相关论文: A mixed basis approach in the SGP-limit
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
In many electron spin qubit systems coherent control is impaired by the fluctuating nuclear spin bath of the host material. Previous experiments have shown dynamic nuclear polarization with feedback to significantly prolong the…
The possibility of comparatively simple and fast determination of characteristic relaxation parameters T1, T2 and T3 for nuclear spin-systems with strong Larmor and Rabi inhomogeneous broadenings of NMR lines using the secondary echo signal…
Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…
We investigate a minimal model for cell propagation involving migration along self-generated signaling gradients and cell division, which has been proposed in an earlier study. The model consists in a system of two coupled parabolic…
How long does a diffusing molecule spend in a close vicinity of a confining boundary or a catalytic surface? This quantity is determined by the boundary local time, which plays thus a crucial role in the description of various…
Swept-frequency pulses have found applications in a wide range of areas including spectroscopic techniques where efficient control of spins is required. For many of these applications, a good understanding of the evolution of spin systems…
We present a systematic treatment of scattering processes for quantum systems whose time evolution is discrete. We define and show some general properties of the scattering operator, in particular the conservation of quasi-energy which is…
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
We report an observation of extremely long-lived spin states in systems of dipolar-coupled nuclear spins in solids. The 'suspended echo' experiment uses a simple stimulated echo pulse sequence and creates non-equilibrium states which live…
A very efficient large-order perturbation theory is formulated for the nuclear motion of a linear triatomic molecule. To demonstrate the method, all of the experimentally observed rotational energies, with values of $J$ almost up to 100,…
The Gaussian phase approximation (GPA) underlies many standard diffusion magnetic resonance (MR) signal models, yet its validity is rarely scrutinized. Here, we assess the validity of the GPA by analytically deriving the excess phase…
We study the asymptotic behavior of a diffusion process with small diffusion in a domain $D$. This process is reflected at $\partial D$ with respect to a co-normal direction pointing inside $D$. Our asymptotic result is used to study the…
Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…
The aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM),…
A numerical method is developed to efficiently calculate the stress (and displacement) field in finite 2D rectangular media. The solution is expanded on a function basis with elements that satisfy the Navier-Cauchy equation. The obtained…
We present a simple approach to predict the main features of optical spectra affected by self-phase modulation (SPM), which is based on regarding the spectrum modification as an interference effect. A two-wave interference model is found…
We present a robust approach to incorporating models for the time-variable broadening of the pulse profile due to scattering in the ionized interstellar medium into profile-domain pulsar timing analysis. We use this approach to…
We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than…
The paper describes the design of band selective excitation and rotation pulses in high resolution NMR by method of double sweep. We first show the design of a pulse sequence that produces band selective excitation to the equator of Bloch…