scholarly journals Using the inverse distribution function method and the modified superposition method in the NMPUD computer system

2021 ◽  
Vol 2099 (1) ◽  
pp. 012071
Author(s):  
D A Cherkashin ◽  
A V Voytishek
Keyword(s):  
Computer System ◽  
Numerical Experiments ◽  
Function Method ◽  
Piecewise Linear ◽  
Computational Modelling ◽  
Random Variables ◽  
Piecewise Linear Approximation ◽  
Weighted Sums ◽  
Superposition Method ◽  
One Dimensional

Abstract This paper presents a computer system for modelling one-dimensional random variables NMPUD, developed in the laboratory of mathematical modelling of Lyceum No. 130 in Novosibirsk. The results of the numerical experiments and the considerations justifying the practicability for using in the NMPUD system: the elementary densities constructed by the technology of sequential (inserted) substitutions, the densities representing weighted sums of elementary densities (which can be simulated using the modified discrete superposition method), the algorithms for a piecewise linear approximation of unknown densities using a given sample, the algorithms of the modified superposition method for computational modelling of random variables with piecewise linear densities, are also presented.

scholarly journals Nonstationary 1D Dynamics Problems for Heteromodular Elasticity with Piecewise-Linear Approximation of Boundary Conditions

2019 ◽  
pp. 37-47
Author(s):  
O V Dudko ◽  
A A Lapteva ◽  
V E Ragozina
Keyword(s):  
Shock Wave ◽  
Boundary Condition ◽  
Elastic Medium ◽  
Half Space ◽  
Linear Approximation ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Time Interval ◽  
One Dimensional ◽  
Small Strains

The paper provides the investigation of a heteromodular elastic medium under dynamic loading. The heteromodularity (when the stress - strain relation depends on the deformation direction) is a distinctive feature of many natural and structural materials: rocks, porous and cohesive bulk media, fibrous and granular composites, some metal alloys, etc. The fact that the listed materials show the heteromodular property at the stage of elastic deformation should be especially taken into account when solving problems of their shock dynamics. To describe the heteromodular behavior of an elastic medium in terms of small strains we use the physically nonlinear model of V.P. Myasnikov. The accepted assumption about the one-dimensional straining reduces the nonlinear relationship of stresses and small strains to piecewise linear equations. In the case of dynamic shock deformation, the initial nonlinearity of the model is concentrated in the equations which define the velocity of the shock wave abruptly transforming the heteromodular medium from a stretched to a compressed state. In this paper we investigate the processes of generation, motion, and possible interactions of plane one-dimensional deformation waves (including shock ones) in a heteromodular elastic half-space. The points of the half-space boundary undergo one-dimensional motions according to a given non-linear law corresponding to the “stretching-compression” mode. We suggest replacing the nonstationary boundary condition of the problem by its piecewise linear approximation and constructing a connected sequence of analytical solutions with a linear boundary condition at each local time interval. The proposed approach is the basis of the numerical solving algorithm for a boundary value problem with a given nonlinear condition. It is shown that the general solution behind the shock wave consists of several local layers, which number is related to the quantity of nodes in the piecewise linear decomposition of the boundary condition. In these layers, the compression deformation is defined by the relevant part of the boundary condition and simultaneously “stores” information on the preliminary tension, which should be considered an important feature of the heteromodular medium dynamics.

scholarly journals An Upwind-Biased Conservative Advection Scheme for Spherical Hexagonal–Pentagonal Grids

2007 ◽  
Vol 135 (12) ◽  
pp. 4038-4044 ◽  
Author(s):  
Hiroaki Miura
Keyword(s):  
Linear Approximation ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
Flux Divergence ◽  
Discrete Form ◽  
One Dimensional ◽  
Advection Scheme ◽  
Regular Grids ◽  
Divergence Operator ◽  
A Cell

Abstract A discrete form of the flux-divergence operator is developed to compute advection of tracers on spherical hexagonal–pentagonal grids. An upwind-biased advection scheme based on a piecewise linear approximation for one-dimensional regular grids is extended simply for spherical hexagonal–pentagonal grids. The distribution of a tracer over the upwind side of a cell face is linearly approximated using a nodal value and a gradient at a computational node on the upwind side. A piecewise linear approximation is relaxed to a local linear approximation, and the relaxation precludes the complicated conditional branching present in remapping schemes. Results from a cosine bell advection test show that the new scheme compares favorably with other upwind-biased schemes for spherical hexagonal–pentagonal grids.

scholarly journals BORDER-COLLISION BIFURCATIONS IN ONE-DIMENSIONAL DISCONTINUOUS MAPS

2003 ◽  
Vol 13 (11) ◽  
pp. 3341-3351 ◽  
Author(s):  
PARAG JAIN ◽  
SOUMITRO BANERJEE
Keyword(s):  
Linear Approximation ◽  
Piecewise Linear ◽  
Piecewise Linear Approximation ◽  
One Dimensional ◽  
Border Collision Bifurcations ◽  
Bifurcation Phenomena ◽  
Existence And Stability ◽  
Parameter Values ◽  
Discrete Domain

We present a classification of border-collision bifurcations in one-dimensional discontinuous maps depending on the parameters of the piecewise linear approximation in the neighborhood of the point of discontinuity. For each range of parameter values we derive the condition of existence and stability of various periodic orbits and of chaos. This knowledge will help in understanding the bifurcation phenomena in a large number of practical systems which can be modeled by discontinuous maps in discrete domain.

Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion

2013 ◽  
Vol 723 ◽  
pp. 190-231 ◽  
Author(s):  
Ignacio Duran ◽  
Stephane Moreau
Keyword(s):  
Euler Equations ◽  
Transfer Functions ◽  
Piecewise Linear ◽  
Strong Dependence ◽  
Piecewise Linear Approximation ◽  
Nozzle Geometry ◽  
Magnus Expansion ◽  
One Dimensional ◽  
Linearized Euler Equations ◽  
Varying Coefficients

AbstractThe acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (J. Sound Vib., vol. 55, 1977, pp. 225–243) and the effective nozzle length proposed by Stow, Dowling & Hynes (J. Fluid Mech., vol. 467, 2002, pp. 215–239) and by Goh & Morgans (J. Sound Vib., vol. 330, 2011, pp. 5184–5198) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewise-linear approximation of the velocity profile in the nozzle proposed by Moase, Brear & Manzie (J. Fluid Mech., vol. 585, 2007, pp. 281–304) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first-order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging–diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers, showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.

scholarly journals On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Xiaochen Ma ◽  
Qunying Wu
Keyword(s):  
Probability Space ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Sublinear Expectation ◽  
Negatively Dependent Random Variables ◽  
Large Numbers ◽  
End Random Variables

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

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