Time dependent Schrödinger equation for black hole evaporation: No information loss

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state”. ¹ This was the starting point of the popular “black hole (BH) information paradox”.     

管理中的Nash平衡与Braess悖论现象

本给出了交通规划、经济贸易以及其它管理中的一些Nash平衡和Braess悖论实例，分析了Nash平衡和Braess悖论现象及其本质特征，指出它们在管理工作中具有普遗性和潜在应用性。     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria

Consider a network where two routes are available for users wishing to travel from a source to a destination. On one route (which could be viewed as private transport) service slows as traffic increases. On the other (which could be viewed as public transport) the service frequency increases with demand. The Downs-Thomson paradox occurs when improvements in service produce an overall decline in performance as user equilibria adjust. Using the model proposed by Calvert [10], with a ⋅|M|1 queue corresponding to the private transport route, and a bulk-service infinite server queue modelling the public transport route, we give a complete analysis of this system in the setting of probabilistic routing. We obtain the user equilibria (which are not always unique), and determine their stability.AMS subject classification: 60K30, 90B15, 90B20, 91A10, 91A13This revised version was published online in June 2005 with corrected coverdate     

The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Lorentz-Compton佯谬与一个双赢判决性散射实验设计

通过对“可见光区域是否存在Compton效应”的讨论而进一步深化到经典条件下“光的量子理论能否包含光的经典电磁理论”的实验验证,发现了Lorentz-Compton佯谬,并基于逆Compton散射设计了一个敏感而又可行的双赢判决性散射实验来解决此佯谬。     

Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

Polystyrene prepared by reactive extrusion: kinetics and effect of processing parameters

The conversion and residence time were investigated during the bulk polymerization of styrene in a twin screw extruder. It was found that polymerization mainly occurred in the zone between 400 and 1000 mm along the screw axis in the extruder, corresponding to the residence time of the reactants ranging from 1 to 4 min in the extruder. Furthermore, the processing conditions (feed rate, screw rotation rate) and average molecular weight of the polymer have a great effect on the residence time. Based on dimensionless analysis, a model of the residence time has been built‐up, which has been confirmed by the results of realistic measurements. A kinetic model of the polymerization has also been established under the assumption that the screw extruder can be regarded as an ideal plug flow reactor. Copyright © 2004 John Wiley & Sons, Ltd.     

IMPACT MODEL RESOLUTION ON PAINLEVE’S PARADOX

Painlevé‘s paradox is one of the basic difficulties for solving LCP of dynamic systems subjected to unilateral constraints. A bi-nonlinear parameterized impact model, consistent with dynamic principles and experimental results, is established on the localized and quasi-static impact model theory. Numerical simulations are carried out on the dynamic motion of Painlevé‘s example. The results confirm ““““impact without collision““““ in the inconsistent states of the system. A ““““critical normal force““““ which brings an important effect on the future movement of the system in the indeterminate states is found. After the motion pattern for the impact process is obtained from numerical results, a rule of the velocity‘s jump that incorporates the tangential impact process is deduced by using an approximate impulse theory and the coefficient of restitution defined by Stronge. The results of the jump rule are quite precise if the system rigidity is big enough.