Asymptotic approximations for swirling turbulent plume rising from circular sources

2021 ◽  
Vol 6 (9) ◽  
Author(s):  
Yuchen Dai ◽  
Alexander Klimenko ◽  
Yuanshen Lu ◽  
Kamel Hooman
Keyword(s):  
Asymptotic Approximations ◽  
Turbulent Plume

scholarly journals A Bayesian solution to the Behrens–Fisher problem

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
Fco. Javier Girón ◽  
Carmen del Castillo
Keyword(s):  
Closed Form ◽  
Hierarchical Model ◽  
Bayes Factor ◽  
Bayes Factors ◽  
Simple Solution ◽  
Asymptotic Approximations ◽  
Normal Distributions ◽  
Fisher Distribution ◽  
Leibler Divergence

AbstractA simple solution to the Behrens–Fisher problem based on Bayes factors is presented, and its relation with the Behrens–Fisher distribution is explored. The construction of the Bayes factor is based on a simple hierarchical model, and has a closed form based on the densities of general Behrens–Fisher distributions. Simple asymptotic approximations of the Bayes factor, which are functions of the Kullback–Leibler divergence between normal distributions, are given, and it is also proved to be consistent. Some examples and comparisons are also presented.

scholarly journals Asymptotic Approximations to the Nodes and Weights of Gauss-Hermite and Gauss-Laguerre Quadratures

2018 ◽  
Vol 140 (3) ◽  
pp. 298-332 ◽  
Author(s):  
Amparo Gil ◽  
Javier Segura ◽  
Nico M. Temme
Keyword(s):  
Asymptotic Approximations

Asymptotic Approximations.

1965 ◽  
Vol 72 (1) ◽  
pp. 94 ◽  
Author(s):  
J. H. Curtiss ◽  
Harold Jeffreys
Keyword(s):  
Asymptotic Approximations

Local Density Approximations for the Energy of a Periodic Coulomb Model

2003 ◽  
Vol 13 (08) ◽  
pp. 1185-1217 ◽  
Author(s):  
Olivier Bokanowski ◽  
Benoît Grebert ◽  
Norbert J. Mauser
Keyword(s):  
Kinetic Energy ◽  
Local Density ◽  
Exchange Energy ◽  
Asymptotic Approximations ◽  
Exchange Potential ◽  
Energy Term ◽  
Local Exchange ◽  
Coulomb Model ◽  
Local Density Approximations ◽  
Number Of Particles

We deal with local density approximations for the kinetic and exchange energy term, ℰ kin (ρ) and ℰ ex (ρ), of a periodic Coulomb model. We study asymptotic approximations of the energy when the number of particles goes to infinity and for densities close to the constant averaged density. For the kinetic energy, we recover the usual combination of the von-Weizsäcker term and the Thomas–Fermi term. Furthermore, we justify the inclusion of the Dirac term for the exchange energy and the Slater term for the local exchange potential.

Analytical Calculation of Deformations and Kinematic Analysis of a Flat Truss with an Arbitrary Number of Panels

2021 ◽  
pp. 113-122
Author(s):  
М. Н. Кирсанов ◽  
О. В. Воробьев
Keyword(s):  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Analytical Calculation ◽  
Middle Part ◽  
Asymptotic Approximations ◽  
Induction Method ◽  
Particular Solutions

Постановка задачи. Разыскиваются аналитические зависимости прогиба и смещения опоры плоской фермы решетчатого вида от числа панелей. Ферма имеет сдвоенную решетку, прямолинейный нижний и приподнятый в средней части верхний пояс. Результаты. Для двух видов нагружения по формуле Максвелла-Мора получены аналитические зависимости прогибов конструкции от нагрузки, размеров и числа панелей. Для обобщения серии частных решений с различным числом панелей ферм на произвольный случай использован метод индукции и аналитические возможности системы компьютерной математики Maple. Для некоторых решений получены асимптотические приближения. Показано распределение усилий в элементах фермы. Выводы. Полученные формулы могут быть использованы в задачах оптимизации и как тестовые для оценки приближенных численных решений. Выявлены случаи геометрической изменяемости фермы при числе панелей, кратном трем. Приведен алгоритм выявления соответствующего распределения возможных скоростей шарниров. Statement of the problem. Analytical dependences of the deflection and displacement of the support of a flat lattice truss on the number of panels are being sought. The truss has a double lattice, a rectilinear lower belt and an upper belt raised in the middle part. Results. For two types of loading, according to the Maxwell-Mohr formula, analytical dependences of the deflections of the structure on the load, dimensions and number of panels are obtained. To generalize a series of particular solutions for trusses with different numbers of panels for an arbitrary case, the induction method and the analytical capabilities of the Maple computer mathematics system were used. For some solutions, asymptotic approximations are obtained. The distribution of forces in the rods of the structure is shown. Conclusions. The obtained formulas can be used in optimization problems and as test ones for evaluating approximate numerical solutions. Cases of geometric variability of the truss with the number of panels being a multiple of three are revealed. An algorithm for identifying the corresponding distribution of possible velocities of the joints is presented.

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