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Coulomb's Law (coulomb + law)
Selected AbstractsThe role of friction and secondary flaws on deflection and re-initiation of hydraulic fractures at orthogonal pre-existing fracturesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2006Xi Zhang SUMMARY In this study, we explore the nature of plane-strain hydraulic fracture growth in the presence of pre-existing fractures such as joints without or with secondary flaws. The 2-D plane-strain fracture studied can be taken as a cross-section through the short dimensions of an elongated 3-D fracture or as an approximate representation of the leading edge of a 3-D fracture where the edge curvature is negligible. The fluid-driven fracture intersects a pre-existing fracture to which it is initially perpendicular and is assumed not to immediately cross, but is rather deflected into the pre-existing fracture. The intersection results in branching of the fracture and associated fluid flow into the pre-existing fracture. Further growth results in opening and frictional sliding along the pre-existing fracture. Fracture propagation in an impermeable homogeneous elastic medium and fluid invasion into a pre-existing fracture are both driven by an incompressible, Newtonian fluid injected at a constant rate. The frictional stress on the surfaces of pre-existing fractures is assumed to obey the Coulomb law. The governing equations for quasi-static fluid-driven fracture growth are given and a scaling is introduced to help identify important parameters. The displacement discontinuity method and the finite difference method are employed to deal with this coupling mechanism of rock fracture and fluid flow. In order to account for fluid lag, a method for separately tracking the crack tip and the fluid front is included in the numerical model. Numerical results are obtained for internal pressure, frictional contact stresses, opening and shear displacements, and fluid lag size, as well as for fracture re-initiation from secondary flaws. After fracture intersection, the hydraulic fracture growth mode changes from tensile to shearing. This contributes to increased injection pressure and to a reduction in fracture width. In the presence of pre-existing fractures, the fluid-driven cracks can be arrested or retarded in growth rate as a result of diversion of fluid flow into and frictional sliding along the pre-existing fractures. Frictional behaviour significantly affects the ability of the fluid to enter or penetrate the pre-existing fracture only for those situations where the fluid front is within a certain distance from the intersecting point. Importantly, fluid penetration requires higher injection pressure for frictionally weak pre-existing fractures. Fracture re-initiation from secondary flaws can reduce the injection pressure, but re-initiation is suppressed by large sliding on pre-existing fractures that are frictionally weak. [source] Thermoelastic rolling contact problem with temperature dependent frictionPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Andrzej Chudzikiewicz The paper is concerned with the numerical solution of a thermoelastic rolling contact problem with wear. The friction between the bodies is governed by Coulomb law. A frictional heat generation and heat transfer across the contact surface as well as Archard's law of wear in contact zone are assumed. The friction coefficient is assumed to depend on temperature. In the paper quasistatic approach to solve this contact problem is employed. This approach is based on the assumption that for the observer moving with the rolling body the displacement of the supporting foundation is independent on time. The original thermoelastic contact problem described by the hyperbolic inequality governing the displacement and the parabolic equation governing the heat flow is transformed into elliptic inequality and elliptic equation, respectively. In order to solve numerically this system we decouple it into mechanical and thermal parts. Finite element method is used as a discretization method. Numerical examples showing the influence of the temperature dependent friction coefficient on the temperature distribution and the length of the contact zone are provided. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] The origins and present status of the radio wave controversy in NMRCONCEPTS IN MAGNETIC RESONANCE, Issue 4 2009D.I. Hoult Abstract The origins, history, and present status of the controversy surrounding a quantum description of the NMR signal as being due to radio waves are traced. With the Principle of Relativity and Coulomb's Law as formal starting points and the minimum of mathematics needed for understanding, the derivation of a classical electromagnetic theory of signal reception is first given. The agreement between that classical theory and a recent NMR experiment is then presented, leading to proof that, except for the highest field imaging experiments, there is no significant contribution of radio waves to the signal. Attention is drawn to the very different properties of the near and far energy, momenta, and fields inherent in the derivation. The role of the Correspondence Principle in formulating a quantum description is then emphasized and it is shown that the standard NMR interpretation of Dicke's theory of coherent spontaneous emission,that the latter is responsible for the NMR signal,cannot be correct. Finally, the author speculates on some of the intriguing relationships found