Generalized Burgers equations and Euler-Painlev transcendents. I

Initial-value problems for the generalized Burgers equation (GBE) ut+u betaux+lambdaualpha =(delta/2)uxx are discussed for the single hump type of initial data both continuous and discontinuous. The numerical solution is carried to the self-similar ``intermediate asymptotic'' regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painlev equations categorize the Kortweg-de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±[infinity], is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient lambda, are also discussed. The results are compared with those holding for the modified KdV equation with damping. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Langevin dynamics of the pure SU(2) deconfining transition

We investigate the dissipative real-time evolution of the order parameter for the deconfining transition in the pure SU(2) gauge theory. The approach to equilibrium after a quench to temperatures well above the critical one is described by a Langevin equation. To fix completely the Markovian Langevin dynamics we choose the dissipation coefficient, that is a function of the temperature, guided by preliminary Monte Carlo simulations for various temperatures. Assuming a relationship between Monte Carlo time and real time, we estimate the delay in thermalization brought about by dissipation and noise. © 2007 The American Physical Society.

Hot Brownian carriers in the Langevin picture: Application to a simple model for the Gunn effect in GaAs

We consider a charged Brownian gas under the influence of external, static and uniform electric and magnetic fields, immersed in a uniform bath temperature. We obtain the solution for the associated Langevin equation, and thereafter the evolution of the nonequilibrium temperature towards a nonequilibrium (hot) steady state. We apply our results to a simple yet relevant Brownian model for carrier transport in GaAs. We obtain a negative differential conductivity regime (Gunn effect) and discuss and compare our results with the experimental results. © 2013.

Portadores quentes: modelo browniano

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Solvabilty of generalized Hammerstein integral equations on unbounded domains, with sign-changing kernels

In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

Preliminary spatiotemporal analysis of the association between socio-environmental factors and suicide

Background: The seasonality of suicide has long been recognised. However, little is known about the relative importance of socio-environmental factors in the occurrence of suicide in different geographical areas. This study examined the association of climate, socioeconomic and demographic factors with suicide in Queensland, Australia, using a spatiotemporal approach. Methods: Seasonal data on suicide, demographic variables and socioeconomic indexes for areas in each Local Government Area (LGA) between 1999 and 2003 were acquired from the Australian Bureau of Statistics. Climate data were supplied by the Australian Bureau of Meteorology. A multivariable generalized estimating equation model was used to examine the impact of socio-environmental factors on suicide. Results: The preliminary data analyses show that far north Queensland had the highest suicide incidence (e.g., Cook and Mornington Shires), while the south-western areas had the lowest incidence (e.g., Barcoo and Bauhinia Shires) in all the seasons. Maximum temperature, unemployment rate, the proportion of Indigenous population and the proportion of population with low individual income were statistically significantly and positively associated with suicide. There were weaker but not significant associations for other variables. Conclusions: Maximum temperature, the proportion of Indigenous population and unemployment rate appeared to be major determinants of suicide at a LGA level in Queensland.

Theoretical investigation of thermal tweezers for parallel manipulation of atoms and nanoparticles on surfaces

A major focus of research in nanotechnology is the development of novel, high throughput techniques for fabrication of arbitrarily shaped surface nanostructures of sub 100 nm to atomic scale. A related pursuit is the development of simple and efficient means for parallel manipulation and redistribution of adsorbed atoms, molecules and nanoparticles on surfaces – adparticle manipulation. These techniques will be used for the manufacture of nanoscale surface supported functional devices in nanotechnologies such as quantum computing, molecular electronics and lab-on-achip, as well as for modifying surfaces to obtain novel optical, electronic, chemical, or mechanical properties. A favourable approach to formation of surface nanostructures is self-assembly. In self-assembly, nanostructures are grown by aggregation of individual adparticles that diffuse by thermally activated processes on the surface. The passive nature of this process means it is generally not suited to formation of arbitrarily shaped structures. The self-assembly of nanostructures at arbitrary positions has been demonstrated, though these have typically required a pre-patterning treatment of the surface using sophisticated techniques such as electron beam lithography. On the other hand, a parallel adparticle manipulation technique would be suited for directing the selfassembly process to occur at arbitrary positions, without the need for pre-patterning the surface. There is at present a lack of techniques for parallel manipulation and redistribution of adparticles to arbitrary positions on the surface. This is an issue that needs to be addressed since these techniques can play an important role in nanotechnology. In this thesis, we propose such a technique – thermal tweezers. In thermal tweezers, adparticles are redistributed by localised heating of the surface. This locally enhances surface diffusion of adparticles so that they rapidly diffuse away from the heated regions. Using this technique, the redistribution of adparticles to form a desired pattern is achieved by heating the surface at specific regions. In this project, we have focussed on the holographic implementation of this approach, where the surface is heated by holographic patterns of interfering pulsed laser beams. This implementation is suitable for the formation of arbitrarily shaped structures; the only condition is that the shape can be produced by holographic means. In the simplest case, the laser pulses are linearly polarised and intersect to form an interference pattern that is a modulation of intensity along a single direction. Strong optical absorption at the intensity maxima of the interference pattern results in approximately a sinusoidal variation of the surface temperature along one direction. The main aim of this research project is to investigate the feasibility of the holographic implementation of thermal tweezers as an adparticle manipulation technique. Firstly, we investigate theoretically the surface diffusion of adparticles in the presence of sinusoidal modulation of the surface temperature. Very strong redistribution of adparticles is predicted when there is strong interaction between the adparticle and the surface, and the amplitude of the temperature modulation is ~100 K. We have proposed a thin metallic film deposited on a glass substrate heated by interfering laser beams (optical wavelengths) as a means of generating very large amplitude of surface temperature modulation. Indeed, we predict theoretically by numerical solution of the thermal conduction equation that amplitude of the temperature modulation on the metallic film can be much greater than 100 K when heated by nanosecond pulses with an energy ~1 mJ. The formation of surface nanostructures of less than 100 nm in width is predicted at optical wavelengths in this implementation of thermal tweezers. Furthermore, we propose a simple extension to this technique where spatial phase shift of the temperature modulation effectively doubles or triples the resolution. At the same time, increased resolution is predicted by reducing the wavelength of the laser pulses. In addition, we present two distinctly different, computationally efficient numerical approaches for theoretical investigation of surface diffusion of interacting adparticles – the Monte Carlo Interaction Method (MCIM) and the random potential well method (RPWM). Using each of these approaches we have investigated thermal tweezers for redistribution of both strongly and weakly interacting adparticles. We have predicted that strong interactions between adparticles can increase the effectiveness of thermal tweezers, by demonstrating practically complete adparticle redistribution into the low temperature regions of the surface. This is promising from the point of view of thermal tweezers applied to directed self-assembly of nanostructures. Finally, we present a new and more efficient numerical approach to theoretical investigation of thermal tweezers of non-interacting adparticles. In this approach, the local diffusion coefficient is determined from solution of the Fokker-Planck equation. The diffusion equation is then solved numerically using the finite volume method (FVM) to directly obtain the probability density of adparticle position. We compare predictions of this approach to those of the Ermak algorithm solution of the Langevin equation, and relatively good agreement is shown at intermediate and high friction. In the low friction regime, we predict and investigate the phenomenon of ‘optimal’ friction and describe its occurrence due to very long jumps of adparticles as they diffuse from the hot regions of the surface. Future research directions, both theoretical and experimental are also discussed.

Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Sit versus stand : can sitting be accurately identified using MTI accelerometer data?

High levels of sitting have been linked with poor health outcomes. Previously a pragmatic MTI accelerometer data cut-point (100 count/min-1) has been used to estimate sitting. Data on the accuracy of this cut-point is unavailable. PURPOSE: To ascertain whether the 100 count/min-1 cut-point accurately isolates sitting from standing activities. METHODS: Participants fitted with an MTI accelerometer were observed performing a range of sitting, standing, light & moderate activities. 1-min epoch MTI data were matched to observed activities, then re-categorized as either sitting or not using the 100 count/min-1 cut-point. Self-report demographics and current physical activity were collected. Generalized estimating equation for repeated measures with a binary logistic model analyses (GEE), corrected for age, gender and BMI, were conducted to ascertain the odds of the MTI data being misclassified. RESULTS: Data were from 26 healthy subjects (8 men; 50% aged <25 years; mean BMI (SD) 22.7(3.8)m/kg2). MTI sitting and standing data mode was 0 count/min-1, with 46% of sitting activities and 21% of standing activities recording 0 count/min-1. The GEE was unable to accurately isolate sitting from standing activities using the 100 count/min-1 cut-point, since all sitting activities were incorrectly predicted as standing (p=0.05). To further explore the sensitivity of MTI data to delineate sitting from standing, the upper 95% confidence interval of the mean for the sitting activities (46 count/min-1) was used to re-categorise the data; this resulted in the GEE correctly classifying 49% of sitting, and 69% of standing activities. Using the 100 count/min-1 cut-point the data were re-categorised into a combined ‘sit/stand’ category and tested against other light activities: 88% of sit/stand and 87% of light activities were accurately predicted. Using Freedson’s moderate cut-point of 1952 count/min-1 the GEE accurately predicted 97% of light vs. 90% of moderate activities. CONCLUSION: The distributions of MTI recorded sitting and standing data overlap considerably, as such the 100 count/min -1 cut-point did not accurately isolate sitting from other static standing activities. The 100 count/min -1 cut-point more accurately predicted sit/stand vs. other movement orientated activities.

Effect of mobile phone distraction on car-following behaviour

Multitasking, such as the concurrent use of a mobile phone and operating a motor vehicle, is a significant distraction that impairs driving performance and is becoming a leading cause of motor vehicle crashes. This study investigates the impact of mobile phone conversations on car-following behaviour. The CARRS-Q Advanced Driving Simulator was used to test a group of young Australian drivers aged 18 to 26 years on a car-following task in three randomised phone conditions: baseline (no phone conversation), hands-free and handheld. Repeated measure ANOVA was applied to examine the effect of mobile phone distraction on selected car-following variables such as driving speed, spacing, and time headway. Overall, drivers tended to select slower driving speeds, larger vehicle spacings, and longer time headways when they were engaged in either hands-free or handheld phone conversations, suggesting possible risk compensatory behaviour. In addition, phone conversations while driving influenced car-following behaviour such that variability was increased in driving speeds, vehicle spacings, and acceleration and decelerations. To further investigate car-following behaviour of distracted drivers, driver time headways were modelled using Generalized Estimation Equation (GEE). After controlling for various exogenous factors, the model predicts an increase of 0.33 seconds in time headway when a driver is engaged in hands-free phone conversation and a 0.75 seconds increase for handheld phone conversation. The findings will improve the collective understanding of distraction on driving performance, in particular car following behaviour which is most critical in the determination of rear-end crashes.