Related papers: Dimensionality effects in Turing pattern formation
Models of diffusion driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of…
The effects of an aperiodic order or a random disorder on phase transitions in statistical mechanics are discussed. A heuristic relevance criterion based on scaling arguments as well as specific results for Ising models with random disorder…
This paper addresses the question of how population diffusion affects the formation of the spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we present theoretical analysis to results of the numerical…
We study transitions from convective to absolute instability near a trivial state in large bounded domains for prototypical model problems in the presence of transport and negative nonlinear feedback. We identify two generic scenarios,…
Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…
Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor--that of the cascade. The…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
In this thesis we deal with the specific collective phenomena in condensed matter - striped-structures formation. Such structures are observed in different branches of condensed matter physics, like surface physics or physics of…
We present a theoretical and numerical investigation of the effect of a time-varying external driving force on interface growth. First, we derive a relation between the roughening exponents which comes from a generalized Galilean…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…
In sorting literature, comparative statics for multidimensional assignment models with general output functions and input distributions is an important open question. We provide a complete theory of comparative statics for technological…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the…
Properties of the two dimensional Ising model with fixed magnetization are deduced from known exact results on the two dimensional Ising model. The existence of a continuous phase transition is shown for arbitrary values of the fixed…
Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a…
Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the…
The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of conformal invariance and universality are established numerically.
We study theoretically the out-of-equilibrium transport properties of a double quantum dot system in the Kondo regime. We model the system by means of a two-impurity Anderson Hamiltonian. The transport properties are characterized by Kondo…
The classical low-dimensional models of thin structures are based on certain a priori assumptions on the three-dimensional deformation and/or stress fields, diverse in nature but all motivated by the smallness of certain dimensions with…