On the Fluid Dependence of Rock Compressibility: Biot-Gassmann Refined
|
|
- MargaretMargaret Burke
- 5 years ago
- Views:
Transcription
1 Downloaded 0/9/3 to Redistribution subject to SEG license or coyright; see Terms of Use at htt://library.seg.org/ On the luid Deendence of Rock Comressibility: Biot-Gassmann Refined Leon Thomsen, Delta Geohysics and University of Houston Introduction n imortant issue in using seismic data to hysically characterize crustal rocks is the deendence of seismic rock velocity uon the comressibility of the fluid in the ore sace. t seismic frequencies, the standard theory for understanding this fluid deendence is that of Biot (94 and Gassmann (95. It is well-known that this theory redicts that the rigidity should be indeendent of fluid content, and that the fluid deendence of the incomressibility is given by an exlicit formula (Eqn. (, below. The urose of this note is to oint out an aroximation in the theory that has not been fully areciated. Below it is shown that avoiding this aroximation leads to a refinement of the standard Biot-Gassmann ( B-G formula for fluid substitution in rock incomressibility, with new requirements (comressibility data for imlementation. This revision has been reorted reviously (Brown and orringa, 975 in a limited context (non-uniform mineralogy; here it is shown to be much more general. The refined formula fits exerimental data better than does the classic formula. Exerimental considerations It is sobering to reach the conclusion that a theory that has been well-acceted for over half a century is in fact not correct. In such a case, we should immediately re-examine the exerimental verification of the theoretical redictions. It turns out that the theory has not, in fact, had strong exerimental verification, desite its wide accetance. The ambiguous state of the exerimental test of the B-G conclusions was discussed e.g. by Thomsen (986, Winkler (986, and Z. Wang (000; this work is not reviewed here. rincial difficulty is that most of the revious exerimental aroaches have measured elastic velocities (P and S at ultrasonic frequencies (in gas-saturated and liquid-saturated rock, whereas the theory is exlicitly limited to quasistatic (or low-frequency measurements, with the assumtion that it alies to elastic velocities at seismic frequencies. Of course, the reason for this indirect exerimental strategy is that direct measurements of comressibility under quasi-static conditions are difficult at the low strains (<0-6 beyond which non-linear effects become imortant. The following analysis shows that in fact static comressibility tests are required in order to fully secify the arameters in the (refined theory; recent work by Hart and Wang (00 enables a fresh assessment. Theoretical considerations The roof of the Biot-Gassmann formula is here recaitulated, following the comact and clear argument of Brown and orringa (975 ( B&, but with an imortant change. The argument is conducted in terms of comressibility rather than of incomressibility, but leads eventually to the classic low-frequency B-G formula: fld sat fld ( dry fld ( sol where sat, dry, fld, sol are the incomressibilities of (resectively: the fluid-saturated rock, the rock with comletely emty ore sace, the ore-filling fluid, and the solid grains of the rock. is orosity, and =- dry / sol. Using mainly just calculus, B& derive the difference between the dry comressibility and the saturated 00 SEG SEG Denver 00 nnual eeting 447
2 comressibility (their Eqn. (3: ( in terms of various measures of comressibility of a mass element ( undrained,,, defined by them. In articular, the unjacketed comressibility and the ore comressibility are: d (3a d (3b where is the volume of the mass element, = is its ore volume, is the fluid ressure in the ore sace, is the total ( confining ressure, and d =- is the differential ressure. Using the Recirocity Theorem (Love, 944, B& obtained =, leading to their rimary scalar result: (4 They remark uon their success in generalizing the B-G result at the cost of only one additional arameter (, but do not emhasize that the aearance in (4 of (instead of the solid comressibility comlicates the imlementation substantially. However, for a rock with homogeneous solid, B& concluded (following arguments discussed below that, = = ( the comressibility of the solid grains, so that Eqn. (4 becomes (5 It is easy to show that Eqn. (5 is exactly the same as the classical B-G result (, written in this notation. Here, we concentrate on B& s conclusion that = = for monomineralic rocks. This conclusion follows from their assertion that equality of stress across all the solid-fluid surfaces of the rock results in a self-similar volume change, with no change in orosity (ore volume/total volume. In fact, it is easy to show that the change in orosity is given by d (6 and that ( ( ( d (7 448 SEG Denver 00 nnual eeting 00 SEG Downloaded 0/9/3 to Redistribution subject to SEG license or coyright; see Terms of Use at htt://library.seg.org/
3 from which it is easy to see that invariance of leads to the conclusion that = =. Downloaded 0/9/3 to Redistribution subject to SEG license or coyright; see Terms of Use at htt://library.seg.org/ B& simly assert that is invariant, with resect to. However that conclusion is clearly roven by Gurevich (004; the roof allows examination of its assumtions. In the roof, is regarded as an indeendent variable (to be adjusted by an exerimenter, whereas in the resent context, it is a deendent variable, determined by the external ressure, by the rock roerties, and by the assumtion of no fluid flow into or out of the mass element. In this undrained context, is linearly related to the volume (through the fluid comressibility ; this connection means that the deformation cannot be self-similar. In the general case, the distortion of the solid by the alication of uniform throughout the rock is a comlicated function of solid incomressibility, rigidity, and micro-geometry. But, it is easy to imagine an artificial case where none of this matters. Imagine the case where the mass element consists of a cube of homogeneous isotroic solid material with volume, surrounded by a cubic shell of fluid with volume. (If it is desired that the solid should be simly connected, imagine very thin sacers, made of the same solid material, which connect the solid cube to other similar cubes in nearby mass elements, but which do not materially distort the stresses. lication of uniform (at constant d throughout this eculiar