Arbitrary Spatial Distribution Research Articles

OPTICAL AMPLITUDE AND PHASE EVOLUTION IN NONLINEAR MAGNETO-OPTICAL BRAGG GRATINGS

We present a theory on stratified nonlinear magneto-photonic crystals, with arbitrary spatial distribution of the refractive index and magneto-optical coefficients. The coupled mode theory is formulated for plane waves inside the crystal, and a perturbation series of integral solutions for the spectral response of the crystal is presented. Material issues and configurations are discussed, and the described theory is applied to the calculation of transmission spectra of binary magneto-photonic crystals.

FIELD THEORY OF TACHYON MATTER

We propose a field theory for describing the tachyon on a brane–antibrane system near the minimum of the potential. This field theory realizes two known properties of the tachyon effective action: (a) absence of plane-wave solutions around the minimum, and (b) exponential fall off of the pressure at late time as the tachyon field evolves from any spatially homogeneous initial configuration towards the minimum of the potential. Classical solutions in this field theory include nonrelativistic matter with arbitrary spatial distribution of energy.

The theory of thermoluminescence with an arbitrary spatial distribution of traps.

There are two basic analytical models for thermoluminescence (TL). The first relates to the uniform distribution of traps. The second relates to the pairs of traps and recombination centres placed close to each other. In both cases, it was possible to formulate a set of differential equations describing charge carriers' kinetics. Some recent results, both experimental and theoretical, show that this simple picture may not be applicable, especially in dosimetric applications of TL. There are strong indications that many measured TL glow curves come from clusters of spatially associated traps and recombination centres. The kinetics of TL and some relevant processes in spatially correlated systems was studied numerically using Monte Carlo simulations. In this paper, new equations are presented for TL in a system with an arbitrary spatial distribution of traps and recombination centres. An analytical formulation allows easier comparison of the theory with experimentally observed data.

Computer simulation of gas generation and transport in landfills—I: quasi-steady-state condition

We develop a comprehensive three-dimensional (3D) model of gas generation and transport in landfills. The model, which is developed for a four-component gas mixture, takes into account the effect of heterogeneity in the distributions of the permeability and porosity in the landfill, as well as that of the soil that surrounds it. It also takes into account the presence of an arbitrary number of gas extraction wells with an arbitrary spatial distribution. The governing non-linear equations of mass transport and reaction are solved by a novel iterative method that bypasses the non-linearity without making any approximation. The model is utilized for investigating gas generation and transport in a model landfill, and the effect of various parameters that control these phenomena.

Solute segregation and coherent nucleation and growth near a dislocation—a phase-field model integrating defect and phase microstructures

A diffuse-interface field model is proposed for describing diffusional processes in coherent systems with arbitrary microstructures and arbitrary spatial distribution of structural defects such as dislocations. It takes into account the effect of both the coherency elastic energy of a microstructure and the elastic coupling between the coherency strains and defect strains. In this model, any arbitrary spatial distribution of defects is described using the micromechanics concept of space-dependent “stress-free” or “eigen” strains. As examples, the solute segregation as well as the nucleation and diffusional growth of a coherent precipitate around an edge dislocation are considered. It is shown that coherent nucleation may become barrierless under the influence of the local elastic field of a dislocation.

Formation and Evolution of Dusty Starburst Galaxies. I. A New Method for Deriving a Spectral Energy Distribution

We present a new numerical code that is designed to derive a spectral energy distribution (SED) for an arbitrary spatial distribution of stellar and gaseous components in a dusty starburst galaxy. We apply a ray-tracing method to numerical simulations and thereby estimate extinction and reemission of stellar light by dusty gas in an explicitly self-consistent manner. By using this code, we can investigate simultaneously dynamical and photometric evolution of a dusty galaxy based on stellar and gaseous dynamical simulations. As an example, we demonstrate when and how a major galaxy merger with dusty starburst becomes an ultraluminous infrared galaxy owing to strong internal dust extinction. We furthermore discuss advantages and disadvantages of the present new code in clarifying the nature and the origin of low- and high-redshift dusty starburst galaxies.

Modulated photocurrents in a sandwich-cell structure

Approximate formulae describing modulated photocurrents in asandwich configuration of sample electrodes are derived. Thecarrier transport is described in terms of the multiple-trappingmodel. The formulae refer to arbitrary spatial distribution ofgenerated carriers. The case of exponential light absorption in thesample is considered in detail. It is shown that for limiting lowand high modulation frequencies, both the amplitude and the phaseshift of the photocurrent are almost independent of the lightabsorption coefficient. In the intermediate-frequency range, forthe case of surface carrier generation, the phase shift of thephotocurrent usually shows oscillations. This makes it possible toobtain the energetic density of states from a simple formula.Examples of calculated frequency dependencies of the photocurrentphase shift and amplitude are given for exponential and Gaussiantrap distributions as well as for a single trap level.

