Non-equilibrium Coexistence Research Articles

Mechanical theory of nonequilibrium coexistence and motility-induced phase separation

Nonequilibrium phase transitions are routinely observed in both natural and synthetic systems. The ubiquity of these transitions highlights the conspicuous absence of a general theory of phase coexistence that is broadly applicable to both nonequilibrium and equilibrium systems. Here, we present a general mechanical theory for phase separation rooted in ideas explored nearly a half-century ago in the study of inhomogeneous fluids. The core idea is that the mechanical forces within the interface separating two coexisting phases uniquely determine coexistence criteria, regardless of whether a system is in equilibrium or not. We demonstrate the power and utility of this theory by applying it to active Brownian particles, predicting a quantitative phase diagram for motility-induced phase separation in both two and three dimensions. This formulation additionally allows for the prediction of novel interfacial phenomena, such as an increasing interface width while moving deeper into the two-phase region, a uniquely nonequilibrium effect confirmed by computer simulations. The self-consistent determination of bulk phase behavior and interfacial phenomena offered by this mechanical perspective provide a concrete path forward toward a general theory for nonequilibrium phase transitions.

Self-sustained non-equilibrium co-existence of fluid and solid states in a strongly coupled complex plasma system

A complex (dusty) plasma system is well known as a paradigmatic model for studying the kinetics of solid-liquid phase transitions in inactive condensed matter. At the same time, under certain conditions a complex plasma system can also display characteristics of an active medium with the micron-sized particles converting energy of the ambient environment into motility and thereby becoming active. We present a detailed analysis of the experimental complex plasmas system that shows evidence of a non-equilibrium stationary coexistence between a cold crystalline and a hot fluid state in the structure due to the conversion of plasma energy into the motion energy of microparticles in the central region of the system. The plasma mediated non-reciprocal interaction between the dust particles is the underlying mechanism for the enormous heating of the central subsystem, and it acts as a micro-scale energy source that keeps the central subsystem in the molten state. Accurate multiscale simulations of the system based on combined molecular dynamics and particle-in-cell approaches show that strong structural nonuniformity of the system under the action of electostatic trap makes development of instabilities a local process. We present both experimental tests conducted with a complex plasmas system in a DC glow discharge plasma and a detailed theoretical analysis.

Competitive coexistence of seasonal breeders.

Many species are annual breeders who, between reproductive events, consume resources and may die. Their resource often reproduces continuously or has short, overlapping generations. An accurate model for such life cycles needs to represent both, the discrete- and the continuous-time processes in the community. The dynamics of a single discrete breeder and its resource can differ significantly from that of a fully continuous consumer-resource community (e.g., Lotka-Volterra) and that of a fully discrete one (e.g., Nicholson-Bailey). We study the dynamics of multiple discrete breeders on a single resource and identify a number of coexistence mechanisms and complex dynamics. The resource grows logistically, resource consumption is linear and consumer reproduction can be linear or nonlinear. We derive explicit conditions for the positive equilibrium state to exist and for mutual invasion to occur at that equilibrium. Stable equilibrium coexistence of more than one consumer is possible only when reproduction is nonlinear. Higher resource growth rate generally allows more consumers to stably coexist. Our explicit formulas allow us to generate communities of many coexisting consumers. Total biomass in the system seems to increase with the number of coexisting consumers. Complex patterns of coexistence arise, including bistability of equilibrium and non-equilibrium coexistence. The mixed continuous-discrete modeling approach can easily be adapted to study how certain aspects of global change affect discrete breeder communities.

Shear melting at the crystal-liquid interface: Erosion and the asymmetric suppression of interface fluctuations.

The influence of an applied shear on the planar crystal-melt interface is modeled by a nonlinear stochastic partial differential equation of the interface fluctuations. A feature of this theory is the asymmetric destruction of interface fluctuations due to advection of the crystal protrusions on the liquid side of the interface only. We show that this model is able to qualitatively reproduce the nonequilibrium coexistence line found in simulations. The impact of shear on spherical clusters is also addressed.

