There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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Table Of Integrals Series And Products

Nanocrystals (NCs) discussed in this Review are tiny crystals of metals, semiconductors, and magnetic material consisting of hundreds to a few thousand atoms each. Their size ranges from 2-3 to about 20 nm. What is special about this size regime that placed NCs among the hottest research topics of the last decades? The quantum mechanical coupling * To whom correspondence should be addressed. E-mail: dvtalapin@uchicago.edu. † The University of Chicago. ‡ Argonne National Lab. Chem. Rev. 2010, 110, 389–458 389

/pdf/prospects-of-colloidal-nanocrystals-for-electronic-and-3dxpyhl3r7.pdf

Prospects of Colloidal Nanocrystals for Electronic and Optoelectronic Applications

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

With the high-temperature superconductors a qualitatively new regime in the phenomenology of type-II superconductivity can be accessed. The key elements governing the statistical mechanics and the dynamics of the vortex system are (dynamic) thermal and quantum fluctuations and (static) quenched disorder. The importance of these three sources of disorder can be quantified by the Ginzburg number $Gi=\frac{{(\frac{{T}_{c}}{{H}_{c}^{2}}\ensuremath{\varepsilon}{\ensuremath{\xi}}^{3})}^{2}}{2}$, the quantum resistance $Qu=(\frac{{e}^{2}}{\ensuremath{\hbar}})(\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\varepsilon}\ensuremath{\xi}})$, and the critical current-density ratio $\frac{{j}_{c}}{{j}_{o}}$, with ${j}_{c}$ and ${j}_{o}$ denoting the depinning and depairing current densities, respectively (${\ensuremath{\rho}}_{n}$ is the normal-state resistivity and ${\ensuremath{\varepsilon}}^{2}=\frac{m}{M}l1$ denotes the anisotropy parameter). The material parameters of the oxides conspire to produce a large Ginzburg number $\mathrm{Gi}\ensuremath{\sim}{10}^{\ensuremath{-}2}$ and a large quantum resistance $\mathrm{Qu}\ensuremath{\sim}{10}^{\ensuremath{-}1}$, values which are by orders of magnitude larger than in conventional superconductors, leading to interesting effects such as the melting of the vortex lattice, the creation of new vortex-liquid phases, and the appearance of macroscopic quantum phenomena. Introducing quenched disorder into the system turns the Abrikosov lattice into a vortex glass, whereas the vortex liquid remains a liquid. The terms "glass" and "liquid" are defined in a dynamic sense, with a sublinear response $\ensuremath{\rho}={\frac{\ensuremath{\partial}E}{\ensuremath{\partial}j}|}_{j\ensuremath{\rightarrow}0}$ characterizing the truly superconducting vortex glass and a finite resistivity $\ensuremath{\rho}(j\ensuremath{\rightarrow}0)g0$ being the signature of the liquid phase. The smallness of $\frac{{j}_{c}}{{j}_{o}}$ allows one to discuss the influence of quenched disorder in terms of the weak collective pinning theory. Supplementing the traditional theory of weak collective pinning to take into account thermal and quantum fluctuations, as well as the new scaling concepts for elastic media subject to a random potential, this modern version of the weak collective pinning theory consistently accounts for a large number of novel phenomena, such as the broad resistive transition, thermally assisted flux flow, giant and quantum creep, and the glassiness of the solid state. The strong layering of the oxides introduces additional new features into the thermodynamic phase diagram, such as a layer decoupling transition, and modifies the mechanism of pinning and creep in various ways. The presence of strong (correlated) disorder in the form of twin boundaries or columnar defects not only is technologically relevant but also provides the framework for the physical realization of novel thermodynamic phases such as the Bose glass. On a macroscopic scale the vortex system exhibits self-organized criticality, with both the spatial and the temporal scale accessible to experimental investigations.

Vortices in high-temperature superconductors

A theory of vortex pinning in high-temperature superconductors by correlated disorder in the form of twin boundaries, grain boundaries, and columnar defects is described. Mapping vortex trajectories onto boson world lines leads to a ``superfluid'' flux liquid at high temperatures, as well as low-temperature ``Bose-glass'' and ``Mott-insulator'' phases, in which the flux lines are localized. Currents perpendicular to the average vortex direction act like an electric field applied to charged bosons, while currents parallel to the field act like an imaginary magnetic field in this approach. We discuss the equilibrium and dynamic properties of these phases, and propose a scaling theory for the flux-liquid to Bose-glass transition, at which the linear resistivity vanishes. Although the Bose-glass predictions share some features with vortex-glass behavior predicted for point disorder, the response to tilting the magnetic field in the two cases differs dramatically, thus allowing the two theories to be distinguished experimentally.

Boson localization and correlated pinning of superconducting vortex arrays.

The lattice of magnetic flux lines that can permeate a type ii superconductor, such as the high-transition-temperature copper oxide materials, melts from a solid-like stale to a liquid-like state at a temperature below the superconducting transition temperature. Contrary to the predictions of mean-field theory, this phase transition in Bi2Sr2CaCu2O8 is found to be first-order. The vortex liquid discontinuously expands on freezing.

Thermodynamic observation of first-order vortex-lattice melting transition in Bi2Sr2CaCu2O8

The physics of flux lines in the cuprate superconductors pinned by columnar defects is mapped onto boson localization in two dimensions. The theory predicts a Bose glass phase with an infinite tilt modulus and zero linear resistivity, as well as an entangled flux liquid. We describe correlations and transport in these phases, and propose a scaling theory for the irreversibility line which separates them.

Boson localization and pinning by correlated disorder in high-temperature superconductors.

We investigate analytically and numerically the melting of the vortex lattice moving in an inhomogeneous environment under the applied current [ital j]. We predict the existence of a dynamic phase transition at some characteristic current [ital j]=[ital j][sub [ital t]] (crystallization current) from the motion of the amorphous vortex configuration at [ital j][lt][ital j][sub [ital t]] to the motion of the vortex crystal at [ital j][gt][ital j][sub [ital t]]. The crystallization current [ital j][sub [ital t]] exceeds essentially the critical current [ital j][sub [ital c]] for strongly disordered systems and diverges as temperature approaches the melting temperature [ital T][sub [ital m]] of the undisturbed lattice.

Valerii M. Vinokur

Papers

Vortices in high-temperature superconductors

Boson localization and correlated pinning of superconducting vortex arrays.

Thermodynamic observation of first-order vortex-lattice melting transition in Bi2Sr2CaCu2O8

Boson localization and pinning by correlated disorder in high-temperature superconductors.

Dynamic Melting of the Vortex Lattice.