Related papers: Moments approaches for asymptotic inverse problems…
The influence of size differences, shape, mass and persistent motion on phase separation in binary mixtures has been intensively studied. Here we focus on the exclusive role of diffusivity differences in binary mixtures of equal-sized…
The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be…
We consider the complex moment problem, that is the problem of constructing a positive Borel measure on $\mathbb{C}$ from a given set of moments. We relate this problem to the dynamic inverse problem for the discrete system associated with…
Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…
Pairs of pseudoscalar neutral mesons from decays of vector resonances are studied as bipartite systems in the framework of density operator. Time-dependent quantum entanglement is quantified in terms of the entanglement entropy and these…
This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…
In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence…
We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some…
Recently several authors studied the segregation of particles for a system composed of mono-dispersed inelastic spheres contained in a box divided by a wall in the middle. The system exhibited a symmetry breaking leading to an…
We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
A high-resolution Eulerian method for simulating high-speed polydisperse granular multiphase flows has been developed. The governing equations include a compressible gas that is coupled to mass-based moment equations for a polydisperse…
Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…
We study methods for reconstructing the momenta of invisible particles in cascade decay chains at hadron colliders. We focus on scenarios, such as SUSY and UED, in which new physics particles are pair produced. Their subsequent decays lead…
In this work, we propose a novel methodology for robustly estimating particle size distributions from optical scattering measurements using constrained Gaussian process regression. The estimation of particle size distributions is commonly…
Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear…
After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure…
We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…