Related papers: Exact Solutions for Small Systems: Urns Models
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
The random vector of frequencies in a generalized urn model is viewed as conditionally independent random variables, given their sum. Such a representation is exploited to derive Edgeworth expansions for a sum of functions of such…
We revisit the problem of parameter estimation for discrete probability distributions with values in $\mathbb{Z}^d$. To this end, we adapt a technique called Stein's Method of Moments to discrete distributions which often gives closed-form…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…
In this paper, calculus of variation methods are generalized to find min-max optimal solution of uncertain dynamical systems with uncertain or certain cost. First, a new form of Euler-Lagrange conditions for uncertain systems is presented.…
We introduce novel high order well-balanced finite volume methods for the full compressible Euler system with gravity source term. They require no a priori knowledge of the hydrostatic solution which is to be well-balanced and are not…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…
A methodology for computing expansion basis functions using discrete harmonic modes is presented. The discrete harmonic modes are determined grain-by-grain for virtual polycrystals for which finite element meshes are available. The…
The unique properties of anisotropic and composite particles are increasingly being leveraged in modern particulate products. However, tailored synthesis of particles characterized by multi-dimensional dispersed properties remains in its…
In this paper, we consider functionals based on moments and non-linear entropies which have a linear growth in time in case of source-type so-lutions to the fast diffusion or porous medium equations, that are also known as Barenblatt…
We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…
The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…
Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and to have locally Lipschitz nonlinearities of at most (slightly…
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich…
We are concerned with the global existence and large time behavior of entropy solutions to the one dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we…
We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…
We study real-space condensation phenomena in a type of classical stochastic processes (site-particle system), such as zero-range processes and urn models. We here study a stochastic process in the Ehrenfest class, i.e., particles in a site…
We develop the method of Maximum Entropy (ME) as a technique to generate approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…