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1.
The field measurements and numerical results for intermittent flow regime in a sandy soil show that the time distributions of the soil water flux q(z, t), and the soil water content θ(z, t)at various depths are periodic in nature, where t is time and z is the depth (i.e., at the surface z = 0 and at depths z = − 5, − 10, − 15 cm, etc). The period of q(z, t) and θ(z, t) variations are generally determined by the sum of the duration of pulse and the duration between the initiation of two consecutive pulses of water at the soil surface. Fourier series models have been given for q(z, t) and θ(z, t) variations. The predicted Fourier results for these variations have been compared with the experimentally verified numerical results—designated as observed values. The results show that the amplitudes of these variations were damped exponentially with depth, and the phase shift increased linearly with depth.  相似文献   

2.
Summary  This paper deals with the theoretical treatment of a three-dimensional elastic problem governed by a cylindrical coordinate system (r,θ,z) for a medium with nonhomogeneous material property. This property is defined by the relation G(z)=G 0(1+z/a) m where G 0,a and m are constants, i.e., shear modulus of elasticity G varies arbitrarily with the axial coordinate z by the power product form. We propose a fundamental equation system for such nonhomogeneous medium by using three kinds of displacement functions and, as an illustrative example, we apply them to an nonhomogeneous thick plate (layer) subjected to an arbitrarily distributed load (not necessarily axisymmetric) on its surfaces. Numerical calculations are carried out for several cases, taking into account the variation of the nonhomogeneous parameter m. The numerical results for displacement and stress components are shown graphically. Received 10 May 1999; accepted for publication 15 August 1999  相似文献   

3.
In this paper, we consider a two-dimensional homogeneous isotropic elastic material state in the arch-like region arb, 0 ≤ θα, where (r, θ) denote plane polar coordinates. We assume that three of the edges r = a, r = b, θ = α are traction-free, while the edge θ = 0 is subjected to an (in plane) self-equilibrated load. We define an appropriate measure for the Airy stress function φ and then we establish a clear relationship with the Saint-Venant's principle on such regions. We introduce a cross-sectional integral function I(θ) which is shown to be a convex function and satisfies a second-order differential inequality. Consequently, we establish a version of the Saint-Venant principle for such a curvilinear strip, without requiring of any condition upon the dimensions of the arch-like region.  相似文献   

4.
We prove a blow-up criterion in terms of the upper bound of (ρ, ρ −1, θ) for a strong solution to three dimensional compressible viscous heat-conductive flows. The main ingredient of the proof is an a priori estimate for a quantity independently introduced in Haspot (Regularity of weak solutions of the compressible isentropic Navier–Stokes equation, arXiv:1001.1581, 2010) and Sun et al. (J Math Pure Appl 95:36–47, 2011), whose divergence can be viewed as the effective viscous flux.  相似文献   

5.
In a celebrated theorem H?lder proved that the Euler Γ-function is differential transcendental, i.e. Γ(z) is not a solution of any (non-trivial) algebraic ordinary differential equation with coefficients that are complex numbers; and we extend his methods to the Riemann ζ-function. Moreover, we conjecture that Γ and ζ are differential independent, i.e. Γ(z) is not a solution of any such algebraic differential equation—even allowing coefficients that are differential polynomials in ζ(z). However, we are able to demonstrate only the partial result that Γ(z) and ζ(sin 2πz) are differential independent.  相似文献   

6.
The flow-induced microstructure of a mesophase pitch was studied within custom-made dies for changing wall shear rates from 20 to 1,100 s − 1, a flow scenario that is typically encountered during fiber spinning. The apparent viscosity values, measured at the nominal wall shear rates ranging from 500 to 2,500 s − 1 using these dies, remain fairly constant. The microstructure was studied in two orthogonal sections: rθ (cross section) and rz (longitudinal mid plane). In these dies, the size of the microstructure gradually decreases toward the wall (to as low as a few micrometers), where shear rate is highest. Furthermore, as observed in the rθ plane of the capillary, for a significant fraction of the cross section, discotic mesophase has a radial orientation. Thus, the directors of disc-like molecules were aligned in the vorticity (θ) direction. As confirmed from the microstructure in the rz plane, most of the discotic molecules remain nominally in the flow plane. Orientation of the pitch molecules in the shear flow conditions is consistent with that observed in controlled low-shear rheometric experiments reported earlier. Microstructral investigation suggests that the radial orientation of carbon fibers obtained from a mesophase pitch originates during flow of pitch through the die.  相似文献   

7.
Summary  This paper deals with interaction problems of elliptical and ellipsoidal inclusions under bending, using singular integral equations of the body force method. The problems are formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the x,y and r,θ,z directions in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy the boundary conditions along the elliptical and the ellipsoidal boundaries, the unknown functions are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield the exact solutions for a single elliptical or spherical inclusion under a bending stress field. It yields rapidly converging numerical results for interface stresses in the interaction of inclusions. Received 9 September 1999; accepted for publication 15 January 2000  相似文献   

8.
Using the stability results of Bressan & Colombo [BC] for strictly hyperbolic 2 × 2 systems in one space dimension, we prove that the solutions of isentropic and non-isentropic Euler equations in one space dimension with the respective initial data (ρ0, u 0) and (ρ0, u 0, &\theta;00 γ− 1) remain close as soon as the total variation of (ρ0, u 0) is sufficiently small. Accepted April 25, 2000?Published online November 24, 2000  相似文献   

9.
In this paper, we study a free boundary problem for compressible Navier-Stokes equations with density-dependent viscosity. Precisely, the viscosity coefficient μ is proportional to ρ θ with , where ρ is the density, and γ > 1 is the physical constant of polytropic gas. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the weak solution, give the uniform bounds (with respect to time) of the solution and show that it converges to a stationary one as time tends to infinity. Moreover, we estimate the stabilization rate in L norm, (weighted) L 2 norm and weighted H 1 norm of the solution as time tends to infinity.  相似文献   

10.
A new method is developed to solve Biot's consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot's consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface (z = 0) and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.  相似文献   

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