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Analytical Relations (analytical + relation)
Selected AbstractsInfluence of liquid bridges on the mechanical behaviour of polydisperse granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2006F. Soulié Abstract We investigate a polydisperse granular material in which the particle interactions are governed by a capillary force law. The cohesion force for a grain-pair with unequal diameters is expressed as an explicit function of the inter-particle distance and the volume of the liquid bridge. This analytical relation is validated by experiments on a reference material. Then, it is completed by a rupture criterion and cast in the form of a force law that accounts for solid contact, capillary force and rupture characteristics of a grain-pair. Finally, in order to evaluate the influence of capillary cohesion on the macroscopic behaviour, radial and axial compression tests on cylindrical assemblies of wet particles are simulated using a 3D distinct element method. Copyright © 2005 John Wiley & Sons, Ltd. [source] Scaling of geological discontinuity normal load,deformation response using fractal geometryINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2001Michael E. Plesha Abstract The mechanical behaviour of discontinuities in rock, such as joints, is known to be size-dependent. It is also suspected that the behaviour of larger size features, such as faults, is also size-dependent. This size dependence has serious implications for performing numerical response simulations of geological media. In this paper, we develop a new mathematical theory for scaling of one particular discontinuity property, namely the interface normal stiffness. To accomplish this, we idealize an interface to have fractal geometry, and we develop analytical relations which show that the interface normal stiffness, which is commonly thought to be a size-independent property, is in fact a size-dependent property and has fractal characteristics that may be exploited to develop a fundamental theory for scaling. Copyright © 2001 John Wiley & Sons, Ltd. [source] Analytical design of a half-mode substrate integrated waveguide Wilkinson power dividerMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 5 2010A. Suntives Abstract This article presents a new approach in designing half-mode substrate integrated waveguide Wilkinson power dividers based on analytical relations. Even- and odd-mode analysis is used to determine the required value of the branch resistance and optimize the power divider performance, namely the output ports' isolation. In this manner, the design process for this microwave component is simplified and expedited, while an excellent correlation with full-wave simulations is maintained. Measurements of the fabricated prototype corroborate the calculated results and demonstrate a wide output-port isolation bandwidth of 71%. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1066,1069, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25145 [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] | ||||||||||