Aberrations of diffracted wave fields: distortion

Near-field diffraction patterns are merely aberrated Fraunhofer diffraction patterns. These aberrations, inherent to the diffraction process, provide insight and understanding into wide-angle diffraction phenomena. Nonparaxial patterns of diffracted orders produced by a laser beam passing through a grating and projected upon a plane screen exhibit severe distortion (W311). This distortion is an artifact of the configuration chosen to observe diffraction patterns. Grating behavior expressed in terms of the direction cosines of the propagation vectors of the incident and diffracted orders exhibits no distortion. Use of a simple direction cosine diagram provides an elegant way to deal with nonparaxial diffraction patterns, particularly when large obliquely incident beams produce conical diffraction.     

Existence of stationary waves of radiation cooling

The solution of the system of equations of gas dynamics and radiation transfer is analyzed and it is shown that a Zel'dovich-Raizer stationary wave of radiation cooling does not exist in a hot gas.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 61, No. 3, pp. 437–442, September, 1991.     

Construction of stationary waves on a falling film

Waves on a film falling down a vertical wall exhibit many distinct features. They tend to be locally stationary over several wavelengths, viz. they travel with constant speeds and shapes over a long distance. In the limit of very long (solitary) waves, these stationary waves also exhibit two length scales with small and short capillary waves running ahead of a large tear-drop shaped hump. We present a spectral-element method for this difficult multi-scale free surface problem. A boundary layer approximation of the equation of motion allows a Fourier expansion in the streamwise direction in conjunction with a domain decomposition in the direction normal to the wall that eliminates numerical instability. This mixed method hence enjoys both the exponential convergence rate of a spectral technique and the numerical advantage provided by a compactly supported basis which yields sparse projected differential operators. All stationary wave families, parameterized by the wavelength, are then constructed using a Newton continuation scheme. The constructed waves are favorably compared to experimentally measured wave shapes.     

Interpretation of stationary well investigations for gas-condensate fields

On the basis of previously obtained solutions for equations of two-phase filtration with phase transitions, we suggest and analyze methods for determining a number of hydromechanical quantities from experimental “depression-output” curves for operating wells of gas-condensate fields. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 3, pp. 375–379, May–June, 1997.     

Measurement of Helmholtz wave fields

A simple formalism is found for the measurement of wave fields that satisfy the Helmholtz equation in free space. This formalism turns out to be analogous to the well-known theory of measurements for quantum-mechanical wave functions: A measurement corresponds to the squared magnitude of the inner product (in a suitable Hilbert space) of the wave field and a field that is associated with the detector. The measurement can also be expressed as an overlap in phase space of a special form of the Wigner function that is tailored for Helmholtz wave fields.     

Theory of thermal waves

An analogy between thermal and electromagnetic waves is established. The conditions under which thermal oscillations can give rise to acoustical oscillations are derived. The coefficients of thermal conductivity in liquid helium are calculated as a function of the temperature below the lambda point.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 3, pp. 431–438, September, 1982.     

On the angular-spectrum representation of multipole wave fields

The closed-form expression of the angular spectrum of multipole fields, both scalar and vectorial, of any order and degree, evaluated across a plane orthogonal to an arbitrary (fixed) direction, is provided. Such a result has been obtained by starting from the Weyl representation of multipole fields and using suitable transformation rules. Moreover, as far as the vectorial case is concerned, knowledge of the (vectorial) transverse angular spectrum allows one to gain some insight into the polarization structure of the multipole fields evaluated across a typical plane. Such information could be useful, for instance, in those problems dealing with the interaction between planar partially reflecting surfaces and waves.     

Determination of stationary temperature fields in intersecting cylindrical shells

This article examines the problem of determining stationary temperature fields in intersecting cylindrical shells. The problem is solved by the finite differences method. It is established that the results obtained by the proposed method agree well with the three-dimensional solution except for a small neighborhood of the line of intersection of the shells. The dimensions of this neighborhood do not exceed the thickness of the shells.Translated from Problemy Prochnosti, No. 12, pp. 65–67, December, 1990.     

