prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does a media application determine the context of an event?

Read the following text and answer briefly.

Context 1: 2015-05-14 Assigned to ROVI GUIDES, INC  reassignment ROVI GUIDES, INC  MERGER (SEE DOCUMENT FOR DETAILS)  Assignors: TV GUIDE, INC 
2015-05-14 Assigned to UV CORP  reassignment UV CORP  MERGER (SEE DOCUMENT FOR DETAILS)  Assignors: UNITED VIDEO PROPERTIES, INC 
2015-05-14 Assigned to TV GUIDE, INC  reassignment TV GUIDE, INC  MERGER (SEE DOCUMENT FOR DETAILS)  Assignors: UV CORP 
Methods and systems are described herein for quickly and easily displaying supplemental information about an event occurring in a media asset  In some embodiments, a media application may use a content-recognition module to determine the context of an event and distribute itemized tasks to multiple entities in order to generate the supplemental information about the event 
While viewing media assets (e g , a television program), users may wish to learn more information about an event (e g , a statement made by a person appearing in the media asset, the validity of a claim in an advertisement, etc ) occurring in the media asset  While some media assets allow a user to select additional options or added features (e g , pop-up biographies about the cast and crew), when the added features appear and what topic the added features concern are determined by the content producer and not the user  Furthermore, as the added feature is derived from the content producer, the added feature may be biased or may present limited viewpoints about an event  Therefore, added features provided by a content producer may not provide the added information about an event that a user desires 
In order to gain the added information that a user desires, the user may use additional devices (e g , a laptop computer) to search (e g , using an Internet search engine) for more information about the event  However, without knowing the proper context (e g , who said the statement, what was the tone of the statement, when was the statement said, etc ) of the event or what search terms to use to describe the context of the event (e g , how to describe the tone of the statement), a user may not be able to determine (even using a search engine) more information about the event  Moreover, the use of general search terms may not provide the accuracy or precision needed by the user  Furthermore, even if a user may eventually determine the information, the effort and time required may distract the user from the media asset 
Accordingly, methods and systems are described herein for quickly and easily displaying supplemental information about an event occurring in a media asset  In some embodiments, a media application may use a content-recognition module to determine the context of an event in a media asset and distribute itemized tasks to multiple users in order to generate the supplemental information about the event  The context-recognition module prevents the user from being distracted from the media asset (e g , while the user attempts to describe the context of the event or search for information about the event)  In addition, by distributing tasks to multiple entities (e g , crowd-sourcing), the media application may collect large amounts of information in relatively short periods of time (or in real-time) and aggregate and/or filter the information to generate the supplemental information about the event based on multiple viewpoints and/or sources  By using multiple viewpoints and/or sources, the media application enhances the completeness (e g , by providing unbiased information) and accuracy of the supplemental information 
For example, when a statement or action is made by a character or person appearing on a media asset (e g , a television program), a user may request supplemental information about the statement or action  In response, the media application may determine the context of the statement (e g , who said the statement and to what the statement was referring) or action (e g , what was the reason for the action)  After determining the context of the statement or action, the media application may itemize into tasks the additional information it requires in order to generate the supplemental information  The media application may then transmit requests including the tasks to a plurality of other users  Based on the responses from the plurality of other users, the media application may generate the supplemental information for display to the user 
In some embodiments, a media application may use multiple types of content-recognition modules and/or algorithms to determine the context of an event  For example, the media application may process data associated with the event in order to determine the context of an event  In some embodiments, processing the various types of data may include cross-referencing the data in a database indicating the different contexts the event may have 
In some embodiments, a media application may generate supplemental information about an event in a media asset in response to a user request  In order to generate the supplemental information, the media application may transmit, to multiple users, a request for additional information regarding a context of an event shown in a media asset  Upon receiving messages from the plurality of users that include the requested additional information, the media application may generate the supplemental information associated with the context of the event based on the messages 
It should be noted, the systems and/or methods described above may be applied to, or used in accordance with, other systems, methods and/or apparatuses 
FIG  9 is a flowchart of illustrative steps for generating supplemental information based on additional information provided by a plurality of users in accordance with some embodiments of the disclosure 
Accordingly, methods and systems are described herein for quickly and easily displaying supplemental information about an event occurring in a media asset  The methods and systems described herein alleviate the need for a user to determine the proper context (e g , who said a statement, what was the tone of the statement, when was the statement said, etc ) of an event in a media asset, or the search terms to use to describe the event (e g , the proper search terms to describe the tone of the statement), in order to determine more information about the event  In addition, the methods and systems increase the completeness and accuracy of the information compared to information gathered using traditional searching methods (e g , an Internet search engine), without distracting the user from the media asset 
In some embodiments, a media application may receive a user input from a user device for supplemental information about the context of an event shown in a media asset  The media application may determine additional information required to generate the supplemental information about the context of the event shown in a media asset, and transmit requests for the additional information to one or more users  The media application may receive one or more messages, which include the requested additional information, from the one or more users and generate the supplemental information based on the one or more message  The media application may then instruct the user device to display the supplemental information 
As used herein, “supplemental information” refers to any information related to or associated with an event in a media asset  For example, supplemental information may include, but is not limited to, the verification of a statement or claim in a media asset, further descriptions and/or information about objects or entities shown and/or described in a media asset, and/or any other information, including, but not limited to, a video or audio segment, that may interest a user about an event in a media asset  In some embodiments, the media application may generate supplemental information based on one or more pieces of additional information 
As used herein, “additional information” refers to any information used to generate supplemental information  For example, in an embodiment in which supplement information is the verification of a statement made by a person displayed in a media asset, and a request for the additional information from the media application includes a request for a fact needed to verify the factual basis of the statement, the additional information may be the fact used to verify the statement  For example, if an advertisement claims to have the best product on the market, the media application may use additional information such as the name of the product in question, a list of all other products in the market, and the results of a comparison study of the product in question to all other products to determine whether or not the product is actually the “best” product on the market  Additionally or alternatively, the media application may request industry and/or user reviews related to the event (e g , reviews indicating the quality of the product)  The media application may then use the information in the reviews to generate the supplemental information 
As used herein, an “event” is any action (e g , a verbal statement, opinion and/or physical movement), segment (e g , a portion of a news broadcast featuring a particular topic), or other occurrence during a media asset that may be of particular interest to a user  For example, in some embodiments an event may be a statement or gesture made by a character or person in a media asset affirming or denying a claim 
As referred to herein, the terms “media asset” and “content” should be understood to mean an electronically consumable user asset, such as television programming, as well as pay-per-view programs, on-demand programs (as in video-on-demand (VOD) systems), Internet content (e g , streaming content, downloadable content, Webcasts, etc ), video clips, audio, content information, pictures, rotating images, documents, playlists, websites, articles, books, electronic books, blogs, advertisements, chat sessions, social media, applications, games, and/or any other media or multimedia and/or combination of the same  Media applications also allow users to navigate among and locate content  As referred to herein, the term “multimedia” should be understood to mean content that utilizes at least two different content forms described above, for example, text, audio, images, video, or interactivity content forms  Content may be recorded, played, displayed or accessed by user equipment devices, but can also be part of a live performance 
As referred to herein, the phrase “user equipment device,” “user equipment,” “user device,” “electronic device,” “electronic equipment,” “media equipment device,” or “media device” should be understood to mean any device for accessing the content described above, such as a television, a Smart TV, a set-top box, an integrated receiver decoder (IRD) for handling satellite television, a digital storage device, a digital media receiver (DMR), a digital media adapter (DMA), a streaming media device, a DVD player, a DVD recorder, a connected DVD, a local media server, a BLU-RAY player, a BLU-RAY recorder, a personal computer (PC), a laptop computer, a tablet computer, a WebTV box, a personal computer television (PC/TV), a PC media server, a PC media center, a hand-held computer, a stationary telephone, a personal digital assistant (PDA), a mobile telephone, a portable video player, a portable music player, a portable gaming machine, a smart phone, or any other television equipment, computing equipment, or wireless device, and/or combination of the same 
In some embodiments, the user equipment device may have a front facing screen and a rear facing screen, multiple front screens, or multiple angled screens  In some embodiments, the user equipment device may have a front facing camera and/or a rear facing camera  On these user equipment devices, users may be able to navigate among and locate the same content available through a television  Consequently, media may be available on these devices, as well  The media provided may be for content available only through a television, for content available only through one or more of other types of user equipment devices, or for content available both through a television and one or more of the other types of user equipment devices  The media applications may be provided as on-line applications (i e , provided on a website), or as stand-alone applications or clients on user equipment devices  Various devices and platforms that may implement media applications are described in more detail below 
In some embodiments, a media application may transmit, to a plurality of users, a request for additional information regarding a context of an event shown in a media asset  As used herein, a “plurality of users” may include, but is not limited to any device, entity, or source of information that may process a request for additional information  For example, the plurality of users may include a person operating a user equipment device  In some embodiments, the person may receive (e g , via e-mail, Internet posting, advertisement, or any other applicable information delivery method) the request from the media application for additional information, and in response generate a message (e g , via a return e-mail, an answer to the Internet posting, a user input in the advertisement, or any other applicable method of transmitting information) that includes the additional information  It should be noted that in some embodiments, transmitting a request to a plurality of users may also include querying one or more databases (e g , an Internet search engine or any other storage device, including, but not limited to, databases containing previously generated supplemental information and/or additional information) or consulting one or more data gathering services (e g , a intelligent personal assistant application) for the additional information 
In some embodiments, a media application may use a content-recognition module or algorithm to determine the context of an event and distribute itemized tasks to multiple users in order to generate the supplemental information about the event  The content-recognition module may use object recognition techniques such as edge detection, pattern recognition, including, but not limited to, self-learning systems (e g , neural networks), optical character recognition, on-line character recognition (including but not limited to, dynamic character recognition, real-time character recognition, intelligent character recognition), and/or any other suitable technique or method to determine the objects and/or characteristics in media assets  For example, the media application may receive media assets in the form of a video  The video may include a series of frames  For each frame of the video, the media application may use a content-recognition module or algorithm to determine the context (e g , the person that is speaking or a facial gesture affirming or denying a statement) of an event occurring during the frame or series of frames 
In some embodiments, the content-recognition module or algorithm may also include speech recognition techniques, including but not limited to Hidden Markov Models, dynamic time warping, and/or neural networks (as described above) to translate spoken words into text  The content-recognition module may also use other techniques for processing audio and/or visual data  For example, the media application may monitor the volume of a statement in a media asset to determine the tone of the statement (e g , a high volume may indicate an angry tone) 
In addition, the media application may use multiple types of optical character recognition and/or fuzzy logic, for example, when determining the context of a keyword(s) retrieved from data (e g , media data, translated audio data, subtitle data, user-generated data, etc ) associated with the media asset (or when cross-referencing various types of data with databases indicating the different contexts of events as described below)  For example, the particular data field may be a textual data field  Using fuzzy logic, the system may determine two fields and/or values to be identical even though the substance of the data field or value (e g , two different spellings) is not identical  In some embodiments, the system may analyze particular data fields of a data structure or media asset frame for particular values or text  The data fields could be associated with characteristics, additional information, and/or any other data required for the function of the embodiments described herein  Furthermore, the data fields could contain values (e g , the data fields could be expressed in binary or any other suitable code or programming language) 
As used herein, the “context” of an event refers to the set of circumstances or facts that surround a particular event that influence or affect the meaning of the event  For example, when determining the context of a written and/or spoken statement, the media application may determine who or what authored/stated the statement, the written and/or spoken words and/or other statements that preceded and/or followed the statement, the tone of the statement, and/or any other conditions that may alter the connotation of the statement 
FIG  1 shows an illustrative example of a media application that may be used to display supplemental information in accordance with some embodiments of the disclosure  Display 100 illustrates a display on a user device displaying a media asset  Display 108 illustrates a display featuring supplemental information as described and/or generated in FIGS  6-9  It should be noted that display 100 and display 108 may be presented on any of the devices shown in FIGS  3-4  For example, in some embodiments, display 100 and display 108 may be displayed on user equipment 402, 404, and/or 406 (FIG  4) 
