In a colored-quark and vector-gluon model of hadrons we show that a quark carrying nearly all the momentum of a nucleon (x f':j 1) must have the same helicity as the nucleon;consequently vWt/vW/-.f as x-1, not .j. as might naively have been expected. Furthermore as x-1, vW 2~~"~ (1-x) 2 and (aL/aT) .. ~J.1~-2 (1-x)-2 +0(g 2 ); the resulting angular dependence for e+e--h±+x is consistent with present data and has a disti,nctive form which can be easily tested when better data are available.There have been two significant paradoxes associated with the interpretation of electron-hadron scattering at large q 2 in terms of quarks:where x=-q 2 /(2q·p), appears to reflect the underlying three-quark structure of the proton at short distances, 1 that same three-quark struc-. ture with the simple dynamics that controls short-distance processes would naively appear to lead to the prediction vW 2 n/vW/-j as x-1, contrary to observation. 2 Furthermore, while for Q 2 ~ 15 GeV 2 the colored-quark model gives the correct value of the famous ratio R =a(e+e--hadrons )/ a(e + e--fJ. + fJ.-), that same model has been thought to predict a (1 +cos 2 8) angular distribution for hadrons having large x=2IPI /Q. Instead, in that same Q 2 range the distribution is roughly isotropic. 3 We show here that the above paradoxes are products of the naive arguments:In fact, when the actual dynamics of the quarkgluon interaction are considered, the predictions are in good agreement with observations. The problem of calculating properties of structure functions is tractable, we believe, for large Q 2 and x"' 1 because in that kinematic configuration the quark which couples to the electromagnetic current necessarily has a very large invariant mass, even in the scaling limit. 4 A wave function in which one quark has. very large invariant mass can be generated from the "normal" wave fun~tion (in which the invariant mass of each quark is limited) by an interaction of the sort shown in Fig. 1, where the incoming quark lines are understood to be convoluted with the normal wave function. Since each propagator marked with a cross has a large invariant mass [p 2 -m 2 /(1-x), where m 2 is some characteristic mass or P 1. scale for the quarks], it is reasonable to imagine that the effective quark-gluon couplings displayed in Fig. 1 are small. 5 Thus we can use lowest-order perturbation theory to 1416 go from the normal to "exceptional" (one quark having large P 2 ) wave functions. We assume that (a) the normal wave function is sufficiently damped at large P 2 ' s that the convolution is dominated by the region in which the p 2 ' s of the incoming quarks are finite, and (b) the spin and SU(3) structure of the normal wave function are what one would have in a nonrelativistic quark model. With these two assumptions, 6 the x-1 properties of hadron structure functions are given to O(m 2 / q 2 ) by lowest-order perturbation theory in which the incoming quarks can be treated as free (Fig. 1), 7 the convolution with the wave function having no effect other than fi...
An experiment conducted in the Mediterranean Sea in April 1996 demonstrated that a time-reversal mirror ͑or phase conjugate array͒ can be implemented to spatially and temporally refocus an incident acoustic field back to its origin. The experiment utilized a vertical source-receiver array ͑SRA͒ spanning 77 m of a 125-m water column with 20 sources and receivers and a single source/receiver transponder ͑SRT͒ colocated in range with another vertical receive array ͑VRA͒ of 46 elements spanning 90 m of a 145-m water column located 6.3 km from the SRA. Phase conjugation was implemented by transmitting a 50-ms pulse from the SRT to the SRA, digitizing the received signal and retransmitting the time reversed signals from all the sources of the SRA. The retransmitted signal then was received at the VRA. An assortment of runs was made to examine the structure of the focal point region and the temporal stability of the process. The phase conjugation process was extremely robust and stable, and the experimental results were consistent with theory. INTRODUCTIONPhase conjugation is a process that has been first demonstrated in nonlinear optics 1 and more recently in ultrasonic laboratory acoustic experiments. 2,3 Aspects of phase conjugation as applied to underwater acoustics also have been explored recently. 4-7 The Fourier conjugate of phase conjugation is time reversal; implementation of such a process over a finite spatial aperture results in a ''time-reversal mirror. 2,3 '' In this paper we describe an ocean acoustics experiment in which a time-reversal mirror was demonstrated.In nonlinear optics, phase conjugation is realized using high intensity radiation propagating in a nonlinear medium. Essentially, the incident radiation imparts its own time dependence on the dielectric properties of the medium. The incident radiation is then scattered from this time-varying dielectric medium. The resulting scattered field is a time reversed replica of this incident field propagating in the opposite direction of the incident field. For example, the scattered field that results from an outgoing spherical wave is a spherical wave converging to the original source point; when it passes through the origin it has the time reversed signature of the signal which was transmitted from that point at the originating time. Clearly, this phenomenon can be thought of as a self-adaptive process, i.e., the process constructs a wavefront of the exact required curvature. ͑An alternative would be to use a concave spherical mirror with the precise radius of curvature of the incident wavefront.͒ There is an assortment of nonlinear optical processes which can result in phase conjugation. 1 In acoustics, however, we need not use the propagation medium nonlinearities to produce a phase conjugate field.Because the frequencies of interest in acoustics are orders of magnitude lower than in optics, phase conjugation can be accomplished using signal processing. As in the optical case, phase conjugation takes advantage of reciprocity which is a property of wave...
The composite roughness model is applied to bottom backscattering in the frequency range 10–100 kHz. For angles near normal incidence, the composite roughness model is replaced by the Kirchhoff approximation which gives better results. In addition, sediment volume scattering is treated, with account taken of refraction and reflection at the randomly sloping interface. In applying the model to published data it is found that sediment volume scattering is dominant in soft sediments except at small and large grazing angles. For coarse sand bottoms, roughness scattering dominates over a wide range of grazing angles. Implications for acoustic remote sensing are discussed.
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