General Theoretical Scheme Research Articles

Modified Chebyshev polynomial (U N ) approximation in the neutron transport theory and computation of critical half thicknesses

Abstract A general theoretical scheme for the UN method and the evolution of a general eigenvalue spectrum are described. The applicability of UN method to one dimensional slab geometry neutron transport problems is discussed. The eigenvalue spectrum is calculated for isotropic scattering with different values of the parameter c, the mean number of secondary neutrons per collision, known as the fundamental eigenvalue. Then the critical slab problem has been studied. The critical half thicknesses are computed for different values of c. For the solution, Mark and Marshak boundary conditions are used. Results are obtained for both, UN and PN approximations for comparison.

Testing the blazar spectral sequence: X-ray-selected blazars

We present simultaneous optical and X-ray data from Swift for a sample of radio-loud flat-spectrum quasars selected from the Einstein Medium Sensitivity Survey (EMSS). We present also a complete analysis of Swift and INTEGRAL data on four blazars recently discussed as possibly challenging the trends of the hypothesized ‘blazar spectral sequence’. The spectral energy distributions (SEDs) of all these objects are modelled in terms of a general theoretical scheme, applicable to all blazars, leading to an estimate of the jets’ physical parameters. Our results show that, in the case of the EMSS broad line blazars, X-ray selection does not lead to find sources with synchrotron peaks in the UV/X-ray range, as was the case for X-ray-selected BL Lacs. Instead, for a wide range of radio powers all the sources with broad emission lines show similar SEDs, with synchrotron components peaking below the optical/UV range. The SED models suggest that the associated inverse Compton (IC) emission should peak below the GeV range, but could be detectable in some cases by the Fermi Gamma-ray Space Telescope. Of the remaining four ‘anomalous’ blazars, two highly luminous sources with broad lines, claimed to possibly emit synchrotron X-rays, are shown to be better described with IC models for their X-ray emission. For one source with weak emission lines (a BL Lac object) a synchrotron peak in the soft X-ray range is confirmed, while for the fourth source, exhibiting narrow emission lines typical of narrow-line Seyfert 1 galaxies, no evidence of X-ray emission from a relativistic jet is found. We re-examine the standing and interpretation of the original ‘blazar spectral sequence’ and suggest that the photon ambient, in which the particle acceleration and emission occur, is likely the main factor determining the shape of the blazar SED. A connection between SED shape and jet power/luminosity can however result through the link between the mass and accretion rate of the central black hole and the radiative efficiency of the resulting accretion flow, thus involving at least two parameters.

Effective medium theory of the one-dimensional resonance phononic crystal

A general theoretical scheme to describe the effective modulus and mass density foracoustic metamaterials is presented. For such a purpose, an effective medium theory of aone-dimensional acoustic waveguide containing subwavelength-sized Helmholtz resonatorsis formulated. It is shown that, when the wavelength is much larger than theperiodic length and the size of the resonators, the whole composite structure canbe treated as an effective homogeneous medium in accounting for its acousticproperties. It is also shown that the acoustic characteristics, such as the effectivemodulus and the effective mass density, can be determined precisely from thetransmission and the reflection data. The calculated effective modulus and effectivemass density confirm that this structure behaves as a homogeneous metamaterialwith a negative effective modulus in a frequency range just above the resonantfrequency.

Physical Limits on Self-Replication Processes

Using few very general axioms which should be satisfied by any reasonable theory consistent with the Second Law of Thermodynamics we argue that: a) "no-cloning theorem" is meaningful for a very general theoretical scheme including both quantum and classical models, b) in order to describe self-replication, Wigner's "cloning" process should be replaced by a more general "broadcasting", c) "separation of species" is possible only in a non-homogeneous environment, d) "parent" and "offspring" must be strongly correlated. Motivated by the existing results on broadcasting which show that only classical information can self-replicate perfectly we discuss briefly a classical toy model with "quantum features" — overlapping pure states and "entangled states" for composite systems.

