Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Differential Pharmacokinetics of Digoxin in Elderly Patients

Digoxin remains one of the most commonly prescribed of all cardiac medications. The main indications for digoxin usage include atrial fibrillation and heart failure; both these conditions are more prevalent in older patients. Given the aging population and the increasing incidence of heart failure we would expect prescribing of digoxin to remain as frequent or to even increase in older patients. Older patients are also more likely to develop toxicity and diagnosis of digoxin toxicity can be difficult in this group. Numerous components contribute to the development of toxicity in older patients, ranging from aging-related changes in renal function or body mass to polypharmacy and possible interactions with digoxin. It is therefore important to understand how the pharmacokinetics of digoxin may be altered in the older population. Application of basic pharmacological principles may be helpful in anticipating these problems. This review describes the pharmacokinetics of digoxin, the changes in pharmacokinetics with increasing age and how concomitant disease states or drug interactions may affect the pharmacokinetics of digoxin. Greater knowledge about the causes and prevention of digoxin toxicity should further reduce the morbidity and mortality arising from digoxin toxicity, especially in the elderly population.
For over 200 years debate has raged regarding the use of digitalis glycosides in cardiac disease. At present digoxin is the most commonly prescribed digitalis compound. This review describes the pharmacokinetics of digoxin and in particular how they are altered with increasing age. When considering the elderly population it is important to recognise the heterogeneity of response in this group, therefore there are no rules, with regards to prescribing, that can apply to the entire elderly population.

Assessment of rolling resistance models in discrete element simulations

Particulate systems are of interest in many disciplines. They are often investigated using the discrete element method because of its capability to investigate particulate systems at the individual particle scale. To model the interaction between two particles and between a particle and a boundary, conventional discrete element models use springs and dampers in both the normal and tangential directions. The significance of particle rotation has been highlighted in both numerical studies and physical experiments. Several researchers have attempted to incorporate a rotational torque to account for the rolling resistance or rolling friction by developing different models. This paper presents a review of the commonly used models for rolling resistance and proposes a more general model. These models are classified into four categories according to their key characteristics. The robustness of these models in reproducing rolling resistance effects arising from different physical situations was assessed by using several benchmarking test cases. The proposed model can be seen to be more general and suitable for modelling problems involving both dynamic and pseudo-static regimes. An example simulation of the formation of a 2D sandpile is also shown. For simplicity, all formulations and examples are presented in 2D form, though the general conclusions are also applicable to 3D systems.

Some current problems in perovskite nano-ferroelectrics and multiferroics: kinetically-limited systems of finite lateral size

We describe some unsolved problems of current interest; these involve quantum critical points in
ferroelectrics and problems which are not amenable to the usual density functional theory, nor to
classical Landau free energy approaches (they are kinetically limited), nor even to the Landau–
Kittel relationship for domain size (they do not satisfy the assumption of infinite lateral diameter)
because they are dominated by finite aperiodic boundary conditions.

Differential evolution combined with clonal selection for dynamic economic dispatch

Dynamic economic load dispatch (DELD) is one of the most important steps in power system operation. Various optimisation algorithms for solving the problem have been developed; however, due to the non-convex characteristics and large dimensionality of the problem, it is necessary to explore new methods to further improve the dispatch results and minimise the costs. This article proposes a hybrid differential evolution (DE) algorithm, namely clonal selection-based differential evolution (CSDE), to solve the problem. CSDE is an artificial intelligence technique that can be applied to complex optimisation problems which are for example nonlinear, large scale, non-convex and discontinuous. This hybrid algorithm combines the clonal selection algorithm (CSA) as the local search technique to update the best individual in the population, which enhances the diversity of the solutions and prevents premature convergence in DE. Furthermore, we investigate four mutation operations which are used in CSA as the hyper-mutation operations. Finally, an efficient solution repair method is designed for DELD to satisfy the complicated equality and inequality constraints of the power system to guarantee the feasibility of the solutions. Two benchmark power systems are used to evaluate the performance of the proposed method. The experimental results show that the proposed CSDE/best/1 approach significantly outperforms nine other variants of CSDE and DE, as well as most other published methods, in terms of the quality of the solution and the convergence characteristics.

The Reliability of the Arc-Length Method in the Analysis of Mode-Jumping Problems

The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial nite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Arc-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence diÆculty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example.

Fixed-boundary constituencies and the principle of equal representation in Ireland

The process of constituency boundary revision in Ireland, designed to satisfy what is perceived as a rigid requirement that a uniform deputy-population ratio be maintained across constituencies, has traditionally consumed a great deal of the time of politicians and officials. For almost two decades after a High Court ruling in 1961, the process was a political one, was highly contentious, and was marked by serious allegations of ministerial gerrymandering. The introduction in 1979 of constituency commissions made up of officials neutralised, for the most part, charges that the system had become too politicised, but it continued the process of micro-management of constituency boundaries. This article suggests that the continuing problems caused by this system – notably, the permanently changing nature of constituency boundaries and resulting difficulties of geographical identification – could be resolved by reversion to the procedure that is normal in proportional representation systems: periodic post-census allocation of seats to constituencies whose boundaries are based on those of recognised local government units and which are stable over time. This reform, replacing the principle of redistricting by the principle of reapportionment, would result in more recognisable constituencies, more predictable boundary trajectories over time, and a more efficient, fairer, and speedier process of revision.