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Trapping model for the low-index ring-shaped micro-object in a focused, lowest-order Gaussian laser-beam profile

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 1997年第4期14卷 782-789页

作者： Gauthier, RC Department of Physics and Astronomy Laurentian University Sudbury Ontario Canada P3E-2C6

The trapping properties of a micron-sized, ring-shaped object are examined with an optical model consisting of ray, wave, electromagnetic, and quantum theoretical components. numerically calculated values for the trapping force vector and the predicted behavior of the ring are in reasonable agreement with reported experimental observations for this object. (C) 1997 Optical Society of America.

关键词： RADIATION PRESSURE OPTICAL TRAP numerical computations PARTICLES FORCE GENERATION numerical calculation ANNULAR BEAM PROFILES optical model RADIATION PRESSURE Force trap model trapping Generations

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Conservation of energy for non-dissipative water waves

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OCEAN ENGINEERING 2015年第Oct.1期107卷 147-156页

作者： Sadeghian, H. Badiei, P. Univ Tehran Sch Civil Engn Coll Engn Tehran Iran

In this paper Reynolds transport theory is applied to obtain energy conservation equation (ECE). Depth integrated ECE is derived considering a control volume extended over water depth. It is demonstrated that mild slope equation (MSE) is derivable from depth integrated ECE for linear waves. Two equations are derived by separating real and imaginary parts of depth integrated ECE for multidirectional wave fields that can properly deal with reflecting waves. Geometrical optics equations, derived for non-reflecting waves, can be obtained from aforementioned equations as well. Depth integrated ECE is averaged over a wave period for monochromatic waves. The result is similar in form to energy transport equation (ETE) governing spectral wave models. The terms of energy density and energy flux, obtained here, are more accurate expressions, comparing to those of ETE. It should be mentioned that ETE is also obtained from ECE, the general form derived here. The strength of newly derived equations in dealing with reflective wave fields has been illustrated by simple numerical computations. In this research MSE has been derived by the new presented method. Besides, coupled equations for multidirectional waves as well as time averaged depth integrated ECE have also been obtained through mentioned new approach. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Energy conservation equation Mild slope equation Geometrical optics equations Energy density Energy flux numerical computations

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A model for a finite memory transport in the Fisher equation

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APPLIED MATHEMATICAL MODELLING 2008年第9期32卷 1883-1893页

作者： Abdel-Gawad, H. I. Cairo Univ Fac Sci Dept Math Cairo Egypt

A model for a finite memory effect in the Fisher equation had been presented by Cattaneo [Acad. Sci. 247 (1958) 431]. By this model the type of the governing equation is transformed from a parabolic type to a hyperbolic one. But the Cattaneo's equation does not reduce to the logistic equation in the homogeneous regime. A new model is presented which conserves the parabolic generic equation as well as the reduction property. Memory effects are visualized in the two models through numerical computations of solutions. (c) 2007 Elsevier Inc. All rights reserved.

关键词： finite memory effect a new model Cattaneo's model numerical computations exact solutions

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Bouncing ball dynamics: Simple model of motion of the table and sinusoidal motion

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INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS 2014年第Oct.期65卷 226-235页

作者： Okninski, Andrzej Radziszewski, Boguslaw Politech Swietokrzyska PL-25314 Kielce Poland Coll Mazovia PL-08110 Siedlce Poland

Non-linear dynamics of a bouncing ball moving vertically in a gravitational field and colliding with a moving limiter is considered. The Poincare map, describing evolution from an impact to the next impact, is used to analyse the original system. Sinusoidal displacement of the table, defining the standard model, is approximated in one period of the limiter's motion by a cubic spline, thus making analytical computations possible. Analytical and numerical results, based on Implicit Function Theorem, obtained for this simplified model, are used to elucidate dynamics of the standard model of the bouncing ball. Finally, the same techniques are applied to investigate dynamics of the standard model. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Bouncing ball models numerical computations Rigorous results

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Doubly uniform semiclassical quantization formula for resonances

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EUROPEAN PHYSICAL JOURNAL D 2009年第3期53卷 283-288页

作者： Linnaeus, I. Jakusjina Thylwe, K. -E. Dalarna Univ Coll S-78188 Borlange Sweden Royal Inst Technol KTH Mech S-10044 Stockholm Sweden

The radial Schrodinger equation with an effective potential containing a single well and a single barrier is treated with an improved uniform semiclassical method. The improved quantization formula for complex energies (or resonances) contains a correction term that originates from a uniform treatment of the classically forbidden region near the origin in addition to the more familiar uniform treatment of the barrier region. In the present case the origin has a second-order pole, due to the centrifugal barrier potential term, and/or a Coulomb-type singularity, and these terms dominate the region inside the innermost classical turning point. numerical results for first-order and third-order approximate complex resonance energies are compared with those of a standard (first- and third-order) barrier-uniform semiclassical method and also with those of 'exact' numerical computations. The improved quantization formula provides results in significantly better agreement with the exact results as the angular momentum quantum number l approaches zero.

