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We present calculations of forces for two dimensional static sandpile models. Using a symbolic calculation software we obtain exact results for several different orientations of the lattice and for different types of supporting surfaces.…
Local strain engineering is an exciting approach to tune the optoelectronic properties of materials. Two dimensional (2D) materials such as 2D transition metal dichalcogenides (TMDs) are particularly well suited for this purpose because…
The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…
SCAN+rVV10 has been demonstrated to be a versatile van der Waals (vdW) density functional that delivers good predictions of both energetic and structural properties for many types of bonding. Recently, the r$^{2}$SCAN functional has been…
The behavior of the bulk two-point correlation function $G({\bf r};T|d)$ in $d$-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such…
We study perturbatively the (conformal) WZNW model. At one loop we compute one-particle irreducible two- and three-point current correlation functions, both in the conventional version and in the classically equivalent, chiral, nonlocal,…
Bilayer two-dimensional (2D) van der Waals (vdW) materials are attracting increasing attention due to their predicted high quality electronic and optical properties. Here we demonstrate dense, selective growth of WSe2 bilayer flakes by…
We reformulate time evolution of systems in mixed states in terms of the classical observables of correlators using the Weyl correspondence rule. The resulting equation of motion for the Wigner functional of the density matrix is found to…
We analyze the Wheeler-DeWitt (WDW) equation in the context of a gravitational collapse. The physics of an expanding/collapsing universe and many details of a collapsing star can classically be described by the Roberston-Walker metric in…
We introduce a simple geometric model which describes the kinetics of fragmentation of d-dimensional objects. In one dimension our model coincides with the random scission model and show a simple scaling behavior in the long-time limit. For…
This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods,…
The width W of the active region around an active moving wall in a directed percolation process diverges at the percolation threshold p_c as W \simeq A \epsilon^{-\nu_\parallel} \ln(\epsilon_0/\epsilon), with \epsilon=p_c-p, \epsilon_0 a…
We derive and validate a quantitative analytical model of the near-field electrostatic effects in the vicinity (>=3\AA) of two-dimensional (2D) materials. In solving the Poisson equation of a near-planar point charge ansatz for the…
The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…
We analyze scaling functions in the $3$-$d$, $Z(2)$, $O(2)$ and $O(4)$ universality classes and their finite size dependence using Monte Carlo simulations of improved $\phi^4$ models. Results for the scaling functions are fitted to the…
To implement the Wigner branching random walk, the particle carrying a signed weight, either $-1$ or $+1$, is more friendly to data storage and arithmetic manipulations than that taking a real-valued weight continuously from $-1$ to $+1$.…
It is shown that a recently conjectured form for the critical scaling function for planar self-avoiding polygons weighted by their perimeter and area also follows from an exact renormalization group flow into the branched polymer problem,…
Recently, the authors have proposed a new approach to the theory of random metrics, making an explicit link between probability measures on the space of metrics on a Kahler manifold and random matrix models. We consider simple examples of…
We consider two random walkers starting at the same time $t=0$ from different points in space separated by a given distance $R$. We compute the average volume of the space visited by both walkers up to time $t$ as a function of $R$ and $t$…
In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity…