A non-dimensional approach to diffraction phenomena in the Fresnel approximation

The paper presents a theoretical and numerical study of the diffraction problem approached in the Fresnel approximation. The problem was formulated by a non-dimensional approach, which implies the definition of two non-dimensional quantities: F and ζ. In particular the parameter F is the well-known Fresnel number, whose value was usually used to classify diffraction regime. In analyzing the numerical approach some limitations imposed by the discretization arise; in particular these limitations constrain the level of sampling to be used for the diffracting field by requiring more and more elements when the diffraction conditions become more severe — i.e. increasing the dimension of the diffracting aperture and/or decreasing the distance of the plane where the diffracted field is observed.     

An alternative approach to quantum phenomena

This paper outlines the qualitative foundations of a quasiclassical theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of quantizing a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum measurement problem; in particular, it is suggested that the unpredictability of quantum phenomena may arise from deterministic chaos in the behavior of the background field.     

A density-matrix approach to critical phenomena

A density-matrix approach to the constrained Hartree-Fock problem is proposed as an alternative to Kümmel's maximum overlap method for the study of critical phenomena, with reference to two different quasi-spin models. Excellent results are obtained.     

A quasi particle approach to relaxation phenomena

An evolution equation for the relaxation of a nucleus in a metal is derived, assuming that the electronic thermostat is the vacuum of quasi-particles. The relaxation originates in the successive creations of quasi-boson excitations of the electronic system.The author's interest in this subject was aroused through a collaboration with Prof. I. Berkes. He wishes to thank him. It is pleasure to thank also Prof. R. Coussement and Dr. P. Put for many helpfull discussions and for their hospitality at the I.K.S. Leuven.     

Mixture approach to plasmas with dissipative phenomena

Summary On appealing to the recent well-established theory of mixtures, plasmas are described in a systematic way as mixtures of interacting charged-fluid constituents. Viscosity and heat conduction of the constituents are accounted for through the formalism of hidden variables so as to allow wave front propagation. A thermodynamic analysis is performed by having recourse to the second law in the form of the Clausius-Duhem inequality, thus providing a thorough scheme of dissipative effects in plasmas. For example, as an outstanding result of the investigation, it follows that, in the case of constituents at different temperatures, a transfer of linear momentum is unavoidably associated with a correspondent transfer of energy. It is then shown how, in the limiting approximation of magnetofluidodynamics, the process of electric conduction may be embodied into the framework of dissipative effects.

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Riassunto Sulla base della teoria delle misture elaborata negli ultimi anni si trattano i plasmi in maniera sistematica come misture di costituenti fluidi carichi interagenti. La viscosità e la conduzione di calore sono descritti mediante il formalismo delle variabili nascoste in modo da rendere ammissibile la propagazione di fronti d'onda. L'analisi della compatibilità del modello con la termodinamica è effettuata considerando la seconda legge nella forma della diseguaglianza di Clausius-Duhem; come risultato si ottiene uno schema completo di effetti dissipativi nei plasmi. Per esempio, si mostra che nel caso di costituenti a temperatura diversa un trasferimento d'impulso è inevitabilmente legato ad un corrispondente trasferimento di energia. Infine si mostra che, nel caso limite della magnetofluidodinamica, il fenomeno della conduzione elettrica può essere inglobato nel contesto degli effetti dissipativi.

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Резюме На основе недавно развитой теории смесей описывается плазма систематическим образом, как смесь взаимодействуюших заряженных жидких компонент. Вязкость и теплопроводность этих компонент объясняются с помошью формализма скрытых переменных, что позволяет описать распространение волнового фронта. Проводится анализ совместимости предложенной модели со вторым законом термодинамики в форме неравенства Клаузиуса-Духема. В результате этого получается полная схема диссипативных эффектов в плазме. Например, показывается, что в случае компонент при различных температурах перенос импульса неизбежно связан с соответствуюшим переносом энергии. Затем показывается, как в предельном случае магнитной гидродинамики процесс электропроводности может быть включен в рамки диссипативных явлений.

     

The Mueller matrix formalism in diffraction phenomena

Electromagnetic diffraction at the edge of a plane screen is described by the use of the Mueller matrix. The transformation law is found for the Stokes parameters of the incident and diffracted wave by applying the Mueller method to several cases of diffraction.     

Directly recording diffraction phenomena in time domain

By making use of a new technique for measuring the complete spatiotemporal electric field of light with micrometer spatial and femtosecond temporal resolution, we directly demonstrate the formation of the so-called boundary diffraction wave and Arago’s spot, as well as the superluminal propagation of a “diffraction-free” pulse. We believe that such spatiotemporally resolved measurements and the time-domain treatment of diffracting waves not only turn out to be useful for modern physical optics, especially in micro- and meso-optics, but also significantly aid in the understanding of diffraction phenomena in general.     

