Approximate Controllability Of Semilinear Systems Using Integral Contractors

In this article, a non-autonomous (time-varying) semilinear system is considered and its approximate controllability is investigated. The notion of 'bounded integral contractor', introduced by Altman, has been exploited to obtain sufficient conditions for approximate controllability. This condition is weaker than Lipschitz condition. The main theorems of Naito [11, 12] are obtained as corollaries of our main results. An example is also given to show how our results weaken the conditions assumed by Sukavanam[17].

Approximate solution of u'=-A2u using a relation between exp(-tA2) and exp(itA)

Let A be a positive definite operator in a Hilbert space and consider the initial value problem for u(t) = -A(2)u. Using a representation of the semigroup exp(-A(2)t) in terms of the group exp(iAt) we express u in terms of the solution of the standard heat equation w(t) = W-yy, with initial values v solving the initial value problem for v(y) = iAv. This representation is used to construct a method for approximating u in terms of approximations of v. In the case that A is a 2(nd) order elliptic operator the method is combined with finite elements in the spatial variable and then reduces the solution of the 4(th) order equation for u to that of the 2(nd) order equation for v, followed by the solution of the heat equation in one space variable.

A probabilistic constrained nonlinear optimization framework to optimize RED parameters

The random early detection (RED) technique has seen a lot of research over the years. However, the functional relationship between RED performance and its parameters viz,, queue weight (omega(q)), marking probability (max(p)), minimum threshold (min(th)) and maximum threshold (max(th)) is not analytically availa ble. In this paper, we formulate a probabilistic constrained optimization problem by assuming a nonlinear relationship between the RED average queue length and its parameters. This problem involves all the RED parameters as the variables of the optimization problem. We use the barrier and the penalty function approaches for its Solution. However (as above), the exact functional relationship between the barrier and penalty objective functions and the optimization variable is not known, but noisy samples of these are available for different parameter values. Thus, for obtaining the gradient and Hessian of the objective, we use certain recently developed simultaneous perturbation stochastic approximation (SPSA) based estimates of these. We propose two four-timescale stochastic approximation algorithms based oil certain modified second-order SPSA updates for finding the optimum RED parameters. We present the results of detailed simulation experiments conducted over different network topologies and network/traffic conditions/settings, comparing the performance of Our algorithms with variants of RED and a few other well known adaptive queue management (AQM) techniques discussed in the literature.

A pseudo-dynamical systems approach to a class of inverse problems in engineering

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Theoretical Optimization of Metal Para-Normal Silicon Schottky-Barrier Solar-Cell

The theoretical optimization of the design parametersN A ,N D andW P has been done for efficient operation of Au-p-n Si solar cell including thermionic field emission, dependence of lifetime and mobility on impurity concentrations, dependence of absorption coefficient on wavelength, variation of barrier height and hence the optimum thickness ofp region with illumination. The optimized design parametersN D =5×1020 m−3,N A =3×1024 m−3 andW P =11.8 nm yield efficiencyη=17.1% (AM0) andη=19.6% (AM1). These are reduced to 14.9% and 17.1% respectively if the metal layer series resistance and transmittance with ZnS antireflection coating are included. A practical value ofW P =97.0 nm gives an efficiency of 12.2% (AM1).

Architecture Optimization of Aerospace Computing Systems

Simultaneous consideration of both performance and reliability issues is important in the choice of computer architectures for real-time aerospace applications. One of the requirements for such a fault-tolerant computer system is the characteristic of graceful degradation. A shared and replicated resources computing system represents such an architecture. In this paper, a combinatorial model is used for the evaluation of the instruction execution rate of a degradable, replicated resources computing system such as a modular multiprocessor system. Next, a method is presented to evaluate the computation reliability of such a system utilizing a reliability graph model and the instruction execution rate. Finally, this computation reliability measure, which simultaneously describes both performance and reliability, is applied as a constraint in an architecture optimization model for such computing systems. Index Terms-Architecture optimization, computation

Steady state optimization of an ammonia reactor

A hybrid simulation technique for identification and steady state optimization of a tubular reactor used in ammonia synthesis is presented. The parameter identification program finds the catalyst activity factor and certain heat transfer coefficients that minimize the sum of squares of deviation from simulated and actual temperature measurements obtained from an operating plant. The optimization program finds the values of three flows to the reactor to maximize the ammonia yield using the estimated parameter values. Powell's direct method of optimization is used in both cases. The results obtained here are compared with the plant data.

