A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Ideal Structure of the Silver Code

The Silver code has captured a lot of attention in the recent past,because of its nice structure and fast decodability. In their recent paper, Hollanti et al. show that the Silver code forms a subset of the natural order of a particular cyclic division algebra (CDA). In this paper, the algebraic structure of this subset is characterized. It is shown that the Silver code is not an ideal in the natural order but a right ideal generated by two elements in a particular order of this CDA. The exact minimum determinant of the normalized Silver code is computed using the ideal structure of the code. The construction of Silver code is then extended to CDAs over other number fields.

A numerical study of the role of the vertical structure of vorticity during tropical cyclone genesis

An eight-level axisymmetric model with simple parameterizations for clouds and the atmospheric boundary layer was developed to examine the evolution of vortices that are precursors to tropical cyclones. The effect of vertical distributions of vorticity, especially that arising from a merger of mid-level vortices, was studied by us to provide support for a new vortex-merger theory of tropical cyclone genesis. The basic model was validated with the analytical results available for the spin-down of axisymmetric vortices. With the inclusion of the cloud and boundary layer parameterizations, the evolution of deep vortices into hurricanes and the subsequent decay are simulated quite well. The effects of several parameters such as the initial vortex strength, radius of maximum winds, sea-surface temperature and latitude (Coriolis parameter) on the evolution were examined. A new finding is the manner in which mid-level vortices of the same strength decay and how, on simulated merger of these mid-level vortices, the resulting vortex amplifies to hurricane strength in a realistic time frame. The importance of sea-surface temperature on the evolution of full vortices was studied and explained. Also it was found that the strength of the surface vortex determines the time taken by the deep vortex to amplify to hurricane strength.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Influence of crossed electric and quantizing magnetic fields on the Einstein relation in nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) under crossed fields' configuration in nonlinear optical materials on the basis of a newly formulated electron dispersion law by incorporating the crystal field in the Hamiltonian and including the anisotropies of the effective electron mass and the spin-orbit splitting constants within the framework of kp formalisms. The corresponding results for III-V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for II-VI and stressed materials on the basis of various appropriate dispersion relations. We have considered n-CdGeAs2, n-Hg1-xCdxTe, n-In1-xGaxAsyP1-y lattice matched to InP, p-CdS and stressed n-InSb materials as examples. The DMR also increases with increasing electric field and the natures of oscillations are totally band structure dependent with different numerical values. It has been observed that the DMR exhibits oscillatory dependences with inverse quantizing magnetic field and carrier degeneracy due to the Subhnikov-de Haas effect. An experimental method of determining the DMR for degenerate materials in the present case has been suggested. (C) 2010 Elsevier B.V. All rights reserved.

A series of transition metal-azido extended complexes with various anionic and neutral co-ligands: synthesis, structure and their distinct magnetic behavior

The crystal structures and magnetic properties of five new transition metal-azido complexes with two anionic [pyrazine-2-carboxylate (pyzc) and p-aminobenzoate (paba)] and two neutral [pyrazine (pyz) and pyridine (py)] coligands are reported All five complexes were synthesized bysolvothermal methods The complex [Co-2(pyzc)(2)(N-3)(2)(H2O)(2)](n) (1) is 1D and exhibit canted antiferromagnetism, while the 3D complex [MnNa(pyzc)(N-3)(2)(H2O)(2)](n) (2) has a complicated structure and is weakly ferromagnetic in nature [Mn-2(paba)(2)(N-3)(2)(H2O)(2)](n) (3). is a 2D sheet and the Mn-II ions are found to be antiferromagnetically coupled The isostructural 2D complexes [Cu-3(pyz)(2)(N-3)(6)](n) (4) and [Cu-3(py)(2)(N-3)(6)](n) (5) resemble remarkably in their magnetic properties exhibiting moderately strong ferromagnetism. Density functional theory calculations (B3LYP functional) have been performed to provide a qualitative theoretical interpietation of the overall magnetic behavior shown by these complexes.

