Theory of Non-Equilibrium Heat Transport in Anharmonic Multiprobe Systems at High Temperatures

We consider the problem of heat transport by vibrational modes between Langevin thermostats connected by a central device. The latter is anharmonic and can be subject to large temperature difference and thus be out of equilibrium. We develop a classical formalism based on the equation of motion method, the fluctuation–dissipation theorem and the Novikov theorem to describe heat flow in a multi-terminal geometry. We show that it is imperative to include a quartic term in the potential energy to insure stability and to properly describe thermal expansion. The latter also contributes to leading order in the thermal resistance, while the usually adopted cubic term appears in the second order. This formalism paves the way for accurate modeling of thermal transport across interfaces in highly non-equilibrium situations beyond perturbation theory.

Hierarchical Computational Anatomy: Unifying the Molecular to Tissue Continuum via Measure Representations of the Brain

This paper presents a unified representation of the brain based on mathematical functional measures integrating the molecular and cellular scale descriptions with continuum tissue scale descriptions. We present a fine-to-coarse recipe for traversing the brain as a hierarchy of measures projecting functional description into stable empirical probability laws that unifies scale-space aggregation. The representation uses measure norms for mapping the brain across scales from different measurement technologies. Brainspace is constructed as a metric space with metric comparison between brains provided by a hierarchy of Hamiltonian geodesic flows of diffeomorphisms connecting the molecular and continuum tissue scales. The diffeomorphisms act on the brain measures via the 3D varifold action representing "copy and paste" so that basic particle quantities that are conserved biologically are combined with greater multiplicity and not geometrically distorted. Two applications are examined, the first histological and tissue scale data in the human brain for studying Alzheimer's disease, and the second the RNA and cell signatures of dense spatial transcriptomics mapped to the meso-scales of brain atlases. The representation unifies the classical formalism of computational anatomy for representing continuum tissue scale with non-classical generalized functions appropriate for molecular particle scales.

Application of the Generalized Hamiltonian Dynamics to Spherical Harmonic Oscillators

Dirac’s Generalized Hamiltonian Dynamics (GHD) is a purely classical formalism for systems having constraints: it incorporates the constraints into the Hamiltonian. Dirac designed the GHD specifically for applications to quantum field theory. In one of our previous papers, we redesigned Dirac’s GHD for its applications to atomic and molecular physics by choosing integrals of the motion as the constraints. In that paper, after a general description of our formalism, we considered hydrogenic atoms as an example. We showed that this formalism leads to the existence of classical non-radiating (stationary) states and that there is an infinite number of such states—just as in the corresponding quantum solution. In the present paper, we extend the applications of the GHD to a charged Spherical Harmonic Oscillator (SHO). We demonstrate that, by using the higher-than-geometrical symmetry (i.e., the algebraic symmetry) of the SHO and the corresponding additional conserved quantities, it is possible to obtain the classical non-radiating (stationary) states of the SHO and that, generally speaking, there is an infinite number of such states of the SHO. Both the existence of the classical stationary states of the SHO and the infinite number of such states are consistent with the corresponding quantum results. We obtain these new results from first principles. Physically, the existence of the classical stationary states is the manifestation of a non-Einsteinian time dilation. Time dilates more and more as the energy of the system becomes closer and closer to the energy of the classical non-radiating state. We emphasize that the SHO and hydrogenic atoms are not the only microscopic systems that can be successfully treated by the GHD. All classical systems of N degrees of freedom have the algebraic symmetries ON+1 and SUN, and this does not depend on the functional form of the Hamiltonian. In particular, all classical spherically symmetric potentials have algebraic symmetries, namely O4 and SU3; they possess an additional vector integral of the motion, while the quantal counterpart-operator does not exist. This offers possibilities that are absent in quantum mechanics.

Interacting Fermions and Supersymmetric Models

Chapter 24 discusses interacting fermions and supersymmetry (SUSY) models. The chapter addresses the semi-classical formalism relative to a fermion field in a bosonic background. It covers topics that include bosonic and fermionic bound states (both Dirac and Majorana), symmetric wells, supersymmetric theory, general results in SUSY theories, integrable SUSY models, non-integrable multi-frequency super Sine–Gordon models, phase transition and meta-stable states. It also discusses the conditions under which the overall theory presents supersymmetry and the consequences thereof. It also covers how semi-classical formulae can help to identify the particle excitations and estimate one of their most important characteristics, i.e. their mass.

Role of kinetics on the couplings between fluid flow, deformation and reaction

<p>Short timescale processes such as earthquakes, tremors and slow slip events may be influenced by reactions, which are known to proceed rapidly in the presence of water (typically several days). Here, we developed a theoretical framework to introduce the influence of mineralogical reactions on fluid flow and deformation. The classical formalism for dissolution/precipitation reactions is used to consider the influence of the distance from equilibrium and of temperature on the reaction rate and a dependence on porosity is introduced to model the evolution of the reacting surface area during reaction. The thermodynamic admissibility of the derived equations is checked and an analytical solution is derived to test the model. The fitting of experimental data for three reactions typically occurring in metamorphic systems (serpentine dehydration, muscovite dehydration and calcite decarbonation) indicates a systematic faster kinetics on the dehydration side than on the hydration side close from equilibrium. This effect is amplified through the porosity term in the reaction rate. Numerical modelling indicates that this difference in reaction rate close from equilibrium plays a key role in microtextures formation during dehydration in metamorphic systems. The developed model can be used in a wide variety of geological systems where couplings between reaction, deformation and fluid flow have to be considered.</p>

Expected values and variances of Bragg peak intensities measured in a nanocrystalline powder diffraction experiment

A rigorous study of sampling and intensity statistics applicable for a powder diffraction experiment as a function of crystallite size is presented. This analysis yields approximate equations for the expected value, variance and standard deviations for both the number of diffracting grains and the corresponding diffracted intensity for a given Bragg peak. The classical formalism published in 1948 by Alexander, Klug & Kummer [J. Appl. Phys.(1948),19, 742–753] appears as a special case, limited to large crystallite sizes, in the present analysis. It is observed that both the Lorentz probability expression and the statistics equations used in the classical formalism are inapplicable for nanocrystalline powder samples.