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Analytical Description (analytical + description)
Selected AbstractsGeneralized treatment of NMR spectra for rapid chemical reactionsCONCEPTS IN MAGNETIC RESONANCE, Issue 4 2007Matthew D. Christianson Abstract Application of NMR spectroscopy to fast irreversible reactions (t1/2 < 0.7 s) has been hampered by limitations in instrumentation and general methods for modeling the complicated spectra that result. Analytical descriptions of nuclear spin dynamics during fast reactions, first solved by Ernst and coworkers, are limited to first-order reaction kinetics. We demonstrate that numeric methods enable simulation of NMR spectra for fast reactions having any form of rate law. Simulated stopped-flow NMR spectra are presented for a variety of common kinetic scenarios including reversible and irreversible reactions of first and second-order, multistep reactions, and catalytic transformations. The simulations demonstrate that a wealth of mechanistic information, including reaction rates, rate laws, and the existence of intermediates, is imbedded in a single NMR spectrum. The sensitivity of modern NMR instrumentation along with robust methods for simulating and fitting kinetic parameters of fast reactions make stopped-flow NMR an attractive method for kinetic studies of fast chemical reactions. © 2007 Wiley Periodicals, Inc. Concepts Magn Reson Part A 30A: 165,183, 2007. [source] SANISAND: Simple anisotropic sand plasticity modelINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2008Mahdi Taiebat Abstract SANISAND is the name used for a family of simple anisotropic sand constitutive models developed over the past few years within the framework of critical state soil mechanics and bounding surface plasticity. The existing SANISAND models use a narrow open cone-type yield surface with apex at the origin obeying rotational hardening, which implies that only changes of the stress ratio can cause plastic deformations, while constant stress-ratio loading induces only elastic response. In order to circumvent this limitation, the present member of the SANISAND family introduces a modified eight-curve equation as the analytical description of a narrow but closed cone-type yield surface that obeys rotational and isotropic hardening. This modification enables the prediction of plastic strains during any type of constant stress-ratio loading, a feature lacking from the previous SANISAND models, without losing their well-established predictive capability for all other loading conditions including the cyclic. In the process the plausible assumption is made that the plastic strain rate decomposes in two parts, one due to the change of stress ratio and a second due to loading under constant stress ratio, with isotropic hardening depending on the volumetric component of the latter part only. The model formulation is presented firstly in the triaxial stress space and subsequently its multiaxial generalization is developed following systematically the steps of the triaxial one. A detailed calibration procedure for the model constants is presented, while successful simulation of both drained and undrained behavior of sands under constant and variable stress-ratio loadings at various densities and confining pressures is obtained by the model. Copyright © 2007 John Wiley & Sons, Ltd. [source] A geometry projection method for shape optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004J. Norato Abstract We present a new method for shape optimization that uses an analytical description of the varying design geometry as the control in the optimization problem. A straightforward filtering technique projects the design geometry onto a fictitious analysis domain to support simplified response and sensitivity analysis. However, the analytical geometry model is referenced directly for all purely geometric calculations. The method thus combines the advantages of direct geometry representations with the simplified analysis procedures that are possible with fictitious domain analysis methods, such as the material distribution methods commonly used in topology optimization. The projected geometry measure converges to the indicator function of the analytical geometry model in the limit of numerical mesh refinement. Consequently, optimal designs obtained with the new method converge to solutions of well-defined continuum optimization problems in the limit of mesh refinement. This property is confirmed in example computations for minimum compliance design of an elastic structure subject to a volume constraint and for minimum volume design subject to a maximum stress constraint. Copyright © 2004 John Wiley & Sons, Ltd. [source] Computational form-finding of tension membrane structures,Non-finite element approaches: Part 1.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003Use of cubic splines in finding minimal surface membranes Abstract This paper, presented in three parts, discusses a computational methodology for form-finding of tension membrane structures (TMS), or fabric structures, used as roofing forms. The term ,form-finding' describes a process of finding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an efficient numerical tool, which will allow a better integration of the design/analysis/manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap films). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping. Part 1 describes a new form-finding approach, based on the Laplace,Young equation and cubic spline fitting to give a full, piecewise, analytical description of a minimal surface. The advantages arising from the approach, particularly with regard to manufacture of cutting patterns for a membrane, are highlighted. Part 2 describes an alternative and novel form-finding approach, based on a constant tension field and faceted (triangular mesh) representation of the minimal surface. It presents techniques for controlling mesh distortion and discusses effects of mesh control on the accuracy and computational efficiency of the solution, as well as on the subsequent stages in design. Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical efficiency of each method, are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] Computational form-finding of tension membrane structures,Non-finite element approaches: Part 2.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003Triangular mesh discretization, control of mesh distortion in modelling minimal surface membranes Abstract This paper, presented in three parts, discusses a computational methodology for form-finding of tension membrane structures (TMS), or fabric structures, used as roofing forms. The term ,form-finding' describes a process of finding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an efficient numerical tool, which will allow a better integration of the design/analysis/manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap films). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping. Part 1 gave a background to the problem of TMS design, described the DR method, and presented a new form-finding methodology, based on the Laplace,Young equation and cubic spline fitting to give a full, piecewise, analytical description of the surface. Part 2 describes an alternative and novel form-finding method, based on a constant tension field and faceted (triangular mesh) representation of the minimal surface. Techniques for controlling mesh distortion are presented, and their effects on the accuracy and computational efficiency of the solution, as well as on the subsequent stages in design, are examined. Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical efficiency of each method, are presented. Copyright © 2002 John Wiley & Sons, Ltd. [source] A novel model for the interpretation of small-angle scattering experiments of self-affine structuresJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 1 2010Gerald J. Schneider A novel theory is presented which allows, for the first time, the analytical description of small-angle scattering experiments on anisotropic shaped clusters of nanoparticles. Experimentally, silica-filled rubber which is deformed is used as an example. The silica can be modelled by solid spheres which form clusters. The experiments demonstrate that the clusters become anisotropic as a result of the deformation whereas the spheres are not affected. A comparison of the newly derived model function and the experiments provides, for the first time, microscopic evidence of the inhomogeneous deformation of clusters in the rubbery matrix. [source] Intracluster light and the extended stellar envelopes of cD galaxies: an analytical descriptionMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007Marc S. Seigar ABSTRACT We have analysed deep R -band images, down to a limiting surface brightness of 26.5 R-mag arcsec,2 (equivalent to ,28 B-mag arcsec,2), of five cD galaxies to determine the shape of the surface brightness profiles of their extended stellar envelopes. Both de Vaucouleurs R1/4 and Sérsic R1/n models, on their own, provide a poor description of the surface brightness profiles of cD galaxies. This is due to the presence of outer stellar envelopes, thought to have accumulated over the merger history of the central cluster galaxy and also from the tidal stripping of galaxies at larger cluster radii. We therefore simultaneously fit two Sérsic functions to measure the shape of the inner and outer components of the cD galaxies. We show that, for three out of our five galaxies, the surface brightness profiles are best fitted by an inner Sérsic model, with indices n, 1 ,6, and an outer exponential component. For these systems, the galaxy-to-envelope size ratio is 0.1,0.4 and the contribution of the stellar envelope to the total R -band light (i.e. galaxy + envelope) is around 60,80 per cent (based on extrapolation to a 300 kpc radius). The exceptions are NGC 6173, for which our surface brightness profile modelling is consistent with just a single component (i.e. no envelope) and NGC 4874 which appears to have an envelope with a de Vaucouleurs, rather than exponential, profile. [source] Radiative torques: analytical model and basic propertiesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2007A. Lazarian ABSTRACT We attempt to get a physical insight into grain alignment processes by studying basic properties of radiative torques (RATs). For this purpose we consider a simple toy model of a helical grain that reproduces well the basic features of RATs. The model grain consists of a spheroidal body with a mirror attached at an angle to it. Being very simple, the model allows analytical description of RATs that act upon it. We show a good correspondence of RATs obtained for this model and those of irregular grains calculated by ddscat. Our analysis of the role of different torque components for grain alignment reveals that one of the three RAT components does not affect the alignment, but induces only for grain precession. The other two components provide a generic alignment with grain long axes perpendicular to the radiation direction, if the radiation dominates the grain precession, and perpendicular to magnetic field, otherwise. The latter coincides with the famous predictions of the Davis,Greenstein process, but our model does not invoke paramagnetic relaxation. In fact, we identify a narrow range of angles between the radiation beam and the magnetic field, for which the alignment is opposite to the Davis,Greenstein predictions. This range is likely to vanish, however, in the presence of thermal wobbling of grains. In addition, we find that a substantial part of grains subjected to RATs gets aligned with low angular momentum, which testifies that most of the