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Keyword: KPZ Equation (7)	27 Mar 2025	Run
Keyword: Spin Polaron (6)	27 Mar 2025	Run
Keyword: Source Nodes (1)	27 Mar 2025	Run
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articleNo Access
DYNAMICS OF EDEN CLUSTERS: CONFIRMATION OF APPERT–DERRIDA UNIVERSALITY
- INGO WEICHSEL
International Journal of Modern Physics C01 Jun 2000
Preview Abstract
Universality of ratios of cumulants depends on the minor changes in the definition of time.
articleNo Access
SIMULATIONS OF KINETIC ROUGHENING WITH POWER-LAW NOISE ON THE CONNECTION MACHINE
- R. BOURBONNAIS,
- H.J. HERRMANN, and
- T. VICSEK
International Journal of Modern Physics C01 Sep 1991
Preview Abstract
We present results of large scale simulations on the Connection Machine (CM) on the scaling behavior of the Zhang model and its variants for the kinetics of self-affine interfaces with power-law noise. Details on implementing this problem on a massively parallel computer such as the CM are given. Our calculations for the case when the amplitude η of the noise has a distribution P(η)~η^−1−µ are in good agreement with earlier findings of non-universality for µ<7. We present data which suggest that for µ≥7 the model is in the universality class of Gaussian noise.
articleNo Access
A Crossover Between Two Growth Universality Classes
- T. J. da Silva
International Journal of Modern Physics C01 Sep 1998
Preview Abstract
We investigated two simple SOS growth models where the roughness of the profile is softened by surface relaxation or by refuse. In the first case, a particle can relax until it reaches a local minimum and this process is described by a linear equation. In the second case, a particle can be evaporated and this process is described by the KPZ equation. In this work, we have mixed both the models in the same growth process. Numerical simulations in (1+1)-dimensions show a process that for short times behaves as the surface relaxation model and for intermediate times, behaves as the refuse model. Numerical simulations indicate for this crossover a dynamical exponent z≈1.4, indicating that it is in the KPZ universality class.
articleNo Access
Cumulant Ratios of Eden Model Surfaces in 1+1 Dimensions
- Dietrich Stauffer
International Journal of Modern Physics C01 Oct 1998
Preview Abstract
Monte Carlo simulations suggest that dimensionless ratios of cumulants for the height of the surface depend on how randomness is used.
articleNo Access
Renormalized-generalized solutions for the KPZ equation
- Pedro Catuogno and
- Christian Olivera
Infinite Dimensional Analysis, Quantum Probability and Related Topics25 Nov 2014
Preview Abstract
This work introduces a new notion of solution for the KPZ equation, in particular, our approach encompasses the Cole–Hopf solution. We set in the context of the distribution theory the proposed results by Bertini and Giacomin from the mid '90s.
This new approach provides a pathwise notion of solution as well as a structured approximation theory. The developments are based on regularization arguments from the theory of distributions.
articleNo Access
Parabolic equations with natural growth approximated by nonlocal equations
Communications in Contemporary Mathematics21 Jan 2020
Preview Abstract
In this paper, we study several aspects related with solutions of nonlocal problems whose prototype is
$\{\begin{matrix} u_{t} = \int_{ℝ^{N}} J (x - y) (u (y, t) - u (x, t)) 𝒢 (u (y, t) - u (x, t)) d y & in Ω \times (0, T), \\ u (x, 0) = u_{0} (x) & in Ω, \end{matrix}$
where we take, as the most important instance, $𝒢 (s) \sim 1 + \frac{μ}{2} \frac{s}{1 + μ^{2} s^{2}}$ with $μ \in ℝ$ as well as $u_{0} \in L^{1} (Ω)$ , $J$ is a smooth symmetric function with compact support and $Ω$ is either a bounded smooth subset of $ℝ^{N}$ , with nonlocal Dirichlet boundary condition, or $ℝ^{N}$ itself. The results deal with existence, uniqueness, comparison principle and asymptotic behavior. Moreover, we prove that if the kernel is rescaled in a suitable way, the unique solution of the above problem converges to a solution of the deterministic Kardar–Parisi–Zhang equation.
articleNo Access
Synchronization for KPZ
- Tommaso C. Rosati
Stochastics and Dynamics03 Nov 2021
Preview Abstract
We study the long-time behavior of Kardar–Parisi–Zhang (KPZ)-like equations:
$\partial_{t} h (t, x) = Δ_{x} h (t, x) + | \nabla_{x} h (t, x) |^{2} + η (t, x),$
$h (0, x) = h_{0} (x), (t, x) \in (0, \infty) \times 𝕋^{d},$
on the $d$ -dimensional torus $𝕋^{d}$ driven by an ergodic noise $η$ (e.g., space-time white in $d = 1$ ). The analysis builds on infinite-dimensional extensions of similar results for positive random matrices. We establish a one force, one solution principle and derive almost sure synchronization with exponential deterministic speed in appropriate Hölder spaces.