Processing of fine size minerals : Studies on some Indian uranium ores

Conventionally uranium ores are processed by direct chemical leaching techniques. However, the application of chemical leaching for lean tenor and high tonnage uranium- ores is being desisted due to obvious environmental concerns. It is in this context that the physical benefi-ciation methods for the pre-concentration of uranium ores, if feasible, are gaining importance. Adoption of physical beneficiation helps in containing uranium and daughter nuclides in a smaller mass of pre-concentrate, which can be further subjected to conventional chemical processing, leaving bulk of the ore safe for disposal. In the application of physical beneficiation techniques, particle size plays a significant role. Both the economic mineral of uranium - uraninite and pitchblend, are brittle and report in very fine sizes during comminution, an oper-ation meant for their liberation.It is well established fact that concentration of particles finer than 25um by conventional physical beneficiation methods is very difficult due to the low mass and high surface area. However with the advent of new fine particle concentrators and techniques the situation has shown tremendous impr-ovement. This paper highlights the studies carried out on the use of both physical (gravity and magnetic) and physico-chemical beneficiation methods for recovering fine size uranium values from some low grade uranium bearing ores of India

The hypothesis of path integral duality II: corrections to quantum field theoretic results

In the path integral expression for a Feynman propagator of a spinless particle of mass $m$, the path integral amplitude for a path of proper length ${\cal R}(x,x'| g_{\mu\nu})$ connecting events $x$ and $x'$ in a spacetime described by the metric tensor $g_{\mu\nu}$ is $\exp-[m {\cal R}(x,x'| g_{\mu\nu})]$. In a recent paper, assuming the path integral amplitude to be invariant under the duality transformation ${\cal R} \to (L_P^2/{\cal R})$, Padmanabhan has evaluated the modified Feynman propagator in an arbitrary curved spacetime. He finds that the essential feature of this `principle of path integral duality' is that the Euclidean proper distance $(\Delta x)^2$ between two infinitesimally separated spacetime events is replaced by $[(\Delta x)^2 + 4L_P^2 ]$. In other words, under the duality principle the spacetime behaves as though it has a `zero-point length' $L_P$, a feature that is expected to arise in a quantum theory of gravity. In the Schwinger's proper time description of the Feynman propagator, the weightage factor for a path with a proper time $s$ is $\exp-(m^2s)$. Invoking Padmanabhan's `principle of path integral duality' corresponds to modifying the weightage factor $\exp-(m^2s)$ to $\exp-[m^2s + (L_P^2/s)]$. In this paper, we use this modified weightage factor in Schwinger's proper time formalism to evaluate the quantum gravitational corrections to some of the standard quantum field theoretic results in flat and curved spacetimes. We find that the extra factor $\exp-(L_P^2/s)$ acts as a regulator at the Planck scale thereby `removing' the divergences that otherwise appear in the theory. Finally, we discuss the wider implications of our analysis.Comment: 26 pages, Revte

UV divergence-free QFT on noncommutative plane

We formulate Noncommutative Qauntum Field Theory in terms of fields defined as mean value over coherent states of the noncommutative plane. No *-product is needed in this formulation and noncommutativity is carried by a modified Fourier transform of fields. As a result the theory is UV finite and the cutoff is provided by the noncommutative parameter theta.Comment: 6 pages, Latex, no figures. Accepted for publication in J.Phys.A. New references adde

Non-Gaussianity of the density distribution in accelerating universes

According to recent observations, the existence of the dark energy has been considered. Even though we have obtained the constraint of the equation of the state for dark energy ($p = w \rho$) as $-1 \le w \le -0.78$ by combining WMAP data with other astronomical data, in order to pin down $w$, it is necessary to use other independent observational tools. For this purpose, we consider the $w$ dependence of the non-Gaussianity of the density distribution generated by nonlinear dynamics. To extract the non-Gaussianity, we follow a semi-analytic approach based on Lagrangian linear perturbation theory, which provides an accurate value for the quasi-nonlinear region. From our results, the difference of the non-Gaussianity between $w = -1$ and $w= -0.5$ is about 4% while that between $w = -1$ and $w= -0.8$ is about $0.9$. For the highly non-linear region, we estimate the difference by combining this perturbative approach with N-body simulation executed for our previous paper. From this, we can expect the difference to be more enhanced in the low-$z$ region, which suggests that the non-Gaussianity of the density distribution potentially plays an important role for extracting the information of dark energy.Comment: 15 pages, 4 figures, accepted for publication in JCAP; v2: smoothing scale has been change