From Habits to Social Structures : Pragmatism and Contemporary Social Theory

Pragmatism has sometimes been taken as a catchphrase for epistemological stances in which anything goes. However, other authors argue that the real novelty and contribution of this tradition has to do with its view of action as the context in which all things human take place. Thus, it is action rather than, for example, discourses that should be our starting point in social theory. The introductory section of the book situates pragmatism (especially the ideas of G. H. Mead and John Dewey) within the field and tradition of social theory. This introductory also contextualizes the main core of the book which consists of four chapters. Two of these chapters have been published as articles in scientific journals and one in an edited book. All of them discuss the core problem of social theory: how is action related to social structures (and vice versa)? The argument is that habitual action is the explanation for the emergence of social structures from our action. Action produces structures and social reproduction takes place when action is habitualized; that is, when we develop social dispositions to act in a certain manner in familiar environments. This also means that even though the physical environment is the same for all of us, our habits structure it into different kinds of action possibilities. Each chapter highlights these general insights from different angles. Practice theory has gained momentum in recent years and it has many commonalities with pragmatism because both highlight the situated and corporeal character of human activity. One famous proponent of practice theory is Margaret Archer who has argued that the pragmatism of G. H. Mead leads to an oversocialized conception of selfhood. Mead does indeed present a socialized view of selfhood but this is a meta-sociological argument rather than a substantial sociological claim. Accordingly, one can argue that in this general sense intersubjectivity precedes subjectivity and not the other way around. Such a view does not indicate that our social relation would necessarily "colonize" individual action because there is a place for internal conversations (in Archer s terminology); it is especially in those phases of action where it meets obstacles due to the changes of the environment. The second issue discussed has the background assumption that social structures can fruitfully be conceptualized as institutions. A general classification of different institution theories is presented and it is argued that there is a need for a habitual theory of institutions due to the problems associated with these other theories. So-called habitual institutionalism accounts for institutions in terms of established and prevalent social dispositions that structure our social interactions. The germs of this institution theory can be found in the work of Thorstein Veblen. Since Veblen s times, these ideas have been discussed for example, by the economist Geoffrey M. Hodgson. His ideas on the evolution of institutions are presented but a critical stance is taken towards his tendency of defining institutions with the help of rules because rules are not always present in institutions. Accordingly, habitual action is the most basic but by no means the only aspect of institutional reproduction. The third chapter deals with theme of action and structures in the context of Pierre Bourdieu s thought. Bourdieu s term habitus refers to a system of dispositions which structure social fields. It is argued that habits come close to the concept of habitus in the sense that the latter consists of particular kinds of habits; those that are related to the reproduction of socioeconomic positions. Habits are thus constituents of a general theory of societal reproduction whereas habitus is a systematic combination of socioeconomic habits. The fourth theme relates to issues of social change and development. The capabilities approach has been associated with the name of Amartya Sen, for example, and it underscores problems inhering in economistic ways of evaluating social development. However, Sen s argument has some theoretical problems. For example, his theory cannot adequately confront the problem of relativism. In addition, Sen s discussion lacks also a theory of the role of the public. With the help of arguments derived from pragmatism, one gets an action-based, socially constituted view of freedom in which the role of the public is essential. In general, it is argued that a socially constituted view of agency does not necessarily to lead to pessimistic conclusions about the freedom of action.

Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.

A theory on the migration of an extraneous electron across hydrogen bonds in polypeptides

The migrating electrons in biological systems normally are extraneous and taking this into account the electron delocalisation across the hydrogen bonds in proteins is re-examined. It is seen that an extraneous electron can travel rapidly via the low-lying virtual orbitals of the hydrogen-bonded π-electronic structure of peptide units in proteins. The frequency of electron transfer decreases slowly with an increase in the path length. However, the coupling of electron and protonic motions enhances this frequency. Transfer of electrons across the hydrogen bonds in accordance with the double-exchange mechanism does not appear to be possible. This theory offers a possibility for an extraneous electron to transfer within protein structures.

