Related papers: A first principle (3+1) dimensional model for micr…
We investigate the dynamics of an idealized model of microtubule growth that evolves by: (i) attachment of guanosine triphosphate (GTP) at rate lambda, (ii) conversion of GTP to guanosine diphosphate (GDP) at rate 1, and (iii) detachment of…
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
In nature interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviours. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active…
We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic…
We derive rigorously the non-linear macroscopic system associated to a microscopic system of coupled quintic Schr\"odinger equations in the framework of discrete wave turbulence under a particular scaling law that describes the limiting…
It has been recently discovered that stabilization of two-dimensional (2D) solitons against the critical collapse in media with the cubic nonlinearity by means of nonlinear lattices (NLs) is a challenging problem. We address the 1D version…
We derive mathematical models of the elementary process of dissolution/growth of bubbles in a liquid under pressure control. The modeling starts with a fully compressible version, both for the liquid and the gas phase so that the entropy…
We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied…
Microtubules are filamentous tubular protein polymers which are essential for a range of cellular behaviour, and are generally straight over micron length scales. However, in some gliding assays, where microtubules move over a carpet of…
We propose a two-dimensional model for the organization of stabilized microtubules driven by molecular motors in an unconfined geometry. In this model two kinds of dynamics are competing. The first one is purely diffusive, with an…
Turbulent mixing layers (TMLs) are ubiquitous in multiphase gas. They can potentially explain observations of high ions such as O VI, which have significant observed column densities despite short cooling times. Previously, we showed that…
An overview is given of basic models combining discreteness in their linear parts (i.e. the models are built as dynamical lattices) and nonlinearity acting at sites of the lattices or between the sites. The considered systems include the…
In this article we use analytical and numerical modeling to describe parallel viscous two-phase flows in microchannels. The focus is on idealized two-dimensional geometries, with a view to validating the various methodologies for future…
We study density waves in the flows of granular particles through vertical tubes and hoppers using both analytic methods and molecular dynamics (MD) simulations. We construct equations of motion for quasi one-dimensional systems. The…
A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in…
Microtubules are highly regulated dynamic elements of the cytoskeleton of eukaryotic cells. One of the regulation mechanisms observed in living cells is the severing by the proteins katanin and spastin. We introduce a model for the dynamics…
We consider the massive Thirring model and establish pointwise long-time behavior of its solutions in weighted Sobolev spaces. For soliton-free initial data we can show that the solution converges to a linear solution modulo a phase…
We study here the nonlinear Schrodinger Equation (NLS) as the first term in a sequence of approximations for an electromagnetic (EM) wave propagating according to the nonlinear Maxwell equations (NLM). The dielectric medium is assumed to be…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
In this paper, the finite volume method is developed to analyze coupled dynamic problems of nonlinear thermoelasticity. The major focus is given to the description of martensitic phase transformations essential in the modelling of shape…