In FIG  1, display 100 represents a display of a media asset (e g , a streaming television program) on a user device (e g , user equipment 402, 404, and/or 406 (FIG  4))  Display 100 includes entity 102 and entity 104  In display 100, entity 104 is currently speaking as indicated by event 106  As shown in FIG  1, event 106 is a statement (e g , “We export a lot of coal”) by a person in the media asset 
In some embodiments, display 108 represents the continued display of the media asset on a user device, after a user has requested supplemental information about event 106  For example, a media application may have received a user input (e g , via user input interface 310 (FIG  3)) while entity 104 was speaking  Using the systems and methods described herein (e g , FIGS  6-9), the media application generated supplemental information 110  Supplemental information 110 represents more information about event 106 
For example, the media application (e g , media application 206 (FIG  2)) may have determined the context of event 106  Specifically, the media application may determine via a content-recognition module or algorithm the words spoken and/or actions by the person during the event  Additionally or alternatively, the media application may analyze the words and/or action during a predetermined amount of time (e g , ten seconds) before and/or after the event (e g , in order to better understand the context of the event)  Furthermore, by cross-referencing the words and/or other information obtained by the content-recognition module (e g , as discussed below in relation to FIG  5) with a database, the content-recognition module determines that the term “we,” the person in the media asset refers to an organization or body  The content-recognition module or algorithm may also determine that the term “export” refers to shipping goods out of a country  The content-recognition module or algorithm may also determine that the term “a lot” refers to a particular numerical amount  Finally, the content-recognition module or algorithm may also determine that the term “coal” refers to a mineral of fossilized carbon 
The content-recognition module or algorithm may also determine the relationships between words and/or other information obtained by the content-recognition module  For example, by processing the relationship between the words, the media application determines that event 106 is a statement regarding a particular amount of a particular substance shipped out of a particular country  Therefore, the media application determines that the request for supplemental information is likely a request to determine the validity of the statement  The media application then generates the supplemental information 
The media application may also have stored supplemental information generated by previous requests (e g , supplemental information generated in response to the same or different user viewing the media asset at an earlier date), and display the supplemental information again during the event (either in response to a user input requesting supplemental information or automatically without a user requesting supplemental information) 
FIG  2 shows an illustrative example of a system that may be used to generate supplemental information (e g , supplemental information 110 (FIG  1)) based on additional information provided by a plurality of users in accordance with some embodiments of the disclosure  For example, in some embodiments, system 200 may be used to generate supplemental information (e g , supplemental information 110 (FIG  1)) on a display (e g , display 108 (FIG  1)) of a user device (e g , user equipment 402, 404, and/or 406 (FIG  4))  It should be noted that in some embodiments, the devices shown in FIG  2 may correspond to one or more devices in FIGS  3-4 
FIG  2 shows system 200  In system 200, a user is currently accessing a media asset on display 202  In some embodiments, display 202 may correspond to display 100 (FIG  1))  During an event (e g , event 106 (FIG  1)) a user may have requested supplemental information about an event (e g , event 106 (FIG  1)) in display 202 using user device 204  Media application 206, which in some embodiments, may be implemented on user device 204 or at a remote location (e g , supplemental information source 418 (FIG  4)), receives the request for supplemental information 
Media application 206 determines the context of the event (e g , who said the statement making up the event and to what the statement was referring)  After determining the context of the statement, the media application may itemize into one or more tasks, additional information (e g , facts) it requires in order to generate the supplemental information (e g , a verification or correction of the factual basis of the statement)  For example, if the event is a statement about the amount of coal that is exported from the United States (e g , as described in relation to FIG  1 above), media application 206 may determine the fact required to generate the supplemental information is the exact numerical amount of coal that is exported from the United States  The media application may then transmit requests for the additional information (e g , a request for the exact numerical amount of coal that is exported from the United States) to a plurality of other users 
In FIG  2, users operating user device 208, user device 210, and user device 212 represent a plurality of users  Having determined the additional information it requires in order to generate the supplemental information, media application 206 requests the additional information from the plurality of users  In system 200, media application 206 has transmitted the same task (e g , the same question) to each of the plurality of users  In some embodiments, one or more of the users may receive different tasks  For example, by breaking the additional information into small, independent tasks, media application 206 may increase the speed (e g , multiple users may work concurrently to solve different parts of a problem) and accuracy (e g , reducing the tasks to smaller, less complex problems reduces the chance of human error) of the additional information returned by the plurality of users 
In addition, by breaking the additional information into small, independent tasks, the plurality of users may not know to what they are contributing (enhancing the privacy of the user that requested the supplemental information), however, the plurality of users can still be effective in their individual tasks  In addition, by breaking the additional information into small, independent tasks, the media application may more easily outsource the requests for additional information  For example, one or more of the tasks used to generate the additional information may be the same as one or more of the tasks used to generate other additional information (e g , additional information used to generate different supplemental information in response to a request for supplemental information about the same or a different event issued by the same or a different user)  The response to each of the request and/or the additional information may be stored (e g , on any of the devices accessible by communications network 414 (FIG  4)) for subsequent retrieval 
Based on the responses, transmitted as messages including the additional information, from the plurality of other users, media application 206 may generate the supplemental information (e g , supplemental information 110 (FIG  1)) for display to the user on the user device 204  For example, media application may aggregate, append, and/or compare the additional information in each of the messages received from the plurality of users  The supplemental information may then be generated based on the aggregated, appended, and/or compared additional information (e g , as described in FIG  9 below) 
In some embodiments, the plurality of users may receive summary information about the event with the request for additional information  (e g , a video clip of a portion or segment of the media asset, a textual description, etc ), which may help the plurality of users provide additional information  For example, in some embodiments, the media application may instead of (or in addition to) determining the context of an event, determine a particular portion of the event that would be needed for the plurality of users to provide additional information about the event 
For example, the media application may use progress information associated with the progress of the media asset (e g , line 506 (FIG  5)) to determine at what point during the progression of the media asset the event occurred, and in response, transmit a portion of the media asset beginning ten second before that point and ending ten seconds after that point  For example, if the event is a statement made by a character or person in a media asset, the media application may determine when the statement began (e g , the point of progress of the media asset in which the statement began) and ended  The media application may then include the portion containing the entire statement (and the event) in the request for additional information sent to the plurality of users 
The selected portion may include any amount of summary information that the media application determines is necessary for the user or any one of the plurality of users to understand the main action sequence  This summary information (e g , a portion of the media asset) may be included with the request for additional information (e g , in a file transmitted with the request), or may be included with the generated supplemental information as a reference for the user  For example, the media application may select a segment of the play length of the media asset or a particular scene of the media asset, which includes the event, for to display to the plurality of users along with the request for additional information 
For example, if an event (e g , a statement) was in response to a question, the media application may also determine when the question began and ended, and send the entire question (or the play length of the media asset corresponding to the question) to the plurality of users as well  After determining the portion to provide to the plurality of users (e g , a segment including the ten seconds before and the ten seconds after the event), the media application may provide the summary information of the event and any other material needed by the plurality of users to understand the event and/or request for supplemental information from the user 
In some embodiments, a portion of the media asset containing the event, as selected by the media application, may also include any amount of the play length of the media asset, or any amount of scenes or segments from the media asset  In some embodiments, the portion may include segments of the play length of the media asset or scenes from the media asset that are not adjacent during the normal playback of the media asset  For example, in some embodiments, a portion of the media asset may include one or more sequences or scenes of interest to the plurality of users, even though the particular sequences or scenes are featured at different points in the play length of the media asset  The media application may determine the segments or scenes to include based on a content recognition file (e g , data structure 500 (FIG  5)) describing the media asset  For example, if a plot point or other information, which may be relevant to an event is displayed earlier in the media asset, the summary information may include a portion of the media asset displaying the plot point 
In some embodiments, the length of a portion may be determined based on the genre of the media asset  In some embodiments, the length of the portion may depend on a user profile for the user or for anyone of the plurality of users  For example, a user profile and/or a content recognition file (e g , data structure 500 (FIG  5)) may indicate that a particular user may require more or less additional content  For example, the user may be aware of particular characters or plot points in the media asset and, therefore, may not require the additional content to introduce those aspects 
In some embodiments, the plurality of users may receive a particular user interface, which organizes the data about the event (e g , a clip of the actual event, summary information about the event, information about the request for supplemental information issued by the user, etc )  The interface may also include an automatic submission form, which may be used to generate a message, which is sent to the media application 
In some embodiments, the media application may also receive user input from the user requesting the supplemental information that further affects the generation of supplemental information by the media application  For example, the user may request the supplemental information includes particular information (e g , the factual basis of a statement), may request a multimedia format of the supplemental information (e g , textual description, a video clip, etc ), may request a form of the supplemental information (e g , a short description about the event, an Internet link to other sources of information on the event, or a true or false designation about the event) by entering user inputs (e g , via user input interface 310 (FIG  3)) 
It should be noted that any information or process referred to in this disclosure that is referred to as being in response to a user input may alternatively and/or additionally be performed automatically by the media application (e g , via control circuitry 304 (FIG  3))  For example, in some embodiments, a user may request a true or false designation (e g , an on-screen pop-up box indicating whether an event was true or false)  Additionally and/or alternatively, in some embodiments, the true or false designation may appear automatically based on predetermined settings indicating to the media application to display a true or false designation in response to detecting an event 
In some embodiments, an indicator that supplemental information has previously been generated or is currently ready to generate (e g , a plurality of users are available) may be displayed to a user (e g , on display 100 (FIG  1) during the event)  The indicator may also indicate the particular information, the multimedia format, and/or the form of supplemental information that is available  An indicator may also appear with the supplemental information (e g , supplemental information 110 (FIG  1)), which allows the user to request additional supplemental information or provide feedback/responses (e g , rating the quality of the supplemental information) to the media application and/or plurality of users 
In some embodiments, a user may also access (e g , via selection of an indicator and/or automatically upon the supplemental information being generated) summary information about the event  For example, in some embodiments (e g , when the supplemental information is not generated in real-time), the media asset may have progressed to a different point by the time the supplemental information is ready for display  Therefore, the media application may need to provide a video clip of the event or other summary information, so that the user remembers about what or why the supplemental information was requested 
FIG  3 is a block diagram of an illustrative user equipment device in accordance with some embodiments of the disclosure  It should be noted that the components shown in FIG  3 may be used to store, receive, transmit, and/or display the media assets, additional information, and/or supplemental information as described herein  For example, media application 206 (FIG  2) may be implemented on user equipment device 300, and may issue instructions (e g , displaying supplemental information 110 (FIG  1)) via control circuitry 304 
Users may access media assets and the media application (and its display screens described above and below) from one or more of their user equipment devices  FIG  3 shows a generalized embodiment of illustrative user equipment device 300  More specific implementations of user equipment devices are discussed below in connection with FIG  4  User equipment device 300 may receive content and data via input/output (hereinafter “I/O”) path 302  I/O path 302 may provide content (e g , broadcast programming, on-demand programming, Internet content, content available over a local area network (LAN) or wide area network (WAN), and/or other content) and data to control circuitry 304, which includes processing circuitry 306 and storage 308  Control circuitry 304 may be used to send and receive commands, requests, and other suitable data using I/O path 302  I/O path 302 may connect control circuitry 304 (and specifically processing circuitry 306) to one or more communications paths (described below)  I/O functions may be provided by one or more of these communications paths, but are shown as a single path in FIG  3 to avoid overcomplicating the drawing 
Control circuitry 304 may be based on any suitable processing circuitry such as processing circuitry 306  As referred to herein, processing circuitry should be understood to mean circuitry based on one or more microprocessors, microcontrollers, digital signal processors, programmable logic devices, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), etc , and may include a multi-core processor (e g , dual-core, quad-core, hexa-core, or any suitable number of cores) or supercomputer  
Context 2: Hugh Hilton Goodwin (December 21, 1900 – February 25, 1980) was a decorated officer in the United States Navy with the rank of Vice Admiral  A veteran of both World Wars, he commanded escort carrier  during the Mariana Islands campaign  Goodwin then served consecutively as Chief of Staff, Carrier Strike Group 6 and as Air Officer, Philippine Sea Frontier and participated in the Philippines campaign in the later part of the War 

