Temporal focusing by use of composite X waves

It is shown that highly focused pulses can be shaped by exciting a finite aperture with a spread-out pulse train of X waves. The basis of the proposed scheme is that the peaks of X waves, characterized by different apex angles, travel at different velocities. This property allows one to vary the temporal starting points of the initial excitations of a sequence of X waves so that all their peaks meet at a chosen focusing point. It is demonstrated that this simple criterion can be effective in producing a highly focused, composite X-wave pulse that exhibits a slower decay behavior than the individual X-wave components used in synthesizing it.     

Generation of sinc wave by a one-dimensional array for applicationsin ultrasonic imaging

A new solution to the 2-D scalar wave equation is presented which describes an ultrasonic beam maintaining the lateral field response expressed by the sinc function over a finite depth of field. This new beam is realizable with a linear array transducer, and less subject to diffraction spreading than conventional focused beams, physically, it is a superposition of plane waves having the same wavelength, but traveling at different angles. It is shown by numerical simulation that the beam can provide more uniform lateral beamwidth and smoother on-axis field magnitude over a greater depth of field than the rectangular transducers and Gaussian apodized transmitters which have been used to increase the limited depth of field of conventional focused beams. Compared with currently developed limited diffraction beams which must be generated by 2-D array transducers, the beam has a wider lateral beamwidth but with lower sidelobe levels. In ultrasonic medical imaging, the beam enables one to obtain a line focus using a 1-D array transducer and to eliminate the diffraction correction required in some applications such as tissue characterization     

An X wave transform

Limited diffraction beams such as X waves can propagate to an infinite distance without spreading if they are produced with an infinite aperture and energy. In practice, when the aperture and energy are finite, these beams have a large depth of field with only limited diffraction. Because of this property, limited diffraction beams could have applications in medical imaging, tissue characterization, blood flow velocity vector imaging, nondestructive evaluation of materials, communications, and other areas such as optics and electromagnetics. In this paper, a new transform, called X wave transform, is developed. In the transform, any well behaved solutions to the isotropic-homogeneous wave equation or limited diffraction beams can he expanded using X waves as basis functions. The coefficients of the expansions can be calculated with the properties that X waves are orthogonal. Examples are given to demonstrate the efficacy of the X wave transform. The X wave transform reveals an intrinsic relationship between any well behaved solutions to the wave equation and X waves, including limited diffraction beams. This provides a theoretical foundation to develop new limited diffraction beams or solutions to the wave equation that may have practical usefulness.     

Comment on the paper: Evanescent waves do contribute to the far field

Abstract

In a series of papers [1], it has been claimed that evanescent waves contribute to the far field of a radiating dipole, i.e. that the amplitude of the sum of the evanescent waves decreases as 1/r with increasing distance, r, from the dipole. In spite of the fact that three recent papers [2] have demonstrated that these claims are incorrect and that they contradict well-established results relating to the farzone behavior of the angular spectrum representation of wavefields [3], the author continues to repeat this claim, most recently in a note with the title ‘Evanescent waves do contribute to the field’. It is the purpose of this note to point out an error in the previous publications [1] which has led to this erroneous conclusion.     

Producing bowtie limited diffraction beams with synthetic arrayexperiment

Limited diffraction beams have a large depth of field and could have applications in medical ultrasound and other wave related areas such as electromagnetics and optics. However, these beams have higher sidelobes than conventional focused beams at their focuses. Recently, a new type of beam, called bowtie limited diffraction beams, was developed. These beams can achieve both low sidelobes and a large depth of field in medical imaging. In this paper, the production of bowtie beams in water with a synthetic array experiment is reported. A broad-band PZT ceramic/polymer composite transducer of about 1 mm diameter and 2.5 MHz central frequency was scanned in a raster format and placed at the centers of elements of an equivalent two-dimensional array of 50 mm diameter aperture. A polyvinylidene fluoride (PVDF) needle hydrophone of 0.5 mm diameter was used to receive the waves produced by the transducer. Proper weighting functions were applied to the received signals to produce various beams. Results show that the bowtie beams produced with the synthetic array experiment are in good agreement with those derived from theory and obtained by computer simulations. The depth of field of these beams is about 216 mm and sidelobes of a tenth derivative bowtie X wave in pulse-echo imaging are about 30 dB lower than those of rotary symmetric limited diffraction beams such as the zeroth-order X wave discovered previously     