Some useful properties of Legendre polynomials and its applications to neutron transport equation in slab geometry

In this paper, we describe a new scattering kernel and general theoretical scheme for the evolution of the discrete and continuum eigenvalue spectrum in one-dimensional slab geometry neutron transport equation. Firstly, some useful properties of the Legendre polynomials which revealed during the definition of the new scattering kernel are discussed. By using the scattering kernel in one-dimensional neutron transport equation we obtained an integral equation for angular part of the angular flux. For the solution of this integral equation and eigenvalue equations, some comments are given.

General Eigenvalue Spectrum in a One-Dimensional Slab Geometry Transport Equation

A general theoretical scheme for the evolution of a general discrete eigenvalue spectrum in a one-dimensional slab geometry neutron transport equation is described. To make a general procedure, we described the consistent scattering kernel. By using this scattering kernel, discrete eigenvalues are computed. Three methods are presented for the calculation of discrete eigenvalues, but the simplest one is chosen for the computation. Numerical results are presented in the tables. Results are discussed and compared with those already obtained using various methods available in the literature.

Shallow-donor wave functions and donor-pair exchange in silicon:Ab initiotheory and floating-phase Heitler-London approach

Electronic and nuclear spins of shallow donors in Silicon are attractive candidates for qubits in quantum computer proposals. Shallow donor exchange gates are frequently invoked to preform two-qubit operations in such proposals. We study shallow donor electron properties in Si within the Kohn-Luttinger envelope function approach, incorporating the full Bloch states of the six band edges of Si conduction band, obtained from {\it ab initio} calculations within the density-functional and pseudopotential frameworks. Inter-valley interference between the conduction-band-edge states of Si leads to oscillatory behavior in the charge distribution of one-electron bound states and in the exchange coupling in two-electron states. The behavior in the donor electron charge distribution is strongly influenced by interference from the plane-wave and periodic parts of the Bloch functions. For two donors, oscillations in the exchange coupling calculated within the Heitler-London (HL) approach are due to the plane-wave parts of the Bloch functions alone, which are pinned to the impurity sites. The robustness of this result is assessed by relaxing the phase pinning to the donor sites. We introduce a more general theoretical scheme, the floating-phase HL, from which the previously reported donor exchange oscillatory behavior is qualitatively and quantitatively confirmed. The floating-phase formalism provides a ``handle'' on how to theoretically anticipate the occurrence of oscillatory behavior in electronic properties associated with electron bound states in more general confining potentials, such as in quantum dots.

Near-field light emission from nano- and micrometric complex structures

We propose a general theoretical scheme for the investigation of light emitted from nano- and micrometric structures of arbitrary shape and composition. More specifically, the proposed fully three-dimensional approach allows to derive the light-intensity distributions around the emitting structures and their modifications in the presence of nearby scattering objects. Our analysis allows to better identify the nontrivial relationship between near-field images and fluorescent objects.

A Stochastic Model of Conductance Transitions in Voltage-Gated IonChannels.

We present a statistical physics model to describe the stochastic behaviorof ion transport and channel transitions under an applied membrane voltage.To get pertinent ideas we apply our general theoretical scheme to ananalytically tractable model of the channel with a deep binding site whichinteracts with the permeant ions electrostatically. It is found that theinteraction is modulated by the average ionic occupancy in the bindingsite, which is enhanced by the membrane voltage increases. Above acritical voltage, the interaction gives rise to a emergence of a newconducting state along with shift of S4 charge residues in the channel.This exploratory study calls for further investigations to correlate thecomplex transition behaviors with a variety of ion channels, withparameters in the model, potential energy parameters, voltage, and ionicconcentration.

Black dots as a detector of self-assembly in thin liquid films

Experiments with different types of amphiphilic substances exhibit two stable tendencies. (1) The surface tension/concentration curves (Δ σ/ C s) display well-defined kink and plateau sectors. (2) Free thin liquid films (foam films) from solutions with concentrations in the plateau regions drain until ‘black dots’ appear and then rupture almost immediately. A general theoretical scheme is developed that suggests a mechanism connecting the formation of black dots with the onset and the reorganization of smaller self-assembled aggregates (premicelles) in the bulk of the solution and on the interfaces. The results show that the black dots in free thin liquid films may serve as an indicator of the presence and reorganization of self-assembled structures in amphiphilic solutions.

