The classical solution of one problem of an absolutely inelastic impact on a long elastic semi-infinite bar

In this article, we study the classical solution of the mixed problem in a quarter of a plane for a one-dimensional wave equation. On the bottom boundary, the Cauchy conditions are specified, meanwhile, the second of them has a discontinuity of the first kind at one point. The smooth boundary condition, which has the first and the second order derivatives, is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. The uniqueness is proved and the conditions are established under which a piecewise-smooth solution exists. The problem with matcing conditions is considered.

Dynamics of Characteristic and One-Point Correlation Functions of Multi-Mode Bosonic Systems: Exactly Solvable Model

In this communication we study dynamics of the open quantum bosonic system governed by the generalized Lindblad equation with both dynamical and environment induced intermode couplings taken into account. By using the method of characteristics we deduce the analytical expression for the normally ordered characteristic function. Analytical results for one-point correlation functions describing temporal evolution of the covariance matrix are obtained.

Method of characteristics for the problems of stages of the serviceability check of elementary section of a gas pipeline for operation

The article is devoted to modeling the gas-dynamic state of an elementary section of a gas pipeline during gas injection and its outflow through the choke in the final section of the pipe and to solving these problems using the method of characteristics. The subject of the study is the gas-dynamic state of an elementary horizontal section of a gas pipeline in the process of checking its serviceability for operation. The processes of gas injection into the section and gas outflow from it, considered in the article, were modeled using the N.E. Zhukovsky formula on gas outflow into unbounded space in a framework of the short pipeline approach. The original equations are linearized by introducing the mass flow rate of gas and waves traveling in two directions. When solving the problem, the method of characteristics was applied; numerical results were obtained and analyzed using an analytical solution to the problem. The research methods are based on the laws of conservation of momentum and gas mass, the d’Alembert method for solving a system of hyperbolic equations and the methods of conducting a computational experiment. An analytical solution to the problem with a rupture caused by an instantaneous change in the gas pressure at the end of the section is obtained. It is shown that the process proceeds with the formation of compression and rarefaction waves, and their multiple reflections at the ends of the section. The gas in the section tends to a state of rest with time, and the changes in the mass flow rate and gas pressure are of exponential nature.

Evaluation of service pressure regulation strategy on the performance of a rural water network based on pulse demand; using the method of characteristics

Reducing the occurrence of pipe bursts, reducing leakage, and reducing energy consumption are the three main goals in implementing pressure control programs in water distribution networks. Service Pressure Regulation Strategy is an evolved approach that encompasses all goals of pressure management. This paper has investigated this approach in a rural network with hydraulic complexities as a case study so that some parts of the network have excess pressure and other low pressure. A computer code based on the Method of Characteristics (MOC) has been developed for network hydraulic analysis. The generated code analyzes unsteady flow, pressure-driven demand analysis, and dynamic adjustment of pressure control valves based on the target node. Also, the experimental results of a laboratory network have been applied to validate and calibrate the numerical simulation. In addition, by measuring the flow rate and pressure of the network and the results of the MNF method, three consumption patterns were used to generate pulsed nodal demands. Studies show that creating Pressure-Management Areas by hydraulic analysis by MOC will determine the best control strategies. The mean pressure has decreased 54% by applying this strategy. Furthermore, the average fluctuations of pressure have reduced from 9.7 meters to 3.5 meters.

Optimal control of a hyperbolic system that describes Slutsky demand

A non-linear optimal control problem for a hyperbolic system of first order equations on a line in the case of degeneracy of the initial condition line is considered. This problem describes many natural, economic and social processes, in particular, the optimality of the Slutsky demand, the theory of bio-population, etc. The research is based on the method of characteristics and the use of nonstandard variations of the increment of target functional, which leads to the construction of efficient computational algorithms.

Accretion and ablation in deformable solids with an Eulerian description: examples using the method of characteristics

Accretion and ablation, i.e., the addition and removal of mass at the surface, are important in a wide range of physical processes, including solidification, growth of biological tissues, environmental processes, and additive manufacturing. The description of accretion requires the addition of new continuum particles to the body, and is therefore challenging for standard continuum formulations for solids that require a reference configuration. Recent work has proposed an Eulerian approach to this problem, enabling side-stepping of the issue of constructing the reference configuration. However, this raises the complementary challenge of determining the stress response of the solid, which typically requires the deformation gradient that is not immediately available in the Eulerian formulation. To resolve this, the approach introduced the elastic deformation as an additional kinematic descriptor of the added material, and its evolution has been shown to be governed by a transport equation. In this work, the method of characteristics is applied to solve concrete simplified problems motivated by biomechanics and manufacturing. Specifically, (1) for a problem with both ablation and accretion in a fixed domain and (2) for a problem with a time-varying domain, the closed-form solution is obtained in the Eulerian framework using the method of characteristics without explicit construction of the reference configuration.

Calculation of the elasticplastic deformation of a solid body by multidimensional nodal method of characteristics

Описан многомерный узловой метод характеристик, предназначенный для численного расчета упругопластической деформации твердого тела в рамках модели Прандтля-Рейса с уравнением состояния небаротропного типа. В качестве критерия перехода из упругого в пластическое состояние применялось условие текучести Мизеса. Рассмотренный численный метод базируется на координатном расщеплении исходной системы уравнений на ряд одномерных подсистем с последующим их интегрированием с помощью одномерного узлового метода характеристик. Метод использован для расчета ряда одно- и двумерных модельных задач A multidimensional nodal method of characteristics is described. The method is designed to numerically calculate the elastoplastic deformation of a solid body within the Prandtl-Reis model with the non-barotropic state equation. The Mises flow condition was used as a criterion for the transition from an elastic to a plastic state. The considered numerical method is based on the coordinate splitting of the original system of equations into a number of one-dimensional subsystems. Then the resulting equations were integrated using a one-dimensional nodal method of characteristics. The proposed method allows calculating a number of one- and two-dimensional model problems. The results of calculations that employ the multidimensional node method of characteristics were compared with data calculated using the Godunov hybrid method in the framework of a model that did not take into account the contribution of potential elastic compression energy to the total energy of the medium. There are some discrepancies in the calculation results that occur at high speeds of interaction of the aluminum striker with the barrier, exceeding 500 m/s, which are associated with omission of the potential energy due to the elastic compression of the solid within the original Prandtl-Reis model