The swirling round laminar jet

The swirling round laminar jet in an unbounded viscous fluid is investigated in this paper. The axisymmetric laminar jet with a swirling velocity is simulated by a linear-momentum source and an angular-momentum source, both located at the origin. The first-order and the second-order solutions in the far field have been obtained by solving the complete Navier—Stokes equations. It is found that the first-order solution is the well-known round-laminar-jet solution without the swirling velocity obtained by Landau [2] and Squire [3]. The second-order solution represents a pure rotating flow. The swirling velocity predicted by the present solution is compared with that obtained by Loitsyanskii [15] and Görtler [16], who solved the corresponding boundary-layer equations. It is found that the swirling velocity predicted by the present theory is smaller than that obtained from the boundary-layer equations.     

Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits

The diffraction of X-waves from a screen containing two slits is investigated. It is shown that when the peak of the incident X-wave hits the screen midway between the slits, two pulses are generated from each slit. These pulses follow laterally skewed trajectories relative to the direction of propagation of the incident X-wave along the central axis of the configuration. One of the two pulses converges on the central axis and the other diverges away from it. A geometrical construction explaining the behavior of these pulses is provided. It is shown that the trajectory of each radiated pulse can be deduced from the intersection of two curved wavefronts emanating from the two edges of each slit. The pulses converging on the central axis meet at a certain range, thus suggesting a novel focusing scheme.     

Determination of soil nitrate and water content using attenuated total reflectance spectroscopy

Direct determination of nitrate and soil moisture can significantly improve N-application management and thus reduce N-derived environmental pollution related to agriculture. Several studies have shown that Fourier transform infrared attenuated total reflectance (FT-IR/ATR) spectroscopy could be used to estimate the nitrate content of standardized soil pastes. Paste standardization appeared to be the main obstacle to in situ application of this approach, and the present study shows how FT-IR/ATR can be used to estimate both water content and nitrate concentration of field soil samples. Water content and nitrate concentration are determined sequentially using two subsamples of the initial soil sample. An a priori determined amount of highly concentrated nitrate solution is added to the first subsample and the ATR spectrum of this paste is used to estimate the sample water content. It is then possible to calculate the amount of water that should be added to the second subsample so that the resulting paste is very close to the ideal standard paste. Nitrate concentration, mg [N]/kg [dry soil], is estimated using the FT-IR/ATR spectrum of this second paste. Results are presented for a laboratory experiment with four agricultural soils, as well as for a field trial with a calcareous soil. For water content, the determination errors range from 0.01 to 0.02 g [water]/g [dry soil]. For nitrate concentration, the errors for three of the soils range from 5.9 to 8.4 mg [N]/kg [dry soil], while for the fourth, calcareous clay soil, the determination error is 13.6 mg [N]/kg [dry soil]. The determination errors obtained for the field trial are similar to the ones obtained for a similar soil under laboratory conditions, which shows the potential usefulness of the approach for improving N-application management and reducing environmental pollution.     

Designing limited diffraction beams

Theoretically, limited diffraction beams can only be produced with an infinite aperture. In practice, they can be closely approximated with a finite aperture over a large depth of field. Because of this property, these beams could have applications in medical imaging, tissue characterization, Doppler velocity estimation, and nondestructive evaluation (NDE) of materials, as well as other physics-related areas such as electromagnetics and optics. In this paper, a new method is developed to design limited diffraction beams of desired beam shapes within a finite aperture of interest. It uses previously discovered limited diffraction beams such as Bessel beams and X waves as basis functions, and constructs new beams with linear superpositions of the bases. To construct a new beam of a desired shape, coefficients of the basis functions in the linear superposition are chosen so that the difference between the new beam and a desired beam is minimized under the criterion of least-squares error within the aperture. This procedure is implemented by digitizing both the basis beams and desired beams in the aperture and solving a system of linear equations from its normal equation. The method is applied to several desired beams that are limited diffraction beams known previously. Results show that the designed beams and the desired beams are virtually identical. If the desired beams are not solutions to the wave equation, the designed beams are new limited diffraction beams that are similar in shapes to the desired beams. This suggests that the method may be a powerful and practical tool for developing new limited diffraction beams of desired properties.     

