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The minimal energy variations of a directed polymer with tilted columnar disorder in two dimensions are shown numerically to obey a multiscaling at short distances which crosses over to global simple scaling at large distances. The scenario…
A new semi-analytic model of the metal rolling process is introduced, which, for the first time, is able to predict the through-thickness stress and strain oscillations present in long thin roll-gaps. The model is based on multiple-scales…
The scaling of the fundamental limits of the second hyperpolarizability is used to define the intrinsic second hyperpolarizability, which aids in identifying material classes with ultralarge nonlinear-optical response per unit of molecular…
Chemical space which encompasses all stable compounds is unfathomably large and its dimension scales linearly with the number of atoms considered. The success of machine learning methods suggests that many physical quantities exhibit…
The predictions of the polymer mode coupling theory for the finite size corrections to the transport coefficients of entangled polymeric systems are tested in comparisons with various experimental data. It is found that quantitative…
Multiple relaxation channels often arise in the dynamics of liquids where the momentum current associated to the particle-conservation law splits into distinct contributions. Examples are strongly confined liquids for which the currents in…
This study investigated, experimentally and numerically, the fracturing behavior of thermoset polymer structures featuring cracks and sharp u-notches. It is shown that, even for cases in which the sharpness of the notch would suggest…
We introduce a new theoretical framework for deriving lower bounds on data movement in bilinear algorithms. Bilinear algorithms are a general representation of fast algorithms for bilinear functions, which include computation of matrix…
The CP^3 spin model is simulated at large correlation lengths in two dimensions. An overrelaxation algorithm is employed which yields reduced critical slowing down with dynamical exponents z around unity. We compare our results with recent…
We calculate numerically the quasiparticle effective mass (m*) renormalization as a function of temperature and electron density in two- and three-dimensional electron systems with long-range Coulomb interaction. In two dimensions, the…
We analyze the conformational properties of polymer macromolecules in solutions in presence of extended structural obstacles of (fractal) dimension $\varepsilon_d$ causing the anisotropy of environment. Applying the pruned-enriched…
We study the asymptotics of recurrence coefficients for monic orthogonal polynomials p_n(z) with the quartic exponential weight exp [-N (1/2 z^2 + t/4 z^4)], where t is complex. Our goals are: A) to describe the regions of different…
The atomic-scale influence of disorder on the topological order can be quantified by a universal topological marker, although the practical calculation of the marker becomes numerically very costly in higher dimensions. We propose that for…
We present description of the DIS structure functions F_1 and F_2 at small $x$ obtained in double-logarithmic approximation (DLA). First we clarify our previous results on F_1 and then obtain explicit expressions for F_2. Our calculations…
In this paper, we study the algebraic formula complexity of multiplying $d$ many $2\times 2$ matrices, denoted $\mathrm{IMM}_{d}$, and show that the well-known divide-and-conquer algorithm cannot be significantly improved at any depth, as…
A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter $\eps^2$, is considered. It can have multiple solutions. An asymptotic expansion is constructed for…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for…
We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyse their range of validity by means of comprehensive Molecular…
Despite topological protection and the absence of magnetic impurities, two-dimensional topological insulators display quantized conductance only in surprisingly short channels, which can be as short as 100 nm for atomically thin materials.…