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This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free…
We construct a monotone continuous $Q^1$ finite element method on the uniform mesh for the anisotropic diffusion problem with a diagonally dominant diffusion coefficient matrix. The monotonicity implies the discrete maximum principle.…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
We propose a quantum algorithm for the linear advection-diffusion equation (ADE) Lattice-Boltzmann method (LBM) that leverages dynamic circuits. Dynamic quantum circuits allow for an optimized collision-operator quantum algorithm,…
Quasicentroid molecular dynamics (QCMD) is a path-integral method for approximating nuclear quantum effects in dynamics simulations, which has given promising results for gas- and condensed-phase water. Here, by simulating the infrared…
Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work we consider time-periodically modulated quantum systems which are in contact with a stationary…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
Leveraging the techniques found in the literature on Quantum Equilibration for finite dimensional systems, we develop the theory of Quantum Equilibration for the case of infinite-dimensional systems, particularly the cases where the…
Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we…
We propose a method to study dynamical response of a quantum system by evolving it with an imaginary-time dependent Hamiltonian. The leading non-adiabatic response of the system driven to a quantum-critical point is universal and…
We address parameter estimation for complex/structured systems and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe for Ohmic…
We formulate a path-integral Monte Carlo algorithm for simulating lattice systems consisting of fictitious particles governed by a generalized exchange statistics. This method, initially proposed for continuum systems, introduces a…
Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are…
Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches…
We develop a quantum relative entropy method for the mean-field limit of quantum many-body systems. For closed systems governed by the von Neumann equation, we prove a quantitative stability estimate between the $N$-body density matrix and…
The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are…
We propose a procedure - partly analytical and partly numerical - to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
In this study a new numerical approach of the fluid dynamic, the lattice Boltzmann method (LBM), is used to solved the stream in a atmospheric Argon-nitrogen plasma jet. The axial symmetry and the variation of density, viscosity and…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…