Dynamic complexity of optimal paths and discount factors for strongly concave problems

We study the relationship between the dynamical complexity of optimal paths and the discount factor in general infinite-horizon discrete-time concave problems. Given a dynamic systemx _t+1=h(x _t ), defined on the state space, we find two discount factors 0 < ^{* **} < 1 having the following properties. For any fixed discount factor 0 < < ^*, the dynamic system is the solution to some concave problem. For any discount factor ^** < < 1, the dynamic system is not the solution to any strongly concave problem. We prove that the upper bound ^** is a decreasing function of the topological entropy of the dynamic system. Different upper bounds are also discussed.This research was partially supported by MURST, National Group on Nonlinear dynamics in Economics and Social Sciences. The author would like to thank two anonymous referees for helpful comments and suggestions.     

Negative-mass instability at nonsymmetrical perturbations

The negative-mass (space-charge) instability is studied within the model of a flat thin electron beam moving along the stationary uniform magnetic field in the case of nonsymmetrical perturbations. It is shown that due to the phenomenon of "phase mixing" of electron bunches the instability increments are small for perturbations with spatial scales smaller than the Larmor diameter.     

Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Effect of surfactants on the stability of thin liquid film flow on a rotating disk

The effect of surfactants on surface instabilities of thin liquid film flow on a rotating disk was studied at different flow rates Q (0.5相似文献   

On the origin of dynamic instability of molecular systems

The vibronic origin of dynamic instability of molecular systems considered earlier, is here given a more complete and rigorous treatment. It is shown that the nonvibronic contribution to the curvature of the adiabatic potential arising due to nuclear displacements under fixed electronic density distribution, is always positive, and hence the only reason for dynamic instability is the pseudo Jahn-Teller effect. For some examples of special interest (planar equilateral NH₃, planar square CH₄ and linear H ₃ ⁺ ) the molecular excited states, responsible for the instability of the ground state, are revealed by means of ab initio calculations.     

Statistical mechanics of a dynamical system based on Conway's game of Life

We study a discrete dynamical system whose evolution is governed by rules similar to those of Conway's game of Life but also include a stochastic element (parametrized by a temperature). Statistical properties that are examined are density as a function of temperature and entropy (suitably defined). A phase transition and a certain thermodynamic constant of the motion are observed.Lady Davis Visiting Scientist at the Technion 1974–75.     

Cl+C2H6→HCl+C2H5反应的准经典轨线研究

用三原子模型的准经典轨线方法研究了Ｃｌ与Ｃ２Ｈ６（ｖ＝０，ｊ）的反应。计算结果表明，反应产物ＨＣｌ的角度分布基本上为各向同性，其振动分布处于基态，与实验结果相一致。对反应轨线的研究表明，该反应为一直接反应，而且反应碰撞在低及高的碰撞参数下的机理不一样，在低碰撞参数下反应碰撞是直接完成的，产物ＨＣｌ以向后散射为主，转动基本上是冷的，但比高碰撞参数下的热。在高的碰撞参数下则生成短寿命的碰撞复合物，产物     

Inherent instabilities of some W5Si3-type binary phases with large electropositive metal atoms: Six examples in the Ba-Pb, Ca-Sn-Mg,Cu,Zn, and La-Ga-Al,Zn systems

A particular pathology of certain W₅Si₃-type A₅B₃ structures (I4/mcm) appears to arise because of unduly close approaches of the A1-type atoms on the cell faces at , 0, () that occur with the larger and more electropositive A and/or in the presence of smaller B atoms. A structure refinement of binary Ba_4.81Pb₃ indicates such a marginal stability in that the Ba atoms in the facial Ba_0.81 chains exhibit an extreme displacement ellipsoid along . Although Ca₅Sn₃ and La₅Ga₃ binaries are unknown in this structure type, five stable ternary derivatives of these have been synthesized via substitution reactions and characterized by single crystal X-ray diffraction means: Ca₄Sn_3.223(4)Mg_0.777, Ca₄Sn₃Cu_1.30(4), Ca_4.66(6)Sn₃Zn_0.704(4), La_4.81(1)Ga_1.38(2)Al_1.62, and La_4.762(5)Ga_1.5(1)Zn_1.5. Only the Ca-Sn-Zn phase exhibits lower symmetry, P4/mbm. The problematic A1 sites exhibit diverse changes in these, whereas the surrounding B2 tetrahedra are largely unaltered. The Ca-Sn results are, respectively: direct Mg/Sn substitution at the Ca1 site; mixed fractional distribution of the smaller Cu at two sites around the A1 position with an unresolved disorder; a pair of apparently independent modes, fractional Ca in the normal position and fractional Zn rectangles thereabout. The two La-Sn phases contain normal Ga,Al (Ga,Zn) tetrahedral chains with pairs of fractional disordered La atoms along , 0, z. Each can be rationalized in terms of a reasonable incommensurate structure. Electronic effects may also be operable.     

聚氯乙烯结构缺陷和热不稳定性之间关系的研究 2.各种结构缺陷含量和热脱氯化氢速率之间的关系

本工作采用溴加成法、酚解法、FTIR法及臭氧裂解法分别测定了五种不饱和蒸气压下聚合的PVC样品(u-PVC)和五种商品PVC样品(s-PVC)的总双键、总不稳定氯、孤立双键和内部双键的含量.通过研究结构缺陷和PVC的平均分子量及脱HCl速率的相互关系,揭示了不饱和总双键值,总不稳定氯和孤立双键含量彼此的相关性是建立在它们分别与1/M_n的相关性基础之上,从而得出了这三种定量值测得的主要都是端基烯丙基氯结构.根据三者对脱HCl速率的良好线性相关性,首次提出了端基烯丙基氯结构在HCl催化作用下异构化成内部烯丙基氯从而成为脱HCl速率主要原因的机理.