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Some examples of Penrose’s quasi-local mass construction 彭罗斯的准局部大规模建筑的一些例子
K. Tod
Penrose’s quasi-local mass (Penrose, Proc.R.Soc.Lond. A 381, 253 (1982)) is calculated for a variety of two-surfaces in particular space-times. The results are compared with other definitions of mass where these are available.
彭罗斯的准局部质量。A 381,253(1982))在特定时空中计算了各种双曲面。这些结果与其他可用的质量定义进行了比较。
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引用次数: 106
The influence of diffusion on the current-voltage curve in a flame ionization detector 扩散对火焰电离检测器电流-电压曲线的影响
H. Bolton, P. Halbherr
An earlier analysis of the electric current carried by positive ions from the flame in a flame ionization detector is extended to include the effect of the diffusion of the ions. It had been noted that the earlier theory gave a current-voltage expression from which the experimental measurements diverged at very low values of the voltages. Solutions of the nonlinear differential equations for the electric field are presented here in both one and two dimensions, the latter being the experimental cylindrical arrangement of the flame ionization detector. A partial explanation is given for the behaviour at low currents.
在火焰电离检测器中,对火焰中正离子携带的电流的早期分析被扩展到包括离子扩散的影响。已经注意到,早先的理论给出了一个电流-电压表达式,在电压非常低的情况下,实验测量结果与之不符。本文给出了一维和二维电场非线性微分方程的解,其中二维是火焰电离探测器的实验圆柱形布置。对低电流下的行为作了部分解释。
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引用次数: 1
Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I 多孔介质中自然对流对热点火的影响。2集总热模型1
V. Balakotaiah, P. Pourtalet
In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t/ln t + t/(t - 1) (1 < t ≼ 3.4955), ψ/R* = (B Ls)2 ((t - 1)/t) exp{ - B Ls + B Ls/t} ln t, where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single-valued, isola, inverse S, mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.
本文研究了在无限大导热系数和零扩散系数假设下一维扩散-对流-反应模型的临界、着火轨迹和温度分岔图随瑞利数的消失。将该模型的预测结果与Semenov模型的预测结果进行了比较,以确定物种扩散项的影响。结果表明,当瑞利数(R* > 1)较大时,引燃轨迹可以用参数形式表示:B Ls = t/ llnt + t/(t - 1) (1 < t - smitr3.4955), ψ/R* = (B Ls)2 ((t - 1)/t) exp{- B Ls + B Ls/t} llnt,其中B为反应热参数,ψ为Semenov数,Ls为(修正)路易斯数。发现临界性在bls = 4.194时消失。将这些结果与Semenov模型的结果进行比较,发现忽略物种扩散项可以得到点火轨迹和临界边界的保守逼近。发现集总热模型- 1具有5种不同类型的温度与瑞利数的分岔图(单值、孤立、逆S、蘑菇、逆S +孤立)。这些图与在无限大热导率和零种扩散率假设下强迫对流问题的温度对流量的分岔图在性质上是相同的。
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引用次数: 3
On the existence of interfacial (Stoneley) waves in bonded piezoelectric half-spaces 结合压电半空间中界面波的存在性
M. Abbudi, D. Barnett
A new definition of the piezoelectric limiting speed, based on the piezoelectrically stiffened acoustical tensor is introduced. The Stoneley wave problem is readily formulated for bonded piezoelectric half-spaces in both the Φ and F representations introduced by Lothe & Barnett. The notion of the F piezoelectric interfacial impedance tensor, which is an extension of the elastic interfacial impedance tensor, is used to show that a maximum of two subsonic Stoneley waves can occur. A definite existence criterion for a single subsonic piezoelectric Stoneley mode is given, and a numerical scheme that searches for Stoneley modes, when they exist for a given geometry and material combination, is also presented along with a numerical example for two joined cadmium sulphide half-spaces.
