Academic literature on the topic 'Molecular Energy - Non-dynamical Correlation'
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Journal articles on the topic "Molecular Energy - Non-dynamical Correlation"
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Feng, Hai-Ran, Xiang-Jia Meng, Peng Li, and Yu-Jun Zheng. "Dynamical correlation between quantum entanglement and intramolecular energy in molecular vibrations: An algebraic approach." Chinese Physics B 23, no. 7 (July 2014): 073301. http://dx.doi.org/10.1088/1674-1056/23/7/073301.
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HWA, RUDOLPH C. "GEOMETRICAL AND DYNAMICAL MULTIPLICITY FLUCTUATIONS IN HIGH-ENERGY NUCLEAR COLLISIONS." International Journal of Modern Physics A 04, no. 02 (January 1989): 481–92. http://dx.doi.org/10.1142/s0217751x89000248.
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General properties of multiplicity fluctuation in high-energy nuclear collisions are considered. Quantities that can directly be related to the geometrical and dynamical sources of the fluctuation are identified. Formalism for treating impact-parameter selection is discussed. The connection with correlation is described. Recent data indicate the absence of any significant collective behavior in the current experiments at the SPS. The observable that can reveal the onset of such behavior is suggested.
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MAKRI, NANCY, AKIRA NAKAYAMA, and NICHOLAS J. WRIGHT. "FORWARD-BACKWARD SEMICLASSICAL SIMULATION OF DYNAMICAL PROCESSES IN LIQUIDS." Journal of Theoretical and Computational Chemistry 03, no. 03 (September 2004): 391–417. http://dx.doi.org/10.1142/s0219633604001112.
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Forward-backward semiclassical dynamics (FBSD) provides a practical methodology for including quantum mechanical effects in classical trajectory simulations of polyatomic systems. FBSD expressions for time-dependent expectation values or correlation functions take the form of phase space integrals with respect to trajectory initial conditions, weighted by the coherent state transform of a corrected density operator. Quantization through a discretized path integral representation of the Boltzmann operator ensures a proper treatment of zero point energy effects and of imaginary components in finite-temperature correlation functions, and extension to systems obeying Bose statistics is possible. Accelerated convergence is achieved via Monte Carlo or molecular dynamics sampling techniques and through the construction of improved imaginary time propagators. The accuracy of the methodology is demonstrated on several model systems, including models of Bose and Fermi particles. Applications to liquid argon, neon and para-hydrogen are presented.
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Jeffreson, Sarah M. R., J. M. Diederik Kruijssen, Benjamin W. Keller, Mélanie Chevance, and Simon C. O. Glover. "The role of galactic dynamics in shaping the physical properties of giant molecular clouds in Milky Way-like galaxies." Monthly Notices of the Royal Astronomical Society 498, no. 1 (July 24, 2020): 385–429. http://dx.doi.org/10.1093/mnras/staa2127.
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ABSTRACT We examine the role of the large-scale galactic-dynamical environment in setting the properties of giant molecular clouds in Milky Way-like galaxies. We perform three high-resolution simulations of Milky Way-like discs with the moving-mesh hydrodynamics code arepo, yielding a statistical sample of ${\sim}80\, 000$ giant molecular clouds and ${\sim}55\, 000$ H i clouds. We account for the self-gravity of the gas, momentum, and thermal energy injection from supernovae and H ii regions, mass injection from stellar winds, and the non-equilibrium chemistry of hydrogen, carbon, and oxygen. By varying the external gravitational potential, we probe galactic-dynamical environments spanning an order of magnitude in the orbital angular velocity, gravitational stability, mid-plane pressure, and the gradient of the galactic rotation curve. The simulated molecular clouds are highly overdense (∼100×) and overpressured (∼25×) relative to the ambient interstellar medium. Their gravoturbulent and star-forming properties are decoupled from the dynamics of the galactic mid-plane, so that the kpc-scale star formation rate surface density is related only to the number of molecular clouds per unit area of the galactic mid-plane. Despite this, the clouds display clear, statistically significant correlations of their rotational properties with the rates of galactic shearing and gravitational free-fall. We find that galactic rotation and gravitational instability can influence their elongation, angular momenta, and tangential velocity dispersions. The lower pressures and densities of the H i clouds allow for a greater range of significant dynamical correlations, mirroring the rotational properties of the molecular clouds, while also displaying a coupling of their gravitational and turbulent properties to the galactic-dynamical environment.
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Finn, Molly K., Remy Indebetouw, Kelsey E. Johnson, Allison H. Costa, C. H. Rosie Chen, Akiko Kawamura, Toshikazu Onishi, et al. "Structural and Dynamical Analysis of the Quiescent Molecular Ridge in the Large Magellanic Cloud." Astronomical Journal 164, no. 2 (July 21, 2022): 64. http://dx.doi.org/10.3847/1538-3881/ac7aa1.
