Sensitivity of nucleation phenomena on range of interaction potential

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.     

Homogeneous operators and projective representations of the Möbius group: A survey

This paper surveys the existing literature on homogeneous operators and their relationships with projective representations ofPS L(2, ℝ) and other Lie groups. It also includes a list of open problems in this area.     

Supersymmetry and the ladder operator technique in quantum mechanics: The radial Schrödinger equation

Using the ladder operator technique, a construction of the supersymmetric Hamiltonian is proposed. We show that the accidental degeneracies associated with the Coulomb and isotropic oscillator problems may be attributed to the existence of a supersymmetry of the Hamiltonians.     

Experimental investigation of real-time scheduling in flexible manufacturing systems

This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.     

2-satisfiability and diagnosing faulty processors in massively parallel computing systems

A fault diagnosis model for multiprocessor computers is proposed. Under normal operating mode each processor executes its own data. When an error occurs, the system is switched to the diagnostic mode. Previous input data for each processor is shifted to a different unit, to obtain a set of comparison results. We show that analysis of the test data to diagnose or locate faulty processors is equivalent to a 2-satisfiability problem. Under the assumption that discrepancy in a comparison result occurs if and only if at least one of the processors (being compared) is faulty, we prove that all the faulty processors can be diagnosed in O(n²) time, where n denotes the number of processors in the system.     

Stochastic Games with Average Payoff Criterion

We study two-person stochastic games on a Polish state and compact action spaces and with average payoff criterion under a certain ergodicity condition. For the zero-sum game we establish the existence of a value and stationary optimal strategies for both players. For the nonzero-sum case the existence of Nash equilibrium in stationary strategies is established under certain separability conditions. Accepted 9 January 1997     

Solutions of anomalous Ward identities in a QCD framework. II

TheSU(3) _F breaking effects are considered to fit the set of anomalous Ward identities in QCD. The solutions are then analysed and compared with a recent work that also deals with such identities.     

Anomalous dielectric relaxation of water molecules at the surface of an aqueous micelle

Dielectric relaxation of aqueous solutions of micelles, proteins, and many complex systems shows an anomalous dispersion at frequencies intermediate between those corresponding to the rotational motion of bulk water and that of the organized assembly or macromolecule. The precise origin of this anomalous dispersion is not well-understood. In this work we employ large scale atomistic molecular dynamics simulations to investigate the dielectric relaxation (DR) of water molecules in an aqueous micellar solution of cesium pentadecafluorooctanoate. The simulations clearly show the presence of a slow component in the moment-moment time correlation function [PhiMW(t)] of water molecules, with a time constant of about 40 ps, in contrast to only 9 ps for bulk water. Interestingly, the orientational time correlation function [Cmu(t)] of individual water molecules at the surface exhibits a component with a time constant of about 19 ps. We show that these two time constants can be related by the well-known micro-macrorelations of statistical mechanics. In addition, the reorientation of surface water molecules exhibits a very slow component that decays with a time constant of about 500 ps. An analysis of hydrogen bond lifetime and of the rotational relaxation in the coordinate frame fixed on the micellar body seems to suggest that the 500 ps component owes its origin to the existence of an extended hydrogen bond network of water molecules at the surface. However, this ultraslow component is not found in the total moment-moment time correlation function of water molecules in the solution. The slow DR of hydration water is found to be well correlated with the slow solvation dynamics of cesium ions at the water-micelle interface.     

Kinetics of densification of powder compacts during the initial stage of sintering with constant rates of heating. A thermal analysis approach. Part I. Theoretical considerations

Densification of powder compacts during sintering (initial stage) under constant heating rate has been studied and methods of analysing the densification kinetic data have been suggested. p]Green compacts can broadly be envisaged to consists of two phases, viz. porosity and solid material. Annihilation of the pores causes densification of the compacts during sintering. So, the kinetics of the initial stage of densification may very well be represented by a densification parameter (α),where

Here, v_s and v_p,respectively, denote the pore volumes of the sintered and the green compact. Continuous and in situ recording of the linear shrinkage (ΔL) of the compacts during the sintering may be done with a dilatometer and using this value of ΔL,the value of α at any temperature (T) may be calculated.These kinetic data (α vs. T)may then be subjected to analysis using the well-known methods of thermal analysis, and the so-called “derived activation energy (E)” of densification may be evaluated therefrom. The exact form of g(α)—governing rate equation—is ascertained by a trial-and-error method.These methods were used to analyse the densification kinetic data of haematite, copper and silver powders (with particles of irregular shapes and sizes). The results of such analyses will appear on other parts of this paper.