On the mechanism of the formation of horizontal cracks in a vertical column of saturated sand

Extended horizontal cracks have! been observed experimentally in a vertical column of saturated sand when a flow of water is forced to percolate upward through it. This paper provides a theory for this phenomenon. It will be shown that the presence of inhomogeneity in permeability along the length of the column is essential for such cracks to develop. It will also be shown that small initial inhomogeneity may be magnified through the transport of the finer component of the sand by percolation. Under certain conditions liquefaction takes place at a section of the sand column causing a crack to initiate and grow there. This theory is found to be in good qualitative agreement with the experimental findings.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

Slightly slanting impact on an elastic cantilever column-an experimental study

Experiments concerning slightly slanting impact between a flat-ended rigid body and a flat-ended elastic cantilever column with a rectangular cross-section have been performed. The experimental results are compared with the theoretical ones. The small angle of incidence was measured by using an optical method. The impact process was studied by using a split disc for the rigid body, with the two halves bonded together and electrically insulated from each other. The disc and the column were parts of an electric circuit. Different contact states could be distinguished according to different voltage levels. Reasonably good agreement between theory and experiment was found. Thus, the impact duration has its minimum under perfectly axial impact as predicted by the theory. Also, the predicted process of alternating line and surface contact was observed. Furthermore, the existence of a small critical angle of incidence was verified. This critical angle of incidence divides the impact processes into two categories: (1) The rigid body and the column end come into surface contact before separation. (2) They separate without surface contact. Comparison of axial strains between theory and experiment shows good agreement.

Short-surface waves radiated by a partially-immersed 3-dimensional oscillating body

The short-surface waves generated by a 3-D arbitrarily oscillating body floating onwater are discussed. In the far-field off the body, the phase and the amplitude functions ofthe radiated waves are determined by the ray method. An undetermined constant is includ-ed in the amplitude function. From the result of Ref. [1], the near-field boundary layersolution near the body waterline is obtained. The amplitude of this solution depends on thewhole wall shape of the body and the slope at the body waterline on the cross-sections per-pendicular to the waterline. By matching the far-field solution with the near-field bound-ary layer solution, the undetermined constant in the amplitude function of the far-fieldradiated waves is determined. For the special case of a half-submerged sphere which per-forms vertical oscillating motion, the result obtained in this paper is in agreement withthat of Ref. [ 2 ].

Steady axi-symmetrical thermocapillary motion of a short melting column

This paper deals with the steady axi-symmetric thermo-capillary motion in a short meltingcolumn.with the assumptions that the Marangoni number M<<1, the Reynolds number Re<<1 andthe capillary number C<<1, at the leading order, the solutions of the problem are obtained inthe form of series. For two kinds of typical cases, symmetric and anti-symmetric distributionof air temperature, the numerical calculations are made. The results describe the effect ofendwalls on thermo-capillary flow.

Non-linear theory of a positive-column in a magnetic-field

A nonlinear theory of an intermediate pressure discharge column in a magnetic field is presented. Motion of the neutral gas is considered. The continuity and momentum transfer equations for charged particles and neutral particles are solved by numerical methods. The main result obtained is that the rotating velocities of ionic gas and neutral gas are approximately equal. Bohm's criterion and potential inversion in the presence of neutral gas motion are also discussed.

Vertical Bearing Capacity of a Partially-Embedded Pipeline on Tresca Soils

Slip-line field solutions are presented for the ultimate load of submarine pipelines on a purely cohesive soil obeying Tresca yield criterion, taking into account of pipe embedment and pipe-soil contact friction. The derived bearing capacity factors for a smooth pipeline degenerate into those for the traditional strip-line footing when the embedment approaches zero. Parametric studies demonstrate that the bearing capacity factors for pipeline foundations are significantly influenced by the pipeline embedment and the pipe-soil frictional coefficient. With the increase of pipeline embedment, the bearing capacity factor Nc decreases gradually, and finally reaches the minimum value (4.0) when the embedment equals to pipeline radius. As such, if the pipeline is directly treated as a traditional strip footing, the bearing capacity factor Nc would be over evaluated. The ultimate bearing loads increase with increasing pipeline embedment and pipe-soil frictional coefficient.

Phase imaging with partially coherent x rays

X-ray phase imaging with illumination by a partially coherent source with a setup similar to in-line holography is considered. Using the optical transform function, we consider the effects of partial coherence on this x-ray phase imaging for a weak phase object. The optimal contrast and the resolution of phase imaging are analyzed. As the coherence decreases, the imaging contrast and the optimal contrast frequency decrease, and the resolution degrades. It is shown that this contrast-enhanced phase-imaging method can be regarded as a linear bandpass filter and that the bandwidth and the image contrast are changeable. The frequency property of the imaging system can be improved if an incoherent x-ray source with the proper shape is used. (C) 1999 Optical Society of America.

Instability of solution of phase retrieval in direct diffraction phase-contrast imaging with partially coherent X-ray source

The theoretical model of direct diffraction phase-contrast imaging with partially coherent x-ray source is expressed by an operator of multiple integral. It is presented that the integral operator is linear. The problem of its phase retrieval is described by solving an operator equation of multiple integral. It is demonstrated that the solution of the phase retrieval is unstable. The numerical simulation is performed and the result validates that the solution of the phase retrieval is unstable.

Generation of a high-quality partially coherent dark hollow beam with a multimode fiber

We report the experimental generation of a high-quality partially coherent dark hollow beam (DHB) by coupling a partially coherent beam into a multimode fiber (MMF) with a suitable incidence angle. The interference experiment of the generated partially coherent DHB passing through double slits is demonstrated. It is found that the coupling efficiency of the MMF, the quality, and the coherence of the generated partially coherent DHB are closely controlled by the coherence of the input beam. (c) 2008 Optical Society of America.

Influence of temperature and salinity fluctuations on propagation behaviour of partially coherent beams in oceanic turbulence

A theoretical study of the behaviour of partially coherent beams propagating through oceanic turbulence has been performed. Based on the previously developed knowledge of beam spreading of a partially coherent beam in the atmosphere and the spatial power spectrum of the refractive index of ocean water, we study the normalized root-mean-square width of a partially coherent beam on propagation through oceanic turbulence and its turbulence distance which may be a measure of turbulence resistance. Our analysis indicates that the behaviour of partially coherent beams on propagation may be described by the rate of dissipation of the mean-squared temperature chi(T) and that of salinity chi(S). In terms of a quantity w that defines the contributions of the temperature and salinity distributions to the distribution of the refractive index, chi(S) could be written as a function of chi(T) and w. Therefore, the behaviour of partially coherent beams on propagation can be characterized only by chi(T) for a given w. The results are shown for curved surfaces, from which one can see that partially coherent beams exhibit robust turbulence resistance when the water volume has a smaller chi(T).

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves. (c) 2006 Elsevier B.V. All rights reserved.