Following the War, he remained in the Navy and rose to the flag rank and held several important commands including Vice Commander, Military Air Transport Service, Commander, Carrier Division Two and Commander, Naval Air Forces, Continental Air Defense Command 

Early life and career

Hugh H  Goodwin was born on December 21, 1900, in Monroe, Louisiana and attended Monroe High School there (now Neville High School)  Following the United States' entry into World War I in April 1917, Goodwin left the school without receiving the diploma in order to see some combat and enlisted the United States Navy on May 7, 1917  He completed basic training and was assigned to the battleship   Goodwin participated in the training of armed guard crews and engine room personnel as the Atlantic Fleet prepared to go to war and in November 1917, he sailed with the rest of Battleship Division 9, bound for Britain to reinforce the Grand Fleet in the North Sea 

Although he did not complete the last year of high school, Goodwin was able to earn an appointment to the United States Naval Academy at Annapolis, Maryland in June 1918  While at the academy, he earned a nickname "Huge" and among his classmates were several future admirals and generals including: Hyman G  Rickover, Milton E  Miles, Robert E  Blick Jr , Herbert S  Duckworth, Clayton C  Jerome, James P  Riseley, James A  Stuart, Frank Peak Akers, Sherman Clark, Raymond P  Coffman, Delbert S  Cornwell, Frederick J  Eckhoff, Ralph B  DeWitt, John Higgins, Vernon Huber, Albert K  Morehouse, Harold F  Pullen, Michael J  Malanaphy, William S  Parsons, Harold R  Stevens, John P  Whitney, Lyman G  Miller and George J  O'Shea 

Goodwin graduated with Bachelor of Science degree on June 3, 1922, and was commissioned Ensign in the United States Navy  He was subsequently assigned to the battleship  and took part in the voyage to Rio de Janeiro, Brazil, before he was ordered to the Naval Torpedo Station at Newport, Rhode Island for submarine instruction in June 1923  Goodwin completed the training several weeks later and was attached to the submarine   He then continued his further training aboard submarine  and following his promotion to Lieutenant (junior grade) on June 3, 1925, he qualified as submariner 

He then served aboard submarine  off the coast of California, before he was ordered for the recruiting duty to San Francisco in September 1927  While in this capacity, Goodwin applied for naval aviation training which was ultimately approved and he was ordered to the Naval Air Station Pensacola, Florida in August 1928  Toward the end of the training, he was promoted to lieutenant on December 11, 1928, and upon the completion of the training in January 1929, he was designated Naval aviator 

Goodwin was subsequently attached to the Observation Squadron aboard the aircraft carrier  and participated in the Fleet exercises in the Caribbean  He was transferred to the Bureau of Aeronautics in Washington, D C  in August 1931 and served consecutively under the architect of naval aviation William A  Moffett and future Chief of Naval Operations Ernest J  King 

In June 1933, Goodwin was ordered to the Naval War College at Newport, Rhode Island, where he completed junior course in May of the following year  He subsequently joined the crew of aircraft carrier  and served under Captain Arthur B  Cook and took part in the Fleet exercises in the Caribbean and off the East Coast of the United States 

He was ordered back to the Naval Air Station Pensacola, Florida in June 1936 and was attached to the staff of the Base Commandant, then-Captain Charles A  Blakely  When Blakely was succeeded by William F  Halsey in June 1937, Goodwin remained in Halsey's staff and was promoted to Lieutenant Commander on December 1, 1937  He also completed correspondence course in International law at the Naval War College 

Goodwin was appointed Commanding officer of the Observation Squadron 1 in June 1938 and attached to the battleship  he took part in the patrolling of the Pacific and 
West Coast of the United States until September 1938, when he assumed command of the Observation Squadron 2 attached to the battleship  

When his old superior from Lexington, now Rear Admiral Arthur B  Cook, was appointed Commander Aircraft, Scouting Force in June 1939, he requested Goodwin as his Aide and Flag Secretary  He became Admiral Cook's protégé and after year and half of service in the Pacific, he continued as his Aide and Flag Secretary, when Cook was appointed Commander Aircraft, Atlantic Fleet in November 1940 

World War II

Following the United States' entry into World War II, Goodwin was promoted to the temporary rank of Commander on January 1, 1942, and assumed duty as advisor to the Argentine Navy  His promotion was made permanent two months later and he returned to the United States in early 1943 for duty as assistant director of Planning in the Bureau of Aeronautics under Rear admiral John S  McCain  While still in Argentina, Goodwin was promoted to the temporary rank of Captain on June 21, 1942 

By the end of December 1943, Goodwin was ordered to Astoria, Oregon, where he assumed command of newly commissioned escort carrier USS Gambier Bay  He was responsible for the initial training of the crew and was known as a strict disciplinarian, but the crew appreciated the skills he taught them that prepared them for combat  Goodwin insisted that everyone aboard has to do every job right every time and made us fight our ship at her best 

During the first half of 1944, Gambier Bay was tasked with ferrying aircraft for repairs and qualified carrier pilots from San Diego to Pearl Harbor, Hawaii, before departed on May 1, 1944, to join Rear admiral Harold B



ground_truth: It uses a content-recognition module or algorithm.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: When did Goodwin become a Naval aviator?

Read the following text and answer briefly.

