Dynamics of Transcendental Entire Maps on Berkovich Affine Line

Dynamics of transcendental entire maps with coefficients in an algebraically closed and complete non-Archimedean field $K$ is studied. It is shown, among other things, that periodic repelling points are dense in Berkovich Julia set, the forward union of any open set which intersects the Julia set is the whole Berkovich affine line, and a multi-connected Fatou component is wandering, in which all points go to infinity under iteration.     

Geodesics in the Space of Measure-Preserving Maps and Plans

We study Brenier’s variational models for incompressible Euler equations. These models give rise to a relaxation of the Arnold distance in the space of measure-preserving maps and, more generally, measure-preserving plans. We analyze the properties of the relaxed distance, we show a close link between the Lagrangian and the Eulerian model, and we derive necessary and sufficient optimality conditions for minimizers. These conditions take into account a modified Lagrangian induced by the pressure field. Moreover, adapting some ideas of Shnirelman, we show that, even for non-deterministic final conditions, generalized flows can be approximated in energy by flows associated to measure-preserving maps.     

On the Dynamics of Bohmian Measures

The present work is devoted to the study of dynamical features of Bohmian measures, recently introduced by the authors. We rigorously prove that for sufficiently smooth wave functions the corresponding Bohmian measure furnishes a distributional solution of a nonlinear Vlasov-type equation. Moreover, we study the associated defect measures appearing in the classical limit. In one space dimension, this yields a new connection between mono-kinetic Wigner and Bohmian measures. In addition, we shall study the dynamics of Bohmian measures associated to so-called semi-classical wave packets. For these type of wave functions, we prove local in-measure convergence of a rescaled sequence of Bohmian trajectories towards the classical Hamiltonian flow on phase space. Finally, we construct an example of wave functions whose limiting Bohmian measure is not mono-kinetic but nevertheless equals the associated Wigner measure.     

航天器计算结构动力学展望

本文通过对结构动力学分析在航天器研制过程中具有极为重要的作用的叙述和未来航天器结构动力学的研究情况的展望,指出结构动力学试验仿真是航天器计算动力学研究发展的趋势,通过对结构功力学试验仿真技术途径和苛刻要求的介绍,提出航天器计算结构动力学前沿研究的几个课题。     

Nonstationary Process: Nonstationary Bifurcation Maps,Evolutionary Dynamics

The study presented in this paper is one of a series of paperspublished by the authors on nonstationary problems. It addresses itselfto the characterization of the types of dynamical responses and theirranges contained in the time flow of the Duffing nonlinear,nonstationary, dissipative, forced oscillator. A new effective method –a Nonstationary Bifurcation Map (EI-Lu map) – has been introduced bythe authors that allows us to do precisely this. This new technique isby far more advantageous than the customary methods in use: the phaseportrait or Poincaré maps. The latter may give inadequate informationbecause of the overlapping dynamical responses contained within rangesof time. The main feature of nonstationary processes is that thenonstationary responses are transient. The phenomena of the transiencyare presented in detail. Significant cases are those when thenonstationary transmission of the signals crosses differentnonstationary bifurcation boundaries. This is significant because mostof dynamical-biological activities occur in the regions between orderand chaos. It characterizes nonstationary dynamical processes. Thepossibility of constructing responses for arbitrary small nonstationaryinputs may be used as nonstationary perturbations, replacing customaryperturbations of integrable Hamiltonians.     

可变结构空间桁架机械臂的动力学建模

可变结构空间桁架机械臂由于具有高承载比和工作空间大等优点,有可能成为下一代空间机械臂的替代形式．本文对可变结构空间桁架机械臂的动力学问题进行建模研究,首先简要介绍了桁架机械臂系统的结构形式,然后采用笛卡尔坐标和变分原理建立系统的动力学模型,其中杆件的转动采用卡尔丹角进行描述,最后通过与ADAMS软件的计算结果对比验证本文所建模型的正确性．     

Order-N Formulation and Dynamics of Multi-Unit Flexible Space Manipulators

As robotic manipulators gain more importance in space operations, it is becoming imperative to understand their distinctive dynamics and control characteristics. With the increasing complexity of space robots, efficient algorithms are now required for their simulation. The present study uses an order-N algorithm, based on the Lagrangian approach and velocity transformations, to simulate the planar dynamics of a novel orbiting manipulator with arbitrary number of slewing and deployable flexible links. The relatively general formulation accounts for interactions between orbital, librational, slewing, deployment, and vibrational degrees of freedom, and thus is applicable to a large class of manipulator systems of contemporary interest. A parametric analysis of the system dynamics is carried out to investigate the effects of initial disturbances, variation of system parameters and maneuver profiles. The study suggests significant coupling between the rigid body motion and structural vibrations. As a result, the system's flexibility can significantly affect the manipulator's performance.     

Protein Folding Dynamics in the Space of Experimentally Measured Variables: Turbulence Phenomena

The process of folding of villin subdomain HP-35 has been studied using the method of molecular dynamics. To characterize protein conformations, two variables are introduced that correspond to the distances between fluorophores in experiments on protein folding with the Förster resonance energy. The simulation results show that the field of probability flows of transitions between protein states is filled with eddies. It has been found that, in contrast to the previously studied cases of hydrodynamic turbulence and turbulence in protein folding in three-dimensional conformational space, the structure functions of the flows of various orders depend linearly on the increment in the conformational space. An explanation of this linear dependence based on the β-model is proposed. It is shown that this dependence is not due to the choice of variables to describe the folding process.     

