Nonequilibrium collective motion is ubiquitous in nature and often results in a rich collection of intriguing phenomena, such as the formation of shocks or patterns, subdiffusive kinetics, traffic jams, and nonequilibrium phase transitions. These stochastic many-body features characterize transport processes in biology, soft condensed matter and, possibly, also in nanoscience. Inspired by these applications, a wide class of lattice-gas models has recently been considered. Building on the celebrated...

Determining amino acid sequences of protein molecules is one of the most important issues in molecular biology. These sequences determine protein structure and functionality. Unfortunately, direct biochemical methods for reading amino acid sequences can be used for reading short sequences only. This is the reason, which makes peptide assembly algorithms an important complement of these methods. In this paper, a genetic algorithm solving the problem of short amino acid sequence assembly is presented....

The self-consistent chemotaxis-fluid system $$\left\{\begin{array}{cc}{n}_t+u·\nabla n=\Delta n-\nabla ·\left(n\nabla c\right)+\nabla ·\left(n\nabla \phi \right),\hfill & x\in \Omega ,t>0,\hfill \\ c_t+u·\nabla c=\Delta c-nc,\hfill & x\in \Omega ,t>0,\hfill \\ u_t+\kappa (u·\nabla )u+\nabla P=\Delta u-n\nabla \phi +n\nabla c,\hfill & x\in \Omega ,t>0,\hfill \\ \nabla ·u=0,\hfill & x\in \Omega ,t>0,\hfill \end{array}\right.$$ is considered under no-flux boundary conditions for $n,c$ and the Dirichlet boundary condition for $u$ on a bounded smooth domain $\Omega \subset {ℝ}^N$$(N=2,3...$

A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.

In this paper we consider a model of chemorepulsion. We prove global existence and uniqueness of smooth classical solutions in space dimension n = 2. For n = 3,4 we prove the global existence of weak solutions. The convergence to steady states is shown in all cases.

A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly...

We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a $(\mu ,\nu )$-pseudo almost automorphic solution. The...

We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous...

We study the chemotaxis system with singular sensitivity and logistic-type source: $u_t=\Delta u-\chi \nabla ·(u\nabla v/v)+ru-\mu u^k$, $0=\Delta v-v+u$ under the non-flux boundary conditions in a smooth bounded domain $\Omega \subset {ℝ}^n$, $\chi ,r,\mu >0$, $k>1$ and $n\ge 1$. It is shown with $k\in (1,2)$ that the system possesses a global generalized solution for $n\ge 2$ which is bounded when $\chi >0$ is suitably small related to $r>0$ and the initial datum is properly small, and a global bounded classical solution for $n=1$.

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...