Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

The Systems Theory Framework of career development: Applications to career counselling and career assessment

Since its inception, the Systems Theory Framework of career development has afforded ready translation into practice, especially into career counselling and qualitative career assessment. Through its clearly articulated constructs and the clarity of its diagrammatic representation, the Systems Theory Framework has facilitated the development of qualitative career assessment instruments as well as a quantitative measure. This article briefly overviews these practical applications of the Systems Theory Framework as well as its application in career counselling through a story telling approach. The article concludes by offering a synthesis of and considering future directions for the Systems Theory Framework’s practical applications.

Dissipative dynamics of a harmonic oscillator: A nonperturbative approach

Starting from a microscopic theory, we derive a master equation for a harmonic oscillator coupled to a bath of noninteracting oscillators. We follow a nonperturbative approach, proposed earlier by us for the free Brownian particle. The diffusion constants are calculated analytically and the positivity of the master equation is shown to hold above a critical temperature. We compare the long time behavior of the average kinetic and potential energies with known thermodynamic results. In the limit of vanishing oscillator frequency of the system, we recover the results of the free Brownian particle.

Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag−Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.

A dynamic renormalization group study of active nematics

We carry out a systematic construction of the coarse-grained dynamical equation of motion for the orientational order parameter for a two-dimensional active nematic, that is a nonequilibrium steady state with uniaxial, apolar orientational order. Using the dynamical renormalization group, we show that the leading nonlinearities in this equation are marginally irrelevant. We discover a special limit of parameters in which the equation of motion for the angle field bears a close relation to the 2d stochastic Burgers equation. We find nevertheless that, unlike for the Burgers problem, the nonlinearity is marginally irrelevant even in this special limit, as a result of a hidden fluctuation-dissipation relation. 2d active nematics therefore have quasi-long-range order, just like their equilibrium counterparts.

Improved procedures for static and dynamic analyses of wrinkled membranes

An analysis of large deformations of flexible membrane structures within the tension field theory is considered. A modification-of the finite element procedure by Roddeman et al. (Roddeman, D. G., Drukker J., Oomens, C. W J., Janssen, J. D., 1987, ASME J. Appl. Mech. 54, pp. 884-892) is proposed to study the wrinkling behavior of a membrane element. The state of stress in the element is determined through a modified deformation gradient corresponding to a fictive nonwrinkled surface. The new model uses a continuously modified deformation gradient to capture the location orientation of wrinkles more precisely. It is argued that the fictive nonwrinkled surface may be looked upon as an everywhere-taut surface in the limit as the minor (tensile) principal stresses over the wrinkled portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. Under dynamic excitations, the governing equations are weakly projected to arrive at a system of nonlinear ordinary differential equations that is solved using different integration schemes. It is concluded that, implicit integrators work much better than explicit ones in the present context.

Stability of scheduled multi-access communication over quasi-static flat fading channels with random coding and independent decoding

The stability of scheduled multiaccess communication with random coding and independent decoding of messages is investigated. The number of messages that may be scheduled for simultaneous transmission is limited to a given maximum value, and the channels from transmitters to receiver are quasistatic, flat, and have independent fades. Requests for message transmissions are assumed to arrive according to an i.i.d. arrival process. Then, we show the following: (1) in the limit of large message alphabet size, the stability region has an interference limited information-theoretic capacity interpretation, (2) state-independent scheduling policies achieve this asymptotic stability region, and (3) in the asymptotic limit corresponding to immediate access, the stability region for non-idling scheduling policies is shown to be identical irrespective of received signal powers.

Knowledge through Discussion : An Interpretation of Epistemology in Plato's Meno

According to Meno s paradox we cannot inquire into what we do not know because we do not know what we are inquiring into. There are many ways to interpret the paradox but the central issue about our ability to reach truth is a profound one. In the dialogue Meno, Plato presents the paradox and an outline of a solution which enables us to reach knowledge (epistēmē) through philosophical discussion. During the last century Meno has often been considered transitional between Socratic thinking and Plato s own philosophy, and thus the dialogue has not been adequately interpreted as an integrated whole. Therefore the distinctive epistemology of the dialogue has not gained due notice. In this thesis the dialogue is analysed as an integrated whole and the philosophical interpretation also takes into account its dramatic features. The thesis emphasises the role of language and definitions in acquiring knowledge. Among the results concerning these subjects is a new interpretation of Socrates s defintion of shape (schēma). The theory of anamnēsis all learning is recollection in the Meno is argued to answer the paradox philosophically although Plato s presentation also contains playful and ironic elements. The background of the way Plato presents his case is that he appreciated the fact that no argument can plausibly demonstrate that argumentation is able to reach truth. In the Meno, Plato makes the earliest explicit distinction between knowledge and true belief in the history of Western philosophy. He also gives a definition of knowledge which is the basis of the so called classical definition of knowledge as justified true belief. In the Meno, true beliefs become knowledge when someone ties them down by reasoning about the explanation. The analysis of the epistemology of the dialogue from this perspective gives an interpretation which integrates the central concepts of the epistemology in the dialogue elenchos, anamnēsis and hypothetical inquiry into a unified whole which contains a plausible argument according to which the ignorant can reach knowledge through discussion. The conception that emerges by such an analysis is interesting both from the point of view of current interests and that of the history of philosophy. The method of knowledge acquisition in the Meno can, for example, be seen as a predecessor of modern scientific methods. The Meno is the earliest Greek mathematical text that has survived in its original form. The analysis presented in the thesis of the geometric passages in the dialogue provides new results both concerning Socrates s geometry lesson with the slave and the example presenting the hypothetical method. Concerning the latter, a new interpretation is presented. Keywords: anamnēsis, epistēmē, knowledge, Meno s paradox, Plato