mass element results in no shear stress at all, only a uniform comression of both solid and fluid, each according to its own comressibility ( or, resectively. This changes the relative volume fraction occuied by solid and by fluid, hence it changes the fluid-filled orosity, /. Hence, from Eqns. (6, 7 it follows that,, and are all different. Of course this artificial case has no significance in itself, but only illustrates, by examle, the rincile that in the general case,,, and are all different. This argument confirms B& s conclusion that differs from and, and generalizes it to include even the secial case of homogenous solid. Hence, it is certainly necessary to consider the comlications osed by the aearance in Eqn. (4 of, and in even the simlest cases. In terms of incomressibilities, Eqn. (4 becomes (comare with B& (: fld sat fld dry fld fld (8 The difficulty in using this exression for seismic fluid substitution is that (unlike the solid comressibility both and are arameters of the rock, and deend uon comosition, rigidity, and micro-geometry in a comlicated way, not suscetible to theoretical resolution. In recent comressibility exeriments, Hart and Wang (00 indeendently measured all the arameters of Eqn. (4 excet for, in Berea sandstone and Indiana limestone, and found that (esecially in the sandstone that differed from, in a stress-deendent way. (Since this aroach assumes the validity of Eqn. (4, it cannot be used as a check of the same equation. They also measured Skemton s B-coefficient, the ratio of fluid ressure to confining ressure in an undrained exeriment, given in terms of comressibilities by (H.. Wang, 000: B and used this overdetermined dataset to rove their oint, conservatively. However, their data can also serve as a validity check of Eqns. (4, 8. In the course of deriving Eqn. (, B& analyze the variation of the ore volume with alied ressure in an undrained exeriment, finding that (their Eqn. (: ( Using their subsequent result that = -, this is (9 (0 00 SEG SEG Denver 00 nnual eeting 449
4 B ( ( ( Downloaded 0/9/3 to Redistribution subject to SEG license or coyright; see Terms of Use at htt://library.seg.org/ so that the ore comressibility is given as B ( ( B Using the sandstone data from Hart and Wang (00, Table, ig. confirms their conclusion that (. This conclusion seems to be firm, even with this less conservative aroach (desite the evidence of scatter in the data, esecially at differential ressures greater than 5 Pa. Because of the ressure-deendence of the differences, they cannot be due to the fact that the sandstone has about 0% of non-quartz minerals, but must be due to the microgeometry of the rock, in articular to the closing of microcracks with increasing ressure. igure. Demonstrating that ig.. Neglect of this comlexity causes systematic error. urther, when these measured values are used to calculate the difference, using the refined B-G Eqn. (4, the agreement with exeriment is fairly good (ig.. When the classic B-G formula (5 is used to calculate this difference, the errors are somewhat larger, and biased low, articularly at low differential ressure. Conclusions In the classic exression ( or 5 of Biot-Gassmann for fluid substitution in the rock comressibility, contains an aroximation reviously identified (by B&, in a limited context, whose generality has not been fully areciated. Correction of this aroximation (using Eqn. (4 relacing Eqn. (5 requires data on rock comressibility. With the correction, agreement of theory and the exerimental data of Hart and Wang (00 is fairly good. By contrast, the classic equation gives redictions which are systematically lower. The significance of the correction deends uon the articular circumstances, and is most imortant where the rock contains cracks or fractures. cknowledgments: The author areciates constructive discussion from J. Berryman (Lawrence Berkeley National Laboratory, Boris Gurevich (Curtin University, Gennady Golushubin (University of Houston, and Herb Wang (University of Wisconsin, as well as material suort from LBNL and UH. 00 SEG SEG Denver 00 nnual eeting 450
5 EDITED REERENCES Note: This reference list is a coy-edited version of the reference list submitted by the author. Reference lists for the 00 SEG Technical Program Exanded bstracts have been coy edited so that references rovided with the online metadata for each aer will achieve a high degree of linking to cited sources that aear on the Web. Downloaded 0/9/3 to Redistribution subject to SEG license or coyright; see Terms of Use at htt://library.seg.org/ REERENCES Biot,.., 94, General Theory of Three-Dimensional Consolidation: Journal of lied Physics,, no., 55 64, doi:0.063/ Brown, R. J. S., and J. orringa, 975, On the deendence of the elastic roerties of a orous rock on the comressibility of the ore fluid: Geohysics, 40, , doi:0.90/ Gassmann,., 95, Uber die Elastizitat oroser edien, itteiluagen aus dem Inst. fur Geohysik (Zurich, 7, l-3. Translated and rerinted as: On elasticity of orous media, in Classics of Elastic Wave Theory,.. Pelissier, Ed., SEG, 007. Hart, D. J., and H.. Wang, 00, ariation of unjacketed ore comressibility using Gassmann s equation and an overdetermined set of volumetric oroelastic measurements: Geohysics, 75, no., N9 N8, doi:0.90/ Love.. E. H., 944, athematical Treatise on the Theory of Elasticity, Dover Books. Thomsen, L., 985, Biot-consistent elastic moduli of orous rocks: Low-frequency limit: Geohysics, 50, , doi:0.90/ Wang, Z., 000, The Gassmann equation revisited: Comaring laboratory data with Gassmann s redictions, in Z. Wang, and. Nur, eds., Seismic and acoustic velocities in reservoir rocks, 3: Recent develoments: SEG, 8 3. Wang, H.., 000, Theory of linear oroelasticity: Princeton University Press. Winkler,. W., 986, Estimates of velocity disersion between seismic and ultrasonic frequencies: Geohysics, 5, 83 89, doi:0.90/ SEG SEG Denver 00 nnual eeting 45
Main Menu. Summary (1)
Elastic roerty changes of bitumen reservoir during steam injection Ayato Kato*, University of Houston, higenobu Onozuka, JOGMEC, and Toru Nakayama, JAPEX ummary Elastic roerty changes of bitumen reservoir
More informationA SIMPLE PLASTICITY MODEL FOR PREDICTING TRANSVERSE COMPOSITE RESPONSE AND FAILURE
THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS A SIMPLE PLASTICITY MODEL FOR PREDICTING TRANSVERSE COMPOSITE RESPONSE AND FAILURE K.W. Gan*, M.R. Wisnom, S.R. Hallett, G. Allegri Advanced Comosites
More informationCasimir Force Between the Two Moving Conductive Plates.
