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In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. However, as…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Cerebral autoregulation plays a key physiological role by limiting blood flow changes in the face of pressure fluctuations. Although the involved cellular processes are mechanically driven, the quantification of haemodynamic forces in…
We investigate a diffusive, stage-structured epidemic model with the maturation delay and freely-moving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is…
Understanding the physics of blood is challenging due to its nature as a suspension of soft particles and the fact that typical problems involve different scales. This is valid also for numerical investigations. In fact, many computational…
The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and Preziosi (2019a). We split the population in two subgroups and perform a linear stability analysis. We show that pattern formation results…
Feedback loops are essential for regulating cell proliferation and maintaining the delicate balance between cell division and cell death. Thanks to the exact solution of a few simple models of cell growth it is by now clear that stochastic…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
This paper is devoted to the stability analysis of a classical three-field formulation of Biot's consolidation model where the unknown variables are the displacements, fluid flux (Darcy velocity), and pore pressure. Specific…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…
Mathematical methods provide useful framework for the analysis and design of complex systems. In newer contexts such as biology, however, there is a need to both adapt existing methods as well as to develop new ones. Using a combination of…
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
We study the asymptotic properties of the solutions of a nonlinear renewal equation. The main contribution of the present article is to provide stability and convergence results around equilibrium solutions, under some local subcritical…
Cells and tissues exhibit oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with cell biochemical signalling, it is yet unclear the role of these…
The glassy dynamics in confluent epithelial monolayers is crucial for several biological processes, such as wound healing, embryogenesis, cancer progression, etc. Several experiments have indicated that, unlike particulate systems, the…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
This paper presents a new generalized Mackey-Glass model with a non-linear harvesting term and mixed delays. The main purpose of this work is to study the existence and the exponential stability of the pseudo almost periodic solution for…