A case for water utilities as cooperatives and the UK experience

This article explores the creation of consumer cooperatives as a means of privatizing water utilities. The first section examines the structure of ownership and sets out Hansmann's theoretical basis for determining which category of persons is most efficiently assigned ownership. The section extends the discussion of market contracting costs by considering the externalities and social costs associated with a water utility. The heart of the paper is the second section which applies the theory of efficiently assigned ownership to the case of water utilities. The third section briefly reviews the literature on the relative efficiency of private and public utilities and also succinctly applies the theory of the firm to the question of vertical integration in the case of water utilities. The fourth section discusses the UK's experience with water utilities. The final section draws together the paper's conclusions. The application of Hansmann's general theoretical scheme for assigning ownership leads to the conclusion that water utilities should be consumer cooperatives. Consumer‐owned utilities would confront lower market contracting and ownership costs, than would investor‐owned utilities. Additionally, the social costs and externalities that are particular to water are better left to consumers who are more prone to take them into account in their decisions.

Tracer-diffusion in colloidal mixtures: A mode-coupling scheme with hydrodynamic interactions

In this work, we develop a general theoretical scheme to study tracer-diffusion in mixtures of interacting colloidal particles where the influence of solvent-mediated hydrodynamic interactions is also considered. Based on the many-body Smoluchowski diffusion equation, we derive in a first step an exact microscopic expression of the irreducible memory function (self-friction function) associated with the self-intermediate scattering function and with the mean squared displacement of a tagged particle. By applying a mode-coupling scheme (MCS) to the irreducible memory function, we obtain explicit expressions for the tracer-diffusion quantities in terms of partial static structure factors and hydrodynamic functions. The influence of hydrodynamic interactions (HI) is accounted for using a far-field expansion of the two-body hydrodynamic diffusivity tensors. For charge-stabilized colloids, this is a good approximation due to strong electrostatic repulsion between the particles. Various applications are discussed in order to illustrate the versatility of our mode-coupling scheme.

Theory of Extremal Dynamics with Quenched Disorder: Self-Organization, Avalanche Dynamics and Critical Exponents

In this paper we discuss a general theoretical scheme, that we have recently proposed, for a class of phenomena characterized by extremal dynamics with quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic dynamics with cognitive memory. This transformation, together with other concepts, permits a mathematical characterization of the self-organized nature of the avalanche type dynamics. By combining the mapping with real space methods, like the fixed scale transformation (FST), it is also possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems with quenched disorder.

Vibrational broadening of x-ray emission spectra: A first-principles study on diamond

We present a general theoretical scheme that allows an accurate account of the vibrational broadening of core-level line shapes in crystals, using state-of-the-art electronic-structure techniques within the Franck-Condon approximation. Electronic and vibrational degrees of freedom are consistently treated using ab initio density-functional theory. Neglecting the core-hole lifetime, anharmonic effects are treated within a self-consistent phonon approach. Finite core-hole lifetime effects are simulated by an independent-boson model, which, however, we have been able to apply only when lattice distortions are treated in the harmonic approximation. We apply the theory to the diamond 1s core-level emission spectrum. In the limit of infinite core-hole lifetime, we find that (i) the Stokes shift is about 3 eV, (ii) the harmonic approximation overestimates the Stokes shift by \ensuremath{\sim}1.4 eV, and (iii) phonon broadening is about 2 eV. A comparison with experiment reveals that the phonon bandwidth is comparable to the core-hole lifetime, which we estimate \ensuremath{\Gamma}\ensuremath{\approx}110 meV.

Implications of an evolutionary biopsychosocial model

AbstractMealey's work has several interesting implications: It refutes the charge that sociobiology paints a cynical portrait of human nature and adopts a one-sided reductionism; it exemplifies a general theoretical scheme for constructing evolutionary biopsychosocial models of human behavior; and it has the practical effect of promoting and informing early intervention in children at risk for psychopathic disorder.

