应用力学进展：祝贺郑哲敏先生八十华诞应用力学报告会

    本书为祝贺郑哲敏先生八十华诞的学术报告会的文集，其中收录邀请报告12篇，定向征文58篇。这些论文涉及爆炸力学、岩土力学、冲击力学、材料力学性能、生物力学、物理力学、海洋工程力学、环境流体力学等几大方面，绝大多数为论文作者科研项目的最新成果。

 

 

力学未来15年国际学术讨论会论文集

Cannabis use and involuntary admission may mediate long-term adherence in first-episode psychosis patients: a prospective longitudinal study

Background: This study aimed to examine factors associated with treatment adherence in first-episode psychosis (FEP) patients followed up over 8 years, especially involuntary first admission and stopping cannabis use. Methods: This prospective, longitudinal study of FEP patients collected data on symptoms, adherence, functioning,and substance use. Adherence to treatment was the main outcome variable and was categorized as ‘good’ or ‘bad’. Cannabis use during follow-up was stratified as continued use, stopped use, and never used. Bivariate and logistic regression models identified factors significantly associated with adherence and changes in adherence over the 8-year follow-up period. Results: Of the 98 FEP patients analyzed at baseline, 57.1% had involuntary first admission, 74.4% bad adherence,and 52% cannabis use. Good adherence at baseline was associated with Global Assessment of Functioning score (p = 0.019), Hamilton Depression Rating Scale score (p = 0.017) and voluntary admission (p < 0.001). Adherence patterns over 8 years included: 43.4% patients always bad, 26.1% always good, 25% improved from bad to good. Among the improved adherence group, 95.7% had involuntary first admission and 38.9% stopped cannabis use. In the subgroup of patients with bad adherence at baseline, involuntary first admission and quitting cannabis use during follow up were associated with improved adherence. Conclusions: The long-term association between treatment adherence and type of first admission and cannabis use in FEP patients suggest targets for intervention to improve clinical outcomes.

水中悬浮隧道管段锚索耦合模型涡激振动的研究

为了分析水中悬浮隧道在水流作用下的动力响应,通过Hamilton 原理推导得到了悬浮隧道 管段和锚索的运动控制方程;同时引入锚索横向和轴向变形之间的耦合作用,建立了悬浮隧道的动 力响应模型,并考虑锚索发生顺流向涡激振动的影响,在时间域内求解运动控制方程。计算结果表 明:若锚索长细比很大,则锚索横向和轴向变形之间的耦合作用不可忽略;锚索发生顺流向涡激振 动时,结构的横荡和横摇响应幅值增大,但垂荡响应基本不受其影响。

深水张力腿平台与系泊系统的耦合动力响应

把张力腿简化为非线性梁结构,运用Hamilton原理,推导出平面情况下平台本体与张力腿系泊系统的耦合运动方程及边界条件;分析了不同流场条件下,两种不同张力腿模型(非线性梁和无质量弹簧模型)对平台动力响应预测结果的影响;分析结果表明:随着流场条件的不同,采用不同的张力腿简化模型得到的平台动力响应预测结果具有明显的不同.阐明了两种模型所得结果产生差异的原因.

Invariants, Lie-Bäcklund operators and Bäcklund transformations

This thesis is mainly concerned with the application of groups of transformations to differential equations and in particular with the connection between the group structure of a given equation and the existence of exact solutions and conservation laws. In this respect the Lie-Bäcklund groups of tangent transformations, particular cases of which are the Lie tangent and the Lie point groups, are extensively used.

In Chapter I we first review the classical results of Lie, Bäcklund and Bianchi as well as the more recent ones due mainly to Ovsjannikov. We then concentrate on the Lie-Bäcklund groups (or more precisely on the corresponding Lie-Bäcklund operators), as introduced by Ibragimov and Anderson, and prove some lemmas about them which are useful for the following chapters. Finally we introduce the concept of a conditionally admissible operator (as opposed to an admissible one) and show how this can be used to generate exact solutions.