Multiple resource limitation: nonequilibrium coexistence of species in a competition model using a synthesizing unit

During the last two decades, the simple view of resource limitation by a single resource has been changed due to the realization that co-limitation by multiple resources is often an important determinant of species growth. Hence, the multiple resource limitation hypothesis needs to be taken into account, when communities of species competing for resources are considered. We present a multiple species–multiple resource competition model which is based on the concept of synthesizing unit to formulate the growth rates of species competing for interactive essential resources. Using this model, we demonstrate that a more mechanistic explanation of interactive effects of co-limitation may lead to the known complex dynamics including nonequilibrium states as oscillations and chaos. We compare our findings with earlier investigations on biological mechanisms that can predict the outcome of multispecies competition. Moreover, we show that this model yields a periodic state where more species than limiting complementary resources can coexist (supersaturation) in a homogeneous environment. We identify two novel mechanisms, how such a state can emerge: a transcritical bifurcation of a limit cycle and a transition from a heteroclinic cycle. Furthermore, we demonstrate the robustness of the phenomenon of supersaturation when the environmental conditions are varied.

Coexistence of Cycling and Dispersing Consumer Species: Armstrong and McGehee in Space

Two competing consumer species may coexist using a single homogeneous resource when the more efficient consumer—the one having the lowest equilibrium resource density—has a more nonlinear functional response that generates consumer‐resource cycles. We extend this model of nonequilibrium coexistence, as proposed by Armstrong and McGehee, by putting the interaction into a spatial context using two frameworks: a spatially explicit individual‐based model and a spatially implicit metapopulation model. We find that Armstrong and McGehee’s mechanism of coexistence can operate in a spatial context. However, individual‐based simulations suggest that decreased dispersal restricts coexistence in most cases, whereas differential equation models of metapopulations suggest that a low rate of dispersal between subpopulations often increases the coexistence region. This difference arises in part because of two potentially opposing effects on coexistence due to the asynchrony in the temporal dynamics at different locations. Asynchrony implies that the less efficient species is more likely to be favored in some spatial locations at any given time, which broadens the conditions for coexistence. On the other hand, asynchrony and dispersal can also reduce the amplitude of local population cycles, which restricts coexistence. The relative influence of these two effects depends on details of the population dynamics and the representation of space. Our results also demonstrate that coexistence via the Armstrong‐McGehee mechanism can occur even when there is little variation in the global densities of either the consumers or the resource, suggesting that empirical studies of the mechanisms should measure densities on several spatial scales.

Coexistence of Cycling and Dispersing Consumer Species: Armstrong and McGehee in Space

Two competing consumer species may coexist using a single homogeneous resource when the more efficient consumer--the one having the lowest equilibrium resource density--has a more nonlinear functional response that generates consumer-resource cycles. We extend this model of nonequilibrium coexistence, as proposed by Armstrong and McGehee, by putting the interaction into a spatial context using two frameworks: a spatially explicit individual-based model and a spatially implicit metapopulation model. We find that Armstrong and McGehee's mechanism of coexistence can operate in a spatial context. However, individual-based simulations suggest that decreased dispersal restricts coexistence in most cases, whereas differential equation models of metapopulations suggest that a low rate of dispersal between subpopulations often increases the coexistence region. This difference arises in part because of two potentially opposing effects on coexistence due to the asynchrony in the temporal dynamics at different locations. Asynchrony implies that the less efficient species is more likely to be favored in some spatial locations at any given time, which broadens the conditions for coexistence. On the other hand, asynchrony and dispersal can also reduce the amplitude of local population cycles, which restricts coexistence. The relative influence of these two effects depends on details of the population dynamics and the representation of space. Our results also demonstrate that coexistence via the Armstrong-McGehee mechanism can occur even when there is little variation in the global densities of either the consumers or the resource, suggesting that empirical studies of the mechanisms should measure densities on several spatial scales.

Simulation of the coexistence of a shearing liquid and a strained crystal

The coexistence between a strained crystal and its shearing melt is studied using nonequilibrium molecular dynamics simulations of Lennard-Jones particles. The coexistence is found to be independent of initial conditions, boundary effects, and the details of the thermostat. The nonequilibrium phase diagram is presented. The shear stress at coexistence is found to be significantly smaller than the yield stress of the crystal. It is demonstrated that there exists no physically reasonable prescription for a nonequilibrium analogue of chemical potential for the shearing liquid by which the coexistence could be attributed to an equality of chemical potentials between the two phases. We conclude that the nonequilibrium coexistence is determined by the stability of the interface.

Factors determining crystal--liquid coexistence under shear.

