相关论文: Scaling Law in Cluster Decay
The stable fragmentation with index of self-similarity $\alpha \in [-1/2,0)$ is derived by looking at the masses of the subtrees formed by discarding the parts of a $(1 + \alpha)^{-1}$--stable continuum random tree below height $t$, for $t…
The interaction potential between the alpha particle and the deformed parent nucleus was used for description of the decay of superheavy nuclei. It consists of centrifugal, nuclear and Coulomb parts suitably modified for deformed nuclei.…
We consider TASEP with two types of particles starting at every second site. Particles to the left of the origin have jump rate $1$, while particles to the right have jump rate $\alpha$. When $\alpha<1$ there is a formation of a shock where…
The critical incompatibility of polymers with different compositions scales inversely with their length. For instance, a mixture of A and B homopolymers of length $N$ segregates at $\chi_{AB}^{cr} = 2/N$. But what if the difference between…
The scaling of the longitudinal velocity structure functions, $S_q(r) = < | \delta u (r) |^q > \sim r^{\zeta_q}$, is analyzed up to order $q=8$ in a decaying rotating turbulence experiment from a large Particle Image Velocimetry (PIV)…
With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here…
Sum rules for exclusive production of heavy meson pairs in $e^+e^-$ annihilation are used to evaluate the $\Upsilon(4S) \to B \bar B$ and $\psi(3770) \to D \bar D$ decay widths. Infinitely heavy quark limit is discussed, so that scaling law…
In the framework of the Statistical Multifragmentation Model, the nuclear isoscaling analysis is extended to constrain the ratio between the sizes of the decaying sources formed in a collision between two heavy ions. It is found that the…
Four groups (even-even, even-odd, odd-even and odd-odd) of heavy and super-heavy nuclei are of interest for the synthesis of the isotopes with $Z=119, 120$. We report calculations of $\alpha$~decay half-lives using four models: AKRA…
In this paper, we propose a method to construct the decay amplitudes in the orbital ($L$) and spin ($S$) coupling scheme for particles with arbitrary spins. For the $1\to 2$ decay with only massive particles involved, the angular dependence…
The scaling behavior of cyclical surface growth (e.g. deposition/desorption), with the number of cycles n, is investigated. The roughness of surfaces grown by two linear primary processes follows a scaling behavior with asymptotic exponents…
To describe the small-scale intermittency of turbulence, a self-similarity is assumed for the probability density function of a logarithm of the rate of energy dissipation smoothed over a length scale among those in the inertial range. The…
A simple relation $(aZ_{c} + b)(Z_{d}/Q)^{1/2} + (cZ_{c} + d)$ of estimation of the half-life of cluster emission is further improved for cluster and $\alpha$-decays, separately, by incorporating isospin of parent nucleus as well as angular…
Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…
Wall turbulence has a sublayer where one-point statistics, e.g., the mean velocity and the variances of some velocity fluctuations, vary logarithmically with the distance from the wall. This logarithmic scaling is found here for two-point…
We investigate Anderson localization on various 1D structures having flat bands. The main focus is on the scaling laws obeyed by the localization length at weak disorder in the vicinity of flat-band energies. A careful distinction is made…
The universal anomalous diffusion scaling is obtained for the semiclassical quantum Hall transition, which has been argued to describe samples with dissipation or correlated impurities. The results explain a discrepancy between existing…
We compute energy distributions of three $\alpha$-particles emerging from the decay of $^{12}$C resonances by means of the hyperspherical adiabatic expansion method combined with complex scaling. The large distance continuum properties of…
The frequency dependence of the Raman coupling coefficient $C(\omega)$ is calculated numerically for square and cubic percolation clusters. No general scaling law in terms of the macroscopic parameters such as the fractal dimension $D$ or…
For a second-order particle system in $\mathbb R^d$ subject to locally-in-space pairwise annihilation, we prove a scaling limit for its empirical measure on position and velocity towards a degenerate elliptic partial differential equation.…