Controllability results for impulsive mixed type functional integro-differential evolution equations with nonlocal conditions

In this paper, we establish the controllability for a class of abstract impulsive mixed-type functional integro-differential equations with finite delay in a Banach space. Some sufficient conditions for controllability are obtained by using the Mönch fixed point theorem via measures of noncompactness and semigroup theory. Particularly, we do not assume the compactness of the evolution system. An example is given to illustrate the effectiveness of our results.

A regulatory framework for short-term stochastic maintenance outage scheduling in smart grids

The current regulatory framework for maintenance outage scheduling in distribution systems needs revision to face the challenges of future smart grids. In the smart grid context, generation units and the system operator perform new roles with different objectives, and an efficient coordination between them becomes necessary. In this paper, the distribution system operator (DSO) of a microgrid receives the proposals for shortterm (ST) planned outages from the generation and transmission side, and has to decide the final outage plans, which is mandatory for the members to follow. The framework is based on a coordination procedure between the DSO and other market players. This paper undertakes the challenge of optimization problem in a smart grid where the operator faces with uncertainty. The results show the effectiveness and applicability of the proposed regulatory framework in the modified IEEE 34- bus test system.

Stochastic short-term maintenance scheduling of GENCOs in an oligopolistic electricity market

In the proposed model, the independent system operator (ISO) provides the opportunity for maintenance outage rescheduling of generating units before each short-term (ST) time interval. Long-term (LT) scheduling for 1 or 2 years in advance is essential for the ISO and the generation companies (GENCOs) to decide their LT strategies; however, it is not possible to be exactly followed and requires slight adjustments. The Cournot-Nash equilibrium is used to characterize the decision-making procedure of an individual GENCO for ST intervals considering the effective coordination with LT plans. Random inputs, such as parameters of the demand function of loads, hourly demand during the following ST time interval and the expected generation pattern of the rivals, are included as scenarios in the stochastic mixed integer program defined to model the payoff-maximizing objective of a GENCO. Scenario reduction algorithms are used to deal with the computational burden. Two reliability test systems were chosen to illustrate the effectiveness of the proposed model for the ST decision-making process for future planned outages from the point of view of a GENCO.

Systems of Navier-Stokes equations on cantor sets

We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.

Combined mutation differential evolution to solve systems of nonlinear equations

This paper presents a differential evolution heuristic to compute a solution of a system of nonlinear equations through the global optimization of an appropriate merit function. Three different mutation strategies are combined to generate mutant points. Preliminary numerical results show the effectiveness of the presented heuristic.

A few what-ifs on using statistical analysis of stochastic simulation runs to extract timeliness properties

Modern real-time systems, with a more flexible and adaptive nature, demand approaches for timeliness evaluation based on probabilistic measures of meeting deadlines. In this context, simulation can emerge as an adequate solution to understand and analyze the timing behaviour of actual systems. However, care must be taken with the obtained outputs under the penalty of obtaining results with lack of credibility. Particularly important is to consider that we are more interested in values from the tail of a probability distribution (near worst-case probabilities), instead of deriving confidence on mean values. We approach this subject by considering the random nature of simulation output data. We will start by discussing well known approaches for estimating distributions out of simulation output, and the confidence which can be applied to its mean values. This is the basis for a discussion on the applicability of such approaches to derive confidence on the tail of distributions, where the worst-case is expected to be.

Dynamical behaviour of multi-particle large-scale systems

Collective behaviours can be observed in both natural and man-made systems composed of a large number of elemental subsystems. Typically, each elemental subsystem has its own dynamics but, whenever interaction between individuals occurs, the individual behaviours tend to be relaxed, and collective behaviours emerge. In this paper, the collective behaviour of a large-scale system composed of several coupled elemental particles is analysed. The dynamics of the particles are governed by the same type of equations but having different parameter values and initial conditions. Coupling between particles is based on statistical feedback, which means that each particle is affected by the average behaviour of its neighbours. It is shown that the global system may unveil several types of collective behaviours, corresponding to partial synchronisation, characterised by the existence of several clusters of synchronised subsystems, and global synchronisation between particles, where all the elemental particles synchronise completely.