The interaction between an imposed shear flow and an order--disorder transition underlies a broad range of phenomena. Under the influence of shear flow, a variety of soft matter is observed to spontaneously form bands characterized by different local order---for example, thermotropic liquid crystals subjected to shear flow exhibit rich phase behaviour. The stability of order under the influence of shear flow is also fundamental to understanding frictional wear and lubrication. Although there exists a well developed theoretical approach to the influence of shear flow on continuous transitions in fluid mixtures, little is known about the underlying principles governing non-equilibrium coexistence between phases of different symmetry. Here we show, using non-equilibrium molecular dynamics simulations of a system of spherical particles, that a stationary coexistence exists between a strained crystal and the shearing liquid, and that this coexistence cannot be accounted for by invoking a non-equilibrium analogue of the chemical potential. Instead of such thermodynamic arguments, we argue that a balancing of the crystal growth rate with the rate of surface erosion by the shearing melt can account for the observed coexistence.

Nonequilibrium coexistence of solid and liquid particles in Arctic stratospheric clouds

Observations of polar stratospheric clouds (PSCs) from Ny Ålesund, Spitsbergen, have been examined to quantify the occurrence of solid particles. The polarized backscatter ratio was found to be a more sensitive indicator of the presence of non‐spherical (solid) particles in a PSC than the aerosol depolarization, which approaches zero for clouds containing a large volume of liquid droplets. The analysis corroborates our previous finding that type Ia PSCs cannot be composed of nitric acid trihydrate particles in equilibrium with the gas phase, which would lead to a much too high backscatter ratio. Conversely, type Ib PSCs, previously thought to be composed solely of liquid droplets, often contain a very small fraction of solid particles. These clouds develop a high parallel backscatter, arising from Mie scattering by droplets, and a nonvanishing perpendicular signal due to the few solid particles. Other type Ib PSCs appear to contain only liquid particles. The mixed liquid/solid clouds are observed on the smallest spatial and temporal scale resolvable by the lidar instrument (30 m, l min), implying that their properties are not a result of spatial averaging of different cloud types. Comparison of the observations with optical calculations shows that such nonequilibrium particle distributions are to be expected, as temperature changes are sufficiently rapid to prevent the particles from assuming equilibrium sizes. The observed optical characteristics of type Ia and type Ib clouds can be reproduced in a model by assuming that a very small fraction of the particles are composed of nitric acid hydrate, with the majority being binary H2SO4/H2O or ternary HNO3/H2SO4/H2O droplets.

Chaotic flow: the physics of species coexistence.

Hydrodynamical phenomena play a keystone role in the population dynamics of passively advected species such as phytoplankton and replicating macromolecules. Recent developments in the field of chaotic advection in hydrodynamical flows encourage us to revisit the population dynamics of species competing for the same resource in an open aquatic system. If this aquatic environment is homogeneous and well-mixed then classical studies predict competitive exclusion of all but the most perfectly adapted species. In fact, this homogeneity is very rare, and the species of the community (at least on an ecological observation time scale) are in nonequilibrium coexistence. We argue that a peculiar small-scale, spatial heterogeneity generated by chaotic advection can lead to coexistence. In open flows this imperfect mixing lets the populations accumulate along fractal filaments, where competition is governed by an "advantage of rarity" principle. The possibility of this generic coexistence sheds light on the enrichment of phytoplankton and the information integration in early macromolecule evolution.

Phyllocladus aspleniifolius: Variability in the Population Structure, the Regeneration Niche and Dispersion Patterns in Tasmanian Forests

This study aimed to determine the range of the regeneration niches of Phyllocladus aspleniifolius (Podocarpaceae) in terms of differential microsite occupation, population structure and dispersion pattern at 50 sites. The distribution and sizes of stems were mapped on belt transects to within 0.5 m, and the microsites of seedlings and saplings were recorded. A variety of population structures exist and are related to community floristics and structure. Community variation provides different microsite opportunities. Phyllocladus aspleniifolius showed a preference for elevated sites, including logs, buttresses and old stump mounds. Aggregation of regeneration is common and is determined by microsite distribution and seed dispersal characteristics. It is concluded that although the regeneration of P. aspleniifolius is favoured by catastrophic disturbance, smaller scale processes such as those evoked in the concept of non-equilibrium coexistence are likely to allow P. aspleniifolius to persist in all communities throughout its range in the absence of large scale disturbances.

