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The study of the evolution of the dynamics of a massive or massless particle shows that in special relativity theory, the energy is not conserved. From the law of evolution of the velocity over time of a particle subjected to a constant…
Debris disc analysis and modelling provide crucial information about the structure and the processes at play in extrasolar planetary systems. In binary systems, this issue is more complex because the disc should in addition respond to the…
Recent computer simulations reveal several intriguing features in the evolution of properties of amorphous solids subjected to repeated cyclic shear deformation. These include the divergence of the number of cycles to reach steady states as…
Sediment transport is studied as a function of the grain to fluid density ratio using two phase numerical sim- ulations based on a discrete element method (DEM) for particles coupled to a continuum Reynolds averaged description of…
Axial segregation of a binary mixture of grains in a rotating drum is studied using Molecular Dynamics (MD) simulations. A force scheme leading to a constant restitution coefficient is used and shows that axial segregation is possible…
Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…
We consider the spreading dynamics of some insoluble surface-active species along an aqueous interface. The model includes both diffusion, Marangoni convection and first-order reaction kinetics. An exact solution of the nonlinear transport…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
The internal energy associated with the defect microstructure of strongly deformed crystals provides an important driving force for grain boundary motion during recrystallization. Typical dislocation microstructures are strongly…
Elastoplastic properties of nanocrystalline metals are non-uniform on the scale of the grain size, and this non-uniformity affects macroscopic quantities as, in these systems, a significant part of the material is at or adjacent to a grain…
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
A threshold dynamics model of grain growth that accounts for the anisotropy in the grain boundary energy has been used to simulate experimentally observed grain growth of polycrystalline Ni. The simulation reproduces several aspects of the…
Scattering of electrons from chiral spin textures such as the skyrmions is an emerging research area due to its richness in topological quantum transport, which is significant for spintronic devices. We study the dynamical process of…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
Liquid crystal skyrmions are topologically protected spatially localized distortions of the director field which are fascinating from both fundamental mathematics and applied physics points of view. Skyrmions are realized in experimental…
In this paper we consider the multispecies stirring process on the discrete torus. We prove a large deviation principle for the trajectory of the vector of densities of the different species. The technique of proof consists in extending the…
The present paper introduces a mathematical model for studying dynamic grain growth. In particular, we show how characteristic measurements, grain volumes, centroids, and central second-order moments at discrete moments in time can be…
Grain boundary (GB) migration plays a crucial role in the thermal and mechanical responses of polycrystalline materials, particularly in ultrafine-grained and nano-grained materials exhibiting grain size-dependent properties. This study…