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Asymptotic estimates for the solutions of boundary-value problems with initial jump for linear differential equations with small parameter in the coefficients of derivatives

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UKRAINIAN MATHEMATICAL JOURNAL 2013年第5期65卷 694-708页

作者： Kasymov, K. A. Nurgabyl, D. N. Uaisov, A. B. Kazakhstan Natl Univ Alma Ata Inst Math & Mech Alma Ata Kazakhstan Zhetysu State Univ Taldykorgan Kazakhstan

We establish asymptotic estimates for the solutions of singularly perturbed boundary-value problems with initial jumps.

关键词： ASYMPTOTIC expansions boundary value problems -- numerical solutions LINEAR differential equations PARAMETER estimation COEFFICIENTS (Statistics) DERIVATIVES (Mathematics) SINGULARITIES (Mathematics)

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The aero-acoustic resonance behavior of partially covered slender cavities

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EXPERIMENTS IN FLUIDS 2011年第5期51卷 1353-1367页

作者： de Jong, Arjen Teake Bijl, Hester Scarano, Fulvio Delft Univ Technol NL-2611 HS Delft Netherlands

The present investigation focuses on the aeroacoustic resonance of cavities with a width much larger than their length or depth and partially covered, as often encountered in automotive door gaps. The cavities are under influence of a low Mach number flow with a relatively thick boundary layer. Under certain conditions, these cavities can acoustically resonate with the flow. The upstream and downstream edge of the opening as well as the cover lip overhang location and boundary layer thickness are parametrically varied in an experimental campaign, and the effect of the parameters on the resonance amplitude is investigated. Slender rectangular cavity geometries with an opening length of 8 mm and spanwise width of 500 mm are used. The cavity flow-induced acoustic response is measured with pressure transducers at different spanwise locations inside the cavity. Hot-wire measurements are performed to quantify the boundary layer characteristics. Furthermore, high-speed time-resolved particle image velocimetry is used to capture the instantaneous velocity field around the opening geometries. When the boundary layer thickness is increased, the cavity resonance amplitude diminishes. The cover lip overhang location has a large influence on the resonance response, which can be attributed to changes in the cavity driven flow properties. Rounding of the upstream edge promotes resonance, whereas rounding of the downstream edge can diminish it. A possible explanation of the phenomenon is given on the basis of the PIV observations.

关键词： boundary value problems -- numerical solutions TRANSDUCERS ACOUSTIC emission FLUID dynamics SPEED

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Use of pseudo-harmonics method coupled with finite differences coarse mesh in the solution of fixed source problems

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ANNALS OF NUCLEAR ENERGY 2005年第12期32卷 1366-1376页

作者： de Lima, ZR da Silva, FC Alvim, ACM Univ Fed Rio de Janeiro Nucl Engn Programme COPPE UFRJ Rio De Janeiro Brazil

A method based in the pseudo-harmonics method was developed to solve the fixed source problem. The pseudo-harmonics method is based on the eigenfunctions associated with the leakage and removal matrix operator of the neutron diffusion equation, which will be treated here in three dimensions and two groups of energy. This matrix is built in this work through the nodal discretization supplied by coarse mesh finite differences method (CMFDM). CMFDM has as input data the average currents and the average fluxes in the faces of the node, and the average flux in the node, previously obtained by the nodal expansion method. The results obtained with the pseudo-harmonics procedure show good accuracy when compared to the reference results of the source problem tested. Moreover, it is a method which can be easily implemented to solve this type of problems. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： EIGENFUNCTIONS boundary value problems -- numerical solutions NEUTRONS PARTICLES (Nuclear physics)

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Car-Parrinello simulation of an O-H stretching envelope and potential of mean force of an intramolecular hydrogen bonded system: Application to a Mannich base in solid state and in vacuum

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JOURNAL OF CHEMICAL PHYSICS 2007年第20期126卷 205101.1-205101.9页

作者： Jezierska, Aneta Panek, Jaroslaw J. Koll, Aleksander Mavri, Janez Natl Inst Chem SI-1001 Ljubljana Slovenia Univ Wroclaw Fac Chem PL-50383 Wroclaw Poland

