Remotely cc-almost periodic type functions in Rn{\mathbb R}^{n}

In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$-almost periodic functions in ${\mathbb R}^{n},$ slowly oscillating functions in ${\mathbb R}^{n},$ and further analyze the recently introduced class of quasi-asymptotically $c$-almost periodic functions in ${\mathbb R}^{n}.$ We provide certain applications of our theoretical results to the abstract Volterra integro-differential equations and the ordinary differential equations

MATLAB

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Development of Stresses in Cohesionless Poured Sand

The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9

Joint microwave and infrared studies for soil moisture determination

The feasibility of using a combined microwave-thermal infrared system to determine soil moisture content is addressed. Of particular concern are bare soils. The theoretical basis for microwave emission from soils and the transport of heat and moisture in soils is presented. Also, a description is given of the results of two field experiments held during vernal months in the San Joaquin Valley of California

Anti-plane Shear of Cylinders and Layered Systems: Cohesive Fracture and Instability

This research examines the mechanics of mode-III cohesive fracture by defect initiation and quasi-static growth in both cylinder and layered systems. The analysis, which is exact, is based on the solution of two fundamental elasticity problems: i) a cylinder subject to an arbitrary shear on one end cap and an equilibrating torque on the other and, ii) a layer subject to arbitrary anti-plane shear traction on one surface and an equilibrating uniform traction on the other. For a particular geometry and defect configuration, these solutions are shown to lead to a pair of interfacial integral equations whose derived cohesive surface fields capture the entire defect evolution process from incipient growth through complete failure. The anti-plane shear separation/slip process is assumed to be modeled by Needleman-type traction-separation relations (e.g., bilinear, Xu-Needleman, frictional) characterized by a shear cohesive strength, a characteristic force length and, in the case of the bilinear law, a finite decohesion cutoff length and possibly other parameters as well. Symmetrically arrayed cohesive surface defects are modeled by a cohesive surface strength function which varies with surface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body movement, are found by eigenfunction approximation of the solution of the governing interfacial integral equations. General features of the solutions to anti-plane shear cohesive fracture in both cylindrical and layered geometries indicate that quasi-static defect initiation and propagation occur under monotonically increasing load. For small values of characteristic force length, brittle behavior occurs that is readily identifiable with the growth of a sharp crack, i.e., the existence of a strong local stress concentration. At larger values of characteristic force length, ductile response occurs which is more typical of a linear “spring” cohesive surface, i.e., more distributed stress and slip distribution. Both behaviors ultimately give rise to abrupt failure of the cohesive surface. Results for the stiff, strong cohesive surface under a small applied load show consistency with static linear elastic fracture mechanics solutions in the literature. By superimposing a frictional part onto the cohesive law, the solution can be used to predict frictional response. Both decohesion and friction dominated cases show similar quasi-static defect propagation process, stable defect growth till a maximum load is reached, then defect growth becomes dynamic and unstable. However, the difference lies in that the friction dominated cohesive surface can still sustain certain load even after response becomes dynamic, but the decohesion dominated case will not. For friction dominated cohesive surfaces, the cylinder cases have smooth deformation processes whereas the layered systems experience a noticeable displacement jump. Both cylinder and layered systems predict the principal plane (perpendicular to principal stress direction) to be close to 45 degrees which helps to explain the orientation of mode-I microcracks in layered systems and the initiation of a spiral crack plane in cylinder geometries. The cohesive fracture solution to layered geometries can be extended to obtaining traction fields for more complicated defect geometries (array of cracks and subsurface cracks in nonuniform bilayer) which can be used to predict the sequence of defect propagation. The bifurcation analysis of the uniform two-sublayer system shows the phenomenon of non-unique slip for the same loading. The bifurcation analysis for the multi-sublayer system with such non-uniqueness gives an explanation of the asymmetric configuration. For the analysis of nonuniform multi-sublayer systems, no additional difficulty occurs in the problem-solving process. By studying different geometries and crack patterns, the current study discussed the combined effects of interlaminar and intralaminar crack interaction which are important in predicting the most vulnerable place in the system while multiple defects exist