bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some Tears in Achilles Tatius (Achilles 6.7.3–7)
Authors: Hutchinson G. O. 
Published: August 2018

AbstractAnother novelist provides in some respects a point in between Chariton and Heliodorus. His elaborate expatiation on tears and the lover put rhythm at the service of an intricate treatment of the mind and body, and a shrewd depiction of amorous self-control and manipulation. The first-person narrative adds a further stratum of sophistication to this handling of the speaker’s rival and enemy. Achilles Tatius demonstrates further, in contrast with Chariton, the range of possibilities for the exploitation of rhythm seen already in the difference of Chariton and Plutarch. Comparison with Heliodorus brings out Achilles’ elegance.
Newton’s Three Laws
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter introduces Newton’s laws, the Newtonian formulation of mechanics and key concepts such as configuration space and phase space for later development. In 1687, the natural philosopher Sir Isaac Newton published the Principia Mathematica and, with it, sparked the revolutionary ideas key to all branches of classical physics. In this chapter, the system is the object of interest and is considered to be either a single or a collection of generic particles that are not governed by quantum mechanics, for quantum systems do not follow these laws explicitly. Results for systems of particles and conservation laws are presented as the invariance of a given quantity under time evolution. The N-body problem, first integrals, initial value problems and Galilean transformations are all introduced and the Picard iteration and the Verlet algorithm are discussed.
Energy and Work
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter discusses the work–energy theorem, which is developed from Newton’s second law, and defines the kinetic and potential energies of the system. While there is some vector calculus involved, it has been kept to the bare minimum and the reader should not require in-depth knowledge to understand the salient points. If there is a net force on the particle, it accelerates in the direction of the unbalanced force. The force is a central force if it depends only on the distance between the point on which the force acts and the coordinate origin. Using Stokes’s theorem, potential energies are thoroughly discussed. The chapter also discusses spherically symmetric potentials, isotropic force, force on systems of particles, centre of mass coordinates and rigid bodies.
Constrained Lagrangian Mechanics
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
Symmetries & Lagrangian-Hamilton-Jacobi Theory
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s theorem’, after Amalie ‘Emmy’ Noether, who first discovered it in 1918. The chapter starts off by discussing Noether’s theorem and symmetry transformations in Lagrangian mechanics in detail. It then moves on to gauge theory and surface terms in the action before isotropic symmetries. continuous symmetry, conserved quantities, conjugate momentum, cyclic coordinates, Hessian condition and discrete symmetries are discussed. The chapter also covers Lie algebra, spontaneous symmetry breaking, reduction theorems, non-dynamical symmetries and Ostrogradsky momentum. The final section of the chapter details Carathéodory–Hamilton–Jacobi theory in the Lagrangian setting, to derive the Hamilton–Jacobi equation on the tangent bundle!
Liouville’s Theorem & Classical Statistical Mechanics
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter returns to the discussion of constrained Hamiltonian dynamics, now in the canonical setting, including topics such as regular Lagrangians, constraint surfaces, Hessian conditions and the constrained action principle. The standard approach to Hamiltonian mechanics is to treat all the variables as being independent; in the constrained case, a constraint function links the variables so they are no longer independent. In this chapter, the Dirac–Bergmann theory for singular Lagrangians is developed, using an action-based approach. The chapter then investigates consistency conditions and Dirac’s different types of constraints (i.e. first-class constraints, second-class constraints, primary constraints and secondary constraints) before deriving the Dirac bracket from simple arguments. The Jackiw–Fadeev constraint formulation is then discussed before the chapter closes with the Güler formulation for a constrained Hamilton–Jacobi theory.
Classical Path-Integrals
Authors: Mann Peter 
Published: August 2018

Abstract
The purpose of this chapter is to formalise functions and set theory. It is often handy to partition a collection of numbers into one package for neatness. This is the idea of a set; it is itself an object. A function is like a number-crunching box: numbers are fed into the function and another number comes out; it is a mapping from a set of numbers to another set of numbers and there are several ways to write it. A functional is a box that takes a function and gives out a number; it is a function of a function of a variable. A real-valued function is a scalar field when it has a scalar quantity as its output; it is called a vector field when the output is a vector. Other concepts associated with sets and functions are discussed, providing background to the other chapters in the book.
Partial Differentiation
Authors: Mann Peter 
Published: August 2018

