相关论文: Coarsening and wavelength selection far from equil…
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…
We study nonlinear systems of hyperbolic (in a wider sense) PDE's in entire d-dimensional space describing wave propagation with the initial data in the form of a finite sum of wavepackets referred to as multi-wavepackets. The problem…
This study investigates chaotic diffusion in multi-scale turbulence driven by nonlinear wave-particle resonance coupling. Turbulent waves with distinct characteristic wavelengths across scales coherently interact with charged particles when…
The present paper studies existence and distributional uniqueness of subclasses of stationary hard-core particle systems arising as thinnings of stationary particle processes. These subclasses are defined by natural maximality criteria. We…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I…
The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We consider the dynamics of weakly nonlinear wave packets, and…
We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
Multicellular organisms comprise a diverse collection of stable tissues built from different cell types. It remains unclear how large numbers of interacting cells can precisely coordinate their gene expression during tissue…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…
This work continues our studies of nonlinear evolution of a system of wavepackets. We study a wave propagation governed by a nonlinear system of hyperbolic PDE's with constant coefficients with the initial data being a multi-wavepacket. By…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…
In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on \textit{collinear dynamical systems} and their variations are…
We present a molecular dynamics study of force patterns, tensile strength and crack formation in a cohesive granular model where the particles are subjected to swelling or shrinkage gradients. Non-uniform particle size change generates…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…