A framework for the response time analysis of fixed-priority tasks with stochastic inter-arrival times

Real-time scheduling usually considers worst-case values for the parameters of task (or message stream) sets, in order to provide safe schedulability tests for hard real-time systems. However, worst-case conditions introduce a level of pessimism that is often inadequate for a certain class of (soft) real-time systems. In this paper we provide an approach for computing the stochastic response time of tasks where tasks have inter-arrival times described by discrete probabilistic distribution functions, instead of minimum inter-arrival (MIT) values.

Self-adaptive combination of global tabu search and local search for nonlinear equations

Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.

Solving nonlinear equations by a tabu search strategy

Solving systems of nonlinear equations is a problem of particular importance since they emerge through the mathematical modeling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a metaheuristic, called Directed Tabu Search (DTS) [16], is able to converge to the solutions of a set of problems for which the fsolve function of MATLAB® failed to converge. We also show the effect of the dimension of the problem in the performance of the DTS.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Project, modelling and simulation of air stripping columns for the treatment of groundwater contaminated with volatile organic compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for the column design for any particular type of packing and contaminant avoiding the necessity of a pre-defined diameter used in the classical approach. It also renders unnecessary the employment of the graphical Eckert generalized correlation for pressure drop estimates. The hydraulic features are previously chosen as a project criterion and only afterwards the mass transfer phenomena are incorporated, in opposition to conventional approach. The design procedure was translated into a convenient algorithm using C++ as programming language. A column was built in order to test the models used either in the design or in the simulation of the column performance. The experiments were fulfilled using a solution of chloroform in distilled water. Another model was built to simulate the operational performance of the column, both in steady state and in transient conditions. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting system of ODE can be solved, allowing for the calculation of the concentration profile in both phases inside the column. In transient state the system of PDE was numerically solved by finite differences, after a previous linearization.

Spectral solution for the air stripping pollutants removal dynamic model with non linear steady state conditions

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

A New Approach in the Design of Air Stripping Columns for the Treatment of Groundwater Contaminated With Volatile Organic Compounds

Volatile organic compounds are a common source of groundwater contamination that can be easily removed by air stripping in columns with random packing and using a counter-current flow between the phases. This work proposes a new methodology for column design for any type of packing and contaminant which avoids the necessity of an arbitrary chosen diameter. It also avoids the employment of the usual graphical Eckert correlations for pressure drop. The hydraulic features are previously chosen as a project criterion. The design procedure was translated into a convenient algorithm in C++ language. A column was built in order to test the design, the theoretical steady-state and dynamic behaviour. The experiments were conducted using a solution of chloroform in distilled water. The results allowed for a correction in the theoretical global mass transfer coefficient previously estimated by the Onda correlations, which depend on several parameters that are not easy to control in experiments. For best describe the column behaviour in stationary and dynamic conditions, an original mathematical model was developed. It consists in a system of two partial non linear differential equations (distributed parameters). Nevertheless, when flows are steady, the system became linear, although there is not an evident solution in analytical terms. In steady state the resulting ODE can be solved by analytical methods, and in dynamic state the discretization of the PDE by finite differences allows for the overcoming of this difficulty. To estimate the contaminant concentrations in both phases in the column, a numerical algorithm was used. The high number of resulting algebraic equations and the impossibility of generating a recursive procedure did not allow the construction of a generalized programme. But an iterative procedure developed in an electronic worksheet allowed for the simulation. The solution is stable only for similar discretizations values. If different values for time/space discretization parameters are used, the solution easily becomes unstable. The system dynamic behaviour was simulated for the common liquid phase perturbations: step, impulse, rectangular pulse and sinusoidal. The final results do not configure strange or non-predictable behaviours.