A dimensional analysis of supersaturated total dissolved gas dissipation

Elevated levels of total dissolved gas (TDG) may occur downstream of dam discharges, leading to increased incidence of gas bubble disease in fish. Accelerating the dissipation of supersaturated TDG in the downstream river can mitigate this negative problem. However, developing effective mitigation techniques is hampered by limitations in present models of TDG dissipation processes. Furthermore, data useful for modelling the dissipation of supersaturated TDG through the free surface in natural rivers are limited. Past studies indicated that the TDG dissipation process is quantitatively different from the reaeration process, and TDG behavior is quantitatively different from dissolved oxygen. However, a correct parameterization of the TDG dissipation process is still missing. The paper presents a novel dimensional analysis of the dissipation of supersaturated TDG. This approach can provide a relationship between the TDG dissipation coefficient and some classical fluid mechanics index-numbers. This dimensional analysis considers some key parameters for the dissipation process both water and TDG properties as well as flow characteristics, including turbulence. These parameters are water kinematic viscosity, TDG molecular diffusivity and vertical turbulent diffusivity, and channel width. The application of dimensional analysis pointed out that the TDG dissipation coefficient is a function of the Schmidt number, the aspect ratio of the channel, and the shear Reynolds number. The dimensional analysis was then verified using both field data collected in some large natural rivers and reservoirs in Sichuan and experimental data in laboratory flume at State Key Laboratory of Hydraulics and Mountain River Engineering of Sichuan University. The analysis revealed the key role of turbulence in controlling the TDG dissipation while the importance of gas/water characteristics remains still unclear and needs further investigations

Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

Small-Recoil Approximation

In this review we discuss a technique to compute and to sum a class of Feynman diagrams, and some of its applications. These are diagrams containing one or more energetic particles that suffer very little recoil in their interactions. When recoil is completely neglected, a decomposition formula can be proven. This formula is a generalization of the well-known eikonal formula, to non-abelian interactions. It expresses the amplitude as a sum of products of irreducible amplitudes, with each irreducible amplitude being the amplitude to emit one, or several mutually interacting, quasi-particles. For abelian interaction a quasi-particle is nothing but the original boson, so this decomposition formula reduces to the eikonal formula. In non-abelian situations each quasi-particle can be made up of many bosons, though always with a total quantum number identical to that of a single boson. This decomposition enables certain amplitudes of all orders to be summed up into an exponential form, and it allows subleading contributions of a certain kind, which is difficult to reach in the usual way, to be computed. For bosonic emissions from a heavy source with many constituents, a quasi-particle amplitude turns out to be an amplitude in which all bosons are emitted from the same constituent. For high-energy parton-parton scattering in the near-forward direction, the quasi-particle turns out to be the Reggeon, and this formalism shows clearly why gluons reggeize but photons do not. The ablility to compute subleading terms in this formalism allows the BFKL-Pomeron amplitude to be extrapolated to asymptotic energies, in a unitary way preserving the Froissart bound. We also consider recoil corrections for abelian interactions in order to accommodate the Landau-Pomeranchuk-Migdal effect.Comment: 21 pages with 4 figure

Viscoelasticity of 2D liquids quantified in a dusty plasma experiment

The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wavenumber-dependent viscosity, $\eta(k)$, which is a quantitative indicator of viscoelasticity. Using an expression generalized here to include friction, $\eta(k)$ is computed from the transverse current autocorrelation function (TCAF), which is found by tracking random particle motion. The TCAF exhibits an oscillation that is a signature of elastic contributions to viscoelasticity. Simulations of a Yukawa liquid are consistent with the experiment.Comment: 5 pages text, 3 figures, 1 supplementary material, in press Physical Review Letters 201

Asymmetric Dark Matter and Effective Operators

In order to annihilate in the early Universe to levels well below the measured dark matter density, asymmetric dark matter must possess large couplings to the Standard Model. In this paper, we consider effective operators which allow asymmetric dark matter to annihilate into quarks. In addition to a bound from requiring sufficient annihilation, the energy scale of such operators can be constrained by limits from direct detection and monojet searches at colliders. We show that the allowed parameter space for these operators is highly constrained, leading to non-trivial requirements that any model of asymmetric dark matter must satisfy.Comment: 6 pages, 1 figure. V2 replacement: Citations added. Shading error in Fig. 1 (L_FV panel) corrected. Addition of direct detection bounds on m_chi <5 GeV added, minor alterations in text to reflect these change

Solid superheating observed in two-dimensional strongly-coupled dusty plasma

It is demonstrated experimentally that strongly-coupled plasma exhibits solid superheating. A 2D suspension of microspheres in dusty plasma, initially self-organized in a solid lattice, was heated and then cooled rapidly by turning laser heating on and off. Particles were tracked using video microscopy, allowing atomistic-scale observation during melting and solidification. During rapid heating, the suspension remained in a solid structure at temperatures above the melting point, demonstrating solid superheating. Hysteresis diagrams did not indicate liquid supercooling in this 2D system.Comment: 9 pages text, 3 figures, in press Physical Review Letters 200

Supersymmetry and the Anomalous Anomalous Magnetic Moment of the Muon

The recently reported measurement of the muon's anomalous magnetic moment differs from the standard model prediction by 2.6 standard deviations. We examine the implications of this discrepancy for supersymmetry. Deviations of the reported magnitude are generic in supersymmetric theories. Based on the new result, we derive model-independent upper bounds on the masses of observable supersymmetric particles. We also examine several model frameworks. The sign of the reported deviation is as predicted in many simple models, but disfavors anomaly-mediated supersymmetry breaking.Comment: 4 pages, 4 figures, version to appear in Phys. Rev. Let

Global behavior of cosmological dynamics with interacting Veneziano ghost

In this paper, we shall study the dynamical behavior of the universe accelerated by the so called Veneziano ghost dark energy component locally and globally by using the linearization and nullcline method developed in this paper. The energy density is generalized to be proportional to the Hawking temperature defined on the trapping horizon instead of Hubble horizon of the Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the fate of the universe and present the bifurcation phenomenon of the dynamical system of the universe. It seems that the universe could be dominated by dark energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE