A three parameter scaling relationship between isotopic distributions for elements with Z< or =8 has been observed. This allows a simple description of the dependence of such distributions on the overall isospin of the system. This scaling law (termed isoscaling) applies for a variety of reaction mechanisms that are dominated by phase space, including evaporation, multifragmentation, and deeply...

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Voronoï cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as funct...

In this note we prove scattering for perturbations of solitons in the scaling space appropriate for the quartic nonlinearity, namely Ḣ− 1 6 . The article relies strongly on refined estimates for a KdV equation linearized at the soliton. In contrast to the work of Tao [19] we are able to work purely in the scaling space without additional regularity assumptions, allowing us to construct wave ope...

Scaling limits of continuous time random walks are used in physics to model anomalous diffusion, in which a cloud of particles spreads at a different rate than the classical Brownian motion. Governing equations for these limit processes generalize the classical diffusion equation. In this article, we characterize scaling limits in the case where the particle jump sizes and the waiting time betw...

We prove the stability of the one dimensional kink solution of the Cahn-Hilliard equation under d-dimensional perturbations for d ≥ 3. We also establish a novel scaling behavior of the large time asymptotics of the solution. The leading asymptotics of the solution is characterized by a length scale proportional to t 1 3 instead of the usual t 1 2 scaling typical to parabolic problems.

In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion equation (NDE) has been suggested and checked for one-dimensional lattices. Here, we apply this approach to two-dimensional strongly nonlinear lattices and find...

We introduce a class of stochastic volatility models (Xt)t≥0 for which the absolute moments of the increments exhibit anomalous scaling: E (|Xt+h −Xt|) scales as hq/2 for q < q∗, but as hA(q) with A(q) < q/2 for q > q∗, for some threshold q∗. This multi-scaling phenomenon is observed in time series of financial assets. If the dynamics of the volatility is given by a mean-reverting equation driv...

Here ψ(E; t) is the energy distribution of a coasting beam. It is often easier in practical applications to follow the evolution of phase space density by tracking a representative distribution of macroparticles using the equations of motion. There are scaling relations derived from the PDE’s which can make dramatic improvements in the efficiency or practical scope of macroparticle models. Scal...

We study waves in convex scalar conservation laws under noisy initial perturbations. It is known that the building blocks of these waves are shock and rarefaction waves, both are invariant under hyperbolic scaling. Noisy perturbations can generate complicated wave patterns, such as diffusion process of shock locations. However we show that under the hyperbolic scaling, the solutions converge in...

The existence of stationary localized spots for the planar and the three-dimensional Swift–Hohenberg equation is proved using geometric blow-up techniques. The spots found in this paper have a much larger amplitude than that expected from a formal scaling in the far field. One advantage of the geometric blow-up methods used here is that the anticipated amplitude scaling does not enter as an ass...