提出了基于压电加筋声张量的压电极限速度的新定义。在Lothe & Barnett引入的Φ和F表示中,结合压电半空间的Stoneley波问题很容易被表述出来。压电界面阻抗张量F的概念是弹性界面阻抗张量的扩展,用来证明最多可以出现两个亚音速斯通利波。给出了单个亚音速压电斯通利模态存在的确定判据,给出了在给定几何形状和材料组合条件下寻找斯通利模态的数值格式,并给出了两个连接的硫化镉半空间的数值实例。
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引用次数: 33
Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition 狄利克雷条件下奇摄动双稳定势的极小值和梯度流
Nicholas C. Owen, J. Rubinstein, P. Sternberg
Minimizers and gradient flows are studied for the functional ∫Ω W(u) + ϵ2∣∇u∣2dx, Ω ⊆ Rn, ϵ > 0, where u satisfies a Dirichlet condition u = hϵ on ∂Ω. Here W is taken to be a double-well potential with minimum value zero attained at u = a and u = b. Questions of existence and structure of minimizers for small ϵ are resolved through the identification of a limiting variational problem, the so-called Γ-limit. A formal asymptotic solution is then constructed for the gradient flow ∂tuϵ = 2ϵ∆uϵ—ϵ-1W'(uϵ), uϵ(x, 0) = g(x), uϵ(x, t) = hϵ on ∂Ω, valid when ϵ is small. Using multiple timescales we show that fronts rapidly develop and then propagate with normal velocity ϵk, where k is mean curvature. At the intersection of a front with ∂Ω, the Dirichlet condition is shown to imply a contact angle condition for the front. This asymptotically correct evolution process represents gradient flow for the Γ-limit.
研究了泛函∫Ω W(u) + ϵ2∣∇u∣2dx, Ω Rn, λ > 0,其中u满足∂Ω上的Dirichlet条件u = hλ的最小化和梯度流。这里,W是在u = a和u = b处达到最小值为零的双阱势。通过识别一个极限变分问题,即Γ-limit,解决了小λ的最小值的存在性和结构问题。然后构造了一个正式的渐近解,用于梯度流∂tue_ (2e_∆ue_ -ϵ-1W’(ue_), ue_ (x, 0) = g(x), ue_ (x, t) = h_在∂Ω上,当ε很小时有效。使用多个时间尺度,我们显示锋面迅速发展,然后以正常速度ϵk传播,其中k是平均曲率。在锋面与∂Ω的交集处,狄利克雷条件暗示了锋面的接触角条件。这个渐近正确的演化过程表示Γ-limit的梯度流。
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引用次数: 77
A theoretical analysis of electrochemical arc machining 电化学电弧加工的理论分析
J. McGeough, H. Rasmussen
Electrochemical arc machining (ECAM) involves the removal of metal from an anodically polarized workpiece by both erosion arising from discharges produced in an aqueous electrolyte and electrolytic dissolution. A theoretical model is derived for the process and analysed for two specific applications, fine-hole drilling and the finishing of components by smoothing of their initially rough surfaces. In the second of these examples, a perturbation procedure for obtaining approximate solutions is used; the model so developed encorporates the effects of current density on current efficiency which are known from experimental electrochemical machining (ECM) studies to influence the rate and mode of smoothing. For fine-hole drilling by ECAM, the analysis predicts that the interelectrode gap width increases with the applied voltage and inversely with the square root of the mechanically driven anode. In the case of smoothing, ECAM is found to remove the surface irregularities at a much faster rate and with lower loss of stock metal than ECM alone, when electrolytes such as sodium chloride solution yielding 100% current efficiency are used for the latter process. The analysis shows that an electrolyte solution with a current density-dependent current efficiency is needed if parent metal loss by ECM is to approach that of ECAM, and even then, machining by the latter is still much faster. Attention is drawn to experimental evidence in support of these predictions of ECAM behaviour. Finally, results from the model are used to verify the practical use of ECM for rapid finishing of the surfaces of components left rough by electrodischarge machining.