Abstract
This short chapter discusses the Legendre transform, which is used in mechanics to convert between the Lagrangian and the Hamiltonian formulations. The Legendre transform is a mathematical tool that can be used to convert the variables of a function through the methods of partial differentiation in a one-to-one fashion. Developed by Adrien-Marie Legendre in the nineteenth century, it is also central to converting between action principles, generating functions and thermodynamic potentials. By using the Legendre transform, two variables can be expressed in four different ways, via the idea of conjugate pairs; it just depends on what differential quantity is subtracted. Variables that are not considered in the transformation are called passive variables, whiles the important ones are the active variables. The information in this chapter provides the background for many of the other chapters in this book.
Differential Equations
Authors: Mann Peter 
Published: August 2018

Abstract
This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used throughout classical mechanics. First developed by Euler to determine the shortest paths between fixed points along a surface, it was applied by Lagrange to mechanical problems in analytical mechanics. The variational problems in the chapter have been simplified for ease of understanding upon first introduction, in order to give a general mathematical framework. This chapter takes a relaxed approach to explain how the Euler–Lagrange equation is derived using this method. It also discusses first integrals. The chapter closes by defining the functional derivative, which is used in classical field theory.
A First Look at Relativity
Authors: Wittman David M. 
Published: August 2018

Abstract
The heart of relativity is the supposition that the laws of physics are the same in all coordinate systems. This chapter builds a foundation by defining coordinate systems (also called frames of reference or simply frames) and examining some quantities that are coordinate‐dependent and others that are coordinate‐independent; the latter turn out to be more physically meaningful. Galileo first considered relationships between coordinate systems moving at different veloCities; in modern terms this could relate a coordinate system attached to the ground to one attached to a moving train. Given your velocity relative to the train, and the train‐ground relative velocity, Galileo developed a law for inferring your velocity relative to the ground. If this Galilean velocity addition law is correct, there are profound implications: nature must have no speed limit, and the laws of motion must be the same in any constant‐velocity frame.
Acceleration and Force
Authors: Wittman David M. 
Published: August 2018

Abstract
This chapter develops crucial distinctions between constant‐velocity (also called inertial) frames of reference and accelerating ones. Inertial frames respect Newton’s first law—objects maintain constant velocity unless acted upon by a net force—while accelerating frames violate this law. Therefore, much of our thinking about whether the laws of physics are the same in all frames will really concern *inertial* frames. Newton’s first law gives us a foolproof test for distinguishing accelerating frames from inertial frames; this testworks even if velocitymeasurements are not directly available. We sometimes invent fictitious forces (such as “centrifugal force”) to explain the acceleration of free objects in accelerating frames, but we know how to determine that these are indeed fictitious.We also examine relationships between acceleration, force, andmass (Newton’s second law).We *define*mass as the ratio of force to acceleration, so mass represents a resistance to acceleration, or inertia.
Reasoning with Frames and Spacetime Diagrams
Authors: Wittman David M. 
Published: August 2018

Abstract
To prepare for the high‐speed world where Galilean relativity breaks down, we now practice the skill of thinking in different frames. Practicing this in our familiar lowspeed world will help us avoid cognitive overload when we enter the more counterintuitive high‐speed world. We examine two problems that illustrate the process of thinking in different frames. Te frst is a brain‐teaser that suddenly becomes easier in a particular frame; the second is a classic problem from introductory physics that we can solve in a new way using symmetry and frame‐based thinking tools alone. Along the way, we will learn how to use the spacetime diagram, a major tool that will appear throughout this book. Te chapter concludes with another look at accelerated vs. inertial frames, from the spacetime diagram point of view
Time Skew
Authors: Wittman David M. 
Published: August 2018

