On managing interference in a one-dimensional space over time-invariant channels

2017 ◽  
Author(s):  
Mohaned Chraiti ◽  
Ali Ghrayeb ◽  
Chadi Assi
Keyword(s):  
Dimensional Space ◽  
One Dimensional ◽  
Time Invariant ◽  
Over Time

scholarly journals Adiabatic Compression of Ideal Collisionless Gas in One-Dimensional Space

2020 ◽  
pp. 6-12
Author(s):  
Д. А. Быковских ◽  
В. А. Галкин
Keyword(s):  
Analytical Solution ◽  
Exact Solutions ◽  
Particle Velocity ◽  
Software Verification ◽  
Distribution Density ◽  
Dimensional Space ◽  
Adiabatic Compression ◽  
One Dimensional ◽  
Over Time

В статье рассматривается задача об адиабатическом сжатии бесстолкновительного газа с подвижной и неподвижной границами в одномерном пространстве. Для этой задачи получен класс точных решений. Идея нахождения класса точных решений заключается в определении плотности распределения молекул в пространстве координат и скоростей с течением времени. Поскольку пространство скоростей дискретное, то для вычисления макроскопических величин необходимо суммировать плотность распределения частиц по скоростям. Представлены результаты сравнения численного исследования методом Монте-Карло и аналитического решения задачи при различном числе частиц и скоростях движения стенки. Выполнена оценка погрешностей результатов. Полученный класс аналитического решения можно использовать для верификации комплексов программ. The study focuses on adiabatic compression of collisionless gas with moving and fixedboundaries in onedimensionalspace. A class of exact solutions is found. The key concept for findingthese exact solutions is the determination of the molecule distribution density in the coordinate and velocityspaces over time. Since the velocity space is discrete, the particle velocity distribution density is integratedover the velocities to obtain the macroscopic gas properties. The analytical solution and numerical MonteCarlo solution results are compared for different particle numbers and boundary velocities, and the errorsare performed. The class of exact solutions can be used for software verification.

Parametric surfaces

1949 ◽  
Vol 45 (1) ◽  
pp. 14-23 ◽  
Author(s):  
A. S. Besicovitch
Keyword(s):  
Dimensional Space ◽  
Parametric Surfaces ◽  
Rectifiable Curve ◽  
One Dimensional ◽  
Dimensional Measure

In 1914 Carathéodory defined m–dimensional measure in n–dimensional space. He considered one-dimensional measure as a generalization of length and he proved that the length of a rectifiable curve coincides with its one-dimensional measure.

scholarly journals Atmospheric Escape and the Evolution of Close-In Exoplanets

2019 ◽  
Vol 47 (1) ◽  
pp. 67-90 ◽  
Author(s):  
James E. Owen
Keyword(s):  
Radiative Transfer ◽  
Lower Mass ◽  
Hydrodynamic Simulations ◽  
One Dimensional ◽  
Hot Jupiters ◽  
Atmospheric Escape ◽  
Hydrodynamic Calculations ◽  
Ionization Chemistry ◽  
Exoplanet Systems ◽  
Over Time

Exoplanets with substantial hydrogen/helium atmospheres have been discovered in abundance, many residing extremely close to their parent stars. The extreme irradiation levels that these atmospheres experience cause them to undergo hydrodynamic atmospheric escape. Ongoing atmospheric escape has been observed to be occurring in a few nearby exoplanet systems through transit spectroscopy both for hot Jupiters and for lower-mass super-Earths and mini-Neptunes. Detailed hydrodynamic calculations that incorporate radiative transfer and ionization chemistry are now common in one-dimensional models, and multidimensional calculations that incorporate magnetic fields and interactions with the interstellar environment are cutting edge. However, comparison between simulations and observations remains very limited. While hot Jupiters experience atmospheric escape, the mass-loss rates are not high enough to affect their evolution. However, for lower-mass planets, atmospheric escape drives and controls their evolution, sculpting the exoplanet population that we observe today. ▪ Observations of some exoplanets have detected atmospheric escape driven by hydrodynamic outflows, causing the exoplanets to lose mass over time. ▪ Hydrodynamic simulations of atmospheric escape are approaching the sophistication required to compare them directly to observations. ▪ Atmospheric escape sculpts sharp features into the exoplanet population that we can observe today; these features have recently been detected.

