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We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
Neutron and x-ray scattering experiments traditionally rely upon histogrammed data sets, which are analysed using least-squares curve fitting of multiple probability distribution components to quantify separately the various scientific…
This paper considers the problem of estimating the cumulative distribution function and probability density function of a random variable using data quantized by uniform and non-uniform quantizers. A simple estimator is proposed based on…
Atomic scale simulations are a key element of modern science in that they allow to understand, and even predict, complex physical or chemical phenomena on the basis of the fundamental laws of nature. Among the different existing atomic…
Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and…
The dynamics of a linear system embedded in a heat bath environment and subject to non- Gaussian noise is studied. Higher order cumulants in coordinate space are derived and their impact on the dynamics and on asymptotic steady state…
The gravitational clustering of collisionless particles in an expanding universe is modelled using some simple physical ideas. I show that it is possible to understand the nonlinear clustering in terms of three well defined regimes: (1)…
We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source…
Pulsar dynamic spectra exhibit high visibility fringes arising from interference between scattered radio waves. These fringes may be random or highly ordered patterns, depending on the nature of the scattering or refraction. Here we…
Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data,…
Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current…
To estimate the smoothing distribution in a nonlinear state space model, we apply the conditional particle filter with ancestor sampling. This gives an iterative algorithm in a Markov chain Monte Carlo fashion, with asymptotic convergence…
Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the…
We theoretically study the propagation of light through a cold atomic medium, where the effects of motion, laser intensity, atomic density, and polarization can all modify the properties of the scattered light. We present two different…
Data assimilation is a technique for increasing the accuracy of simulations of solutions to partial differential equations by incorporating observable data into the solution as time evolves. Recently, a promising new algorithm for data…
In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available…
The method of photon distribution function (PDF) is used to study fluctuations of light beams propagating through a turbulent atmosphere. Our analysis concerns the regime of saturated fluctuations. The focus is on the phenomena of beam…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image…