Car-Parrinello molecular dynamics (CPMD) study was performed for an anharmonic system - an intramolecularly hydrogen bonded Mannich-base-type compound, 4,5-dimethyl-2(N,N-dimethylaminemethyl)phenol, to investigate the vibrational spectrum associated with the O-H stretching. Calculations were carried out for the solid state and for an isolated molecule. The classical CPMD simulation was performed and then the proton potential snapshots were extracted from the trajectory. The vibrational Schrodinger equation for the snapshots was solved numerically, and the (O-H) envelope was calculated as a superposition of the 0 -> 1 transitions. The potential of mean force for the proton stretching mode was calculated from the proton vibrational eigenfunctions and eigenvalues incorporating statistical sampling, nuclear quantum effects, and effects of the environment. Perspectives for application of the presented methodology in the computational support of biocatalysis are given in the study. (C) 2007 American Institute of Physics.

关键词： MANNICH bases MOLECULAR dynamics SOLID state physics AMINO compounds CARBONYL compounds VIBRATIONAL spectra boundary value problems -- numerical solutions

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Existence of solutions for nonlinear fractional q-difference integral equations with two fractional orders and nonlocal four-point boundary conditions

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2014年第5期351卷 2890-2909页

作者： Ahmad, Bashir Nieto, Juan J. Alsaedi, Ahmed Al-Hutami, Hana King Abdulaziz Univ Fac Sci Dept Math Jeddah 21589 Saudi Arabia Univ Santiago de Compostela Fac Matemat Dept Anal Matemat Santiago De Compostela 15782 Spain

We investigate the existence of solutions for a nonlinear fractional q-difference integral equation (q-variant of the Langevin equation) with two different fractional orders and nonlocal four-point boundary conditions. Our results are based on some classical fixed point theorems. An illustrative example is also presented. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

关键词： INTEGRAL equations EXISTENCE theorems NONLINEAR differential equations -- numerical solutions FRACTIONAL calculus boundary value problems -- numerical solutions FIXED point theory

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FEM/BEM for simulation of LSAW devices

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 2007年第10期54卷 2060-2069页

作者： Taziev, R. A. Russian Acad Sci Inst Semicond Phys Siberian Branch Novosibirsk 630090 Russia

This paper presents a modeling of the propagation of surface acoustic, leaky acoustic, and surface skimming bulk waves in piezoelectrics with a finite array of metallic electrodes over their surface. A combined method of matrix Green's function and the finite element method for computation of all acoustic wave fields is an effective tool for simulation of the propagation of acoustic waves in such structures. The proposed method is optimized in the speed of computation of all matrix Green's function components originally obtained. The Fourier transformations of Green's function from k-space domain to real space domain are performed by combined trapezoidal and Filon's integration methods for rapidly oscillating functions. The trapezoidal integration method is used on a distance from a point source from zero to a few wavelengths long, but the other has the advantage for a distance from some wavelength to infinity. That allows one, by selectively condensing computation grids around branch and singular points of the sharp behavior of Green's function, to maximize speed and accuracy of computation of integrals. FEM is used, modified originally to achieve acceleration without loss accuracy. Because of the simple geometry of the electrodes, unknown elastic fields are presented as a series of known eigenfunctions with unknown coefficients over the whole region of electrodes. All unknown coefficients are determined by applying the Galerkin method. There is good agreement between numerical and experimental conductances of acoustic wave transducers on materials such as lithium niobate and lithium tantalate.

关键词： RADIO wave propagation ACOUSTIC surface wave devices boundary value problems -- numerical solutions ELECTRODES VIBRATION transducers

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Klein-Gordon particles in mixed vector-scalar inversely linear potentials

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PHYSICS LETTERS A 2005年第2期338卷 81-89页

作者： de Castro, AS UNESP Dept Fis & Quim BR-12516410 Guaratingueta SP Brazil

The problem of a spinless particle subject to a general mixing of vector and scalar inversely linear potentials in a two-dimensional world is analyzed. Exact bounded solutions are found in closed form by imposing boundary conditions on the eigenfunctions which ensure that the effective Hamiltonian is Hermitian for all the points of the space. The nonrelativistic limit of our results adds a new support to the conclusion that even-parity solutions to the nonrelativistic one-dimensional hydrogen atom do not exist. (c) 2005 Elsevier B.V. All rights reserved.

