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Первый авторSerdyukova
Страниц6
ID404437
АннотацияA detailed investigation of the IVC breakpoint and the breakpoint region width gives important information concerning the peculiarities of stacks with a finite number of intrinsic Josephson junctions. The current-voltage characteristics for a stack of n Josephson junctions is defined from solving the system of n nonlinear differential equations. The current voltage characteristic has the shape of a hysteresis loop. On the back branch of the Hysteresis loop, near the breakpoint Ib, voltage V (I) decreases to zero rapidly. The goal of this work is to accelerate the computation of IVC based on numerical solution of the system. A numericalanalytical method was proposed in. This method showed perfect results in IVC calculations for a stack of 9 and 19 intrinsic Josephson junctions and the computation time reduced by five times approximately. The question of choosing a change-over point from “analytical” to numerical calculation was open. In testing computations the change-over point was taken equal to 2Ib. In the case of periodic boundary conditions an equation, determining the approximate location of Ib, was obtained. This moment we succeeded to develop an algorithm determining the approximate value Ib in more complicated technically case of non-periodic boundary conditions with γ = 1. All calculations were performed using the REDUCE 3.8 system.
УДК519.6
Serdyukova, S.I. Solving the Hysteresis Loop Calculation Problem for Josephson Junction Stacks / S.I. Serdyukova // Вестник Российского университета дружбы народов. Серия: Математика, информатика, физика .— 2014 .— №2 .— С. 297-302 .— URL: https://rucont.ru/efd/404437 (дата обращения: 25.09.2021)

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UDC 519.6 Solving the Hysteresis Loop Calculation Problem for Josephson Junction Stacks S. I. Serdyukova Laboratory of Information Technologies Joint Institute for Nuclear Research 6, Joliot-Curie str., Dubna, Moscow region, Russia, 141980 A detailed investigation of the IVC breakpoint and the breakpoint region width gives important information concerning the peculiarities of stacks with a finite number of intrinsic Josephson junctions. <...> The current-voltage characteristics for a stack of n Josephson junctions is defined from solving the system of n nonlinear differential equations. <...> The current voltage characteristic has the shape of a hysteresis loop. <...> On the back branch of the Hysteresis loop, near the breakpoint Ib, voltage V (I) decreases to zero rapidly. <...> This method showed perfect results in IVC calculations for a stack of 9 and 19 intrinsic Josephson junctions and the computation time reduced by five times approximately. <...> The question of choosing a change-over point from “analytical” to numerical calculation was open. <...> In testing computations the change-over point was taken equal to 2Ib. <...> In the case of periodic boundary conditions an equation, determining the approximate location of Ib, was obtained. <...> This moment we succeeded to develop an algorithm determining the approximate value Ib in more complicated technically case of non-periodic boundary conditions with γ = 1. <...> Key words and phrases: stack of Josephson junctions, computation of current-voltage characteristics, hysteresis loop, Cauchy problem for a system of nonlinear differential equations, fourth-order Runge-Kutta method, long-time asymptotic formulas, a numerical-analytical method, computation of formulas using the REDUCE 3.8 system. 1. <...> For each next I : I = Ik+1, found already ϕl(Ik,Tmax), ˙ϕl(Ik,Tmax) are used as initial data. <...> The dynamics of phase differences ϕl(t) had been simulated by solving the equation system (2) using the fourth order Runge-Kutta method [2]. <...> After simulation of the phase differences dynamics the voltages on each junction were calculated as ∂ϕl/∂t = The average of the voltage ¯ Vl is given by ¯ Vl = ∑ l′=1 n Al,l′ Vl′ . 1 TmaxTmin ∑ l=1 n TmaxTmin Finally the total voltage V of the stack is obtained by summing these averages: V = Vl. <...> The fundamental matrices D (whose <...>