Breakdown of Hydrodynamics in a Simple One-Dimensional Fluid

We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches, e.g., the hydrodynamic profiles relax algebraically toward their equilibrium values. Deviations from local thermodynamic equilibrium are persistent, decaying as a power law of the distance to the shock layer. Non-equipartition is observed infinitely far from the shock wave, and the velocity-distribution moments exhibit multiscaling. These results question the validity of simple hydrodynamic theories to understand collective behavior in 1d fluids.Comment: 4 pages, 5 figure

Modeling M-Theory Vacua via Gauged S-Duality

We construct a model of M-theory vacua using gauged S-duality and the Chan-Paton symmetries by introducing an infinite number of open string charges. In the Bechi-Rouet-Stora-Tyutin formalism, the local description of the gauged S-duality on its moduli space of vacua is fully determined by one physical state condition on the vacua. We introduce the string probe of the spatial degrees of freedom and define the increment of the cosmic time. The dimensionality of space-time and the gauge group of the low energy effective theory originate in the symmetries (with or without their breakdown) in our model. This modeling leads to the derived category formulation of the quantum mechanical world including gravity and to the concept of a non-linear potential of gauged and affinized S-duality which specifies the morphism structure of this derived category.Comment: 31 pages, version reflecting the erratum. arXiv admin note: substantial text overlap with arXiv:1102.460

Nonresponse of native Cottonwood trees to water additions during summer drought

Studies have demonstrated that some riparian trees may switch their reliance on surface soil water (unsaturated or vadose zone) to groundwater (saturated zone) sources during the growing season in association with changes in moisture availability. A closely related question is: How do these trees respond to pulse increases in water availability in previously dry zones? We tested the whole-tree physiological response of 6 natural Populus genotypes to water additions during the peak of summer drought in northern Utah, USA. We found clear evidence that trees were insensitive to water additions to the surface soil that were twice the magnitude of whole-tree transpiration rates. Our results suggest that some cottonwoods may have little immediate transpiration of leaf conductance response to pulse soil moisture increases. This lack of response may be related to water-use strategy associated with regional climate patterns (i.e. genetic or environmental programming), cavitation recovery, or other physical determinants of water use such as depth to groundwater. Our data suggest that it is important to consider potential nonresponsiveness to changes in soil water availability when evaluating the impact of climate change on these important and productive ecosystems

The Modulation of Multiple Phases Leading to the Modified KdV Equation

This paper seeks to derive the modified KdV (mKdV) equation using a novel approach from systems generated from abstract Lagrangians that possess a two-parameter symmetry group. The method to do uses a modified modulation approach, which results in the mKdV emerging with coefficients related to the conservation laws possessed by the original Lagrangian system. Alongside this, an adaptation of the method of Kuramoto is developed, providing a simpler mechanism to determine the coefficients of the nonlinear term. The theory is illustrated using two examples of physical interest, one in stratified hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to illustrate how the criterion for the mKdV equation to emerge may be assessed and its coefficients generated.Comment: 35 pages, 5 figure

A conditional trophic cascade: Birds benefit faster growing trees with strong links between predators and plants