Casimir Force Between the Two Moving Conductive Plates. Jaroslav Hynecek 1 Isetex, Inc., 95 Pama Drive, Allen, TX 751 ABSTRACT This article resents the derivation of the Casimir force for the two moving
More information8.7 Associated and Non-associated Flow Rules
8.7 Associated and Non-associated Flow Rules Recall the Levy-Mises flow rule, Eqn. 8.4., d ds (8.7.) The lastic multilier can be determined from the hardening rule. Given the hardening rule one can more
More informationEffective conductivity in a lattice model for binary disordered media with complex distributions of grain sizes
hys. stat. sol. b 36, 65-633 003 Effective conductivity in a lattice model for binary disordered media with comlex distributions of grain sizes R. PIASECKI Institute of Chemistry, University of Oole, Oleska
More informationPaper C Exact Volume Balance Versus Exact Mass Balance in Compositional Reservoir Simulation
Paer C Exact Volume Balance Versus Exact Mass Balance in Comositional Reservoir Simulation Submitted to Comutational Geosciences, December 2005. Exact Volume Balance Versus Exact Mass Balance in Comositional
More informationFE FORMULATIONS FOR PLASTICITY
G These slides are designed based on the book: Finite Elements in Plasticity Theory and Practice, D.R.J. Owen and E. Hinton, 1970, Pineridge Press Ltd., Swansea, UK. 1 Course Content: A INTRODUCTION AND
More informationA compression line for soils with evolving particle and pore size distributions due to particle crushing
Russell, A. R. (2011) Géotechnique Letters 1, 5 9, htt://dx.doi.org/10.1680/geolett.10.00003 A comression line for soils with evolving article and ore size distributions due to article crushing A. R. RUSSELL*
More informationLower bound solutions for bearing capacity of jointed rock
Comuters and Geotechnics 31 (2004) 23 36 www.elsevier.com/locate/comgeo Lower bound solutions for bearing caacity of jointed rock D.J. Sutcliffe a, H.S. Yu b, *, S.W. Sloan c a Deartment of Civil, Surveying
More informationChurilova Maria Saint-Petersburg State Polytechnical University Department of Applied Mathematics
Churilova Maria Saint-Petersburg State Polytechnical University Deartment of Alied Mathematics Technology of EHIS (staming) alied to roduction of automotive arts The roblem described in this reort originated
More informationFlexible Pipes in Trenches with Stiff Clay Walls
Flexible Pies in Trenches with Stiff Clay Walls D. A. Cameron University of South Australia, South Australia, Australia J. P. Carter University of Sydney, New South Wales, Australia Keywords: flexible
More informationPROCESSING OF LOW-VISCOSITY CBT THERMOPLASTIC COMPOSITES: HEAT TRANSFER ANALYSIS
PROCESSING OF LOW-VISCOSITY CBT THERMOPLASTIC COMPOSITES: HEAT TRANSFER ANALYSIS Dr. Adrian Murtagh, Siora Coll and Dr. Conchúr Ó Brádaigh Comosites Research Unit Det. of Mechanical & Biomedical Engineering,
More informationCharacteristics of Beam-Based Flexure Modules
Shorya Awtar e-mail: shorya@mit.edu Alexander H. Slocum e-mail: slocum@mit.edu Precision Engineering Research Grou, Massachusetts Institute of Technology, Cambridge, MA 039 Edi Sevincer Omega Advanced
More informationPreconditioning techniques for Newton s method for the incompressible Navier Stokes equations
Preconditioning techniques for Newton s method for the incomressible Navier Stokes equations H. C. ELMAN 1, D. LOGHIN 2 and A. J. WATHEN 3 1 Deartment of Comuter Science, University of Maryland, College
More informationPressure-sensitivity Effects on Toughness Measurements of Compact Tension Specimens for Strain-hardening Solids
American Journal of Alied Sciences (9): 19-195, 5 ISSN 1546-939 5 Science Publications Pressure-sensitivity Effects on Toughness Measurements of Comact Tension Secimens for Strain-hardening Solids Abdulhamid
More informationUnjacketed bulk compressibility of sandstone in laboratory experiments. R. M. Makhnenko 1 and J. F. Labuz 1
481 Unjacketed bulk compressibility of sandstone in laboratory experiments R. M. Makhnenko 1 and J. F. Labuz 1 1 Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55455; PH (612)
More informationSAMARIS. Draft report
SAMARIS Work Package 5 - Performance based secifications Selection and evaluation of models for rediction of ermanent deformations of unbound granular materials in road avements Draft reort Pierre Hornych
More informationThe Second Law: The Machinery
The Second Law: The Machinery Chater 5 of Atkins: The Second Law: The Concets Sections 3.7-3.9 8th Ed, 3.3 9th Ed; 3.4 10 Ed.; 3E 11th Ed. Combining First and Second Laws Proerties of the Internal Energy
More informationKeywords: pile, liquefaction, lateral spreading, analysis ABSTRACT
Key arameters in seudo-static analysis of iles in liquefying sand Misko Cubrinovski Deartment of Civil Engineering, University of Canterbury, Christchurch 814, New Zealand Keywords: ile, liquefaction,
More informationRe-entry Protocols for Seismically Active Mines Using Statistical Analysis of Aftershock Sequences
Re-entry Protocols for Seismically Active Mines Using Statistical Analysis of Aftershock Sequences J.A. Vallejos & S.M. McKinnon Queen s University, Kingston, ON, Canada ABSTRACT: Re-entry rotocols are
More informationarxiv: v1 [physics.data-an] 26 Oct 2012
Constraints on Yield Parameters in Extended Maximum Likelihood Fits Till Moritz Karbach a, Maximilian Schlu b a TU Dortmund, Germany, moritz.karbach@cern.ch b TU Dortmund, Germany, maximilian.schlu@cern.ch
More informationdn i where we have used the Gibbs equation for the Gibbs energy and the definition of chemical potential
Chem 467 Sulement to Lectures 33 Phase Equilibrium Chemical Potential Revisited We introduced the chemical otential as the conjugate variable to amount. Briefly reviewing, the total Gibbs energy of a system
More informationA Note on Massless Quantum Free Scalar Fields. with Negative Energy Density
Adv. Studies Theor. Phys., Vol. 7, 13, no. 1, 549 554 HIKARI Ltd, www.m-hikari.com A Note on Massless Quantum Free Scalar Fields with Negative Energy Density M. A. Grado-Caffaro and M. Grado-Caffaro Scientific
More informationA General Damage Initiation and Evolution Model (DIEM) in LS-DYNA
9th Euroean LS-YNA Conference 23 A General amage Initiation and Evolution Model (IEM) in LS-YNA Thomas Borrvall, Thomas Johansson and Mikael Schill, YNAmore Nordic AB Johan Jergéus, Volvo Car Cororation
More informationNumerical simulation of bird strike in aircraft leading edge structure using a new dynamic failure model
Numerical simulation of bird strike in aircraft leading edge structure using a new dynamic failure model Q. Sun, Y.J. Liu, R.H, Jin School of Aeronautics, Northwestern Polytechnical University, Xi an 710072,
More informationCOMSOL in a New Tensorial Formulation of Non-Isothermal Poroelasticity
Excert rom the Proceedings o the COMSOL Conerence 009 oston COMSOL in a New Tensorial Formulation o Non-Isothermal Poroelasticity Mario-César Suárez A. *, 1 and Fernando Samaniego. 1 Faculty o Sciences
More informationIdentification of the source of the thermoelastic response from orthotropic laminated composites
Identification of the source of the thermoelastic resonse from orthotroic laminated comosites S. Sambasivam, S. Quinn and J.M. Dulieu-Barton School of Engineering Sciences, University of Southamton, Highfield,
More informationNotes on pressure coordinates Robert Lindsay Korty October 1, 2002
Notes on ressure coordinates Robert Lindsay Korty October 1, 2002 Obviously, it makes no difference whether the quasi-geostrohic equations are hrased in height coordinates (where x, y,, t are the indeendent
More informationWave Drift Force in a Two-Layer Fluid of Finite Depth
Wave Drift Force in a Two-Layer Fluid of Finite Deth Masashi Kashiwagi Research Institute for Alied Mechanics, Kyushu University, Jaan Abstract Based on the momentum and energy conservation rinciles, a
More informationEvaluation of Seismic Earth Pressures at the Passive Side
The 1 th World Conference on Earthquake Engineering October -17,, Beijing, China Evaluation of Seismic Earth Pressures at the Passive Side Fei SONG 1 and Jian-Min ZHANG 1 PhD. Candidate, Institute of Geotechnical
More information1 University of Edinburgh, 2 British Geological Survey, 3 China University of Petroleum
Estimation of fluid mobility from frequency deendent azimuthal AVO a synthetic model study Yingrui Ren 1*, Xiaoyang Wu 2, Mark Chaman 1 and Xiangyang Li 2,3 1 University of Edinburgh, 2 British Geological
More informationSome consideration about fluid substitution without shear wave velocity Fuyong Yan*, De-Hua Han, Rock Physics Lab, University of Houston
ain enu Some consideration about fluid substitution without shear wave velocity Fuyong Yan*, De-Hua Han, Rock Physics Lab, University of Houston Summary When S-wave velocity is absent, approximate Gassmann
More information2. Keywords Topology optimization, stress constraints, Raghava criterion, Ishai criterion.
