The Hamiltonian Analysis for Yang-Mills Theory on R×S2R\times S^2

Pure Yang-Mills theory on ${\mathbb R} \times S^2$ is analyzed in a gauge-invariant Hamiltonian formalism. Using a suitable coordinatization for the sphere and a gauge-invariant matrix parametrization for the gauge potentials, we develop the Hamiltonian formalism in a manner that closely parallels previous analysis on ${\mathbb R}^3$. The volume measure on the physical configuration space of the gauge theory, the nonperturbative mass-gap and the leading term of the vacuum wave functional are discussed using a point-splitting regularization. All the results carry over smoothly to known results on ${\mathbb R}^3$ in the limit in which the sphere is de-compactified to a plane

Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis

A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N\leq 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass-gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge invariant variables is also presented.Comment: 31 pages, References added, typos correcte

Reply to comment on "Simple one-dimensional model of heat conduction which obeys Fourier's law"

In this reply we answer the comment by A. Dhar (cond-mat/0203077) on our Letter "Simple one dimensional model of heat conduction which obeys Fourier's law" (Phys. Rev. Lett. 86, 5486 (2001), cond-mat/0104453)Comment: 1 pag., 1 fi

Classical limit of master equation for harmonic oscillator coupled to oscillator bath with separable initial conditions

The equation for the Wigner function describing the reduced dynamics of a single harmonic oscillator, coupled to an oscillator bath, was obtained by Karrlein and Grabert [Phys. Rev. E, vol. 55, 153 (1997)]. It was shown that for some special correlated initial conditions the equation reduces, in the classical limit, to the corresponding classical Fokker-Planck equation obtained by Adelman [J. Chem Phys., vol. 64, 124 (1976)]. However for separable initial conditions the Adelman equations were not recovered. We resolve this problem by showing that, for separable initial conditions, the classical Langevin equation obtained from the oscillator bath model is somewhat different from the one considered by Adelman. We obtain the corresponding Fokker-Planck equation and show that it exactly matches the classical limit of the equation for the Wigner function obtained from the master equation for separable initial conditions. We also discuss why the special correlated initial conditions correspond to Adelman's solution.Comment: 12 page

Simultaneous adsorption and biodegradation of reactive dyes using jatropha deoiled cakes

© BEIESP. Endemic pollution problems due to discharge of wastewaters are affecting all the aspects of human life. The poor quality effluents coming from industries is destroying the fragile ecosystem, leading to various apprehensions amongst researchers and scientific communities. Treatment of wastewaters have become an urgent need of the society, which cannot be ignored. Incineration, absorption on solid matrices and biological treatment are some of the effluent treatment methods available. These methods, however, have their own disadvantages. This work explores the application of jatropha deoiled cakes on the concurrent adsorption and biological degradation of reactive dyes. Reactive blue, reactive yellow, reactive red were used for the experiments. The combined experiments were tested for effect of glucose concentrations as well as initial concentrations. Glucose concentrations of 1 g/l, 2 g/l and 3 g/l were taken. All the dyes were varied from 100 ppm to 600 ppm. It was observed that combined degradation yielded higher degradation compared to biological degradation alone. The degradation rate varied with the variation of glucose concentration and it also varied with the initial concentration

Exploratory studies on beneficiation of low-grade Banded Iron ore Formations (BIF) of Karnataka, India

Iron ore is the basic raw material for production of metallic iron. With depletion of high-grade resources and fine dissemination of valuable minerals in the abundantly available low-grade banded iron ore formations (BIF), liberation is achieved at finer sizes. Hence, it necessitated all beneficiation techniques to be operated at this finer size. However, physical separation techniques have limitations in separation efficiency. A combination of pre-concentration technique such as magnetic separation followed by flotation of magnetic fraction proved to be promising in achieving the respectable grade. A low-grade iron ore sample (BIF) of Karnataka, India was subjected to high intensity magnetic separation followed by flotation for enhancing its grade and recovery. Laboratory scale studies on this ore assaying 39.80 Fe%, 39.62 SiO2% and 1.73 Al2O3% indicated that it could be improved to 63.78 Fe%, 3.10 SiO2% and 1.01 Al2O3% at an overall iron recovery of 24% only. However, attempts are being made to further improve the iron recovery

Eulerian Walkers as a model of Self-Organised Criticality

We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an abelian group, same as the group for the Abelian Sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.Comment: 4 pages, RevTex, 4 figure

Demineralization of phenol derivatives using sequential adsorption and biological degradation process

The present investigation was undertaken to assess the degradation of phenol derivatives by sequential adsorption and biological process. Phenols and their derivatives are recognized toxic compounds and known for their carcinogenic and other toxic properties even in trace quantity. Biological treatment is considered more environmentally friendly and cost-effective in comparison with physicochemical treatment. However, the process is less effective for high concentration pollutants. Activated carbons, prepared from Jatropha having micropore size under 125 microns, have been used to carry out the adsorption of Phenol and Chlorophenol in aqueous solution. Observations revealed that the rate of phenol biodegradation was increased because of pretreatment, i.e., adsorption, temperature and glucose concentration. The optimal conditions for Phenol and CP removal were found to be temperature 350C (58-65% removal) and two gpl glucose levels (70-78% removal). The importance of the study is the pretreatment of recalcitrant chemicals with adsorption followed by biodegradation and thus provided with an alternative bioremediation approach