Strain localization in two-dimensional lattices

Two-dimensional localized strain wave solutions of the nonlinear equation for shear waves in two-dimensional lattices are studied. The corresponding equation does not possess an invariance in one of the spatial direction while its exact plane traveling wave solution does not reflect that. However, the numerical simulation of a two-dimensional localized wave reveals a non-symmetric evolution.DFG, 405631704, Anormaler Energietransfer in kristallinen Materialien vom Standpunkt der diskreten Mechanik und der Kontinuumstheori

Разработка легкого коммерческого электромобиля

The paper describes the process and results of the development of the light commercial electric vehicle. In order to ensure maximum energy efficiency of the developed vehicle the key parameters of the original electric motor. The article also presents the results of power electronic thermal calculation. For the mathematical model of the vehicle, the driving cycle parameters of the electric platform were determined in accordance with UNECE Regulations No 83, 84. The driving cycle was characterized by four successive urban and suburban cycles. The mathematical model also takes into account the time phases of the cycle, which include idling, vehicle idling, acceleration, constant speed movement, deceleration, etc. The model of the electric part of the vehicle was developed using MatLab-Simulink (SimPowerSystems library) in addition to the mechanical part of the electric car. The electric part included the asynchronous electric motor, the motor control system and the inverter. This model at the output allows to obtain such characteristics of the electric motor as currents, flows and voltages of the stator and rotor in a fixed and rotating coordinate systems, electromagnetic moment, angular speed of rotation of the motor shaft. The developed model allowed to calculate and evaluate the performance parameters of the electric vehicle. Technical solutions of the electric vehicle design were verified by conducting strength calculations. In conclusion, the results of field tests of a commercial electric vehicle are presented.В статье описаны процесс и результаты создания легкого коммерческого электромобиля. С целью обеспечения максимальной энергоэффективности разрабатываемого транспортного средства определены основные параметры оригинального электродвигателя. Представлены результаты теплового расчета силовой электроники. Для математической модели транспортного средства определены параметры ездового цикла электрической платформы в соответствии с Правилами № 83, 84 ЕЭК ООН. Цикл движения характеризовался четырьмя последовательными циклами городского и пригородного режимов движения. Математическая модель также учитывает временные фазы цикла, которые включают холостой ход транспортного средства, ускорение, движение с постоянной скоростью, замедление и т. д. Модель электрической части транспортного средства разработана с использованием MatLab-Simulink (библиотека SimPowerSystems) в дополнение к механической части электромобиля. Электрическая часть включала асинхронный электродвигатель, систему управления двигателем и инвертор. Данная модель на выходе позволяет получить такие характеристики электродвигателя, как токи, поведение магнитного поля, напряжения статора и ротора в неподвижной и вращающейся системах координат, электромагнитный момент, угловая скорость вращения вала двигателя. Разработанная модель позволила рассчитать и оценить параметры производительности электромобиля. Технические решения конструкции электромобиля были проверены на прочность путем расчетов. Представлены результаты полевых испытаний коммерческого электромобиля

Construction of Special Solutions for Nonintegrable Systems

The Painleve test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized Henon-Heiles system that the use of the Laurent series solutions of the initial differential equation assists to solve the obtained algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial differential equation in the form of the Laurent or Puiseux series we use the Painleve test. This test can also assist to solve the inverse problem: to find the form of a polynomial potential, which corresponds to the required type of solutions. We consider the five-dimensional gravitational model with a scalar field to demonstrate this.Comment: LaTeX, 14 pages, the paper has been published in the Journal of Nonlinear Mathematical Physics (http://www.sm.luth.se/math/JNMP/

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation

The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg-Landau equation (CGLE5) allows to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5. Using the investigation of the CGLE5 as an example, we demonstrate that to find elliptic solutions the analysis of a system of differential equations is more preferable than the analysis of the equivalent single differential equation.Comment: LaTeX, 21 page

A generic travelling wave solution in dissipative laser cavity

A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the notso-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussianwith variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics andlocalization in semiconductor laser cavity

On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations

We study the scattering of a long longitudinal radiating bulk strain solitary wave in the delaminated area of a two-layered elastic structure with soft (“imperfect”) bonding between the layers within the scope of the coupled Boussinesq equations. The direct numerical modelling of this and similar problems is challenging and has natural limitations. We develop a semi-analytical approach, based on the use of several matched asymptotic multiple-scale expansions and averaging with respect to the fast space variable, leading to the coupled Ostrovsky equations in bonded regions and uncoupled Korteweg-de Vries equations in the delaminated region. We show that the semi-analytical approach agrees well with direct numerical simulations and use it to study the nonlinear dynamics and scattering of the radiating solitary wave in a wide range of bi-layers with delamination. The results indicate that radiating solitary waves could help us to control the integrity of layered structures with imperfect interfaces. Long longitudinal bulk strain solitary waves observed in elastic waveguides, such as rods, bars, plates, and shells, can be modelled with Boussinesq-type equations. Radiating solitary waves, that is solitary waves radiating a co-propagating one-sided oscillatory tail, emerge in layered elastic waveguides with soft ("imperfect") bonding between the layers. In this paper, we study the scattering of a radiating solitary wave in delaminated areas of imperfectly bonded bi-layers within the scope of the coupled Boussinesq equations. We develop direct and semi-analytical numerical approaches and demonstrate that radiating solitary waves undergo changes which could be used to control the quality of the interfaces