In Chapter II we establish the group nature of all separable solutions and conserved quantities in classical mechanics by analyzing the group structure of the Hamilton-Jacobi equation. It is shown that consideration of only Lie point groups is insufficient. For this purpose a special type of Lie-Bäcklund groups, those equivalent to Lie tangent groups, is used. It is also shown how these generalized groups induce Lie point groups on Hamilton's equations. The generalization of the above results to any first order equation, where the dependent variable does not appear explicitly, is obvious. In the second part of this chapter we investigate admissible operators (or equivalently constants of motion) of the Hamilton-Jacobi equation with polynornial dependence on the momenta. The form of the most general constant of motion linear, quadratic and cubic in the momenta is explicitly found. Emphasis is given to the quadratic case, where the particular case of a fixed (say zero) energy state is also considered; it is shown that in the latter case additional symmetries may appear. Finally, some potentials of physical interest admitting higher symmetries are considered. These include potentials due to two centers and limiting cases thereof. The most general two-center potential admitting a quadratic constant of motion is obtained, as well as the corresponding invariant. Also some new cubic invariants are found.

In Chapter III we first establish the group nature of all separable solutions of any linear, homogeneous equation. We then concentrate on the Schrodinger equation and look for an algorithm which generates a quantum invariant from a classical one. The problem of an isomorphism between functions in classical observables and quantum observables is studied concretely and constructively. For functions at most quadratic in the momenta an isomorphism is possible which agrees with Weyl' s transform and which takes invariants into invariants. It is not possible to extend the isomorphism indefinitely. The requirement that an invariant goes into an invariant may necessitate variants of Weyl' s transform. This is illustrated for the case of cubic invariants. Finally, the case of a specific value of energy is considered; in this case Weyl's transform does not yield an isomorphism even for the quadratic case. However, for this case a correspondence mapping a classical invariant to a quantum orie is explicitly found.

Chapters IV and V are concerned with the general group structure of evolution equations. In Chapter IV we establish a one to one correspondence between admissible Lie-Bäcklund operators of evolution equations (derivable from a variational principle) and conservation laws of these equations. This correspondence takes the form of a simple algorithm.

In Chapter V we first establish the group nature of all Bäcklund transformations (BT) by proving that any solution generated by a BT is invariant under the action of some conditionally admissible operator. We then use an algorithm based on invariance criteria to rederive many known BT and to derive some new ones. Finally, we propose a generalization of BT which, among other advantages, clarifies the connection between the wave-train solution and a BT in the sense that, a BT may be thought of as a variation of parameters of some. special case of the wave-train solution (usually the solitary wave one). Some open problems are indicated.

Most of the material of Chapters II and III is contained in [I], [II], [III] and [IV] and the first part of Chapter V in [V].

Knowledge modelling in aerospace design

This paper addresses the need for computer support in aerospace design. A review of current design methodologies and computer support tools is presented and the need for further support in aerospace design, particularly in the early formative stages of the design process, is discussed. A parameter-based model of design, founded on the assumption that a design process can be constructed from a predefined set of tasks, is proposed for aerospace design. This is supported by knowledge of possible tasks in which the confidence in key design parameters is used as a basis for identifying, or signposting, the next task. A prototype implementation of the signposting model, for use in the design of helicopter rotor blades, is described and results from trials of the tool are presented. Further areas of research are discussed

An Alternative View of the US Price-Dividend Ratio Dynamics

As a necessary condition for the validity of the present value model, the price-dividend ratio must be stationary. However, significant market episodes seem to provide evidence of prices significantly drifting apart from dividends while other episodes show prices anchoring back to dividends. This paper investigates the stationarity of this ratio in the context of a Markov- switching model à la Hamilton (1989) where an asymmetric speed of adjustment towards a unique attractor is introduced. A three-regime model displays the best regime identification and reveals that the first part of the 90’s boom (1985-1995) and the post-war period are characterized by a stationary state featuring a slow reverting process to a relatively high attractor. Interestingly, the latter part of the 90’s boom (1996-2000), characterized by a growing price-dividend ratio, is entirely attributed to a stationary regime featuring a highly reverting process to the attractor. Finally, the post-Lehman Brothers episode of the subprime crisis can be classified into a temporary nonstationary regime.