Analytical studies of gain optimization in CO2-N2 gasdynamic lasers employing two-dimensional wedge nozzles

An analytical method has been proposed to optimise the small-signaloptical gain of CO2-N2 gasdynamic lasers (gdl) employing two-dimensional (2D) wedge nozzles. Following our earlier work the equations governing the steady, inviscid, quasi-one-dimensional flow in the wedge nozzle of thegdl are reduced to a universal form so that their solutions depend on a single unifying parameter. These equations are solved numerically to obtain similar solutions for the various flow quantities, which variables are subsequently used to optimize the small-signal-gain. The corresponding optimum values like reservoir pressure and temperature and 2D nozzle area ratio also have been predicted and graphed for a wide range of laser gas compositions, with either H2O or He as the catalyst. A large number of graphs are presented which may be used to obtain the optimum values of small signal gain for a wide range of laser compositions without further computations.

Ant Colony Optimization Algorithms for Shortest Path Problems

We propose four variants of recently proposed multi-timescale algorithm in [1] for ant colony optimization and study their application on a multi-stage shortest path problem. We study the performance of the various algorithms in this framework. We observe, that one of the variants consistently outperforms the algorithm [1].

Numerical simulation of conductive particle behaviour at the surface of a plate electrode affected by a DC corona field

The electric field in certain electrostatic devices can be modeled by a grounded plate electrode affected by a corona discharge generated by a series of parallel wires connected to a DC high-voltage supply. The system of differential equations that describe the behaviour (i.e., charging and motion) of the conductive particle in such an electric field has been numerically solved, using several simplifying assumptions. Thus, it was possible to investigate the effect of various electrical and mechanical factors on the trajectories of conductive particles. This model has been employed to study the behaviour of coalparticles in fly-ash corona separators.

Statistical Optimization of Iron Electrodes for Alkaline Storage Batteries

A pressed-plate Fe electrode for alkalines storage batteries, designed using a statistical method (fractional factorial technique), is described. Parameters such as the configuration of the base grid, electrode compaction temperature and pressure, binder composition, mixing time, etc. have been optimised using this method. The optimised electrodes have a capacity of 300 plus /minus 5 mA h/g of active material (mixture of Fe and magnetite) at 7 h rate to a cut-off voltage of 8.86V vs. Hg/HgO, OH exp 17 ref.

On an analytical-numerical procedure for the analysis of cylindrical shells with arbitrarily oriented cracks

An analytical-numerical procedure for obtaining stress intensity factor solutions for an arbitrarily oriented crack in a long, thin circular cylindrical shell is presented. The method of analysis involves obtaining a series solution to the governing shell equation in terms of Mathieu and modified Mathieu functions by the method of separation of variables and satisfying the crack surface boundary conditions numerically using collocation. The solution is then transformed from elliptic coordinates to polar coordinates with crack tip as the origin through a Taylor series expansion and membrane and bending stress intensity factors are computed. Numerical results are presented and discussed for the pressure loading case.

Numerical simulations of void growth near a notch tip in ductile single crystals

The objective of this work is to study the growth of a cylindrical void ahead of a notch tip in ductile FCC single crystals under mode I, plane strain, small scale yielding (SSY) conditions. To this end, finite element simulations are performed within crystal plasticity framework neglecting elastic anisotropy. Attention is focussed on the effects of crystal hardening, ratio of void diameter to spacing from the notch and crystal orientation on plastic flow localization in the ligament connecting the notch and the void as well as their growth. The results show strong interaction between shear bands emanating from the notch and angular sectors of single slip forming around the void leading to intense plastic strain development in the ligament. Further, the ductile fracture processes are retarded by increase in hardening of the single crystal and decrease in ratio of void diameter to spacing from the notch. Also, a strong influence of crystal orientation on near-tip void growth and plastic slip band development is observed. Finally, the synergistic, cooperative growth of multiple voids ahead of the notch tip is examined.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.