in the classical electrodynamics of NMR signal reception and attempts to relate them to a common quantum electrodynamic precept of near field interaction: that the free induction decay voltage present at the terminals of an open-circuit receiving coil is based on an exchange of virtual photons between the nuclei in a sample and the free electrons in a receiving coil. © 2009 Crown in the right of Canada. Concepts Magn Reson Part A 34A: 193,216, 2009. [source] Explicitly correlated SCF study of anharmonic vibrations in (H2O)2INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2002Donald D. Shillady Abstract Modeling solvation in high-pressure liquid chromatography (HPLC) requires calculation of anharmonic vibrational frequencies of solvent clusters for a statistical partition function. An efficient computational method that includes electron correlation is highly desirable for large clusters. A modified version of the "soft Coulomb hole" method of Chakravorty and Clementi has recently been implemented in a Gaussian-lobe-orbital (GLO) program (PCLOBE) to include explicit electron,electron correlation in molecules. The soft Coulomb hole is based on a modified form of Coulomb's law: An algorithm has been developed to obtain the parameter "w" from a polynomial in the effective scaling of each primitive Gaussian orbital relative to the best single Gaussian of the H1s orbital. This method yields over 90% of the correlation energy for molecules of low symmetry for which the original formula of Chakravorty and Clementi does not apply. In this work, all the vibrations of the water dimer are treated anharmonically. A quartic perturbation of the harmonic vibrational modes is constrained to be equal to the exact Morse potential eigenvalue based on a three-point fit. This work evaluates the usefulness of fitting a Morse potential to a hydrogen bond vibrational mode and finds it to be slightly better than using MP2 vibrational analysis for this important dimer. A three-point estimate of the depth, De, of a Morse potential leads to a correction formula for anharmonicity in terms of the perturbed harmonic frequency: When scaled by 0.9141, the harmonic Morse method leads to essentially the same results as scaling the BPW91 local density method by 0.9827. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Lubricants under high local pressure: Liquids act like solidsMATERIALWISSENSCHAFT UND WERKSTOFFTECHNIK, Issue 10-11 2004M. H. MüserArticle first published online: 21 OCT 200 Schmierstoff; Druck; plastisches Fliessen; Reibungsgesetz Abstract A lubricant layer solidifies when it is confined between two walls at large normal pressures. The atomic scale motion that occurs when the two confining surfaces slide past each other induces flow in the lubricant layer that is akin of plastic flow. This results in friction-velocity relationships similar to Coulomb's law of friction. Moreover, the lubricant layer does not necessarily melt, even when the two solids are in stick slip motion. In this paper, atomic-scale details of the plastic flow mechanism are investigated by means of molecular dynamics simulations. Schmierstoffe unter hohem lokalem Druck: Flüssigkeiten verhalten sich wie Feststoffe Eine molekular dünne Schicht Schmierstoff verfestigt sich, wenn sie zwischen zwei Festkörpern großen Drücken ausgesetzt ist. Die atomaren Bewegungsmechanismen, die in dem Schmierstofffilm auftreten, wenn die Festkörper gegeneinander verschoben werden, können als plastisches Fliessen verstanden werden. Dieser Mechanismus führt zu einer Kraft-Geschwindigkeitsrelation, die dem Coulomb'schen Reibungsgesetz ähnlich ist. Selbst wenn die beiden Wände in Stick-Slip Bewegung sind, verflüssigt sich der Schmiermittelfilm nicht automatisch. In dieser Arbeit werden die Details des angesprochenen plastischen Fliessens anhand von Molekular-Dynamik Simulationen im Detail untersucht. [source] Distance dependence and salt sensitivity of pairwise, coulombic interactions in a proteinPROTEIN SCIENCE, Issue 5 2002Kelly K. Lee Abstract Histidine pKa values were measured in charge-reversal (K78E, K97E, K127E, and K97E/K127E) and charge-neutralization (E10A, E101A, and R35A) mutants of staphylococcal nuclease (SNase) by 1H-NMR spectroscopy. Energies of interaction between pairs of charges (,Gij) were obtained from the shifts in pKa values relative to wild-type values. The data describe the distance dependence and salt sensitivity of pairwise coulombic interactions. Calculations with a continuum electrostatics method captured the experimental ,Gij when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The ,Gij when rij , 10 Å were exaggerated slightly in the calculations. Coulomb's law with a dielectric constant near 80 and a Debye-Hückel term to account for screening by the ionic strength reproduced the salt sensitivity and distance dependence of ,Gij as well as the structure-based method. In their interactions with each other, surface charges behave as if immersed in water; the Debye length describes realistically the distance where interactions become negligible at a given ionic strength. On average, charges separated by distances (rij) ,5 Å interacted with ,Gij , 0.6 kcal/mole in 0.01 M KCl, but ,Gij decayed to ,0.10 kcal/mole when rij = 20 Å. In 0.10 M KCl, ,Gij , 0.10 kcal/mole when rij = 10 Å. In 1.5 M KCl, only short-range interactions with rij , 5 Å persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 Å are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects. [source] | ||||||||||