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Abstract We present a comparison of low-J 13CO and CS observations of four different regions in the LMC—the quiescent Molecular Ridge, 30 Doradus, N159, and N113, all at a resolution of ∼3 pc. The regions 30 Dor, N159, and N113 are actively forming massive stars, while the Molecular Ridge is forming almost no massive stars, despite its large reservoir of molecular gas and proximity to N159 and 30 Dor. We segment the emission from each region into hierarchical structures using dendrograms and analyze the sizes, masses, and line widths of these structures. We find that the Ridge has significantly lower kinetic energy at a given size scale and also lower surface densities than the other regions, resulting in higher virial parameters. This suggests that the Ridge is not forming massive stars as actively as the other regions because it has less dense gas and not because collapse is suppressed by excess kinetic energy. We also find that these physical conditions and energy balance vary significantly within the Ridge and that this variation appears only weakly correlated with distance from sites of massive-star formation such as R136 in 30 Dor, which is ∼1 kpc away. These variations also show only a weak correlation with local star formation activity within the clouds.
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Inoue, Hajime. "Wandering of the central black hole in a galactic nucleus and correlation of the black hole mass with the bulge mass." Publications of the Astronomical Society of Japan 73, no. 2 (February 16, 2021): 431–38. http://dx.doi.org/10.1093/pasj/psab009.
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Abstract We investigate a mechanism for a super-massive black hole at the center of a galaxy to wander in the nucleus region. A situation is supposed in which the central black hole tends to move by the gravitational attractions from the nearby molecular clouds in a nuclear bulge but is braked via the dynamical frictions from the ambient stars there. We estimate the approximate kinetic energy of the black hole in an equilibrium between the energy gain rate through the gravitational attractions and the energy loss rate through the dynamical frictions in a nuclear bulge composed of a nuclear stellar disk and a nuclear stellar cluster as observed from our Galaxy. The wandering distance of the black hole in the gravitational potential of the nuclear bulge is evaluated to get as large as several 10 pc, when the black hole mass is relatively small. The distance, however, shrinks as the black hole mass increases, and the equilibrium solution between the energy gain and loss disappears when the black hole mass exceeds an upper limit. As a result, we can expect the following scenario for the evolution of the black hole mass: When the black hole mass is smaller than the upper limit, mass accretion of the interstellar matter in the circumnuclear region, causing the AGN activities, makes the black hole mass larger. However, when the mass gets to the upper limit, the black hole loses the balancing force against the dynamical friction and starts spiraling downward to the gravity center. From simple parameter scaling, the upper mass limit of the black hole is found to be proportional to the bulge mass, and this could explain the observed correlation of the black hole mass with the bulge mass.
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Bonačič-Koutecký, Vlasta, Detlef Reichardt, Jiří Pittner, Piercarlo Fantucci, and Jaroslav Koutecký. "Ab initio Molecular Dynamics for Determination of Structures of Alkali Metal Clusters and Their Temperatures Behavior; An Example of Li9+." Collection of Czechoslovak Chemical Communications 63, no. 9 (1998): 1431–46. http://dx.doi.org/10.1135/cccc19981431.
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It will be shown that an ab initio molecular dynamics procedure based on gradient corrected density functionals for exchange and correlation and using a Gaussian atomic basis (AIMD-GDF) implemented for parallel processing represents a suitable tool for detailed and accurate investigation of structural and dynamical properties of small systems. Gradients of the Born-Oppenheimer ground state energy, obtained by iterative solution of the Kohn-Sham equations, are used to calculate the forces acting on atoms at each instantaneous configuration along trajectories generated by solving classical equations of motion. Dynamics of different isomers of the Li9+ cluster have been investigated as a function of excess energy. It is shown that different isomers, even those similar in energy, can exhibit different structural and dynamical behavior. The analysis of the simulations leads to the conclusion that structures with a central atom, in particular the centered antiprism of Li9+ exhibit concerted mobility of the peripheral atoms at relatively low excess energy. In contrast, compact tetrahedral type structures show much more rigid behavior at low excess energy. However, the former ones need larger excess of internal energy to undergo isomerizations to geometrically different structures than the latter ones. At the time scale of our simulations we found that for the intermediate excess energies it is "easier" to carry the cluster in the basin of the lowest energy isomer than in the reverse direction. It has been found that the liquid-like behavior in small Li clusters becomes apparent at relatively high temperature in spite of large mobility of their atoms.
