Balinese Temples

There is a temple; the name is Pura Dalem. It is the Kerambitan Temple by the post office. The name of the god there is Dewi Durga. Dewi Durga is like a body guard, and protects all of Kerambitan. [excerpt

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach

Increased bradykinesia in Parkinson’s disease with increased movement complexity: elbow flexion-extension movements

The present research investigates factors contributing to bradykinesia in the control of simple and complex voluntary limb movement in Parkinson’s disease (PD) patients. The functional scheme of the basal ganglia (BG)–thalamocortical circuit was described by a mathematical model based on the mean firing rates of BG nuclei. PD was simulated as a reduction in dopamine levels, and a loss of functional segregation between two competing motor modules. In order to compare model simulations with performed movements, flexion and extension at the elbow joint is taken as a test case. Results indicated that loss of segregation contributed to bradykinesia due to interference between competing modules and a reduced ability to suppress unwanted movements. Additionally, excessive neurotransmitter depletion is predicted as a possible mechanism for the increased difficulty in performing complex movements. The simulation results showed that the model is in qualitative agreement with the results from movement experiments on PD patients and healthy subjects. Furthermore, based on changes in the firing rate of BG nuclei, the model demonstrated that the effective mechanism of Deep Brain Stimulation (DBS) in STN may result from stimulation induced inhibition of STN, partial synaptic failure of efferent projections, or excitation of inhibitory afferent axons even though the underlying methods of action may be quite different for the different mechanisms

Efficient computation of two-dimensional steady free-surface flows

We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable techniques, these problems are formulated in terms of a coupled system of Bernoulli's equation and an integral equation. When applying a numerical collocation scheme, the Jacobian for the system is dense, as the integral equation forces each of the algebraic equations to depend on each of the unknowns. We present here a strategy for overcoming this challenge, which leads to a numerical scheme that is much more efficient than what is normally employed for these types of problems, allowing for many more grid points over the free surface. In particular, we provide a simple recipe for constructing a sparse approximation to the Jacobian that is used as a preconditioner in a Jacobian-free Newton-Krylov method for solving the nonlinear system. We use this approach to compute numerical results for a variety of prototype problems including flows past pressure distributions, a surface-piercing object and bottom topographies.Comment: 20 pages, 13 figures, under revie

Drug diffusion from polymeric delivery devices: a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective

Spectrograms of ship wakes: identifying linear and nonlinear wave signals

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher order effects in a spectrogram and, while the high speed ferry data is very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceleration.Comment: 21 pages, 10 figures, submitte

The relationship between obsessive-compulsive disorder and depression in the general population

Though much is known about obsessive-compulsive disorder and depression individually, not much research has been done to look at the comorbidity of the two mental illnesses. This study seeks to review the comorbidity of obsessive-compulsive disorder (OCD) and depression in a college sample. Comorbidity between mental illnesses like OCD and depression is important to study because results will implicate what symptoms should be of concern, and these symptoms should be used to consider treatment. Understanding symptoms of both illnesses, and how they relate, can drive future research on what the best treatment options are for individuals diagnosed with these illnesses. This study measured depression with various subtypes of OCD through an online SONA survey. Data was collected from a sample of l 05 college students. Furthermore, results showed an overall correlation between depression and OCD rates overall. Obsessive subtypes had higher correlations within those with depressive symptoms than did compulsive subtypes. This study indicates that further research needs to be done to understand treatment outcomes of those with comorbid OCD and depression. More studies should take into account for the complexity of OCD subtypes when measuring comorbidity

Beacon-Based Gaming

Today, scavenger-hunt gaming applications on mobile devices navigate a player through multiple locations in a physical world via global positioning system (GPS) locating technologies. A scavenger-hunt gaming application that relies on alternate locating technologies, e.g., beacons, is described. A group of beacons can be associated to a series of points of interest (POIs) of a particular venue (such as a park or museum). The group of beacons, as well as the POIs, are subsequently indexed, recorded, and either downloaded as part of the scavenger-hunt gaming application or accessed via a cloud-based gaming service. The scavenger-hunt gaming application, referencing a group of beacons specific to a venue, is capable of being played at multiple venues in the physical world

More exceedingly comparative: Adverbial and attributive Exceed comparatives

Novel fieldwork data from Shan (Kra-Dai) adds to the cross-linguistic account of comparative constructions, especially Exceed-type comparatives. Shan can form comparative expressions from adverbs, which had not been analyzed in previous accounts of Exceed-type comparatives (Bochnak 2013; Howell 2013; Clem 2019; a.o.). Synthesizing previous semantic accounts of phrasal comparatives can account for the presented data