Threshold condition for traveling wave excitation in an annular prime-mover

The threshold condition for thermoacoustic instability in an annular prime-mover is derived. The region of spatially inhomogeneous temperature distribution (due to the presence of a stack and hot and cold heat exchangers) is assumed to be acoustically thin. The interaction of acoustic waves with the stack is assumed to be quasiadiabatic. Theoretical approach (based on the transformation of differential wave equation into Volterra integral equation, which is solved by iterative procedure) is valid for arbitrary spatial temperature distribution. Nevertheless, it was found that the threshold for the excitation of a traveling acoustic wave does not depend on the details of temperature spatial distribution but just on the ratio of the temperatures of hot and cold heat exchangers. Moreover, the critical temperature ratio does not depend on the thickness of the stack if the acoustic losses inside the heated region are negligible in comparison with acoustic losses in the rest part of the annular system. In this important limiting case critical temperature ratio diminishes when the dimensions of the system are scaled up. [Work supported by DGA.]

Dependence of scattered acoustical signal intensity on the form of distribution of plankton concentration

Sounding of the plankton aggregation which consists of identical statistically uncorrelated particles by a plane monochromatic wave has been studied. Analytical formulas for scattered signal intensity and interference coefficient have been obtained for an arbitrary plankton spatial distribution form. The role of interference of waves scattered by individual plankton targets has been under investigation. The influence of the plankton probability density function form on the sounding signal mean intensity has also been considered.

A backward Monte Carlo estimator for the multiple scattering of a narrow light beam

A backward Monte Carlo estimator is derived for the multiple scattering of a narrow light beam of arbitrary spatial distribution incident on a plane parallel layer. A means of obtaining an error estimate which provides an upper bound on the actual error is suggested. The intuitively clear result that the higher order intensities asymptotically approach each other for all optical radii was observed. It is observed that at reasonably modest optical distances from the beam, consideration of only the first or second orders of scatter in the evaluation of the diffuse light field will lead to erroneous results.

Modeling approach for two-dimensional distributed transducers of arbitrary spatial distribution

A new modeling method for two-dimensional distributed transducers with arbitrary spatial distribution is presented. The spatial weighting of a distributed transducer is defined using multidimensional distributions with composite functions as arguments. A differentiation theorem is derived for one-dimensional distributions of composite functions and is extended to multidimensions through the use of partial distributional derivatives and the product rule. The resulting theory is used to determine the differential operator describing the distributed transducer’s spatial dynamics. The methodology, which is valid for both uniaxial and biaxial transducers, is applied to several two-dimensional problems.

Heat flux measurement from the temperature field of a heated surface. 2. Inhomogeneous flux

Based on the previously obtained analytical solutions of the three-dimensional space-time problem of recalculating boundary conditions, algorithms are developed and a computational experiment is carried out to reconstruct the heat flux with arbitrary spatial distribution of the temperature field of the heated surface.

Analytical solution of two-dimensional diffusion in a composite medium with application to cooling of reactor fuel elements

A special eigenfunction expansion is applied to the solution of two-dimensional, steady state, heat transfer from a composite medium to a well-stirred fluid. The composite medium may consist of an arbitrary number of parallel slabs or cylinders, possibly with contact resistance between them, and heat sources or sinks of an arbitrary spatial distribution. The composite medium is treated in a unified way as a single region with discontinuities. The advantages of the present solution method are demonstrated through its application to a well-known problem of heat transfer in reactor fuel elements. Results of the current solution compare favorably with a previous analytical solution by Fourier series expansions for a slab geometry.

Mathematical modelling of the chronoamperometric response of an array of rectangular microelectrodes

A general mathematical model describing the response of an array of flat amperometric electrodes with arbitrary size and spatial distribution at the bottom of a measuring cell with rectangular walls and finite dimensions is outlined. It is based on the three-dimensional diffusion equation with initial and boundary conditions corresponding to the physical situation which was numerically solved by the implicit alternating-direction finite-difference method. The accuracy of the numerical solution was confirmed by theoretical and experimental results obtained by other authors. By comparing the chronoamperometric curves of the individual electrodes and by examining the spatial concentration distribution in the measuring cell conclusions can be drawn concerning the mutual influence of the individual electrodes for a given geometry of the array and the dimensions of the measuring cell. This will allow the designing of arrays and selecting the proper measuring cell dimensions resulting in minimal sensor interferences. Chronoamperometric curves show the time required for attaining quasi steady state and the corresponding current value. Illustrative examples are presented.