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Yuan, Qiang, and Xi-Wen Hou. "Entropy, energy, and entanglement of localized states in bent triatomic molecules." International Journal of Modern Physics B 31, no. 12 (May 10, 2017): 1750088. http://dx.doi.org/10.1142/s0217979217500886.
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The dynamics of quantum entropy, energy, and entanglement is studied for various initial states in an important spectroscopic Hamiltonian of bent triatomic molecules H2O, D2O, and H2S. The total quantum correlation is quantified in terms of the mutual information and the entanglement by the concurrence borrowed from the theory of quantum information. The Pauli entropy and the intramolecular energy usually used in the theory of molecules are calculated to establish a possible relationship between both theories. Sections of two quantities among these four quantities are introduced to visualize such relationship. Analytic and numerical simulations demonstrate that if an initial state is taken to be the stretch- or the bend-vibrationally localized state, the mutual information, the Pauli entropy, and the concurrence are dominant-positively correlated while they are dominantly anti-correlated with the interacting energy among three anharmonic vibrational modes. In particular, such correlation is more distinct for the localized state with high excitations in the bending mode. The nice quasi-periodicity of those quantities in D2O molecule reveals that this molecule prepared in the localized state in the stretching or the bending mode can be more appreciated for molecular quantum computation. However, the dynamical correlations of those quantities behave irregularly for the dislocalized states. Moreover, the hierarchy of the mutual information and the Pauli entropy is explicitly proved. Quantum entropy and energy in every vibrational mode are investigated. Thereby, the relation between bipartite and tripartite entanglements is discussed as well. Those are useful for the understanding of quantum correlations in high-dimensional states in polyatomic molecules from quantum information and intramolecular dynamics.
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Falgarone, E. "Turbulence in Interstellar Clouds." International Astronomical Union Colloquium 120 (1989): 68–79. http://dx.doi.org/10.1017/s0252921100023496.
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Above masses of the order of lOO M⊙, molecular clouds have masses and sizes which scale like those of self-gravitating polytropes bounded by an external pervading pressure. It is unlikely that this scaling is due to mere observational bias. But the physics underlying this behaviour is far from being understood. In particular, the possible contribution of turbulence to both the ambient pressure and the internal pressure (whose dependence with the density would mimic a polytropic behavior) is a difficult and much debated issue. The clouds mass, size and internal velocity dispersion are such that they are observed to be in approximate virial balance between their self-gravity, the surface energy term due to the ambient pressure and their internal energy. The latter is dominated by the kinetic energy of disordered internal motions. However, there has been little evidence so far that these motions are actually turbulent rather than simply disordered. The transition to turbulence in a flow occurs when the non linear advection term in the momentum equation, v.Δv, considerably exceeds the viscous dissipation term, vΔv (where v is the kinematic viscosity). Non linearities therefore dominate the physics of a turbulent flow and the velocities are not randomly distributed. Most of the previous attempts to determine a well-defined correlation length in the velocity field (Kleiner and Dickman 1985, a and b; Scalo 1984), which is predicted to be close to the scale at which the energy is injected, or to characterize the expected hierarchical structure (Pérault et al. 1986) have been plagued by the lack of dynamical range in the data set and the range of scales over which the correlation functions have been computed. The most plausible determination, that of Kleiner and Dickman (1987) who claim to have found a correlation length of 0.2 pc in the Taurus cloud, gives a result which is so close to the angular resolution of the observations that it is doubtful.
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Toscano, Giuseppe, and Daniele Duca. "RENEWABLE ENERGY CONTENT OF FATTY ACID METHYL ESTERS (FAME) AND GLYCEROL." Journal of Agricultural Engineering 40, no. 4 (December 31, 2009): 47. http://dx.doi.org/10.4081/jae.2009.90.
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Fatty acid methyl esters (FAME) and glycerol produced by transesterification reaction contain atoms that in the reagents belong to methanol and, therefore, are not renewable. A method to evaluate the content of the renewable and non-renewable energetic fraction, released during their combustion, was 52 Fig. 2 - Correlation between EFNR and NCM of FAME. Fig. 3 - Correlation between NCM and NS. Fig. 4 - Correlations between EFNR and NS. 07_Toscano(541)_47 26-01-2010 9:35 Pagina 52 developed using a thermochemical criteria, based on bond dissociation energies and the knowledge of the molecular structure of the reagents and the products. Results show that the fraction of non-renewable energy in the most diffused FAME is lower than 1% depending on the lengths of the carbonaceous methyl esters. Meanwhile, the energetic supply for the GL of this fraction is about 1.6%. The data reported in this document can be used to develop a criteria that corrects the fiscal mechanism aspects of some renewable energy products.
