Thermally driven acoustic oscillations,part IV: Tubes with variable cross-section

Summary The problem of thermally driven acoustic oscillations is treated for tubes with variable cross-section, with particular emphasis on the possible reduction of the necessary temperature ratio for excitation. Tubes with optimal conditions in the vicinity of the temperature jump, and with big cross-sections in parts with constant temperature are found to give the best performance in this respect. Included in the family of devices which were treated is the classical Sondhauss-tube. Experiments which give a striking confirmation of the theory are reported.

---

Zusammenfassung Das Problem der thermisch getriebenen akustischen Schwingungen wird für Rohre mit veränderlichem Querschnitt behandelt, mit besonderer Berücksichtigung der Frage der Reduktion des für die Anfachung nötigen Temperaturverhältnisses. Rohre, die optimale Radien in der Umgebung des Temperatursprunges haben, und möglichst grosse Querschnitte in Teilen mit konstanter Temperatur aufweisen, erweisen sich am besten in dieser Hinsicht. In der Familier der untersuchten Anordnungen its das klassische Sondhauss-Rohr miteinbezogen. Experimente gaben überzeugende Bestätigung für die verwendeten Theorien.

     

An optimization technique for the transient response of passively stable satellites

The principal result of this paper is an analytical technique for optimizing the transient response characteristics for a class of passively stabilized satellites in the presence of practical design parameter constraints. The technique developed is directed at linearized models and is treated in detail only for quartic characteristic equations. The results, even for the special case treated, are sufficiently broad to provide a generalization of some techniques which have appeared in the literature. Briefly, it is shown that certain coalescent root configuration represent a hierarchy of transient optima, and conditions are derived which give the optimum transient characteristics as functions of the available variable system parameters.     

Analysis of two stationary magnetohydrodynamics systems of equations including Joule heating

We study the coupling of the equations of steady-state magnetohydrodynamics (MHD) with the heat equation when the buoyancy effects due to temperature differences in the flow as well as Joule effect and viscous heating are (all) taken into account. Two models for the gravity force are considered: the first one is the well-known Boussinesq approximation; in the second one density is assumed to be constant except in the gravity force, where it is assumed to be a non-increasing function of the temperature. The equations are posed in a bounded three-dimensional domain. We give existence results of weak solutions to both models under certain conditions on the data. We also give some uniqueness results.     

Tanker chartering: A system dynamics case study

This paper describes a practical system dynamics case study. It attempts to show how this OR technique can be applied to a practical problem and the results which it can, and cannot, be expected to give.Although the paper is based on a real project, the details have been altered for commercial secrecy, and the emphasis in this paper is, for the same reason, rather different from that of the original work. The aim of the paper is, therefore, to give enough of a “real” background to contrast the industrial application of SD with some of its other applications.For the sake of reasonable brevity, the emphasis in this paper is on the managerial viewpoint, and the extent to which an SD model provides helpful answers to managerial questions. The model paper is described only briefly as full details, and a model listing are given by Coyle. Some other aspects of the system are treated by Winch.     

A reaction-diffusion model for autocatalytic polymerization: II. The initial value problem

An initial-boundary value problem arising from a simple modelfor radical chain polymerization is discussed in detail. Generalproperties of the solution are derived first and it is shownthat a moving interface develops. This separates a region wherethe polymer is sufficiently concentrated for it to be immobilefrom one where it is still free to diffuse. An asymptotic analysisis performed in this latter region, where it is shown that apermanent-form travelling wave (treated in Part I) developsin the long time structure and that this wave travels with itsminimum possible speed. Numerical results for the full initial-boundaryvalue problem are presented which confirm the asymptotic theoryand give results in regions not accessible to this analysis.     

Generalized fourier transform and its applications

We consider the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space. We give a definition of this operator and establish its basic properties. Special attention is paid to cases in which the range of the generalized Fourier transform coincides with a weighted space of entire functions. The results are applied to finding the orders and types of operators in various spaces.     