Non-Equilibrium Phase Transitions in Nematic Liquid Crystals under Shear Flow†

Abstract We discuss the impact of shear flow on the isotropic-nematic transition in crystalline liquids, paying particular attention to the notion of a non-equilibrium coexistence line. We establish a non-equilibrium phase diagram spanned by temperature and externally applied shear stress, by interpreting thc locally stable solutions to the equations of motion for the entire nematic order parameter and fluid velocity, in the case of planar Couette flow. This system displays several characteristics reminiscent of homogeneous equilibrium phenomena: a region in the phase diagram in which two states are locally stable; a critical point at which this two-state region vanishes; and singularities associated with this non- equilibrium critical point. By analyzing inhomogeneous solutions of the equations of motion we address the issue of whether a particular state is selected within the two state region. We find state selection throughout the two-state region, except on a coexistence line interpolating between the...

Studies in SE Fennoscandian mires, with special regard to the use of multivariate techniques and the scaling of ecological gradients.

Abstract The study presents the results from an integrated approach to hydromorphology, species distribution, and ecological conditions in SE Fennoscandian bogs and poor fens. Patterns of distribution are observed on spatial scales ranging from 0.25 m2 to whole mires (1 km2), and the scope of the study extended to include the regional perspective. Detailed ecological studies studies are performed within a restricted part (0.3 km2) of one mire complex, N. Kisselbergmosen, R{lkienes, SE Norway, while the distribution of plant species and hydromorphological mire types is studied within parts (1000 km2) of Akershus and Østfold counties, SE Norway. Patterns are interpreted by use of multivariate techniques, in particular ordination by detrended correspondence analysis (DCA). On the scale of one mire, four complex-gradients are shown to account for most of the vegetational variation. The relative merits of different sampling procedures and classification systems are discussed. On a broader scale, gradient relationships of vegetation, hydromorphology and species distributions can mostly be ascribed to variation in thermal and hygric factors, often operating in conjunction. Their effects on the vegetation are often mediated by differential water supply. Structuring factors in boreal mires are discussed, and interspecfic interaction as well as abiotic factors are important. The importance of interactions is higher in the bottom layer in the field layer. On a fine scale, boreal mires are considered to conform to the patch dynamics theory of non-equilibrium coexistence of species. On a broad scale, boreal mires appear to be in a dynamic equilibrium with present climatic conditions east of the limit for the onset of erosion. The common conceptual basis for descriptive biogeography and vegetation ecology is emphasized. Arguments in favour of scaling ecological gradients in units of compositional turnover are forwarded, and the properties of one such scaling method, the nonlinear rescaling procedure in DCA ordination, is outlined. The advantage of an integrated approach to ecological problems is emphasized.

Predator-mediated, non-equilibrium coexistence of tree-hole mosquitoes in southeastern North America.

Mosquito populations in tree holes in northern Florida (30.6° N lat.), USA are held below their carrying capacities by a self-limiting, cannabalistic predator. Within tree holes, extinctions and reinvasions are common; in the system as a whole, extinctions and immigrations occur without regard to community composition, tree-hole size or stability, or average number of species present. Little, if any, density-dependent development takes place. There is no evidence that the community ever reaches equilibrium, that competition is taking place, or that competition has been an important factor structuring this mosquito community. Rather, examination of related species in the same genera suggests that the principal determinants of their coexistence relate to the adaptations already possessed by each species at the time of their first encounter. Thus, unless experimentally demonstrated or reasonably inferred from circumstantial evidence, competition and coevolved niche shifts cannot be invoked to explain the coexistence of a diversity of species within a habitat type, no matter how circumscribed or discrete that habitat.

Non-Equilibrium Coexistence of Plants

PICKETT, S. T. A. (Botany Dept., Rutgers Univ., New Brunswick, NJ 08903). Nonequilibrium coexistence in plants. Bull. Torrey Bot. Club 107: 238-248. 1980.-Equilibrium plant communities are established by uninterrupted successions over several centuries. However, these equilibrium communities are often relatively poorer in species than some non-equilibrium community that preceded them. This, coupled with the paucity of confirmed within-community niche differentiation, suggests that factors preventing the establishment of a competitive equilibrium are critical to the coexistence of plants. Disturbance occurs frequently enough in many systems to destroy or disadvantage the competitive dominants of late successional communities and so allow the coexistence of species with many degrees of competitive ability. Without disturbance the persistence of certain species is threatened. The concept of patch dynamics is used to generalize and emphasize non-equilibrium coexistence.