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Equilibrium Configurations (equilibrium + configuration)
Selected AbstractsEquilibrium states of magnetized toroid,central compact object systemsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2009Jun Otani ABSTRACT Equilibrium configurations of self-gravitating magnetized toroid,central compact object systems have been constructed in the framework of the Newtonian gravity. We have succeeded in including not only poloidal but also toroidal magnetic fields under the ideal magnetohydrodynamic approximation. We find two new and interesting results about the critical equilibrium states of such systems beyond which no equilibrium states are allowed to exist. First, there appear critical distances from the central compact objects to the inner surfaces of the magnetized toroids. Furthermore, these critical distances are much larger than the distances of the innermost stable circular orbits. It implies that even if these systems would be treated in the framework of general relativity, there would appear cusp structures of the effective total potential of the gravitational and magnetic forces for strongly magnetized toroids which are different from the general relativistic cusp structures. Secondly, since the strength of the magnetic field for the critical equilibrium configurations is roughly 1015 G if the mass of the central object is 1.4 M, and the maximum density of the toroid is 1011 g cm,3, the existence of equilibrium states of toroids around compact objects seems to set limit to the maximum value of the magnetic field of the system to be ,1015 G, i.e. no stronger magnetic fields can be realized for the systems consisting of magnetized toroids and central compact objects with the masses around the typical neutron star mass. The value of the maximum density of the toroid, 1011 g cm,3, is taken from the theoretical computational results of binary neutron star merging simulations in full general relativity. [source] Bifurcation and second-order work in geomaterialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2007François Nicot Abstract In this paper, the ability of a material rate-independent system to evolve toward another mechanical state from an equilibrium configuration, with no change in the control parameters, is investigated. From a mechanical point of view, this means that the system can spontaneously develop kinetic energy with no external disturbance from an equilibrium state, which corresponds to a particular case of bifurcation. The existence of both conjugate incremental strain and stress such that the second-order work vanishes is established as a necessary and sufficient condition for the appearance of this bifurcation phenomenon. It is proved that this fundamental result is independent of the constitutive relation of the rate-independent material considered. Then the case of homogeneous loading paths is investigated, and, as an illustration, the subsequent results are applied to interpret the well-known liquefaction observed under isochoric triaxial loading conditions with loose granular materials. Copyright © 2006 John Wiley & Sons, Ltd. [source] A phase-space method for arbitrary bimolecular gas-phase reactions: Theoretical descriptionINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2001A. Gross Abstract A theoretical model for the calculation of rate constants for arbitrary bimolecular gas-phase reactions was developed. The method is based on the phase-space statistical method developed by Light and co-workers 1,6. In the present article this method is extended to arbitrary molecular systems. The new method requires knowledge of the molecular properties in the reaction and products channels of the chemical system. The properties are the vibrational frequencies, moments of inertia, and potential energy for the interacting species in their ground state equilibrium configuration. Furthermore, we have to calculate either the energy barrier or the long-range potential for the chemical system (if the reaction channel does not have an energy barrier). The usefulness of the method is that it can be applied to all bimolecular reactions, trimolecular reactions, and even reactions of higher orders. Therefore, it can be applied to cases where rate constants of complex chemical reactions are required, but reliable laboratory measurements or other means to estimate rate parameters are not yet possible. Even if spectroscopic data are not available for the reactants and products, it is possible to use electronic structure theory to calculate the required data. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 [source] Passivity-based control of a magnetically levitated flexible beamINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 6 2009T. Shimizu Abstract This paper solves the asymptotic stabilization problem for a magnetically levitated flexible beam using a nested-loop passivity-based controller design. Passivity analyses reveal that the system can be decomposed into two passive subsystems: a mechanical subsystem that consists of a flexible beam with both ends free and that defines a passive map from external forces to the velocity of the points on the flexible beam at which the external forces act; and an electrical subsystem that consists of a pair of electromagnets and that defines a strictly output-passive map from voltages applied across the electromagnets to magnetic fluxes. The standard method for designing passivity-based controllers leads to a nonlinear feed-forward controller for the electrical subsystem, which enables the electrical subsystem to generate given desired magnetic forces, and an output feedback compensator for the mechanical subsystem, which computes the desired forces required to regulate the position and vibration of the beam. The asymptotic stability of each controller may be proven using Lyapunov's stability theory and LaSalle's invariant set theorem. Numerical simulations confirm the asymptotic stability of the equilibrium configuration of the closed-loop system formed by the magnetically levitated flexible beam together with the proposed controllers. Copyright © 2008 John Wiley & Sons, Ltd. [source] Stress-Driven Morphological Instabilities in Rocks, Glass, and CeramicsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 3 2007M. A. Grinfeld The purpose of this study is to further investigate the classical Gibbs analysis of the heterogeneous system "stressed crystal,melt." It is demonstrated that each equilibrium configuration is stable with respect to a special class of variations introduced by Gibbs. This basic result is compared with the opposite result on the universal morphological instability of phase interface separating a stressed crystal with its melt. Some plausible manifestations of the instabilities implied by the Gibbs model are qualitatively discussed. [source] Differences in Wetting Characteristics of Bi2O3 Polymorphs in ZnO Varistor MaterialsJOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 9 2000Mattias Elfwing Detailed analysis of the microstructure of grain boundaries, especially triple-grain and multiple-grain junctions, in ZnO varistor materials has been performed using transmission electron microscopy. Different polymorphs of Bi2O3 are shown to exhibit different wetting properties on ZnO interfaces. Recent investigations suggest that the equilibrium configuration