Macroscopic description of particle systems with non-local density-dependent diffusivity

In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear between the density equations that are derived from different representations of the Langevin equation describing a system of interacting Brownian particles. Linear stability analysis demonstrates that under some circumstances the density equation interpreted like Ito has pattern solutions, which never appear for the Hanggi-Klimontovich interpretation, which is the other one typically appearing in the context of nonlinear diffusion processes. We also introduce a discrete-time microscopic model of particles that confirms the results obtained at the macroscopic density level.Comment: 4 pages, 3 figure

Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2

Fermi-surface collapse and dynamical scaling near a quantum critical point

Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh2Si2, a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the quantum-critical point from a smooth background contribution; the latter exists away from the quantum-critical point and is detectable through our studies only over a wide range of magnetic field. Importantly, the width of the critical crossover is proportional to temperature, which violates the predictions of conventional theory and is instead consistent with an energy over temperature, E/T, scaling of the quantum-critical single-electron fluctuation spectrum. Our results provide evidence that the quantum-dynamical scaling and a critical Kondo breakdown simultaneously operate in the same material. Correspondingly, we infer that macroscopic scale-invariant fluctuations emerge from the microscopic many-body excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finite-temperature behavior in a broad range of strongly correlated quantum systems.Comment: 5 pages, plus supporting materia

On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation

In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the hamiltonian system $u_{xx} + f(u) = 0$ and the asymptotic speed of propagation of fronts of the reaction diffusion equation. Based on this conjecture an explicit expression for the speed of the front is given. We give a counterexample to this conjecture and conclude that additional restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure

Development of condenser mathematical model for research and development of ways to improve its efficiency

The condensing unit is one of the most important elements of the steam turbine of a combined heat and power plant. Defects in elements of the condensing unit lead to disturbances in the steam turbine operation, its failures and breakdowns, as well as efficiency losses of the plant. Therefore, the operating personnel need to know the cause of the malfunction and to correct it immediately. There are no diagnostic models of condensers in the Republic of Kazakhstan at the moment. In this regard, a mathematical model of a condenser based on the methodology of Kaluga Turbine Plant (KTP) has been developed. The mathematical model makes it possible to change the input parameters, plot dependency diagrams, and calculate the plant efficiency indicators. The mathematical model of the condenser can be used to research ways for the improvement of the condensing unit efficiency, for diagnostic purposes of the equipment condition, for the energy audit conduction of the plant, and in the training when performing virtual laboratory research. Using static data processing by linear regression method we obtain that the KTP methodology of condenser calculation is fair at cooling water temperature from 20 °C to 24 °C, but at cooling water temperature from 20 °C to 28 °C, the methodology of JSC "All-Russia Thermal Engineering Institute" (JSC "VTI") is used. One of the ways to increase the condenser efficiency has been proposed. It is the heat transfer augmentation with riffling annular grooves on tubes. This method increases the heat transfer coefficient by 2%, reduces the water subcooling of the heating steam by 0.9 °C, and decreases the cooling area by 2%. © 2020 Institut za Istrazivanja. All rights reserved

Perturbative Linearization of Reaction-Diffusion Equations

We develop perturbative expansions to obtain solutions for the initial-value problems of two important reaction-diffusion systems, viz., the Fisher equation and the time-dependent Ginzburg-Landau (TDGL) equation. The starting point of our expansion is the corresponding singular-perturbation solution. This approach transforms the solution of nonlinear reaction-diffusion equations into the solution of a hierarchy of linear equations. Our numerical results demonstrate that this hierarchy rapidly converges to the exact solution.Comment: 13 pages, 4 figures, latex2