Korobov Spaces with Respect to Digital Orthonormal Bases

 For an orthonormal basis (ONB) of we define classes of functions according to the order of decay of the Fourier coefficients with respect to the considered ONB . The rate is expressed in the real parameter α. We investigate the following problem: What is the order of decay, if any, when we consider with respect to another ONB ? If the function is expressable as an absolutely convergent Fourier series with respect to , we give bounds for the new order of decay, which we call . Special attention is given to digital orthonormal bases (dONBs) of which the Walsh and Haar systems are examples treated in the present paper. Bounding intervals and in several cases explicit values for are given for the case of dONBs. An application to quasi-Monte Carlo numerical integration is mentioned.     

Shock-induced ignition of thermally sensitive explosives

The process of planar detonation ignition, induced by a constant-velocitypiston or equivalently by a shock reflected from a stationarywall, is investigated using high-resolution one-dimensionalnumerical simulations. The standard one-step model with Arrheniuskinetics, which models thermally sensitive explosives, is employed.Emphasis is on comparing and contrasting the results of thefinite activation temperature simulations with high activationtemperature asymptotic predictions and previous simulations.During the induction phase, it is shown that the asymptoticresults give qualitatively good predictions. However, for parametersrepresentative of gaseous explosives, subsequent to thermalrunaway at the piston and the formation of a reaction wave,the high activation temperature asymptotic theory is qualitativelyincorrect for moderately high activation temperatures. It isshown that the results are very sensitive to the value of theactivation temperature, especially the distance from the pistonat which a secondary shock forms and the degree of unsteadinessin the reaction wave which moves away from the piston. The dependenceof the ignition evolution on the other parameters (initial shockMach number, heat of reaction and polytropic index) is alsoinvestigated. It is shown that qualitative predictions regardingthe dependence of the ignition evolution on each of the parameterscan be elucidated from finite activation temperature homogeneousexplosion calculations together with the high activation temperatureasymptotic shock ignition results. It is found that for sufficientlystrong initiating shocks the ignition evolution is qualitativelydifferent from cases studied previously in that no secondaryshock forms. For a high polytropic index, corresponding to asimple equation of state model for condensed phase explosives,the results are in much better qualitative agreement with theasymptotic theory.     

Minimax Methods for Open-Loop Equilibra in $N$-Person Differential Games Part II: Duality and Penalty Theory

The equilibrium strategy for $N$-person differential games can be obtained from a min-max problem subject to differential constraints. The differential constraints are treated here by the duality and penalty methods. We first formulate the duality theory. This involves the introduction of $N+1$ Lagrange multipliers: one for each player and one commonly shared by all players. The primal min-max problem thus results in a dual problem, which is a max-min problem with no differential constraints. We develop the penalty theory by penalizing $N+1$ differential constraints. We give a convergence proof which generalizes a theorem due to B.T. Polyak.     

Remarks on Nonlinear Schrödinger Equations with Harmonic Potential

Bose-Einstein condensation is usually modeled by nonlinear Schrödinger equations with harmonic potential. We study the Cauchy problem for these equations. We show that the local problem can be treated as in the case with no potential. For the global problem, we establish an evolution law, which is the analogue of the pseudo-conformal conservation law for the nonlinear Schrödinger equation. With this evolution law, we give wave collapse criteria, as well as an upper bound for the blow up time. Taking the physical scales into account, we finally give a lower bound for the breaking time. This study relies on two explicit operators, suited to nonlinear Schrödinger equations with harmonic potential, already known in the linear setting.     

Indecomposable Representations of the Superalgebra B(1,2)

Finite-dimensional indecomposable superbimodules over the superalgebra B(1,2) are treated. We propound a method for constructing indecomposable alternative superbimodules over B(1,2) containing a given socle (such can be presented by any irreducible module over B(1,2)). The method is based on adding on the Jordan basis. Also, for the characteristic 3 case, we give examples of Jordan indecomposable superbimodules which are not alternative.     

DEPENDENCE OF QUALITATIVE BEHAVIOR OF THE NUMERICAL SOLUTIONS ON THE IGNITION TEMPERATURE FOR A COMBUSTION MODEL

We study the dependence of qualitative behavior of the numerical solutions （obtained by a projective and upwind finite difference scheme） on the ignition temperature for a combustion model problem with general initial condition. Convergence to weak solution is proved under the Courant-Friedrichs-Lewy condition. Some condition on the ignition temperature is given to guarantee the solution containing a strong detonation wave or a weak detonation wave. Finally, we give some numerical examples which show that a strong detonation wave can be transformed to a weak detonation wave under some well-chosen ignition temperature.     

