Transient behavior of entangled polymers at high shear rates

A new model is presented for describing the time-dependent flow of entangled polymer liquids at high shear rates. The results were obtained by extending the Doi and Edwards theory to include the effect of chain stretching. This nonlinear phenomenon is predicted to occur when the product of the shear rate and longitudinal relaxation time of the polymer exceeds one. If a constant-shear-rate flow is started under these conditions, it is shown that the shear stress and the normal stress are considerably larger than that predicted by the original reptation model. We also find that both of these stresses can pass through maxima before reaching a steady state and that the times required to reach these maxima are constants independent of the shear rate. In general the new model requires the numerical solution of coupled partial differential equations. However, at the highest shear rates where reptative relaxation is no longer important, an analytical solution for the stresses is found. The results obtained here are shown to agree well with experimental data and to be an improvement over a simpler model recently proposed.     

Interrelation between crystallization and liquid crystal formation: A calorimetric and polarizing microscopical study on a monotropic polymer system

The crystallization of the monotropic liquid crystal forming polyether, poly-n-nonyl-4 4′-biphenyl-2-chloroethane, was investigated using DSC calorimetry and polarizing optical microscopy. The principal theme was the nature of crystallization from the nematic liquid crystalline state, which in the monotropic system could be directly compared with the more familiar crystallization from the isotropic melt using one and the same compound. Novel, polarizing optical structures were observed that combine features of both the usual LCPs (fine “grains”) and those of the conventional crystallizeable polymers (spherulites) with differing degrees of prominence of each according to crystallization conditions. The considerations of such structural observations, combined with the calorimetric results and the newly gained information on the kinetics of the crystallization process, reveal an acceleration of the overall crystallization rate at the stage where liquid crystal formation sets in as assessed by calorimetry but not as registered with the polarizing microscope, leading to wider issues regarding the conception of “amorphous crystalline ratio” and its extension to the liquid crystal state. Beyond polymers, the new findings lead to the more general considerations on metastable phases, specifically to their emergence and competition with the phases of ultimate stability. In this respect the present study on a monotropic LCP provides an illustrative example of a more general treatment presented previously. © 1995 John Wiley & Sons, Inc.     

Hierarchical controls in stochastic manufacturing systems with convex costs

This paper presents an extension of earlier research on heirarchical control of stochastic manufacturing systems with linear production costs. A new method is introduced to construct asymptotically optimal open-loop and feedback controls for manufacturing systems in which the rates of machine breakdown and repair are much larger than the rate of fluctuation in demand and rate of discounting of cost. This new approach allows us to carry out an asymptotic analysis on manufacturing systems with convex inventory/backlog and production costs as well as obtain error bound estimates for constructed open loop controls. Under appropriate conditions, an asymptotically optimal Lipschitz feedback control law is obtained.This work was partly supported by the NSERC Grant A4619, URIF, General Motors of Canada, and Manufacturing Research Corporation of Ontario.     

Quasi-reversible multiclass queues with order independent departure rates

This paper introduces a new class of queues which are quasi-reversible and therefore preserve product form distribution when connected in multinode networks. The essential feature leading to the quasi-reversibility of these queues is the fact that the total departure rate in any queue state is independent of the order of the customers in the queue. We call such queues order independent (OI) queues. The OI class includes a significant part of Kelly's class of symmetric queues, although it does not cover the whole class. A distinguishing feature of the OI class is that, among others, it includes the MSCCC and MSHCC queues but not the LCFS queue. This demonstrates a certain generality of the class of OI queues and shows that the quasi-reversibility of the OI queues derives from causes other than symmetry principles. Finally, we examine OI queues where arrivals to the queue are lost when the number of customers in the queue equals an upper bound. We obtain the stationary distribution for the OI loss queue by normalizing the stationary probabilities of the corresponding OI queue without losses. A teletraffic application for the OI loss queue is presented.     

Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates

We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.Supported in part by The Israel Science Foundation, grant no. 372/93-1.     

Sojourn time distribution in a MAP/M/1 processor-sharing queue

This paper considers the sojourn time distribution in a processor-sharing queue with a Markovian arrival process and exponential service times. We show a recursive formula to compute the complementary distribution of the sojourn time in steady state. The formula is simple and numerically feasible, and enables us to control the absolute error in numerical results. Further, we discuss the impact of the arrival process on the sojourn time distribution through some numerical examples.     

Convergence rates in monotone separable stochastic networks

We study bounds on the rate of convergence to the stationary distribution in monotone separable networks which are represented in terms of stochastic recursive sequences. Monotonicity properties of this subclass of Markov chains allow us to formulate conditions in terms of marginal network characteristics. Two particular examples, generalized Jackson networks and multiserver queues, are considered.     

Stabilization by memory effects: Kirchhoff plate versus Euler–Bernoulli plate

In this paper we study the asymptotic behavior of solutions of a dissipative coupled system where we have interactions between a Kirchhoff plate and an Euler–Bernoulli plate. The dissipative mechanism is given by memory terms that act either collaboratively (in both equations) or unilaterally (in only one equation). We show that the solutions of this system decay to zero sometimes exponentially and other times polynomially. We found explicit decay rates that depend on the fractional exponents of the memory in each of the following cases: when the memory only acts in the Kirchhoff equation, or only in the Euler–Bernoulli equation, or in both. We also show that all decay rates found are the best. The results obtained are surprising for the following facts: in the collaborative case, the best decay rates of the system are given by the worst decay rates of the uncoupled equations, and in the unilateral case, we conclude that the memory effects in the Euler–Bernoulli equation dissipate the system more slowly than memory effects in the Kirchhoff equation.     

Atom Tunneling in Chemistry

Quantum mechanical tunneling of atoms is increasingly found to play an important role in many chemical transformations. Experimentally, atom tunneling can be indirectly detected by temperature‐independent rate constants at low temperature or by enhanced kinetic isotope effects. In contrast, the influence of tunneling on the reaction rates can be monitored directly through computational investigations. The tunnel effect, for example, changes reaction paths and branching ratios, enables chemical reactions in an astrochemical environment that would be impossible by thermal transition, and influences biochemical processes.