grains in diffuse interstellar medium do not rotate fast, that is, rotate with thermal or even subthermal velocities. This tendency of RATs to decrease grain angular velocity as a result of the RAT alignment decreases the degree of polarization, by decreasing the degree of internal alignment, that is, the alignment of angular momentum with the grain axes. For the radiation-dominated environments, we find that the alignment can take place on the time-scale much shorter than the time of gaseous damping of grain rotation. This effect makes grains a more reliable tracer of magnetic fields. In addition, we study a self-similar scaling of RATs as a function of ,/aeff. We show that the self-similarity is useful for studying grain alignment by a broad spectrum of radiation, that is, interstellar radiation field. [source] Defect Tolerance and Nanomechanics in Transistors that Use Semiconductor Nanomaterials and Ultrathin Dielectrics,ADVANCED FUNCTIONAL MATERIALS, Issue 17 2008Jong-Hyun Ahn Abstract This paper describes experimental and theoretical studies of the mechanics of free-standing nanoribbons and membranes of single-crystalline silicon transfer printed onto patterned dielectric layers. The results show that analytical descriptions of the mechanics agree well with experimental data, and they explicitly reveal how the geometry of dielectric layers (i.e., the width and depth of the features of relief) and the silicon (i.e., the thickness and widths of the ribbons) affect mechanical bowing (i.e., "sagging") in the suspended regions of the silicon. This system is of practical importance in the use of semiconductor nanomaterials for electronic devices, because incomplete sagging near defects in gate dielectrics provides a level of robustness against electrical shorting in those regions which exceeds that associated with conventional deposition techniques for thin films. Field effect transistors formed using silicon nanoribbons transferred onto a range of ultrathin gate dielectrics, including patterned epoxy, organic self-assembled monolayers, and HfO2, demonstrate these concepts. [source] Halo model at its best: constraints on conditional luminosity functions from measured galaxy statisticsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2006Asantha Cooray ABSTRACT Using the conditional luminosity function (CLF; the luminosity distribution of galaxies in a dark matter halo) as the fundamental building block, we present an empirical model for the galaxy distribution. The model predictions are compared with the published luminosity function (LF) and clustering statistics from the Sloan Digital Sky Survey (SDSS) at low redshifts, galaxy correlation functions from the Classifying Objects by Medium-Band Observations 17 (COMBO-17) survey at a redshift of 0.6, the Deep Extragalactic Evolutionary Probe 2 (DEEP2) survey at a redshift of unity, the Great Observatories Deep Origins Survey (GOODS) at a redshift around 3 and the Subaru/XMM,Newton Deep Field data at a redshift of 4. The comparison with statistical measurements allows us to constrain certain parameters related to analytical descriptions on the relation between a dark matter halo and its central galaxy luminosity, its satellite galaxy luminosity, and the fraction of early- and late-type galaxies of that halo. With the SDSS r -band LF at Mr < ,17, the lognormal scatter in the central galaxy luminosity at a given halo mass in the central galaxy,halo mass, Lc(M), relation is constrained to be 0.17+0.02,0.01, with 1, errors here and below. For the same galaxy sample, we find no evidence for a low-mass cut-off in the appearance of a single central galaxy in dark matter haloes, with the 68 per cent confidence level upper limit on the minimum mass of dark matter haloes to host a central galaxy, with luminosity Mr < ,17, is 2 × 1010 h,1 M,. If the total luminosity of a dark matter halo varies with halo mass as Lc(M) (M/Msat),s when M > Msat, using SDSS data, we find that Msat= (1.2+2.9,1.1) × 1013 h,1 M, and power-law slope ,s= 0.56+0.19,0.17 for galaxies with Mr < ,17 at z < 0.1. At z, 0.6, the COMBO-17 data allows these parameters for MB < ,18 galaxies to be constrained as (3.3+4.9,3.0) × 1013 h,1 M, and (0.62+0.33,0.27), respectively. At z, 4, Subaru measurements constrain these parameters for MB < ,18.5 galaxies as (4.12+5.90,4.08) × 1012 h,1 M, and (0.55+0.32,0.35), respectively. The redshift evolution associated with these parameters can be described as a combination of the evolution associated with the halo mass function and the luminosity,halo mass relation. The single parameter well constrained by clustering measurements is the average of the total satellite galaxy luminosity corresponding to the dark matter halo distribution probed by the galaxy sample. For SDSS, ,Lsat,= (2.1+0.8,0.4) × 1010 h,2 L,, while for GOODS at z, 3, ,Lsat, < 2 × 1011 h,2 L,. For SDSS, the fraction of galaxies that appear as satellites is 0.13+0.03,0.03, 0.11+0.05,0.02, 0.11+0.12,0.03 and 0.12+0.33,0.05 for galaxies with luminosities in the r, band from ,22 to ,21, ,21 to ,20, ,20 to ,19 and ,19 to ,18, respectively. In addition to constraints on central and satellite CLFs, we also determine model parameters of the analytical relations that describe the fraction of early- and late-type galaxies in dark matter haloes. We use our CLFs to establish the probability distribution of halo mass in which galaxies of a given luminosity could be found either at halo centres or as satellites. Finally, to help establish further properties of the galaxy distribution, we propose the measurement of cross-clustering between galaxies divided into two distinctly different luminosity bins. Our analysis shows how CLFs provide a stronger foundation to built-up analytical models of the galaxy distribution when compared with models based on the halo occupation number alone. [source] | ||||||||||