Attenuation of flexural phonons in free-standing crystalline two-dimensional materials

We develop the theory for dynamics of the out-of-plane deformations in flexible two-dimensional materials. We focus on study of attenuation of flexural phonons in free-standing crystalline membranes. We demonstrate that the dynamical renormalization does not involve the ultraviolet divergent logarithmic contributions contrary to the static ones. This fact allows us to find the scaling form of the attenuation, determine its small and large frequency asymptotes, and to derive the exact expression for the dynamical exponent of flexural phonons in the long wave limit: $\textsf{z}{=}2{-}\eta/2$. Here $\eta$ is the universal exponent controlling the static renormalization of the bending rigidity. Also we determine the dynamical exponent for the long-wave in-plane phonons: $\textsf{z}^\prime{=}(2{-}\eta)/(1{-}\eta/2)$. We discuss implication of our results to experiments on phonon spectra in graphene and dynamics of graphene-based nanomechanical resonators.Comment: 20 pages, 10 figures; see related arXiv

Screening in Space: Rich and Poor Consumers in a Linear City

Unlike standard models of monopolistic screening (second-degree price discrimination), we consider a situation where consumers are heterogeneous not only vertically, in their willingness to pay, but also horizontally, in their tastes or "addresses'' a la Hotelling's Linear City. For such a screening game, a novel model is composed. We formulate the game as an optimization program, prove the existence of equilibria, develop a method to calculate equilibria, and characterize their properties. Namely, the solution structure of the resulting menu of contracts can be either a "chain of envy'' like in usual screening or a number of disconnected chains. Unlike usual screening, "almost all'' consumers get positive informational rent. Importantly, the model can be extended to oligopoly screening.The authors are grateful to Pavel Ilinov, Igor Bykadorov, Mikhail Martyanov,Pavel Molchanov for discussions and help in checking the proofs. The study was financed by the HSE University Basic Research. Program

Why are losses from trade unlikely?

© 2015. Examining a standard monopolistic competition model with unspecified utility/cost functions, we find necessary and sufficient conditions on their elasticities for welfare losses to arise from trade or market expansion. Two numerical examples explain the losses (under unrealistic elasticities)

Painful Birth of Trade Under Classical Monopolistic Competition

In the standard Krugman (1979) non-CES trade model, several asymmetric countries typically lose from increasing trade costs. However, all countries transiently benefit from such increase at the moment of closing trade, under almost-prohibitive trade costs (i.e., near autarky, which is possible only under non-CES preferences). In other words, during trade liberalization the first step from autarky to trade is necessarily harmful. Our explanation rests on market distortion and business destruction effects

Narrowing of the flexural phonon spectral line in stressed crystalline two-dimensional materials

We develop the microscopic theory for the attenuation of out-of-plane phonons in stressed flexible two-dimensional crystalline materials. We demonstrate that the presence of nonzero tension strongly reduces the relative magnitude of the attenuation and, consequently, results in parametrical narrowing of the phononspectral line. We predict the specific power-law dependence of the spectral-line width on temperature and tension. We speculate that suppression of the phonon attenuation by nonzero tension might be responsible for high quality factors of mechanical nanoresonators based on flexural two-dimensional materials.Comment: 6+4 pages, 5 figures; see related arXiv

Submicrosecond atmospheric electric discharge from the non-uniform electrode (tip) towards the plane electrode / Субмикросекундный разряд атмосферного давления с неоднородного электрода (острия) в направлении плоского электрода / Pražnjenje u nanosekundama pri atmosferskom pritisku od neuniformne elektrode (vrh) prema ravnoj elektrodi

This paper deals with the results of a numerical simulation of the fast atmospheric pressure discharge in a strongly non-uniform configuration of a tip-to-plane diode filled with a nitrogen and oxygen mixture. The simulation is based on the advanced hydrodynamic plasma discharge accounting also gas photoionization. It was shown that, in the absence of photoionization, discharge develops similarly to the case with photoionization, except the case of reversed voltage polarity. The theoretical results correspond to the existing experimental data for the spatial discharge structure and the current/voltage discharge characteristics. / В данной работе рассматриваются результаты численного моделирования быстрого разряда при атмосферном давлении в сильно неоднородной конфигурации диода «острие-плоскость», заполненного смесью азота и кислорода. Моделирование основано на современной гидродинамической модели разрядной плазмы, учитывающей также фотоионизацию газа. Было показано, что при отсутствии фотоионизации разряд развивается аналогично случаю с фотоионизацией (за исключением случая обратной полярности приложенного напряжения). Теоретические результаты соответствуют существующим экспериментальным данным для структуры пространственного разряда и для временных характеристик тока / напряжения разряда. / U radu se razmatraju rezultati numeričke simulacije brzog pražnjenja pri atmosferskom pritisku u visoko nehomogenoj konfiguraciji diode tipa vrh‒ravan napunjene smešom azota i kiseonika. Simulacija se zasniva na savremenom hidrodinamičkom modelu pražnjenja plazme, koji takođe uzima u obzir fotojonizaciju gasa. Pokazano je da se, u odsustvu fotojonizujućeg pražnjenja, on razvija slično kao i kod fotojonizacije, sa izuzetkom napona inverzne polarizacije. Teorijski rezultati su konzistentni sa postojećim eksperimentalnim podacima za prostornu strukturu pražnjenja i za karakteristike pražnjenja napona/struje

Influence of runaway electrons on the formation time of nanosecond discharge

In this paper, we present the theoretical results of a self-consistent kinetic simulation, clarifying the influence of runaway electron flows on a delay time of the switching stage of a nanosecond discharge. The simulation is based on an accurate numerical solution of the Boltzmann kinetic equation, with model collision integrals that take into account elastic and ionization collisions of the electrons with neutral atoms. As an example, the breakdown of a cylindrical gap is investigated with respect to the variations of the voltage rise time value. The current and voltage time profiles, power spectrum, and current of high-energy electrons, as well as the electron distribution function, are calculated accordingly. Our numerical solution agrees with the existent experimental data