Related papers: Truncation of contact defects in reaction-diffusio…
Topological defects are singularities in material fields that play a vital role across a range of systems: from cosmic microwave background polarization to superconductors, and biological materials. Although topological defects and their…
Topological defects are produced during phase transitions in the very early Universe. They arise in most unified theories of strong, weak and electromagnetic interactions. These lectures focus on the role of topological defects in…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is…
The supercritical series expansion of the survival probability for the one-dimensional contact process in heterogeneous and disordered lattices is used for the evaluation of the loci of critical points and critical exponents $\beta$. The…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
Statistics and thermally activated dynamics of crack nucleation and propagation in a two-dimensional heterogeneous material containing quenched randomly distributed defects are studied theoretically. Using the generalized Griffith criterion…
We study the dynamics and equilibrium profile shapes of contact lines for wetting in the case of a spatially inhomogeneous solid wall with stripe defects. Using a phase-field model with conserved dynamics, we first numerically determine the…
We consider scattering waves through truncated periodic potentials with perturbations that support localized gap eigenstates. In a small complex neighborhood around an assumed positive bound state of the model operator, we prove the…
A reaction-diffusion equation is studied in a time-dependent interval whose length varies with time. The reaction term is either linear or of KPP type. On a fixed interval, it is well-known that if the length is less than a certain critical…
The aim of this paper is to present the analysis of influence of defects in 1D photonic crystal (PC) on the density of states and simultaneously spontaneous emission, in both spatial and frequency domains. In our investigations we use an…
We consider a general class of contact processes on $\mathbb{Z}^d$ with potentially long-range interactions. By adapting well established renormalization arguments to the long-range setting we extend by now classical results for…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
Reduced transport and localization in isolated quantum systems are typically attributed to spatially-extended disorder, but may also emerge from the influence of a few controllable defects. We show here how a single defect profoundly…
Contact has been well established as an important quantity to govern dilute quantum systems, in which the pairwise correlation at short distance traces a broad range of thermodynamic properties. So far, studies have been focusing on contact…
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…
Periodic boundary conditions are a common theoretical and computational tool used to emulate effectively infinite domains. However, two-dimensional periodic domains are topologically distinct from the infinite plane, eliciting the question:…
The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary $d$-dimensional reaction-diffusion system of the activator-inhibitor type are asymptotically derived. It is shown that…
We show that defect-mediated turbulence can exist in media where the underlying local dynamics is deterministically chaotic. While many of the characteristics of defect-mediated turbulence, such as the exponential decay of correlations and…
We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish criteria…