Input: Why does Craig want to find his own place?

Context:
My Aspergers Child: COMMENTS & QUESTIONS [for Feb., 2017]
I emailed you a while back and you mentioned that I could email when I needed to. Thank you. I last wrote you in December that my son became involved in a dispute involving the local police. We have had 3 court dates. It keeps delaying due to not being able to come to an agreement. But the attorney, even though he was just vaguely familiar with Aspergers, has been very good with Craig. He has the compassion and excellence that is needed here. What started out very bad is turning into a good thing. It will probably take another 90 days or more.
But Craig is working hard. Too hard sometimes. He goes to therapy 3 times a week. Doing excellent. He's more focused and can calm down easier. He's got a lot on his plate but has support from his family. From his attorney. From therapy. And from his work.
He has been renting a room from a lady who has a son with ADHD. It is good for him. I'm a little worried though because since she smokes he wants to find his own place. With all the costs he has to balance it out financially. That is good. I can't help him more than I am which is good. He is stepping up and taking responsibility. He is listening much better.
He is going to have an evaluation today to get an accurate diagnosis. I understand that is a little difficult since he is an adult. Also the PTSD may cover it over. The attorney stated it would help to have the diagnosis.
Aware this is a long update, but thanks for reading. I am fighting much guilt still but I have a lot of peace now. My daughter and her 4 year old son also have Aspergers symptoms. So my life chapters may not close for a while. :-)
My name is Mac. I'm sure you're quite busy, so I'll get right to it I just wanted to pass on compliments on My Aspergers Child and your post, How to Implement the GFCF Diet: Tips for Parents of Autistic Children.
Me and my wife absolutely loved it!
I got a facebook message from him today begging to be able to come home saying he misses home and he will change. He says he will follow rules now. I stated to him the simple rules he has to follow which were - No weed in my house, or smoked in my house, coming home at curfew, going to school, no skipping, no drugs at school, and to drop the attitude of I am 17 I can do whatever I want.
I have made it very clear that if I see any drugs in my home I will be calling the police, as well as if I see signs of it being sold by him I will report him. (He has never had selling amounts in my house, ... I believe it's being kept at his "friends" which of course I have no proof of....I just know it is not here.
I know my battle is not over by a long shot, I am sure we will have more consequences and possibly another being kicked out, but I am going to think positive and hope that he learned some form of a valuable lesson here.
Thank you so much for the guidance, never in a million years did I ever think I'd be on this side, (the one needing the help, as I am the one who helps.)
I am going to go back to the start of the program like I said earlier and keep notes close by for reference.
Thanks for all you do, helping us all with ODD children/teens
I have a small company providing educational support services to a few families who have children with various disabilities in Ohio. One of the families has multiple adopted children of whom several have significant attachment disorders including RAD. As an experienced teacher and foster parent I have some experience in working with children who have extensive trauma backgrounds. However, I could use additional training. Also working with these children are two staff members with minimal background in attachment disorders who would also benefit from training primarily in behavior management. The primary caregiver to the children does a wonderful job managing their needs. In order to further develop team cohesion, I'm hoping to include her in any training as well.
Is it possible to schedule such a training session with you? If so, please let us know what will work for you including time, place, and cost. Thank you for your assistance.
I just listed to your tapes on dealing with an out of control, defiant teen. I'd like to ask your advice on a particular situation we have. Our 15 year old daughter is smoking pot almost every day at school. Because we had no way to control the situation, we told her, fine, go ahead and smoke weed. However, you will no longer receive the same support from us. You will not have your phone, lunch money to go off campus (she has an account at the school for the cafeteria she can use), and you will be grounded until you can pass a drug test. We will not be testing you except for when you tell us you are ready to be tested. She is now saying she's suicidal because she feels so isolated, yet she continues to smoke weed. In fact, she tried to sneak out last night but was foiled by our alarm system. For the particular drug test we have, I read it takes about 10 days of not smoking to pass the test. What would you do? Please advise.
I am having a problem with my 18 year old son, Danny, with high functioning autism. We finally had him diagnosed when he was 16 years old. I always knew something was going on with him but the doctors misdiagnosed him as bipolar. It's been 2 years now and he will not accept his diagnosis. He won't talk about it and when I try to bring it up he gets very angry. I've tried telling him that it's not a bad thing, that there's been many, many very successful people with Aspergers. He won't tell anyone and refuses to learn about managing life with it. He once shared with me that the other kids at school use it as an insult, like saying someone is so autistic when they do something they don't approve of. So he doesn't want anyone to know. He's turned down services that could help him. He has a girlfriend, going on 8 months. He won't tell her and they're having problems arguing a lot and I wonder if it would help for her to know.
