Related papers: Morse theory for the uniform energy
We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
We use discrete Morse theory to give a new proof of the Degree Theorem in Auter space A_n. There is a filtration of A_n into subspaces A_{n,k} using the degree of a graph, and the Degree Theorem says that each A_{n,k} is (k-1)-connected.…
In this work, we investigate the quantum dynamics of a particle subject to the Morse potential within the framework of Dunkl quantum mechanics. By employing the Dunkl derivative operator, which introduces reflection symmetry, we construct a…
In this work, we use the JKO scheme to approximate a general class of diffusion problems generated by Darcy's law. Although the scheme is now classical, if the energy density is spatially inhomogeneous or irregular, many standard methods…
Charge and heat transport through a single molecule tunnel-coupled to external normal electrodes have been studied. The molecule with sufficiently strong interaction between lectrons and vibrational internal degrees of freedom can be…
Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from…
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking…
We present an analytic construction of nonlocal energies on the unit interval. The energies are defined using a new graph-directed construction of discrete energies on dyadic approximations of the interval. When the discrete jump kernels…
This is a survey article on Morse theory based on lectures to graduate students and advanced undergraduates. After a brief review of standard material, mostly without proofs, the Morse theory of complex Grassmannian manifolds is worked out…
In the past decade, classical dynamical density functional theory (DDFT) has been developed and widely applied to the Brownian dynamics of interacting colloidal particles. One of the possible derivation routes of DDFT from the microscopic…
We study probability measures that minimize the Riesz energy with respect to the geodesic distance $\vartheta (x,y)$ on projective spaces $\mathbb{FP}^d$ (such energies arise from the 1959 conjecture of Fejes T\'oth about sums of non-obtuse…
Ray flow methods provide efficient tools for modelling wave energy transport in complex systems at high-frequencies. We compare two Petrov-Galerkin discretizations of a phase-space boundary integral model for stationary wave energy…
We consider the well-known minimizing-movement approach to the definition of a solution of gradient-flow type equations by means of an implicit Euler scheme depending on an energy and a dissipation term. We perturb the energy by considering…
We develop a systematic approach to construct energy functionals of the one-particle reduced density matrix (1RDM) for equilibrium systems at finite temperature. The starting point of our formulation is the grand potential $\Omega…
Thermal forces drive several nonequilibrium phenomena able to set a fluid in motion without pressure gradients. Although the most celebrated effect is thermophoresis, also known as Ludwig-Soret effect, probably the simplest example where…
Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via relaxation departing either from energies associated with…
We study the long-time behaviour of the temperature-driven compressible flows. We show that numerical solutions of a structure-preserving finite volume method generate a discrete attractor that consists of entire discrete trajectories.…
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…