Abstract:
Exclusive diffusion on a one-dimensional lattice is studied. In the model particles hop stochastically into both directions with different rates. At the ends of the lattice particles are injected and removed. The exact stationary probability measure is represented in form of a matrix product as a generalization of the solution given by Derrida et al \cite{dehp} for the fully asymmetric process. The phase diagram of the current on the infinite lattice is obtained. Analytic expressions for the current in the different phases are derived. The model is equivalent to a $XXZ$-Heisenberg chain with a certain type of boundary terms the ground state of which corresponds to the stationary solution of the master equation.

Abstract:
The study assesses the spatial distribution and sources of mercury contamination in the Ankobra River Basin in southwestern Ghana and discusses possible remediation options and challenges. Eighty-two (82) samples of water and streambed sediments from areas of active and historic artisanal mining and historic mine spoil from large-scale mining were analysed for their total mercury content using cold vapour Atomic Fluorescence Spectrometry (CV-AAS). The highest Hg concentrations were recorded from historic mine tailings, legacy of large scale mines in the area, which averaged 795 ppb but ranged from 80 ppb to 2500 ppb. Concentrations in streambed sediments averaged 139 ppb, but ranged from 63 ppb to 270 ppb. Water, expectedly, gave the lowest Hg concentrations with a mean value of 1.5 ppb, but ranged from below detection to 8 ppb. Areas worked by artisanal miners and historic tailings dumps at Bondaye and Prestea recorded the highest mercury values. These high mercury concentration sites constitute potential sources of major mercury pollution in the area and therefore require major and urgent clean up to mitigate any major health risks. However, any remediation strategy would require further and detailed study of the contaminated sites and an evaluation of known remediation techniques to achieve maximum results.

Abstract:
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is manifested by the existence of a phase in which the densities of the two species are not equal. In order to provide a more rigorous basis to these observations we consider the limit of the process when the rate at which particles leave the system goes to zero. In this limit the process reduces to a biased random walk in the positive quarter plane, with specific boundary conditions. The stationary probability measure of the position of the walker in the plane is shown to be concentrated around two symmetrically located points, one on each axis, corresponding to the fact that the system is typically in one of the two states of broken symmetry in the exclusion process. We compute the average time for the walker to traverse the quarter plane from one axis to the other, which corresponds to the average time separating two flips between states of broken symmetry in the exclusion process. This time is shown to diverge exponentially with the size of the chain.

Abstract:
We show that all zero energy eigenstates of an arbitrary $m$--state quantum spin chain Hamiltonian with nearest neighbor interaction in the bulk and single site boundary terms, which can also describe the dynamics of stochastic models, can be written as matrix product states. This means that the weights in these states can be expressed as expectation values in a Fock representation of an algebra generated by $2m$ operators fulfilling $m^2$ quadratic relations which are defined by the Hamiltonian.

Abstract:
We study a one-dimensional anisotropic exclusion model describing particles moving deterministically on a ring with a single defect across which they move with probability 0 < q < 1. We show that the stationary state of this model can be represented as a matrix-product state.

Abstract:
We study analytically a model where particles with a hard-core repulsion diffuse on a finite one-dimensional lattice with space-dependent, asymmetric hopping rates. The system dynamics are given by the \mbox{U$_{q}$[SU(2)]}-symmetric Hamiltonian of a generalized anisotropic Heisenberg antiferromagnet. Exploiting this symmetry we derive exact expressions for various correlation functions. We discuss the density profile and the two-point function and compute the correlation length $\xi_s$ as well as the correlation time $\xi_t$. The dynamics of the density and the correlations are shown to be governed by the energy gaps of a one-particle system. For large systems $\xi_s$ and $\xi_t$ depend only on the asymmetry. For small asymmetry one finds $\xi_t \sim \xi_s^2$ indicating a dynamical exponent $z=2$ as for symmetric diffusion.

Abstract:
We consider systems of particles hopping stochastically on $d$-dimensional lattices with space-dependent probabilities. We map the master equation onto an evolution equation in a Fock space where the dynamics are given by a quantum Hamiltonian (continuous time) or a transfer matrix resp. (discrete time). We show that under certain conditions the time-dependent two-point density correlation function in the $N$-particle steady state can be computed from the probability distribution of a single particle moving in the same environment. Focussing on exclusion models where each lattice site can be occupied by at most one particle we discuss as an example for such a stochastic process a generalized Heisenberg antiferromagnet where the strength of the spin-spin coupling is space-dependent. In discrete time one obtains for one-dimensional systems the diagonal-to-diagonal transfer matrix of the two-dimensional six-vertex model with space-dependent vertex weights. For a random distribution of the vertex weights one obtains a version of the random barrier model describing diffusion of particles in disordered media. We derive exact expressions for the averaged two-point density correlation functions in the presence of weak, correlated disorder.

Abstract:
We study the one dimensional partially asymmetric simple exclusion process (ASEP) with open boundaries, that describes a system of hard-core particles hopping stochastically on a chain coupled to reservoirs at both ends. Derrida, Evans, Hakim and Pasquier [J. Phys. A 26, 1493 (1993)] have shown that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra, closely related to the deformed oscillator-algebra. We construct all finite dimensional irreducible representations of this algebra. This enables us to compute the stationary bulk density as well as all correlation lengths for the ASEP on a set of special curves of the phase diagram.

Abstract:
The vascular endothelium plays a critical role in the control of blood flow. Altered endothelium-mediated vasodilator and vasoconstrictor mechanisms underlie key aspects of cardiovascular disease, including those in obesity. Whilst the mechanism of nitric oxide (NO)-mediated vasodilation has been extensively studied in obesity, little is known about the impact of obesity on vasodilation to the endothelium-derived hyperpolarization (EDH) mechanism; which predominates in smaller resistance vessels and is characterized in this study.

Abstract:
Stream sediment samples were analyzed for the concentrations of some trace metals in the Obuasi gold mining environment, Ghana. The objectives were to determine the possible impacts of mining operations in the area on sediments’ trace metal load, and the resulting effects on agriculture and livelihoods. The concentrations of arsenic (As), copper (Cu), lead (Pb), zinc (Zn), iron (Fe), with calcium (Ca) as reference element, were compared to their respective background concentrations to calculate the enrichment and contamination factors, and also geo-accumulation and pollution load indices of each trace metal. These were in turn compared to standard tables to determine the status of contamination. Q-mode hierarchical cluster analysis (HCA) was then applied to the samples for spatial classification. This study suggests probable contribution of mining and associated activities in the Obuasi area to the concentrations of trace metals especially arsenic, in the stream sediments. Three spatial relationships were revealed based on the concentrations of these trace metals from the Q-mode HCA. The samples presented generally high concentrations, which were more profound for samples taken closer to holding pond and tailings dams, and decreased downstream.