相关论文: Coarse graining of master equations with fast and …
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…
The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles…
Generalized Ising models, also known as cluster expansions, are an important tool in many areas of condensed-matter physics and materials science, as they are often used in the study of lattice thermodynamics, solid-solid phase transitions,…
Chemical reactions often proceed through the formation and the consumption of intermediate species. An example is the creation and subsequent degradation of the substrate-enzyme complexes in an enzymatic reaction. In this paper we provide a…
A new method to remove the stiffness of partial differential equations is presented. Two terms are added to the right-hand-side of the PDE : the first is a damping term and is treated implicitly, the second is of the opposite sign and is…
We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on timescales that are unreachable in standard simulations.…
We describe compressible two-phase flows by a single-velocity six-equation flow model, which is composed of the phasic mass and total energy equations, one volume fraction equation, and the mixture momentum equation. The model contains…
Chemical master equation plays an important role to describe the time evolution of homogeneous chemical system. In addition to the reaction process, it is also accompanied by physical diffusion of the reactants in complex system that is…
Master equations describing open quantum dynamics are typically first order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the…
We investigate the adiabatic elimination of fast variables in relativistic stochastic mechanics, which is analyzed by using the equation of motion and the distribution function, with relativistic corrections explicitly derived. A new…
Graph-based diffusion models have shown promising results in terms of generating high-quality solutions to NP-complete (NPC) combinatorial optimization (CO) problems. However, those models are often inefficient in inference, due to the…
Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the…
A master equation approach is applied to a reversible and conservative cellular automata model (Q2R). The Q2R model is a dynamical variation of the Ising model for ferromagnetism that possesses quite a rich and complex dynamics. The…
We present and discuss a general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems, able to overcome the intrinsic limitations of the conventional Markov approximation. In particular, the…
We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the…
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the existence of a global branch of nonnegative stationary…
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or…
It is increasingly realized that taking stochastic effects into account is important in order to study biological cells. However, the corresponding mathematical formulation, the chemical master equation (CME), suffers from the curse of…
We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the…
The mixed states are important in quantum optics since they frequently appear in the decoherence problems. When one of the components of the system is prepared in the mixed state and the evolution operator of this system is not available,…