consists of crystalline Bi2O3 in the triple-grain and multiple-grain junctions and an amorphous bismuth-rich film in the ZnO/ZnO grain boundaries. The present investigation supports this suggestion for ,-Bi2O3 and also adds to the microstructural image and wetting properties of ,-Bi2O3. [source] Frictional granular mechanics: A variational approachINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010R. Holtzman Abstract The mechanical properties of a cohesionless granular material are evaluated from grain-scale simulations. Intergranular interactions, including friction and sliding, are modeled by a set of contact rules based on the theories of Hertz, Mindlin, and Deresiewicz. A computer-generated, three-dimensional, irregular pack of spherical grains is loaded by incremental displacement of its boundaries. Deformation is described by a sequence of static equilibrium configurations of the pack. A variational approach is employed to find the equilibrium configurations by minimizing the total work against the intergranular loads. Effective elastic moduli are evaluated from the intergranular forces and the deformation of the pack. Good agreement between the computed and measured moduli, achieved with no adjustment of material parameters, establishes the physical soundness of the proposed model. Copyright © 2009 John Wiley & Sons, Ltd. [source] A relaxed model and its homogenization for nematic liquid crystals in composite materialsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2004Quan Shen Abstract We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen,Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non-linear. We employ two-scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd. [source] Equilibrium states of magnetized toroid,central compact object systemsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2009Jun Otani ABSTRACT Equilibrium configurations of self-gravitating magnetized toroid,central compact object systems have been constructed in the framework of the Newtonian gravity. We have succeeded in including not only poloidal but also toroidal magnetic fields under the ideal magnetohydrodynamic approximation. We find two new and interesting results about the critical equilibrium states of such systems beyond which no equilibrium states are allowed to exist. First, there appear critical distances from the central compact objects to the inner surfaces of the magnetized toroids. Furthermore, these critical distances are much larger than the distances of the innermost stable circular orbits. It implies that even if these systems would be treated in the framework of general relativity, there would appear cusp structures of the effective total potential of the gravitational and magnetic forces for strongly magnetized toroids which are different from the general relativistic cusp structures. Secondly, since the strength of the magnetic field for the critical equilibrium configurations is roughly 1015 G if the mass of the central object is 1.4 M, and the maximum density of the toroid is 1011 g cm,3, the existence of equilibrium states of toroids around compact objects seems to set limit to the maximum value of the magnetic field of the system to be ,1015 G, i.e. no stronger magnetic fields can be realized for the systems consisting of magnetized toroids and central compact objects with the masses around the typical neutron star mass. The value of the maximum density of the toroid, 1011 g cm,3, is taken from the theoretical computational results of binary neutron star merging simulations in full general relativity. [source] Models of S/, interactions in protein structures: Comparison of the H2S,benzene complex with PDB dataPROTEIN SCIENCE, Issue 10 2007Ashley L. Ringer Abstract S/, interactions are prevalent in biochemistry and play an important role in protein folding and stabilization. Geometries of cysteine/aromatic interactions found in crystal structures from the Brookhaven Protein Data Bank (PDB) are analyzed and compared with the equilibrium configurations predicted by high-level quantum mechanical results for the H2S,benzene complex. A correlation is observed between the energetically favorable configurations on the quantum mechanical potential energy surface of the H2S,benzene model and the cysteine/aromatic configurations most frequently found in crystal structures of the PDB. In contrast to some previous PDB analyses, configurations with the sulfur over the aromatic ring are found to be the most important. Our results suggest that accurate quantum computations on models of noncovalent interactions may be helpful in understanding the structures of proteins and other complex systems. [source] On the Thermodynamic Stability of Liquid Capillary BridgesTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 5 2007Janet Aw Elliott Abstract Capillary condensation is important in the behaviour of various materials encountered in nature and in industrial processes. The behaviour of liquid capillary bridges has mostly been investigated from a mechanical perspective, with an emphasis on computing the relevant adhesion forces. In the present paper, a thermodynamic approach is used, computing the free energy of such systems (based on numerically constructed shapes of liquid bridges) in order to determine the nature and properties of their equilibrium states. The dependence of the thermodynamic equilibrium configurations on the geometry of the system is investigated, and comparisons are made with experimental findings reported in the literature. La condensation capillaire est importante dans le comportement de divers matériaux rencontrés dans la nature et dans les procédés industriels. Le comportement des ponts capillaires liquides a surtout été étudié d'un point de vue mécanique, l'accent étant mis sur le calcul par ordinateur des forces d'adhésion pertinentes. Dans le présent article, on utilise une approche thermodynamique utilisant le calcul par ordinateur de l'énergie libre de tels systèmes (d'après les formes numériquement construites des ponts liquides), dans le but de déterminer la nature et les propriétés de leurs états d'équilibre. La dépendance des configurations d'équilibre thermodynamique sur la géométrie du système est étudiée, et des comparaisons sont faites avec les résultats expérimentaux présentés dans la littérature scientifique. [source] Link, twist, energy, and the stability of DNA minicirclesBIOPOLYMERS, Issue 2 2003Kathleen A. Hoffman Abstract We describe how the stability properties of DNA minicircles can be directly read from plots of various biologically intuitive quantities along families of equilibrium configurations. Our conclusions follow from extensions of the mathematical theory of distinguished bifurcation diagrams9, 21 that are applied within the specific context of an elastic rod model of minicircles. Families of equilibria arise as a twisting angle , is varied. This angle is intimately related to the continuously varying linking number Lk for nicked DNA configurations that is defined as the sum of Twist and Writhe. We present several examples of such distinguished bifurcation diagrams involving plots of the energy E, linking number Lk, and a twist moment m3, along families of cyclized equilibria of both intrinsically straight and intrinsically curved DNA fragments. © 2003 Wiley Periodicals, Inc. Biopolymers 70: 145,157, 2003 [source] | |||||||||||||