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Third Order (third + order)
Selected AbstractsAn adaptive multiresolution method for parabolic PDEs with time-step controlINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009M. O. Domingues Abstract We present an efficient adaptive numerical scheme for parabolic partial differential equations based on a finite volume (FV) discretization with explicit time discretization using embedded Runge,Kutta (RK) schemes. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. Compact RK methods of second and third order are then used to choose automatically the new time step while controlling the approximation error in time. Non-admissible choices of the time step are avoided by limiting its variation. The implementation of the multiresolution representation uses a dynamic tree data structure, which allows memory compression and CPU time reduction. This new numerical scheme is validated using different classical test problems in one, two and three space dimensions. The gain in memory and CPU time with respect to the FV scheme on a regular grid is reported, which demonstrates the efficiency of the new method. Copyright © 2008 John Wiley & Sons, Ltd. [source] An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged bodyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2007Christopher P. Kent Abstract An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave,body interaction problem into body and free-surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free-surface problem satisfies modified nonlinear free-surface boundary conditions. It is then shown that the nonlinear free-surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free-surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo-spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd. [source] On the influence of numerical schemes and subgrid,stress models on large eddy simulation of turbulent flow past a square cylinderINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2002A. Nakayama Abstract Influence of finite difference schemes and subgrid-stress models on the large eddy simulation calculation of turbulent flow around a bluff body of square cylinder at a laboratory Reynolds number, has been examined. It is found that the type and the order of accuracy of finite-difference schemes and the subgrid-stress model for satisfactory results are dependent on each other, and the grid resolution and the Reynolds number. Using computational grids manageable by workstation-level computers, with which the near-wall region of the separating boundary layer cannot be resolved, central-difference schemes of realistic orders of accuracy, either fully conservative or non-conservative, suffer stability problems. The upwind-biased schemes of third order and the Smagorinsky eddy-viscosity subgrid model can give reasonable results resolving much of the energy-containing turbulent eddies in the boundary layers and in the wake and representing the subgrid stresses in most parts of the flow. Noticeable improvements can be obtained by either using higher order difference schemes, increasing the grid resolution and/or by implementing a dynamic subgrid stress model, but each at a cost of increased computational time. For further improvements, the very small-scale eddies near the upstream corners and in the laminar sublayers need to be resolved but would require a substantially larger number of grid points that are out of the range of easily accessible computers. Copyright © 2002 John Wiley & Sons, Ltd. [source] Solvent and substituent effects on the reaction of 2- and 4-chloro-3,5-dinitrobenzotrifluorides with substituted anilinesINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 12 2009Basim H. M. Asghar The solvent effect on a nucleophilic substitution reaction of 2- and 4-chloro-3,5-dinitrobenzotrifluoride with substituted anilines was studied in methanol, acetonitrile, and toluene at 25°C. This reaction is of second order, except 2-chloro-3,5-dinitrobenzotrifluoride in toluene shows third order. The kA values are found to be dependent on the substituent in aniline and give good Hammett correlations. The obtained , values are ,4.07 and ,4.62, for the reaction of anilines with 2-chloro-3,5-dinitrobenzotrifluoride in methanol and acetonitrile, respectively. The , values for the reaction of the anilines with 4-chloro-3,5-dinitrobenzotrifluoride are ,3.38, ,4.11, and ,4.34 in methanol, acetonitrile, and toluene, respectively. The reaction of the former compound with anilines in toluene shows a second order in aniline. The dependence of the reaction on the external base such as DABCO suggests a proton transfer controlling step. © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 777,786, 2009 [source] Competing kinetic pathways in the bromine addition to allylic ethers in 1,2-dichloroethane: Opposite temperature effectsINTERNATIONAL JOURNAL OF CHEMICAL KINETICS, Issue 4 2007Alessandro Cecchi The kinetics of the electrophilic bromination of three allylic ethers in a nonprotic solvent, 1,2-dichloroethane, has been investigated. Two of them followed a prevalent second-order pathway, while the third one exhibited a classical, clean third order. The second-order pathway in the first two olefins is attributed to electrophilic assistance of the ethereal oxygen to the attacking bromine molecule. In the molecular bromination of 2,4- cis -dimethyl-8-oxabicyclo[3.2.1]-6-octen-3- cis -ol, opposite temperature dependences were found for the two different kinetic pathways. An exoergonic process for the second-order reaction was explained by the lesser stability of the bromiranium,bromide ionic intermediate, compared to the bromiranium,tribromide in the third-order profile. © 2007 Wiley Periodicals, Inc. 39: 197,203, 2007 [source] Efficient calculation of configurational entropy from molecular simulations by combining the mutual-information expansion and nearest-neighbor methods,,JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2008Vladimir Hnizdo Abstract Changes in the configurational entropies of molecules make important contributions to the free energies of reaction for processes such as protein-folding, noncovalent association, and conformational change. However, obtaining entropy from molecular simulations represents a long-standing computational challenge. Here, two recently introduced approaches, the nearest-neighbor (NN) method and the mutual-information expansion (MIE), are combined to furnish an efficient and accurate method of extracting the configurational entropy from a molecular simulation to a given order of correlations among the internal degrees of freedom. The resulting method takes advantage of the strengths of each approach. The NN method is entirely nonparametric (i.e., it makes no assumptions about the underlying probability distribution), its estimates are asymptotically unbiased and consistent, and it makes optimum use of a limited number of available data samples. The MIE, a systematic expansion of entropy in mutual information terms of increasing order, provides a well-characterized approximation for lowering the dimensionality of the numerical problem of calculating the entropy of a high-dimensional system. The combination of these two