Related papers: How disorder originates and grows inside order
In this study, the analytic expressions of the steady probability distribution of tumor cells were established based on the steady state solution to the corresponding Fokker-Planck equation. Then, the effects of two uncorrelated white…
Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent…
We propose an explanation for the onset of oscillations seen in numerical simulations of dense, inclined flows of inelastic, frictional spheres. It is based on a phase transition between disordered and ordered collisional states that may be…
We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the…
We perform a comprehensive study of noise-induced effects in a stochastic model of reaction-diffusion type, describing nano-structured thin films growth at condensation. We introduce an external flux of adsorbate between neighbour…
We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This…
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…
We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…
We study numerically the phase-ordering kinetics of the site-diluted and bond-diluted Ising models after a quench from an infinite to a low temperature. We show that the speed of growth of the ordered domain's size is non-monotonous with…
Relationships between inter-cluster synchronization phenomena and external noise are studied on the basis of noise level-free analysis. We consider a mean-field model of ensembles of coupled limit cycle oscillators with two natural…
We discuss the Euclidean quantum $O(N)$ model with $N=2$ in a continuous broken symmetry phase. We study the system at low temperatures in the presence of quenched disorder linearly coupled to the scalar field. Performing an average over…
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established.…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
Recent studies of active colloidal matter have revealed that a global polar order can arise from chemorepulsive interactions among particles without any explicit alignment interaction between them. In this work, we investigate such…
Non-motile elongated bacteria confined in two-dimensional open micro-channels can exhibit collective motion and form dense monolayers with nematic order if the cells proliferate, i.e., grow and divide. Using soft molecular dynamics…
A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell…
In quenched disordered systems, the existence of ordering is generally believed to be only possible in the weak disorder regime (disregarding models of spin-glass type). In particular, sufficiently large random field is expected to prohibit…
We develop a mean-field approach for multicomponent stochastic spatially extended systems and use it to obtain a multivariate nonlinear self-consistent Fokker-Planck equation defining the probability density of the state of the system,…
Living systems implement and execute an extraordinary plethora of computational tasks. The inherent degree of large scale coordination emerges as a global property, from the intricate sea of microscopic interactions. The brain, with its…
The noise power spectra of spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg-Landau equation with a stochastic term. Analytical and numerical investigations show that the spatial spectra of the…