I'm sad that he thinks it's a life sentence to something horrible instead of accepting, embracing it and learning about it more so he maybe can understand why he's struggling. I told him that he doesn't need to shout it out to the whole world but he won't even accept it himself.
I don't know how to help him with it and because he's almost 19 I have limited control now. It's made my life easier knowing what we're dealing with and I think his life would be easier is he accepted it.
Please help me help him.
I am a clinical psychologist in NYC who now has several (!!) children I see who have RAD. In 20 years of practice, I’d seen only one case. Now, I have at least three children with this. I have no training, per se, in working with this children though I know about setting structure, consistency, etc. I do a lot of work with parents about parenting. I work primarily within the school setting in a charter school whose mission is to educate children on the autism spectrum in a mainstream setting. We use Michelle Garcia Winner’s social thinking program with our ASD kids. I also work with gen ed kids in the school who are at-risk; the school is in the inner city from where the majority of our non-ASD kids live.
It would have been so much easier to mention to my adult son that I think (I know he does, but want to ease into the subject)
he has Asperger's when we were living together two years ago. He has since moved to Tennessee working in his field of interest
which is 3-D printing and software development. I am so happy for him that he has found his way into a job that he truly enjoys
even though he's socially isolated.
He's not diagnosed and does not know he has it. How I know is his classic symptoms being sensory issues (fabric feeling like sandpaper)
communication difficulties, meltdowns and much more. Throughout his childhood I just felt he was a bit different. Nothing major stood out and time
just passes, misdiagnosis of ADHD, low frustration, etc. We've talked about his ADHD numerous times (which I now know he doesn't have).
It's so much easier to communicate with him now that I know he has Asperger's. I keep it "slow and low" in talking, with long moments
of silence and then we connect. It's really too bad that Asperger's got a diagnostic code back in the 90's, yet all the so called doctors,
physiologist's, etc, didn't know how to diagnose it. Too bad.
There seems to be no one answer to "should I tell my adult son he has Asperger's" from a few specialists I asked. He is typical Asperger,
complicated, highly intelligent (high IQ), anxiety at times, socially isolated, hard to make friends. Not knowing how he will react is the hard part.
How will he be better off knowing he has it? Do I wait to tell him in person, or ease into it with him over Skype? He likes direct, honest, concrete communication.
Why is this so hard for me? Maybe because no one know's if he is going to be better off knowing or not. Do you know if people are better off
knowing? I try to get up the courage to just let him know, then I back down.
I have been searching the web looking for advice and came upon your site. I am trying to read blogs, websites, books, and articles to help guide me. I was so happy when you said that I could ask you a question. My husband and I are struggling with my 27 year old son who lives with us.
Kyle is the youngest of 4 sons. He is a college graduate but never could find the "right" job. He has always been quiet and never had a lot of friends. Two years ago, his girlfriend broke up with him. Kyle had an online gambling addiction and was using pot all the time. After the breakup, Kyle was very depressed and started using heroin and finally told my husband he was using. He is now seeing a psychiatrist who has him on suboxone and antidepressants. He is also seeing a psychologist weekly for counseling but it does not seem to be helping.
Last October,, Kyle lost his job, got drunk, and was agitated and came home , fighting with us, damaging our home and being verbally abusive. My other son , age 32, who also lives with us called the police and Kyle got arrested. He is currently in the family court system. He went through an anger management course and now is in substance abuse classes. Kyle continues to verbally abusive to me and blame me for everything. He says he "hates me "and calls me terrible names. At times, he pushes my husband and intimidates me. My husband and I are so upset. We just hired an attorney for him because since he has been going to these classes, he is getting more depressed and not getting better. Kyle continues to drink while taking his meds prescribed by the psychiatrist and then he has his "moods." My husband and I have met once with the psychiatrist just to give him background information when Kyle started with him.
