Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences最新文献_第6页

Exponential trend to equilibrium for discrete coagulation equations with strong fragmentation and without a balance condition 具有强破碎且无平衡条件的离散混凝方程的指数趋向平衡

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI: 10.1098/rspa.2004.1294

N. Fournier, S. Mischler

引用次数: 23

Continuity theorems and chance distribution of random fuzzy variables 连续性定理与随机模糊变量的机会分布

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI: 10.1098/rspa.2004.1280

Yuanguo Zhu, Baoding Liu

引用次数: 29

Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics 通过非线性时变气泡云的传播和由测量的声学特性估计气泡群

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI: 10.1098/rspa.2004.1298

T. Leighton, S. D. Meers, P. White

{"title":"Propagation through nonlinear time-dependent bubble clouds and the estimation of bubble populations from measured acoustic characteristics","authors":"T. Leighton, S. D. Meers, P. White","doi":"10.1098/rspa.2004.1298","DOIUrl":"https://doi.org/10.1098/rspa.2004.1298","url":null,"abstract":"For several decades the propagation characteristics of acoustic pulses (attenuation and sound speed) have been inverted in attempts to measure the size distributions of gas bubbles in liquids. While this has biomedical and industrial applications, most notably it has been attempted in the ocean for defence and environmental purposes, where the bubbles are predominantly generated by breaking waves. Such inversions have required assumptions, and the state–of–the–art technique still assumes that the bubbles undergo linear, steady–state monochromatic pulsations in the free field, without interacting. The measurements always violate, to a greater or lesser extent, these assumptions. The errors incurred by the use of such assumptions have been difficult to quantify, but are expected to be most severe underneath breakers in the surf zone, where the void fraction is greatest. Very few measurements have been made in this important region of the ocean. This paper provides a method by which attenuation can be predicted through clouds of bubbles which need not be homogeneous, nor restricted to linear steady–state monochromatic pulsations. To allow inversion of measured surf zone attenuations to estimate bubble populations with current computational facilities, this model is simplified such that the bubble cloud is assumed to be homogeneous and the bubbles oscillating in steady state (although still nonlinearly). The uses of the new methods for assessing the errors introduced in using state–of–the–art inversions are discussed, as are their implications for oceanographic and industrial nonlinear bubble counters, for biomedical contrast agents, and for sonar target detection in the surf zone.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80399969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 102

Uniform asymptotic expansion of the Jacobi polynomials in a complex domain 复域上Jacobi多项式的一致渐近展开式

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI: 10.1098/rspa.2004.1296

R. Wong, Yuqiu Zhao

引用次数: 8

Bounds for the effective constitutive relation of a nonlinear composite 非线性复合材料有效本构关系的界

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI: 10.1098/rspa.2004.1309

D. Talbot, John R. Willis

{"title":"Bounds for the effective constitutive relation of a nonlinear composite","authors":"D. Talbot, John R. Willis","doi":"10.1098/rspa.2004.1309","DOIUrl":"https://doi.org/10.1098/rspa.2004.1309","url":null,"abstract":"For a nonlinear composite, a bound on its effective energy density does not induce a corresponding bound on its constitutive relation, because differentiating a bound on a function does not automatically bound its derivative. In this work, a method introduced by Milton and Serkov for bounding directly the constitutive relation is refined by employing a linear comparison material, in a way similar to that employed by the present authors to obtain bounds of ‘Hashin–Shtrikma’ type for the effective energy of a nonlinear composite. The original Milton–Serkov approach produces bounds with a close relationship to the classical energy bounds of Voigt and Reuss type. The bounds produced in the present implementation are closely related to bounds of Hashin–Shtrikman type for the composite. Indeed, in the case of a linear composite, the present method delivers the Hashin–Shtrikman bounds in their generalized form, valid for any two–point statistics. It is demonstrated for nonlinear examples that the approximate constitutive relation that is obtained by differentiating the energy bound can be on the boundary of the bounding set for the exact constitutive relation, but a simple counterexample is presented to show that this is not always the case.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76552702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 31