Books on the topic "Molecular Energy - Non-dynamical Correlation"
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Thygesen, K. S., and A. Rubio. Correlated electron transport in molecular junctions. Edited by A. V. Narlikar and Y. Y. Fu. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199533046.013.23.
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This article focuses on correlated electron transport in molecular junctions. More specifically, it considers how electronic correlation effects can be included in transport calculations using many-body perturbation theory within the Keldysh non-equilibrium Green’s function formalism. The article uses the GW self-energy method (G denotes the Green’s function and W is the screened interaction) which has been successfully applied to describe quasi-particle excitations in periodic solids. It begins by formulating the quantum-transport problem and introducing the non-equilibrium Green’s function formalism. It then derives an expression for the current within the NEGF formalism that holds for interactions in the central region. It also combines the GW scheme with a Wannier function basis set to study electron transport through two prototypical junctions: a benzene molecule coupled to featureless leads and a hydrogen molecule between two semi-infinite platinum chains. The results are analyzed using a generic two-level model of a molecular junction.
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Nitzan, Abraham. Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.001.0001.
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This text provides a uniform and consistent approach to diversified problems encountered in the study of dynamical processes in condensed phase molecular systems. Given the broad interdisciplinary aspect of this subject, the book focuses on three themes: coverage of needed background material, in-depth introduction of methodologies, and analysis of several key applications. The uniform approach and common language used in all discussions help to develop general understanding and insight on condensed phases chemical dynamics. The applications discussed are among the most fundamental processes that underlie physical, chemical and biological phenomena in complex systems. The first part of the book starts with a general review of basic mathematical and physical methods (Chapter 1) and a few introductory chapters on quantum dynamics (Chapter 2), interaction of radiation and matter (Chapter 3) and basic properties of solids (chapter 4) and liquids (Chapter 5). In the second part the text embarks on a broad coverage of the main methodological approaches. The central role of classical and quantum time correlation functions is emphasized in Chapter 6. The presentation of dynamical phenomena in complex systems as stochastic processes is discussed in Chapters 7 and 8. The basic theory of quantum relaxation phenomena is developed in Chapter 9, and carried on in Chapter 10 which introduces the density operator, its quantum evolution in Liouville space, and the concept of reduced equation of motions. The methodological part concludes with a discussion of linear response theory in Chapter 11, and of the spin-boson model in chapter 12. The third part of the book applies the methodologies introduced earlier to several fundamental processes that underlie much of the dynamical behaviour of condensed phase molecular systems. Vibrational relaxation and vibrational energy transfer (Chapter 13), Barrier crossing and diffusion controlled reactions (Chapter 14), solvation dynamics (Chapter 15), electron transfer in bulk solvents (Chapter 16) and at electrodes/electrolyte and metal/molecule/metal junctions (Chapter 17), and several processes pertaining to molecular spectroscopy in condensed phases (Chapter 18) are the main subjects discussed in this part.
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Holubec, Viktor. Non-Equilibrium Energy Transformation Processes: Theoretical Description at the Level of Molecular Structures. Springer London, Limited, 2014.
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Non-equilibrium Energy Transformation Processes: Theoretical Description at the Level of Molecular Structures. Springer, 2014.
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Holubec, Viktor. Non-Equilibrium Energy Transformation Processes: Theoretical Description at the Level of Molecular Structures. Springer International Publishing AG, 2016.
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Henriksen, Niels E., and Flemming Y. Hansen. Theories of Molecular Reaction Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.001.0001.
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This book deals with a central topic at the interface of chemistry and physics—the understanding of how the transformation of matter takes place at the atomic level. Building on the laws of physics, the book focuses on the theoretical framework for predicting the outcome of chemical reactions. The style is highly systematic with attention to basic concepts and clarity of presentation. Molecular reaction dynamics is about the detailed atomic-level description of chemical reactions. Based on quantum mechanics and statistical mechanics or, as an approximation, classical mechanics, the dynamics of uni- and bimolecular elementary reactions are described. The first part of the book is on gas-phase dynamics and it features a detailed presentation of reaction cross-sections and their relation to a quasi-classical as well as a quantum mechanical description of the reaction dynamics on a potential energy surface. Direct approaches to the calculation of the rate constant that bypasses the detailed state-to-state reaction cross-sections are presented, including transition-state theory, which plays an important role in practice. The second part gives a comprehensive discussion of basic theories of reaction dynamics in condensed phases, including Kramers and Grote–Hynes theory for dynamical solvent effects. Examples and end-of-chapter problems are included in order to illustrate the theory and its connection to chemical problems. The book has ten appendices with useful details, for example, on adiabatic and non-adiabatic electron-nuclear dynamics, statistical mechanics including the Boltzmann distribution, quantum mechanics, stochastic dynamics and various coordinate transformations including normal-mode and Jacobi coordinates.
