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1.
Variational self-consistent estimates for nonlinearproblems are formulated, building on a variational formulationpreviously developed by the authors. The formulation employsa linear comparison medium for whose propertiessome self-consistent choice is made. In contrastto linear problems, three possible self-consistent choices presentthemselves. The results that they give are analysed for twoparticular systems (a nonlinear dielectric and a nonlinear lossycomposite) for which bounds are already available. Estimatesbased on self-consistent embedding of a single inclusion ina homogeneous matrix composed of comparison materialare also developed. 相似文献
2.
Discretization of autonomous ordinary differential equationsby numerical methods might, for certain step sizes, generatesolution sequences not corresponding to the underlying flowso-calledspurious solutions or ghost solutions.In this paper we explain this phenomenon for the case of explicitRunge-Kutta methods by application of bifurcation theory fordiscrete dynamical systems. An important tool in our analysisis the domain of absolute stability, resulting from the applicationof the method to a linear test problem. We show that hyperbolicfixed points of the (nonlinear) differential equation are inheritedby the difference scheme induced by the numerical method whilethe stability type of these inherited genuine fixed points iscompletely determined by the method's domain of absolute stability.We prove that, for small step sizes, the inherited fixed pointsexhibit the correct stability type, and we compute the correspondinglimit step size. Moreover, we show in which way the bifurcationsoccurring at the limit step size are connected to the valuesof the stability function on the boundary of the domain of absolutestability, where we pay special attention to bifurcations leadingto spurious solutions. In order to explain a certain kind ofspurious fixed points which are not connected to the set ofgenuine fixed points, we interprete the domain of absolute stabilityas a Mandeibrot set and generalize this approach to nonlinearproblems. 相似文献
3.
Lukyanov A. V.; Shikhmurzaev Y. D.; King A. C. 《IMA Journal of Applied Mathematics》2008,73(1):199-224
A numerical algorithm for the biharmonic equation in domainswith piecewise smooth boundaries is presented. It is intendedfor problems describing the Stokes flow in the situations whereone has corners or cusps formed by parts of the domain boundaryand, due to the nature of the boundary conditions on these partsof the boundary, these regions have a global effect on the shapeof the whole domain and hence have to be resolved with sufficientaccuracy. The algorithm combines the boundary integral equationmethod for the main part of the flow domain and the finite-elementmethod which is used to resolve the corner/cusp regions. Twoparts of the solution are matched along a numerical internalinterface or, as a variant, two interfaces, and theyare determined simultaneously by inverting a combined matrixin the course of iterations. The algorithm is illustrated byconsidering the flow configuration of curtain coating,a flow where a sheet of liquid impinges onto a moving solidsubstrate, which is particularly sensitive to what happens inthe corner region formed, physically, by the free surface andthe solid boundary. The moving contact line problemis addressed in the framework of an earlier developed interfaceformation model which treats the dynamic contact angle as partof the solution, as opposed to it being a prescribed functionof the contact line speed, as in the so-called slip models. 相似文献
4.
On sait associer à certaines structures de Poisson surRn, de 1-jet nul en 0, des actions de R2 sur Rn, donnéespar le rotationnel de leur partie quadratiqueet un autre champ de vecteurs. Lorsque ces actions sont nonrésonantes et hyperboliques, onmontre que ces structures sont quadratisables,en ce sens qu'il existe des coordonnées dans lesquelles,elles sont quadratiques. Dans le cas de la dimension 3, nosrésultats mènent à la non-dégénérescencegénérique des structures de Poisson quadratiquesà rotationnels inversibles. We can associate with some Poisson structures defined on Rnwith a zero 1-jet at zero, actions from R2 on Rn, given by thecurl of their quadratic part and another vectorfield. Assuming that those actions are hyperbolicsand without resonances, we give a normal formfor those structures. On R3, we prove that every quadratic Poissonstructure with invertible curl, is generically non degenerate. 相似文献
5.
On the Existence and Stability of Spatially Structured Solutions of the Reaction-Diffusion Equations
The reaction-diffusion equations for the well-known Brusselatorchemical kinetic model are investigated when the model is madeconsistent with the principle of detailed balance. In contrastto the original model, the corrected one does not show solutionswith spatial structure i.e. solutions with multipleinternal maxima and multiple internal global minima in bothdependent variables. Sufficient conditions for stability ofthe solutions are given in terms of a Rayleigh quotient forgeneral boundary conditions for nonlinear reaction-diffusionequations in general. For the particular case of the Brusselatorit is shown that conditions for a change of stability are muchmore unlikely to be attained as a result of the restrictionsof detailed balancing. The detailed sufficiency condition forthe stability of any steady-state solution and for no branchingfrom the equilibrium branch solution depends onwhether the solution has global extrema inside the region, onits boundary, or both 相似文献
6.