methods enables obtaining well-converged estimations of the configurational entropy that capture many-body correlations of higher order than is possible with the simple histogramming that was used in the MIE method originally. The combined method is tested here on two simple systems: an idealized system represented by an analytical distribution of six circular variables, where the full joint entropy and all the MIE terms are exactly known, and the R,S stereoisomer of tartaric acid, a molecule with seven internal-rotation degrees of freedom for which the full entropy of internal rotation has been already estimated by the NN method. For these two systems, all the expansion terms of the full MIE of the entropy are estimated by the NN method and, for comparison, the MIE approximations up to third order are also estimated by simple histogramming. The results indicate that the truncation of the MIE at the two-body level can be an accurate, computationally nondemanding approximation to the configurational entropy of anharmonic internal degrees of freedom. If needed, higher-order correlations can be estimated reliably by the NN method without excessive demands on the molecular-simulation sample size and computing time. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Deficiency indices and spectral theory of third order differential operators on the half lineMATHEMATISCHE NACHRICHTEN, Issue 12-13 2005Horst Behncke Abstract We investigate the spectral theory of a general third order formally symmetric differential expression of the form acting in the Hilbert space ,2w(a ,,). A Kummer,Liouville transformation is introduced which produces a differential operator unitarily equivalent to L . By means of the Kummer,Liouville transformation and asymptotic integration, the asymptotic solutions of L [y ] = zy are found. From the asymptotic integration, the deficiency indices are found for the minimal operator associated with L . For a class of operators with deficiency index (2, 2), it is further proved that almost all selfadjoint extensions of the minimal operator have a discrete spectrum which is necessarily unbounded below. There are however also operators with continuous spectrum. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Scattering and absorption of electromagnetic waves on a plane with hemispherical bossesMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 11 2007Xiaoxiong Gu Abstract We apply multiple scattering equations to study the scattering of electromagnetic waves on a perfectly conducting plane surface with a random dense distribution of hemispherical bosses. We derive a multipole solution up to third order to analyze close range interactions between nearby bosses. Results show significant improvement of accuracy compared with the traditional dipole approximation solution. Absorption on a lossy embossed surface is obtained from the field solution for the perfectly conducting surface. The surface current and absorption enhancement factor are further computed numerically. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2681,2686, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22855 [source] A low voltage highly linear 24-GHz down conversion mixer in 0.18-,m CMOSMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 10 2007Masum Hossain Abstract A K-band low voltage, highly linear folded Gilbert cell mixer in 0.18-,m CMOS is presented. An optimization technique been introduced which is particularly applicable to Gilbert cell type mixers. This technique has been experimentally verified with a down conversion mixer fabricated in a 0.18-,m CMOS process. Utilizing PMOS devices in the transconductance stage and using a 2-V supply voltage, the mixer can down convert from 24 GHz to 10 MHz with an input referred third order intercept of +20 dBm and a conversion gain of 2 dB. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2547,2552, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22759 [source] Computer simulation study on propagation of nonlinear waves through heavily defective crystalsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 11 2004Y. Hiki Abstract A molecular dynamics computer simulation has been performed for a monatomic, anharmonic, and two-dimensional hexagonal crystal. Central forces between the nearest neighbor atoms and anharmonic forces up to the third order are considered. Pulse displacements are applied to the line of atoms at the left end of a rectangular model crystal, in the right half of which a number of light or heavy mass defects are randomly placed. Phonons or solitons propagating in the crystal and scattered by the defects are observed. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Stability analysis of the constant temperature anemometer with frequency depended amplifier gainPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003ajn M.Sc. In this paper we are concerned with the stability and the dynamic response of the constant temperature anemometer. The amplifier of the presented hot,wire anemometer has one pole with high time constant, which affect the presented amplifier to behave in the anemometer working frequency bandwidth with the frequency depended gain. For precise description of the anemometer dynamical response the used transfer function of the amplifier is first order of zeros and third order of poles. The hot,wire response to the sine-wave voltage perturbation was calculated and measured. The root curves of the transfer function were presented. [source] Morphology and development of the subterranean organs of the achlorophyllous Sciaphila polygyna (Triuridaceae)BOTANICAL JOURNAL OF THE LINNEAN SOCIETY, Issue 3 2004STEPHAN IMHOF The subterranean organs of the achlorophyllous Sciaphila polygyna (Triuridaceae) are described, depicted, and structurally explained for the first time. Unlike other Triuridaceae, the subterranean system of S. polygyna appears as a complex star-like structure of short, but thickened, roots as well as scale leaves and shoots. A complete series of sections revealed the following construction. In the axil of a scale leaf at a shoot of first order, a side shoot of second order as well as a pair of endogenous shoot-borne roots arise. This side shoot of second order also develops a scale leaf very early in ontogeny, which again gives rise to a side shoot of third order and a pair of shoot-borne roots. Other scale leaves at shoots of any order may also bear shoots and root pairs. This growth pattern occurs in a very close manner without internode elongation, resulting in the clumped, star-like appearance. The structures described superficially resemble the root systems of many mycoheterotrophic plants from other families. Comparisons with respect to how they develop, however, show that these similar root systems can result from distinct developmental patterns, suggesting independent evolutionary pathways and a considerable evolutionary pressure towards abbreviated and thickened roots in mycoheterotrophic plants. Possible advantages as well as evolutionary implications of the structures described are discussed. © 2004 The Linnean Society of London, Botanical Journal of the Linnean Society, 2004, 146, 295,301. 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