Phase transitions in self-gravitating systems. Self-gravitating fermions and hard spheres models

We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of self-gravitating fermions and hard spheres models. Three kinds of phase transitions (of zeroth, first and second order) are evidenced. They separate a ``gaseous'' phase with a smoothly varying distribution of matter from a ``condensed'' phase with a core-halo structure. We propose a simple analytical model to describe these phase transitions. We determine the value of energy (in the microcanonical ensemble) and temperature (in the canonical ensemble) at the transition point and we study their dependance with the degeneracy parameter (for fermions) or with the size of the particles (for a hard spheres gas). Scaling laws are obtained analytically in the asymptotic limit of a small short distance cut-off. Our analytical model captures the essential physics of the problem and compares remarkably well with the full numerical solutions.Comment: Submitted to Phys. Rev. E. New material adde

Dark Energy and Gravity

I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as the candidate and emphasises why no other approach really solves the conceptual problems usually attributed to the cosmological constant. Part 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract the key ingredients which must be present in any viable solution. I argue that (i)the cosmological constant problem cannot be satisfactorily solved until gravitational action is made invariant under the shift of the matter lagrangian by a constant and (ii) this cannot happen if the metric is the dynamical variable. Hence the cosmological constant problem essentially has to do with our (mis)understanding of the nature of gravity. Part 3 discusses an alternative perspective on gravity in which the action is explicitly invariant under the above transformation. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy, edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure

Fluctuations in the current and energy densities around a magnetic flux carrying cosmic string

We calculate the fluctuations in the current and energy densities for the case of a quantized, minimally coupled, massless, complex scalar field around a straight and infinitesimally thin cosmic string carrying magnetic flux. At zero temperature, we evaluate the fluctuations in the current and energy densities for arbitrary flux and deficit angle. At a finite temperature, we evaluate the fluctuations in the energy density for the special case wherein the flux is absent and the deficit angle equals $\pi$. We find that, quite generically, the dimensionless ratio of the variance to the mean-squared values of the current and energy densities are of order unity which suggests that the fluctuations around cosmic strings can be considered to be large.Comment: RevTeX, 13 Pages, 3 Figure

Detectability of Weakly Interacting Massive Particles in the Sagittarius Dwarf Tidal Stream

Tidal streams of the Sagittarius dwarf spheroidal galaxy (Sgr) may be showering dark matter onto the solar system and contributing approx (0.3--23)% of the local density of our Galactic Halo. If the Sagittarius galaxy contains WIMP dark matter, the extra contribution from the stream gives rise to a step-like feature in the energy recoil spectrum in direct dark matter detection. For our best estimate of stream velocity (300 km/sec) and direction (the plane containing the Sgr dwarf and its debris), the count rate is maximum on June 28 and minimum on December 27 (for most recoil energies), and the location of the step oscillates yearly with a phase opposite to that of the count rate. In the CDMS experiment, for 60 GeV WIMPs, the location of the step oscillates between 35 and 42 keV, and for the most favorable stream density, the stream should be detectable at the 11 sigma level in four years of data with 10 keV energy bins. Planned large detectors like XENON, CryoArray and the directional detector DRIFT may also be able to identify the Sgr stream.Comment: 26 pages, 4 figure

Mean Field Theory of Spherical Gravitating Systems

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems confined in a finite domain consisting of either point masses, or rotating mass shells of different dimension. We establish a direct connection between the spherically symmetric equilibrium states of a self-gravitating point mass system and a shell model of dimension 3. We construct the equilibrium density functions by maximizing the entropy subject to the usual constraints of normalization and energy, but we also take into account the constraint on the sum of the squares of the individual angular momenta, which is also an integral of motion for these symmetric systems. Two new statistical ensembles are introduced which incorporate the additional constraint. They are used to investigate the possible occurrence of a phase transition as the defining parameters for each ensemble are altered

Relevance of Induced Gauge Interactions in Decoherence

Decoherence in quantum cosmology is shown to occur naturally in the presence of induced geometric gauge interactions associated with particle production.A new 'gauge '-variant form of the semiclassical Einstein equations is also presented which makes the non-gravitating character of the vacuum polarisation energy explicit.Comment: 10 pages, LATEX, IC/94/16