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This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well…
This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
The purpose of this paper is to model mathematically mechanical aspects of cardiac tissues. The latter constitute an elastic domain whose total volume remains constant. The time deformation of the heart tissue is modeled with the…
We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive {\it master equations} for the dynamics of the expected power in the discrete modes. In…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…
The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…
Since the early 1900s, numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as solved when a complete or partial probabilistic description on…
We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…
Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…
Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The…
Numerical analysis is conducted for a generalized particle method for a Poisson equation. Unique solvability is derived for the discretized Poisson equation by introducing a connectivity condition for particle distributions. Moreover, by…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
This paper worked towards modeling blood platelets. Blood platelets, also known as thrombocytes, play a key role in blood clotting which is a vital human function. Furthermore, the role of these entities in strokes, myocardial infarctions,…
Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction…
We propose a novel partitioned scheme based on Eikonal equations to model the coupled propagation of the electrical signal in the His-Purkinje system and in the myocardium for cardiac electrophysiology. This scheme allows, for the first…