Average cost Markov decision processes under the hypothesis of Doeblin

Average cost Markov decision processes (MDPs) with compact state and action spaces and bounded lower semicontinuous cost functions are considered. Kurano [7] has treated the general case in which several ergodic classes and a transient set are permitted for the Markov process induced by any randomized stationary policy under the hypothesis of Doeblin and showed the existence of a minimum pair of state and policy. This paper considers the same case as that discussed in Kurano [7] and proves some new results which give the existence theorem of an optimal stationary policy under some reasonable conditions.     

Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

Vibrations of a beam can be described as an Euler-Bernoulli beam,or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.     

The Shapley value for cooperative games under precedence constraints

Cooperative games are considered where only those coalitions of players are feasible that respect a given precedence structure on the set of players. Strengthening the classical symmetry axiom, we obtain three axioms that give rise to a unique Shapley value in this model. The Shapley value is seen to reflect the expected marginal contribution of a player to a feasible random coalition, which allows us to evaluate the Shapley value nondeterministically. We show that every exact algorithm for the Shapley value requires an exponential number of operations already in the classical case and that even restriction to simple games is #P-hard in general. Furthermore, we outline how the multi-choice cooperative games of Hsiao and Raghavan can be treated in our context, which leads to a Shapley value that does not depend on pre-assigned weights. Finally, the relationship between the Shapley value and the permission value of Gilles, Owen and van den Brink is discussed. Both refer to formally similar models of cooperative games but reflect complementary interpretations of the precedence constraints and thus give rise to fundamentally different solution concepts.     

等离子体反应器流场的数值模拟

本文采用颗粒轨道模型对等离子体反应器进行数值模拟.数值格式用SIMPLER法.湍流模型用简单的次网格模型.计算结果给出速度场、温度场及颗粒轨道,对工程设计和工艺过程参数控制有参考价值.     

Korobov Spaces with Respect to Digital Orthonormal Bases

 For an orthonormal basis (ONB) of we define classes of functions according to the order of decay of the Fourier coefficients with respect to the considered ONB . The rate is expressed in the real parameter α. We investigate the following problem: What is the order of decay, if any, when we consider with respect to another ONB ? If the function is expressable as an absolutely convergent Fourier series with respect to , we give bounds for the new order of decay, which we call . Special attention is given to digital orthonormal bases (dONBs) of which the Walsh and Haar systems are examples treated in the present paper. Bounding intervals and in several cases explicit values for are given for the case of dONBs. An application to quasi-Monte Carlo numerical integration is mentioned. (Received 21 February 2000; in revised form 19 October 2000)     

Thermal analysis of a longitudinal trapezoidal fin with temperature-dependent thermal conductivity and heat transfer coefficient

A homotopy analysis method (HAM) is used to develop analytical solution for the thermal performance of a straight fin of trapezoidal profile when both the thermal conductivity and the heat transfer coefficient are temperature dependent. Results are presented for the temperature distribution, heat transfer rate, and fin efficiency for a range of values of parameters appearing in the mathematical model. Since the HAM algorithm contains a parameter that controls the convergence and accuracy of the solution, its results can be verified internally by calculating the residual error. The HAM results were also found to be accurate to at least three places of decimal compared with the direct numerical solution of the mathematical model generated using a fourth–fifth-order Runge–Kutta–Fehlberg method. The HAM solution appears in terms of algebraic expressions which are not only easy to compute but also give highly accurate results covering a wide range of values of the parameters rather than the small values dictated by the perturbation solution.     

Fully discrete approximation of a velocity and temperature tracking problem for the Boussinesq equations with piecewise distributed controls

In this article, we study the dynamics of a fully discrete piecewise optimal distributed control problem for the Boussinesq equations which models a velocity tracking over time coupled to thermal dynamics. We prove that the rates of velocity and‐ temperature tracking are exponential. We also give some computational results which reinforces the theoretical results derived. Copyright © 2005 John Wiley & Sons, Ltd.