Context 2:  Sallada's Carrier Support Group 2, staging in the Marshalls for the invasion of the Marianas 

The air unit, VC-10 Squadron, under Goodwin's command gave close air support to the initial landings of Marines on Saipan on June 15, 1944, destroying enemy gun emplacements, troops, tanks, and trucks  On the 17th, her combat air patrol (CAP) shot down or turned back all but a handful of 47 enemy planes headed for her task group and her gunners shot down two of the three planes that did break through to attack her 

Goodwin's carrier continued in providing of close ground support operations at Tinian during the end of July 1944, then turned her attention to Guam, where she gave identical aid to invading troops until mid-August that year  For his service during the Mariana Islands campaign, Goodwin was decorated with Bronze Star Medal with Combat "V" 

He was succeeded by Captain Walter V  R  Vieweg on August 18, 1944, and appointed Chief of Staff, Carrier Division Six under Rear admiral Arthur W  Radford  The Gambier Bay was sunk in the Battle off Samar on October 25, 1944, during the Battle of Leyte Gulf after helping turn back a much larger attacking Japanese surface force 

Goodwin served with Carrier Division Six during the Bonin Islands raids, the naval operations at Palau and took part in the Battle of Leyte Gulf and operations supporting Leyte landings in late 1944  He was later appointed Air Officer of the Philippine Sea Frontier under Rear admiral James L  Kauffman and remained with that command until the end of hostilities  For his service in the later part of World War II, Goodwin was decorated with Legion of Merit with Combat "V"  He was also entitled to wear two Navy Presidential Unit Citations and Navy Unit Commendation 

Postwar service

Following the surrender of Japan, Goodwin assumed command of Light aircraft carrier  on August 24, 1945  The ship was tasked with air missions over Japan became mercy flights over Allied prisoner-of-war camps, dropping food and medicine until the men could be rescued  She was also present at Tokyo Bay for the Japanese surrender on September 2, 1945 

Goodwin returned with San Jacinto to the United States in mid-September 1945 and he was detached in January 1946  He subsequently served in the office of the Chief of Naval Operations until May that year, when he entered the instruction at National War College  Goodwin graduated in June 1947 and served on Secretary's committee for Research on Reorganization  Upon promotion to Rear admiral on April 1, 1949, Goodwin was appointed Chief of Staff and Aide to Commander-in-Chief, Atlantic Fleet under Admiral William H  P  Blandy 

Revolt of the Admirals

In April 1949, the budget's cuts and proposed reorganization of the United States Armed Forces by the Secretary of Defense Louis A  Johnson launched the wave of discontent between senior commanders in the United States Navy  Johnson proposed the merging of the Marine Corps into the Army, and reduce the Navy to a convoy-escort force 

Goodwin's superior officer, Admiral Blandy was call to testify before the House Committee on Armed Services and his harsh statements for the defense of the Navy, costed him his career  Goodwin shared his views and openly criticized Secretary Johnson for having power concentrated in a single civilian executive, who is an appointee of the Government and not an elected representative of the people  He also criticized aspects of defense unification which permitted the Joint Chiefs of Staff to vote on arms policies of individual services, and thus "rob" the branches of autonomy 

The outbreak of the Korean War in summer 1950 proved the proposal of Secretary Johnson as incorrect and he resigned in September that year  Also Secretary of the Navy, Francis P  Matthews resigned one month earlier 

Later service

Due to the Revolts of the admirals, Blandy was forced to retire in February 1950 and Goodwin was ordered to Newport, Rhode Island for temporary duty as Chief of Staff and Aide to the President of the Naval War College under Vice admiral Donald B  Beary in April 1950  Goodwin was detached from that assignment two months and appointed member of the General Board of the Navy  He was shortly thereafter appointed acting Navy Chief of Public Information, as the substitute for Rear Admiral Russell S  Berkey, who was relieved of illness, but returned to the General Board of the Navy in July that year  Goodwin served in that capacity until February 1951, when he relieved his Academy class, Rear admiral John P  Whitney as Vice Commander, Military Air Transport Service (MATS) 

While in this capacity, Goodwin served under Lieutenant general Laurence S  Kuter and was co-responsible for the logistical support of United Nations troops fighting in Korea  The MATS operated from the United States to Japan and Goodwin served in this capacity until August 1953, when he was appointed Commander Carrier Division Two  While in this assignment, he took part in the Operation Mariner, Joint Anglo-American exercise which encountered very heavy seas over a two-week period in fall 1953 

Goodwin was ordered to the Philippines in May 1954 and assumed duty as Commander, U S  Naval Forces in the Philippines with headquarters at Naval Station Sangley Point near Cavite  He held that command in the period of tensions between Taiwan and China and publicly declared shortly after his arrival, that any attack on Taiwan by the Chinese Communists on the mainland would result in US participation in the conflict  The naval fighter planes under his command also provided escort for passing commercial planes  Goodwin worked together with retired Admiral Raymond A  Spruance, then-Ambassador to the Philippines, and accompanied him during the visits to Singapore, Bangkok and Saigon in January 1955 

On December 18, 1955, Goodwin's classmate Rear admiral Albert K  Morehouse, then serving as Commander, Naval Air Forces, Continental Air Defense Command (CONAD), died of heart attack and Goodwin was ordered to CONAD headquarters in Colorado Springs, Colorado to assume Morehouse's position  While in this capacity, he was subordinated to Army General Earle E  Partridge and was responsible for the Naval and Marine Forces allocated to the command designated for the defense of the Continental United States 

Retirement

Goodwin retired on June 1, 1957, after 40 years of active service and was advanced to the rank of Vice admiral on the retired list for having been specially commended in combat  A week later, he was invited back to his Monroe High School (now Neville High School) and handed a diploma showing that he had been graduated with the class of 1918  He then settled in Monterey, California where he taught American history at Stevenson school and was a member of the Naval Order of the United States 

Vice admiral Hugh H  Goodwin died at his home on February 25, 1980, aged 79  He was survived by his wife, Eleanor with whom he had two children, a daughter Sidney and a son Hugh Jr , who graduated from the Naval Academy in June 1948, but died one year later, when the Hellcat fighter he was piloting collided with another over the Gulf of Mexico during training 

Decorations

Here is the ribbon bar of Vice admiral Hugh H  Goodwin:

References

1900 births
1980 deaths
People from Monroe, Louisiana
Military personnel from Louisiana
United States Naval Academy alumni
Naval War College alumni
United States Naval Aviators
United States Navy personnel of World War I
United States Navy World War II admirals
United States Navy vice admirals
United States submarine commanders
Recipients of the Legion of Merit



ground_truth: Goodwin became a Naval aviator in January 1929.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the specific-heat ratio affect the average motion of the bubble?

Read the following text and answer briefly.

Context 3: Paper Info

Title: Specific-heat ratio effects on the interaction between shock wave and heavy-cylindrical bubble: based on discrete Boltzmann method
Publish Date: May 29, 2023
Author List: Yanbiao Gan (from School of Liberal Arts and Sciences, Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle, North China Institute of Aerospace Engineering), Yudong Zhang (from School of Mechanics and Safety Engineering, Zhengzhou University)

Figure

Figure 1: Research orientation and tasks of DBM 
Figure 2: Sketch of D2V16 model The numbers in the figure represent the index i in Eq  (3) 
Figure 3: The computational configuration of the shock-bubble interaction 
In the figure, results from odd rows are experimental, and the even rows indicate DBM simulation results The typical wave patterns and bubble's main characteristic structures are marked out in the figures Numbers in the pictures represent the time in µs Schlieren images of DBM results are calculated from the density gradient formula, i e , |∇ρ|/|∇ρ| max , with |∇ρ| = (∂ ρ/∂ x) 2 + (∂ ρ/∂ y)2  At t = 0µs, the incident shock wave impacts the upstream interface, and subsequently generates a transmitted shock (TS) propagating downstream in the bubble and a reflected shock wave moving upward in ambient gas The incident shock wave travels downstream contin-
The definitions and the corresponding physical meanings of the common TNE quantities in DBM, where the operator ∑ ix,iy indicates integrating over all the fluid units and multiply the unit area dxdy From a certain perspective, the TNE strength is increasing; While from a different perspective, the TNE strength, on the other hand, may be decreasing It is one of the concrete manifestations of the complexity of non-equilibrium flow behavior 
Figure 4: Snapshots of schlieren images of the interaction between a shock wave and a heavy-cylindrical bubble The odd rows represent experimental results from Ref  [31] with permission, and the even rows are DBM simulation results The typical wave patterns and the bubble's main characteristic structure are marked out in the figures Numbers in the picture represent the time in µs 
Figure 5: The temporal variations of length and width of the bubble The symbols represent DBM results and the lines are experimental The definition of the length and the width of the bubble can be seen in the illustration Experimental results are obtained from Fig  12, in Ref  [31] with permission 
Figure 6: Density contours and particle tracer images at three different moments (i e , t = 0 07,t = 0 11, and t = 0 16) with various specific-heat ratios The odd rows represent density contours, and the even rows are tracer particle images 
Figure 9: Vorticity contours at t = 0 134, with various specific-heat ratios The arrows in the vorticity image point out the apparent difference between case γ = 1 4 and case γ = 1 09 
Figure 11: Density contours (first row) and mixing degree M (second row) at several typical moments 
Figure 13: (a) Temporal evolution of D * 3,1 and D * 4,2  (b) Temporal evolution of D * 2 and D * 3  Lines with different colors represent the cases with various specificheat ratios 
The development of schemes for checking TNE state, extracting TNE information and describing corresponding TNE effects in DBM 

abstract

Specific-heat ratio effects on the interaction between a planar shock wave and a two-dimensional heavy-cylindrical bubble are studied by the discrete Boltzmann method  Snapshots of schlieren images and evolutions of characteristic scales, being consistent with experiments, are obtained  The specific-heat ratio effects on some relevant dynamic behaviors such as the bubble shape, deformation process, average motion, vortex motion, mixing degree of the fluid system are carefully studied, as well as the related Thermodynamic Non-Equilibriums (TNE) behaviors including the TNE strength, entropy production rate of the system 
Specifically, it is found that the influence of specific-heat ratio on the entropy production contributed by non-organized energy flux (NOEF) is more significant than that caused by non-organized momentum flux (NOMF)  Effects of specific-heat ratio on entropy production caused by NOMF and NOEF are contrary 
The effects of specific-heat ratio on various TNE quantities show interesting differences  These differences consistently show the complexity of TNE flows which is still far from clear understanding 