At this point, we do not know what to do. We never thought at this stage of our life, we would be supporting and spending our retirement money on adult children. I do not know why Kyle hates me, I could not have been a better mom. My husband and I have no life and just do not know what it the right path we should take. Kyle does not want anything to do with us. He spends all his time in his room playing football online.We have tried tough love versus caring and love and understanding. Do you have any advice for me?
This whole ODD and ADHD is killing me as a parent. I work in the field of adult psych and addictions so I am well educated. I have been dealing with my teen being like this for almost 3 years and I totally lost my cool today with my 17-year-old son to the point I told him he is out of the house. He can never simple rules, comes and goes as he pleases sometimes doesn't come home, just recently back in school from several suspension for drug related... I am just so exhausted. He has made me hate life, hate being a parent and sometimes I just feel like not even being here. I bought your program in hopes to it would help, I am at week three and I feel things are getting worse... what am I doing wrong??
My partner hasn't been diagnosed yet but I know he has aspergers ..day to day is a struggle . I feel I'm going crazy with how he makes me feel.Feel let down constantly. He lies alot but I've been told they can't but I know he does.I just feel trapped and unloved.We have a 4yr old daughter together and my main worry with how he is that it will effect our daughter ; (his skills as a parent are so weak.He can't disapline at all.Feel so alone .he hides it well too.I just wondered if things will get worse? He's angry so quick in arguments.Scares me etc.I can't leave as he's the main bread winner and our daughter loves him to bits.Don't know why I'm writing this..Sorry if I'm going on and not making sense :(
I wanted to let you know about a research opportunity for children, teens, and young adults with autism. I am studying the effects of Brazilian Jiu Jitsu, and psychotherapy on helping people with autism develop subjective awareness of others.
I am writing you to see if this might help someone in your practice, or to see if you might know of someone with autism who may benefit from participating in this study. The requirements of the study will be:
1. A participant should be between 7-21 years of age and have a diagnosis of Autism Spectrum Disorder.
2. The participant should enroll in an approved Jiu Jitsu Academy and attend at least two sessions a week for a period of six months.
3. The participant should enroll in social skills groups, provided by my office or be in a steady psychotherapeutic relationship in your office, at least once a week, or minimally two to three times a month.
4. The participant will be given a SRS (Social Responsiveness Scale) test at the beginning of the study, at three months, and again at six months.
If you know of anyone who might benefit from this novel approach to helping to develop social awareness in autism, please do not hesitate to contact me for further information.
I have a 10 year old daughter who has outbursts with prolonged crying almost like tantrums that 2 year olds have when they cannot express themselves.
I had her in therapy from age 6-8 years old for the same thing but I feel that the sessions didn't really help much.
She has severe sensitivities to light, sound, vibration, frequencies which trigger irritability and crying.
We changed her diet and tried getting her involved with activities but she is anti-social and prefers reading than being social. She is terrified of change even in daily routine (even that will trigger prolonged crying).
It frustrates me because I don't know what else to do with her behavior.
I've tried acupuncture (she refused at the first session); she refuses massage too.
She is an honor-roll student at school and has very minimal issues at school but if she has had a bad day it does result in a tantrum or crying and defiance.
How can I get her tested for Asperger's Syndrome?
Last night our 24 year old son with Aspergers told his dad and I that he is pulling out of the 4 college classes that he recetnly enrolled in because he has not been attending class or turning in his assignments. He paid $2800 (his own money) for tuition and I reminded him of this when he told us but it did not seem to bother him.
This is the 3rd time he has started college courses and has not completed them. (He also took some concurrent college classes while he was in high school that he failed). This is a son who basically had a 4.0 grade point average through 10th grade and got a 34 on the ACT the first time he took it.
With the news that he was once again not sticking with college courses I did not sleep well. When I got up this mornning I began looking online for help in how to deal with his situation. I found your "Launching Adult Children With Aspergers" and purchased it. Most of what is included are things we have done or did with our son throughout his life. I was hoping for more help so I am emailing you now in hopes of more specific ideas.
We noticed some things with our son, Taylor, as a yound child but as we had not heard of Aspergers at that time we just did what we thought would help him. As a toddler and a child at pre-school he generally went off on his own to play. When I talked to his pre-school teacher about my concerns (that I was worried he would end up a hermit) she said she did not see him being a loner and that he seemed to interact fine with others in many situations. We worked with him on making eye contact when talking with others. We explained different emotions in people's faces and mannerisms to help him know how to interact with others. We discussed the fact that people would say things that did not mean what they souneded like - such as "I'm so hungry I could eat a horse". As we did these things he worked hard to better understand communication with others.
