Physics

Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a many-body state, alongside several experimental realizations. In this work, we provide a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators. In our analysis, we use classical period-doubling bifurcation theory and present a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition. We experimentally demonstrate this paradigm using coupled mechanical oscillators, thus providing a clear route for time crystals realizations in real materials.

A general half-plane contact problem in which the geometry is specified in a piecewise-quadratic sense over three segments is solved in closed form. This includes the effects of a moment applied sufficient to introduce separation of one segment and the application of a shearing force sufficient or insufficient to cause sliding. Extending existing solutions to asymmetrical problems is necessary in order to broaden our understanding of the behaviour of dovetail roots of gas turbine fan blades. In previous studies symmetrical contacts have often been used to represent a dovetail flank contact. In the asymmetrical case, the contact pressure may be considerably higher at one of the contact edges compared to the corresponding symmetrical case. Exploiting the generality provided with the solution presented in this study, several simpler indenter problems are investigated making use of an algebraic manipulator. The Mathematica code is made available for download.

In order to describe the velocity of two bodies after they collide, Newton developed a phenomenological equation known as "Newton\' s Experimental Law" (NEL). In this way, he was able to practically bypass the complication involving the details of the force that occurs during the collision of the two bodies. Today, we use NEL together with momentum conservation to predict each bodyś velocity after collision. This, indeed, avoids the complication of knowing the forces involved in the collision, making NEL very useful. Whereas in Newtonś days the quantity of kinetic energy was not known, today it is a basic quantity that is in use. In this paper we will use the loss (or gain) of kinetic energy in a collision to show how NEL can be derived.

The symmetric tensor energy-impulse of interaction of collective of electric charges with an electromagnetic field is received. A system of covariant energy and momentum conservation equations or a system of equations for the collective motion of charged particles is derived from this tensor. From this system Expressions are derived for collective electrodynamics forces. From the energy-momentum tensor derived the tensor of collective electrodynamics forces is.

When two identical balls collide with equal inital speed on a horizontal groove, one can observe three trajectory types depending on the groove width. To explain this observation, we derive velocity diagrams of the balls motions from Newton's laws of translation and rotation and kinematics of rigid bodies in a three-dimensional vectorial representation and compare them with experimental results. The velocity diagrams and an introduced determinant allow to discriminate between the trajectory types and to understand the interplay between translation and rotation after the collision of the balls.

We show that the "defective" terms in the expression that Dondera [Phys. Rev. D 98, 096008 (2018)] obtained for the momentum of the retarded field of an accelerating point charge are mathematically well justified. The repair should not be sought in assigning an accelerating "bare" charge ad hoc compensating attributes. We advance a conjecture, supported by published work, concerning the Hadamard finite part of the divergent integral for the retarded-field momentum in question.

In this comment it is argued that the argument for a unique determination of the electromagnetic potentials in classical electrodynamics in [1] is flawed. To the contrary the "gauge freedom" of the electromagnetic potentials has proven as one of the most important properties in the development of modern physics, where local gauge invariance with its extension to non-Abelian gauge groups is a key feature in the formulation of the Standard Model of elementary particles in terms of a relativistic quantum field theory. [1] A. Davis, Eur. J. Phys. 41, 045202 (2020)

In the paper "The relativistic Doppler effect: when a zero-frequency shift or a red shift exists for sources approaching the observer, Ann. Phys. (Berlin) 523, No. 3, 239-246 (2011), DOI 10.1002/andp.201000099 by C. Wang the use of an erroneous equation ended up at a number of faulty conclusions which are corrected in the present Comment.

A number of errors, both mathematical and conceptual, are identified, in a recent article by Farhat \textit{et al.}\ [Phys.\ Rev.\ Appl.\ \textbf{11}, 044089 (2019)] on cloaking of thermal waves in solids, and corrected. The differences between the two thermal flux laws considered in the latter article are also critically discussed, specifically showing that the chosen model does not, in fact, correspond to the Maxwell--Cattaneo hyperbolic (wave) theory of heat transfer.

This paper presents a comparative study between two micro-macro modeling approaches to simulate stress-induced martensitic transformation in shape memory alloys (SMA). One model is a crystal plasticity based model and the other describes the evolution of the microstructure with a Boltzmann-type statistical approach. Both models consider a self-consistent scheme to perform the scale transition from the local thermomechanical behavior to the global one. The way the two modeling approaches describe the local behavior is analyzed. Similarities and differences are pointed out. Numerical simulations of the thermo-mechanical behavior of an isotropic titanium-niobium SMA are performed. These alloys have known a growing interest of scientific community given their high potential for application in the biomedical field. Stress-strain curves obtained from the two simulations are compared with experimental results. Evolutions of volume fractions of martensite variants predicted by the two approaches are compared for <100>, <110> and <111> tensile directions. Due to the absence of comparative studies between multiscale models dedicated for SMA, this paper fills a gap in the state of the art in this field and provides a significant step toward the definition of an efficient numerical tool for the analysis of SMA behavior under multiaxial loadings.