A multiple-scattering approach to X-ray photoelectron diffraction

We present an alternative method for multiple scattering calculations of X-ray photoelectron diffraction from periodic surfaces. The technique uses a time-reversed RHEED wave function as the final state in a one-step model of the photoemission process. We apply the method to the Ni(001)c(2×2)S system and find an excellent agreement with the experimental data for vertical height of the S overlayer of 1.35±0.05 Å above the top Ni layer. Our calculations display a much better agreement with the experimental data than has been previously reported.     

Non-equilibrium approach to transport phenomena in quantum crystals

A pure dielectric quantum crystal subjected to an external mechanical force is described by non-equilibrium Green’s functions. In equilibrium the leading approximation leads to the definition of elementary excitations, the phonons in the renormalized harmonic approximation. Their temperature dependent energies are to be determined as solutions of an integral equation. For hydrodynamic disturbances a generalized transport equation for a phonon number density is derived. A similar approximation for the spectral function yields an integral equation for space and time dependent quasiparticle energies which are expressed as functionals of the displacement field and the phonon distribution. The Boltzmann equation for the latter includes the quasi-particle interaction.     

The influence of progressive light diffraction in Debye-Sears phenomena

Two previous theories of Debye-Sears diffraction of light by plane ultrasonic waves are summarized. The theories assume that significant modulation of the light wave occurs in both phase and amplitude. In our own approach account is taken of both curvature of the light rays inside the ultrasonic beam and diffraction of the system alone at the exit plane, neglecting any diffraction effect in the liquid itself. In the Hargrove's method progressive diffraction in the medium is considered. Results from these theories are compared with experimental data obtained at a frequency of 5 MHz with ultrasonic waves having large amplitude and beamwidth (50 mm).     

Field-theoretical approach to static critical phenomena in semi-infinite systems

The critical behaviour of a semi-infinite system withO(n) spin symmetry is studied in 4- dimensions near the ordinary transition using renormalization-group methods of field theory and -expansion techniques. It is found that, to all orders in , all surface exponents can be expressed in terms of two bulk exponents and a single surface exponent which follows from the anomalous dimension of the derivative (x ,0) of The order parameter (x,x ) at the surface (x =0). As a byproduct, Barber's scaling law 2₁ – ₁₁ = + is obtained. The surface exponents are calculated to second order in . Our results show that the scaling relation = ^–1 proposed by Bray and Moore is incorrect. The behaviour of various scaling functions close to the surface (i.e. forx correlation length) is determined with the help of short-distance expansions. We also treat corrections to scaling and logarithmic corrections in four dimensions. Our results for the logarithmic corrections of the layer and local susceptibilities disagree with those obtained by Guttmann and Reeve.A brief account of some of the results presented here was given in [1]. The surface exponents were independently calculated to order ² by Reeve and Guttmann [2] using an alternative method     

A matrix approach to grazing-incidence X-ray diffraction in multilayers

A method for computation of X-ray grazing-incidence diffraction (GID) in multilayers and superlattices is presented. The method is based on X-ray dynamical diffraction theory and a matrix from a boundary equations and provides a simple numerical solution of the problem. The application of the method to simulating GID measurements taken from A1As/GaAs superlattice (20 periods of 14.6 nm A1As and 6.8 nm GaAs) demonstrates the principal validity of the theory. A perfect matching between the theory and the experiment requires the real-structure effects of sample to be taken into account.     

A practical approach to ultrasonic imaging using diffraction tomography

A technique for ultrasonic imaging based on the theory of diffraction tomography is presented. The method utilizes a fixed, circular configuration of transmitters and detectors. This configuration was selected because it avoids many practical limitations associated with the design of a medical imaging device. Practical considerations also motivated the inclusion of effects associated with the transmitter beam pattern rather than pursuing the more conventional approach in which plane-wave illumination is required. In addition, the problem of separately imaging both density and compressibility variations is considered.     

A nonconventional approach to describe classical-quantum crossover phenomena near criticality

A nonconventional renormalization group procedure, which involves fixed points and eigenvectors depending on temperature T, is proposed to describe classical-quantum crossover phenomena for quantum systems near criticality. In this new picture, T-dependent critical exponents occur, where T assumes the role of a natural crossover parameter.     

A new approach to treating pressure oscillations in combustion instability phenomena

Developing exact models of combustion instabilities is not an easy task to carry out and requires a great deal of time prior to obtaining success. The present study proposes a low-order model for pressure oscillations that does not require any knowledge of the systems, any new physical findings nor intricate details regarding its operating condition. This new approach is obtained using a Modified Van der Pol’s equation (MVDP) which is tuned by use of a Dual Extended Kalman Filter (DKEF) as a recursive estimator with perspectives in control by computer. This phenomenological model is used to predict the pressure signal from a variety of different combustors. Input data were taken from experimental cases such as a Rijke tube, a gas turbine and a liquid-fuel aero-engine combustor. Furthermore, a simulation considering high frequency oscillations to show the capability of the new approach is presented. In all cases, the results demonstrated the feasibility of applying the tractable model MVDP and DKEF running together to investigate pressure oscillations in practical cases.