Nonlinear stability of boundary layers for the Boltzmann equation with cutoff soft potentials

The study on the boundary layer is important in both mathematics and physics. This paper considers the nonlinear stability of boundary layer solutions for the Boltzmann equation with cutoff soft potentials when the Mach number of the far field is less than −1. Unlike the collision frequency is strictly positive in the hard potential or hard sphere model, the collision frequency has no positive lower bound for the cutoff soft potentials, so the decay in time cannot be expected. Instead, the present paper proves that the solution will always be in a small region around the boundary layer by noticing the decay property of collision operator in velocity.     

The Boltzmann equation with potential force in the whole space

In this paper, we consider the Cauchy problem of the Boltzmann equation with potential force in the whole space. When some more natural assumptions compared with those of the previous works are made on the potential force, we can still obtain a unique global solution to the Boltzmann equation even for the hard potential cases by energy method, if the initial data are sufficiently close to the steady state. Moreover, the solution is uniformly stable. Copyright © 2010 John Wiley & Sons, Ltd.     

Multimethodology in series and parallel: strategic planning using hard and soft OR

This paper examines two distinct ways in which hard and soft operational research (OR) methodologies can be combined, in series and in parallel. Multimethodology in series is acknowledged as the simpler and more common approach. Multimethodology in parallel is identified as having the potential to provide significant benefits to projects in political, changing, or ‘wicked’ contexts that multimethodology in series cannot. Observations regarding these approaches to multimethodology are examined in light of an information systems strategic planning project in the Australian public sector. Two distinct methodologies were combined in the project: soft systems methodology and project management. These methodologies are based on the soft and hard paradigms, respectively. However, findings in this paper have the potential to be transferred to combinations of other hard and soft OR methodologies.     

Stationary solutions of the linearized Boltzmann equation in a half-space

Stationary half-space solutions of the linearized Boltzmann equation are studied by energy estimates methods. We extend the results of Bardos, Caflisch and Nicolaenko for a gas of hard spheres to a general potential. Asymptotic behaviour is obtained for hard as well as soft potentials and compared to the case of hard spheres.     

Point source excitation in direct and inverse scattering: The soft and the hard small sphere

A spherical wave emanating from a point source is scatteredby either a soft or a hard body. The incident spherical wavehas a wavelength which is much larger than the characteristicdimension of the scatterer and it is modified in such a wayas to recover the plane wave incidence when the source pointrecedes to infinity. Using low frequency expansions the scatteringproblem is transformed to a sequence of exterior potential problemsin the presence of a monopole singularity located at the sourceof the incident wave field. Complete expansions for the scatteringamplitude are provided. The method is applied to the cases ofa soft and a hard sphere and the first three approximationsfor the near, as well as the far, field are evaluated. It isobserved that every one, after the first, low frequency approximationof the far field, involves one spherical multipole more thanthe corresponding approximation for the case of an incidentplane wave. As the point singularity tends to infinity, therelative results recover all the known expressions for planeincidence. It is shown that for point excitation the Rayleighapproximation of the scattering amplitude for a hard sphereis of the second order, in contrast to the case of plane excitationwhich is of the third order. Simple algorithms that specifythe radius and the position of a soft and a hard sphere areproposed, which are based on the additional dependence of thescattering amplitude represented by the distance from the pointsource to the centre of the scatterer. The inversion algorithmis shown to be stable whenever the source point is not too faraway from the target sphere. A simple way to decide whetherthe sphere is a soft or a hard body is also provided.     

A fast BIE iteration method for an arbitrary body in a flow of incompressible inviscid fluid

The paper is concerned with the new iteration algorithm to solve boundary integral equations arising in boundary value problems of mathematical physics. The stability of the algorithm is demonstrated on the problem of a flow around bodies placed in the incompressible inviscid fluid. With a discrete numerical treatment, we approximate the exact matrix by a certain Töeplitz one and then apply a fast algorithm for this matrix, on each iteration step. We illustrate the convergence of this iteration scheme by a number of numerical examples, both for hard and soft boundary conditions. It appears that the method is highly efficient for hard boundaries, being much less efficient for soft boundaries.     

