Related papers: Scaling theory for two-dimensional single domain g…
We study the spreading dynamics on graphs with a power law degree distribution p_k ~ k^-gamma with 2<gamma<3, as an example of a branching process with diverging reproductive number. We provide evidence that the divergence of the second…
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical…
The principle of smooth fit is probably the most used tool to find solutions to optimal stopping problems of one-dimensional diffusions. It is important, e.g., in financial mathematical applications to understand in which kind of models and…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
The effect of diffusively correlated spatial fluctuations on the proliferation-extinction transition of autocatalytic agents is investigated numerically. Reactants adaptation to spatio-temporal active regions is shown to lead to…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
We study domain walls in 2d Ising spin glasses in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of domain walls, which describes via $<\ell…
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…
Strain-inducing deformations in graphene alter charge distributions and provide a new method to design specific features in the band structure and transport properties. Novel approaches implement engineered substrates to induce specifically…
The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous…
We investigated the kinetics of domain growth on liposomes consisting of a ternary mixture (unsaturated phospholipid, saturated phospholipid, and cholesterol) by temperature jump. The domain growth process was monitored by fluorescence…
X-Ray microtomography was used to follow the coarsening of the structure of a ternary silicate glass experiencing phase separation in the liquid state. The volumes, surfaces, mean and Gaussian curvatures of the domains of minority phase…
We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling…
We study experimentally the slow growth of a single crack in polycarbonate films submitted to uniaxial and constant imposed stress. For this visco-plastic material, we uncover a dynamical law that describes the dependence of the…
In this paper a simple (2+1) solid-on-solid model of the epitaxial films growth based on random deposition followed by breaking particle-particle lateral bonds and particles surface diffusion is introduced. The influence of the critical…
The vertical gradient freeze crystal growth process is the main technique for the production of high quality compound semiconductors that are vital for today's electronic applications. A simplified model of this process consists of two 1D…
We have demonstrated a new method for the large-area graphene growth, which can lead to a scalable low-cost high-throughput production technology. The method is based on growing single-layer or few-layer graphene films from a molten phase.…
The coarsening dynamics of three-dimensional islands on a growing film is discussed. It is assumed that the origin of the initial instability of a planar surface is the Ehrlich-Schwoebel step-edge barrier for adatom diffusion. Two…
In this work, we present and analyse a system of coupled partial differential equations, which models tumour growth under the influence of subdiffusion, mechanical effects, nutrient supply, and chemotherapy. The subdiffusion of the system…
Strongly correlated amorphous solids are a class of glass-formers whose inter-particle potential admits an approximate inverse power-law form in a relevant range of inter-particle distances. We study the steady-state plastic flow of such…