During his 4th grade year I had a teacher from the gifted program ask me if I had ever heard of Aspergers. I told her that I had not heard of it. She proceeded to read me some of the charateristics and so many of them described my son. So we had him tested by the school district during the summer between 4th and 5th grade and they did find that he had Aspergers but that he was high functioning. We then set him up with and EIP which stayed with him until his sophomore year. We pulled him from it at that time because we had moved and the new district was requiring him to take one class a day that was a study class. This reduced the number of required classes he could take and he was doing fine with his studies at the time.
It was during the 2nd half of his Junior year that we noticed some of his grades going down. Then during his Senior year is when he started skipping classes and not doing assignments. We had not realized it before then but we soon became aware that he was addicted to gaming. He would go to the library or somewhere else on campus and play games on the computer rather than go to class. It was also at this time that he began lying about his actions (so as not to get in trouble).
Based on his grades and his ACT score he received offers from colleges for full tuition scholarships. He chose the college where he had taken concurrent classes during his high school years. But he proceeded to skip class and not turn in assignments so he lost his scholarship and quit attending college. During this time he was only able to find employment through an employment agency where he was mostly sent to manuel labor type jobs (which is not something he enjoys but he did it anyway). It was during this time that at one place had gone to on numerous occasions he was told if he came late one more time they would tell the emplyment agency they did not want him to come there anymore. (This seemed to make an impression on him because he has continued to be reliable and responsbile at his places of employment).
At 19 1/2 he left to serve a 2 year full-time mission for our church. He completed his mission successfully. (I don't think it was without some struggle, stress and depression, but he was able to pick himself up and move on from those times).
When he came home he started working for the employment agency again but began looking for employment elsewhere. He got a job at a local Chick Fil-A where he has worked for 3 years. He started college again shortly after he came home but as before it was short lived. He did finish out the semester but failed most of the classes due to his skipping class and not turning in assignments. When he skipped class he would usually sleep in his car.
Taylor's life consists of working (where to the best of our knowledge) he does well, he is reliable and his employer likes him. When he comes home from work he either sleeps or plays video games or other games - such as kakuro. He spendes most of his time in the basement where his bedroom is and this is where he games. Taylor owns his own car, bought his own laptop and very rarely spends money. He pays us $200 /month to still live at home, unloads the dishwasher on a regular basis and does the weekly garbage. However, his room is a mess and he only cleans his bathroom when I tell him he needs to clean it.
Taylor used to read quite a bit and loved to learn. It has just been in his adult years that he has not read as much - I think because of his gaming addiction. Taylor goes to church on a regular basis but sleeps through the main meeting. In Sunday class room settings he stays awake - I think because he is able to particpate in discussions.
Taylor has only had 2 real friends since entering Junior High school. And as of now he only keeps in contact with one of them who still lives in Georgia. We have lived in Utah since the summer of 2007 and he has never had a friend to do things with since we have lived here. He has two younger siblings, a brother 22 and a sister 20. They love Taylor and spend time with him when they are home. They are both at college and doing well.
Throughout Taylor's school years he has seen a counsleor on a fairly regular basis. One summer during junior high he attended a weekly class where he interacted with other kids with Aspergers. We did see a lot of change in him from this group. After he returned from his mission he went to see a counselor for a short period - this counselor tried to help him with some social skills. His dad and I went with him the first 3 or 4 times but we found out that after we quit going with him he only went a few more times and then scheduled appointments but did not show a couple of the times. We only found this out when a bill came for a "no show" appointment.
I don't know if this is too much information but were are in dire need of help for him. In the information that we purchased from you you mentioned that you do coaching for Aspergers adults. I don't know if you can help us but I thought I would check with you just in case.
Alas I think I have found your information too late to save my marriage but I am hoping to save myself.
I am currently going through a very very painful separation after a 27 year relationship with my husband whom I am convinced has aspergers syndrome. It is a long and painful story and I am desperately trying to process it all alongside dealing with a very conflictual separation. My partner is angry non communicative and totally dismissive of me and our long shared history.
He walked out last year after I discovered he had been visiting massage parlours and developed a relationship with an illegal Chinese escourt whom he subsequently moved in with. He had been seeing this woman behind my back for over 18 months. The pain of all this indescribable and his dismissal of my pain and very existence beyond belief.