Density functional theory of phase transitions in diblock copolymer systems

A general theoretical scheme is presented which allows the characterization of microphase separation of A-B diblock copolymer systems at all degrees of segregation. Our method is based on the density functional theory of Melenkevitz and Muthukumar and uses the technique of density profile parameterization to greatly reduce the technical complexity of the solution. The microphase-separated systems are observed to pass through three stages of ordering as the system is quench intermediate, and strong segregation regimes. These are the weak; intermediate and strong segregation regimes

Unemployment and the real wage: the economic basis for contesting political ideologies

Using the Keynesian theory of effective demand, this paper demonstrates how particular models, such as that of cooperative capitalism enunciated by the left Keynesian social democrats, the Marxian model of profit squeeze emphasizing distributive conflict, and even the conservative model relying on supply side stimulus, fit in as particular variants of a more general theoretical scheme through a reconstruction of the familiar IS schedule. The argument is weaved around the theme of the relations between unemployment and real wage in the context of both a closed and an open economy to explain the common macroeconomic basis of contesting ideologies. Copyright 1990 by Oxford University Press.

IBA-1 calculation of [formula omitted] mixing ratios in 154Gd

The general theoretical scheme, with various special cases, is presented for calculating γ- ray E2 M mixing ratios for even nuclei on the IBA-1 model. The M1 transition operator needed for unconstrained algebraic signs contains three parameters. Numerical results for 154Gd are compared with Warner;s simplified IBA treatment and with Kumar's model. Sign flexibility is demonstrated by 168Er.

Resonance Fluorescence from Large Molecules

In this paper we apply the T matrix formalism of scattering theory to derive general expressions for the absorption cross sections, the cross sections for resonance fluorescence and the emission quantum yields from large molecules in the statistical limit. In the simple case of an isolated molecular resonance both the absorption line shape and the photon scattering cross section exhibit a Lorentzian distribution on the photon energy, the emission quantum yields are distributed among the ground state vibronic levels according to their radiative widths and, most important, the emission quantum yields are independent of the photon energy and of the spectral width of the exciting light. We were able to derive general expressions for the resonance scattering from a pair of overlapping resonances, including radiative corrections to infinite order. The absorption cross section does not vanish in the region of destructive interference but assumes a finite value which depends on the radiative widths. A sharp maximum in the partial and in the total emission quantum yields is exhibited in the destructive interference regions. This general scheme was applied to a pair of zero order discrete states, one of which is optically active, which interact with an optically inactive quasicontinuum. The energy dependent quantum yield depends on the total width of the radiatively impotent state and may exhibit a minimum. We have demonstrated that when interference effects are involved the decay characteristics of this system will differ for coherent and for narrow band excitation. The general formalism was utilized to derive approximate relations for the resonance fluorescence cross sections and for the quantum yield in the case of a Fano absorption line shape which are valid away from the interference region. Finally, we have applied the general theoretical scheme to the case of the direct photodissociation spectrum of molecules. We have demonstrated that a finite energy dependent emission quantum yield will be observed when a molecule is optically pumped into a dissociative continuum.

Recent Reactions between Theory and Experiment. The Raman Effect: The Constitution of Hydrogen Gas

IN watching the advance of science, and particularly of the physical sciences to-day, one cannot fail to be struck by the very close connexion between theory and experiment—a relation which is probably more intimate than at any other period of scientific history. Every new experimental observation is at once seized upon to test whether it can be explained by existing theories, and if not, to find the modifications necessary to include it in the general theoretical scheme of natural processes. The mathematical analysis often suggests the possibility of unexpected relations which can be made the subject of fruitful experimentation. These two, in a sense, complementary branches of physics profoundly react and interact with each other, and their united efforts lead to a greatly accelerated rate of advance in knowledge and understanding of the essential principles involved. The rapidity of advance in physics, which has been so marked a feature in the last decade, is mainly due to this close combination of theory with experiment.