Continuous distribution kinetics for ultrasonic degradation of poly(methyl methacrylate)

Ultrasonic degradation of poly(methyl methacrylate) (PMMA) was carried out in several solvents and some mixtures of solvents. The time evolution of molecular weight distribution (MWD), determined by gel permeation chromatography, is analysed by continuous distribution kinetics. The rate coefficients for polymer degradation are determined for each solvent. The variation of rate coefficients is correlated with the vapour pressure of the solvent, kinematic viscosity of the solution and solvent-polymer interaction parameters. The vapour pressure and the kinematic viscosity of the solution are found to be more critical than other parameters (such as the Huggins and Flory-Huggins constants) in determining the degradation rates. (C) 2001 Society of Chemical Industry.

The extended Enskog operator for simple fluids with continuous potentials: single particle and collective properties

We generalized the Enskog theory originally developed for the hard-sphere fluid to fluids with continuous potentials, such as the Lennard–Jones. We derived the expression for the k and ω dependent transport coefficient matrix which enables us to calculate the transport coefficients for arbitrary length and time scales. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and to the conventional k dependent Enskog theory in the hard-sphere limit. As examples, the self-diffusion of a single atom, the vibrational energy relaxation, and the activated barrier crossing dynamics problem are discussed.

Continued self-similar breakup of drops in viscous continuous phase in agitated vessels

Drop breakup inviscous liquids in agitated vessels occurs in elongational flow around impeller blade edges. The drop size distributions measured over extended periods for impellers of different sizes show that breakup process continues up to 15-20 h, before a steady state is reached. The size distributions evolve in a self-similar way till the steady state is reached. The scaled size distributions vary with impeller size and impeller speed, in contrast with the near universal scaling known for drop breakup in turbulent flows. The steady state size of the largest drop follows inverse scaling with impeller tip velocity. The breadth of the scaled size distributions also shows a monotonic relationship with impeller tip velocity only. (C) 2011 Elsevier Ltd. All rights reserved.

Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.

Computationally Efficient Sub-optimal Mid Course Guidance Using Model Predictive Static Programming (MPSP)

For a homing interceptor, suitable initial condition must be achieved by mid course guidance scheme for its maximum effectiveness. To achieve desired end goal of any mid course guidance scheme, two point boundary value problem must be solved online with all realistic constrain. A Newly developed computationally efficient technique named as MPSP (Model Predictive Static Programming) is utilized in this paper for obtaining suboptimal solution of optimal mid course guidance. Time to go uncertainty is avoided in this formulation by making use of desired position where midcourse guidance terminate and terminal guidance takes over. A suitable approach angle towards desired point also can be specified in this guidance law formulation. This feature makes this law particularly attractive because warhead effectiveness issue can be indirectly solved in mid course phase.

Register Allocation and Optimal Spill code Scheduling in Software Pipelined Loops using 0-1 Integer Linear Programming Formulation

In achieving higher instruction level parallelism, software pipelining increases the register pressure in the loop. The usefulness of the generated schedule may be restricted to cases where the register pressure is less than the available number of registers. Spill instructions need to be introduced otherwise. But scheduling these spill instructions in the compact schedule is a difficult task. Several heuristics have been proposed to schedule spill code. These heuristics may generate more spill code than necessary, and scheduling them may necessitate increasing the initiation interval. We model the problem of register allocation with spill code generation and scheduling in software pipelined loops as a 0-1 integer linear program. The formulation minimizes the increase in initiation interval (II) by optimally placing spill code and simultaneously minimizes the amount of spill code produced. To the best of our knowledge, this is the first integrated formulation for register allocation, optimal spill code generation and scheduling for software pipelined loops. The proposed formulation performs better than the existing heuristics by preventing an increase in II in 11.11% of the loops and generating 18.48% less spill code on average among the loops extracted from Perfect Club and SPEC benchmarks with a moderate increase in compilation time.

On continuous timed automata with input-determined guards

We consider a general class of timed automata parameterized by a set of “input-determined” operators, in a continuous time setting. We show that for any such set of operators, we have a monadic second order logic characterization of the class of timed languages accepted by the corresponding class of automata. Further, we consider natural timed temporal logics based on these operators, and show that they are expressively equivalent to the first-order fragment of the corresponding MSO logics. As a corollary of these general results we obtain an expressive completeness result for the continuous version of MTL.

Minimization of Constraint Violation in Fuzzy Multiobjective Programming

Fuzzy multiobjective programming for a deterministic case involves maximizing the minimum goal satisfaction level among conflicting goals of different stakeholders using Max-min approach. Uncertainty due to randomness in a fuzzy multiobjective programming may be addressed by modifying the constraints using probabilistic inequality (e.g., Chebyshev’s inequality) or by addition of new constraints using statistical moments (e.g., skewness). Such modifications may result in the reduction of the optimal value of the system performance. In the present study, a methodology is developed to allow some violation in the newly added and modified constraints, and then minimizing the violation of those constraints with the objective of maximizing the minimum goal satisfaction level. Fuzzy goal programming is used to solve the multiobjective model. The proposed methodology is demonstrated with an application in the field of Waste Load Allocation (WLA) in a river system.

On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.