Ion shell distributions as free energy source for plasma waves on auroral field lines mapping to plasma sheet boundary layer

Ion shell distributions are hollow spherical shells in velocity space that can be formed by many processes and occur in several regions of geospace. They are interesting because they have free energy that can, in principle, be transmitted to ions and electrons. Recently, a technique has been developed to estimate the original free energy available in shell distributions from in-situ data, where some of the energy has already been lost (or consumed). We report a systematic survey of three years of data from the Polar satellite. We present an estimate of the free energy available from ion shell distributions on auroral field lines sampled by the Polar satellite below 6 <i>R<sub>E</sub></i> geocentric radius. At these altitudes the type of ion shells that we are especially interested in is most common on auroral field lines close to the polar cap (i.e. field lines mapping to the plasma sheet boundary layer, PSBL). Our analysis shows that ion shell distributions that have lost some of their free energy are commonly found not only in the PSBL, but also on auroral field lines mapping to the boundary plasma sheet (BPS), especially in the evening sector auroral field lines. We suggest that the PSBL ion shell distributions are formed during the so-called Velocity Dispersed Ion Signatures (VDIS) events. Furthermore, we find that the partly consumed shells often occur in association with enhanced wave activity and middle-energy electron anisotropies. The maximum downward ion energy flux associated with a shell distribution is often 10mWm<sup>-2</sup> and sometimes exceeds 40mWm<sup>-2</sup> when mapped to the ionosphere and thus may be enough to power many auroral processes. Earlier simulation studies have shown that ion shell distributions can excite ion Bernstein waves which, in turn, energise electrons in the parallel direction. It is possible that ion shell distributions are the link between the X-line and the auroral wave activity and electron acceleration in the energy transfer chain for stable auroral arcs

Bethe--Salpeter equation in QCD

We extend to regular QCD the derivation of a confining $q \bar{q}$ Bethe--Salpeter equation previously given for the simplest model of scalar QCD in which quarks are treated as spinless particles. We start from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by ${1\over m^2}$ expansion the corresponding Wilson loop potential can be reobtained, spin--dependent and velocity--dependent terms included. We also show that, on the contrary, neglecting spin--dependent terms, relativistic flux tube model is reproduced.Comment: 23 pages, revte

Discreteness-induced Transition in Catalytic Reaction Networks

Drastic change in dynamics and statistics in a chemical reaction system, induced by smallness in the molecule number, is reported. Through stochastic simulations for random catalytic reaction networks, transition to a novel state is observed with the decrease in the total molecule number N, characterized by: i) large fluctuations in chemical concentrations as a result of intermittent switching over several states with extinction of some molecule species and ii) strong deviation of time averaged distribution of chemical concentrations from that expected in the continuum limit, i.e., $N \to \infty$. The origin of transition is explained by the deficiency of molecule leading to termination of some reactions. The critical number of molecules for the transition is obtained as a function of the number of molecules species M and that of reaction paths K, while total reaction rates, scaled properly, are shown to follow a universal form as a function of NK/M

Generation of Bernstein waves by ion shell distributions in the auroral region

International audienceHot ion shell distributions could possibly contain enough free energy for waves that could power electron energisation above auroral inverted-V regions. Using both linear theory (WHAMP) and two-dimensional electrostatic simulations, we show that ion shell distributions can cause unstable ion Bernstein mode emissions with high temporal growth rates, as well as perpendicular and parallel e-folding distances, that are in accordance with the tranverse dimensions of auroral arcs and the parallel size of the energisation region, respectively. The phase velocities of the waves are in the proper range to give parallel energisation to electrons with a Landau resonance. The simulation shows that about 90% of the energy goes into electrons and 10% goes into cold ion perpendicular heating. An electron heating rate of ~ 80 eV/s is obtained

Switching Dynamics in Reaction Networks Induced by Molecular Discreteness

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states.Comment: 11 pages, 5 figure

From scalar to string confinement

We outline a connection between scalar quark confinement, a phenomenologically successful concept heretofore lacking fundamental justification, and QCD. Although scalar confinement does not follow from QCD, there is an interesting and close relationship between them. We develop a simple model intermediate between scalar confinement and the QCD string for illustrative purposes. Finally, we find the bound state masses of scalar, time-component vector, and string confinement analytically through semi-classical quantization.Comment: ReVTeX, 9 pages, 5 figure

Finite-Size-Scaling at the Jamming Transition: Corrections to Scaling and the Correlation Length Critical Exponent

We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $\nu\approx 1$, and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $\nu<1$ are due to the improper neglect of these corrections.Comment: 5 pages, 4 figures -- slightly revised version as accepted for Phys. Rev. E Rapid Communication

Heterogeneous Dynamics, Marginal Stability and Soft Modes in Hard Sphere Glasses

In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define normal modes. In this Letter we use these tools to analyze the activated transitions between meta-bassins, both in the aging regime deep in the glass phase and near the glass transition. We observe numerically that structural relaxation occurs mostly along a very small number of nearly-unstable extended modes. This number decays for denser packing and is significantly lowered as the system undergoes the glass transition. This observation supports that structural relaxation and marginal modes share common properties. In particular theoretical results [2, 3] show that these modes extend at least on some length scale $l^*\sim (\phi_c-\phi)^{-1/2}$ where $\phi_c$ corresponds to the maximum packing fraction, i.e. the jamming transition. This prediction is consistent with very recent numerical observations of sheared systems near the jamming threshold [4], where a similar exponent is found, and with the commonly observed growth of the rearranging regions with compression near the glass transition.Comment: 6 pages, improved versio

Effects of elevated temperature and pore pressure on the mechanical behavior of Bullfrog tuff

Samples of the Bullfrog Member of the Crater Flat Tuff from the depth interval 758.9 to 759.2 m in hole USW-G1 on the Nevada Test Site were tested in triaxial compression. Test conditions were: (1) effective confining pressure to 20 MPa; (2) temperature of 200{sup 0}C; (3) both dry and with pore water pressures from 3.4 to 5 MPa; and (4) a strain-rate of 10{sup -4}/s. The results suggest that the presence of water causes the strength to decrease. In addition, the brittle-ductile transition pressure for this rock was found to be about 15 MPa, regardless of saturation. Below this pressure deformation is characterized by unstable stress drops and the development of a single fracture, and above this pressure deformation is stable and distributed more uniformly throughout the sample