Introduction

The applications of shock-accelerated inhomogeneous flows (SAIFs) are of significant value in biomedicine, energy utilization, and astrophysics fields, including but not limited to scenarios such as the impact of shock waves on kidney stones, the interaction between shock waves with foams, the impacting of detonation wave with burning flames in supersonic combustion systems, the formation of supernova remnants, etc  
Shock-bubble interaction (SBI) is one of the most fundamental problems in the research of SAIFs  Its applications and academic research are interdisciplinary  Generally, there are two kinds of problems encountered in SBI research: (i) The geometry of shock waves, the shape of material interfaces, and the structure of container are complex in the actual scene 
They will result in various wave patterns and significantly affect the flow morphology and bubble's evolution  (ii) There usually exist multi-physics coupling problem in the engineering application of SBI  Such as the supersonic combustion machines  When the shock waves passing through the reactants, it may lead to phase transition and chemical reactions, making the flow morphology more complex and inducing small structure (or fast-changing pattern)  
In an underwater explosion experiment, the interaction between shock waves and bubbles may refer to the cavitation and annihilation effects  The other scene is the inertial confinement fusion (ICF), in which the laser ablation, electron heat conduction, self-generated electromagnetic field, radiation, and many other factors may complicate the investigation of hydrodynamic instabilities  
Commonly, research on SBI mainly includes three methods: theoretical derivation, experiment, and numerical simulation  As a fundamental research method, theoretical research can provide a clear understanding of physical processes  In 1960, Rudinger et al  developed a theory that permits computing the response of bubbles to accelerations  
In order to describe the formation and evolution processes of vortex structure quantitatively, many scholars have developed circulation models   However, theoretical works provide limited information  Meanwhile, in the late stage of SBI evolution, the bubble deformation and flow morphology dominated by the developed Richtmyer-Meshkov instability (RMI) and Kelvin-Helmholtz instability (KHI) are difficult to be predicted accu-rately 
As the research method closest to engineering application, the experimental results are often regarded as standard results to verify the rationality and accuracy of theoretical and numerical works  To study the SBI process accurately, the scholars have made a series of improvements to experimental equipment or technique, including the generation techniques of different types of shock waves, interface formation methods, schlieren facilities, and image recognition techniques  
Among these, two of important and valuable works are performed by Ding et al   Based on the soap film technique, they formed kinds of initial interfaces with different curvatures through the wire-restriction method and captured the wave patterns and interface evolution with high-speed schlieren photography  
Other works, such as evolutions of a spherical gas interface under reshock conditions , developments of a membrane-less SF 6 gas cylinder under reshock conditions , and interactions of a cylindrical converging shock wave with an initially perturbed gaseous interface , are also performed by many other scholars 
However, we know that the experimental studies mainly depend on the experimental platform  When studying some complex and demanding condition problems, it takes much work to build the experimental platform  In this situation, numerical simulation research becomes an option  Generally, there are three kinds of physical modeling methods (or models) for SBI numerical research, i e , the macroscopic, mesoscopic, and microscopic modeling methods 
Most of the existing numerical researches on SBI are related to the macroscopic modeling methods (such as the Euler and Navier-Stokes (NS) models) based on the continuous hypothesis (or equilibrium and nearequilibrium hypothesis)   For example, presented the computational results on the evolution of the shock-accelerated heavy bubbles through the multi-fluid Eulerian equation  
There also exist a few SBI works based on the mesoscopic modeling method, such as the Direct Simulation Monte Carlo method   The microscopic modeling methods such as the Molecular dynamics (MD) simulation, is capable of capturing much more flow behaviors but restricted to smaller spatiotemporal scales because of its huge computing costs 
In the numerical research on SBI, three points need to be concerned  (i) Investigation of kinetic modeling that describes the non-continuity/non-equilibrium flows  Most of the current researches are based on macroscopic models  However, there exist abundant small structure (and fast-changing patterns) behaviors and effects such as the shock wave, boundary layer, material defects, etc 
For cases with small structures, the mean free path of molecules cannot be ignored compared to the characteristic length, i e , the non-continuity (discreteness) of the system is pronounced, which challenge the rationality and physical function of the macroscopic models based on the continuity hypothesis 
For cases with fast-changing patterns, the system dose not have enough time to relax to the thermodynamic equilibrium state, i e , the system may significantly deviate from the thermodynamic equilibrium state  Therefore, the rational-ity and physical function of the macroscopic models based on the hypothesis of thermodynamic equilibrium (or near thermodynamic equilibrium) will be challenged 
(ii) Improvement of method that describes the evolution characteristics of bubbles and flows morphology  Most of the studies describe bubble characteristics and flows morphology from a macroscopic view  The mesoscopic characteristics such as the kinetic effects which help understand the kinetic process, are rarely to be studied 
(iii) Further studies of effects of specific-heat ratio on SBI process  The specific-heat ratio is an essential index for studying the compressibility of the gas  Research from Igra et al  has shown that the differences in the specific-heat ratio of bubbles would cause various wave patterns and pressure distribution inside the bubbles during the interaction process  
Besides, many works on hydrodynamic instability have also demonstrated the importance of investigating the specific-heat ratio effect   Among these, Chen et al  investigated the specific-heat ratio effects on temperature gradient and the TNE characteristics of compressible Rayleigh-Taylor (RT) system  
For the above three points, in this work we apply the recently proposed discrete Boltzmann method (DBM)   The Lattice Boltzmann Method (LBM) research has two complementary branches   One aims to work as a kind of new scheme for numerical solving various partial differential equation(s)  The other aims to work as a kind of new method for constructing kinetic model to bridge the macro and micro descriptions 
The two branches have different goals and consequently have different rules  The current DBM is developed from the second branch of LBM and focusing more on the Thermodynamic Non-Equilibrium (TNE) behaviors that the macro modeling generally ignore  It breaks through the continuity and near-equilibrium assumptions of traditional fluid modeling, discards the lattice gas image of standard LBM, and adds various methods based on phase space for checking, exhibiting, describing and analyzing the non-equilibrium state and resulting effects 
More information extraction technologies and analysis methods for complex field are introduced with time  The numerical simulation includes three parts, as shown in Fig    (1) Physical modelling, (2) Algorithm design, (3) Numerical experiments and analysis of complex physical fields  The research of equation algorithm corresponds to the part (2) of the above three parts 
The DBM aims at parts (1) and (3) of the three mentioned above  It belongs to a physical model construction method rather than a numerical solution for the equations  The tasks of DBM are to: (i) Ensure the rationality of the physical model (theoretical model) and balance the simplicity for the problem to be studied; (ii) Try to extract more valuable physical information from massive data and complex physical fields 
Based on the coarse-grained modeling method of nonequilibrium statistical physics, the DBM aims to solve the following dilemma: (i) The traditional hydrodynamic modelings are based on the continuous hypothesis (or near-equilibrium hypothesis)  They only concern the evolution of three conserved kinetic moments of the distribution function, i e  the density, momentum and energy, so their physical functions are insufficient 
(ii) The situation that the MD can be used is restricted to too small spatial-temporal scales  The physical requirement for the modeling is that except for the Hydrodynamic Non-Equilibriums (HNE), the most related TNE are also needed to be captured  Theoretically, the Boltzmann equation is suitable for all-regime flows, including the continuum regime, slip regime, transition regime, and free molecule flow regime 
Based on the Chapman-Enskog (CE) multiscale analysis , through retaining various orders of Kn number (or considering different orders of TNE effects), the Boltzmann equation can be reduced to the various orders of hydrodynamic equations  They can be used to describe the hydrodynamic behaviors, i e , the conservations of mass, momentum and energy , in corresponding flow regimes 
Because what the traditional hydrodynamic equations describe are only the conservation laws of mass, momentum and energy  Consequently, it should be pointed out that, the information lost in the traditional hydrodynamic equations increases sharply with increasing the Kn number  With increasing the Kn number, to ensure the describing capability not to decrease significantly, the more appropriate hydrodynamic equations should be the Extended Hydrodynamic Equations (EHEs) which include not only the evolution equations of conserved kinetic moments but also the most relevant nonconserved kinetic moments of distribution function 
For convenience of description we refer the modeling method that derives EHEs from the fundamental kinetic equation to Kinetic Macroscopic Modeling (KMM) method  It is clear that, the complex process of CE expansion is necessary and the simulation is still based on the macroscopic equations in KMM  As a comparison, the DBM is a kind of Kinetic Direct Modeling (KDM) method 
In DBM modeling, the CE analysis is only used to quickly determine which kinetic moments should keep values unchanged, the final EHEs are not needed, and the simulation is not based on the complicated EHEs  As the TNE degree of the flow to be described rises gradually, the complexity of the derivation process and difficulty of numerical simulation in the KMM method increase sharply 
However, in the DBM method, to describe flows in a one-order more deeper depth of TNE, only two more related kinetic moments need to be added  Since without needing to derive and solve the EHEs, as the TNE degree deepens, the complexity of the DBM approach increases much slower than that of KMM method 
The core step in DBM modeling is to provide a feasible scheme for detecting, describing, presenting, and analyzing TNE effects and behaviors beyond traditional macroscopic modeling  Based on the non-equilibrium statistical physics, we can use the non-conservative moments of ( f − f eq ) to describe how and how much the system deviates from the thermodynamic equilibrium state and to check corresponding effects due to deviating from the thermodynamic equilibrium 
The non-conservative moments of ( f − f eq ) open a phase space, and this space and its subspaces provide an intuitive geometric correspondence for describing complex TNE system properties  The development of schemes for checking TNE state, extracting TNE information and describing corresponding TNE effects in DBM are seen in Table  
Actually, this set of TNE describing methods has been applied in many kinds of complex fluid systems such as hydrodynamic instability system , combustion and detonation systems , multiphase flow system , plasma system , etc  Besides the scheme for detecting, describing, presenting, and analyzing TNE effects and behaviors, the DBM incorporates other methods for analyzing the complex physical field 
One of them is the tracer particle method  The introduction of the tracer particle method makes the gradually blurred interface appear clearly   The rest of the paper is structured as follows  Section 2 shows Year Scheme for investigating TNE effects and behaviors Before 2012 Two classes of LBMs did not show a significant difference in physical function 
2012 Use the non-conservative moments of ( f − f eq ) to check and describe TNE   This is the starting point of current DBM approach  2015 Open TNE phase space based on non-conservative moments of ( f − f eq ) and define a TNE strength using the distance from a state point to the origin  This is the starting point of the phase space description method  
2018 Extend the distance concepts in phase space to describe the TNE difference/similarity of TNE states and kinetic processes   2021 Further extend the phase space description methodology to any set of system characteristics   the modeling method  Then, the numerical simulations and results are presented in Section 3, which includes two subsections 
Section 4 concludes the paper  Other complementary information is given in the Appendix 