The preceding paper Strong statements of analysisby A. R. D. Mathias defends a so-called full-blooded set theorywithout full detail [3]. He again objects to a weak set theorywhich he calls Mac, in which the usual ZermeloFraenkelseparation scheme is required only for formulas with suitablyrestricted quantifiers. I had proposed that suchseparation is adequate for all standard uses of set theory inmathematics. But Mathias has not produced any counter examplesof actual mathematics which requires the use of a stronger separation. 相似文献
7.
A timeout scheme is considered for controlling an infinite firstcome, first served overloaded single-server queue. Inthe overload situation, a customer-rejection mechanism is usedfor timing out older customers in the queue, i.e.excluding those who have waited longer than a certain time.Applying level-crossing analysis to an M/E2/1queue, exact analytic expressions of performance such as thedensity and distribution functions of waiting time of the customerswho get served, the mean delay of customers, successful throughput,and goodput are determined for this queue. 相似文献
8.
9.
** Email: rovas{at}uiuc.edu*** Email: luc_machiels{at}mckinsey.com**** Corresponding author. Email: maday{at}ann.jussieu.fr In this paper, we extend reduced-basis output bound methodsdeveloped earlier for elliptic problems, to problems describedby parameterized parabolic partial differentialequations. The essential new ingredient and the novelty of thispaper consist in the presence of time in the formulation andsolution of the problem. First, without assuming a time discretization,a reduced-basis procedure is presented to efficientlycompute accurate approximations to the solution of the parabolicproblem and relevant outputs of interest. In addition,we develop an error estimation procedure to a posteriorivalidate the accuracy of our output predictions. Second,using the discontinuous Galerkin method for the temporal discretization,the reduced-basis method and the output bound procedure areanalysed for the semi-discrete case. In both cases the reduced-basisis constructed by taking snapshots of the solutionboth in time and in the parameters: in that sense the methodis close to Proper Orthogonal Decomposition (POD). 相似文献
10.
The Galerkin Method for Integral Equations of the First Kind with Logarithmic Kernel: Theory 总被引:4,自引:0,他引:4
The aim of this paper is to develop a straightforward analysisof the Galerkin method for two-dimensional boundary integralequations of the first kind with logarithmic kernels. A distinctivefeature of the analysis is that no appeal is made to coercivity,as a result of which some existence questions cannot be answereddirectly. In return, however, the analysis has no special difficultyin handling corners, cusps, or open arcs. Instead of coercivity,the central feature of the analysis is the positive-definiteproperty of the integral operator for small enough contours.Rates of convergence are predicted theoretically and, in particular,certain linear functionals are shown to exhibit superconvergence.Numerical results supporting the theory are given in the companionpaper Sloan & Spence (1987) for problems on both open andclosed polygonal arcs. 相似文献
11.
In Markov reliability modelling, a partitioned state space isused to describe the behaviour of a system each state of whichis associated with the system either being functional or underrepair. Such a system alternates between working and repairperiods indefinitely. Recent research results on the distributionof the sequences of the lengths of working and repair periodsafford the reliability analyst a set of system characteristicswhich can be used in addition to the traditional ones (reliability,point availability, etc.) to describe the systems transientbehaviour. In this paper, we present a concise derivation ofclosed-form expressions for the probability mass function andthe factorial moments of the total cumulative timespent in a subset of the state space by an irreducible or absorbingdiscrete-parameter Markov chain during the first n time instances.This result is then applied to analyse the sequence of repairevents categorized as minor and majorof a Markov model of a power transmission system. The numericalimplementation using the Macintosh version of MatLab is alsodiscussed. 相似文献
12.
Nochetto Ricardo H.; Veeser Andreas; Verani Marco 《IMA Journal of Numerical Analysis》2009,29(1):126-140
13.