oology Otimization with Different Stress Limits in ension and Comression P. Duysinx Robotics and Automation, Institute of Mechanics, C3, University of Liège, 1 Rue Solvay, B-4 Liège, Belgium, el: +3.4.366.91.94,
More informationQuantitative estimates of propagation of chaos for stochastic systems with W 1, kernels
oname manuscrit o. will be inserted by the editor) Quantitative estimates of roagation of chaos for stochastic systems with W, kernels Pierre-Emmanuel Jabin Zhenfu Wang Received: date / Acceted: date Abstract
More informationExact Solutions in Finite Compressible Elasticity via the Complementary Energy Function
Exact Solutions in Finite Comressible Elasticity via the Comlementary Energy Function Francis Rooney Deartment of Mathematics University of Wisconsin Madison, USA Sean Eberhard Mathematical Institute,
More informationCompressible Flow Introduction. Afshin J. Ghajar
36 Comressible Flow Afshin J. Ghajar Oklahoma State University 36. Introduction...36-36. he Mach Number and Flow Regimes...36-36.3 Ideal Gas Relations...36-36.4 Isentroic Flow Relations...36-4 36.5 Stagnation
More informationA Qualitative Event-based Approach to Multiple Fault Diagnosis in Continuous Systems using Structural Model Decomposition
A Qualitative Event-based Aroach to Multile Fault Diagnosis in Continuous Systems using Structural Model Decomosition Matthew J. Daigle a,,, Anibal Bregon b,, Xenofon Koutsoukos c, Gautam Biswas c, Belarmino
More informationA Bound on the Error of Cross Validation Using the Approximation and Estimation Rates, with Consequences for the Training-Test Split
A Bound on the Error of Cross Validation Using the Aroximation and Estimation Rates, with Consequences for the Training-Test Slit Michael Kearns AT&T Bell Laboratories Murray Hill, NJ 7974 mkearns@research.att.com
More informationSEISMIC PERFORMANCE LIMITS OF THE SKYWAY PIERS FOR THE NEW EAST BAY SPANS OF THE SAN FRANCISCO-OAKLAND BAY BRIDGE
SEISMIC PERFORMANCE LIMITS OF THE SKYWAY PIERS FOR THE NEW EAST BAY SPANS OF THE SAN FRANCISCO-OAKLAND BAY BRIDGE Eric M. HINES Frieder SEIBLE Ph.D., Structural Engineer, LeMessurier Consultants, 675 Massachusetts
More informationIntroduction to Landau s Fermi Liquid Theory
Introduction to Landau s Fermi Liquid Theory Erkki Thuneberg Deartment of hysical sciences University of Oulu 29 1. Introduction The rincial roblem of hysics is to determine how bodies behave when they
More informationKEY ISSUES IN THE ANALYSIS OF PILES IN LIQUEFYING SOILS
4 th International Conference on Earthquake Geotechnical Engineering June 2-28, 27 KEY ISSUES IN THE ANALYSIS OF PILES IN LIQUEFYING SOILS Misko CUBRINOVSKI 1, Hayden BOWEN 1 ABSTRACT Two methods for analysis
More information1. INTRODUCTION. Fn 2 = F j F j+1 (1.1)
CERTAIN CLASSES OF FINITE SUMS THAT INVOLVE GENERALIZED FIBONACCI AND LUCAS NUMBERS The beautiful identity R.S. Melham Deartment of Mathematical Sciences, University of Technology, Sydney PO Box 23, Broadway,
More informationMathematics as the Language of Physics.
Mathematics as the Language of Physics. J. Dunning-Davies Deartment of Physics University of Hull Hull HU6 7RX England. Email: j.dunning-davies@hull.ac.uk Abstract. Courses in mathematical methods for
More informationPreliminary Uncertainty Estimation of the Pressure Distortion Coefficient of a Pressure. Balance by FEM Calculations
Preliminary Uncertainty Estimation of the Pressure Distortion Coefficient of a Pressure Balance by FEM Calculations G. Molinar*, M. Bergoglio*, G. Mosso*,G. Buonanno**, M. Dell Isola** * Istituto di Metrologia
More informationNumerical and experimental investigation on shot-peening induced deformation. Application to sheet metal forming.
Coyright JCPDS-International Centre for Diffraction Data 29 ISSN 197-2 511 Numerical and exerimental investigation on shot-eening induced deformation. Alication to sheet metal forming. Florent Cochennec
More informationChapter 1 Fundamentals
Chater Fundamentals. Overview of Thermodynamics Industrial Revolution brought in large scale automation of many tedious tasks which were earlier being erformed through manual or animal labour. Inventors
More informationHomogeneous and Inhomogeneous Model for Flow and Heat Transfer in Porous Materials as High Temperature Solar Air Receivers
Excert from the roceedings of the COMSOL Conference 1 aris Homogeneous and Inhomogeneous Model for Flow and Heat ransfer in orous Materials as High emerature Solar Air Receivers Olena Smirnova 1 *, homas
More informationModeling Volume Changes in Porous Electrodes
Journal of The Electrochemical Society, 53 A79-A86 2006 003-465/2005/53/A79/8/$20.00 The Electrochemical Society, Inc. Modeling olume Changes in Porous Electrodes Parthasarathy M. Gomadam*,a,z John W.
More information4. Score normalization technical details We now discuss the technical details of the score normalization method.
