Leitmann's direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales

The fundamental problem of the calculus of variations on time scales concerns the minimization of a delta-integral over all trajectories satisfying given boundary conditions. This includes the discrete-time, the quantum, and the continuous/classical calculus of variations as particular cases. In this note we follow Leitmann's direct method to give explicit solutions for some concrete optimal control problems on an arbitrary time scale.Comment: Accepted for publication (9/January/2010) in Applied Mathematics and Computatio

How to collect data on household energy consumption

The existence of reliable, disaggregated information on residential fuel consumption and supply is essential to the formulation of sound household energy strategies. This report presents guidelines for designing and administering household energy surveys. The report is composed of four chapters. Following the introduction, chapter 1 presents the existing methodologies and the advantages and disadvantages of each. Chapter 3 discusses household energy surveying, from survey and questionaire design through fieldwork and data processing/analysis. Finally, in chapter 4, a checklist is presented for use as a quick reference during the creation of a household energy survey.Energy and Environment,Social Analysis,Energy Conservation&Efficiency,Engineering,Transport and Environment

Fractional Noether's theorem in the Riesz-Caputo sense

We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.Comment: Accepted (25/Jan/2010) for publication in Applied Mathematics and Computatio

Market Power, Resource Extraction and Pollution: Some Paradoxes and a Unified View

We adopt a stepwise approach to the analysis of a dynamic oligopoly game in which production makes use of a natural resource and pollutes the environment, starting with simple models where firms' output is not a function of the natural resource to end up with a full-fledged model in which (i) the resource is explicitly considered as an input of production and (ii) the natural resource and pollution interact via the respective state equations. This allows us to show that the relationship between the welfare properties of the economic system and the intensity of competition is sensitive to the degree of accuracy with which the model is constructed.

Intermediate scattering function of an anisotropic active Brownian particle

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.Comment: 10 pages, 4 figure

Avoidance control

Dynamical systems were considered, subject to control by two agents, one of whom desires that no trajectory of the system, emanating from outside a given set, intersects the set no matter what the admissible actions of the other agent. Conditions are given whose satisfaction assures that a given control results in avoidance. Furthermore, these conditions are constructive in that they yield an avoidance feedback control. Some examples are presented

Evasion in the plane

Dynamic systems were considered subject to control by two agents, one of whom desires that no trajectory of the system emanating from outside a given set, intersects that set no matter what the admissible actions of the other agent. Constructive conditions sufficient to yield a feedback control for the agent seeking avoidance were employed to deduce an evader control for the planar pursuit-evasion problem with bounded normal accelerations