The electromagnetic (EM) scattering of a layered sphere is a canonical problem. Mie theory is suitable for plane wave incidence cases, whereas spherically layered media theory (SLMT) can deal with arbitrary incident w...
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The electromagnetic (EM) scattering of a layered sphere is a canonical problem. Mie theory is suitable for plane wave incidence cases, whereas spherically layered media theory (SLMT) can deal with arbitrary incident waves. Both Mie theory and SLMT suffer from numerical instabilities due to the involved spherical Bessel functions when the order is large, the argument is small, or the medium is lossy. The logarithmic derivative method had been proposed to solve this numerical issue with Mie theory successfully, while the numerical issue with SLMT has not been solved fully so far. Computations of reflection and transmission coefficients are the key part of SLMT. In this article, we first define the renormalized reflection and transmission coefficients, which enjoy the feature of having an ordinary level of magnitude. Then, borrowing the idea of the logarithmic derivative method, the expressions for the renormalized canonical reflection and transmission coefficients as well as other terms in the theory are rearranged. Recursive formulas for the product or division of Bessel functions with some common combinations of order and argument are derived. numerical tests show that the proposed approach, validated by the full wave numerical method, is more stable than the conventional formulation.
Through a theoretical analysis for coefficients in the general expressions of stresses and displacements for a two-layer layered elastic half-space system (LEHS), the paper develops a modified method for these coeffic...
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Through a theoretical analysis for coefficients in the general expressions of stresses and displacements for a two-layer layered elastic half-space system (LEHS), the paper develops a modified method for these coefficients and new modified general expressions of stresses and displacements for LEHSs. The modified method is then applied to Love's displacement function. The derived results show that the modified expressions of stresses and displacements for LEHSs no longer contain any positive exponential function. Theoretical derivation and numerical calculation suggest that the modified coefficients tend to zeroth, linear, or quadratic polynomial functions and that the positive exponential functions in the original general expressions of stresses and displacements for LEHSs, which result in numerical overflow, are just a balance to the quick vanishing of some coefficients. The modified method can reasonably avoid the overflow problem in the numerical integration for LEHSs. The numerical verification shows that the modified method is effective and reliable.
Gamma-gamma distribution model was widely used in numerical simulations of the free-space optical communication system. The simulations are often interrupted by numerical overflow exception due to excessive parameters...
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ISBN:
(纸本)9780819493064
Gamma-gamma distribution model was widely used in numerical simulations of the free-space optical communication system. The simulations are often interrupted by numerical overflow exception due to excessive parameters. Based on former researches, two modified models are presented using mathematical calculation software and computer program. By means of substitution and recurrence, factors of the original model are transformed into corresponding logarithmic formats, and potential overflow in calculation is eliminated. By numerical verification, the practicability and accuracy of the modified models are proved and the advantages and disadvantages are listed. The proper model should be selected according to practical conditions. The two models are also applicable to other numerical simulations based on gamma-gamma distribution such as outrage probability and mean fade time of the free-space optical communication.
We describe an optimized algorithm, which is faster and more accurate compared to previously described algorithms, for computing the statistical mechanics of denaturation of nucleic acid sequences according to the cla...
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We describe an optimized algorithm, which is faster and more accurate compared to previously described algorithms, for computing the statistical mechanics of denaturation of nucleic acid sequences according to the classical Poland-Scheraga type of model. Nearest neighbor thermodynamics has been included in a complete and general way, by rigorously treating nearest neighbor interactions, helix end interactions, and isolated base-pairs. This avoids the simplifications of previous approaches and achieves full generality and controllability with respect to thermodynamic modeling. The algorithm computes subchain partition functions by recursion, from which various quantitative aspects of the melting process are easily derived, for example the base-pairing probability profiles. The algorithm represents an optimization with respect to algorithmic complexity of the partition function algorithm of Yeramian et al. (Biopolymers 1990, 30, 481-497): we reduce the computation time for a base-pairing probability profile from O(N-2) to O(N), where N is the sequence length. This speed-up comes in addition to the speed-up due to a multiexponential approximation of the loop entropy factor as introduced by Fixman and Freire(22) and applied by Yeramian et al.(25) The speed-up, however, is independent of the multiexponential approximation and reduces time from O(N-3) to O(N-2) in the exact case. A method for representing very large numbers is described, which avoids numerical overflow in the partition Junctions for genomic length sequences. In addition to calculating the standard base-pairing probability profiles, we propose to use the algorithm to calculate various other probabilities (loops, helices, tails) for a more direct view of the melting regions and their positions and sizes. This can provide a better understanding of the physics of denaturation and the biology of genomes. (C) 2003 Wiley Periodicals, Inc.
NewSpeak is a language designed for use in safety-critical programs. It tries to limit the freedom of the programmer to the kind of ideas in programming that are reasonably easy to formalise, without making these rest...
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NewSpeak is a language designed for use in safety-critical programs. It tries to limit the freedom of the programmer to the kind of ideas in programming that are reasonably easy to formalise, without making these restrictions unduly onerous. Its principal characteristic is that it has no exceptional values or states. Incorrect constructions which would lead to exceptional behaviour, such as range violations or numerical overflow, are all dealt with at compile time.
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