Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation and Fragmentation

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady state mass distribution decays exponentially for large mass in one phase. On the contrary, in the other phase it has a power law tail and in addition an infinite aggregate. The model is solved exactly within a mean field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent $\chi$ and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.Comment: revtex file with 7 figure

Passive Sliders on Fluctuating Surfaces: Strong-Clustering States

We study the clustering properties of particles sliding downwards on a fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo simulations on a discrete version of the problem in one dimension reveal that particles cluster very strongly: the two point density correlation function scales with the system size with a scaling function which diverges at small argument. Analytic results are obtained for the Sinai problem of random walkers in a quenched random landscape. This equilibrium system too has a singular scaling function which agrees remarkably with that for advected particles.Comment: To be published in Physical Review Letter

Conservation Laws and Integrability of a One-dimensional Model of Diffusing Dimers

We study a model of assisted diffusion of hard-core particles on a line. The model shows strongly ergodicity breaking : configuration space breaks up into an exponentially large number of disconnected sectors. We determine this sector-decomposion exactly. Within each sector the model is reducible to the simple exclusion process, and is thus equivalent to the Heisenberg model and is fully integrable. We discuss additional symmetries of the equivalent quantum Hamiltonian which relate observables in different sectors. In some sectors, the long-time decay of correlation functions is qualitatively different from that of the simple exclusion process. These decays in different sectors are deduced from an exact mapping to a model of the diffusion of hard-core random walkers with conserved spins, and are also verified numerically. We also discuss some implications of the existence of an infinity of conservation laws for a hydrodynamic description.Comment: 39 pages, with 5 eps figures, to appear in J. Stat. Phys. (March 1997

Finite-size effects on the dynamics of the zero-range process

We study finite-size effects on the dynamics of a one-dimensional zero-range process which shows a phase transition from a low-density disordered phase to a high-density condensed phase. The current fluctuations in the steady state show striking differences in the two phases. In the disordered phase, the variance of the integrated current shows damped oscillations in time due to the motion of fluctuations around the ring as a dissipating kinematic wave. In the condensed phase, this wave cannot propagate through the condensate, and the dynamics is dominated by the long-time relocation of the condensate from site to site.Comment: 5 pages, 5 figures, version published in Phys. Rev. E Rapid Communication

Dynamics of Shock Probes in Driven Diffusive Systems

We study the dynamics of shock-tracking probe particles in driven diffusive systems and also in equilibrium systems. In a driven system, they induce a diverging timescale that marks the crossover between a passive scalar regime at early times and a diffusive regime at late times; a scaling form characterises this crossover. Introduction of probes into an equilibrium system gives rise to a system-wide density gradient, and the presence of even a single probe can be felt across the entire system.Comment: Accepted in Journal of Statistical Mechanics: Theory and Experimen

Steady State and Dynamics of Driven Diffusive Systems with Quenched Disorder

We study the effect of quenched disorder on nonequilibrium systems of interacting particles, specifically, driven diffusive lattice gases with spatially disordered jump rates. The exact steady-state measure is found for a class of models evolving by drop-push dynamics, allowing several physical quantities to be calculated. Dynamical correlations are studied numerically in one dimension. We conjecture that the relevance of quenched disorder depends crucially upon the speed of the kinematic waves in the system. Time-dependent correlation functions, which monitor the dissipation of kinematic waves, behave as in pure system if the wave speed is non-zero. When the wave speed vanishes, e.g. for the disordered exclusion process close to half filling, disorder is strongly relevant and induces separation of phases with different macroscopic densities. In this case the exponent characterizing the dynamical correlation function changes.Comment: 4 pages, RevTeX, 4 eps figures included using 'psfig.sty

