Related papers: A Kinetic Model for Grain Growth
A multiscale mathematical model is presented to describe the de novo granulation and the evolution of multispecies granular biofilms within a continuous reactor. The granule is modelled as a spherical free boundary domain with radial…
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
Nanocrystalline (NC) materials are intrinsically unstable against grain growth. Significant research efforts have been dedicated to suppressing the grain growth by solute segregation, including the pursuit of a special NC structure that…
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…
The energy-momentum tensor coming from one-parameter effective Yang- Mills theory is here used to describe the matter-energy content of the homogeneous and isotropic Friedmann cosmology in its early stages. The behavior of all solutions is…
Although big bang cosmology effectively models even the most puzzling observational data, it offers no insight into why the cosmological expansion should occur at all. In this paper it is suggested that a finite Universe poses particular…
Simulation of a Langevin-dynamics model demonstrates emergence of critical fluctuations and anomalous grain transport which have been observed in experiments on "soft" quasi-two-dimensional dusty plasma clusters. It has been suggested that…
Grain boundary (GB) kinetics is important for many applications in 2d materials and metal thin films. To study how the substrate shape affects GB mobility and kinetics, we develop a kinetic Monte Carlo (kMC) simulation method and an…
Recent experimental developments in multimode nonlinear photonic circuits (MMNPC), have motivated the development of an optical thermodynamic theory that describes the equilibrium properties of an initial beam excitation. However, a…
We propose a non-linear extension of the Fierz-Pauli mass for the graviton through a functional of the vielbein and an external Minkowski background. The functional generalizes the notion of the measure, since it reduces to a cosmological…
In this work, we study the pattern solutions of doubly nonlocal logistic map that include spatial kernels in both growth and competition terms. We show that this map includes as a particular case the nonlocal Fisher-Kolmogorov equation, and…
Kinetic theory of dissipative particle dynamics is developed in terms of a Boltzmann pair collision theory. The kinetic transport coefficients are computed from explicit collision integrals and compared favourably with detailed simulations.…
We discuss the mathematical modeling and numerical discretization of transport problems on one-dimensional networks. Suitable coupling conditions are derived that guarantee conservation of mass across network junctions and dissipation of a…
We study a moving boundary model of non-conserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin film production by…
We study the solutions of Von Neumann's expanding model with reversible processes for an infinite reaction network. We show that, contrary to the irreversible case, the solution space need not be convex in contracting phases (i.e. phases…
The Vlasov equation is analyzed for coarse grained distributions resembling a finite width of test-particles as used in numerical implementations. It is shown that this coarse grained distribution obeys a kinetic equation similar to the…
Intermediate filaments form an essential structural network, spread throughout the cytoplasm and play a key role in cell mechanics, intracellular organization and molecular signaling. The maintenance of the network and its adaptation to the…
Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…