Discontinuous Galerkin Methods on hp-Anisotropic Meshes I: A Priori Error Analysis

We consider the a priori error analysis of hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form under weak assumptions on the mesh design and the local finite element spaces employed. In particular, we prove a priori hp-error bounds for linear target functionals of the solution, on (possibly) anisotropic computational meshes with anisotropic tensor-product polynomial basis functions. The theoretical results are illustrated by a numerical experiment.

Analgesic Effects of Fatty Acid Amide Hydrolase Inhibition in a Rat Model of Neuropathic Pain

Cannabinoid-based medicines have therapeutic potential for the treatment of pain. Augmentation of levels of endocannabinoids with inhibitors of fatty acid amide hydrolase (FAAH) is analgesic in models of acute and inflammatory pain states. The aim of this study was to determine whether local inhibition of FAAH alters nociceptive responses of spinal neurons in the spinal nerve ligation model of neuropathic pain. Electrophysiological studies were performed 14-18 days after spinal nerve ligation or sham surgery, and the effects of the FAAHinhibitor cyclohexylcarbamic acid 3-carbamoyl biphenyl-3-yl ester (URB597) on mechanically evoked responses of spinal neurons and levels of endocannabinoids were determined. Intraplantar URB597 (25 _g in 50 _l) significantly ( p _ 0.01) attenuated mechanically evoked responses of spinal neurons in sham-operated rats. Effects of URB597 were blocked by the cannabinoid 1 receptor (CB1 ) antagonist AM251 [N-1-(2,4-dichlorophenyl)-5-(4-iodophenyl)-4-methyl-N-1-piperidinyl-1H-pyrazole-3-carboxamide] (30_g in50_l) and the opioid receptor antagonist naloxone. URB597 treatment increased levels of anandamide, 2-arachidonyl glycerol, and oleoyl ethanolamide in the ipsilateral hindpaw of shamoperated rats. Intraplantar URB597 (25 _g in 50 _l) did not, however, alter mechanically evoked responses of spinal neurons in spinal nerve ligated (SNL) rats or hindpaw levels of endocannabinoids. Intraplantar injection of a higher dose of URB597 (100 _g in 50 _l) significantly ( p_0.05) attenuated evoked responses of spinal neurons in SNL rats but did not alter hindpaw levels of endocannabinoids. Spinal administration of URB597 attenuated evoked responses of spinal neurons and elevated levels of endocannabinoids in shamoperated and SNL rats. These data suggest that peripheral FAAH activity may be altered or that alternative pathways of metabolism have greater importance in SNL rats.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual o-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving nonclassical damping is proposed. An example of modal control sucessfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

Optimal Controller Designs for Rotating Machines - Penalising the Rate of Change of Control Forcing

In the context of active control of rotating machines, standard optimal controller methods enable a trade-off to be made between (weighted) mean-square vibrations and (weighted) mean-square currents injected into magnetic bearings. One shortcoming of such controllers is that no concern is devoted to the voltages required. In practice, the voltage available imposes a strict limitation on the maximum possible rate of change of control force (force slew rate). This paper removes the aforementioned existing shortcomings of traditional optimal control.

Modal Control of Vibration in Rotating Machines and Other Generally Damped Systems

Second order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper a method to utilise modal control using the decoupled second order matrix equations involving non-classical damping is proposed. An example of modal control successfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.

Exotic dynamics in a firing rate model of neural tissue with threshold accommodation

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognized that more realistic models of neural tissue can be obtained with the introduction of state-dependent dynamic thresholds. In this paper we treat a specific phenomenological model of threshold accommodation that mimics many of the properties originally described by Hill. Importantly we explore the consequences of this dynamic threshold at the tissue level, by modifying a standard neural field model of Wilson-Cowan type. As in the case without threshold accommodation classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps) in both one and two dimensions. Importantly an analysis of bump stability in one dimension, using recent Evans function techniques, shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. In the regime where a bump solution does not exist direct numerical simulations show the possibility of self-replicating bumps via a form of bump splitting. Simulations in two space dimensions show analogous localized and traveling solutions to those seen in one dimension. Indeed dynamical behavior in this neural model appears reminiscent of that seen in other dissipative systems that support localized structures, and in particular those of coupled cubic complex Ginzburg-Landau equations. Further numerical explorations illustrate that the traveling pulses in this model exhibit particle like properties, similar to those of dispersive solitons observed in some three component reaction-diffusion systems. A preliminary account of this work first appeared in S Coombes and M R Owen, Bumps, breathers, and waves in a neural network with spike frequency adaptation, Physical Review Letters 94 (2005), 148102(1-4).