SMT SCORING SYSTEM This document describes the scoring system for the Stanford Math Tournament We begin by giving an overview of the changes to scoring and a non-technical descrition of the scoring rules
More informationMATHEMATICAL MODELLING OF THE WIRELESS COMMUNICATION NETWORK
Comuter Modelling and ew Technologies, 5, Vol.9, o., 3-39 Transort and Telecommunication Institute, Lomonosov, LV-9, Riga, Latvia MATHEMATICAL MODELLIG OF THE WIRELESS COMMUICATIO ETWORK M. KOPEETSK Deartment
More informationVIBRATION ANALYSIS OF BEAMS WITH MULTIPLE CONSTRAINED LAYER DAMPING PATCHES
Journal of Sound and Vibration (998) 22(5), 78 85 VIBRATION ANALYSIS OF BEAMS WITH MULTIPLE CONSTRAINED LAYER DAMPING PATCHES Acoustics and Dynamics Laboratory, Deartment of Mechanical Engineering, The
More informationONE. The Earth-atmosphere system CHAPTER
CHAPTER ONE The Earth-atmoshere system 1.1 INTRODUCTION The Earth s atmoshere is the gaseous enveloe surrounding the lanet. Like other lanetary atmosheres, it figures centrally in transfers of energy between
More informationMultiscale Surfaces and Amontons Law of Friction
Tribol Lett (23) 49:539 543 DOI.7/s249-2-94-6 ORIGINAL PAPER Multiscale Surfaces and Amontons Law of Friction J. R. Barber Received: 4 December 22 / Acceted: 24 December 22 / Published online: 26 January
More informationVersion 1.0. klm. General Certificate of Education June Mathematics. Statistics 4. Mark Scheme
Version.0 klm General Certificate of Education June 00 Mathematics MS04 Statistics 4 Mark Scheme Mark schemes are reared by the Princial Examiner and considered, together with the relevant questions, by
More informationOn the Prediction of Material Failure in LS-DYNA : A Comparison Between GISSMO and DIEM
13 th International LS-YNA Users Conference Session: Constitutive Modeling On the Prediction of Material Failure in LS-YNA : A Comarison Between GISSMO and IEM Filie Andrade¹, Markus Feucht², Andre Haufe¹
More informationON THE DEVELOPMENT OF PARAMETER-ROBUST PRECONDITIONERS AND COMMUTATOR ARGUMENTS FOR SOLVING STOKES CONTROL PROBLEMS
Electronic Transactions on Numerical Analysis. Volume 44,. 53 72, 25. Coyright c 25,. ISSN 68 963. ETNA ON THE DEVELOPMENT OF PARAMETER-ROBUST PRECONDITIONERS AND COMMUTATOR ARGUMENTS FOR SOLVING STOKES
More informationINTRODUCING THE SHEAR-CAP MATERIAL CRITERION TO AN ICE RUBBLE LOAD MODEL
Symosium on Ice (26) INTRODUCING THE SHEAR-CAP MATERIAL CRITERION TO AN ICE RUBBLE LOAD MODEL Mohamed O. ElSeify and Thomas G. Brown University of Calgary, Calgary, Canada ABSTRACT Current ice rubble load
More informationDomain Dynamics in a Ferroelastic Epilayer on a Paraelastic Substrate
Y. F. Gao Z. Suo Mechanical and Aerosace Engineering Deartment and Princeton Materials Institute, Princeton University, Princeton, NJ 08544 Domain Dynamics in a Ferroelastic Eilayer on a Paraelastic Substrate
More informationPhase transition. Asaf Pe er Background
Phase transition Asaf Pe er 1 November 18, 2013 1. Background A hase is a region of sace, throughout which all hysical roerties (density, magnetization, etc.) of a material (or thermodynamic system) are
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 5 Jul 1998
arxiv:cond-mat/98773v1 [cond-mat.stat-mech] 5 Jul 1998 Floy modes and the free energy: Rigidity and connectivity ercolation on Bethe Lattices P.M. Duxbury, D.J. Jacobs, M.F. Thore Deartment of Physics
More informationSession 5: Review of Classical Astrodynamics
Session 5: Review of Classical Astrodynamics In revious lectures we described in detail the rocess to find the otimal secific imulse for a articular situation. Among the mission requirements that serve
More informationPolarization Mode Dispersion Mitigation through Spun Fibers
INTERNATIONAL JOURNAL O MICROWAVE AND OPTICAL TECHNOLOGY, 176 VOL.5 NO.3 MAY 1 Polarization Mode Disersion Mitigation through Sun ibers Dowluru Ravi Kumar*, Dr.. Prabhakara Rao * Lecturer in ECE, Deartment
More informationSystem Reliability Estimation and Confidence Regions from Subsystem and Full System Tests
009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 0-, 009 FrB4. System Reliability Estimation and Confidence Regions from Subsystem and Full System Tests James C. Sall Abstract
More informationFluid model for relativistic, magnetized plasmas
PHYSICS OF PLASMAS 15, 0611 008 Fluid model for relativistic, magnetized lasmas J. M. TenBarge, R. D. Hazeltine, and S. M. Mahajan Institute for Fusion Studies, University of Texas at Austin, Austin, Texas
More informationKinetics of Protein Adsorption and Desorption on Surfaces with Grafted Polymers
1516 Biohysical Journal Volume 89 Setember 2005 1516 1533 Kinetics of Protein Adsortion and Desortion on Surfaces with Grafted Polymers Fang Fang,* Javier Satulovsky, y and Igal Szleifer* *Deartment of
More informationLow frequency modes in strongly coupled dusty plasmas
PHYSICS OF PLASMAS VOLUME 5, NUMBER 10 OCTOBER 1998 Low frequency modes in strongly couled dusty lasmas P. K. Kaw and A. Sen a) Institute for Plasma Research, Bhat 38 44, India Received 6 October 1997;
