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Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction…
A two species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behavior which…
Modelling the dynamics of dense granular media is a long standing challenge and essential to many natural phenomena and technological applications. Here, we trace back puzzling experimental observation of detailed-balanced steady states to…
A living polymers transition is found in molecular dynamics simulations of a charge-symmetric size-asymmetric electrolyte with no anisotropic interactions. The fluid has strong polymeric character at low temperatures, where it consists of…
A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very…
Biological systems commonly combine intrinsically out-of-equilibrium active components with passive polymeric inclusions to produce unique material properties. To explore these composite systems, idealized models - such as polymers in…
We consider a generational and continuous-time two-phase model of the cell cycle. The first model is given by a stochastic operator, and the second by a piecewise deterministic Markov process. In the second case we also introduce a…
In this paper we present recent results on parametric analysis of biological models. The underlying method is based on the algorithms for computing trajectory sets of hybrid systems with polynomial dynamics. The method is then applied to…
In an attempt to explain the uniqueness of the coding mechanism of living cells as contrasted with multi-species structure of ecosystems we examine two models of individuals with some replicative properties. In the first model the system…
An autocatalytic pattern matching polymer system is studied as an abstract model for chemical ecosystem evolution. Highly ordered populations with particular sequence patterns appear spontaneously out of a vast number of possible states.…
The thermodynamic (TD) properties of biological membranes play a central role for living systems. It has been suggested, for instance, that nonlinear pulses such as action potentials (APs) can only exist if the membrane state is in vicinity…
Quantitative modeling has become an essential tool in modern biophysics, driven by advances in both experimental techniques and theoretical frameworks. Powerful high-resolution techniques now provide detailed datasets spanning molecular to…
To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
Biomaterial systems have allowed for the in vitro production of complex, emergent tissue behaviors that were not possible with conventional 2D culture systems allowing for analysis of the normal development as well as disease processes. We…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
In this work, we compare the structural and dynamic behavior of active filaments in two dimensions using tangential and push-pull models, including a variant with passive end monomers. These models serve as valuable frameworks for…
Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
We study dynamics and scaling exponents in a nonlinear network model inspired by the formation of planetary systems. Dynamics of this model leads to phase separation to two types of condensate, light and heavy, distinguished by how they…