相关论文: A mixed basis approach in the SGP-limit

Recently a number of analytic prescriptions for computing the non-linear matter power spectrum have appeared in the literature. These typically involve resummation or closure prescriptions which do not have a rigorous error control, thus…

We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses…

We demonstrate that CPMG and XYXY decoupling sequences with non-ideal $\pi$ pulses can reduce dipolar interactions between spins of the same species in solids. Our simulations of pulsed electron spin resonance (ESR) experiments show that…

Recovering high-dimensional statistical structure from limited measurements is a fundamental challenge in hyperspectral imaging, where capturing full-resolution data is often infeasible due to sensor, bandwidth, or acquisition constraints.…

We adapt Stein's method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of…

Changes in the nervous system due to neurological diseases take place at very small spatial scales, on the order of the micro and nanometers. Developing non-invasive imaging methods for obtaining this microscopic information as quantitative…

A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized…

Nuclear Magnetic Resonance (NMR) spectrometry uses electro-frequency pulses to probe the resonance of a compound's nucleus, which is then analyzed to determine its structure. The acquisition time of high-resolution NMR spectra remains a…

We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the $L^2$- and $H^1$-norms of the error. The proposed method is built on…

In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…

One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or…

Nonlinear signal distortions are one of the primary factors limiting the capacity and reach of optical transmission systems. Currently, several approaches exist for compensating nonlinear distortions, but for practical implementation,…

The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent…

We derive various approximations for the solutions of nonlinear hyperbolic systems with fastly oscillating initial data. We first provide error estimates for the so-called slowly varying envelope, full dispersion, and Schr\"odinger…

Lattice diffusion and internal local magnetic field gradients in solids are investigated by numerical simulation of nuclear mangetic resonance(NMR) spin echo experiments. The Fourier-spectrum method is employed in order to solve the…

When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately…

Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…

Long-range magnetic interactions in highly magnetised liquids (laser-polarised 3He-4He dilute mixtures at 1 K in our experiment) introduce a significant non-linear and non-local contribution to the evolution of nuclear magnetisation that…

We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line. By taking the large particle limit we establish existence and uniqueness for the limiting empirical measure valued process…

A spin-echo-type technique is applied to an artificial two-level system that utilizes charge degree of freedom in a small superconducting electrode. Gate-voltage pulses are used to produce the necessary pulse sequence in order to eliminate…