Annihilation of Immobile Reactants on the Bethe Lattice

Two-particle annihilation reaction, A+A -> inert, for immobile reactants on the Bethe lattice is solved exactly for the initially random distribution. The process reaches an absorbing state in which no nearest-neighbor reactants are left. The approach of the concentration to the limiting value is exponential. The solution reproduces the known one-dimensional result which is further extended to the reaction A+B -> inert.Comment: 12 pp, TeX (plain

A Novel, Contactless, Portable “Spot-Check” Device Accurately Measures Respiratory Rate

Respiratory rate (RR) is an important vital sign used in the assessment of acutely ill patients. It is also used as to predict serious deterioration in a patient's clinical condition. Convenient electronic devices exist for measurement of pulse, blood pressure, oxygen saturation and temperature. Although devices which measure RR exist, none has entered everyday clinical practice. We developed a contactless portable respiratory rate monitor (CPRM) and evaluated the agreement in respiratory rate measurements between existing methods and our new device. The CPRM uses thermal anemometry to measure breath signals during inspiration and expiration. RR data were collected from 52 healthy adult volunteers using respiratory inductance plethysmography (RIP) bands (established contact method), visual counting of chest movements (established non-contact method) and the CPRM (new method), simultaneously. Two differently shaped funnel attachments were evaluated for each volunteer. Data showed good agreement between measurements from the CPRM and the gold standard RIP, with intra-class correlation coefficient (ICC): 0.836, mean difference 0.46 and 95% limits of agreement of -5.90 to 6.83. When separate air inlet funnels of the CPRM were analysed, stronger agreement was seen with an elliptical air inlet; ICC 0.908, mean difference 0.37 with 95% limits of agreement -4.35 to 5.08. A contactless device for accurately and quickly measuring respiratory rate will be an important triage tool in the clinical assessment of patients. More testing is needed to explore the reasons for outlying measurements and to evaluate in the clinical setting

Locating the minimum : Approach to equilibrium in a disordered, symmetric zero range process

We consider the dynamics of the disordered, one-dimensional, symmetric zero range process in which a particle from an occupied site $k$ hops to its nearest neighbour with a quenched rate $w(k)$. These rates are chosen randomly from the probability distribution $f(w) \sim (w-c)^{n}$, where $c$ is the lower cutoff. For $n > 0$, this model is known to exhibit a phase transition in the steady state from a low density phase with a finite number of particles at each site to a high density aggregate phase in which the site with the lowest hopping rate supports an infinite number of particles. In the latter case, it is interesting to ask how the system locates the site with globally minimum rate. We use an argument based on local equilibrium, supported by Monte Carlo simulations, to describe the approach to the steady state. We find that at large enough time, the mass transport in the regions with a smooth density profile is described by a diffusion equation with site-dependent rates, while the isolated points where the mass distribution is singular act as the boundaries of these regions. Our argument implies that the relaxation time scales with the system size $L$ as $L^{z}$ with $z=2+1/(n+1)$ for $n > 1$ and suggests a different behaviour for $n < 1$.Comment: Revtex, 7 pages including 3 figures. Submitted to Pramana -- special issue on mesoscopic and disordered system

Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation

We investigate a non-equilibrium reaction-diffusion model and equivalent ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The exact energy spectrum and the n-point hole correlations are considered with the help of the Jordan-Wigner fermionization and the inter-particle distribution function method. Although the Hamiltonian has no explicit translational symmetry, the translational invariance is recovered after long time due to the diffusion. We see the scaling relations for the concentration and the two-point function in finite size analysis.Comment: 7 pages, LaTeX file, to appear in J. Phys. A: Math. and Ge

A Novel Approach for the Particle-in-Cell Modelling of Gridded Ion Engine Plume Neutralisation

The Particle-in-Cell modelling of gridded ion engine plume neutralisation has been simplified when compared to traditional methods. This results in significantly less computational resources being required. The NSTAR engine was modelled as a reference, where simulated specific impulse values were found to be 5% higher than the real engine. This method will be most suited to rapid prototyping and optimisation studies, where speed of simulations is an important factor

Jamming transition in a homogeneous one-dimensional system: the Bus Route Model

We present a driven diffusive model which we call the Bus Route Model. The model is defined on a one-dimensional lattice, with each lattice site having two binary variables, one of which is conserved (``buses'') and one of which is non-conserved (``passengers''). The buses are driven in a preferred direction and are slowed down by the presence of passengers who arrive with rate lambda. We study the model by simulation, heuristic argument and a mean-field theory. All these approaches provide strong evidence of a transition between an inhomogeneous ``jammed'' phase (where the buses bunch together) and a homogeneous phase as the bus density is increased. However, we argue that a strict phase transition is present only in the limit lambda -> 0. For small lambda, we argue that the transition is replaced by an abrupt crossover which is exponentially sharp in 1/lambda. We also study the coarsening of gaps between buses in the jammed regime. An alternative interpretation of the model is given in which the spaces between ``buses'' and the buses themselves are interchanged. This describes a system of particles whose mobility decreases the longer they have been stationary and could provide a model for, say, the flow of a gelling or sticky material along a pipe.Comment: 17 pages Revtex, 20 figures, submitted to Phys. Rev.

