Classical Problem (classical + problem)

Distribution by Scientific Domains

Selected Abstracts

Asymptotic Back Strain Approach for Estimation of Effective Properties of Multiphase Materials

A. Gusev
Estimation of the effective properties of composite materials from those of the constituents and the material's morphology is a classical problem of both theoretical and technological interest. In this work, the authors have introduced an asymptotic back strain finite element approach for numerical estimation of effective properties of multiphase materials. The proposed approach should open an appealing pathway to rational and effective computer aided design of random microstructure composite materials. [source]

The Mandel,Cryer effect in chemoporoelasticity

A. P. Bunger
Abstract Chemoporoelastic theory is an extension of classical Biot poroelasticity that accounts for coupling with the presence and the transport of ions in the pore fluid. The impact of this extra level of coupling can be both substantial and complex. This paper relies on the two variations of Mandel's classical problem, which has become a canonical illustration of the complexity that poromechanical coupling can bring to an otherwise straightforward system. To this end, solutions for a chemoporoelastic shale cylinder and a spherical shale ball are derived. These solutions are then used to demonstrate that chemoporoelastic coupling leads to a coupled pore pressure response that is not only non-monotonic, as in Mandel's classical case, but also demonstrates the consequences of the semi-permeable membrane-like nature of the shale and of the problem's two diffusion-related timescales. This paper concludes with a discussion of the implications of these results for experimentation and modeling of so-called reactive shales using chemoporoelastic theory. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Solving limit analysis problems: an interior-point method

F. Pastor
Abstract This paper exposes an interior-point method used to solve convex programming problems raised by limit analysis in mechanics. First we explain the main features of this method, describing in particular its typical iteration. Secondly, we show and study the results of its application to a concrete limit analysis problem, for a large range of sizes, and we compare them for validation with existing results and with those of linearized versions of the problem. As one of the objectives of the work, another classical problem is analysed for a Gurson material, to which linearization or conic programming does not apply. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Lawrence J. De Chant
Abstract Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical,numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A generalization of the weighted set covering problem

Jian Yang
Abstract We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b -matching problem. In general, we may use a polynomial-time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256,278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383,390], and V. Chvatal [A greedy heuristic for the set-covering problem, Math Oper Res 4(3) (1979), 233,235] to get an approximate solution for the problem. We find a worst-case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005 [source]

Robust Design of Fault Detection and Isolation Systems

Daniele Romano
Abstract Inspired by the rationale of Robust Design, a novel methodology is presented for the design of diagnostic systems for fault detection and isolation (FDI). Detection/isolation capability and robustness, i.e. sensitivity to faults and insensitivity to noise, are addressed in an integrated way within a fully stochastic framework. Although FDI is a classical problem in control engineering, this new approach improves the current state of the art both in terms of general applicability and optimality of the design solution. It demonstrates the potential of robust design in fostering innovation in a variety of technical sectors. For illustrative purposes, the methodology is applied to the design of a FDI system for a fluid mixer. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Spheroidal coordinate systems for modelling global atmospheres

A. A. White
Abstract In meteorological dynamics it is common practice to represent the potential surfaces of apparent gravity (the geopotentials) as spheres, and consequently the use of spherical polar coordinates in models of the global atmosphere is widespread. Several writers have considered how oblate spheroidal coordinates might be used instead, thus enabling the Figure of the Earth to be better represented. It is observed here that oblate spheroidal coordinate systems are conventionally defined using confocal oblate spheroids, and that such spheroids are inappropriate representations of the geopotentials because they imply the wrong sign for the latitudinal variation of apparent gravity. Re-examination of a classical problem of Newtonian gravitation shows that, near the Earth, the geopotentials are to a very good approximation spheroids, but not spheroids of an analytically simple type. However, similar oblate spheroids are a qualitatively correct model of the near-Earth geopotentials, and are a quantitatively good approximation in so far as Newton's uniform-density model adequately describes the real Earth. An orthogonal curvilinear coordinate system based on similar oblate spheroids is proposed and examined. © Crown Copyright 2008. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd [source]

Colour constancy based on texture similarity for natural images

Bing Li
Colour constancy is a classical problem in computer vision. Although there are a number of colour constancy algorithms based on different assumptions, none of them can be considered as universal. How to select or combine these available methods for different natural image characteristics is an important problem. Recent studies have shown that the texture feature is an important factor to consider when selecting the best colour constancy algorithm for a certain image. In this paper, Weibull parameterisation is used to identify the texture characteristics of colour images. According to the texture similarity, the best colour constancy method (or best combination of methods) is selected out for a specific image. The experiments were carried out on a large data set and the results show that this new approach outperforms current state-of-the-art single algorithms, as well as some combined algorithms. [source]

Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium

Marcello Lucia
We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction-diffusion equations with one linearly stable and one linearly unstable equilibrium. For a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension. We introduce a variational characterization of these traveling wave solutions and give a necessary and sufficient condition for linear versus nonlinear selection mechanism. We obtain sufficient conditions for the linear and nonlinear selection mechanisms that are easily verifiable. Our method also allows us to obtain efficient lower and upper bounds for the propagation speed. © 2004 Wiley Periodicals, Inc. [source]

Numerical evaluation of the damping-solvent extraction method in the frequency domain