One-dimensional linear stability of curved detonations 弯曲爆轰的一维线性稳定性

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI: 10.1098/rspa.2004.1290

S. Watt, G. Sharpe

引用次数: 14

Confinement of interstitial cluster diffusion by oversized solute atoms 超大溶质原子对间隙团簇扩散的限制

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI: 10.1098/rspa.2004.1289

T. Hudson, S. Dudarev, A. Sutton

引用次数: 26

Semi-analytical solutions for one- and two-dimensional pellet problems 一维和二维颗粒问题的半解析解

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-08-08 DOI: 10.1098/rspa.2004.1286

T. Marchant, M. I. Nelson

{"title":"Semi-analytical solutions for one- and two-dimensional pellet problems","authors":"T. Marchant, M. I. Nelson","doi":"10.1098/rspa.2004.1286","DOIUrl":"https://doi.org/10.1098/rspa.2004.1286","url":null,"abstract":"The problem of heat and mass transfer within a porous catalytic pellet in which an irreversible first–order exothermic reaction occurs is a much–studied problem in chemical–reactor engineering. The system is described by two coupled reaction–diffusion equations for the temperature and the degree of reactant conversion. The Galerkin method is used to obtain a semi–analytical model for the pellet problem with both one– and two–dimensional slab geometries. This involves approximating the spatial structure of the temperature and reactant–conversion profiles in the pellet using trial functions. The semi–analytical model is obtained by averaging the governing partial differential equations. As the Arrhenius law cannot be integrated explicitly, the semi–analytical model is given by a system of integrodifferential equations. The semi–analytical model allows both steady–state temperature and conversion profiles and steady–state diagrams to be obtained as the solution to sets of transcendental equations (the integrals are evaluated using quadrature rules). Both the static and dynamic multiplicity of the semi–analytical model is investigated using singularity theory and a local stability analysis. An example of a stable limit cycle is also considered in detail. Comparison with numerical solutions of the governing reaction–diffusion equations and with other results in the literature shows that the semi–analytical solutions are extremely accurate.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85613218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 17

The effects of the contact angle on sloshing in containers 接触角对容器内晃动的影响

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-08-08 DOI: 10.1098/rspa.2004.1281

R. Kidambi, P. Shankar

引用次数: 9

On the nature of shear horizontal wave propagation in elastic plates coated with viscoelastic materials 粘弹性材料包覆弹性板中剪切水平波传播特性研究

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-08-08 DOI: 10.1098/rspa.2004.1284

F. Simonetti, P. Cawley

{"title":"On the nature of shear horizontal wave propagation in elastic plates coated with viscoelastic materials","authors":"F. Simonetti, P. Cawley","doi":"10.1098/rspa.2004.1284","DOIUrl":"https://doi.org/10.1098/rspa.2004.1284","url":null,"abstract":"The possibility of using long–range ultrasonic guided–wave non–destructive testing for the inspection of metallic structures coated with attenuative layers is extremely attractive. However, the material damping may cause severe attenuation of the acoustic signal, resulting in reduction of the test range. This paper addresses the dispersion of shear horizontal waves propagating in metallic plates coated with viscoelastic layers. It is shown that the bilayer modes can be viewed as an interaction between the free elastic plate modes and the modes of the viscoelastic layer if it were clamped on its lower surface. For low–attenuation materials the interaction is strong and the trajectories of the bilayer dispersion curves jump between the two families as the frequency increases. However, as the material damping increases the interaction becomes weak and most of the energy is confined in either the metallic plate or in the attenuative layer, and modes no longer jump. The guided–wave attenuation is related to the strain energy in the viscoelastic layer per unit in–plane power flow by means of an energy–balance argument. The guided–wave attenuation of the modes whose energy travels primarily in the elastic plate exhibits periodic peaks in the frequency domain, which occur at roughly equally spaced critical frequencies. These frequencies are close to the through–thickness resonance frequencies of the clamped–free viscoelastic layer if it is considered to be elastic. Minima of the guided–wave attenuation occur around the Love transition frequencies.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2004-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83941559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 44