Model construction

Based on the Bhatnagar-Gross-Krook (BGK) singlerelaxation model, a two-fluid DBM with a flexible specific-heat ratio is presented in this part  From the origin Boltzmann equation to a DBM, four fundamental steps are needed: (i) Simplification and modification of the Boltzmann equation according to the research requirement 
(ii) Discretization of the particle velocity space under the condition that the reserved kinetic moments keep their values unchanged  (iii) Checking the TNE state and extracting TNE information  (iv) The selection/design of the boundary conditions 

Simplification and modification of the Boltzmann equation

As we know, the collision term in the original Boltzmann contains high dimensional distribution functions  Therefore, the direct solution to it needs too much computing consumption  The most common method to simplify the collision operator is to introduce a local equilibrium distribution function ( f eq ) and write the complex collision operator in a linearized form, i e , the original BGK collision operator − 1 τ ( f − f eq ), where τ is the relaxation time  
The original BGK operator describes the situation where the system is always in the quasi-equilibrium state  Namely, it characterizes only the situation where the Kn number of the system is small enough and f ≈ f eq   The currently used BGK operator for non-equilibrium flows in the field is a modified version incorporating the meanfield theory description  
Based on the above considerations, the simplified Boltzmann equation describing the SBI process is where the two-dimensional equilibrium distribution function is ) where ρ, T , v, u, I, R, and η are the mass density, temperature, particle velocity vector, flow velocity vector, the number of the extra degrees of freedom including molecular rotation and vibration inside the molecules, gas constant, and a free parameter that describes the energy of the extra degrees of freedom, respectively 
The specific-heat ratio is flexible by adjusting parameter I, i e , γ = (D + I + 2)/(D + I), where D = 2 represents the two-dimensional space 

Discretization of the particle velocity space and determination of f σ ,eq i

The continuous Boltzmann equation should be discretized for simulating  Specifically, the continuous velocity space can be replaced by a limited number of particle velocities  So that the values of continuous kinetic moments can be obtained from the summation form of kinetic moments  In this process, it requires the reserved kinetic moments, which are used to characterize the system behaviors, keep their values unchanged after discretizing the velocity space 
Namely, f the reserved kinetic moments  According to the CE analysis, f can be expressed by f eq   Therefore, in the process of discretization, the reserved kinetic moments of f eq should keep their values unchanged, i e , where i represents the kind of discrete velocities and α (α = x or y) is the direction in cartesian coordinate 
To simulate the interaction between two different fluids, a two-fluid DBM should be constructed  Based on the singlerelaxation model, the discrete two-fluid Boltzmann equation can be written as : where σ represents the types of material particle and f σ ,eq i = f σ ,eq i (ρ σ , u, T)  In two-fluid DBM, the macroscopic quantities of the mixture and each component are
where ρ σ and u σ are the mass density and flow velocity of the component σ , respectively  ρ and u represent the mass density and flow velocity of the mixture, respectively  There exist two kinds of temperature (internal energy) definitions in two-fluid DBM because the definition of temperature (internal energy) depends on the flow velocity to be chosen as a reference 
The first definition is by choosing the velocity of the mixture to be a reference, i e , So that the expressions of temperature of component σ and mixture are where We can also choose the flow velocity of component as a reference, i e , , where u σ is the flow velocity of component σ   The corresponding definitions of temperature for component σ and the mixture are
where ∆E * I is It is clear to see that these two definitions of temperature for mixture are the same, but for temperature of component σ are different  We choose the first definition in this manuscript  To solve the Eq  ( ), it is necessary to determine the values of f σ ,eq i   Its values depend on the reserved kinetic moments which characterize the main system behaviors 
In DBM modeling, the CE multiscale analysis is used to determine quickly the reserved kinetic moments  Specifically, when constructing a DBM which only the first order term of Kn number is retained (i e , only the first order TNE effects are retained), seven kinetic moments should be reserved, i e , the M 0 , M 1 , M 2,0 , M 2 , M 3,1 , M 3 , M 4,2  
Two more kinetic moments ( M 4 and M 5,3 ) are needed when the second order TNE is considered   However, it should be noted that the function of CE analysis in DBM modeling is only to determine the kinetic moments that need to be preserved  Whether or not to derive the hydrodynamic equations does not affect the DBM simulation 
The kinetic moments used in our physical modeling are shown in the Appendix B  Their expressions can be obtained by integrating v and η with continuous-form f eq   For better understanding, the Appendix C gives the two-fluid hydrodynamic equations recovered from the Boltzmann equation  The kinetic moments in Appendix B can be written in matrix form, i e , C • f σ ,eq = fσ,eq , (
where C is the matrix of discrete velocity and feq represents the kinetic moments  A proper discrete velocity model is needed to confirm the values of f σ ,eq i   The f σ ,eq can be obtained by solving the inverse matrix, i e , f σ ,eq = C −1 • fσ,eq , where C −1 is the inverse matrix of C  It is very convenient to obtain the inverse matrix of C through some mathematical softwares such as Mathematica, etc 
The D2V16 model is chosen in this paper, its sketches can be seen in Fig    The specific values of D2V16 are given in the following equations: where "cyc" indicates cyclic permutation and c is an adjustable parameter of the discrete velocity model  The sketch of η in D2V16 is η i = η 0 for i = 1 − 4, and η i = 0 for i = 5 − 16 

Checking the TNE state and extracting TNE information

Many physical quantities can characterize the degree of TNE in a fluid system, such as relaxation time, Kn number, viscosity, heat conduction, the gradients of macroscopic quantity, etc  They are all helpful to characterize the TNE strength and describe the TNE behaviors of a fluid system from their perspectives 
But it is not enough only relying on these quantities  Besides the above physical quantities describing the TNE behaviors, in DBM modeling, we can also use the non-conservative moments of ( f − f eq ) to characterize the TNE state and extract TNE information from the fluid system  Fundamentally, four TNE quantities can be defined in a firstorder DBM, i e , ∆ σ * 2 , ∆ σ * 3,1 , ∆ σ * 3 , and ∆ σ * 4,2  
Their definitions can be seen in Table , where v * i = v i − u represents the central velocity and u is the macro flow velocity of the mixture  Physically, ∆ σ * 2 = ∆ σ * 2,αβ e α e β and ∆ σ * 3,1 = ∆ σ * 3,1 e α represent the viscous stress tensor (or non-organized momentum flux, NOMF) and heat flux tensor (or non-organized energy flux, NOEF), respectively 
The e α (e β ) is the unit vector in the α (β ) direction  The later two higher-order TNE quantities contain more condensed information  Specifically, and it indicates the flux information of ∆ σ * 2   To describe the TNE strength of the whole fluid system, some TNE quantities contained more condensed information are also defined, i e ,
Other TNE quantities can be defined based on specific requirements  All the independent components of TNE characteristic quantities open a highdimensional phase space, and this space and its subspaces provide an intuitive image for characterizing the TNE state and understanding TNE behaviors   It should be emphasized that: (i) The TNE strength/intensity/degree is the most basic parameter of non-equilibrium flow description; And any definition of non-equilibrium strength/intensity/degree depends on the research perspective 
(ii) The physical meaning of D * m,n is the TNE strength of this perspective  (iii) From a certain perspective, the TNE strength is increasing; While from a different perspective, the TNE strength, on the other hand, may be decreasing  It is normal, one of the concrete manifestations of the complexity of non-equilibrium flow behavior 
Strictly speaking, those TNE intensity and effect descriptions that do not account for the research perspective are not correct  Do not explain the research perspective, the corresponding is not dependent on the research perspective 

Numerical simulations and results

In this section, we first validate the DBM code by comparing the DBM results with experimental results  Then, the effects of specific-heat ratio on the dynamic process and TNE behaviors on SBI are investigated 