Leading up to this I had been battling anxiety and depression which my husband found very hard to cope with.
Over the years of our relationship I knew something was off but I just could not put my finger on it. I often felt a complete lack of validation and empathy. Communication was also difficult as my husband was defensive and unwilling to look at issues in our marriage.
Please Mark could you help me validate some of this pain and try and make dense of 27 years of my life without drowning in fear guilt and despair about my future.
Thank you for listening and your site.
I have had problems with drunkenness, being late for school, not handing in school work, buying pot from a dealer etc. I chose to focus on the drinking and did the grounding then (grounding happened 3 times). I also stopped sleep overs at friends 100%. I have stopped handing out money for no reason or even buying treats like chocolate.
I did lose it one evening (and didn't do the poker face) when I was trying to unplug the internet at midnight on a school night (she’s always late for school so I am trying to get her to sleep at a reasonable hour). I was physically stopped and pushed around so I slapped my daughter (it was not hard). This ended up with her saying she didn’t want to come home (the next day after school). By this stage, I also had enough and didn’t go get her. I thought I am not begging. You will run out of money soon. It was quite a relief to have some peace. Daughter’s Dad was in town (from another country) and called a family meeting with the counsellor. To cut a long story short, daughter and her counsellor put it on the table that daughter wants to go live somewhere else (with her friends family) because of the stress at home with me (we live on our own) (i.e. stricter rules and her bucking up against it).
I didn’t really want this but made a compromise that daughter would go there Tues morning – Friday afternoon as the friend is an A student whereas my daughter is failing. They do the same subjects. I made the decision at the end of the day based on what is good for me – some time away from the daughter. I also thought of your book when the child went to live with the grandparents – daughter will dig her own hole over at the friend’s house. They have a week day no going out policy which made me think it is OK. I went and discussed with them the problems experienced (drinking, pot, late nights, not handing in work)
I am also trying to follow the let go of school thing per your book. I find it really difficult to remain calm when I can see daughter on her phone and watching series (when I have her on the weekends) when I know there are projects due. I hired her a private tutor once a week for help with a subject. The tutor has just fired my daughter for not handing in work and being not committed. It’s not the first time private tutoring has not been appreciated. The school give me a report back on a Friday as to whether everything is handed in. The deal is – if the work is not handed in – no pocket money and no Friday night out). Her school is a "progressive" school and there are no repercussions for her being late or not handing in work. I would change schools if I could but there are only 8 months left of school (she turns 18 in August).
We have just completed the first week and beginning week two of your material. We are agreeing with your take and see our son and ourselves in most of what you are saying. Prior to finding your material and starting your program we had been having extreme out of control behaviors and had to call the police because he was breaking things in our house and pushed my husband. This happened three weeks ago. After that incident we took away privileges ie. PS4, phone (which had already been taken for a few days), and friends. So, last week while doing your program he already didn’t have privileges and has continued with poor behavior – name calling, throwing things, slamming doors. We are not sure when to give privileges back. He has been given the privilege of playing with friends on occasion. His 13th birthday is tomorrow. This past weekend, for his birthday my husband and he went boar hunting. Of course we debated about it but decided to go ahead since it was his bday. We are cooking some of the meet on the grill tomorrow night for his bday and inviting a couple of his friends over for a cookout. No more gifts other than cards and balloons. We are wondering if we should go ahead and give him his privileges back and not sure how to do it. Last Friday morning we attempted to talk giving him a date to return privileges and that conversation ended with him getting angry but he gathered from our conversation that he is getting his stuff back on his bday. We are starting week 2 assignments today but not sure how to handle what was already in place. Of course, we aren’t seeing the respect and responsibility we are looking for but realize it has been a long time. We were wanting him to pay for his phone and thought it might be a good time to introduce that idea. Allowing him to earn his phone. We expect that he will be angry with this idea and not sure how to implement.
My son and myself are interested in a inpatient Aspergers program. We line in Calif which is preferable. My son is very high functioning and was diagnosed dry late. He was eight years old. He has never been in or attended a full day of class. Partially due to depression,anxiety, and trouble with his ADHD also his aversion and being bullied and of course his Aspergers. He will not attend his freshmen year due to surgery on both Achilles' tendons from walking on his toes. With physical therapy he should be ready by his sophomore year! We all feel he needs in patient therapy to give him the tools on how to work with his issues in a structured setting and a place that will give him tools for the rest of his life.