Phases of a conserved mass model of aggregation with fragmentation at fixed sites

To study the effect of quenched disorder in a class of reaction-diffusion systems, we introduce a conserved mass model of diffusion and aggregation in which the mass moves as a whole to a nearest neighbour on most sites while it fragments off as a single monomer (i.e. chips off) from certain fixed sites. Once the mass leaves any site, it coalesces with the mass present on its neighbour. We study in detail the effect of a \emph{single} chipping site on the steady state in arbitrary dimensions, with and without bias. In the thermodynamic limit, the system can exist in one of the following phases -- (a) Pinned Aggregate (PA) phase in which an infinite aggregate (with mass proportional to the volume of the system) appears with probability one at the chipping site but not in the bulk. (b) Unpinned Aggregate (UA) phase in which \emph{both} the chipping site and the bulk can support an infinite aggregate simultaneously. (c) Non Aggregate (NA) phase in which there is no infinite cluster. Our analytical and numerical studies show that the system exists in the UA phase in all cases except in 1d with bias. In the latter case, there is a phase transition from the NA phase to the PA phase as density is increased. A variant of the above aggregation model is also considered in which total particle number is conserved and chipping occurs at a fixed site, but the particles do not interact with each other at other sites. This model is solved exactly by mapping it to a Zero Range Process. With increasing density, it exhibits a phase transition from the NA phase to the PA phase in all dimensions, irrespective of bias. Finally, we discuss the likely behaviour of the system in the presence of extensive disorder.Comment: RevTex, 19 pages including 11 figures, submitted to Phys. Rev.

Long Days Enhance Recognition Memory and Increase Insulin-like Growth Factor 2 in the Hippocampus

Light improves cognitive function in humans; however, the neurobiological mechanisms underlying positive effects of light remain unclear. One obstacle is that most rodent models have employed lighting conditions that cause cognitive deficits rather than improvements. Here we have developed a mouse model where light improves cognitive function, which provides insight into mechanisms underlying positive effects of light. To increase light exposure without eliminating daily rhythms, we exposed mice to either a standard photoperiod or a long day photoperiod. Long days enhanced long-term recognition memory, and this effect was abolished by loss of the photopigment melanopsin. Further, long days markedly altered hippocampal clock function and elevated transcription of Insulin-like Growth Factor2 (Igf2). Up-regulation of Igf2 occurred in tandem with suppression of its transcriptional repressor Wilm’s tumor1. Consistent with molecular de-repression of Igf2, IGF2 expression was increased in the hippocampus before and after memory training. Lastly, long days occluded IGF2-induced improvements in recognition memory. Collectively, these results suggest that light changes hippocampal clock function to alter memory, highlighting novel mechanisms that may contribute to the positive effects of light. Furthermore, this study provides insight into how the circadian clock can regulate hippocampus-dependent learning by controlling molecular processes required for memory consolidation

A coarse grained model of granular compaction and relaxation

We introduce a theoretical model for the compaction of granular materials by discrete vibrations which is expected to hold when the intensity of vibration is low. The dynamical unit is taken to be clusters of granules that belong to the same collective structure. We rigourously construct the model from first principles and show that numerical solutions compare favourably with a range of experimental results. This includes the logarithmic relaxation towards a statistical steady state, the effect of varying the intensity of vibration resulting in a so-called `annealing' curve, and the power spectrum of density fluctuations in the steady state itself. A mean-field version of the model is introduced which shares many features with the exact model and is open to quantitative analysi

Kinetics of catalysis with surface disorder

We study the effects of generalised surface disorder on the monomer-monomer model of heterogeneous catalysis, where disorder is implemented by allowing different adsorption rates for each lattice site. By mapping the system in the reaction-controlled limit onto a kinetic Ising model, we derive the rate equations for the one and two-spin correlation functions. There is good agreement between these equations and numerical simulations. We then study the inclusion of desorption of monomers from the substrate, first by both species and then by just one, and find exact time-dependent solutions for the one-spin correlation functions.Comment: LaTex, 19 pages, 1 figure included, requires epsf.st