Thermally stimulated currents due to multiple-trapping carrier transport. II. Dispersive transport

For pt.I see ibid., vol.4, p.3967 (1992). This paper deals with non-isothermal dispersive carrier transport in an insulator with trapping states. The approximate solutions of the transport equations derived previously are extended here to include an arbitrary spatial distribution of generated carriers as well as the temperature and energy dependences of some trap parameters and the temperature dependence of the microscopic carrier mobility. The accuracy of the formulae describing thermally stimulated currents (TIC) is verified by Monte Carlo calculations for exponential and Gaussian trap distributions. Methods of determining the shape of the trap distribution and the trap parameters from the TSC data are discussed.

Laser-induced thermoelectric effects in an STM junction

The spatial and temporal temperature distribution for a conical shape metal emitter under laser irradiance is obtained analytically using the Green function method. In this study the tip is modeled as an infinite cone of half angle θ 0 which can vary between 0 and 1 2 π . The full three-dimensional heat diffusion equation is solved simultaneously with the Fourier equation for the heat flux assuming no radiation losses. The general solution is obtained for an arbitrary temporal and spatial distribution of the irradiance. With uniform irradiance the temperature rise in the conical tip varies almost linearly with the laser intensity and heating time and depends strongly on cone angle and thermal properties. For a tungsten tip, the temperature increase is about 2–3 orders of magnitude above ambient for a typical laser intensity of about 1 MW/cm 2 in a time of a few hundred nanoseconds. To study Joule heating and the Thomson thermoelectric effect in the STM junction we first obtained the current distribution inside the emitter. Using this as a volume heat source, we used the Green function method to solve the heat conduction equation. The resulting temperature gradient was then used to obtain the thermoelectric potential. For a tungsten tip at ∼ 1000 K the thermoelectric effect generates a bias voltage on the order of 10 mV.

Ac-conductance of an infinite ideal quantum wire in an electric field with arbitrary spatial distribution

In a purely ballistic quantum wire exposed to a monochromatic longitudinal electric field E( x)e -1 wt , each open sub-band channel is predicted to contribute ( e 2 h )L( ω v F ) L(0) to the conductance Φ(ω), where v F is the sub-band Fermi velo city and L is the Fourier transformed auto-correlation function of the field, ∫d x' E( x') E( x' + x). This reproduces the universal static limit e 2 h and the ω-dependence for known special cases. Estimates using the parameters realised in GaAlAs-heterostructures show that the predicted effects should be detectable in quasi-one-dimensional inversion layers.

Photothermal waves in anisotropic media

The coupled 3-D thermoacoustic equations, describing wave propagation in anisotropic solids, are derived. While solutions to these equations predict the behavior of both thermal and acoustic waves, a specific formulation is presented for the analysis of thermal wave generation, and propagation, in the decoupled mode. The approach is based on a transfer function formalism, and can easily be adapted to accommodate external sources with arbitrary spatial distribution. Simulations pertaining to the case of thermal wave propagation in a semi-infinite sample, as well as a slab of material are presented. Results predict anisotropy-induced asymmetric field formation and thermal beam-steering effects.

Determination of bulk minority-carrier lifetime and surface/interface recombination velocity from photoluminescence decay of a semi-infinite semiconductor slab

The analytical expression is derived for the time dependence of the total minority-carrier content in a semi-infinite semiconductor slab, after excitation with a delta function light pulse. It is shown that to this end it is sufficient to solve the continuity equation for the minority carriers in one dimension only. This implies that the excitation may have an arbitrary lateral spatial distribution. The photoluminescence, probing the total minority-carrier content, turns out to be a nonexponential function of time when the surface/interface recombination velocity differs from zero. A practical method is developed to deduce accurate values of the bulk lifetime and the interface recombination velocity from such a nonexponential decay curve, based on a special way of plotting. Moreover, the analytical expressions are derived for the photoluminescence decay in the case of finite slab thicknesses and finite interface recombination velocities. From these results it is evident that only for large ratios (>10) of slab thickness and minority-carrier diffusion length can the semiconductor be considered as being semi-infinite.

Boundary effects on transient radiation fields from vibrating surfaces

The transient radiation or diffraction from a planar source imbedded in an infinite baffle is analyzed for three different baffle conditions (rigid, free-space, and soft). For an excitation separable in time and space, it is shown that the field is related to the normal derivative of the input field only. A method is also given for computing the transient fields based on a wave decomposition in the spatial frequency domain. This method is a time generalization of the angular spectrum theory that presents transient wave propagation as a time-varying spatial filter, allowing a linear systems interpretation of the diffraction. The formalism is shown to easily include the effects of a finite receiving aperture. The method is amenable to computing the field from an arbitrary time excitation and an arbitrary spatial distribution. The method is valid for arbitrary distances to the observation point and uses computationally efficient FFT calculations.