Comparison with experimental results

In the following part, we use a first-order two-fluid DBM to simulate the interaction between a planar shock wave with a 2-D heavy-cylindrical bubbles, and compare the DBM results with the experimental results from Ref    The computational configuration can be seen in Fig    In a flow field which is filled with Air, there is a static bubble composed of 26% Air and 74% SF 6  
A shock with Ma = 1 2 would pass through the bubble from left to right  The initial conditions of ambient gas are ρ 0 = 1 29kg/m 3 , T 0 = 293K, p 0 = 101 3kPa  Ignoring the pressure difference between interior gas and ambient gas, the initial parameters of the bubble are ρ bubble = 4 859kg/m 3 , p bubble = 101 3kPa,
and T 0 = 293K  For simulating, these actual physical quantities should be transferred to dimensionless parameters  This process can refer to the Appendix A  The dimensionless conditions of macroscopic quantities of the fluid field in initial time are (ρ, T, u x , u y ) bubble = (4 0347, 1 0, 0 0, 0 0), (ρ, T, u x , u y ) 1 = (1 3416,
1 128, 0 3616, 0 0), (ρ, T, u x , u y ) 0 = (1 0, 1 0, 0 0, 0 0), where the subscript "0" ("1") represents downstream (upstream) region  In two-fluid DBM code, the distribution function f Air is used to describe the ambient gas, i e , Air  The f bubble characters the bubble which is a mixture that composed of Air and SF 6  
The grid number is N x × N y = 800 × 400, where the N x and N y are grid number in x and y direction, respectively  This grid size has passed the mesh convergence test  The below results also show that it is sufficient to meet the requirements of the following research problem  Other parameters used for the simulation are: c = 1 0, η Air = η bubble = 10 0,
I Air = 3, I bubble = 15, ∆x = ∆y = 1 2 × 10 −4 and ∆t = 1 × 10 −6   The viscosity effect is feeble compared to the shock compression effect, so it does not significantly affect the deformation of the bubble  Therefore, in this part, the relaxation time τ is set sufficiently small  The inflow (outflow) boundary condition is used in the left (right) boundary, and the periodic boundary is adopted in the y direction 
The first-order forward difference scheme is used to calculate the temporal derivative, and the second-order nonoscillatory nonfree dissipative scheme is adopted to solve the spatial derivative in Eq  ( )   Two quantitative comparisons between experimental results and DBM simulations are shown in the following part, including snapshots of schlieren images and evolutions of characteristic scales for the bubble 
The first is shown in Fig  non-organized momentum flux (NOMF) uously to form a diffracted shock (DS)  As TS propagates, it will split into three branches due to the considerable pressure perturbations caused by the gradual decay of the DS strength   Afterward, as shown in the subfigure at about t = 128µs, two high pressure regions (ROH) generate because of the interaction of these branches 
Subsequently, at about t = 148µs, the two ROHs meet, causing the shock focusing  On the one hand, at about t = 168µs, the shock focusing causes the generation of downstream-propagating second transmitted shock (STS) and upward-moving rarefaction wave  On the other hand, it will produce high pressure region inside the bubble, which later leads to a jet structure, as shown at about t = 288µs 
At about t = 428µs, due to the deposited vorticity, there will produce a pair of counter-rotating vortexes at the pole region of the bubble  The further development of the vortex pair and the effect of viscosity decrease the amplitude of the jet  Finally, the jet structure disappears  The second quantitative comparison is the interface structure described by the length and width of the bubble, as shown in Fig   
The experimental data are extracted from Fig  , in Ref    Quantitative agreements between DBM simulation and experimental results are seen  For the profile of bubble width, there are mainly two stages  At an early time (t < 150µs), it decreases to a minimum value because of the shock compression effect 
After the shock wave passes through the bubble (t > 150µs), the developed vortex pair caused by the deposited vorticity gradually dominates the growth of bubble width  Different from width evolution, the temporal variation of length experiences three stages  In the early stages (t < 150µs), it decreases quickly due to the shock compression effect 
Then, the jet structure emerges, which results in a growth in length (150µs < t < 250µs)  Because the upstream interface moves faster than the downstream interface, the bubble length would decrease at 250µs < t < 500µs  In the third stage (t > 500µs), the vortex pair forms and then leads to a continuous development of bubble length 
Both the length and width experience oscillations in the later stages due to complex wave patterns  The quantitative agreements between DBM simulation and experimental results indicate the following two facts: (i) the order of TNE considered in the current DBM is sufficient, (ii) the choosing of discrete velocities and spatial-temporal steps and simulation parameters like the relaxation times is suitable for characterizing the deformation of bubble, wave patterns, main characteristics of flow morphology 

Effects of specific-heat ratio on SBI

The major of current works on SBI research have not focused on specific-heat ratio effects  In this part, the simulation parameters are fine-adjusted based on the parameters in Section 3 1 to highlight the influence of specific-heat ratio  Through adjusting the extra degree of freedom I, five cases with various specific-heat ratios of the bubble are simulated, i e , γ = 1 4,
1 28, 1 18, 1 12, and 1 09  Two kinds of analysis methods, including tracer particle method and two-fluid model, are used to characterize qualitatively the macroscopic behaviors such as the shape, deformation process, mixing degree, etc  The related TNE behaviors are also studied 

Effects of specific-heat ratio on jet shape, deformation process, and average motion

We first observe the specific-heat ratio effect on the bubble shape from the view of density contour and images of particle tracer visually  As shown in Fig  , pictures with three typical moments are plotted, i e , t = 0 07,t = 0 11, and t = 0 16  The odd rows represent density contours and the even rows are tracer particle images 
It can be seen that the specific-heat ratio significantly affects the length and shape of the jet structure  The smaller the specific-heat ratio is, the stouter the jet structure can be seen  The reason is that the specific-heat ratio significantly changes the propagation speed of shock waves and wave patterns inside the bubble 
The specific-heat ratio also influences the vortex structure in early stage but contributes little effects to it in later stage  In the later stage, for cases with different specific-heat ratios, the differences in vortex pairs are almost invisible  Then, the effects of specific-heat ratio on deformation process are analyzed 
Shown in Fig  are the evolutions of characteristic scales which used to describe the bubble size, i e , width and length  It can be seen that the smaller the specific-heat ratio of bubble, the smaller the bubble width and length  For the fluid with smaller specific-heat ratio, it is easier to be compressed 
Therefore, the characteristic scales of bubbles with smaller specific-heat ratio tend to be compressed smaller  It can also be seen that the case with the largest specific-heat ratio reaches the minimum characteristic scales firstly  The reason is that the shock wave propagates faster in case with larger specific-heat ratio 
Through the method of tracer, information on the average motion of the bubble is easy to obtain  Shown in Fig  are the average position and average velocity of the bubble, with different specific-heat ratios  It is found that, in the shock compression stage (t < 0 03), the effect of specific-heat ratio contributes little to the average motion 
However, when the shock wave passes through the bubble (t > 0 03), a larger specific-heat ratio speeds up the average motion of the bubbles  The reason is that the bubbles with smaller specific-heat ratio need more energy to compress their size, so their translational energy is smaller 

Effects of specific-heat ratio on vortex motion

Vorticity is one of the most important physical quantities in describing the vortex motion  In the 2-D case, the vorticity can be calculated by the following equation: The positive (negative) value of ω represents the positive (negative) direction along the z axis  Vorticity contours at t = 0 134, with various specific-heat ratios, are shown in Fig   
The discernable difference between cases with various specific-heat ratios can be observed  The arrows in the vorticity images point out the obvious differences around the interface between case γ = 1 4 and case γ = 1 09  That is to say, there exists influences of specific-heat ratio on the rotational motion of the bubble 
The strength of vorticity is described by circulation Γ, where Γ = ∑ ω∆x∆y  Γ + = ∑ ω| ω>0 ∆x∆y is the positive circulation and Γ − = ∑ ω| ω<0 ∆x∆y represents the negative circulation  Figure shows the temporal evolution of circulations on SBI process  It can be seen that the values of Γ are equal to zero all the time because the values of Γ + and Γ − are the same 
But they point in the opposite direction  In the shock compression stage (t < 0 03), the specific-heat ratio effect contributes little to the circulation of the bubble  When the shock wave sweeps through the bubble (t > 0 03), the specific-heat ratio affects the value of circulation obviously  The cases with a smaller specific-heat ratio experiences a larger range of amplitude of change, which is caused by its good compressibility 

Effects of specific-heat ratio on mixing degree

The mixing process is a fundamental research content on SBI  In two-fluid DBM, the mixing degree at each fluid unit can be defined as M = 4 • M A M B , where M σ represents the mass fraction of component σ   The higher the value of M, the higher the mixing amplitude  Images of density (first cow) and mixing degree M (second row) at several typical moments are shown in Fig   
As can be seen, the mass mixing occurs in the region where two media contact  In addition, the mixing degree M g described the whole fluid field can be defined where the symbol "−" indicates integrating the M σ over the whole fluid field and then dividing the grid size N x • N y   Shown in Fig  is the temporal evolution of the global mixing degree M g  
As can be seen, temporal profiles of the global mixing degree show two stages: t < 0 03 and t > 0 03  When t < 0 03, there is almost no difference between cases with various specific-heat ratios  But for t > 0 03, the stronger the specific-heat ratio effect, the larger the mixing degree  Actually, there are mainly two indicators that measure the global mixing degree: the amplitude of mixing and the area of the mixing zone between two fluids 
At the stage t > 0 03, the shock compression dominates the mix by enhancing the mixing amplitude and increasing the area of the mixing zone simultaneously  In this stage, the specific-heat ratio effect contributes little to the mix  However, when the shock passes through the bubble, the deformation of interface and the evolution of vortex core both significantly raise the area of the mixing zone 
As can be seen in Fig  , the smaller specific-heat ratio of bubble, the stronger global mixing degree of fluid field  Intuitively, for the fluid with smaller specific-heat ratio, it is easier to deform and compress, which is beneficial for the fluid mixing  It can also be explained by the diffusion formula, i e ,  
The specific-heat ratio affects both the temperature T and the gradient of density simultaneously  Therefore, these two aspects comprehensively influence the material diffusion between the two fluids  Due to the complex reflected shock wave, the global mixing degree shows a tendency for oscillating growth 