Ushnish Basu
Abstract The damping-solvent extraction method for the analysis of unbounded visco-elastic media is evaluated numerically in the frequency domain in order to investigate the influence of the computational parameters,domain size, amount of artificial damping, and mesh density,on the accuracy of results. An analytical estimate of this influence is presented, and specific questions regarding the influence of the parameters on the results are answered using the analytical estimate and numerical results for two classical problems: the rigid strip and rigid disc footings on a visco-elastic half-space with constant hysteretic material damping. As the domain size is increased, the results become more accurate only at lower frequencies, but are essentially unaffected at higher frequencies. Choosing the domain size to ensure that the static stiffness is computed accurately leads to an unnecessarily large domain for analysis at higher frequencies. The results improve by increasing artificial damping but at a slower rate as the total (material plus artificial) damping ratio ,t gets closer to 0.866. However, the results do not deteriorate significantly for the larger amounts of artificial damping, suggesting that ,t,0.6 is appropriate; a larger value is not likely to influence the accuracy of results. Presented results do not support the earlier suggestion that similar accuracy can be achieved by a large bounded domain with small damping or by a small domain with larger damping. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Optimum adaptive OFDM systems

Lorenzo Piazzo
When Orthogonal Frequency Division Multiplexing (OFDM) is used to transmit information over a frequency selective channel, it is convenient to vary the power and the number of bits allocated to each subcarrier in order to optimize the system performance. In this paper, the three classical problems of transmission power minimization, error rate minimization and throughput maximization are investigated in a unified manner. The relations existing among these three problems are clarified and a precise definition of optimum system is given. A general and rigorous way to extend the solution of any of the three problems in order to obtain the solution of the other two is presented. This result is used to devise an efficient algorithm for the error rate minimization. Copyright © 2003 AEI. [source]

A new mixed finite element method for poro-elasticity

Maria Tchonkova
Abstract Development of robust numerical solutions for poro-elasticity is an important and timely issue in modern computational geomechanics. Recently, research in this area has seen a surge in activity, not only because of increased interest in coupled problems relevant to the petroleum industry, but also due to emerging applications of poro-elasticity for modelling problems in biomedical engineering and materials science. In this paper, an original mixed least-squares method for solving Biot consolidation problems is developed. The solution is obtained via minimization of a least-squares functional, based upon the equations of equilibrium, the equations of continuity and weak forms of the constitutive relationships for elasticity and Darcy flow. The formulation involves four separate categories of unknowns: displacements, stresses, fluid pressures and velocities. Each of these unknowns is approximated by linear continuous functions. The mathematical formulation is implemented in an original computer program, written from scratch and using object-oriented logic. The performance of the method is tested on one- and two-dimensional classical problems in poro-elasticity. The numerical experiments suggest the same rates of convergence for all four types of variables, when the same interpolation spaces are used. The continuous linear triangles show the same rates of convergence for both compressible and entirely incompressible elastic solids. This mixed formulation results in non-oscillating fluid pressures over entire domain for different moments of time. The method appears to be naturally stable, without any need of additional stabilization terms with mesh-dependent parameters. Copyright © 2007 John Wiley & Sons, Ltd. [source]

P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problems

Emmanuel Perrey-Debain
Abstract The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Boom in the development of non-peptidic ,-secretase (BACE1) inhibitors for the treatment of Alzheimer's disease

Romano Silvestri
Abstract ,-Amyloid cleaving enzyme-1 (BACE1) has become a significant target for the therapy of Alzheimer's disease. After the discovery of the first non-peptidomimetic ,-secretase inhibitors by Takeda Chemicals in 2001, several research teams focused on SAR development of these agents. The non-peptidic BACE1 inhibitors may potentially overcome the classical problems associated with the peptide structure of first generation, such as blood,brain barrier crossing, poor oral bioavailability and susceptibility to P-glycoprotein transport. In the past 6 years a boom in research of non-peptidic BACE1 inhibitors has disseminated findings over hundreds of publications and patents. The rapidly growing literature has been reviewed with particular emphasis on literature of pharmaceutical companies. © 2008 Wiley Periodicals, Inc. Med Res Rev, 29, No. 2, 295,338, 2009 [source]

Variances Are Not Always Nuisance Parameters

BIOMETRICS, Issue 2 2003
Raymond J. Carroll
Summary In classical problems, e.g., comparing two populations, fitting a regression surface, etc., variability is a nuisance parameter. The term "nuisance parameter" is meant here in both the technical and the practical sense. However, there are many instances where understanding the structure of variability is just as central as understanding the mean structure. The purpose of this article is to review a few of these problems. I focus in particular on two issues: (a) the determination of the validity of an assay; and (b) the issue of the power for detecting health effects from nutrient intakes when the latter are measured by food frequency questionnaires. I will also briefly mention the problems of variance structure in generalized linear mixed models, robust parameter design in quality technology, and the signal in microarrays. In these and other problems, treating variance structure as a nuisance instead of a central part of the modeling effort not only leads to inefficient estimation of means, but also to misleading conclusions. [source]

The Algebra of Geometric Impossibility: Descartes and Montucla on the Impossibility of the Duplication of the Cube and the Trisection of the Angle

CENTAURUS, Issue 1 2010
Jesper Lützen
Today we credit Pierre Wantzel with the first proof (1837) of the impossibility of doubling a cube and trisecting an arbitrary angle by ruler and compass. However two centuries earlier Descartes had put forward what probably counts as the first proof of these impossibilities. In this paper I analyze this proof, as well as the later related proof given by Montucla (1754) and the brief version of this proof published by Condorcet (1775). I discuss the many novelties of these early arguments and highlight the problematic points addressed by Gauss (1801) and Wantzel. In particular I show that although Descartes developed many of the algebraic techniques used in later proofs he failed to provide an algebraic impossibility proof and resorted to a geometric argument. Montucla and Condorcet turned this proof into an algebraic one. I situate the analysis of the early proof of the impossibility of the two classical problems in the general context of early modern mathematics where mathematics was primarily viewed as a problem solving activity. Within such a paradigm of mathematics impossibility results arguably do not play the role of proper mathematical results, but rather the role of meta-results limiting the problem solving activity. [source]