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Billing, Gert D., ed. The Quantum Classical Theory. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195146196.001.0001.
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Over a period of fifty years, the quantum-classical or semi-classical theories have been among the most popular for calculations of rates and cross sections for many dynamical processes: energy transfer, chemical reactions, photodissociation, surface dynamics, reactions in clusters and solutions, etc. These processes are important in the simulation of kinetics of processes in plasma chemistry, chemical reactors, chemical or gas lasers, atmospheric and interstellar chemistry, as well as various industrial processes. This book gives an overview of quantum-classical methods that are currently used for a theoretical description of these molecular processes. It gives the theoretical background for the derivation of the theories from first principles. Enough details are provided to allow numerical implementation of the methods. The book gives the necessary background for understanding the approximations behind the methods and the working schemes for treating energy transfer processes from diatomic to polyatomic molecules, reactions at surfaces, non-adiabatic processes, and chemical reactions.
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Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.
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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.
Book chapters on the topic "Molecular Energy - Non-dynamical Correlation"
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Pulay, Péter, and Svein Saebø. "Strategies of Gradient Evaluation for Dynamical Electron Correlation." In Geometrical Derivatives of Energy Surfaces and Molecular Properties, 95–107. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4584-5_7.
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Ramane, Harishchandra S. "Energy of Graphs." In Handbook of Research on Advanced Applications of Graph Theory in Modern Society, 267–96. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-5225-9380-5.ch011.
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The energy of a graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The graph energy has close correlation with the total pi-electron energy of molecules calculated with Huckel molecular orbital method in chemistry. A graph whose energy is greater than the energy of complete graph of same order is called hyperenergetic graph. A non-complete graph having energy equal to the energy of complete graph is called borderenergetic graph. Two non-cospectral graphs are said to be equienergetic graphs if they have same energy. In this chapter, the results on graph energy are reported. Various bounds for graph energy and its characterization are summarized. Construction of hyperenergetic, borderenergetic, and equienergetic graphs are reported.
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Tuck, Adrian F. "Temperature Intermittency and Ozone Photodissociation." In Atmospheric Turbulence. Oxford University Press, 2008. http://dx.doi.org/10.1093/oso/9780199236534.003.0008.
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During the last two missions performed by the ER-2 in the Arctic lower stratosphere, POLARIS in the summer of 1997 and SOLVE during the winter of 1999–2000, an unexpected correlation emerged when the data were subjected to analysis by generalized scale invariance. It was between the intermittency of temperature, a number which can be determined for each segment of analysable flight from the temperature measurements, and the average over the flight segment of the photodissociation rate of ozone, which was calculable as a time series along the flight segment by taking the product of the 1Hz measurements of the local ozone concentration and the 1Hz measurements of the ozone photodissociation coefficient. In searching for a physical explanation of this correlation, it was realized that the common link between the quantities was that ozone photodissociation produces photofragments of atomic and molecular oxygen that recoil very fast, while temperature itself is the integral of the translational energy of all air molecules. The next step therefore was to ask if the intermittency of temperature was correlated with the average of the temperature itself over the flight segment: it was. One might think that because ozone is present at about 20km altitude in mixing ratios of about 2−3×10−6, the rapid quenching of the translational energies of the recoiling photofragments by molecular nitrogen and molecular oxygen would prevent any possible effects from showing up in the bulk, observed temperature. However, during the POLARIS mission, it was possible to fly the ER-2 near the terminator, the boundary between day and night, because at Arctic latitudes the planet was rotating slowly enough that it could fly legs in the same, stagnant air mass in both sunlight and darkness. These flights showed that the heating rate was significant, about 0.2Kper hour, and since heating in the stratosphere arises from the absorption of solar radiation by ozone, which leads to photodissociation, there is a prima facie case for considering non-local thermodynamic equilibrium effects from the recoiling fast photofragments. Two arguments may be deployed at this point, both from the theoretical literature; there are as yet no experiments on the translational speed distributions of atmospheric molecules.
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Dyall, Kenneth G., and Knut Faegri. "Correlation Methods." In Introduction to Relativistic Quantum Chemistry. Oxford University Press, 2007. http://dx.doi.org/10.1093/oso/9780195140866.003.0018.
