Numerical three-dimensional free surface circulation model for the South Biscayne Bay,Florida

A three– dimensional, time dependent free surface model has been developed for predicting circulation and surface height variations in a tidal bay. An explicit finite difference numerical solution is obtained by transforming the vertical coordinate in the governing model equations. The transformed geometry consists of a fixed, flat free surface and a constant depth basin for easy computation. The ocean–bay interface open boundary condition is incorporated into this hydrodynamic model without approximation, and yields rather accurate results for the bay circulation and tide level variations. The numerical method employs a staggered grid Richardson lattice, which has the inherent property of not requiring calculation of the tangential velocity components on solid surfaces. The momentum equations ignore horizontal diffusion which is small for the South Biscayne Bay, for which vertical diffusion and advection dominate.     

Asymptotic behaviour for wave equation with time-dependent coefficients

Abstract We shall find asymptotic profiles for strictly hyperbolic equations with time-dependent coefficients which are of Lipschitz class and have some stability condition. More precisely, it will be shown that there exists a solution which is not asymptotically free provided that the coefficient tends slowly to some constant. Keywords: Wave equation, Asymptotic profiles, Asymptotic integrations     

Molecular static simulations of ferroelectric material hysteresis behaviour

The present contribution deals with molecular static modelling and the simulation of ferroelectric material hysteresis behaviour. Therefore the core-shell model is implemented in a molecular static algorithm. Moreover the algorithm is implemented as a finite element method for nonlinear trusses. Thereby the computational costs are reduced significantly compared to molecular dynamics. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some remarks on time-dependent variational problems and their asymptotic behaviour

The subject matter of this paper is the asymptotic behaviour of quasi-static variational inequalities, as regards physical parameters like the friction coefficient, compliance coefficient, etc. By convex duality, the quasi-static problems can be recast into the forms of standard evolution problems, whose study relies on well-known methods. In this framework the stability with respect to small friction coefficients reduces to long time behaviour for evolution problems.     

Using the discrete time modelling approach to evaluate the time-dependent behaviour of queueing systems

Many real-life queueing problems exhibit time-dependent behaviour, but the corresponding theoretical models are hard to handle. The overall purpose of this paper is to describe a discrete time modelling (DTM) approach to solving problems of this sort, and to outline the research opportunities and challenges associated with it. The DTM approach is placed alongside other related research and is shown in particular to have strong links with some aspects of the matrix-geometric methods. The main research issues that have arisen in applying the DTM approach to problems of the form M(t)/G/1, M(t)/G/c and M(t)/G^0.c/1 are described. This then provides a basis for outlining ongoing research into systems such as M(t)/G/c/K and tandem queues. Finally DTM research opportunities and challenges for more complex problems such as priority queues, server vacation models and queueing networks are delineated.     

Three-dimensional phase field simulations of grain growth in materials containing finely dispersed second-phase particles

Phase field modelling has proven to be a versatile tool for simulating microstructural evolution phenomena, such as grain growth in polycrystalline materials. However, the computational requirements of a phase field model impose strong limitations on the number of phase field variables employed in a practical implementation. In this paper, a bounding box algorithm is proposed allowing the use of a large number of phase field variables without excessive computational requirements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The value of rolling-horizon policies for risk-averse hydro-thermal planning

We consider the optimal management of a hydro-thermal power system in the mid and long terms. From the optimization point of view, this amounts to a large-scale multistage stochastic linear program, often solved by combining sampling with decomposition algorithms, like stochastic dual dynamic programming. Such methodologies, however, may entail prohibitive computational time, especially when applied to a risk-averse formulation of the problem. We propose instead a risk-averse rolling-horizon policy that is nonanticipative, feasible, and time consistent. The policy is obtained by solving a sequence of risk-averse problems with deterministic constraints for the current time step and future chance and CVaR constraints.The considered hydro-thermal model takes into account losses resulting from run-of-river plants efficiencies as well as uncertain demand and streamflows. Constraints aim at satisfying demand while keeping reservoir levels above minzones almost surely. We show that if the problem uncertainty is represented by a periodic autoregressive stochastic process with lag one, then the probabilistic constraints can be computed explicitly. As a result, each one of the aforementioned risk-averse problems is a medium-size linear program, easy to solve.For a real-life power system we compare our approach with three alternative policies. Namely, a robust nonrolling-horizon policy and two risk-neutral policies obtained by stochastic dual dynamic programming, implemented in nonrolling- and rolling-horizon modes, respectively. Our numerical assessment confirms the superiority of the risk-averse rolling-horizon policy that yields comparable average indicators, but with reduced volatility and with substantially less computational effort.     

Structure formation and phase behaviour in ferrofluid monolayers: theory and computer simulations

In order to investigate the peculiarities brought by the quasi-2D geometry into the aggregation processes in ferrofluids, a combination of density functional theory (DFT), and molecular dynamics (MD) simulations is presented. The microstructure formation and the phase behaviour of monodisperse ferrofluid monolayers is studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximation of time-dependent free boundaries

Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.     