电化学电弧加工(ECAM)涉及通过水电解质和电解溶解产生的放电产生的侵蚀从阳极极化工件上去除金属。推导了该工艺的理论模型,并对两种具体应用进行了分析,即细孔钻孔和通过光滑其最初粗糙的表面对部件进行精加工。在第二个例子中,用摄动法求近似解;所建立的模型包含了电流密度对电流效率的影响,电流密度对电流效率的影响是由实验电化学加工(ECM)研究得出的,它会影响平滑的速率和方式。对于ECAM钻小孔,分析预测电极间隙宽度随施加电压的增加而增加,与机械驱动阳极的平方根成反比。在平滑的情况下,ECAM被发现以更快的速度去除表面不规则性,并且比单独使用ECM更低的金属损失,当电解质(如氯化钠溶液)用于后一种工艺时,电流效率为100%。分析表明,如果ECM的母材损耗接近ECAM,则需要具有电流密度相关电流效率的电解质溶液,即使这样,后者的加工速度仍然要快得多。注意被吸引到实验证据,以支持这些预测的ECAM行为。最后,利用该模型的结果验证了电解加工对电火花加工留下的零件表面进行快速精加工的实际应用。
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引用次数: 8
On the solutions of a class of dual integral equations occurring in diffraction problems 衍射问题中一类对偶积分方程的解
K. Eswaran
It is shown that there exists a category of two-dimensional diffraction problems, which can be put into a ‘standard form‘ of dual integral equations. These diffraction problems include: diffraction of electromagnetic waves by a finite strip, a finite slit, the diffraction of scalar or vector elastic waves by a rigid strip or crack, etc. A general method for solving such dual integral equations is given by the artifice of constructing a set of functions of compact support biorthogonal to another given set of functions. The sufficient conditions for a given dual integral equations to be solvable in this manner are also determined. Hence, the method forms a complement to the Weiner-Hopf method. To illustrate the method solutions are obtained for a bench-mark problem : the diffraction of light by a finite perfectly conducting strip (or equivalently the diffraction of SH waves by a crack). Comparison with results obtained by others for low, intermediate and high frequencies show the utility and accuracy of the method for the entire range of frequencies. Both the near field and the far field are obtained, the latter is shown to correspond to the Fraunhoffer diffraction pattern for high frequency. It is also shown that for the equivalent crack problem the stress intensity factor (SIF) fluctuates rapidly with changes in the angle of incidence for high frequencies, thus making the SIF especially sensitive to angle of incidence at high frequencies.
结果表明,存在一类二维衍射问题,可以化为对偶积分方程的“标准形式”。这些衍射问题包括:电磁波通过有限条、有限缝的衍射,标量或矢量弹性波通过刚性条或裂纹的衍射等。通过构造紧支撑函数集与另一给定函数集双正交的技巧,给出了求解这类对偶积分方程的一般方法。给出了对偶积分方程用这种方法可解的充分条件。因此,该方法是对Weiner-Hopf方法的补充。为了说明该方法,得到了一个基准问题的解:光通过有限完全导电带的衍射(或等效的SH波通过裂纹的衍射)。与其它低频、中频和高频的结果比较,表明了该方法在整个频率范围内的实用性和准确性。得到了近场和远场,远场与高频的夫琅和费衍射图相对应。对于等效裂纹问题,应力强度因子(SIF)在高频时随入射角的变化而快速波动,从而使SIF对高频入射角特别敏感。
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引用次数: 49
Computer simulation studies of anisotropic systems. XVIII. Re-entrant phase separation in nematogenic mixtures of cylindrical and spherical particles 各向异性系统的计算机模拟研究。十八。圆柱形和球形颗粒致线虫混合物的再入相分离
R. Hashim, G. R. Luckhurst, S. Romano
Addition of a solute composed of quasi-spherical molecules to a nematic liquid crystal is known to depress the nematic–isotropic transition temperature. A biphasic régime, consisting of coexisting nematic and isotropic phases, is also created at the transition. A molecular field theory of such mixtures, developed by Humphries and Luckhurst, predicts, in addition, the appearance of a re-entrant biphasic region following the nematic phase for a narrow range of compositions. This unusual re-entrant phase separation has not been observed for real nematogenic mixtures, presumably because the system freezes before the re-entrant phases can be formed. Here we report the observation of this biphasic régime for a model nematogenic mixture, formed from cylindrical and spherical particles, which was studied using the Monte Carlo technique of computer simulation. The particles are confined to the sites of a simple cubic lattice but still retain their rotational freedom; in consequence the mixture is unable to freeze in the conventional sense. The temperature variation of the heat capacity and the solute–solute radial distribution function reveal the predicted transition to the re-entrant biphasic régime. The internal energy and the second-rank orientational order parameter were also determined as a function of temperature. The predictions of the Humphries–Luckhurst theory are found to be in good qualitative accord with the results of the simulation.