Effects of specific-heat ratio on TNE behaviors

The investigation of TNE behaviors is of great importance for understanding the kinetics process on SBI  These TNE quantities describe the fluid system deviating from the thermodynamic state from their own perspectives  The effects of specific-heat ratio on global TNE strength, i e , D * 2 , D * 3 , D * 3,1 , and D * 4,2 , are shown in Fig   
It can be seen that the effects of specific-heat ratios on various TNE quantities are different  Theoretically, the influence of specific-heat ratio on the non-equilibrium effect is reflected in two aspects: transport coefficient and macroscopic quantity gradient  For example, on the one hand, the specific-heat ratio reduces heat conductivity, while on the other hand, it enhances the temperature gradient 
Therefore, the effect of specific heat ratio on NOEF is the comprehensive result of the competition between the two aspects  As shown in Fig  , the smaller the specific-heat ratio, the stronger strength of D * 3,1   It indicates that the specific-heat ratio increase the strength of D * 3,1 by raising the heat conductivity  
For the strength of D * 3 , as shown in Fig  (b), it is seen that it decreases as the specific-heat ratio becomes small  The reason is that a smaller specific-heat ratio decreases the temperature gradient  Effects of specific-heat ratio on D * 4,2 show two-stage  In the shock compression stage (t < 0 03), the smaller specificheat ratio, the larger the strength of D * 4,2  
But the situation is reversed at the stage t > 0 03  For strength of D * 2 , the specificheat effects are more significant in later stage 

Effects of specific-heat ratio on entropy production rate

and entropy production The concepts of entropy are commonly used in complex flows   In DBM, there are two kinds of en- tropy production rates, i e , ṠNOEF and ṠNOMF   They are key factors in compression science field  The former is induced by temperature gradient and the NOEF (∆ * 3,1 )  The latter is affected by velocity gradient and the NOMF (∆ * 2 ) 
The entropy production rates are defined by the following formulas : Integrating the ṠNOEF and ṠNOMF over time t, the entropy generations over this period of time are obtained, i e , S NOEF = t 0 ṠNOEF dt and S NOMF = t 0 ṠNOMF dt  Plotted in Fig  ) and 14(b) are the temporal evolution of ṠNOMF and ṠNOEF , respectively 
The evolution of entropy generation rate is related to two aspects: (i) the propagation of the shock wave, and (ii) the deformation of the bubble  The former generates a macroscopic quantity gradient, and the latter makes the contact interface wider, longer, and deformed  Depending on the location of the shock wavefront, there exist two critical moments in this SBI process: (i) at around t = 0 03, the shock wave just sweeps through the bubble, and (ii) at t = 0 06, the shock wave exits the flow field 
Therefore, the temporal evolution of the entropy production rate shows three stages, i e , t < 0 03, 0 03 < t < 0 06, and t > 0 06  At the stage t < 0 03, the shock compression stage, the shock effects compress the bubble  It generates the large macroscopic quantity gradients, resulting in a quick increase of ṠNOMF  
At around t = 0 03, the shock wave passed through the bubble  So the values of ṠNOMF decreases  The values of ṠNOMF would continue to decrease due to the gradually wider contact interface caused by the diffusion effect  At around t = 0 06, the shock wave comes out of the flow field so that the values of ṠNOMF drops rapidly 
In the third stage, i e , t > 0 06, because of the diffusive effect, the general trend of ṠNOMF is downward  However, it shows an oscillatory trend due to the influence of various reflected shock waves  The specific heat ratio indirectly changes the value of ṠNOMF by changing the velocity gradient  The smaller the specific-heat ratio, the larger ṠNOMF  
Different understanding can be seen in Fig  , where the temporal evolution of ṠNOEF is plotted  In the first stage (t < 0 03), cases with different specific-heat ratios show various trends  At the stage where the bubble deformation is not very large, i e , 0 03 < t < 0 06, values of ṠNOEF fluctuate near the average value 
In the third stage (t > 0 06), evolutions of ṠNOEF in cases with larger specific-heat ratios show an apparent growing tendency  Differently, the values of ṠNOEF in cases with smaller specific-heat ratios remain almost unchanged  The influence of specific heat ratio on the ṠNOEF , similar with the effect on NOEF, is also affected by the heat conductivity and the temperature gradient 
It can be seen that, except for the case of γ = 1 09, the larger the specific-heat ratio, the higher entropy production rate ṠNOEF   The temporal evolutions of ṠNOEF of case γ = 1 09 and case γ = 1 12 are very similar  Consequently, the specific-heat ratio increases the ṠNOEF by raising the temperature gradient 
Further understanding can be seen in Fig  , where the entropy productions over this period are plotted  For convenience, the sum and difference between S NOMF and S NOEF are also plotted in the figure  The variation range of S NOEF is larger than that of S NOMF   It indicates that the influence of specific-heat ratio on S NOEF is more significant than that on S NOMF  
Effects of specific-heat ratio on entropy production caused by NOMF and NOEF are contrary  Specifically, it can be seen that the entropy production contributed by NOMF increases with re- duced specific-heat ratio  But the entropy production caused by NOEF first reduces with decreasing specific-heat ratio and then approaches to a saturation value 
The S NOEF in case γ = 1 09 is almost the same with it in case γ = 1 12  When the specificheat ratio γ is smaller than a threshold value γ c (γ c ≈ 1 315), the entropy production induced by NOEF is more significant than that caused by NOMF  However, in the case of γ > γ c , the situation reverses  The temporal evolution of the total entropy production (S NOMF +S NOEF ) is similar to the S NOEF profile 
The difference between S NOMF and S NOEF increases with decreasing specific-heat ratio 

Conclusions

Specific-heat ratio effects on the interaction between a planar shock wave and a 2-D heavy-cylindrical bubble are studied by a two-fluid DBM which has a flexible specific-heat ratio and includes several schemes for analyzing the complex physical fields  Besides the HNE that NS easily describes, the DBM pays more attention to the related TNE that NS is not convenient to describe 
First, both the snapshots of schlieren images and evolutions of characteristic scales from DBM simulation are compared with those from experiment  The quantitative agreements between them indicate the following two facts: (i) the order of TNE considered in the current DBM is sufficient, (ii) the choosing of discrete velocities, spatial-temporal steps, and simulation parameters like the relaxation times are suitable for the following physical researches 
Then, five cases with various specific-heat ratios are simulated  Several analysis methods for complex physical fields, including the description scheme of TNE behaviors, tracer particle method, and two-fluid model, are used to characterize the effects of specific-heat ratio on the bubble shape, deformation process, average motion, vortex motion, mixing degree of the fluid system, TNE strength, and entropy production 
Specifically, for bubble shape, bubbles with different specific-heat ratios display various jet structures  The smaller the specific-heat ratio is, the stouter the jet structure can be seen  For the case with smaller specific-heat ratio, the fluid is easier to be compressed  So, the characteristic scales of bubbles with smaller specific-heat ratio tend to be compressed smaller 
For the bubble, the smaller the specific-heat ratio, the slower average motion  In the shock compression stage, the specific-heat ratio contributes little effects to the vortex motion  Differently, after the shock passes through the bubble, it significantly influences the vorticity around the interface and the corresponding amplitude of circulation due to the development of KHI 
The larger the difference in specific-heat ratio between the bubble and ambient gas, the higher the degree of material mixing  Effects of specific-heat ratio on various TNE quantities are different  These differences consistently show the complexity of TNE flows which is still far from a clear understanding 
In addition, it is found that the temporal evolution of the entropy production rates ṠNOMF and ṠNOEF both show three stages because of the influence of the shock wave location  The smaller the specific-heat ratio, the larger the velocity gradient, which indirectly enhances the strength of ṠNOMF   The specific-heat ratio increases the ṠNOEF by raising the temperature gradient 
The influence of specific-heat ratio on S NOEF is more significant than that on S NOMF   Effects of specific-heat ratio on entropy production caused by NOMF and NOEF are contrary  Specifically, the entropy production contributed by NOMF increases with reduced specific-heat ratio  But the entropy production caused by NOEF first reduces with decreasing specific-heat ratio and then approaches to a saturation value 
When the specific-heat ratio γ is smaller than a threshold value γ c (γ c ≈ 1 315), the entropy production induced by NOEF is more significant than that caused by NOMF  However, in the case of γ > γ c , the situation reverses  The fundamental research in this paper helps to understand the interaction mechanism between shock waves and bubbles in ICF, supersonic combustors, underwater explosions, etc 
The effects of viscosity and heat conduction on the interaction between shock waves and bubbles will be studied in the following work  where the subscript "m, n" means that the m-order tensor is contracted to n-order tensor  According to the CE multiscale analysis, the Boltzmann-BGK equation can be reduced to the hydrodynamic equations 
In the following part, the derivation process from Boltzmann-BGK equation to a two-fluid hydrodynamic equation are shown  More details can see the reference presented by Zhang et al    The discrete Boltzmann equation for component σ is (C 1) In Eq  C 1 there are two equilibrium distribution functions, i e , f σ ,seq = f σ ,seq (ρ σ , u σ , T σ ) and f σ ,eq = f σ ,eq (ρ σ , u, T ) 
For convenience, S σ i is defined as We perform the CE expansion around the f σ ,seq   That is, the distribution function f σ i can be expanded as where ε is a coefficient referring to Knudsen number  The partial derivatives of time and space can also be expanded to Substituting the above four equations into Eq 
(C 1), we can obtain (C 6) When retaining to ε terms, the following equation is obtained When retaining to ε 2 terms, we can obtain where M 2,αβ ( f σ ,(1) ) = ∑ i v iα v iβ f σ ,(1) i and M 3,1,α ( f σ ,(1) ) =   Substituting Eq  (C 14) into the above three equations, and replacing the time derivatives with the space derivatives, we obtain It should be noted that the ability to recover the corresponding level of macroscopic fluid mechanics equations is only part of the physical function of DBM 
The corresponding to the physical functions of DBM is the EHEs, which, in addition to the conserved moments evolution equations corresponding to the three conservation laws of mass, momentum and energy, also includes some of the most closely related nonconserved moments evolution equations  We refer the EHEs derivation based on kinetic equation to as KMM 
The necessity of the expanded part, the evolution equations of the relevant non-conserved moments, increases rapidly as increasing the degree of non-continuity/non-equilibrium  As the degree of non-continuity/non-equilibrium increases, the complexity will rapidly make KMM simulation studies, deriving and solving EHE, impossible 



ground_truth: The specific-heat ratio affects the average motion of the bubble. The bubbles with smaller specific-heat ratios have slower average motion.