126,750 research outputs found

    Criticality and Condensation in a Non-Conserving Zero Range Process

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    The Zero-Range Process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real-space condensation. Within this model the system is critical only at the transition point. Here we consider a non-conserving Zero-Range Process which is shown to exhibit generic critical phases which exist in a range of creation and annihilation parameters. The model also exhibits phases characterised by mesocondensates each of which contains a subextensive number of particles. A detailed phase diagram, delineating the various phases, is derived.Comment: 15 pages, 4 figure, published versi

    Factorised steady states for multi-species mass transfer models

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    A general class of mass transport models with Q species of conserved mass is considered. The models are defined on a lattice with parallel discrete time update rules. For one-dimensional, totally asymmetric dynamics we derive necessary and sufficient conditions on the mass transfer dynamics under which the steady state factorises. We generalise the model to mass transfer on arbitrary lattices and present sufficient conditions for factorisation. In both cases, explicit results for random sequential update and continuous time limits are given.Comment: 11 page

    Construction of the factorized steady state distribution in models of mass transport

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    For a class of one-dimensional mass transport models we present a simple and direct test on the chipping functions, which define the probabilities for mass to be transferred to neighbouring sites, to determine whether the stationary distribution is factorized. In cases where the answer is affirmative, we provide an explicit method for constructing the single-site weight function. As an illustration of the power of this approach, previously known results on the Zero-range process and Asymmetric random average process are recovered in a few lines. We also construct new models, namely a generalized Zero-range process and a binomial chipping model, which have factorized steady states.Comment: 6 pages, no figure

    Phase Transitions in one-dimensional nonequilibrium systems

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    The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which may allow phase transitions and phase ordering in one dimension are identified. We then give an overview of the one-dimensional phase transitions which we have been studied in nonequilibrium systems. A particularly simple model, the zero-range process, for which the steady state is know exactly as a product measure, is discussed in some detail. Generalisations of the model, for which a product measure still holds, are also discussed. We analyse in detail a condensation phase transition in the model and show how conditions under which it may occur may be related to the existence of an effective long-range energy function. Although the zero-range process is not well known within the physics community, several nonequilibrium models have been proposed that are examples of a zero-range process, or closely related to it, and we review these applications here.Comment: latex, 28 pages, review article; references update

    Factors affecting colour and cloud stability in a wildberry herbal drink : a thesis presented in partial fulfilment of the requirements for the degree of M. Tech. in Food Science at Massey University, Albany, New Zealand

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    An investigation was undertaken into the stability of the natural colour, from anthocyanins, and cloud in a Wildberry Herbal fruit drink. The fruit drinks consisted of cloudy apple and berry fruit juice with natural herb extracts and flavours. The objectives of the research were to identify the cause of cloud instability and sediment formation in the drink; determine the effect of ascorbic acid, berryfruit juice volume, storage temperature and light on anthocyanin stability; investigate the use of stabilisers to prevent sediment formation and determine consumer acceptability of a modified drink. The cause of sediment formation was determined by analysing the contribution of the major ingredients to the total amount of sediment formed. To minimise the sediment, a range of commercially available polysaccharide stabilisers were added to the drink and the amount of sediment formed determined. A consumer sensory evaluation was undertaken to determine consumer acceptability of drinks in which stabilisers had been added to improve the cloud stability. The factors affecting the anthocyanin's in the drink were analysed using a fractional factorial experimental design. The effect of the commercial pasteurisation process on the colour was also investigated. The formation of sediment was identified as being the result of complexing between the unstable cloud of the cloudy apple juice and polyphenolics, including anthocyanins, in the berryfruit juice. No sediment formed during eight weeks storage when clarified apple juice was substituted for cloudy apple juice. The sediment was reduced by approximately 45% using stabiliser systems consisting of either xanthan or a xanthan/propylene glycol alginate mixture. Consumer sensory evaluation of the modified drinks found no significant difference in liking from the standard drink. The anthocyanin loss in the drink was found to be significantly affected by increased storage temperature. Elderberry juice was found to have better colour stability over blackcurrant juice. Pasteurisation did not initially affect the colour stability of the drink. It was recommended that the composition of the Wildberry Herbal drink remain unchanged. The product should be stored at as low a temperature as possible. The drinks should be cooled to ambient temperature as quickly as possible after the pasteurisation process

    Bose-Einstein Condensation In Disordered Exclusion Models and Relation to Traffic Flow

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    A disordered version of the one dimensional asymmetric exclusion model where the particle hopping rates are quenched random variables is studied. The steady state is solved exactly by use of a matrix product. It is shown how the phenomenon of Bose condensation whereby a finite fraction of the empty sites are condensed in front of the slowest particle may occur. Above a critical density of particles a phase transition occurs out of the low density phase (Bose condensate) to a high density phase. An exponent describing the decrease of the steady state velocity as the density of particles goes above the critical value is calculated analytically and shown to depend on the distribution of hopping rates. The relation to traffic flow models is discussed.Comment: 7 pages, Late

    Condensation Transitions in Nonequilibrium systems

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    Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium- for example phase transitions in one-dimensional systems. In this talk I will review several `condensation' transitions that occur when a conserved quantity is driven through the system. Although the condensation is spatial, i.e. a finite fraction of the conserved quantity condenses into a small spatial region, useful comparison can be made with usual Bose-Einstein condensation. Amongst some one-dimensional examples I will discuss the `Bus Route Model' where the condensation corresponds to the clustering together of buses moving along a bus-route.Comment: 10 pages. Lecture from TH-2002, Pari

    Episcopal Advisor\u27s Page

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