关键词： boundary value problems DIFFERENTIAL equations -- numerical solutions INTEGRAL equations -- numerical solutions boundary value problems -- numerical solutions

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The Idea of the Selection of PZT-Beam Interaction Forces in Active Vibration Protection Problem

ACTA PHYSICA POLONICA A

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ACTA PHYSICA POLONICA A 2010年第1期118卷 17-22页

作者： Branski, A. Borkowski, M. Szela, S. WEil Rzeszow Univ Technol Acoust Lab PL-35959 Rzeszow Poland Univ Rzeszow Inst Technol PL-35959 Rzeszow Poland

The paper concerns an active vibration protection (p-reduction) of the structure. This problem corresponds to the active vibration reduction (a-reduction). The quantity and effectivness of the a-/p- reduction, measured with reduction and effectiveness coefficient respectively, depends on, inter alia, the PZT distribution on the structure subdomains with the largest curvatures (quasi optimal distribution) are considered. The aim of this paper is to determine such interacting forces PZT-structure, assuming QO distribution of PZTs, which maximize the effectiveness of p-reduction. The beam clamped at one end, vibrating separately with first three modes, is chosen as the research object. The interacting forces are searched requiring that the shear force and bending moment at the clamped side are equal to zero. The total p-reduction is achieved for separate modes. Assuming the QO distribution of the PZTs, the best, p-effectiveness is achieved. The validation of theoretical considerations is confirmed numerically.

关键词： ACTIVE noise & vibration control FREQUENCIES of oscillating systems EIGENFUNCTIONS boundary value problems -- numerical solutions MATHEMATICAL analysis CURVATURE SHEAR (Mechanics) BENDING (Metalwork) ACTUATORS

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Hall effects on hydromagnetic flow of an Oldroyd 6-constant fluid between concentric cylinders

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CHAOS SOLITONS & FRACTALS 2009年第1期39卷 204-213页

作者： Rana, M. A. Siddiqui, A. M. Qamar, Rashid PINSTECH Management Informat Syst Islamabad 44000 Pakistan Penn State Univ Dept Math York PA 17403 USA

The hydromagnetic flow of an electrically conducting, incompressible Oldroyd 6-constant fluid between two concentric cylinders is investigated. The flow is generated by moving inner cylinder and/or application of the constant pressure gradient. Two non-linear boundary value problems are solved numerically. The effects of material parameters, pressure gradient, magnetic field and Hall parameter on the velocity are studied. The graphical representation of velocity reveals that characteristics for shear thinning/shear thickening behaviour of a fluid is dependent upon the rheological properties. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： HALL effect MAGNETOHYDRODYNAMICS ELECTRIC conductivity SHEAR flow boundary value problems -- numerical solutions MAGNETIC fields

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Studies on the 3D confined potentials using generalized pseudospectral approach

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PHYSICS LETTERS A 2006年第2期357卷 112-119页

作者： Sen, K. D. Roy, Amlan K. Univ Hyderabad Sch Chem Hyderabad 500046 Andhra Pradesh India Univ Calif Irvine Dept Chem Los Angeles CA 90095 USA

In presence of the spherically confined three-dimensional potentials with impenetrable boundaries, the generalized pseudospectral method is shown to provide accurate eigenvalues, eigenfunctions, and radial expectation values for (a) the isotropic harmonic oscillator, (b) the H atom and (c) the Davidson oscillator. Several novel degeneracy conditions are obtained for (a) when the radius of confinement is suitably chosen at the radial nodes corresponding to the free states. (c) 2006 Elsevier B.V. All rights reserved.

关键词： EIGENvalueS DIFFERENTIAL equations -- numerical solutions boundary value problems -- numerical solutions HARMONIC oscillators

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