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In this work, we study the Bloch wave homogenization for the Stokes system with periodic viscosity coefficient. In particular, we obtain the spectral interpretation of the homogenized tensor. The presence of the incompressibility constraint…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…
By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels and stimulated by a laser and we compute its fluorescence spectrum; let us stress that, once the model for the unitary atom-field dynamics…
We study a homogenization question for stochastic divergence type operator
Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL),…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
The development of surrogate models to study uncertainties in hydrologic systems requires significant effort in the development of sampling strategies and forward model simulations. Furthermore, in applications where prediction time is…
The multi-energy management framework of industrial parks advocates energy conversion and scheduling, which takes full advantage of the compensation and temporal availability of multiple energy. However, how to exploit elastic loads and…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
Analytical method for the second-order homogenization of two-phase composites within Mindlin-Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce the homogenization…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
We study the asymptotic behavior of thin heterogeneous elastoplastic plates in the framework of linearized elastoplasticity, focusing on the regime where the plate thickness vanishes much faster than the characteristic scale of the…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
Stochastic hybrid systems are dynamic systems that undergo both random continuous-time flows and random discrete jumps. Depending on how randomness is introduced into the continuous dynamics, discrete transitions, or both, stochastic hybrid…
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle…
We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle…