Related papers: How to compute the atomic stress objectively?
Statistical average of the axial current is evaluated on the basis of the covariant Wigner function. In the resulting formula, chemical potential $\mu$, angular velocity $\Omega$ and acceleration $a$ enter in combination $\mu \pm (\Omega…
Stable estimation of rigid body pose and velocities from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange-d'Alembert principle from variational mechanics. With body-fixed optical and inertial…
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. As is pointed out by [8], in this combination, the frictional damping term is dominant for the viscoelastic one for the…
In this paper we analyze a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. We consider the classic velocity-pressure formulation which allows us to…
At present, whenever we work in newtonian mechanics we consider momentum to be a three-dimensional vector or a 4-dimensional one when we work in relativistic mechanics. However, this mathematical vector model has barely 200 years and its…
A modified quantum kinetic equation which takes account of the noninertial features of rotating frame is proposed. The vector and axial-vector field components of the Wigner function for chiral fluids are worked out in a semiclassical…
In a particle physics dynamics, we assume a uniform distribution as the physical measure and a measure-theoretic definition of entropy on the velocity configuration space. This distribution is labeled as the physical solution in the…
The Lagrangian formulation of classical mechanics is widely applicable in solving a vast array of physics problems encountered in the undergraduate and graduate physics curriculum. Unfortunately, many treatments of the topic lack…
This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for each $t, x$ the principal symbol is hyperbolic. No hypothesis…
The Unruh effect is essential to keep the consistency of quantum field theory in inertial and uniformly accelerated frames. Thus, the Unruh effect must be considered as well tested as quantum field theory itself. In spite of it, it would be…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
Kinetic simulations based on the Eulerian Hybrid Vlasov-Maxwell (HVM) formalism permit the examination of plasma turbulence with useful resolution of the proton velocity distribution function (VDF). The HVM model is employed here to study…
It is well known that Cauchy problem for Laplace equations is an ill-posed problem in Hadamard's sense. Small deviations in Cauchy data may lead to large errors in the solutions. It is observed that if a bound is imposed on the solution,…
We compute explicitly the equations of motion of the Hamiltonian formulation of quadratic gravity. This is the theory with the most general Lagrangian with terms of quadratic order in the curvature tensor. We employ the symbolic…
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. Stress (tension) tensors are considered, obtained by the use of the method of Lagrangians with covariant derivatives (MLCD). On the…
We present a simple example in which the importance of the inertial effects of stress is evident. The system is an insulating solid narrow disc whose faces are uniformly charged with charges of equal magnitude and opposite signs. The motion…
The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven…
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable restitution coefficients depending on the kinetic energy and…
Most approaches in Lagrangian fluid dynamics simulations proceed from the definition of particle volumes, from which discrete versions of the spatial differential operators are derived. Recently, Gallou\"et and M\'erigot [1] simultaneously…
The dynamic atomic polarizability describes the response of the atom to incoming electromagnetic radiation. The functional form of the imaginary part of the polarizability for small driving frequencies omega has been a matter of…