Influence of drying on the liquid limit behaviour of a marine clay

The possible mechanisms of particle aggregation and reduction in liquid limit of the Cochin marine clay on drying are investigated. Mineralogical analysis showed the absence of halloysite in the marine specimen. Experimental results also ruled out the possibility of cementitious material being responsible for particle aggregation and reduction in clay plasticity on drying. The presence of calcium and magnesium as the predominant exchangeable ions and of a high pore salt concentration facilitates strong interparticle attraction and small particle separations; the latter leads to development of significant capillary stresses that permits an intimate contact of particles and growth of strong van der Waals' and Coulombic bonds.

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.

Tibetan Written Images : A Study of Imagery in the Writings of Dhondup Gyal

Dhondup Gyal (Don grub rgyal, 1953 - 1985) was a Tibetan writer from Amdo (Qinghai, People's Republic of China). He wrote several prose works, poems, scholarly writings and other works which have been later on collected together into The Collected Works of Dhondup Gyal, in six volumes. He had a remarkable influence on the development of modern Tibetan literature in the 1980s. Examining his works, which are characterized by rich imagery, it is possible to notice a transition from traditional to modern ways of literary expression. Imagery is found in both the poems and prose works of Dhondup Gyal. Nature imagery is especially prominent and his writings contain images of flowers and plants, animals, water, wind and clouds, the heavenly bodies and other environmental elements. Also there are images of parts of the body and material and cultural images. To analyse the images, most of which are metaphors and similes, the use of the cognitive theory of metaphor provides a good framework for making comparisons with images in traditional Tibetan literature and also some images in Chinese, Indian and Western literary works. The analysis shows that the images have both traditional and innovative features. The source domains of images often appear similar to those found in traditional Tibetan literature and are slow to change. However, innovative shifts occur in the way they are mapped on their target domains, which may express new meanings and are usually secular in nature if compared to the religiosity which often characterizes traditional Tibetan literature. Dhondup Gyal's poems are written in a variety of styles, ranging from traditional types of verse compositions and poems in the ornate kāvya-style to modern free verse poetry. The powerful central images of his free verse poems and some other works can be viewed as structurally innovative and have been analysed with the help of the theory of conceptual blending. They are often ambiguous in their meaning, but can be interpreted to express ideas related to creativity, freedom and the need for change and development.

Computational Methods for Studies of Quantum Dots and Boson Condensates

This thesis presents ab initio studies of two kinds of physical systems, quantum dots and bosons, using two program packages of which the bosonic one has mainly been developed by the author. The implemented models, \emph{i.e.}, configuration interaction (CI) and coupled cluster (CC) take the correlated motion of the particles into account, and provide a hierarchy of computational schemes, on top of which the exact solution, within the limit of the single-particle basis set, is obtained. The theory underlying the models is presented in some detail, in order to provide insight into the approximations made and the circumstances under which they hold. Some of the computational methods are also highlighted. In the final sections the results are summarized. The CI and CC calculations on multiexciton complexes in self-assembled semiconductor quantum dots are presented and compared, along with radiative and non-radiative transition rates. Full CI calculations on quantum rings and double quantum rings are also presented. In the latter case, experimental and theoretical results from the literature are re-examined and an alternative explanation for the reported photoluminescence spectra is found. The boson program is first applied on a fictitious model system consisting of bosonic electrons in a central Coulomb field for which CI at the singles and doubles level is found to account for almost all of the correlation energy. Finally, the boson program is employed to study Bose-Einstein condensates confined in different anisotropic trap potentials. The effects of the anisotropy on the relative correlation energy is examined, as well as the effect of varying the interaction potential.}

The velocity dispersion of giant molecular clouds. II - Mathematical and numerical refinements

The energy input to giant molecular clouds is recalculated, using the proper linearized equations of motion, including the Coriolis force and allowing for changes in the guiding center. Perturbation theory yields a result in the limit of distant encounters and small initial epicyclic amplitudes. Direct integration of the motion equations allows the strong encounter regime to be studied. The present perturbation theory result differs by a factor of order unity from that of Jog and Ostriker (1988). The result of present numerical integrations for the 2D (planar) velocity dispersion is presented. The accretion rate for a molecular cloud in the Galactic disk is calculated.