Development and computational tests of an undecoupled optimum short-term hydro-thermal schedulling code using network flows

Summary Optimizing the thermal production of electricity in the short term in an integrated power system when a thermal unit commitment has been decided means coordinating hydro and thermal generation in order to obtain the minimum thermal generation costs over the time period under study. Fundamental constraints to be satisfied are the covering of each hourly load and satisfaction of spinning reserve requirements. A nonlinear network flow model with linear side constraints with no decomposition into hydro and thermal subproblems was used to solve the hydrothermal scheduling. Hydrogeneration is linearized with respect to network variables and a novel thermal generation network is introduced. Computational results are reported.     

Exact solution of theP 1 time-dependent equations with time-dependent cross-sections for slab and spherical geometry

The monoenergetic, one-dimensional, time-dependentP ₁ equations with time-dependent cross sections are solved using the technique of the generalized Lie series. A few numerical results are given and compared with those obtained by theS ₂ method.     

On homogenization of time-dependent random flows

We study a diffusion with a random, time dependent drift. We prove the invariance principle when the spectral measure of the drift satisfies a certain integrability condition. This result generalizes the results of [13, 7]. Received: 25 February 2000 / Revised version: 11 December 2000 /?Published online: 14 June 2001     

Scope of stationary multi-objective evolutionary optimization: a case study on a hydro-thermal power dispatch problem

Many engineering design and developmental activities finally resort to an optimization task which must be solved to get an efficient and often an intelligent solution. Due to various complexities involved with objective functions, constraints, and decision variables, optimization problems are often not adequately suitable to be solved using classical point-by-point methodologies. Evolutionary optimization procedures use a population of solutions and stochastic update operators in an iteration in a manner so as to constitute a flexible search procedure thereby demonstrating promise to such difficult and practical problem-solving tasks. In this paper, we illustrate the power of evolutionary optimization algorithms in handling different kinds of optimization tasks on a hydro-thermal power dispatch optimization problem: (i) dealing with non-linear, non-differentiable objectives and constraints, (ii) dealing with more than one objectives and constraints, (iii) dealing with uncertainties in decision variables and other problem parameters, and (iv) dealing with a large number (more than 1,000) variables. The results on the static power dispatch optimization problem are compared with that reported in an existing simulated annealing based optimization procedure on a 24-variable version of the problem and new solutions are found to dominate the solutions of the existing study. Importantly, solutions found by our approach are found to satisfy theoretical Kuhn–Tucker optimality conditions by using the subdifferentials to handle non-differentiable objectives. This systematic and detail study demonstrates that evolutionary optimization procedures are not only flexible and scalable to large-scale optimization problems, but are also potentially efficient in finding theoretical optimal solutions for difficult real-world optimization problems. Kalyanmoy Deb, Deva Raj Chair Professor. Currently a Finland Distinguished Professor, Department of Business Technology, Helsinki School of Economics, 00101 Helsinki, Finland.     

Stochastic Simulation and Monte Carlo methods applied to the assessment of hydro-thermal generating system operation

Summary Simulation can be defined as a numerical technique for conducting experiments on a digital computer, which involves certain types of mathematical and logical models that describe the behaviour of a system over extended periods of real time. Simulation is, in a wide sense, a technique for performing sampling experiments on a model of the system. Stochastic simulation implies experimenting with the model over time including sampling stochastic variates from probability distributions. This paper describes the main concepts of the application of Stochastic Simulation and Monte Carlo methods to the analysis of the operation of electric energy systems, in particular to hydro-thermal generating systems. These techniques can take into account virtually all contingencies inherent in the operation of the system. Also, the operating policies that have an important effect on the performance of these systems can be realistically represented.     

The equations of thermoelasticity with time-dependent coefficients

We consider an inhomogeneous thermoelastic system with second sound in one space dimension where the coefficients are space- and time-dependent. For Dirichlet-Neumann type boundary conditions the global existence of smooth solutions is proved by using the theory of Kato. Then the asymptotic behavior of the solutions is discussed.     

Stability of time-dependent diffusion semigroups and kernels

The main result of this paper is that when the coefficients of the time-dependent divergence form operators are Hölder continuous in time with order not too much smaller than 1/2, the distance of the semigroups of two operators is bounded by the L ₂ distance of the coefficients of their corresponding operators.     

On the scattering frequencies of time-dependent potentials

This paper discusses the scattering frequencies associated with the scalar wave equation and a time-periodic, real, potential. It is shown that the scattering frequencies form a discrete set in the complex plane and depend continuously on the potential. Existence of the scattering frequencies is proved for periodic potentials which are perturbations of a time independent, nonnegative, potential.