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It is well known from nonrelativistic quantum chemistry that mean-field methods, such as the Hartree–Fock (HF) model, provide mainly qualitative insights into the electronic structure and bonding of molecules. To obtain reliable results of “chemical accuracy” usually requires models that go beyond the mean field and account for electron correlation. There is no reason to expect that the mean-field approach should perform significantly better in this respect for the relativistic case, and so we are led to develop schemes for introducing correlation into our models for relativistic quantum chemistry. There is no fundamental change in the concept of correlation between relativistic and nonrelativistic quantum chemistry: in both cases, correlation describes the difference between a mean-field description, which forms the reference state for the correlation method, and the exact description. We can also define dynamical and nondynamical correlation in both cases. There is in fact no formal difference between a nonrelativistic spin–orbital-based formalism and a relativistic spinor-based formalism. Thus we should be able to transfer most of the schemes for post-Hartree–Fock calculations to a relativistic post-Dirac–Hartree–Fock model. Several such schemes have been implemented and applied in a range of calculations. The main technical differences to consider are those arising from having to deal with integrals that are complex, and the need to replace algorithms that exploit the nonrelativistic spin symmetry by schemes that use time-reversal and double-group symmetry. In addition to these technical differences, however, there are differences of content between relativistic and nonrelativistic methods. The division between dynamical and nondynamical correlation is complicated by the presence of the spin–orbit interaction, which creates near-degeneracies that are not present in the nonrelativistic theory. The existence of the negative-energy states of relativistic theory raise the question of whether they should be included in the correlation treatment. The first two sections of this chapter are devoted to a discussion of these issues. The main challenges in the rest of this chapter are to handle the presence of complex integrals and to exploit time-reversal symmetry.
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Drickamer, H. G. "Pressure-Tuning Spectroscopy: A Tool for Investigating Molecular Interactions." In High Pressure Effects in Molecular Biophysics and Enzymology. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195097221.003.0005.
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Pressure-tuning spectroscopy is a powerful tool for investigating molecular interactions. These interactions may involve organic or inorganic materials in liquid, polymeric, or crystalline media. In this article we confine our attention to organic molecules, largely in dilute solution in polymers or liquids. We demonstrate the use of high-pressure luminescence to study the effect of the environment on π* →π, π* →n and charge-transfer excitations, as well as the interaction between singlet and triplet states. In addition, we provide tests of the energy gap law for non-radiative dissipation of excitation, the role of viscosity in luminescent efficiency, and the internal consistency of various means of predicting and correlating energy transfer. Over the past 40 years, it has been amply demonstrated that high pressure is a powerful tool for studying electronic phenomena in condensed phases. The basic concept is as follows. The optical, electrical, magnetic, and chemical properties—collectively the electronic properties—of condensed phases depend on the interactions of the outer electrons on the atoms, molecules, or ions that make up the phase. Different kinds of electronic orbitals have different spatial characteristics—different radial extent, different shape (orbital angular momentum), and different diffuseness; therefore, pressure perturbs the energies associated with these orbitals in different degrees. This relative perturbation we call “pressure tuning,” and the measurement and explanation of the tuning is “pressure-tuning spectroscopy.” Pressure-tuning spectroscopy of the vibrational and rotational excitations of atoms in molecular and in crystal lattices is also an active and important field, but in this article we arc concerned mainly with electronic phenomena. We further limit this discussion primarily to organic molecules in solid polymers or liquid solutions, as these have the greatest relevance to biologically active systems. A variety of probes are used for studying electronic phenomena under high pressure, but the emphasis here is on luminescence. The presentation consists of a series of examples of various types of excitations on interactions where high pressure has been an effective tool. Only references directly relevant to each example are included. Two general references to pressure studies of molecular luminescence have been published (Drickamer, 1982, 1990).
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Liu, S., I. Grinberg, and A. M. Rappe. "Multiscale Simulations of Domains in Ferroelectrics." In Domain Walls, 311–39. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198862499.003.0014.
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This chapter focuses on recent studies of ferroelectrics, where large-scale molecular dynamics (MD) simulations using first-principles-based force fields played a central role in revealing important physics inaccessible to direct density functional theory (DFT) calculations but critical for developing physically-based free energy functional for coarse-grained phase-field-type simulations. After reviewing typical atomistic potentials of ferroelectrics for MD simulations, the chapter describes a progressive theoretical framework that combines DFT, MD, and a mean-field theory. It then focuses on relaxor ferroelectrics. By examining the spatial and temporal polarization correlations in prototypical relaxor ferroelectrics with million-atom MD simulations and novel analysis techniques, this chapter shows that the widely accepted model of polar nanoregions embedded in a non-polar matrix is incorrect for Pb-based relaxors. Rather, the unusual properties of theses relaxor ferroelectrics stem from the presence of a multi-domain state with extremely small domain sizes (2–10 nanometers), giving rise to a greater flexibility for polarization rotations and the ultrahigh dielectric and piezoelectric responses. Finally, this chapter discusses the challenges and opportunities for multiscale simulations of ferroelectric materials.
