相关论文: A Modica-Mortola approximation for branched transp…
A method is presented which allows the exact construction of conserved (i.e. divergence-free) current vectors from appropriate sets of multipole moments. Physically, such objects may be taken to represent the flux of particles or electric…
We present atomic-scale computer simulations in equiatomic L1$_0$-CoPt where Molecular Dynamics and Monte Carlo techniques have both been applied to study the vacancy-atom exchange and kinetics relaxation. The atomic potential is determined…
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…
This paper proposes a linear approximation of the alternating current optimal power flow problem for multiphase distribution networks with voltage-dependent loads connected in both wye and delta configurations. We establish a set of linear…
Though sufficient for local conservation of charge, Maxwells displacement current is not necessary. An alternative to the Ampere-Maxwell equation is exhibited and the alternatives electric and magnetic fields and scalar and vector…
An indirect, hybrid Monte Carlo discretization of general relativistic kinetic theory suitable for the development of numerical schemes for radiation transport is presented. The discretization is based on surface flux estimators obtained…
We present a primal--dual memory efficient algorithm for solving a relaxed version of the general transportation problem. Our approach approximates the original cost function with a differentiable one that is solved as a sequence of…
We present a variational optimization approach for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and conductivity functions in time-dependent Maxwell's system using limited…
We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a $\delta$…
The Derivative Source Method (DSM) takes derivatives of a particle transport equation with respect to selected parameters and solves them via the standard Monte Carlo random walk simulation along with the original transport problem. The…
Why does the mammalian vascular tree maintain a conserved branching exponent $\alpha^* \approx 2.72$ across a $10^7$-fold range in body mass, despite a fundamental shift from viscous to wave-dominated transport? We prove this universality…
We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of the velocity fields generated by the remaining point vortices.…
We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double-well. In classical (thermal)…
The ultra-cold and weakly-coupled Fermi gas in two spatial dimensions is studied in an effective field theory framework. It has long been observed that universal corrections to the energy density to two orders in the interaction strength do…
We prove estimates for the transport exponents associated with the weakly coupled Fibonacci Hamiltonian. It follows in particular that the upper transport exponent $\tilde \alpha^\pm_u$ approaches the value one as the coupling goes to zero.…
Inhomogeneous dynamical mean-field theory is employed to calculate the vertex-corrected electronic charge transport for multilayered devices composed of semi-infinite metallic lead layers coupled through a strongly correlated material…
We extend the analysis by Esedo\={g}lu and Otto (2015) of thresholding energies for the celebrated multiphase Bence-Merriman-Osher algorithm for computing mean curvature flow of interfacial networks, to the case of differing space-dependent…
We investigate the quadratic Schr\"odinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity bounds on Schr\"odinger potentials under mild assumptions on the marginals that are…