Probabilistic models for stochastic elliptic partial differential equations

Mathematical requirements that the random coefficients of stochastic elliptical partial differential equations must satisfy such that they have unique solutions have been studied extensively. Yet, additional constraints that these coefficients must satisfy to provide realistic representations for physical quantities, referred to as physical requirements, have not been examined systematically.     

A reliable high efficiency atmospheric pressure CO2 laser

A reliably operating high efficiency CO₂ laser is discussed. By adding small amounts of xylene to the laser mixture, a very homogeneous discharge can be sustained in a flowing gas system at pressures slightly above 1 atm. Maximum efficiency is 11.5% and highest energy density is 21 J/1.     

Silicone polymer deposition by CO2 laser induced decomposition of silane in the presence of methyl methacrylate

Infrared multiphoton decomposition of monosilane in the presence of methyl methacrylate results in the formation of gaseous methane, acetylene, butenes and carbon monoxide along with a solid polymer whose chemical mechanism of formation is discussed in line of the poly(dimethylsiloxane) structure inferred from ESCA and IR spectral analysis.     

Lase action on resonant molecular flows through capillaries

New experimental results are reported pointing to the possibility of a laser control of the resonant gases transit through capillaries in the Knudsen and intermediate regimes.     

Safety of structural systems with correlated resistances

In this paper, the reliability of basic structural systems is examined. For elementary chain and ductile parallel systems, the effects of equal correlation between element strengths is established assuming normality. A special case involving a choice between statically determinate and indeterminate structural systems is examined and an ‘optimum’ design approach is presented. In this optimal solution, the correlation structure between elements is controlled so as to maximize the system reliability for given element safety. Reliability analysis is based on a two moment safety index.     

Scheduling on same-speed processors with at most one downtime on each machine

We consider the problem of scheduling a set of independent tasks on multiple same-speed processors with planned shutdown times with the aim of minimizing the makespan. We give an LPT-based algorithm, LPTX, which yields a maximum completion time that is less than or equal to 3/2 the optimal maximum completion time or 3/2 the time that passes from the start of the schedule until the latest end of a downtime. For problems where the optimal schedule ends after the last downtime, and when the downtimes represent fixed jobs, the LPTX maximum completion time is within 3/2 of the optimal maximum completion time. In addition, we show that this result is asymptotically tight for the class of polynomial algorithms assuming that P≠NP. We also show that the bound obtained previously for a similar problem, when no more than half of the machines are shut down at the same time, for the LPT algorithm is asymptotically tight in the class of polynomial algorithms if P≠NP.     

Particles movement and surface quality in PLD/PR systems

A three-dimensional model based on Monte-Carlo and Finite Elements techniques has been used for simulating plume behavior, ‘micron-sized particles’ movement and interaction with obstacles in a Pulsed Laser Deposition with Plasma Reflection (PLD/PR) system. Have been investigated the influences of mass, surface size and emission time on trajectory and film surface quality as well. Droplet and ‘big-size particles’ deposition statistics are presented and a comparison between theoretical and experimental results upon thin film surface quality as well. One can observe that particles mass and surface size have a strong influence on the particles trajectory by affecting the collisions parameters during the entire propagation process. The emission time should influence the particles trajectory by affecting the probability of interaction with other particles. By making a 10,000 particles statistic for a normal distribution of these investigated parameters, we obtain reasonable good results in modeling ‘big-size particles’ tendency to be deposited at lower reflection angles. These results sustain assumption of ‘big particles’ deflection by plume fine particles during the propagation process.     

Alignment Properties of Some Polymeric Layers

Orientational properties of rubbed thin polymer layers with vinylic backbone and different side groups are presented. Some of these polymers lead to the alignment of LC molecules parallel to the rubbing direction whereas other polymers impose a perpendicular orientation. The stability of the obtained alignment as function of the temperature was tested.     

Dynamic Systems with Poisson White Noise

Methods are developed for finding properties of the output of linear and nonlinear dynamic systems to random actions represented by Poisson white noise and filtered Poisson processes. The Poisson white noise can be viewed as a sequence of independent, identically distributed pulses arriving at random times. The filtered Poisson process is the output of a linear filter to Poisson white noise. Three methods are considered for finding output properties. If the input has infrequent or frequent pulses, output properties can be obtained from a Markov model or the assumption that the input is a Gaussian white noise, respectively. Otherwise, a method based on Itô's formula for semimartingales is used to find output properties. Examples are used to illustrate the proposed methods.     

Controllability analysis of quantum systems immersed within an engineered environment

The problem of controllability of quantum systems interacting with an engineered environment, whose dynamics are described by a non-Markovian master equation is addressed. The manipulations of the dynamics is realized with both a laser field and a tailored non-equilibrium, and generally time-dependent, state of the surrounding environment. Lie algebra theory is used to characterize the structures of the reachable state sets and to prove controllability. The theoretical results are supported by examples.