Related papers: Liesegang patterns : Studies on the width law
It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…
We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas…
The Einstein Equivalence Principle has as one of its implications that the non-gravitational laws of physics are those of special relativity in any local freely-falling frame. We consider possible tests of this hypothesis for systems whose…
We investigate the distribution of the resonance widths ${\cal P}(\Gamma)$ and Wigner delay times ${\cal P}(\tau_W)$ for scattering from two-dimensional systems in the diffusive regime. We obtain the forms of these distributions (log-normal…
We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state,…
In [Compositio Math. 155 (2019)] Kleinbock and Wadleigh proved a "zero-one law" for uniform inhomogeneous Diophantine approximations. We generalize this statement with arbitrary weight functions and establish a new and simple proof of this…
We studied the band gap of {\beta}-PtO2 using first-principles calculations based on density functional theory (DFT). The results are obtained within the framework of generalized gradient approximation (GGA), GGA+U, GW and the hybrid…
We investigate the threshold widths of some symmetric properties which range asymptotically between 1/\sqrt{n} and 1/(log n). These properties are built using a combination of failure sets arising from reliability theory. This combination…
We derive statistical distributions for the degrees of freedom in wave packet molecular dynamics models. Specifically, a theory is developed for the width distributions of Gaussian wavepackets in both isotropic and anisotropic formulations.…
The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…
This paper adapts the recently developed rigorous application of the supersymmetric transfer matrix approach for the 1d band matrices to the case of the orthogonal symmetry. We consider $N\times N$ block band matrices consisting of $W\times…
Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although…
Finding models for linear-time properties is a central problem in verification and planning. We study the distribution of linear-time models by investigating the density of linear-time properties over the space of ultimately periodic words.…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…
We study large $N\times N$ power-law random band matrices $H=(H_{ij})$ with centered complex Gaussian entries, where the variances satisfy a power-law decay $\mathbb{E}|H_{ij}|^2\propto (|i-j|/W+1)^{-1-\alpha}$, for some exponent…
Consider a random graph process where vertices are chosen from the interval $[0,1]$, and edges are chosen independently at random, but so that, for a given vertex $x$, the probability that there is an edge to a vertex $y$ decreases as the…
Based on the band theory of Bloch waves, a modified Bragg's law is established for Class I Bragg resonances when linear long waves are reflected by a finite periodic array of artificial bars, including rectangular, parabolic, rectified…
The ripening kinetics of bubbles is studied by performing molecular dynamics simulations. From the time evolution of a system, the growth rates of individual bubbles are determined. At low temperatures, the system exhibits a $t^{1/2}$ law…
When reading peer-reviewed scientific literature describing any analysis of empirical data, it is natural and correct to proceed with the underlying assumption that experiments have made good faith efforts to ensure that their analyses…
A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear…