A simplified two-dimensional acoustic diffusion model for predicting sound levels in enclosures

A new concept for the enclosure-acoustic prediction derived from the mathematical theory of diffusion was proposed some years ago [J. Picaut et al., Acustica 1997]. This model has been applied to predict the sound level distribution in rooms of simple geometries with good accuracy and a relatively low calculation time. However, in situations related with (optimal) acoustic design, the need to evaluate multiple simulations may increase the computational cost. The aim of this work is to provide an approximately equivalent two-dimensional diffusion model achieving similar results with a significant reduction of the execution time. The proposed simplified model is obtained by means of the Kantorovich method. Comparisons of numerical simulations performed with the full diffusion model and the software CATT-Acoustic® are presented to show the efficiency of the simplified diffusion model.     

计算二维声腔传递矩阵的正方形线声源模型

在比较现有二维矩形声腔的声源计算模型特点的基础上,提出了一种新的正方形线声源计算模型,用于计算基于模态级数叠加法的压力响应函数.分析表明,此模型不仅可以克服点声源模型的奇异性,而且在合理选择模型的几何尺寸的前提下能得到比面源模型更为均匀的压力分布,提高了传递函数计算的准确率.数值试验考察了此模型的实际应用效果,表明新的线声源数学模型较圆形线声源更为简便,可以提高计算效率. 关键词： 传递矩阵 正方形线声源模型 二维声腔 模态级数叠加法     

A new simplified ordered upwind method for calculating quasi-potential

We present a new method for calculation of quasi-potential,which is a key concept in the large deviation theory.This method adopts the"ordered"idea in the ordered upwind algorithm and different from the finite difference upwind scheme,the first-order line integral is used as its update rule.With sufficient accuracy,the new simplified method can greatly speed up the computational time.Once the quasi-potential has been computed,the minimum action path(MAP)can also be obtained.Since the MAP is of concern in most stochastic situations,the effectiveness of this new method is checked by analyzing the accuracy of the MAP.Two cases of isotropic diffusion and anisotropic diffusion are considered.It is found that this new method can both effectively compute the MAPs for systems with isotropic diffusion and reduce the computational time.Meanwhile anisotropy will affect the accuracy of the computed MAP.     

A two-dimensional model for mesons

A recently proposed gauge theory for strong interactions, in which the set of planar diagrams play a dominant role, is considered in one space and one time dimension. In this case, the planar diagrams can be reduced to self-energy and ladder diagrams, and they can be summed. The gauge field interactions resemble those of the quantized dual string, and the physical mass spectrum consists of a nearly straight “Regge trajectory”.     

A second-order accurate numerical method for the two-dimensional fractional diffusion equation

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank–Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method.     

A diffusion model for the Dirac equation

In previous work the author was able to derive the Schrödinger equation by an analytical approach built around a physical model that featured a special diffusion process in an ensemble of particles. In the present work, this approach is extended to include the derivation of the Dirac equation. To do this, the physical model has to be modified to make provision for intrinsic electric and magnetic dipoles to be associated with each ensemble particle.     

A simplified post-soft-breakdown current model for MOS devices

Based on the tunneling current model, a simplified current model is developed for MOS devices after soft breakdown (SBD). The post-soft-breakdown current consists of modified direct tunneling current and Fowler Nordheim (FN) tunneling current. Considering the change of gate oxide after soft breakdown, impacts of soft breakdown on the dielectric constant, and effective electron mass of the gate oxide are discussed, and their values are obtained by fitting simulation results to experimental data. It is found that the effective electron mass is decreased after soft breakdown due to damaged oxide, while the dielectric constant is increased after soft breakdown due to interface distortion. In this way, the leakage current after soft breakdown can be accurately calculated. The validity of the proposed model is confirmed by experimental results. Z.L. Li currently is with the Department of Electrical and Electronic Engineering, University of Hong Kong.     

A two-dimensional model of the distribution of trace gases in the stratosphere and troposphere

Summary We report the results of computations of the distribution of trace gases in the troposphere and stratosphere with a two-dimensional photochemical transport model. The region covered by the model extends from pole to pole and from 0 to 50 km. Atmospheric transport is included by using seasonal averaged values for mean meridional and vertical winds and eddy diffusion. The compounds transported in the model are N₂O, NO _x (NO+NO₂), NO _y (NO_x+HNO₃), N₂O₅, H₂O, CH₄ and H₂O₂. Odd hydrogen (OH+HO₂+H) is assumed in photoequilibrium. A simple scheme is proposed to simulate the condensation of H₂O and scavenging of other gases. Rayleigh scattering is included in the calculation of the photodissociation rates. The resulting distributions are compared whenever possible with experimental data. We attempt to discuss the stratospheric budget of water vapour taking into account photochemical sources (e.g. CH₄ oxidation) and sinks. It is shown that similarly to other models serious disagreement seems to exist between the calculated and observed mixing ratios of NO _x , NO _y and the ratios of the different compound within the family. The amount of experimental data is, however, too sparse to draw any definite conclusion.

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Riassunto Si riportano i rusultati sulla distribuzione di gas minori nella stratosfera e troposfera, ottenuti con un modello bidimensionale, fotochimico con trasporto. Il modello si estende da 0 a 50 km in quota e da polo a polo in latitudine. Del trasporto si tiene conto usando i valori medi stagionali dei venti meridionali e verticali e dei coefficienti di diffusione turbolenta. Il modello tratta il trasporto per i seguenti composti: N₂O, NO _x (NO+NO₂), NO _y (NO _x +HNO₃), N₂O₅, H₂O, CH₄ e H₂O₂. L'idrogeno dispari (H+OH+HO₄) è calcolato all'equilibrio fotochimico. Un semplice meccanismo è proposto per simulare la condensazione del vapor d'acqua e di altri gas. I coefficienti di fotodissociazione sono calcolati tenendo conto dello scattering di Rayleigh. Le distribuzioni ottenute per i vari gas sono confrontate, ove ciò è possible, con i dati sperimentali. Si discute inoltre il bilancio stratosferico del vapor d'acqua tenendo conto delle sorgenti fotochimiche (cioè l'ossidazione del CH₄) e dei pozzi. Si conclude che, analogamente ad altri modelli, esistono delle importanti differenze fra i rappporti di mescolamento calcolati e qualli osservati di NO _x e NO _y . I dati sperimentali sono comunque ancora troppo scarsi per arrivare a conclusioni definitive.

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Резюме Мы приводим результаты вычислений распределения прослеживаемых газов в тропосфере и стратосфере с помощью двумерной фотохимической модели переноса. Область, которую покрывает модель, распостраняется от полюса до полюса и от нуля до 50 км. Атмосферный перенос включает сезонные усредненные значения для средних меридиональных и вертикальных ветров и диффзию вихрей. Переносимые соединения в этой модели являются: N₂O, NO _x (NO+NO₂), NO _y (NO _x +HNO₃), N₂O₅, H₂O, CH₄ и H₂O₂. Предполагается, что нечетный водород (OH+HO₂+H) находится в фоторавновесии. Предлагается простая схема для моделирования конденсации H₂O и удаления другин газов. При вьчислении интенсивностей фотодиссоциации учитывается релеевское рассеяние. Полученные распределения сравниваются с имеющимися экспериментальными данными. Мы пытаемся обсудить стратосферный бюджет водяных паров, учитывая фотохимические источники (т.е. окисление CH₄) и стоки. Показывается, что аналогично другим моделям, по-видимому, существует существенное расхождение между вычисленными и измеренными отношениями перемешивания NO _x , NO _y и отношениями для различных соединений. Однако экспериментальные данные являются слишком разбросанными, чтобы сделать определенные выводы.

     

Multi-parameter global calculations of fission fragments using a simplified two-dimensional scission-point model

Exploiting the concept of the dinuclear system,the interaction potential energy of two fragments that are quite close to each other is analyzed.A semi-classical method is used to calculate fission fragment yields using a simplified two-dimensional scission-point model.By considering the tip-to-tip orientation at the scission point of the fission process,we investigate the mass,charge,and kinetic-energy distributions of the fission fragments,for excitation energies in the 0-20 MeV range.Our results show that the fission fragment distributions are reproduced quite well,including the recent experimental results for the isotone chain[D Ramos et al.Phys.Rev.C 97,054612(2018)].Thus,the simplified model is useful for multi-parameter global measurements of fission products.     

A review of chemical diffusion: Criticism and limits of simplified methods for diffusion coefficient calculation

A review of the physics and modelling of mass diffusion involving different gaseous chemical species is firstly proposed. Both accurate and simplified models for mass diffusion involve the calculation of individual species diffusion coefficients. Since these are computationally expensive, in CFD they are commonly estimated by assuming constant Lewis or Schmidt numbers for each chemical species. The constant Lewis number assumption is particularly used. As a matter of fact, these assumptions have never been theoretically justified nor verified in practical flames. The only published information are the first observations by Smooke and Giovangigli about the Lewis number against temperature distributions in methane–air premixed and counterflow diffusion one-dimensional flames. The aim of this work is to verify these assumptions. Functional dependences of molecular properties appearing in these numbers are made explicit to show that while Sc _i depends only on composition, Le _i depends also on temperature and therefore it certainly cannot be assumed constant in a flame. Then, accurately calculating molecular properties, distributions of these characteristic numbers against temperature are obtained a posteriori from numerical simulations of different flames, premixed and non-premixed, and burning different fuels. For non-premixed flames, individual species Lewis number distributions are broad for most of the species considered in this article, whilst they are tight for premixed flames. Some attention is focused on the particular shape of Lewis distributions in non-premixed flames: they are characterized by four or five (when extinction is experienced) branches associated to precise regions in the flame (basically, lean, rich and stoichiometric combusting zones). Instead, the Schmidt distributions are always tighter, also when extinctions take place: for many species they can be approximatively assumed constant. Finally, a simplified procedure to estimate individual species diffusion coefficients is suggested, assuming the median of non-premixed flame Schmidt distributions has a constant value for each chemical species.     

Comparison of methods for calculating turbulent diffusion coefficients

Different methods for calculating the turbulent diffusion coefficient D _T of a passive scalar impurity in an infinite homogeneous isotropic stationary turbulent medium are examined. The values of D _T calculated by these methods are compared for two limiting types of turbulence, viz., turbulence with a δ-function spectrum and turbulence with a Kolmogorov-type spectrum. The temporal dependence of the velocity correlators is assumed to be exponential. It is shown that the most accurate method is based on the use of the solution of the nonlinear equation for the averaged Green’s function with consideration of the contribution from the four-point turbulent velocity correlators. A comparison with the results of other methods that are simpler from the mathematical standpoint shows that some of them also permit the calculation of D _T with relatively good accuracy. Zh. éksp. Teor. Fiz. 111, 871–881 (March 1997)     

A model for solid state diffusion

Classical self-diffusion is discussed in the context of a model single particle Hamiltonian containing a periodic potential and a stochastic time dependent potential. Solutions are given in the Gaussian white noise approximation in terms of a Fokker-Planck equation. The effects of spatial dependence in the time dependent potential are illustrated by calculations of the frequency dependent mobility in a simple one dimension example.     

包含液相扩散方程简化的锂离子电池电化学模型

锂离子电池的电化学模型对于电池特性分析和电池管理具有重要意义,但是准二维(P2D)模型复杂度太高,为了在保证模型精度的基础上尽量降低复杂度,本文提出了一种包含液相简化的P2D (LSP2D)模型,该模型首先基于电化学平均动力学将电池端电压化简成为仅耦合固相Li+浓度c_s和液相Li+浓度c_e的方程,然后进一步对表达c_s和c_e演化规律的偏微分方程进行抛物线近似化简,使得最终的模型由多项式组成.COMSOL仿真表明在放电倍率为1C时该模型与单粒子(SP)模型的估算精度和速度相当,但在放电倍率为3C时,该模型的估算时间比P2D模型减少了99.73%,与SP模型相当,估算精度相比SP模型有大幅度提升.     

A spacecraft shielding model for calculating exposures to radiation

A spacecraft shielding model for calculating exposure to radiation is proposed. This model is based on the concept of the randomly inhomogeneous character of the material thickness distribution both in separate equipment units and the spacecraft as a whole. This concept has made it possible to obtain the shielding function of an arbitrary point in a spacecraft necessary to calculate the radiation exposure using its mean density, geometry and the ratio of the shielding function dispersion to its mean. This is constant for the spacecraft. This conclusion was verified for several Soviet and U.S.A. spacecraft, including the Space Shuttle.     

A simplified tether model for molecular motor transporting cargo

Molecular motors are proteins or protein complexes which function as transporting engines in biological cells. This paper models the tether between motor and its cargo as a symmetric linear potential. Different from Elston and Peskin's work for which performance of the system was discussed only in some limiting cases, this study produces analytic solutions of the problem for general cases by simplifying the transport system into two physical states, which makes it possible to discuss the dynamics of the motor--cargo system in detail. It turns out that the tether strength between motor and cargo should be greater than a threshold or the motor will fail to transport the cargo, which was not discussed by former researchers yet. Value of the threshold depends on the diffusion coefficients of cargo and motor and also on the strength of the Brownian ratchets dragging the system. The threshold approaches a finite constant when the strength of the ratchet tends to infinity.     

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基于托卡马克实验的L-H模转换过程中等离子体的输运特征,建立了一种简化的非线性等离子体输运模型。通过数值求解输运方程,得到了等离子体稳态温度分布剖面,成功模拟了托卡马克边缘输运势垒(ETB)的形成以及高辅助加热功率下的内部输运势垒(ITB)现象,并对比了有无输运势垒两种情况下托卡马克的能量约束效率。     

A note on the two-dimensional radial distribution function

An analytical equation for radial distribution of a two-dimensional fluid is examined.