Liquid film dynamics in horizontal and tilted tubes: dry spots and sliding drops

Using a model derived from lubrication theory, we consider the evolution of a thin viscous film coating the interior or exterior of a cylindrical tube. The flow is driven by surface tension and gravity and the liquid is assumed to wet the cylinder perfectly. When the tube is horizontal, we use large-time simulations to describe the bifurcation structure of the capillary equilibria appearing at low Bond number. We identify a new film configuration in which an isolated dry patch appears at the top of the tube and demonstrate hysteresis in the transition between rivulets and annular collars as the tube length is varied. For a tube tilted to the vertical, we show how a long initially uniform rivulet can break up first into isolated drops and then annular collars, which subsequently merge. We also show that the speed at which a localized drop moves down the base of a tilted tube is non-monotonic in tilt angle.

Effect of nitric oxide donors on blood pressure and pulse pressure in acute and subacute stroke

High blood pressure (BP), pulse pressure (PP), and rate pressure product (RPP) areeach associated independently with a poor outcome in acute ischemic stroke. Whereas nitric oxide (NO) donors, such as glyceryl trinitrate (GTN), lower blood pressure in acute ischemic stroke, their effect on other hemodynamic measures is not known. We performed a systematic review of the effects of NO donors on systemic hemodynamic measures in patients with acute/subacute stroke. Randomized controlled trials were identified from searches of the Cochrane Library, Pubmed, and Embase. Information on hemodynamic measures, including systolic BP (SBP), diastolic BP (DBP), and heart rate, were assessed, and hemodynamic derivatives of these were calculated: PP (PP SBP DBP), mean arterial pressure (MAP DBP PP/3), mid blood pressure (MBP (SBP DBP)/2), pulse pressure index (PPI PP/MAP), and RPP (RPP SBP HR). The effect of treatment on hemodynamic measures was calculated as the weighted mean difference (WMD) between treated and control groups with adjustment for baseline. Results: Three trials involving 145 patients were identified; 93 patients received the NO donor, GTN, and 52 control. As compared with placebo, GTN significantly reduced SBP (WMD -9.80 mmHg, p< 0.001), DBP (WMD -4.43 mmHg, p<0.001), MAP (WMD -6.41 mmHg, p< 0.001), MBP (WMD -7.33 mmHg,p<0.001), PP (WMD -6.11 mmHg, p<0.001 ) and PPI (WMD -0.03, p=0.04 ). 3 GTN increased HR (WMD +3.87 bpm, p<0.001) and non-significantly lowered RPP (WMD -323 mmHg.bpm, p=0.14). Conclusion: The NO donor GTN reduces BP, PP and other derivatives in acute and subacute stroke whilst increasing heart rate.

Internal mammary artery smooth muscle cells resist migration and possess high antioxidant capacity

Objective- This study investigated whether differences exist in atherogen-induced migratory behaviors and basal antioxidant enzyme capacity of vascular smooth muscle cells (VSMC) from human coronary (CA) and internal mammary (IMA) arteries. Methods- Migration experiments were performed using the Dunn chemotaxis chamber. The prooxidant [NAD(P)H oxidase] and antioxidant [NOS, superoxide dismutase, catalase and glutathione peroxidase] enzyme activities were determined by specific assays. Results- Chemotaxis experiments revealed that while both sets of VSMC migrated towards platelet-derived growth factor-BB (1-50 ng/ml) and angiotensin II (1-50 nM), neither oxidized-LDL (ox-LDL, 25-100 �g/ml) nor native LDL (100 �g/ml) affected chemotaxis in IMA VSMC. However, high dose ox-LDL produced significant chemotaxis in CA VSMC that was inhibited by pravastatin (100 nM), mevastatin (10 nM), losartan (10 nM), enalapril (1 �M), and MnTBAP (a free radical scavenger, 50��M). Microinjection experiments with isoprenoids i.e. geranylgeranylpyrophosphate (GGPP) and farnesylpyrophosphate (FPP) showed distinct involvement of small GTPases in atherogen-induced VSMC migration. Significant increases in antioxidant enzyme activities and nitrite production along with marked decreases in NAD(P)H oxidase activity and O2 .- levels were determined in IMA versus CA VSMC. Conclusions- Enhanced intrinsic antioxidant capacity may confer on IMA VSMC resistance to migration against atherogenic agents. Drugs that regulate ox-LDL or angiotensin II levels also exert antimigratory effects.