Geophysical well-logging techniques for environmental problems - a review

Men’s desires for prosperity and better quality of life prelude to more and more domestic and industrial wastes. There is serious waste disposal problems in developed countries, India started experiencing these problems since the onset of waste disposal is to decide the dumping site which must not be detrimental The pith of the above discussion is that if the dumping site underlays with fractured and permeable sediments or rocks, migration of the wastes will contaminate surface and groundwater. In view of serious water pollution in industrial area and also contaminated groundwater due to leaching from the wastes, the selection of appropriate dumping site is an important aspect. Here, geophysical well logging techniques can play an important role. This review paper covers the principles and applications of different well logging techniques for determining porosity, permeability, density and temperature of the underground environment

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Avalanche Dynamics in Evolution, Growth, and Depinning Models

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and evolution is presented. Specifically, we include the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models into a unified treatment encompassing a large class of far from equilibrium processes. The formation of fractal structures, the appearance of $1/f$ noise, diffusion with anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be related to the same underlying avalanche dynamics. This dynamics can be represented as a fractal in $d$ spatial plus one temporal dimension. We develop a scaling theory that relates many of the critical exponents in this broad category of extremal models, representing different universality classes, to two basic exponents characterizing the fractal attractor. The exact equations and the derived set of scaling relations are consistent with numerical simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the manuscript supplied on reques

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons

We report on the generation of coherent phonon polaritons in ZnTe, GaP and LiTaO$_{3}$ using ultrafast optical pulses. These polaritons are coupled modes consisting of mostly far-infrared radiation and a small phonon component, which are excited through nonlinear optical processes involving the Raman and the second-order susceptibilities (difference frequency generation). We probe their associated hybrid vibrational-electric field, in the THz range, by electro-optic sampling methods. The measured field patterns agree very well with calculations for the field due to a distribution of dipoles that follows the shape and moves with the group velocity of the optical pulses. For a tightly focused pulse, the pattern is identical to that of classical Cherenkov radiation by a moving dipole. Results for other shapes and, in particular, for the planar and transient-grating geometries, are accounted for by a convolution of the Cherenkov field due to a point dipole with the function describing the slowly-varying intensity of the pulse. Hence, polariton fields resulting from pulses of arbitrary shape can be described quantitatively in terms of expressions for the Cherenkov radiation emitted by an extended source. Using the Cherenkov approach, we recover the phase-matching conditions that lead to the selection of specific polariton wavevectors in the planar and transient grating geometry as well as the Cherenkov angle itself. The formalism can be easily extended to media exhibiting dispersion in the THz range. Calculations and experimental data for point-like and planar sources reveal significant differences between the so-called superluminal and subluminal cases where the group velocity of the optical pulses is, respectively, above and below the highest phase velocity in the infrared.Comment: 13 pages, 11 figure