Doppler-shifted acoustic cyclotron resonance in aluminum

Doppler-shifted cyclotron resonances (DSCR) have been observed with longitudinal and transverse acoustic waves propagating along the [001], [111], and [110] axes of pure aluminum crystals. One to three distinct series of resonance peaks have been observed in each field direction. The harmonic numbers of most DSCR series follow the selection rules for propagation along high symmetry axes. Except in the case ofB parallel to [110], the peak fields of the harmonics are inversely proportional to the harmonic numbers. Most of the DSCR series are identifiable with known DSCR zones on the Fermi surface, the area derivatives of which are then deduced. The area derivative data obtained are either more accurate or are complementary to those measured by helicon DSCR and magnetomorphic size-effect experiments. Values for Fermi surface area derivatives are compared with those calculated from two current models for the aluminum Fermi surface. Both the caps in [001] and [111] directions are shown to be free-electron-like.Work supported by the National Science Foundation.     

Similarity solutions for two-dimensional weak shock waves

The general forms of self-similar solutions for two-dimensional weak shock waves in fluid dynamics are obtained. The functional form describing the area under the initial pulse is characterized under which the general system of PDEs admits similarity solutions. It is shown how one can construct new solutions with shock discontinuity from these self-similar solutions. In particular, a plane-wave solution is joined with a self-similar solution across a non-trivial shock. Furthermore, a new class of non-trivial simple wave solutions is presented.     

An accurate solution method for the static and dynamic deflections of orthotropic plates with general boundary conditions

Extending the previous work on isotropic beams and plates by the second author [Li WL, et al. An exact series solution for the transverse vibration of rectangular plates with general elastic boundary supports. J Sound Vib 2009;321:254–69], this paper describes an accurate analytical method for calculating the static deflections and modal characteristics of orthotropic plates with general elastic boundary supports. The displacement function is expressed as a 2-D Fourier cosine series supplemented with several terms in the form of 1-D series. The series expansions for all the relevant derivatives can be directly obtained through term-by-term differentiations of the displacement series. Thus, a classical solution can be derived by letting the series exactly satisfy the governing differential equation at every field point and all the boundary conditions at every boundary point, respectively. Several numerical examples are presented to demonstrate the excellent accuracy and convergence of the current solutions.     

On the elasto-plastic stress concentration at a circular hole in an anisotropic sheet

Summary The classical problem of determining the stress concentration factor at a circular hole embedded in an infinite sheet subjected to remote uniform tension is investigated. A finite strain elasto-plastic deformation theory based on Hill's new anisotropic flow theory [7] is used. It is shown that the governing field equations can be reduced to a single first order differential equation from which the stress concentration factor is obtained by a standard numerical method. The solution covers the entire elasto-plastic range and is valid for any strain hardening function. Comparison with experimental results, for a few materials, shows good agreement.With a pure power hardening law and within the framework of small strain plasticity, our results agree with those obtained from a more general solution discovered by Budiansky [8].With 3 Figures     

A bound for the range of a narrow light beam in the near field

We investigate the possibility of light beams that are both narrow and long range with respect to the wavelength. On the basis of spectral electromagnetic field representations, we have studied the decay of the evanescent waves, and we have obtained some bounds for the width and range of a light beam in the near-field region. The range determines the spatial bound of the near field in the direction of propagation. For a number of representative examples we found that narrow beams have a short range. Our analysis is based on the uncertainty relations between spatial position and spatial frequency.     

A new formulation of the magnetic vector potential method for three dimensional magnetostatic field problems

A novel formulation of the magnetic vector potential method for three dimensional magnetostatic field calculations is derived. Rigorously defining the interface and boundary conditions of the gauge of the vector potential, the new method gives a unique solution to the problem. The new field equation does not contain the gauge condition against the usual formulations[1], [2], [3], and takes the form of the diffusion equation. Computed results are favorably compared with the analytic solution of a test problem. This formulation is directly applicable to three dimensional eddy current problems.     