Abstract
This chapter explores one major consequence of the invariance of c: events that are simultaneous in one frame are not necessarily simultaneous in other frames.We will find that the time coordinates of events are just as frame‐dependent as their positions. This is no accident, but a symmetry between space and time. Viewed in a spacetime diagram, a frame change rotates the grid lines marking time just as much as it rotates the grid lines marking position; this preserves c as the same speed in all frames. Along the way, we practice using skewed grids in spacetime diagrams: identifying the time coordinates of events, identifying events that are simultaneous in a given frame, and adding velocities. Although the skewed grids change the time coordinates of events and even their order in time, we show that they do not change causal relationships between events.
Special Relativity: Putting it All Together
Authors: Wittman David M. 
Published: August 2018

Abstract
We have introduced the ideas of special relativity in quick succession because none of those ideas can really be understood in isolation. This chapter works through examples in some detail so you can practice applying the ideas and solidifying your understanding.We start with an overview of how to use spacetime diagrams to solve problems in special relativity, then we walk through examples ofmeasuring the length of a moving object; the train‐in‐tunnel paradox; velocity addition; and how clock readings are arranged so that each observer measures the other’s clocks as ticking slowly.
The Twin Paradox
Authors: Wittman David M. 
Published: August 2018

Abstract
To prepare for the high‐speed world where Galilean relativity breaks down, we now practice the skill of thinking in different frames. Practicing this in our familiar lowspeed world will help us avoid cognitive overload when we enter the more counterintuitive high‐speed world. We examine two problems that illustrate the process of thinking in different frames. Te frst is a brain‐teaser that suddenly becomes easier in a particular frame; the second is a classic problem from introductory physics that we can solve in a new way using symmetry and frame-based thinking tools alone. Along the way, we will learn how to use the spacetime diagram, a major tool that will appear throughout this book. Te chapter concludes with another look at accelerated vs. inertial frames, from the spacetime diagram point of view.
Spacetime Geometry
Authors: Wittman David M. 
Published: August 2018

Abstract
This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.
The Equivalence Principle
Authors: Wittman David M. 
Published: August 2018

Abstract
The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.
Newtonian Gravity
Authors: Wittman David M. 
Published: August 2018

Abstract
Having developed a framework for subsuming gravity into relativity, we examine how gravity behaves as a function of the source mass (Earth, Sun, etc.) and distance from that sourcemass.We develop Newton’s inverse‐square law of gravity, and we examine the consequences in terms of acceleration fields, potentials, escape velocities, and surface gravity. Chapter 17 will build on these ideas to show how orbits are used to probe gravity throughout the universe.We also develop a tool for exposing variations in the acceleration field: the tidal acceleration field in any region is defined as the acceleration field in that region minus the average acceleration. This enables us to restate Newton’s lawof gravity as: the acceleration arrows surrounding any point show a net convergence that is proportional to the density of mass at that point. Chapter 18 will use this to develop a frame‐independent law of gravity.
General Relativity and the Schwarzschild Metric
Authors: Wittman David M. 
Published: August 2018

Abstract
Previously, we saw that variations in the time part of the spacetime metric cause free particles to accelerate, thus unifying gravity and relativity; and that orbits trace those accelerations, which follow the inverse‐square law around spherical source masses. But a metric that empirically models orbits is not enough; we want to understand how any arrangement of mass determines the metric in the surrounding spacetime. This chapter describes thinking tools, especially the frame‐independent idea of spacetime curvature, that helped Einstein develop general relativity. We describe the Einstein equation, which determines the metric given a source or set of sources. Solving that equation for the case of a static spherical mass (such as the Sun) yields the Schwarzschild metric. We compare Schwarzschild and Newtonian predictions for precession, the deflection of light, and time delay of light; and we contrast the effects of variations in the time and space parts of the metric.
Beyond the Schwarzschild Metric
Authors: Wittman David M. 
Published: August 2018

Abstract
General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.
Black Holes
Authors: Wittman David M. 
Published: August 2018

