Related papers: Truncation of contact defects in reaction-diffusio…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
We explore the necessary conditions for 1-form symmetries to emerge in the long-distance limit when they are explicitly broken at short distances. A minimal requirement is that there exist operators which become topological at long…
The topology of space is usually assumed simply connected, but could be multi-connected. We review in the latter case the possibility that topological defects arising at high energy phase transitions might still be present and find that…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
We discuss the structure of topological defects in the context of extra dimensions where the symmetry breaking terms are localized. These defects develop structure in the extra dimension which differs from the case where symmetry breaking…
Energy dissipation by fast crystalline defects takes place mainly through the resonant interaction of their cores with periodic lattice. We show that the resultant effective friction can be reduced to zero by appropriately tuned acoustic…
The paper deals with the homogenization of reaction-diffusion equations with large reaction terms in a multi-scale porous medium. We assume that the fractures and pores are equidistributed and that the coefficients of the equations are…
Dispersion relations provide a powerful tool to describe the electromagnetic form factors of the nucleon both in the spacelike and timelike regions with constraints from unitarity and perturbative QCD. We give a brief introduction into…
We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
Point defects in self-assembled crystals, such as vacancies and interstitials, attract each other and form stable clusters. This leads to a phase separation between perfect crystalline structures and defect conglomerates at low…
A field-theoretical description of the behavior of a disordered Ising system with long-range interaction is presented. The description is performed in the two-loop approximation in three dimensions using the Pade-Borel resummation…
We consider quantum phase transitions with global symmetry breakings that result in the formation of topological defects. We evaluate the number densities of kinks, vortices, and monopoles that are produced in $d=1,2,3$ spatial dimensions…
Drifting pattern domains (DPDs), moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this…
We study a number of domain wall forming models where various types of defect junctions can exist. These illustrate some of the mechanisms that will determine the evolution of defect networks with junctions. Understanding these mechanisms…
An important tool for understanding the effects of interactions in harmonically trapped atomic gases is the examination of their collective modes. One such mode is the breathing or monopole mode, which is special as it is constrained to…
The phenomenon of photonic band gaps in one-dimensional optical lattices is reviewed using a microscopic approach. Formally equivalent to the transfer matrix approach in the thermodynamic limit, a microscopic model is required to study…