Terrestrial systems are thought to be organized predominantly from the bottom-up, but there is a growing literature documenting top-down trophic cascades under certain ecological conditions. We conducted an experiment to examine how arthropod community structure on a foundation riparian tree mediates the ability of insectivorous birds to influence tree growth. We built whole-tree bird exclosures around 35 mature cottonwood (Populus spp.) trees at two sites in northern Utah, USA, to measure the effect of bird predation on arthropod herbivore and predator species richness, abundance, and biomass, and on tree performance. We maintained bird exclosures over two growing seasons and conducted nondestructive arthropod surveys that recorded 63652 arthropods of 689 morphospecies representing 19 orders. Five major patterns emerged: (1) We found a significant trophic cascade (18% reduction in trunk growth when birds were excluded) only at one site in one year. (2) The significant trophic cascade was associated with higher precipitation, tree growth, and arthropod abundance, richness, and biomass than other site–year combinations. (3) The trophic cascade was weak or not evident when tree growth and insect populations were low apparently due to drought. (4) Concurrent with the stronger trophic cascade, bird predation significantly reduced total arthropod abundance, richness, and biomass. Arthropod biomass was 67% greater on trees without bird predation. This pattern was driven largely by two herbivore groups (folivores and non-aphid sap-feeders) suggesting that birds targeted these groups. (5) Three species of folivores (Orthoptera: Melanoplus spp.) were strong links between birds and trees and were only present in the site and the year in which the stronger trophic cascade occurred. Our results suggest that this trophic system is predominately bottom-up driven, but under certain conditions the influence of top predators can stimulate whole tree growth. When the most limiting factor for tree growth switched from water availability to herbivory, the avian predators gained the potential to reduce herbivory. This potential could be realized when strong links between the birds and plant, i.e., species that were both abundant herbivores and preferred prey, were present

Thermodynamic phase transitions and shock singularities

We show that under rather general assumptions on the form of the entropy function, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of the characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of non-hydrodynamic type such as the classical plasma and the ideal Bose gas are also discussed.Comment: revised version, 18 pages, 6 figure

Towards a continuum theory of clustering in a freely cooling inelastic gas

We performed molecular dynamics simulations to investigate the clustering instability of a freely cooling dilute gas of inelastically colliding disks in a quasi-one-dimensional setting. We observe that, as the gas cools, the shear stress becomes negligibly small, and the gas flows by inertia only. Finite-time singularities, intrinsic in such a flow, are arrested only when close-packed clusters are formed. We observe that the late-time dynamics of this system are describable by the Burgers equation with vanishing viscosity, and predict the long-time coarsening behavior.Comment: 7 pages, 5 eps figures, to appear in Europhys. Let

Attempted density blowup in a freely cooling dilute granular gas: hydrodynamics versus molecular dynamics

It has been recently shown (Fouxon et al. 2007) that, in the framework of ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a granular gas can produce an infinite gas density in a finite time. Exact solutions that exhibit this property have been derived. Close to the singularity, the granular gas pressure is finite and almost constant. This work reports molecular dynamics (MD) simulations of a freely cooling gas of nearly elastically colliding hard disks, aimed at identifying the "attempted" density blowup regime. The initial conditions of the simulated flow mimic those of one particular solution of the IGHD equations that exhibits the density blowup. We measure the hydrodynamic fields in the MD simulations and compare them with predictions from the ideal theory. We find a remarkable quantitative agreement between the two over an extended time interval, proving the existence of the attempted blowup regime. As the attempted singularity is approached, the hydrodynamic fields, as observed in the MD simulations, deviate from the predictions of the ideal solution. To investigate the mechanism of breakdown of the ideal theory near the singularity, we extend the hydrodynamic theory by accounting separately for the gradient-dependent transport and for finite density corrections.Comment: 11 pages, 9 figures, accepted for publication on Physical Review

Kink Solution in a Fluid Model of Traffic Flows

Traffic jam in a fluid model of traffic flows proposed by Kerner and Konh\"auser (B. S. Kerner and P. Konh\"auser, Phys. Rev. E 52 (1995), 5574.) is analyzed. An analytic scaling solution is presented near the critical point of the hetero-clinic bifurcation. The validity of the solution has been confirmed from the comparison with the simulation of the model.Comment: RevTeX v3.1, 6 pages, and 2 figure

Can Naked Singularities Yield Gamma Ray Bursts?

Gamma-ray bursts are believed to be the most luminous objects in the Universe. There has been some suggestion that these arise from quantum processes around naked singularities. The main problem with this suggestion is that all known examples of naked singularities are massless and hence there is effectively no source of energy. It is argued that a globally naked singularity coupled with quantum processes operating within a distance of the order of Planck length of the singularity will probably yield energy burst of the order of M_pc^2\approx2\times 10^{16} ergs, where M_p is the Planck mass.Comment: 4 pages, TeX, no figure