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Zinn-Justin, Jean. "O(2) spin model and the Kosterlitz–Thouless’s phase transition." In Quantum Field Theory and Critical Phenomena, 747–59. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198834625.003.0031.
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At low temperature, the large distance properties of the O(2) spin lattice model can be described by the O(2) non-linear σ-model. The latter model is free and massless in two dimensions. The origin of this peculiarity can be found in the local structure of the field manifold: for N = 2, the O(N) sphere reduces to a circle, which cannot be distinguished locally from a straight line. Because the physical fields are sin θ or cos θ, or equivalently e± iθ, instead of θ, a field renormalization is necessary, and temperature-dependent anomalous dimensions are generated. However, the free θ action cannot describe the long-distance properties of the lattice model for all temperatures, since a high temperature analysis of the corresponding spin model shows that the correlation length is finite at high temperature, and thus a phase transition is required. In fact, it is necessary to take into account the property that θ is a cyclic variable. This condition is irrelevant at low temperature, but when the temperature increases, classical configurations with singularities at isolated points, around which θ varies by a multiple of 2π become important. The action of these configurations (vortices) can be identified with the energy of a neutral Coulomb gas, which exhibits a transition between a low temperature of bound neutral molecules and a high temperature phase of a plasma of free charges. The Coulomb gas can be mapped onto the sine-Gordon (sG) model, mapping in which the low- and high-temperature regions of the models are exchanged. This correspondence helps to understand some properties of the famous Kosterlitz-Thouless (KT) phase transition, which separates an infinite correlation length phase without order, the low-temperature phase of the O(2) spin model, from a finite correlation length phase, the high-temperature phase of the O(2) spin model.
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Schäfer, Lothar, and John D. Ewbank. "On Comparing Experimental and Calculated Structural Parameters." In Molecular Orbital Calculations for Biological Systems. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195098730.003.0010.
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The tacit assumption underlying all science is that, of two competing theories, the one in closer agreement with experiment is the better one. In structural chemistry the same principle applies but, when calculated and experimental structures are compared, closer is not necessarily better. Structures from ab initio calculations, specifically, must not be the same as the experimental counterparts the way they are observed. This is so because ab initio geometries refer to nonexistent, vibrationless states at the minimum of potential energy, whereas structural observables represent specifically defined averages over distributions of vibrational states. In general, if one wants to make meaningful comparisons between calculated and experimental molecular structures, one must take recourse of statistical formalisms to describe the effects of vibration on the observed parameters. Among the parameters of interest to structural chemists, internuclear distances are especially important because other variables, such as bond angles, dihedral angles, and even crystal spacings, can be readily derived from them. However, how a rigid torsional angle derived from an ab initio calculation compares with the corresponding experimental value in a molecule subject to vibrational anharmonicity, is not so easy to determine. The same holds for the lattice parameters of a molecule in a dynamical crystal, and their temperature dependence as a function of the molecular potential energy surface. In contrast, vibrational effects are readily defined and best described for internuclear distances, bonded and non-bonded ones. In general, all observed internuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. To illustrate how the operations of an experimental technique affect the nature of its observables, gas electron diffraction shall be used as an example.
Conference papers on the topic "Molecular Energy - Non-dynamical Correlation"
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Bronk, Burt V., Michael J. Smith, and Steve Arnold. "Inclusions in a Micron Sized Electrodynamically Levitated Droplet." In Photon Correlation and Scattering. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/pcs.1992.pd1.
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The development of the quadrupole levitation balance, has led spectroscopic studies of the characteristics of levitated micron-sized droplets(1-7). Experiments not available for other systems arise with this "world's smallest test-tube". In one example it was shown that very high-Q modes occuring for electromagnetic radiation in these nearly perfect spheres permits highly efficient transfer of energy between molecules seperated by distances far larger than those characteristic for Foerster transfer(8). In another application, the possibility of using a sufficiently small droplet consisting of a non-fluorescent solvent as host with one or a few fluorescent molecules present was shown to allow detection of the presence of a single molecule of rhodamine(9).
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THOMAS, FRANK DAVID, SREEHARI RAJAN, MICHAEL A. SUTTON, STEPHEN L. ALEXANDER, TUSIT WEERASOORIYA, and SUBRAMANI SOCKALINGAM. "INTERLAMINAR SHEAR BEHAVIOR OF UHMWPE TENSYLON® COMPOSITES IN QUASI-STATIC MODE II LOADING." In Proceedings for the American Society for Composites-Thirty Seventh Technical Conference. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/asc37/36482.