An Analytical Model of the Dynamics of the Liquefied Vitreous Induced by Saccadic Eye Movements

An analytical model of the dynamics of the vitreous humour induced by saccadic movements within the eye globe is presented. The vitreous is treated as a weakly viscous Newtonian incompressible fluid, an assumption which is appropriate when the vitreous is liquefied or when it is replaced by aqueous humour after surgery. The thin viscous boundary layer generated during a saccadic movement on the side wall is neglected and the flow field is assumed to be irrotational. The vitreous chamber is described as a weakly deformed sphere and this assumption allows a linear treatment of the problem. An analytical solution is found in the form of an expansion of spherical harmonics. Results show that the non-spherical shape of the container generates a flow field characterised by significant velocities and strong three-dimensionality. The model allows the computation of the dynamic pressure on the wall, which may play a role in the generation of retinal detachments. Moreover, results suggest that the irregular shape of the globe may significantly modify tangential stresses on the boundary with respect to the case of motion within a sphere. A simplified analytical solution, for the case of two-dimensional flow within an impulsively rotated container, shows that boundary layer detachment is expected to occur for angles of rotation larger than a threshold value of 15° circa.     

On the Deviation of Computed Permeability Induced by Unresolved Morphological Features of the Pore Space

Transport in Porous Media - This article describes how much the computed absolute permeability is impacted by the slip effect at the fluid/solid interface, in the context of single-phase pore-scale...     

Study on Dynamics, Stability and Control of Multi-Body Flexible Structure System in Functional Space

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Slow Dynamics for the Cahn‐Hilliard Equation in Higher Space Dimensions: The Motion of Bubbles

It is known that the Van der Waals‐Cahn‐Hilliard (W‐C‐H) dynamics can be approximated by a Quasi‐static Stefan problem with surface tension. It turns out that the Stefan problem has a manifold of equilibria equal in dimension to that of the domain Ω: any sphere of fixed radius with interface contained in the domain is an equilibrium (indistinguishable from the point of view of the perimeter functional). We resolve this degeneracy by showing that at the W‐C‐H level this manifold is replaced by a quasi‐invariant stable manifold, on which the typical solution preserves its “bubble” like shape until it reaches the boundary. Moreover, we show that the “bubble” moves superslowly. We also obtain an equation that determines those special spheres that correspond to equilibria at the W‐C‐H level. Our work establishes the phenomenon of superslow motion in higher space dimensions in the class of single interface solutions. (Accepted February 12, 1996)     

Nonuniqueness for the Heat Flow¶of Harmonic Maps on the Disk

We prove that for suitable initial data the heat flow of harmonic maps, from the disk to the sphere, admits infinitely many solutions, characterised by “backward bubbling” at some arbitrarily large time, all having uniformly bounded energy.     

Bounds on the Probability of Failure in Random Vibration

A new method to construct upper and lower bounds for the failure probability of a structure exposed to random excitations is presented. The method is based on an extension of the classical inclusion-exclusion series of Rice where the main idea is to take into consideration only realizations which are in the safe area at a number of previous instants of time. By a numerical example it is demonstrated that this method may lead to rather sharp bounds.     

Lower Semicontinuity for Integral Functionals in the Space of Functions of Bounded Deformation Via Rigidity and Young Measures

We establish a general weak* lower semicontinuity result in the space BD(Ω) of functions of bounded deformation for functionals of the form

Global Wave Maps on Robertson–Walker Spacetimes

We prove the global existence and uniqueness of wave maps onexpanding universes of dimension three or four, that is Robertson–Walkerspacetimes whose inverse radius is integrable with respect to the cosmictime. A result is obtained for small initial data by using the first andsecond energy estimates.     

Regularity of Optimal Maps on the Sphere: the Quadratic Cost and the Reflector Antenna

Building on the results of Ma et al. (in Arch. Rational Mech. Anal. 177(2), 151–183 (2005)), and of the author Loeper (in Acta Math., to appear), we study two problems of optimal transportation on the sphere: the first corresponds to the cost function d ²(x, y), where d(·, ·) is the Riemannian distance of the round sphere; the second corresponds to the cost function ?log |x ? y|, known as the reflector antenna problem. We show that in both cases, the cost-sectional curvature is uniformly positive, and establish the geometrical properties so that the results of Loeper (in Acta Math., to appear) and Ma et al. (in Arch. Rational Mech. Anal. 177(2), 151–183 (2005)) can apply: global smooth solutions exist for arbitrary smooth positive data and optimal maps are Hölder continuous under weak assumptions on the data.     

Space time on the Poincare diagrams

Relations between the experience of space technology and theory of space and time arefound in this paper.A nontraditional approach to the concepts of space and time isintroduced.The approach is based upon the the analysis of the detailed mechanism of radarmeasurement and nonlinear Doppler effects as measured by an astronaut.The Lorentzfactor and four-dimensional interval t~2-x~2/c~2 may be interpreted fromthe point of view of a space technologist.A“geometrical mean”notion for computing timeinterval is introduced parallelly with the usual arithmetic mean formulas,giving resultscomparable with those of special relativity theory.Space time relationships aredemonstrated on the Poincare diagrams.     

Complete Orbits for Twist Maps on the Plane: Extensions and Applications

Twist maps (θ ₁, r ₁) = f (θ, r) on the plane are considered which do not exhibit any kind of periodicity in their dependence on θ. Some general results are obtained which typically yield the existence of infinitely many complete and bounded orbits. Examples that can be treated with this theory include oscillators of the type [(x)\ddot]+V￠(x)=p(t){\ddot{x}+V'(x)=p(t)} under appropriate hypotheses, the bouncing ball system, and the standard map.