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Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…

In this paper, we consider a class of optimal control problems for a one-dimensional time-discrete constrained quasilinear diffusion state-systems of singular Allen--Cahn types and its regularized approximating problems. We note that the…

Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…

We study the dynamics of diffusion processes acting on directed multiplex networks, i.e., coupled multilayer networks where at least one layer consists of a directed graph. We reveal that directed multiplex networks may exhibit a faster…

Caching and multicasting at base stations are two promising approaches to support massive content delivery over wireless networks. However, existing analysis and designs do not fully explore and exploit the potential advantages of the two…

One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove…

We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffusion processes in the context of the vapor deposition of thin…

In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel…

We study a problem when a solution to optimal stopping problem for one-dimensional diffusion will generate by threshold strategy. Namely, we give necessary and sufficient conditions under which an optimal stopping time can be specified as…

The control of structured waves has recently opened innovative scenarios in the perspective of radiation propagation and light-matter interaction. In particular, the transmission of customized electromagnetic fields is investigated for…

We consider processes that coincide with a given diffusion process except on the boundaries of a finite collection of domains. The behavior on each of the boundaries is asymmetric: the process is much more likely to enter the interior of…

Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…

Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…

In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work,…

Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…

Physical wireless transceivers suffer from a variety of impairments that distort the transmitted and received signals. Their degrading impact is particularly evident in modern systems with multiuser transmission, high transmit power, and…

Constrained diffusions in convex polyhedral domains with a general oblique reflection field, and with a diffusion coefficient scaled by a small parameter, are considered. Using an interior Dirichlet heat kernel lower bound estimate for…

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…

The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the whole process of determining model parameters from data. We impose a sensitivity-based approach for choosing optimal design…