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In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the…
Single-round multiway join algorithms first reshuffle data over many servers and then evaluate the query at hand in a parallel and communication-free way. A key question is whether a given distribution policy for the reshuffle is adequate…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
Percolation plays an important role in fields and phenomena as diverse as the study of social networks, the dynamics of epidemics, the robustness of electricity grids, conduction in disordered media, and geometric properties in statistical…
The nucleation of vapor bubbles within a superheated fluid is studied using density functional theory. The nudged elastic band technique is used to find the minimum energy pathway from the metastable uniform liquid to the stable uniform gas…
This comment is devoted to the paper "Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry approach" (CNSNS, vol. 67 (2019), 253-263) in which several results are not new because were derived much earlier.…
I present briefly some facts about nonequilibrium renormalized perturbation theory, correcting recent misleading statements in [E. Mu\~noz, F. Zamani, L. Merker, T. A. Costi, and S. Kirchner, Journal of Physics: Conf. Series 807, 092001…
This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving…
Disagreement percolation connects a Gibbs lattice gas and i.i.d. site percolation on the same lattice such that non-percolation implies uniqueness of the Gibbs measure. This work generalises disagreement percolation to the hard-sphere model…
The formation mechanism of ice banding in the system of freezing colloidal suspensions, which is of significance in frost heaving, ice-templating porous materials and biological materials, still remains a mystery. Recently, the theory of…
We use a sticky particle method to show global existence of (energy) conservative sticky $N$-peakon solutions to the modified Camassa-Holm equation. A dispersion regularization is provided as a selection principle for the uniqueness of…
Jaramillo et al. (2018) (hereafter JMR1) asserted that our theory, henceforth known as CIAD (condensation-induced atmospheric dynamics), modifies the equation of vertical motion in a manner that violates Newton's third law. Jaramillo et al.…
We discuss a classical mistake, made in earlier publications on the stick percolation problem in 3D, for generating the right isotropic configuration of sticks. We explain the observed systematic deviations from the excluded volume rule.…
We prove that, the diffusivity and conductivity on $\mathbb{Z}^d$-Bernoulli percolation ($d \geq 2$) are infinitely differentiable in supercritical regime. This extends a result by Kozlov [Uspekhi Mat. Nauk 44 (1989), no. 2(266), pp 79 -…
It is shown that a suspension of particles in a partially-filled, horizontal, rotating cylinder is linearly unstable towards axial segregation and an undulation of the free surface at large enough particle concentrations. Relying on the…
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It…
We investigate variations of the well-known Achlioptas percolation problem, which uses the method of probing sites when building up a lattice system, or probing links when building a network, ultimately resulting in the delay of the…
We reveal the connection of the recent numerical observations of Krstulovic and Brachet [arXiv:1007.4441] with the general theory of relaxation kinetics of the strongly non-equilibrium Bose-Einstein condensates.
Percolation theory is applied to the phase-transition dynamics of domain pattern formation in segregating binary Bose--Einstein condensates in quasi-two-dimensional systems. Our finite-size-scaling analysis shows that the percolation…
We use a simple Colour Glass Condensate/String Percolation Model argument to show the existence, due to energy conservation, of bounds to the violation of Feynman scaling and limiting fragmentation.