In my utter desperation to find a way to get some help for my daughter's increasingly challenging behaviour I trawled the internet to see if I could find some strategies that would provide specific methods on dealing with teenagers with Asperger's syndrome. When I came across your website, I couldn't believe that every statement you made was exactly what I have been going through with my daughter. She has just turned 14 last week, and was diagnosed with Asperger's/ Autism Spectrum Disorder 15 months ago. I have already been seeing a child psychologist for the past five months, however the methods she has been advising have not been very effective.
Our main difficulty with our daughter is her overwhelming obsession to use her cell phone (and to a lesser extent her laptop) constantly. Without any restriction, she will be on it every minute of the day, and will be awake until the early hours every day. We have tried to incorporate her input around rules as to when she has to give in her phone, but she is unwilling to compromise on a time that she should give it to us, believing that she should have unlimited use. I believe she is unable to do any adequate study or homework, as she is constantly having to look at the phone. We have tried to put rules in place that she has to give in her phone and laptop on school nights at 22:15. If she is able to do this then she is given rewards, and if she doesn't then she knows that there will be consequences. The consequence has been restricted use the following day. However, this is usually where we fail, because taking her phone away from her results in tantrums, screaming, and even threatening to harm herself. This behaviour is relentless to the point where the whole family becomes deeply distressed, and inevitably results in her getting the phone back.
This obsession is affecting her schoolwork, and more severely her eyesight. She has become very shortsighted, and her eyesight continues to deteriorate as a result of holding the phone or laptop very close, and mostly in the dark without any lights on. My husband and I have a constant battle on our hands daily, in all areas of discipline with our daughter, but our main concern is that we have been unable to find a way to minimise this obsessive behaviour centred around her phone and laptop. Please can you provide some strategies that can help us specifically with this problem.
First of all, I thank you for developing this program and I am only at the first stage of assignment 1. I have loads of books I have bought, attended psychiatrists for my son and myself, family therapy, occupational therapy, begged and prayed for change but have been dealing with behavioural issues for so long I am definitely exhausted and resentful.
I am a mum to a 15 yr old boy with ASD, dyslexia, OCD and ODD. Sorry to focus on the labels but just to give you an idea of what I am dealing with. I also have a 13 yr old son whom finds his brother’s behaviours difficult, embarassing and challenging. My husband whom is not in great health ( he had a cerebral aneurysm clamped two years ago and has two further aneurysms that are inoperable so endures fatigue, headaches and stress). We have however a pet cat that is very social and a calming influence in the home! I was fortunate enough to have loving parents but I lost both my mum and dad in 2008 and 2015. My inlaws are elderly and quite directly say they are too old to help us so it feels we are alone in dealing with the issues we have.
I am desperate for change as the household is one of stress and anger and I feel all the control lies in my son Patrick’s hands. I am hopeful your programme can make life better for all of us but I wonder if it is too early to ask you two questions?
The first lies with what to do when Patrick goes into my other son Brendan’s room and will either turn on a light when he is sleeping, yell when he is on his phone or create some disturbance. He will not leave the room when asked to do so and the situation always escalates into yelling and Brendan attempting to physically remove him. This happens regularly and always ends badly with doors slamming, my husband being woken and myself in tears feeling the lack of control and also I admit I seem to think “Why me?” which rationally I know is of no help.
The second problem is leaving the house for school. Patrick refuses personal hygiene (either morning or night) and any request to even brush his teeth is fraught with swearing and abuse. If I can get him to shower, he will watch the water roll down the drain and turn up the water really high temp (mu husband has had to turn down the thermostat on the hot water service) without so much as getting wet. My husband leaves for work at 6am but I leave at 745 to work as a nurse in a busy outpatients department in the Alfred Hospital (Melbourne). My work is my sanity as it is a paid break from home but most days I am late which is causing considerable stress and anxiety not to mention my responsibility to do my job. Patrick simply refuses to leave the house and as much as I am tempted to just walk out and leave I know the house would be left unlocked and wonder if Patrick would even attend school. The time I need to leave is not negotiable but Patrick uses this to his advantage and seems to delight in stressing me out and subsequently speeding to work in a frazzled mess.
The interesting and frustrating element in all of this is that although he is socially isolated at school (he has no friends) and academically challenged his behaviour at school is not a problem. He is quiet and his teachers report he does his best and is compliant and well mannered. It is like a Jekyll and Hyde situation where another side of him at home is so angry and abusive yet at school this behaviour does not happen.
I’m Jackie, I now work primarily as a freelance tech writer, after starting my career in software development and moving on to teach IT to young adults at a variety of colleges and schools.
My freelance work is pretty varied and looks at many aspects of the computer industry as a whole, and I’ve just recently completed a piece which gives help and advice to anyone wanting to become a game designer, which you can read here: http://www.gamedesigning.org/become-a-game-designer/. It highlights the hard work and effort it takes to get into such a role, and also how you can further your career and continue to learn and improve as you go. I hope you’ll agree it shows that starting work in the industry takes dedication and skill and that becoming a game designer isn’t just a fly-by-night job!
If you’d be interested in sharing a quick mention of my work on your blog that would be really wonderful and I’d appreciate the chance to get my work out there to a wider audience. Alternatively, I’d be happy to write a short blurb or paragraph or two (or a longer piece - just let me know) highlighting the key points because I think some of your readers might get a lot of value from it.
My son just turned 15 and is a freshman in high school. Although this is his first year in a general ed environment, he is struggling with behaviors in school. He has meltdowns and does not express why he would have them until much later. Once we all know what caused it, the school will accommodate him and try to "change up" things so as not to cause his meltdown. Once that is resolved, another issue comes up and causes him to melt down. He is a high functioning and academically does well, when he wants to do the work. We battle at home over homework. He does not care how it is done, as long as he hands it in. He thinks failing a test is ok, at least he took the test. Homework is never on his mind when he gets home from school. If I never prompt him, he would never open is backpack. He can be aggressive but is never intentionally trying to hurt anyone. He may push over a chair in school, but it is not directed at anyone. We know how that in itself could hurt someone who gets hit by it though. He is defiant in that he only wants to do what interests him. He does not go out by himself (still immature), or abuse alcohol or drugs and never curses. He is a very funny kid and very talented. His main problems are task avoidance and seeking attention. He can be disrespectful to adults in that he is "cheeky" with them, trying to be funny or cute. And he has no "filters".
I’ve just finished reading your Living with an Aspergers Partner ebook. I found it so informative, thank you.
You offered some personal advise, and i wanted to run a situation past you and seek your input as to a strategy for what to do next.
I’ve been seeing a guy for about 7 months now who I believe has Aspergers. I came to this conclusion months ago and I don’t think he realizes, (or acknowledges) although he is aware he has some traits.
He’s highly intelligent and successful, a pattern seeker, has a tendency to focus on the project to hand to the total exclusion of all else for as long sit takes (work or home) socially awkward (has learned coping strategies), sensitive to loud noise, high anxiety with control strategies, black and white thinking etc. He’s currently not working and I’ve seen a slow withdrawal over the last 6 weeks, including the need to ‘escape’ and leave a situation at least once.
He also has a bipolar ex overseas who has primary custody one daughter where there has been ongoing patterns of drama which has recently increased.
Over the past couple of months (since stopping work and drama increase) I’ve gone from being ‘wonderful’ in his eyes to him now being sorry and not having the ‘urge’ to spend close/intimate time with me and offering friendship. Since he shared that with me in a message he’s stonewalled and has retreated to the safety of minimal messages and talks about not knowing what best to say and not being able to find the right words somehow.
He’s a good kind man who I feel is struggling. I’m concerned about his anxiety and possibly the risk of depression. I’m fairly resilient and whilst i’m disappointed he doesn’t want to pursue a relationship with me, i’m concerned for him and his well being. One of his very few close friends is also just leaving the country to live overseas.
The strategy I’ve used so far is simply to back off and give him space. I’ve asked to take him up on an original offer he made to talk but haven’t pushed it. I also haven’t been aggressive or accusatory in the few messages i’ve sent.
Any advise you could give would be greatly appreciated,
Carli who is 10 years old and has had behavioral issues her whole life. The other night she came home very upset after having a conflict with a friend. She was at her friend's house and her and her friend wanted to get on the computer and the older sister was using it. Carli made up a story that someone was at the door to get the older sister off the computer. Her friend didn't understand that she was making up a story to get the sister off the computer. She got excited that someone was at the door and ran downstairs to answer the door. In the process of getting the door, she fell and yelled at Carli. Carli became extremely upset. She was able to control her feelings at her friend's house, but when she came home, she proceeded to cry extremely loudly for over an hour. Her dad spent most of that time with her, talking to her and trying to calm her down. After an hour, I asked him if he could please tell her to be more quiet because the other members of the household were trying to go to sleep.
