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In this paper we propose a numerical procedure for the prediction of capillary forces in polydisperse granular assemblies at a degree of moisture content that corresponds to the so-called pendular regime. The capillary force model is adopted within the Laplace-Young framework with a toroidal approximation of the liquid bridge geometry. Governing equations are first derived in a form that highlights the role of intrinsic parameters such as inter-particle separation distance, ratio of particle radii and liquid volume. A proper scaling of these equations is adopted so that the solution applies to any particle pair configuration. Numerical integration algorithms are provided in a way that facilitates implementations in macroscopic procedures for computer simulations. A qualitative evaluation is undertaken to highlight model predictions of the effects on capillary force of various intrinsic parameters that characterise the particle pair and liquid bridge. The model is validated against the experimental results provided by Willet et al. (Langmuir 16:9396-9405, ) for a wide range of liquid volumes and particle-pair polydispersity. [ABSTRACT FROM AUTHOR]

In this paper, we derive an algorithm to solve the linear quadratic (LQ) optimal regulator problems. The new approach is based on efficient Legendre and Chebyshev formulae at the Chebyshev-Gauss-Lobatto points. The technique enjoys advantages of both the Legendre and Chebyshev approximations near the end points. To show the numerical behavior of the proposed method, the simulation results of an example are presented. [ABSTRACT FROM AUTHOR]

We study the waiting-time distributions in cyclic polling models with renewal arrivals, general service and switch-over times, and exhaustive service at each of the queues. The assumption of renewal arrivals prohibits an exact analysis and reduces the available analytic results to heavy-traffic asymptotics, limiting results for large switch-over times and large numbers of queues, and some numerical algorithms. Motivated by this, the goal of this paper is to propose a new method for deriving simple closed-form approximations for the complete waiting-time distributions that work well for arbitrary load values. Extensive simulation results show that the approximations are highly accurate over a wide range of parameter settings. [ABSTRACT FROM AUTHOR]

Abstract: Computer modeling of radiation deep penetration problems is historically based on the discrete ordinates (S N) formulation. For efficiency reasons, besides accuracy, coarse-mesh spatial discretization is desirable. The spectral Green''s function (SGF) methods form a class of accurate coarse-mesh numerical methods as they use polynomial approximations only for the node-edge transverse leakage terms; the scattering source terms are treated analytically in the numerical algorithm. Therefore, algebraic work and the computational algorithms of the spectral nodal methods are rather complicated. To alleviate this negative feature, we offer in this paper a composite spatial grid SGF nodal method for the numerical solution of one-speed deep penetration S N problems with isotropic scattering in X,Y geometry. This method uses a rectangular coarse spatial grid, that is coincident with the material region distribution within the shielding structure. We first transverse integrate the S N equations separately in the x- and y-coordinate directions inside each material region, and then we introduce flat approximations for the transverse leakage terms. Furthermore, we use a fine spatial grid to discretize each set of “one-dimensional”S N nodal equations. As the spatial directions are coupled by the transverse leakage terms, we use an explicit alternate direction technique to converge the numerical solution. In order to verify the offered method''s accuracy, we present numerical results for typical model problems. Moreover, we compare the computing performance of this method with the conventional SGF-constant nodal method. [Copyright &y& Elsevier]

In this paper, we present a new approach of-spline curve fitting to a set of ordered points, which is motivated by an insight that properly selected points called dominant points can play an important role in producing better curve approximation. The proposed approach takes four main steps: parameterization, dominant point selection, knot placement, and least-squares minimization. The approach is substantially different from the conventional approaches in knot placement and dominant point selection. In the knot placement, the knots are determined by averaging the parameter values of the dominant points, which basically transforms-spline curve fitting into the problem of dominant point selection. We describe the properties of the knot placement including the property of local modification useful for adaptive curve refinement. We also present an algorithm for dominant point selection based on the adaptive refinement paradigm. The approach adaptively refines a-spline curve by selecting fewer dominant points at flat regions but more at complex regions. For the same number of control points, the proposed approach can generate a-spline curve with less deviation than the conventional approaches. When adopted in error-bounded curve approximation, it can generate a-spline curve with far fewer control points while satisfying the desired shape fidelity. Some experimental results demonstrate its usefulness and quality. [Copyright &y& Elsevier]