More information16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE
16. CHARACTERISTICS OF SHOCK-WAVE UNDER LORENTZ FORCE AND ENERGY EXCHANGE H. Yamasaki, M. Abe and Y. Okuno Graduate School at Nagatsuta, Tokyo Institute of Technology 459, Nagatsuta, Midori-ku, Yokohama,
More informationThe Quark-Parton Model
The Quark-Parton Model Before uarks and gluons were generally acceted Feynman roosed that the roton was made u of oint-like constituents artons Both Bjorken Scaling and the Callan-Gross relationshi can
More informationANALYSIS OF ULTRA LOW CYCLE FATIGUE PROBLEMS WITH THE BARCELONA PLASTIC DAMAGE MODEL
XII International Conerence on Comutational Plasticity. Fundamentals and Alications COMPLAS XII E. Oñate, D.R.J. Owen, D. Peric and B. Suárez (Eds) ANALYSIS OF ULTRA LOW CYCLE FATIGUE PROBLEMS WITH THE
More informationA Comparison between Biased and Unbiased Estimators in Ordinary Least Squares Regression
Journal of Modern Alied Statistical Methods Volume Issue Article 7 --03 A Comarison between Biased and Unbiased Estimators in Ordinary Least Squares Regression Ghadban Khalaf King Khalid University, Saudi
More informationUniversal Finite Memory Coding of Binary Sequences
Deartment of Electrical Engineering Systems Universal Finite Memory Coding of Binary Sequences Thesis submitted towards the degree of Master of Science in Electrical and Electronic Engineering in Tel-Aviv
More informationA numerical assessment of the random walk particle tracking method for heterogeneous aquifers
288 Calibration and Reliability in Groundwater Modelling: From Uncertainty to Decision Making (Proceedings of ModelCARE 2005, The Hague, The Netherlands, June 2005). IAHS Publ. 304, 2006. A numerical assessment
More informationQuasi-particle Contribution in Thermal Expansion and Thermal Conductivity in Metals
e-issn:-459 -ISSN:47-6 Quasi-article Contribution in Thermal Exansion and Thermal Conductivity in Metals Edema OG * and Osiele OM ederal Polytechnic, Auchi, Nigeria Delta State University, Abraka, Nigeria
More informationStudy on Characteristics of Sound Absorption of Underwater Visco-elastic Coated Compound Structures
Vol. 3, No. Modern Alied Science Study on Characteristics of Sound Absortion of Underwater Visco-elastic Coated Comound Structures Zhihong Liu & Meiing Sheng College of Marine Northwestern Polytechnical
More informationResearch Article An iterative Algorithm for Hemicontractive Mappings in Banach Spaces
Abstract and Alied Analysis Volume 2012, Article ID 264103, 11 ages doi:10.1155/2012/264103 Research Article An iterative Algorithm for Hemicontractive Maings in Banach Saces Youli Yu, 1 Zhitao Wu, 2 and
More informationPartially Quenched Chiral Perturbation Theory and the Replica Method
Partially Quenched Chiral Perturbation Theory and the Relica Method P. H. Damgaard and K. Slittorff The Niels Bohr Institute Blegdamsvej 7 DK-200 Coenhagen Ø Denmark March 24, 2000 Abstract We describe
More informationA Simple And Efficient FEM-Implementation Of The Modified Mohr-Coulomb Criterion Clausen, Johan Christian; Damkilde, Lars
Aalborg Universitet A Simle And Efficient FEM-Imlementation Of The Modified Mohr-Coulomb Criterion Clausen, Johan Christian; Damkilde, Lars Published in: Proceedings of the 9th Nordic Seminar on Comutational
More informationNotes on Instrumental Variables Methods
Notes on Instrumental Variables Methods Michele Pellizzari IGIER-Bocconi, IZA and frdb 1 The Instrumental Variable Estimator Instrumental variable estimation is the classical solution to the roblem of
More informationThe non-stochastic multi-armed bandit problem
Submitted for journal ublication. The non-stochastic multi-armed bandit roblem Peter Auer Institute for Theoretical Comuter Science Graz University of Technology A-8010 Graz (Austria) auer@igi.tu-graz.ac.at
More informationEquivalence of Wilson actions
Prog. Theor. Ex. Phys. 05, 03B0 7 ages DOI: 0.093/te/tv30 Equivalence of Wilson actions Physics Deartment, Kobe University, Kobe 657-850, Jaan E-mail: hsonoda@kobe-u.ac.j Received June 6, 05; Revised August
More informationt 0 Xt sup X t p c p inf t 0
SHARP MAXIMAL L -ESTIMATES FOR MARTINGALES RODRIGO BAÑUELOS AND ADAM OSȨKOWSKI ABSTRACT. Let X be a suermartingale starting from 0 which has only nonnegative jums. For each 0 < < we determine the best
More informationThickness and refractive index measurements using multiple beam interference fringes (FECO)
Journal of Colloid and Interface Science 264 2003 548 553 Note www.elsevier.com/locate/jcis Thickness and refractive index measurements using multile beam interference fringes FECO Rafael Tadmor, 1 Nianhuan
More informationPositivity, local smoothing and Harnack inequalities for very fast diffusion equations
Positivity, local smoothing and Harnack inequalities for very fast diffusion equations Dedicated to Luis Caffarelli for his ucoming 60 th birthday Matteo Bonforte a, b and Juan Luis Vázquez a, c Abstract
More informationModeling and Estimation of Full-Chip Leakage Current Considering Within-Die Correlation
