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991.
Kari Lumme Antti Penttilä 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(11):1658-4352
We analyze both the intensity and linear polarization of cosmic dust particles by using the physically exact superposition T-matrix method in a fixed orientation for various aggregates of spheres and DDA for the aggregates of Gaussian random spheres. We study both the spherical geometry (in cometary comae) and cylindrical slabs (for regoliths) up to 2000 monomers with size parameters less than ∼3. It is straightforward to produce the observed linear polarization in both geometries while the typically convex and strong opposition spike seems to require wide regolith geometries. The dependence of various parameters on light scattering has also been studied in a rather detailed form. In applications to the cometary polarization we can fit the data in six colors from UV to the J band at a very good accuracy. We, however, emphasize that we do not claim our model to be unique. The most important parameters here are the refractive index and the size distribution of submicron particles. Rest of the parameters has only a minor role. We also found that it is critically important to use several realizations from any assumed particle geometry model because corresponding scattering characteristics can vary quite a lot. 相似文献
992.
Maxim A. Yurkin Alfons G. Hoekstra 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(13):2234-2247
The open-source code ADDA is described, which implements the discrete dipole approximation (DDA), a method to simulate light scattering by finite 3D objects of arbitrary shape and composition. Besides standard sequential execution, ADDA can run on a multiprocessor distributed-memory system, parallelizing a single DDA calculation. Hence the size parameter of the scatterer is in principle limited only by total available memory and computational speed. ADDA is written in C99 and is highly portable. It provides full control over the scattering geometry (particle morphology and orientation, and incident beam) and allows one to calculate a wide variety of integral and angle-resolved scattering quantities (cross sections, the Mueller matrix, etc.). Moreover, ADDA incorporates a range of state-of-the-art DDA improvements, aimed at increasing the accuracy and computational speed of the method. We discuss both physical and computational aspects of the DDA simulations and provide a practical introduction into performing such simulations with the ADDA code. We also present several simulation results, in particular, for a sphere with size parameter 320 (100-wavelength diameter) and refractive index 1.05. 相似文献
993.
Existence of a positive solution to a system of discrete fractional boundary value problems 总被引:1,自引:0,他引:1
Christopher S. Goodrich 《Applied mathematics and computation》2011,217(9):4740-4753
We analyze a system of discrete fractional difference equations subject to nonlocal boundary conditions. We consider the system of equations given by -Δνiyi(t)=λiai(t+νi-1)fi(y1(t+ν1-1),y2(t+ν2-1)), for t∈[0,b]N0, subject to yi(νi − 2) = ψi(yi) and yi(νi + b) = ?i(yi), for i = 1, 2, where ψi,?i:Rb+3→R are given functionals. We also assume that νi ∈ (1, 2], for each i. Although we assume that both ai and fi(y1, y2) are nonnegative for each i, we do not necessarily presume that each ψi(yi) and ?i(yi) is nonnegative for each i and each yi ? 0. This generalizes some recent results both on discrete fractional boundary value problems and on discrete integer-order boundary value problems, and our techniques provide new results in each case. 相似文献
994.
Emilio Carlos Gomes Wille Eduardo YabcznskiHeitor Silvério Lopes 《Applied mathematics and computation》2011,217(12):5338-5346
This paper presents a design methodology for IP networks under end-to-end Quality-of-Service (QoS) constraints. Particularly, we consider a more realistic problem formulation in which the link capacities of a general-topology packet network are discrete variables. This Discrete Capacity Assignment (DCA) problem can be classified as a constrained combinatorial optimization problem. A refined TCP/IP traffic modeling technique is also considered in order to estimate performance metrics for networks loaded by realistic traffic patterns. We propose a discrete variable Particle Swarm Optimization (PSO) procedure to find solutions for the problem. A simple approach called Bottleneck Link Heuristic (BLH) is also proposed to obtain admissible solutions in a fast way. The PSO performance, compared to that one of an exhaustive search (ES) procedure, suggests that the PSO algorithm provides a quite efficient approach to obtain (near) optimal solutions with small computational effort. 相似文献
995.
This paper introduces a threshold policy with hysteresis (TPH) for the control of the logistic one-species model, the Lotka-Volterra and Rosenzweig-MacArthur two species density-dependent predator-prey models. A nonstandard scheme is used for the discretization of the models since it results in preservation of the qualitative characteristics of the continuous-time models. Two theorems that establish the global stability of the discrete logistic model subject to the threshold policy (TP) and the TPH are proved. The proposed policy (TPH) is more realistic than a pure threshold policy (TP) proposed earlier in the literature and changes the dynamics of the system in such a way that a low amplitude bounded oscillation, far from the extinction region, is achieved. Furthermore, it can be designed by a suitable choice of so called virtual equilibrium points in a simple and intuitive manner. 相似文献
996.
In this paper, we apply the Adomian decomposition method and Padé-approximate to solving the differential-difference equations (DDEs) for the first time. A simple but typical example is used to illustrate the validity and the great potential of the Adomian decomposition method (ADM) in solving DDEs. Comparisons are made between the results of the proposed method and exact solutions. The results show that ADM is an attractive method in solving the differential-difference equations. 相似文献
997.
Miguel Couceiro Jean-Luc Marichal 《Fuzzy Sets and Systems》2011,181(1):28-38
Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity conditions, these functions coincide with the Lovász extensions vanishing at the origin, which subsume the discrete Choquet integrals. We also propose a simultaneous generalization of horizontal min-additivity and horizontal max-additivity, called horizontal median-additivity, and we describe the corresponding function class. Additional conditions then reduce this class to that of symmetric Lovász extensions, which includes the discrete symmetric Choquet integrals. 相似文献
998.
We consider the problem of coloring a grid using p colors with the requirement that each row and each column has a specific total number of entries of each color.Ryser (1957) [20], and independently Gale (1957) [10], obtained a necessary and sufficient condition for the existence of such a coloring when two colors are considered. This characterization yields a linear-time algorithm for constructing the coloring when it exists. Later, Gardner et al. (2000) [11], and Chrobak and Dürr (2001) [5], showed that the problem is NP-hard when p?7 and p?4, respectively.The case p=3 was an open problem for several years and has been recently settled by Dürr et al. (2009) [9]: it is NP-hard too. This grid coloring problem is equivalent to finding disjoint realizations of two degree sequences d1,d2 in a complete bipartite graph KX,Y. These kinds of questions are well studied when one of the degree sequences has span zero or one, where the span of a function is the difference between its maximum and its minimum values. In [4], Chen and Shastri (1989) showed a necessary and sufficient condition for the existence of a coloring when d1+d2 restricted to X or Y has span at most one. In terms of discrete tomography this latter condition means that for two colors, the sum of the number of occurrences of these colors in each row is k or k+1, for some integer k.In the present paper we prove an analog to Chen and Shastri’s characterization when d1+d2 restricted to X and to Y has span at most two. That is, there exist integers k1 and k2 such that the sum of the number of occurrences of two of the colors in each row is k1−1,k1 or k1+1, and in each column is k2−1,k2 or k2+1. Our characterization relies on a new natural condition called the total saturation condition which, when not satisfied, gives a non-existence certificate of such a coloring that can be checked in polynomial time. 相似文献
999.
Adrien Richard 《Discrete Applied Mathematics》2011,159(11):1085-1093
Given a Boolean function F:{0,1}n→{0,1}n, and a point x in {0,1}n, we represent the discrete Jacobian matrix of F at point x by a signed directed graph GF(x). We then focus on the following open problem: Is the absence of a negative circuit in GF(x) for every x in {0,1}n a sufficient condition for F to have at least one fixed point? As result, we give a positive answer to this question under the additional condition that F is non-expansive with respect to the Hamming distance. 相似文献
1000.
J.-O. Lachaud 《Discrete Applied Mathematics》2011,159(18):2229-2250
The Minimum Length Polygon (MLP) is an interesting first order approximation of a digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity of the shape, its perimeter is a good estimate of the perimeter of the digitized shape. We present here two novel equivalent definitions of MLP, one arithmetic, one combinatorial, and both definitions lead to two different linear time algorithms to compute them. This paper extends the work presented in Provençal and Lachaud (2009) [26], by detailing the algorithms and providing full proofs. It includes also a comparative experimental evaluation of both algorithms showing that the combinatorial algorithm is about 5 times faster than the other. We also checked the multigrid convergence of the length estimator based on the MLP. 相似文献