Abstract
Black holes seem like something out of science fiction, but they are real. Now that we understand the relevant properties of gravity we can separate fact from fiction. We start by defining black holes and showing how they differ fromthe simple Newtonian idea of “no escape.” Time and space seem to swap meaning inside the black hole, so that “forward in time” is a direction that points toward the center of the black hole. We then look at the astrophysical evidence that black holes really exists: how we can observe them, as well as the limits to our observations.We then examine facts andmyths about black holes, including tidal effects such as spaghettification. Finally, because black holes in nature spin rapidly, we look at gravitomagnetic effects around rapidly spinning black holes.
First application of 3D design custom-made uncemented prosthetic stem for distal femoral cemented megaprosthesis revision
Authors: Min Li , Yao Kai , Lu Minxun , Zhou Yong , Wang Jie , Tang Fan , Zhang Wenli , Luo Yi , Duan Hong , Tu Chongqi 
Published: August 2018

AbstractObjectives3D design, which is widely used in orthopedics, can be applied for precise distal femoral megaprosthetic revision. This research aimed to present and evaluate the design, perioperative management, and mid-term clinical outcomes of a 3D design custom-made uncemented prosthetic stem.MethodsBetween January 2014 and January 2016, seven patients received 3D design custom-made uncemented prosthetic stem revision at our institution. Clinical records and radiographs were evaluated retrospectively.ResultsThere were no hardware-related complications during the follow-up (average 24.3 months; range 24–48 months). The average Musculoskeletal Tumor Society (MSTS) score at the last follow-up after revision (27.7 points, range 25–28 points) was significantly higher than that before (16.0 points, range 13–18 points). In addition, the range of motion (ROM) of the affected knee, and the scores of pain, function, emotional acceptance, support, walking and gait all improved significantly. The antecurvature radian of the revision stem averaged at 3.6°. Of the seven patients, three received femoral stem revision and four received revision of the femoral stem and the femoral component; three of them used longer prostheses than the others. There were no significant differences in function between these two groups at the last follow-up after revision.ConclusionThe 3D design custom-made prosthesis is a typical precision medicine technology in oncologic orthopedics. Characterized by its individually and precisely designed uncemented stem, it offers an alternative option for distal femoral cemented prosthesis revision. Besides the 3D design itself, the perioperative management, especially the techniques for stem implantation, and long-term follow-up are also crucial.
Coordinated regulation of skeletal muscle mass and metabolic plasticity during recovery from disuse
Authors: Kneppers Anita , Leermakers Pieter , Pansters Nicholas , Backx Evelien , Gosker Harry , Van Loon Luc , Schols Annemie , Langen Ramon , Verdijk Lex 
Published: August 2018

ABSTRACTSkeletal muscle regeneration after disuse is essential for muscle maintenance and involves the regulation of both mass‐ and metabolic plasticity–related processes. However, the relation between these processes during recovery from disuse remains unclear. In this study, we explored the potential interrelationship between the molecular regulation of muscle mass and oxidative metabolism during recovery from disuse. Molecular profiles were measured in biopsies from the vastus lateralis of healthy men after 1‐leg cast immobilization and after 1 wk reloading, and in mouse gastrocnemius obtained before and after hindlimb suspension and during reloading (RL‐1, ‐2, ‐3, ‐5, and ‐8 d). Cluster analysis of the human recovery response revealed correlations between myogenesis and autophagy markers in 2 clusters, which were distinguished by the presence of markers of early myogenesis, autophagosome formation, and mitochondrial turnover vs. markers of late myogenesis, autophagy initiation, and mitochondrial mass. In line with these findings, an early transient increase in B‐cell lymphoma‐2 interacting protein‐3 and sequestosome‐1 protein, and GABA type A receptor‐associated protein like‐1 protein and mRNA and a late increase in myomaker and myosin heavy chain‐8 mRNA, microtubule‐associated protein 1 light chain 3‐II:I ratio, and FUN14 domain‐containing‐1 mRNA and protein were observed in mice. In summary, the regulatory profiles of protein, mitochondrial, and myonuclear turnover are correlated and temporally associated, suggesting a coordinated regulation of muscle mass‐ and oxidative metabolism‐related processes during recovery from disuse.—Kneppers, A., Leermakers, P., Pansters, N., Backx, E., Gosker, H., van Loon, L., Schols, A., Langen, R., Verdijk, L. Coordinated regulation of skeletal muscle mass and metabolic plasticity during recovery from disuse. FASEB J. 33, 1288–1298 (2019). www.fasebj.org