6.3 Modeling and Estimation of Full-Chi Leaage Current Considering Within-Die Correlation Khaled R. eloue, Navid Azizi, Farid N. Najm Deartment of ECE, University of Toronto,Toronto, Ontario, Canada {haled,nazizi,najm}@eecg.utoronto.ca
More informationThe effect of dynamic bending moments on the ratchetting behavior of stainless steel pressurized piping elbows
International Journal of echanical Engineering and Alications 2014; 2(2): 31-37 Published online ay 30, 2014 (htt://www.scienceublishinggrou.com/j/ijmea) doi: 10.11648/j.ijmea.20140202.12 The effect of
More informationAbstract. We perform a perturbative QCD analysis of the quark transverse momentum
BIHEP-TH-96-09 The erturbative ion-hoton transition form factors with transverse momentum corrections Fu-Guang Cao, Tao Huang, and Bo-Qiang Ma CCAST (World Laboratory), P.O.Box 8730, Beijing 100080, China
More informationMaximum Entropy and the Stress Distribution in Soft Disk Packings Above Jamming
Maximum Entroy and the Stress Distribution in Soft Disk Packings Above Jamming Yegang Wu and S. Teitel Deartment of Physics and Astronomy, University of ochester, ochester, New York 467, USA (Dated: August
More informationInformation collection on a graph
Information collection on a grah Ilya O. Ryzhov Warren Powell February 10, 2010 Abstract We derive a knowledge gradient olicy for an otimal learning roblem on a grah, in which we use sequential measurements
More informationA unified method to predict diffuse and localized instabilities in sands
Geomechanics and Geoengineering: An International Journal, 3 Vol. 8, No., 65 75, htt://dx.doi.org/.8/74865..69543 A unified method to redict diffuse and localized instabilities in sands WaiChing Sun* Mechanics
More informationGeneralized analysis method of engine suspensions based on bond graph modeling and feedback control theory
Generalized analysis method of ine susensions based on bond grah modeling and feedback ntrol theory P.Y. RICHARD *, C. RAMU-ERMENT **, J. BUION *, X. MOREAU **, M. LE FOL *** *Equie Automatique des ystèmes
More informationAdiabatic Shear Bands in Simple and Dipolar Plastic Materials
Adiabatic Shear Bands in Simle and Diolar Plastic Materials T W \-1RIGHT us Army Ballistic Research Laboratory Aberdeen Proving Ground, MD 215 R C BATRA University of Missouri-Rolla Rolla, Missouri 6541
More informationCanadian Geotechnical Journal. Dynamic modulus characteristics of saturated clays under variable confining pressure
Dynamic modulus characteristics of saturated clays under variable confining ressure Journal: Canadian Geotechnical Journal Manuscrit ID cgj-216-441.r1 Manuscrit Tye: Note Date Submitted by the Author:
More informationCONCRETE MATERIAL MODELING IN EXPLICIT COMPUTATIONS ABSTRACT
Worksho on Recent Advances in Comutational Structural Dynamics and High Performance Comuting USAE Waterways Exeriment Station Aril 24-26 1996 CONCRETE MATERIAL MODELING IN EXPLICIT COMPUTATIONS L. Javier
More informationMarangoni Convection in a Fluid Saturated Porous Layer with a Prescribed Heat Flux at its Lower Boundary
Euroean Journal of Scientific Research ISSN 145-16X Vol.4 No.4 (8),.477-486 EuroJournals Publishing, Inc. 8 htt://www.eurojournals.com/ejsr.htm Marangoni Convection in a Fluid Saturated Porous Layer with
More informationProbability Estimates for Multi-class Classification by Pairwise Coupling
Probability Estimates for Multi-class Classification by Pairwise Couling Ting-Fan Wu Chih-Jen Lin Deartment of Comuter Science National Taiwan University Taiei 06, Taiwan Ruby C. Weng Deartment of Statistics
More informationFlow liquefaction instability prediction using finite elements
Acta Geotechnica (215) 1:83 1 DOI 1.17/s1144-14-342-z RESEARCH PAPER Flow instability rediction using finite elements Toktam Mohammadnejad José E. Andrade Received: 14 November 213 / Acceted: 6 June 214
More informationINVESTIGATION OF CRACK OPENING IN ISOTROPIC STRAIN HARDENING MATERIAL
INVESTIGATION OF CRACK OPENING IN ISOTROPIC STRAIN HARDENING MATERIAL D. Pustaic ), M. Lovrenic-Jugovic ), H. Wolf ) ) University of Zagre, Faculty of Mechanical Engineering and Naval Architecture, Ivana
More informationON THE LEAST SIGNIFICANT p ADIC DIGITS OF CERTAIN LUCAS NUMBERS
#A13 INTEGERS 14 (014) ON THE LEAST SIGNIFICANT ADIC DIGITS OF CERTAIN LUCAS NUMBERS Tamás Lengyel Deartment of Mathematics, Occidental College, Los Angeles, California lengyel@oxy.edu Received: 6/13/13,
More informationShort Note. A simple derivation of the effective stress coefficient for seismic velocities in porous rocks. Boris Gurevich. n = 1 K 0 /K s, (4)
GEOPHYSICS, VOL. 69, NO. 2 (MARCH-APRIL 2004); P. 393 397, 1 FIG. 10.1190/1.1707058 Short Note A simple derivation of the effective stress coefficient for seismic velocities in porous rocks Boris Gurevich
More informationChapter-6: Entropy. 1 Clausius Inequality. 2 Entropy - A Property
hater-6: Entroy When the first law of thermodynamics was stated, the existence of roerty, the internal energy, was found. imilarly, econd law also leads to definition of another roerty, known as entroy.
More information