相关论文: Asymptotically Exact Solution of the Fredrickson-A…

Exact solutions of quantum lattice models serve as useful guides for interpreting physical phenomena in condensed matter systems. Prominent examples of integrability appear in one dimension, including the Heisenberg chain, where the Bethe…

The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…

Glauber dynamics of a bond-diluted Ising model on a Bethe lattice (a random graph with fixed connectivity) is investigated by an approximate theory which provides exact results for equilibrium properties. The time-dependent solutions of the…

We introduce the fermionized time-dependent Hartree-Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact…

Understanding the quasi-static fracture formation and evolution is essential for assessing the mechanical properties and structural load-bearing capacity of materials. Peridynamics (PD) provides an effective computational method to depict…

We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the…

We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce…

Objective: We propose a novel approach for modelling the inter-dependence of electrical and mechanical phenomena in nervous cells, by using electro-thermal equivalences in finite element (FE) analysis so that existing thermo-mechanical…

We perform a numerical study of the F-model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size…

We present a convex formulation of compliant frictional contact and a robust, performant method to solve it in practice. By analytically eliminating contact constraints, we obtain an unconstrained convex problem. Our solver has proven…

Exact solutions of interacting random walk models, such as 1D lattice gases, offer precise insight into the origin of nonequilibrium phenomena. Here, we study a model of run-and-tumble particles on a ring lattice interacting via hardcore…

Sensitivity analysis with forced optimally time dependent (f-OTD) modes is introduced and its application for skeletal model reduction is demonstrated. f-OTD expands the sensitivity coefficient matrix into a lowdimensional, time dependent,…

This paper investigates the asymptotic behavior of a forward-backward-forward (FBF) type differential equation and its discrete counterpart for solving quasimonotone variational inequalities (VIs). Building on recent continuous-time…

In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…

We map Eigen model of biological evolution [Naturwissenschaften {\bf 58}, 465 (1971)] into a one-dimensional quantum spin model with non-Hermitean Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen…

We test the quasi-equilibrium picture of the aging dynamics -strictly valid in the asymptotic dynamical regime of aging systems- in the pre-asymptotic aging regime of the two dimensional Edwards-Anderson spin glass model. We compare the…

We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density…

We consider a simplified model of protein folding, with binary degrees of freedom, whose equilibrium thermodynamics is exactly solvable. Based on this exact solution, the kinetics is studied in the framework of a local equilibrium approach,…

We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method…

We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…