On the fundamentals of coherence theory

In the thesis I study various quantum coherence phenomena and create some of the foundations for a systematic coherence theory. So far, the approach to quantum coherence in science has been purely phenomenological. In my thesis I try to answer the question what quantum coherence is and how it should be approached within the framework of physics, the metatheory of physics and the terminology related to them. It is worth noticing that quantum coherence is a conserved quantity that can be exactly defined. I propose a way to define quantum coherence mathematically from the density matrix of the system. Degenerate quantum gases, i.e., Bose condensates and ultracold Fermi systems, form a good laboratory to study coherence, since their entropy is small and coherence is large, and thus they possess strong coherence phenomena. Concerning coherence phenomena in degenerate quantum gases, I concentrate in my thesis mainly on collective association from atoms to molecules, Rabi oscillations and decoherence. It appears that collective association and oscillations do not depend on the spin-statistics of particles. Moreover, I study the logical features of decoherence in closed systems via a simple spin-model. I argue that decoherence is a valid concept also in systems with a possibility to experience recoherence, i.e., Poincaré recurrences. Metatheoretically this is a remarkable result, since it justifies quantum cosmology: to study the whole universe (i.e., physical reality) purely quantum physically is meaningful and valid science, in which decoherence explains why the quantum physical universe appears to cosmologists and other scientists very classical-like. The study of the logical structure of closed systems also reveals that complex enough closed (physical) systems obey a principle that is similar to Gödel's incompleteness theorem of logic. According to the theorem it is impossible to describe completely a closed system within the system, and the inside and outside descriptions of the system can be remarkably different. Via understanding this feature it may be possible to comprehend coarse-graining better and to define uniquely the mutual entanglement of quantum systems.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Structure of the rhenium X-ray LIII absorption edge in caesium hexachlororhenate(IV)

The X-ray LIII absorption-edge structure of rhenium in Cs2[ReCl6] has been measured with a bent-crystal X-ray spectrograph. An analysis in terms of molecular-orbital (m.o.) theory has been attempted. The energies of the m.o. levels, crystal-field splitting parameter, effective magnetic moment, magnetic susceptibility, and Landég parameter have been determined from this analysis. An estimate of the Re–Cl bond length has also been made.

Structure and representation of correlation functions and the density matrix for a statistical wave field in optics

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two‐point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.

Birth of the European individual : Outline of a theory of legal practice

The modern subject is what we can call a self-subjecting individual. This is someone in whose inner reality has been implanted a more permanent governability, a governability that works inside the agent. Michel Foucault s genealogy of the modern subject is the history of its constitution by power practices. By a flight of imagination, suppose that this history is not an evolving social structure or cultural phenomenon, but one of those insects (moth) whose life cycle consists of three stages or moments: crawling larva, encapsulated pupa, and flying adult. Foucault s history of power-practices presents the same kind of miracle of total metamorphosis. The main forces in the general field of power can be apprehended through a generalisation of three rationalities functioning side-by-side in the plurality of different practices of power: domination, normalisation and the law. Domination is a force functioning by the rationality of reason of state: the state s essence is power, power is firm domination over people, and people are the state s resource by which the state s strength is measured. Normalisation is a force that takes hold on people from the inside of society: it imposes society s own reality its empirical verity as a norm on people through silently working jurisdictional operations that exclude pathological individuals too far from the average of the population as a whole. The law is a counterforce to both domination and normalisation. Accounting for elements of legal practice as omnihistorical is not possible without a view of the general field of power. Without this view, and only in terms of the operations and tactical manoeuvres of the practice of law, nothing of the kind can be seen: the only thing that practice manifests is constant change itself. However, the backdrop of law s tacit dimension that is, the power-relations between law, domination and normalisation allows one to see more. In the general field of power, the function of law is exactly to maintain the constant possibility of change. Whereas domination and normalisation would stabilise society, the law makes it move. The European individual has a reality as a problem. What is a problem? A problem is something that allows entry into the field of thought, said Foucault. To be a problem, it is necessary for certain number of factors to have made it uncertain, to have made it lose familiarity, or to have provoked a certain number of difficulties around it . Entering the field of thought through problematisations of the European individual human forms, power and knowledge one is able to glimpse the historical backgrounds of our present being. These were produced, and then again buried, in intersections between practices of power and games of truth. In the problem of the European individual one has suitable circumstances that bring to light forces that have passed through the individual through centuries.

A parity-violatingU4-gravitation theory

The general structure of a metric-torsion theory of gravitation allows a parity-violating contribution to the complete action which is linear in the curvature tensor and vanishes identically in the absence of torsion. The resulting action involves, apart from the constant ¯K E =8pgr/c4, a coupling (B) which governs the strength of the parity interaction mediated by torsion. In this model the Brans-Dicke scalar field generates the torsion field, even though it has zero spin. The interesting consequence of the theory is that its results for the solar-system differ very little from those obtained from Brans-Dicke (BD) theory. Therefore the theory is indistinguishable from BD theory in solar-system experiments.