Independent Assessment of the 2018–19 fish deaths in the lower Darling

Three significant fish death events occurred in the Darling River near Menindee between December 2018 and January 2019. The three events took place within two adjacent weir pools in a 30 km reach of river between Texas Downs Station and Weir 32 (DPI NSW Fisheries, 2019). The main native fish species involved included Murray Cod, Silver Perch, Golden Perch, Bony Herring, with mortality estimates in the range of hundreds of thousands to over a million fish. Though post-event fish population sampling is yet to be conducted, we expect that these mortalities will impact populations in the lower Darling River, and perhaps beyond, for many years. These events constitute a serious ecological shock to the lower Darling and reverse positive ecological outcomes that had accrued from environmental watering programs. We have determined that fish deaths events were primarily caused by local hydrological and climatic conditions (Figure 1-1). The extreme hot and dry climate during 2018, extending into 2019, shaped the conditions that saw a large fish biomass, which had flourished since favourable spawning conditions in 2016, isolated in the weir pools around Menindee, with no means of escaping upstream or downstream. Those adverse climate conditions also shaped the subsequent algal bloom development and the strong and persistent thermal stratification of the weir pools, which created hypoxic conditions in the bottom waters of the pools. All that was needed for this to have a fatal impact on the fish was a trigger for the weir pool waters to become destratified and deprive the fish of oxygen. That trigger duly arrived with a series of sudden cool changes in the weather, with temperature drops and wind action initiating the turnover of the weir pool waters. This sudden depletion of oxygen, combined with the already high water and air temperatures, would have offered the large biomass of stressed fish no means of escape. For each fish death event, the weir pool in which the fish were trapped was bordered downstream by an impenetrable barrier (a weir) and upstream by a dry channel. Ultimately, it was the rapid transition from very favourable conditions to very adverse ones that resulted in such high numbers of fish deaths. We have also determined that the fish death events were shaped by a broader climatic, hydrologic and basin management context that placed the lower Darling River at risk of such fish deaths. The preceding six years (since 2012) had seen two high flow events that had delivered water into Menindee Lakes (2012 and 2016) and offered opportunities for substantial fish breeding and recruitment. Fish populations were further enhanced by the judicious use of environmental water. The end result was a considerable biomass of fish within the Menindee Lakes, post 2016. Outside of these high flow events there were minimal flows in the Darling River below Bourke. This period was preceded by the Millennium drought (2000-2010), during which time flows across the entire northern Murray– Darling Basin were reduced. All of the hydroclimatic evidence available indicates that the years since 2000 have been some of the driest on record, in terms of inflows into major upstream storages, combined with an increased number of extreme heat days, which would have had a major impact on water quality in remnant pools. Soon after the events, Basin government officials met and developed an action plan to respond to the crisis. Immediate actions underway include additional water quality monitoring in the lower Darling, the use of aerators and targeted fish relocations. These immediate actions are welcomed, however, the current situation remains critical – without significant inflows, further deaths of surviving fish may be expected. We consider that priorities and actions in the short-term should focus on anticipating a repeat of ‘worst-case scenario’ outcomes with responses focussed at the site scale. In addition, the Minister for Agriculture and Water Resources announced a Native Fish Management and Recovery Strategy to help manage and recover fish populations across the Basin. We consider that this provides a good opportunity to enhance native fish management and support native fish population recovery and should be developed and implemented through a genuine collaboration between governments, communities, and Traditional Owners. The strategy needs to build on existing and lapsed native fish programs across the Basin. Through our investigations, it became evident to us that, over the long-term, the extant water access arrangements in the northern Basin, as well as limitations in the river models used to plan water sharing, place the lower Darling River at a higher risk of conditions that can lead to fish deaths during droughts than has previously been anticipated. Given that we are witnessing an increasing frequency of low inflow sequences in the northern Basin, this presents a serious problem for safeguarding fish populations, and populations of other resident biota, during drought in the lower Darling. We have identified that changes to Barwon–Darling water access arrangements made by NSW just prior to the commencement of the Basin Plan in 2012 have enhanced the ability of irrigators to access water during low flow periods and during the first flow event immediately after a cease-to-flow period. Further, it appears that the river models used to develop water sharing arrangements have a tendency to overestimate streamflows during dry sequences, and hence underestimate the impacts of extractions during dry times