scholarly journals A new method for solving a class of heat conduction equations

2015 ◽  
Vol 19 (4) ◽  
pp. 1205-1210
Author(s):  
Yi Tian ◽  
Zai-Zai Yan ◽  
Zhi-Min Hong
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Dimensional Space ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Governing Equations ◽  
One Dimensional ◽  
Sparse System ◽  
Linear Algebraic Equations ◽  
Crank Nicolson

A numerical method for solving a class of heat conduction equations with variable coefficients in one dimensional space is demonstrated. This method combines the Crank-Nicolson and Monte Carlo methods. Using Crank-Nicolson method, the governing equations are discretized into a large sparse system of linear algebraic equations, which are solved by Monte Carlo method. To illustrate the usefulness of this technique, we apply it to two problems. Numerical results show the performance of the present work.

Periodic Models of Seasonality

2013 ◽  
Author(s):  
Lars Peter Hansen ◽  
Thomas J. Sargent
Keyword(s):  
Spectral Density ◽  
Competitive Equilibrium ◽  
Information Flows ◽  
Periodic Functions ◽  
Third Way ◽  
Monthly Data ◽  
The Third ◽  
Periodic Models ◽  
Time Invariant ◽  
Over Time

Until now, each of the matrices defining preferences, technologies, and information flows has been specified to be constant over time. This chapter relaxes this assumption and lets the matrices be strictly periodic functions of time. The aim is to apply and extend an idea of Denise Osborn (1988) and Richard Todd (1983, 1990) to arrive at a model of seasonality as a hidden periodicity. Seasonality can be characterized in terms of a spectral density. A variable is said to “have a seasonal” if its spectral density displays peaks at or in the vicinity of the frequencies commonly associated with the seasons of the year, for example, every 12 months for monthly data, every four quarters for quarterly data. Within a competitive equilibrium, it is possible to think of three ways of modeling seasonality. The first two ways can be represented within the time-invariant setup of our previous chapters, while the third way departs from the assumption that the matrices that define our economies are time invariant. The chapter focuses on a third model of seasonality following Todd. It specifies an economy in terms of matrices whose elements are periodic functions of time.

scholarly journals Discontinuity Capture in One-Dimensional Space Using the Numerical Manifold Method with High-Order Legendre Polynomials

2020 ◽  
Vol 10 (24) ◽  
pp. 9123
Author(s):  
Yan Zeng ◽  
Hong Zheng ◽  
Chunguang Li
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Volume Method ◽  
Difference Method ◽  
Legendre Polynomials ◽  
Dimensional Space ◽  
Numerical Manifold Method ◽  
One Dimensional ◽  
Numerical Manifold ◽  
Volume Method

Traditional methods such as the finite difference method, the finite element method, and the finite volume method are all based on continuous interpolation. In general, if discontinuity occurred, the calculation result would show low accuracy and poor stability. In this paper, the numerical manifold method is used to capture numerical discontinuities, in a one-dimensional space. It is verified that the high-degree Legendre polynomials can be selected as the local approximation without leading to linear dependency, a notorious “nail” issue in Numerical Manifold Method. A series of numerical tests are carried out to evaluate the performance of the proposed method, suggesting that the accuracy by the numerical manifold method is higher than that by the later finite difference method and finite volume method using the same number of unknowns.

Institutions, culture and migrants’ preference for state-provided welfare. Longitudinal evidence from Germany

2017 ◽  
Vol 27 (2) ◽  
pp. 197-212 ◽  
Author(s):  
Alexander W. Schmidt-Catran ◽  
Romana Careja
Keyword(s):  
Welfare Regime ◽  
Host Countries ◽  
Difference In Differences ◽  
The Difference ◽  
Time Invariant ◽  
Over Time

Using the difference-in-differences estimator and data provided by the German Socio-Economic Panel, this article explores migrants’ preferences for state-provided welfare. The study finds evidence that over time, the preferences of immigrants and natives become more similar. We interpret this finding as evidence that the culture of home countries does not have a time-invariant effect, and that immigrants’ welfare preferences are subject to a socializing effect of the host countries’ welfare regime.

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