Compressive Space-Time Galerkin Discretizations of Parabolic Partial Differential Equations

We study linear parabolic initial-value problems in a space-time variational formulation based on fractional calculus. This formulation uses "time derivatives of order one half" on the bi-infinite time axis. We show that for linear, parabolic initial-boundary value problems on $(0,\infty)$, the corresponding bilinear form admits an inf-sup condition with sparse tensor product trial and test function spaces. We deduce optimality of compressive, space-time Galerkin discretizations, where stability of Galerkin approximations is implied by the well-posedness of the parabolic operator equation. The variational setting adopted here admits more general Riesz bases than previous work; in particular, no stability in negative order Sobolev spaces on the spatial or temporal domains is required of the Riesz bases accommodated by the present formulation. The trial and test spaces are based on Sobolev spaces of equal order $1/2$ with respect to the temporal variable. Sparse tensor products of multi-level decompositions of the spatial and temporal spaces in Galerkin discretizations lead to large, non-symmetric linear systems of equations. We prove that their condition numbers are uniformly bounded with respect to the discretization level. In terms of the total number of degrees of freedom, the convergence orders equal, up to logarithmic terms, those of best $N$-term approximations of solutions of the corresponding elliptic problems.Comment: 26 page

Variational properties of a pumped dynamical system

We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial state of the system. In this paper, we generalize the treatment to the case when population is pumped into the system from levels not explicitly considered. These populations then pass through the coupled levels and exit by decay to levels outside the system. We derive the form of the equation of motion and relate it to our earlier treatments. It turns out that the formalism can be generalized to the new situation. Its physically relevant features are demonstrated, and the behaviour obtained is illustrated by numerical treatment of the standard two-level system with pumping and relaxation included.Comment: 10 pages, 2 figure

Weak convergence for a spatial approximation of the nonlinear stochastic heat equation

We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation has a solution only in one space dimension. In order to obtain results for higher dimensions, colored noise is considered here, besides white noise in one dimension. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence.Comment: 19 page

Equal Educational Opportunity for Children With Special Needs: The Federal Role in Australia

A control engineering benchmark problem with industrial relevance is presented. The process is a simulation model of a nonlinear four-mass system, which should be controlled by a discrete-time controller that optimizes performance for given robustness requirements. The control problem concerns only the so-called regulator problem

Foreword

This paper considers identification of unknown parameters in elastic dynamic models of industrial robots. Identifying such models is a challenging task since an industrial robot is a multivariable, nonlinear, resonant, and unstable system. Unknown parameters (mainly spring-damper pairs) in a physically parameterized nonlinear dynamic model are identified in the frequency domain, using estimates of the nonparametric frequency response function (FRF) in different robot configurations/positions. The nonlinear parametric robot model is linearized in the same positions and the optimal parameters are obtained by minimizing the discrepancy between the nonparametric FRFs and the parametric FRFs (the FRFs of the linearized parametric robot model). In order to accurately estimate the nonparametric FRFs, the experiments must be carefully designed. The selection of optimal robot configurations for the experiments is also part of the design. Different parameter estimators are compared and experimental results show the usefulness of the proposed identification procedure. The weighted logarithmic least squares estimator achieves the best result and the identified model gives a good global description of the dynamics in the frequency range of interest

Parasite problems in organic livestock and options for control

ABSTRACT: Organic livestock production has increased dramatically in recent years in Europe and other parts of the world. The aim of producing livestock under more natural conditions has led to a reversion to primarily outdoor production systems and less intensive housing when indoor, more forage-based diets, and a reduced reliance on external inputs like antiparasiticides. These major changes in livestock production systems may potentially result in re-emergence (or emergence) of parasitic infections. The basic objective of this paper is to give an overview of the available information on parasitic problems in organic livestock production with a focus on northern temperate regions. Furthermore, options for control that target these problems and are acceptable within the framework of organic farming will be discussed. The large majority of conventional pigs and poultry are raised in highly intensive production systems which differ dramatically from organic housing systems and especially outdoor runs and pastures. A comparably pronounced difference between conventional and organic systems is not found for ruminants. Thus, organic rearing may be a higher risk factor for pigs and poultry than for ruminants, however this may partly be counteracted by the fact that pigs and poultry never rely on pasture vegetation for feeding, while ruminants do so with associated potential problems of insufficient nutritional status and increased parasite transmission. Several studies have indicated higher parasite infections rates in organic herds vs. and conventional herds, and many of these differences may be explained by environmental factors favourable to the development of parasite oocysts/eggs/larvae and perhaps for intermediate hosts, while fewer differences may be due to the lack of chemical intervention. However, parasite species have to overcome many very diverse constraints in their attempts to complete their life cycles and it may therefore be risky to generalize. Thus, helminths and Eimeria sp. infections are most prevalent in organic swine herds whereas infections with Isospora suis seems less common than in intensive herds. A higher risk of helminth infections has also been documented in organic poultry. In organic dairy production, gastrointestinal parasites may pose a problem, and lungworm infection remains a major problem, not only in grazing heifers and steers but also in adult milking cows. This is not different from conventional herds but control measures are restricted. Many problems can be controlled by appropriate management routines, e.g. pasture management. However, avoiding chemotherapeutics for control in certain regions, e.g. in relation to ectoparasitic infections, remains a major challenge. Future research has to actively exploit new, promising avenues for control like forages or diets with anti-parasitic activities, biological control and selection for resistance, using approaches compatible with organic farming principles

First and subsequent return stroke properties of cloud-to-ground lightning

Lightning properties obtained by a network of magnetic direction finders and by electric field measurements for distances from 50 to 500 km are compared for three summer thunderstorms in Sweden. The data from direct field recordings indicate 31, 17, and 26 pcts. of negative subsequent return strokes with peak current (as inferred from the peak electric field) higher than the first. Electric fields from first strokes are compared with normalized amplitudes registered by the magnetic direction finding system. The efficiency of detection by the magnetic direction finding system is discussed in terms of the percentage of lightning flashes observed by electric field measurements that are not localized. Statistics of the number of strokes per flash and the interstroke time intervals are presented