Availability and maintenance modeling for systems subject to dependent hard and soft failures

This paper develops availability and maintenance models for single‐unit systems subject to dependent hard and soft failures. A hard failure stops the system immediately, whereas a soft failure only reduces the performance capacity of the system. Dependence between these 2 types of failures is reflected in the fact that each soft failure directly increases the hazard rate of the hard failure. On the basis of such interaction, we derive recursive equations for the system reliability and availability functions. To detect both types of failures, inspections are executed periodically. Furthermore, we investigate the optimal inspection policy via the minimization of the expected cost per unit time. The applicability of the developed availability and maintenance models is validated by a case study on an electrical distribution system.     

一类单自由度非自治系统的非线性振动

本文用奇异摄动理论多尺度法的导数展开法[1],求解了在微粘性阻尼作用下,连结在一个非线性弹簧上的一个质点的受迫振动方程.研究的是四次非线性问题,讨论了四种情况:非共振的软激发;非共振的硬激发;共振的软激发;共振的硬激发.     

A pair of stream functions for three-dimensional vortex flows

Introducing a vector potential, that is based on a pair of stream functions, and a velocity potential, antisymmetric equations for the stream functions are derived with the help of a variational principle. It is found that the equations are in a suitable form to investigate flows with helical symmetry, and, for example, to connect upstream axisymmetric flows with downstream helical flows. The special case of a transition from an upstream solid-body vortex to a downstream helical flow is investigated in detail. Furthermore, the stream-function equations are particularly useful to investigate general small-amplitude inertia waves on vortex flows. Time-dependent helical flows that are time-independent in a suitably rotating frame of reference can also be discussed with the proposed method.     

Combining PSMs with hard OR methods: the philosophical and practical challenges

Combinations of problem structuring methods with hard OR methodologies are seldom described in the literature. This paper will reflect on the barriers to such combinations that can be seen at the philosophical level—paradigm incommensurability—and cognitive level—type of personality and difficulty of switching paradigm. This paper examines the combination of Soft Systems Methodology and Discrete Event Simulation within an Intermediate Care case study. The paper will argue, by way of the practical application, that these problems are not insurmountable and that the result can be seen as interplay of the soft and hard paradigms. The idea of yin and yang is proposed as a metaphor for this process.     

From Optimizing to Learning: A Development of Systems Thinking for the 1990s

In any subject concerned with rational intervention in human affairs, theory must lead to practice; but practice is the source of theory: neither theory nor practice is prime. We can examine this ‘groundless’ relation by asking what intellectual framework F is applied in what methodology M to what area of application A? If we do this for O.R., systems analysis, systems engineering etc., we see that F and M have changed dramatically between the 1950s and the 1980s, yielding the ‘hard’ and ‘soft’ traditions of systems thinking. The ‘hard’ tradition, based on goal seeking, is examined in the work of Simon and contrasted with the ‘soft’ tradition, based on learning, as exemplified in the work of Vickers and the development of soft systems methodology. The two are complementary, but the relation between them is that the ‘hard’ is a special case of ‘soft’ systems thinking. This analysis makes sense of the recent history of management science and helps to prepare us for the 1990s.     

On the geometry of a steady two dimensional potential flow and its physics

The paper studies the geometrical aspects of steady, two-dimensional potential flows and their relation to the physics that governs them. To achieve this, the streamline curvature of a flow is determined when the vector velocity field describing it, is known. Two methods, which allow the calculation of streamline curvature at every point of a flow field, are developed: the ‘Method of Rotation’ and the ‘Method of Directional Derivative’. Especially the first method reveals an interesting feature of curvature, allowing it to be interpreted kinematically. Furthermore, an attempt has been made towards the formulation of a potential theory from a geometrical perspective. For this reason the concept of ‘Global Curvature’ is introduced, being a measure of both stream and potential line curvature. It has been proven that it contains all the information needed to determine the physical quantities of velocity and static pressure throughout a potential flow, thus depicting the strong link between geometry and physics.     