The purpose of this note is initially to present an elementarybut surprising connectedness principle pertaining to the intersectionof a fixed subvariety X of some ambient space Z with anothersubvariety Y which is mobile (in the sense ofbeing movable, rather than actually moving). It is via thismobility that monodromy enters the picture, permitting the crucialpassage from relative or total-space irreducibilityto absolute or fibrewise connectedness (and sometimesirreducibility). A general form of this principle is given inTheorem 2 below. 1991 Mathematics Subject Classification 14C99,15N05. 相似文献
14.
The Hausdorff dimension is obtained for exceptional sets associatedwith linearising a complex analytic diffeomorphism near a fixedpoint, and for related exceptional sets associated with obtaininga normal form of an analytic vector field near a singular point.The exceptional sets consist of eigenvalues which do not satisfya certain Diophantine condition and are closeto resonance. They are related to lim-sup setsof a general type arising in the theory of metric Diophantineapproximation and for which a lower bound for the Hausdorffdimension has been obtained. 相似文献
15.
The high cost of maintenance encourages managers to optimizetheir maintenance schemes. A facet of the optimizingperformance is being able to predict more precisely the timeto failure of components and equipment. In many cases, failureresults from degradation. Modelling the degradation processis likely to give rise to better prediction of failure times.There has been a variety of approaches to the modelling, andmore recent authors have considered the issues of estimationThis paper reviews some of the models used, and the criteriafor selecting models, and considers some of the practical issues.The maintenance context of the modelling is also considered. 相似文献
16.
RAO M. P. R. V.; MCLAUGHLIN J. P. 《IMA Journal of Mathematical Control and Information》1995,12(2):145-155
A combination of direct and indirect methods of adaptive controlthat yielded an improved performance (over its constituent methods)is considered in this paper. This combined method has been recentlydeveloped; it was considered that the improvement was due tothe use of a new kind of errorcalled the closed-loopestimation error. Earlier papers on this combined method useda Lyapunov function and developed stable adaptation laws ofintegral (I) form. Using the same errors, this paper suggestsa new Lyapunov function and its associated adaptation laws ofproportional plus integral (P + I) form, showing that furtherimprovement in the performance can be obtained. Digital simulationresults are presented, indicating that the P termimproves the performance in those cases where the Iterm alone is not adequate. 相似文献
17.
We prove that there are no pseudoholomorphic theories of anythingother than curves, even if one allows more general spaces thanalmost complex manifolds. The proof is elementary, except fortheories of pseudoholomorphic hypersurfaces, where topologicaltechniques are needed. Surprisingly, hypersurface theories existmicrolocally (in great abundance) to all ordersperturbatively, but not locally. 相似文献
18.
Numerical analysis of boundary integral solution of the Helmholtz equation in domains with non-smooth boundaries 总被引:1,自引:0,他引:1
In the paper we carry out a complete analysis of several efficientnumerical methods for the solution of boundary integral equationsdefined on a non-smooth boundary. In particular the solutionof the Helmholtz equation in the exterior of a closed wedgeis studied. The analytical behaviour of the solution of theresulting boundary integral equation (with a non-compact operator)near the wedge is investigated. Numerical analysis of the collocationand iterated collocation method for the problem is presented.Graded meshes are used to reflect the singularbehaviour of the analytical solution, as well as the degreeof the polynomial approximant, in order to yield results withoptimal convergence rates. Finally the convergenceanalysis of some modified two-grid iterative methods for thefast solution of the resulting linear systems is given and numericalresults are presented which agree with the theoretical predictions. 相似文献
19.
Although a function in the Bloch space may have no radial limits,it is shown that there exist bounded linear functionals whichgive average radial limits over an interval onthe boundary. An abeliantauberian theoremis proved, characterizing the existence of a radial limit ata given boundary point in terms of these functionals. 相似文献
20.
Griffiths J. D.; Price-Lloyd N.; Smithies M.; Williams J. 《IMA Journal of Management Mathematics》2006,17(3):277-288
** Email: griffiths{at}cardiff.ac.uk Activities in an intensive care unit (ICU) at a major teachinghospital are modelled by means of a queue-theoretic approach.Using data supplied by the ICU relating to the admissions process,the bed availability and the length of stay of patients, itwas possible to fit theoretical distributions to the observedarrival and service distributions.Queueing equations relevant to a multi-channel system havingrandom arrivals and hyper-exponential service times for eachchannel are set up, and solved iteratively. Results obtainedmatch well with observations, and the model is then utilisedto investigate several what if? scenarios. Referenceis made to a simulation model developed in conjunction withthe queueing model. 相似文献