My question is....how do I as the girlfriend, handle this? He did not like that I asked her to be quiet. We have a rule that if she is having bad behavior, and can't calm down in 5 minutes, he takes her out of the house because her yelling doesn't stop for a long time and is very upsetting to everyone in the household. I would like to ask him to do this with this kind of situation as well. Is this a reasonable request? His thought was that she shouldn't be made to calm down, because everyone handles being upset in a different way. But, she was literally sobbing and wailing very loudly.
My other question is should she have been told that if she wouldn't have lied, this wouldn't have happened? She has a history of lying and of not accepting responsibility for her actions. My boyfriend became very upset with me when I brought this up. He was being very sympathetic and understanding to her. I feel like he was giving her negative attention, and being an over indulgent parent by not putting his foot gown and saying, "you can't carry on like this, even though you are upset". Please let me know how we can handle these situations better.
I am contacting you for help with adult AS. I am taking initiative to pre screen potential therapists to help my current boyfriend get therapy and help with Adult AS.
He has seen many therapists, but it seems like they aren’t really helping him with his problems. They don’t seem to understand how his (undiagnosed) AS would affect therapy approaches. For example, he may not share enough in therapy session and I’m assuming an AS therapist would recognize that is part of the AS and employ strategies to get information from him that helps with treatment. Sometime he tunes out when he is processing something heavy or that he doesn’t want to hear necessarily, or he gets distracted and I’m hoping an As therapist would recognize that and get that he may need repeated something for example, if this is happening.
He is currently suffering from depression that appears clinical in nature as well as reoccurring negative thoughts about something specific that has been worrying him about our relationship. Today he told me these reoccurring thoughts happen during all waking hours unless he watches TV, he never gets a break from them and they make him feel like he is going crazy. As his girlfriend, I am extremely concerned that he cannot get relief from these thoughts and that the therapists he is seeing are unable to help him with his problems. Therefore, I am taking initiative to try and help him find better therapy options, because I want to see him someone who can better help him get to the bottom of things and help him with the challenges he is facing. He really needs an advocate that will help him go deep to figure things out and not just assume therapies are working well, without seeing changes or getting supporting feedback from him in that regard.
Here are some questions I am trying to ask in advance to find the right people to help us with this. As you may know, insurance for these therapies are not often available. We don’t have a lot of money to go from therapist to therapist to find the right person and are hoping prescreening will help.
I recently downloaded your e-book and listened to your talks and your information is by far the most helpful I have been able to find to date. It's very accurately describes my situation as an NT wife married to a very probable AS husband. I think you for taking the time to write this and sharing your insights as well as the experiences of many of your clients. It has really helped me understand the last 32 years of our marriage and get a grasp on how to move forward.
One area that is of primary concern to me, that I did not see addressed, is stimming. I believe that is the behavior my husband is showing through constant vocal singing, repetition of words, shouting out, as well as slapping himself in the chest and general nervous activity. It is very loud and disruptive to our household and it is often a relief when he is not at home. I think there may be a level of Tourette's syndrome as well.
I did some searches on the Internet and could not find anything that really describes his behavior. Most of what I found was flapping or children's behavior. I understand that it is a release of nervous tension but I am really trying to find some strategies to help him stop this behavior as it is extremely frustrating and builds my resentment in dealing with it daily. A lot of it is embarrassing as well and sounds childish to me.
He usually does this when close family members are around and will reign himself in if he is around other people besides us. When we are home it is constant. He also has a lot of anger, mostly at himself, and blows up at unimportant things, it is as if he has a ton of negative energy inside him that need to get out and stimming is one outlet.
I will try to build my acceptance of it, but I also would just like him to stop especially the loudest and most annoying portions. Would you have any resources you could point me to?

Answer: Because his roommate smokes.


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

Context:
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.

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


Input: What is the research opportunity that is mentioned?

Answer: A study on the effects of Brazilian Jiu Jitsu and psychotherapy on people with autism.