Propagation-invariant electromagnetic fields: Theory and experiment

Abstract

The vector concept of the propagation invariance is formulated to be applied to the stationary electromagnetic fields. The analysed exact solutions of the Maxwell equations are obtained on the basis of general propagation-invariant solutions of the scalar Helmholtz equation. A possible classification of the propagation-invariant fields based on quantities which appear in the complex Poynting theorem is proposed. The longitudinal periodicity of the electromagnetic field obtained due to the superposition of two Bessel beams is verified by a simple experiment.     

Application of the finite element technique to continuation problems of stationary fields

The paper deals with the application of the finite element technique to the extrapolation of stationary fields. The problem of continuation of the field potentials derived from the experimental data has been solved. The main idea is based on the application of one of the regularisation methods for solving an ill-conditioned, under- or overdetermined algebraic system of equations. Numerical calculations performed in the paper show the possible applications of the proposed method.     

On the existence of stationary solitary waves in a dissipative bubbly liquid

The formation of a solitary wave during the propagation of acoustic perturbations in a liquid containing heat-conducting gas bubbles is revealed for the first time by means of numerical modeling. A physical mechanism explaining the existence of a nondecaying solitary wave in this dissipative medium is proposed, which is based on the reverse influence of the bubble motion dynamics on the heat balance between gas and liquid. This phenomenon is called the moving boundary effect.     

Analogs of Brewster's angles for surface acoustic waves: the dependence on the strip shape

The analogs of Brewster's angles for surface acoustic waves (SAW) were found 30 years ago. Considering the reflection of classical Rayleigh waves in an isotropic half-space at oblique incidence by long topographic irregularities of small thickness, such as projections and grooves, it was found by a perturbation method that, independently from the shape of the irregularities, the reflection coefficient is equal to zero for some angle of incidence. The problem was never treated more accurately than by the first order perturbation method using the thickness/wavelength ratio as a small perturbation parameter. In this work, the impedance method is used for a correct investigation of the problem in the case of periodic projections. A strong dependence of the angle on the thickness/wavelength ratio is observed, if this parameter is more than 0.03. Moreover, a second such angle appears and both angles become closer and disappear for thick projections. The practically important cases of aluminum strips on piezoelectric STX-quartz and on 128 degrees YX-LiNbO3 crystals are also considered.     

Analysis of temperature fields of bodies in the shape of shells

The temperature fields in axisymmetric thick-walled shells with different middle surface shape are investigated.300th Anniversary of the Union of Ukraine and Russia Dnepropetrovsk State University.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 4, pp. 637–641, October, 1982.     

Polarization-rich continuous wave direct imaging: modeling and visualization

We report a study and comparison of continuous-wave, optical polarization difference imaging (PDI) and polarization modulation imaging (PMI) for imaging through scattering media. The problem is cast in the framework of a theoretical estimation, and the comparison is based on three visualization parameters, namely, the magnitude, the degree, and the orientation of the polarization. We show that PDI is superior in estimating the first two parameters in active imaging under specific conditions, while the PMI is suitable for passive imaging and is the only way to estimate polarization orientation. We also propose new schemes for rendering polarization information as a color image and for applying the newly introduced polarization-orientation imaging for segmentation. Simulation and experimental results verify the theoretical conclusions.     

Capturing a rebel: modeling the Harley-Davidson brand through a motorcycle shape grammar

The potential for capturing brand identity within a shape grammar is discussed. A two-dimensional motorcycle shape grammar is presented, along with constraints that associate the resulting designs with the Harley-Davidson brand. Confirmation of the grammar's brand representation is shown through a customer-based survey.     

Population modeling of the emergence and development of scientific fields

We analyze the temporal evolution of emerging fields within several scientific disciplines in terms of numbers of authors and publications. From bibliographic searches we construct databases of authors, papers, and their dates of publication. We show that the temporal development of each field, while different in detail, is well described by population contagion models, suitably adapted from epidemiology to reflect the dynamics of scientific interaction. Dynamical parameters are estimated and discussed to reflect fundamental characteristics of the field, such as time of apprenticeship and recruitment rate. We also show that fields are characterized by simple scaling laws relating numbers of new publications to new authors, with exponents that reflect increasing or decreasing returns in scientific productivity.