Series expansion studies of random sequential adsorption with diffusional relaxation

We obtain long series (28 terms or more) for the coverage (occupation fraction) $\theta$, in powers of time $t$ for two models of random sequential adsorption with diffusional relaxation using an efficient algorithm developed by the authors. Three different kinds of analyses of the series are performed for a wide range of $\gamma$, the rate of diffusion of the adsorbed particles, to investigate the power law approach of $\theta$ at large times. We find that the primitive series expansions in time $t$ for $\theta$ capture rich short and intermediate time kinetics of the systems very well. However, we see that the series are still not long enough to extract the kinetics at large times for general $\gamma$. We have performed extensive computer simulations employing an efficient event-driven algorithm to confirm the $t^{-1/2}$ saturation approach of $\theta$ at large times for both models, as well as to investigate the short and intermediate time behaviors of the systems.Comment: 35 pages. revtex. 16 eps figures. Series expansion coefficients are attached at the end of the soure/LaTex file (named diff.tex). uses fleqn.st

An investigation into the role of proteinase-activated receptor 2 on neuronal excitability and synaptic transmission in the hippocampus

Proteinase-activated receptor 2 (PAR-2) belongs to a novel family of G-protein coupled receptors that are unique in their activation mechanism by which a proteolytic cleavage at N-terminus by a proteinase reveals a ‘tethered ligand’ to activate the receptor. Albeit at a low level, PAR-2 is extensively expressed in normal and pathological brains, including the hippocampus. Qualitative studies into the expression of PAR-2 in several disease conditions, including ischaemia, HIV-associated dementia, Parkinson’s disease, Alzheimer’s disease, as well as multiple sclerosis, have suggested that PAR-2 plays either degenerative or protective role depending on in which cell type an increase in PAR-2 expression is observed. However, its potential roles in modulating neuronal excitability, synaptic transmission as well as network activities remain to be determined. Utilising the whole-cell patch clamp recording technique, I demonstrate, for the first time, that the activation of PAR-2 leads to a depolarisation of cultured hippocampal neurones following application of SLIGRL (100microM), a selective PAR-2 activating peptide (5.52 ± 1.48mV, n=16, P<0.05) and paradoxically a reduction of spontaneous action potential (AP) frequency (29.63 ± 5.03% of control, n=13, P<0.05). Pharmacological manipulation reveals that the PAR-2-mediated depolarisation is most likely dependent on astrocytic glutamate release, which takes effect on ionotropic glutamate receptors. In addition, an overt depression of synaptic transmission among the cultured neurones upon PAR-2 activation is more likely to cause the reduction of spontaneous APs. In further experiments, I show, for the first time, that the activation of PAR-2 induces a long term depression (LTD) of glutamatergic synaptic transmission at the Schaffer collateral-to-CA1 synapse in acute hippocampal slices following SLIGRL (100microM) application (80.75 ± 2.54% of control at 30 minute, n=12, P<0.05). Additionally, this novel form of LTD is independent of metabotropic glutamate receptors but mediated by NR2B subunit-containing N-methyl-D-aspartic acid (NMDA) receptors. It is also suggested from these experiments that glial-neuronal signalling is contributing to this novel form of LTD. In the final set of experiments, by monitoring field potentials in the stratum pyramidale of the CA3 area in acute hippocampal slices, I demonstrate that PAR-2 activation depresses the frequency of epileptiform activities induced by the application of 4-AP/0 Mg2+, an in vitro model of epilepsy (1.53 ± 0.21Hz to 1.18 ± 0.17Hz, n=13, P0.05, 100microM SLIGRL). In summary, in this thesis, I demonstrate that PAR-2 modulates neuronal excitability and depresses excitatory synaptic transmission in the hippocampus. These data indicate that PAR-2 may play a regulatory role in neuronal signalling at single cell level by controlling neuronal intrinsic properties, as well as at synaptic level by tuning excitatory synaptic strength, which ultimately affects global excitability in the neural circuits as a whole. Therefore, this investigation suggests a novel physiological/pathophysiological role for PAR-2 in the brain. These data may reveal valuable clues for the development of drugs targeting a novel and potentially promising candidate

A kinematic wave theory of capacity drop

Capacity drop at active bottlenecks is one of the most puzzling traffic phenomena, but a thorough understanding is practically important for designing variable speed limit and ramp metering strategies. In this study, we attempt to develop a simple model of capacity drop within the framework of kinematic wave theory based on the observation that capacity drop occurs when an upstream queue forms at an active bottleneck. In addition, we assume that the fundamental diagrams are continuous in steady states. This assumption is consistent with observations and can avoid unrealistic infinite characteristic wave speeds in discontinuous fundamental diagrams. A core component of the new model is an entropy condition defined by a discontinuous boundary flux function. For a lane-drop area, we demonstrate that the model is well-defined, and its Riemann problem can be uniquely solved. We theoretically discuss traffic stability with this model subject to perturbations in density, upstream demand, and downstream supply. We clarify that discontinuous flow-density relations, or so-called "discontinuous" fundamental diagrams, are caused by incomplete observations of traffic states. Theoretical results are consistent with observations in the literature and are verified by numerical simulations and empirical observations. We finally discuss potential applications and future studies.Comment: 29 pages, 10 figure

Engineering Nanostructured MnO2 for High Performance Supercapacitors

Manganese oxides (MnO2) have particularly received increasing attention owing to their high theoretical specific capacitance of 1370 F/g, low-cost, natural abundance, and environmental benignity. However, MnO2 suffers from low electrical conductivity (10−5 to 10−6 S/cm), low ionic diffusion constant (~10−13 cm2/V s), and low structural stability, which results in low electrochemical utilization and poor cycling life. It is therefore important to explore new strategies to improve the electrochemical performance of MnO2. The effective methods to maximize the performance involve (i) reducing MnO2 structures to a nanoscale range and (ii) compositing MnO2 with highly conductive materials. In this chapter, we will first introduce the rapid development of MnO2 nanostructures for supercapacitors. Then the fundamental charge storage mechanism of MnO2 will be specifically clarified. The preparation methods of MnO2 nanostructures and their composites will be subsequently summarized. Then, we will pay great attention to the most recent development of MnO2-based nanostructures for supercapacitors, which is the main body of this chapter. The practical application of MnO2 nanostructures for symmetric and asymmetric supercapacitors will be discussed. Finally, we will present a brief perspective regarding the rational design and synthesis of MnO2-based nanostructures

Evolution of particle size distribution in air in the rainfall process via the moment method

Population balance equation is converted to three moment equations to describe the dynamical behavior of particle size distribution in air in the rainfall. The scavenging coefficient is expressed as a polynomial function of the particle diameter, the raindrop diameter and the raindrop velocity. The evolutions of particle size distribution are simulated numerically and the effects of the raindrop size distribution on particle size distribution are studied. The results show that the raindrops with smaller geometric mean diameter and geometric standard deviation of size remove particles much more efficiently. The particles which fall in the “greenfield gap” are the most difficult to be scavenged from the air