软计算与硬计算融合的含油性属性与样本约简

随着石油勘探领域的不断扩大,含油性识别的研究对象也越来越复杂,传统的基于单一硬计算或软计算的方法在含油性识别中面临着严峻挑战.首先提出了软计算与硬计算融合的4种模式,然后运用GA-FCM对含油性的测井属性进行约简,将约简后的测井属性结合软计算与硬计算融合的分离模式对某油田Oilsk81,Oilsk83,Oilsk85三口井进行含油性模式识别,去掉出错率较高的样本,达到样本约简的目的;最后利用判别分析法对约简后的样本集进行检验分析.实验表明:第一,在这几个油区可以用声波时差和含油饱和度两个测井属性进行含油性识别;第二,将出错率高的样本进行约简可以提高样本集识别的正确率.     

GEVREY REGULARITY FOR SOLUTION OF THE SPATIALLY HOMOGENEOUS LANDAU EQUATION

In this paper, we study the Gevrey class regularity for solutions of the spatially homogeneous Landau equations in the hard potential case and the Maxwellian molecules case.     

Well‐posedness of nonlinear wave equation with combined power‐type nonlinearities

In this paper, we study the initial boundary‐value problem with combined power‐type nonlinearities by utilizing potential well method. We provide an algorithm to compute the depth of the potential well with the help of Mathematica, and derive the invariant subsets, global existence and blowup of solutions. Moreover, we obtain the invariant subsets, global existence and blowup of solutions for the critical case. Copyright © 2011 John Wiley & Sons, Ltd.     

Fast Soliton Scattering by Attractive Delta Impurities

We study the Gross–Pitaevskii equation with an attractive delta function potential and show that in the high velocity limit an incident soliton is split into reflected and transmitted soliton components plus a small amount of dispersion. We give explicit analytic formulas for the reflected and transmitted portions, while the remainder takes the form of an error. Although the existence of a bound state for this potential introduces difficulties not present in the case of a repulsive potential, we show that the proportion of the soliton which is trapped at the origin vanishes in the limit.     

Enhancing case-based reasoning for personnel rostering with selected tabu search concepts

In this paper, we investigate the advantages of using case-based reasoning (CBR) to solve personnel rostering problems. Constraints for personnel rostering problems are commonly categorized as either ‘hard’ or ‘soft’. Hard constraints are those that must be satisfied and a roster that violates none of these constraints is considered to be ‘feasible’. Soft constraints are more flexible and are often used to measure roster quality in terms of staff satisfaction. We introduce a method for repairing hard constraint violations using CBR. CBR is an artificial intelligence paradigm whereby new problems are solved by considering the solutions to previous similar problems. A history of hard constraint violations and their corresponding repairs, which is captured from human rostering experts, is stored and used to solve similar violations in new rosters. The soft constraints are not defined explicitly. Their treatment is captured implicitly during the repair of hard constraint violations. The knowledge in the case-base is combined with selected tabu search concepts in a hybrid meta-heuristic algorithm. Experiments on real-world data from a UK hospital are presented. The results show that CBR can guide a meta-heuristic algorithm towards feasible solutions with high staff satisfaction, without the need to explicitly define soft constraint objectives.     

Contemporary OR/MS in strategy development and policy-making: some reflections

It is now widely accepted that strategy-making and policy development require both rational analysis and an ability to work with insights that are sometimes hard to pin down. Can operational research (OR) contribute to this process in which soft and hard are interwoven? Simon's longstanding distinction between substantive and procedural rationality is helpful in addressing this question. Undoubtedly, OR has made major contributions to strategy development, although there has been a marked tendency to argue for even greater use of substantive rationality. In addition, some soft OR methods are also successfully used in strategy development as ways to provide procedural rationality. Add to this the suggestion of Sagasti that metaphor and language are powerful tools in strategizing, then there is a powerful case for the greater use of OR/management science is strategy development and policy-making.