关键词： semiclassical formula numerical computations COMPLEX ENERGY numerical calculation provenance Quantization Uniform barrier region correct entry formula single opening Uniforms

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Turbulent transfer coefficients model for flows over permeable rough surfaces

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JOURNAL OF ENHANCED HEAT TRANSFER 2000年第1期7卷 11-22页

作者： Sivykh, GF Novosibirsk State Pedag Univ Dept Phys Novosibirsk 630126 Russia

This paper submits a wall region model of turbulent transfer coefficients for flows over a permeable rough surface. The model takes into account violation of the analogy between the transfer processes of heat and momentum in the vicinity of a rough wall. The results of friction and heat transfer computations both in boundary layers and pipe flows are compared with measurements for different types of roughness, In particular, results show that increases in the roughness height undertaken for heat transfer intensification can lead to the opposite effect for fluids with high Prandtl numbers.

关键词： rough surfaces turbulent transfer coefficients model roughness functions numerical computations

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ESTIMATIONS FOR NONSYMMETRIC EFFECTIVE COEFFICIENTS

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SIAM JOURNAL ON APPLIED MATHEMATICS 1994年第3期54卷 731-737页

作者： PASA, GI Inst of Mathematics of the Romanian Acad Bucharest Romania

During the past several years, several papers have been devoted to the study of composite periodic materials. In a simpler manner, the thermic conductivity of a composite material is considered here. If the periodicity directions do not coincide with the coordinate axes, the elastic matrix of components is not symmetric. In this case, estimations are obtained for the effective coefficients that do not contain the inverse of an elastic and effective matrix. Also, nonsymmetry may be related to the position of the fiber (inclusion), to which it is nonsymmetric with respect to the symmetry axes of the periodicity cell (generally a parallelepipedon). In this case. a configuration is given for which the effective coefficients a12 = a21 may be negative or positive, even if the initial corresponding coefficients are equal to zero. This fact agrees with the numerical results given at the beginning of sectional sign 2.

关键词： PERIODIC COMPOSITES FIBER RESIN numerical computations CHARACTERIZATION ESTIMATIONS

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Computing the indices of Sturm-Liouville eigenvalues for coupled boundary conditions (the EIGENIND-SLP codes)

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第1-2期220卷 490-507页

作者： Wang, Guixia Wang, Zhong Wu, Hongyou Inner Mongolia Univ Dept Math Hohhot 010021 Peoples R China Inner Mongolia Univ Dept Math Hohhot 010022 Peoples R China No Illinois Univ Dept Math De Kalb IL 60115 USA

The main purpose of the EIGENIND-SLP codes is to compute the indices of known eigenvalues of self-adjoint Sturm-Liouville problems with coupled boundary conditions (BCs). The spectrum of the problems can be unbounded from both below and above. Using some recent theoretical results. the computation is converted to that of the indices of the same eigenvalues for appropriate separated BCs, and is then carried out in terms of the Prufer angle. The algorithm so generated and its implementation are discussed, and numerous examples are presented to illustrate the theoretical results and various aspects of the implementation. (c) 2007 Elsevier B.V. All rights reserved.

关键词： self-adjoint Sturm-Liouville problems indices of eigenvalues coupled boundary conditions Prufer angle numerical computations

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Bayesian prediction bounds from the scaled Burr type X model

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2002年第5-6期44卷 587-594页

作者： Jaheen, ZF Al-Matrafi, BN Umm Al Qura Univ Fac Sci Math Dept At Taif Saudi Arabia

The two-parameter Burr type X distribution is proposed to be the underlying model, and prediction bounds for future lifetimes are obtained using the Bayesian approach. Prediction intervals are derived for unobserved lifetimes in the same sample (one-sample prediction) and in a future sample from the same population (two-sample prediction) based on type-II censored samples. A numerical example is given to illustrate the procedures, and the accuracy of prediction intervals is investigated via Monte Carlo simulation. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： Burr X model type-2 censoring Bayesian prediction one- and two-sample techniques numerical computations

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Exponential and polynomial decay results for a swelling porous elastic system with a single nonlinear variable exponent damping: theory and numerics

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ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 2023年第2期74卷 1-28页

作者： Al-Mahdi, A. M. Al-Gharabli, M. M. Kissami, I. Soufyane, A. Zahri, M. King Fahd Univ Petr & Minerals Preparatory Year Program Dhahran 31261 Saudi Arabia King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Construct & Bldg Mat Dhahran 31261 Saudi Arabia Mohammed VI Polytech Univ Lot 990 Hay Moulay Rachid Benguerir 43150 Morocco Univ Sharjah Dept Math Res Grp MASEP & BioInformat FG Sharjah U Arab Emirates

We consider a swelling porous elastic system with a single nonlinear variable exponent damping. We establish the existence result using the Faedo-Galerkin approximations method, and then, we prove that the system is stable under a natural condition on the parameters of the system and the variable exponent. We obtain exponential and polynomial decay results by using the multiplier method, and these results generalize the existing results in the literature. In addition, we end our paper with some numerical illustrations.

关键词： Swelling porous problem Multiplier method Stability Variable exponents Galerkin method numerical computations

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