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We discuss a nonlinear model for the relaxation by energy redistribution within an isolated, closed system composed of non-interacting identical particles with energy levels e_i with i=1,2,...,N. The time-dependent occupation probabilities…
The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory…
In this paper, we derive an effective macroscale description suitable to describe the growth of biological tissue within a porous tissue-engineering scaffold. As in our recent work (Holden \textit{et al.} "A multiphase multiscale model for…
This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known…
Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical…
This paper deals with the large-time analysis of a PDE system modelling contact with adhesion, in the case when thermal effects are taken into account. The phenomenon of adhesive contact is described in terms of phase transitions for a…
One of the key characteristics of multicellular organisms is the ability to establish and maintain shapes, or morphologies, under a variety of physical and chemical perturbations. A quantitative description of the underlying morphological…
Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…
The shape of a cell influences and it is influenced by interactions with its neighbouring partners. Here, we introduce a coarse-grained model of non-reciprocal interactions between single-cell organisms to study emergent morphologies during…
We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed…
We consider a model of dynamics of the immune system. The model is based on three factors: occasional boosting and continuous waning of immunity and a general description of the period between subsequent boosting events. The antibody…
Spatially confined rigid membranes reorganize their morphology in response to the imposed constraints. A crumpled elastic sheet presents a complex pattern of random folds focusing the deformation energy while compressing a membrane resting…
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of…
We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
A mathematical model of the metabolic process of atherosclerosis is constructed.
In this Note, we describe the stationary equilibria and the asymptotic behaviour of an heterogeneous logistic reaction-diffusion equation under the influence of autonomous or time-periodic forcing terms. We show that the study of the…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
Atherosclerotic plaques are fatty, cellular lesions that form in artery walls. The early plaque contains monocyte-derived macrophages, which are recruited to consume locally bound lipid deposits. Plaque progression is characterised by an…
Multicellular tissues are the building blocks of many biological systems and organs. These tissues are not static, but dynamically change over time. Even if the overall structure remains the same there is a turnover of cells within the…