Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.

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.

Grönlannin mannerjäätikön tulevaisuus: merenpinnan nousu maailmanlaajuisesti ja Itämerellä

Sea level rise is among the most worrying consequences of climate change, and the biggest uncertainty of sea level predictions lies in the future behaviour of the ice sheets of Greenland and Antarctica. In this work, a literature review is made concerning the future of the Greenland ice sheet and the effect of its melting on Baltic Sea level. The relation between sea level and ice sheets is also considered more generally from a theoretical and historical point of view. Lately, surprisingly rapid changes in the amount of ice discharging into the sea have been observed along the coastal areas of the ice sheets, and the mass deficit of Greenland and West Antarctic ice sheets which are considered vulnerable to warming has been increasing from the 1990s. The changes are probably related to atmospheric or oceanic temperature variations which affect the flow speed of ice either via meltwater penetrating to the bottom of the ice sheet or via changes in the flow resistance generated by the floating parts of an ice stream. These phenomena are assumed to increase the mass deficit of the ice sheets in the warming climate; however, there is no comprehensive theory to explain and model them. Thus, it is not yet possible to make reliable predictions of the ice sheet contribution to sea level rise. On the grounds of the historical evidence it appears that sea level can rise rather rapidly, 1 2 metres per century, even during warm climate periods. Sea level rise projections of similar magnitude have been made with so-called semiempirical methods that are based on modelling the link between sea level and global mean temperature. Such a rapid rise would require considerable acceleration of the ice sheet flow. Stronger rise appears rather unlikely, among other things because the mountainous coastline restricts ice discharge from Greenland. The upper limit of sea level rise from Greenland alone has been estimated at half a metre by the end of this century. Due to changes in the Earth s gravity field, the sea level rise caused by melting ice is not spatially uniform. Near the melting ice sheet the sea level rise is considerably smaller than the global average, whereas farther away it is slightly greater than the average. Because of this phenomenon, the effect of the Greenland ice sheet on Baltic Sea level will probably be rather small during this century, 15 cm at most. Melting of the Antarctic ice sheet is clearly more dangerous for the Baltic Sea, but also very uncertain. It is likely that the sea level predictions will become more accurate in the near future as the ice sheet models develop.

On the Epistemology of Narrative Theory: Narratology and Other Theories of Fictional Narrative

In this article, I propose to analyze narrative theory from an epistemological standpoint. To do so, I will draw upon both Genettian narratology and what I would call, following Shigeyuki Kuroda, “non-communicational” theories of fictional narrative. In spite of their very unequal popularity, I consider these theories as objective, or, in other words, as debatable and ripe for rational analyses; one can choose between them. The article is made up of three parts. The first part concerns the object of narrative theory, or the narrative as a constructed object, both in narratology (where narrative is likened to a narrative discourse) and in non-communicational narrative theories (where fictional narrative and discourse are mutually exclusive categories). The second part takes up the question of how the claims of these theories do or do not lend themselves to falsification. In particular, Gérard Genette’s claim that “every narrative is, explicitly or not, ‘in the first person’”, will be considered, through the lens of Ann Banfield’s theory of free indirect style. In the third part the reductionism of narrative theory will be dealt with. This leads to a reflection on the role of narrative theory in the analysis of fictional narratives.

Kinetic theory for the density plateau in the granular flow down an inclined plane

The striking lack of observable variation of the volume fraction with height in the center of a granular flow down an inclined plane is analysed using constitutive relations obtained from kinetic theory. It is shown that the rate of conduction in the granular energy balance equation is O(delta(2)) smaller than the rate of production of energy due to mean shear and the rate of dissipation due to inelastic collisions, where the small parameter delta = (d/(1 - e(n))H-1/2), d is the particle diameter, en is the normal coefficient of restitution and H is the thickness of the flowing layer. This implies that the volume fraction is a constant in the leading approximation in an asymptotic analysis in small delta. Numerical estimates of both the parameter delta and its pre-factor are obtained to show that the lack of observable variation of the volume fraction with height can be explained by constitutive relations obtained from kinetic theory.

Infrared Spectra of Dimethylquinolines in the Gas Phase: Experiment and Theory

Infrared spectra of atmospherically important dimethylquinolines (DMQs), namely 2,4-DMQ, 2,6-DMQ, 2,7-DMQ, and 2,8-DMQ in the gas phase at 80 degrees C were recorded using a long variable path-length cell. DFT calculations were carried out to assign the bands in the experimentally observed spectra at the B3LYP/6-31G* level of theory. The spectral assignments particularly for the C-H stretching modes could not be made unambiguously using calculated anharmonic or scaled harmonic frequencies. To resolve this problem, a scaled force field method of assignment was used. Assignment of fundamental modes was confirmed by potential energy distributions (PEDs) of the normal modes derived by the scaled force fields using a modified version of the UMAT program in the QCPE package. We demonstrate that for large molecules such as the DMQs, the scaling of the force field is more effective in arriving at the correct assignment of the fundamentals for a quantitative vibrational analysis. An error analysis of the mean deviation of the calculated harmonic, anharmonic, and force field fitted frequencies from the observed frequency provides strong evidence for the correctness of the assignment.

A singularity-free cosmological model in ECSK theory

In the framework of the ECSK [Einstein-Cartan-Sciama-Kibble] theory of cosmology, a scalar field nonminimally coupled to the gravitational field is considered. For a Robertson-Walker open universe (k=0) in the radiation era, the field equations admit a singularity-free solution for the scale factor. In theory, the torsion is generated through nonminimal coupling of a scalar field to the gravitation field. The nonsingular nature of the cosmological model automatically solves the flatness problem. Further absence of event horizon and particle horizon explains the high degree of isotropy, especially of 2.7-K background radiation.

Capillary-gravity waves against a corrugated vertical cliff

An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

Diesel Engine Driven Stand-Alone Variable Speed Constant Frequency Slip Ring Induction Generator - Theory and Experimental Results

The operation of a stand-alone, as opposed to grid connected generation system, using a slip-ring induction machine as the electrical generator, is considered. In contrast to an alternator, a slip-ring induction machine can run at variable speed and still deliver constant frequency power to loads. This feature enables optimization of the system when the prime mover is inherently variable speed in nature eg. wind turbines, as well as diesel driven systems, where there is scope for economizing on fuel consumption. Experimental results from a system driven by a 44 bhp diesel engine are presented. Operation at subsynchronous as well as super-synchronous speeds is examined. The measurement facilitates the understanding of the system as well as its design.

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.