Design support for turbomachinery

From the steam turbines which provide most of our electricity to the jet engines which have shrunk our World, turbomachines undoubtedly play a major role in life today. Competition in the turbomachinery industry is fiercely strong [Wisler, 1998], hence good aerodynamic design is vital. However, with efficiency levels already close to their theoretical maxima, companies are increasingly looking to reduce costs and increase reliability through improved design practice. Computational Fluid Dynamics (CFD) can make a strong contribution to assisting this process as it has the potential to increase performance while reducing cost. The situation is, however, complicated by an ever decreasing number of engineers with sufficient design experience to reap the full benefits offered by CFD. With the large risks involved, novice designers of today are increasingly confined to refining old designs rather than gaining experience, like their forebears, through 'clean sheet' exercises. Hence it is desirable to capture the knowledge and experience of older designers, before it is lost, to assist the engineers of tomorrow. It is therefore the aim of this project to produce a design support tool which will not only store the appropriate CFD codes, but also provide a dynamic signpost (based on elicited knowledge and experience) to advise the engineer in their use. The signposting methodology developed for the aerospace industry [Clarkson and Hamilton, 1997] will provide the basic framework for the tool. This paper reviews current turbomachinery design practice (including an examination of the relevant CFD) in order to establish the important issues which a support tool must address. Current design support methodologies and their propriety are then reviewed, followed by a detailed description of the signposting concept. It then sets out a clear statement of the objectives for the research and the methods proposed to meet them. The paper concludes with a timetable of the work.

Efficient methods for stochastic optimal control

The Hamilton Jacobi Bellman (HJB) equation is central to stochastic optimal control (SOC) theory, yielding the optimal solution to general problems specified by known dynamics and a specified cost functional. Given the assumption of quadratic cost on the control input, it is well known that the HJB reduces to a particular partial differential equation (PDE). While powerful, this reduction is not commonly used as the PDE is of second order, is nonlinear, and examples exist where the problem may not have a solution in a classical sense. Furthermore, each state of the system appears as another dimension of the PDE, giving rise to the curse of dimensionality. Since the number of degrees of freedom required to solve the optimal control problem grows exponentially with dimension, the problem becomes intractable for systems with all but modest dimension.

In the last decade researchers have found that under certain, fairly non-restrictive structural assumptions, the HJB may be transformed into a linear PDE, with an interesting analogue in the discretized domain of Markov Decision Processes (MDP). The work presented in this thesis uses the linearity of this particular form of the HJB PDE to push the computational boundaries of stochastic optimal control.

This is done by crafting together previously disjoint lines of research in computation. The first of these is the use of Sum of Squares (SOS) techniques for synthesis of control policies. A candidate polynomial with variable coefficients is proposed as the solution to the stochastic optimal control problem. An SOS relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function. It is shown that these results extend to arbitrary parabolic and elliptic PDEs, yielding a novel method for Uncertainty Quantification (UQ) of systems governed by partial differential constraints. Domain decomposition techniques are also made available, allowing for such problems to be solved via parallelization and low-order polynomials.

The optimization-based SOS technique is then contrasted with the Separated Representation (SR) approach from the applied mathematics community. The technique allows for systems of equations to be solved through a low-rank decomposition that results in algorithms that scale linearly with dimensionality. Its application in stochastic optimal control allows for previously uncomputable problems to be solved quickly, scaling to such complex systems as the Quadcopter and VTOL aircraft. This technique may be combined with the SOS approach, yielding not only a numerical technique, but also an analytical one that allows for entirely new classes of systems to be studied and for stability properties to be guaranteed.

The analysis of the linear HJB is completed by the study of its implications in application. It is shown that the HJB and a popular technique in robotics, the use of navigation functions, sit on opposite ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. Analytical solutions to the HJB in these settings are available in simplified domains, yielding guidance towards optimality for approximation schemes. Finally, the use of HJB equations in temporal multi-task planning problems is investigated. It is demonstrated that such problems are reducible to a sequence of SOC problems linked via boundary conditions. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.

Modelando evolução por endossimbiose

Nesta dissertação é apresentada uma modelagem analítica para o processo evolucionário formulado pela Teoria da Evolução por Endossimbiose representado através de uma sucessão de estágios envolvendo diferentes interações ecológicas e metábolicas entre populações de bactérias considerando tanto a dinâmica populacional como os processos produtivos dessas populações. Para tal abordagem é feito uso do sistema de equações diferenciais conhecido como sistema de Volterra-Hamilton bem como de determinados conceitos geométricos envolvendo a Teoria KCC e a Geometria Projetiva. Os principais cálculos foram realizados pelo pacote de programação algébrica FINSLER, aplicado sobre o MAPLE.