For spacetimes with timelike Killing fields, we introduce a “Fermi-WalkerKilling” coordinate system and use it to prove a Liouville Theorem for an appropriate volume element of phase space for a statistical mechanical system of particles. We derive an exact relativistic formula for the Helmholtz free energy of an ideal gas and compare it, for a class of spacetimes, to its Newtonian analog, deri...

A computational multiscale method is proposed to simulate coupled, nonequilibrium thermomechanical processes. This multiscale framework couples together thermomechanical equations at the coarse scale with nonequilibrium molecular dynamics at the fine scale. The novel concept of distributed coarse scale thermostats enables subsets of fine scale atoms to be attached to different coarse scale node...

[1] Phonon dispersions and vibrational density of states of MgSiO3 postperovskite, the new high-pressure phase of MgSiO3 perovskite, are calculated as a function of pressure up to 180 GPa using density-functional perturbation theory. The calculated frequencies are then used to determine the thermal contribution to the Helmholtz free energy within the quasi-harmonic approximation. The equation o...

We study some aspects of the quantum theory of a charged particle moving in a time-independent, uni-directional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and momentum eigenstates with the diamagnetism of a free electron gas as an example. When the field is non-uniform but weakly varying, we discuss both perturbative an...

Analytic expressions for the equation of state and internal energy of poly-exponential solids are derived based on the analytic mean field potential (AMFP) method. The formalism is applied to fcc C61D2. Two sets of potential parameters are determined by fitting the experimental compression data of C61D2 up to 1 GPa at 343 and 307 K, respectively. The difference between the two sets of parameter...

We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method, it is shown that the grand potential is a functional of both distributions, that it is minimal in equilibrium, and that the minimizing fields are those at equilibrium. The functional splits into a ...

This paper1 gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms for solving the equations. It leads also to a new interpretation of classical algorithms, enhancing convergence. The algorithms are given and convergence is ...

3 1 The syntax of planetary structure 5 1.1 The basics of planetary and stellar structure . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1.1 Mass conservation and Lagrangian coordinate . . . . . . . . . . . . . . . . . . . 8 1.1.2 Momentum equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.3 Energy conservation . . . . . . . . . . . . . . . . . . . . . . . . . ....

We present a temperature-independent Monte Carlo method for the determination of the density of states of lattice proteins that combines the fast ground-state search strategy of the new pruned-enriched Rosenbluth chain-growth method and multicanonical reweighting for sampling the complete energy space. Since the density of states contains all energetic information of a statistical system, we ca...

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algor...