在向列相液晶中加入由准球形分子组成的溶质可以降低向列相各向同性转变温度。在过渡阶段还形成了由共存的向列相和各向同性相组成的双相体制。此外,汉弗莱斯和卢克赫斯特提出的这种混合物的分子场理论预测,在一个狭窄的组合物范围内,向列相之后会出现一个重新进入的双相区域。这种不寻常的再入相分离在真正的线虫源混合物中没有观察到,可能是因为系统在再入相形成之前就冻结了。本文报道了用计算机模拟蒙特卡罗技术研究了由圆柱形和球形颗粒形成的模型线虫混合物的双相结构的观察结果。粒子被限制在一个简单的立方晶格的位置,但仍然保持它们的旋转自由;因此,混合物不能在传统意义上冻结。热容的温度变化和溶质-溶质径向分布函数揭示了预测的向再入双相体系的转变。并确定了内能和二级取向参数随温度的变化规律。汉弗莱斯-卢克赫斯特理论的预测结果与模拟结果在定性上是一致的。
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引用次数: 8
Analysis of chemical kinetic systems over the entire parameter space. III. A wet combustion system 整个参数空间的化学动力学系统分析。3湿式燃烧系统
B. F. Gray
A simple generalization of Semenov thermal explosion theory is studied here; one exothermic reaction taking place at the same time as a second one involving water as a reactant. Evaporation and condensation are also considered. The resulting two ordinary differential equations containing three parameters are treated by recently developed methods outlined in the first paper of this series. This model is a simple representation of the combustion of wet cellulosic materials such as bagasse, cotton and sawdust. The theory predicts an amazing variety of behaviour arising in association with the degenerate singularities that occur. These include degeneracies up to and including the quartic fold, H32 bifurcation and degenerate double zero eigenvalue points.
本文研究了塞门诺夫热爆炸理论的一个简单推广;一个放热反应与另一个以水为反应物的放热反应同时发生。蒸发和冷凝也被考虑在内。所得到的两个包含三个参数的常微分方程用本系列第一篇文章中概述的最近发展的方法来处理。这个模型是一个简单的燃烧湿纤维素材料,如甘蔗渣,棉花和锯末的表示。该理论预测了与退化奇点相关的各种惊人的行为。这些包括退化到并包括四次褶皱,H32分岔和退化双零特征值点。
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引用次数: 14
Finite deformation of flexible composites 柔性复合材料的有限变形
S. Luo, T. Chou
This paper examines the nonlinear elastic behaviour of flexible composites under finite deformation. The constitutive relations have been derived based on a strain-energy density which, in a fourth-order polynomial form, is assumed to be a function of the lagrangian strain components referring to the initial principal material coordinates. The constitutive equations thus obtained are verified by the following experiments: (1) off-axis tension and simple shear for unidirectional composites, and (2) uniaxial tension for flexible composites with wavy fibres. Good agreement has been found between the theory and experiments.
本文研究了有限变形下柔性复合材料的非线性弹性行为。本构关系是基于四阶多项式形式的应变能密度推导出来的,假设应变能密度是初始主材料坐标下拉格朗日应变分量的函数。通过以下实验验证了所得的本构方程:(1)单向复合材料的离轴张力和简单剪切,(2)波浪纤维柔性复合材料的单轴张力。理论和实验结果吻合得很好。
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引用次数: 29
期刊
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
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