Formation of cylindrical shock waves in radiation-magneto gas dynamics

The propagation of acceleration waves in radiation-magneto gas dynamic flow which is induced by the motion of a piston advancing with finite acceleration into a constant state of rest has been studied along with the characteristic path by using the characteristics of the governing quasilinear system as the reference coordinate system. It is shown that a linear solution in the characteristic plane can exhibit nonlinear behaviour in the physical plane. A differential equation governing the growth and decay of an acceleration wave is derived. The critical time is obtained when all the characteristics will pile up at the wave front to form a shock wave. It is found that the effect of magnetic field on compressive waves which owe their origin to radiation is to cause an early shock formation, while on those of expansion waves which owe their origin to radiation the effect of magnetic field is to decrease the decay rate. However, the effect of coupling of radiation and magnetic field on waves (compressive) which are emanating from piston movement is to slow down the motion of a breakdown point and thus increase the cylindrical shock formation time, while on those of expansion waves, the effect is to enhance the decay rate.     

Gaussian beams in hollow metal waveguides

Various families of Gaussian beams have been explored previously to represent the propagation of nearly plane electromagnetic waves in media having at most quadratic transverse variations of the index of refraction and the gain or loss in the vicinity of the beam. However, such beams cannot directly represent the wave solutions for propagation in planar or rectangular waveguides, and sinusoidal mode functions are more commonly used for such waveguides. On the other hand, it is also useful to consider the possibility of recurring Gaussian beams that have an approximately Gaussian transverse profile at certain distinct planes along the propagation path. It is shown here that under some conditions recurring Gaussian beams can describe wave propagation in hollow metal waveguides, and they can also lead to efficient coupling between the waveguide fields and free-space beams.     

Davies’ surface condition and singularities of deep water waves

Davies’ surface condition is an approximate free-surface condition on gravity waves progressing in permanent form on water of infinite depth. It is known that this condition preserves essential features of finite-amplitude waves including the highest one. This paper proposes a new surface condition that generalizes Davies’ idea of approximation and covers a fully nonlinear condition. Analytic continuation of the proposed surface condition allows us to explore singularities of solutions that dominate the flow. The results of singularity analysis elucidate the connection between Davies’ approximate solution and the fully nonlinear solution. In addition, it is shown that the nonmonotonic variation of wave speed with wave steepness can be predicted using a linear sum of a relatively small number of singularities. This suggests that a suitable choice of a parameter in the proposed surface condition can move singularities away from the flow field without changing their structure and may reduce numerical difficulties due to singularities for large-amplitude waves.     

Design shear strength formula for high strength concrete beams

After a brief review on the concrete shear strength mechanisms, two very reliable expressions for predicting the shear strength of beams without transverse reinforcement are reported: the one proposed by Ba?ant and Kim [7], which is valid for Normal strength Concrete (NSC) beams, and the other recently proposed by the authors, which is valid for High Strength Concrete (HSC) beams. Hence a summary of a shear strength model for beams with stirrups is provided, which was derived [27] on the basis of the Ba?ant and Kim expression and therefore is adequate only for NSC beams.On the basis of the expression obtained for HSC without stirrups and of the model already proposed for NSC with stirrups, a shear strength expression for HSC beams with stirrups is derived. The obtained expression is applied to an experimental program of 116 HSC beams with stirrups, and is found to predict the test results better than ACI Code [1], Eurocode [12] and CEB/FIP Model Code [9].A design formula is hence proposed, which is adequately conservative and accurate.A design example of a HSC beam with stirrups is carried out, and the various design expressions previously considered are compared.     

The energy transport by the propagation of sound waves in wave guides with a moving medium

Summary The problem of the propagation of sound waves radiated by a source in a fluid moving with subsonic velocity between two parallel walls or inside a cylindrical tube is considered in [2], The most interesting thing of this problem is that waves may occur with constant amplitude coming from infinity. This article gives the calculation of the energy transport in the wave guides.It is shown that it is not possible to gain energy from infinity.