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Ultrahigh molecular weight polyethylene (UHMWPE) film composite materials such as Tensylon® HSBD30A are useful for ballistic applications, but quantification of their interlaminar shear behavior is necessary to inform design considerations. This study investigates a double lap shear specimen to determine mode II interlaminar shear properties. Average shear stresses calculated from measured loads and relative displacements calculated from full-field displacement data obtained via digital image correlation are used to produce an approximate traction-separation law. For a representative specimen, interfacial shear strength is calculated to be 3.18 MPa, mode II critical energy release rate is 465 J/m2, and interfacial stiffness is 36.8 MPa/mm. The double lap shear specimen is found to be appropriate for approximating these values, but the potential for complex loading states caused by non-simultaneous crack growth necessitates further investigation into alternative specimen configurations.
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Banjak, Sary, and Vadim Savva. "Coherent Dynamics of Quantum Systems with Non-Uniform Fourier Space Excited by Laser Radiation." In 3rd International Conference of Mathematics and its Applications. Salahaddin University-Erbil, 2020. http://dx.doi.org/10.31972/ticma22.09.
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The algorithm is presented to solve dynamical equations for excitation of molecular models with multiple energy levels. It uses only discrete structures: discrete orthogonal polynomials constructed specially in Fourier space of the probability amplitudes, discrete Fourier transform and leads to exact solution of the differential equations and to discrete distribution of the quantum systems by energy levels.
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Pollard, W. Thomas, and Richard A. Mathies. "Wavepacket Theory of Femtosecond Dynamic Absorption Spectroscopy." In International Conference on Ultrafast Phenomena. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/up.1990.wc18.
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By measuring the spectrum of the probe pulse, rather than just its energy, Shank and coworkers have demonstrated how to take advantage of the large spectral width of the fastest femtosecond pulses to obtain complete time-resolved absorption spectra of coherently evolving molecules on a 6 fs timescale.1 To provide a quantitative analysis of these experiments, we have formulated the perturbative density matrix theory for the third order susceptibility of a multi-level system in terms of four-time correlation functions which can be interpreted as the time-dependent overlap of bra and ket vibrational wavepackets propagating independently on the ground and excited state electronic potential surfaces.2 When vibrational motion during the excitation is minimal, or when the pump pulse is shorter than the optical T2, the system will be prepared in an essentially pure state. The time-resolved differential absorption spectrum can then be treated as the first-order spectroscopy of the non-stationary state created by the pump pulse.
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Gupta, T. C., and K. Gupta. "Correlation of Parameters to Instability and Chaos of a Horizontal Flexible Rotor Ball Bearing System." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-95308.
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The higher order effects from ball bearing nonlinearities cause complex vibration characteristics in rotor ball bearing systems. The sources of nonlinearities are internal radial clearance, Hertzian contact forces between balls and races and varying compliance effect. The same authors in their earlier work have identified the sets of parameters corresponding to instability and chaos for a horizontal flexible rotor supported on deep groove ball bearing. To the best of author’s knowledge, there is not much work reported in the literature on the dynamic analysis for instability and chaos, which is based on energy functions and bearing loads. Extending the preceding research work in the present paper by using a typical set of parameters and specifications of rotor ball bearing system, a correlation of parameters to instability and chaos is attempted using different energy functions associated with the dynamical system. A generalized Timoshenko beam finite element formulation is used to model the flexible rotor shaft. To achieve the convergence of solution with smaller number of elements, shape functions are derived from the exact solutions of governing differential equations of Timoshenko beam element. The sources of excitation are rotating unbalance and parametric excitation due to varying compliance of ball bearing during motion. For the bearing used in the present paper, the ratio of these excitation frequencies comes out to be an irrational number. Therefore, the dynamic response would be quasi-periodic with time period equal to infinity. To extend the use of non-autonomous shooting method to derive quasi-periodic solution, the fixed point algorithm (FPA) proposed in the literature is used to deduce the time period for non-autonomous shooting algorithm. The shooting method otherwise is used only to derive periodic solutions. Thus the non-autonomous shooting method coupled with fixed point algorithm (FPA) is used to compute the quasi-periodic solution, which also gives the monodromy matrix. The eigenvalues of the monodromy matrix, called Floqoet multipliers, give information about instability. The chaotic nature of the dynamic response is established by the maximum value of Lyapunov exponent. Once the instability and chaos is confirmed based on computed values of Floquet multipliers and Lyapunov exponents, the nature of the work done (positive or negative) by different conservative and non-conservative forces and moments during motion are analyzed and the fundamental causes, which make the system response unstable and / or chaotic, are established.
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Passino, Sean A., Yutaka Nagasawa, Taiha Joo, and Graham R. Fleming. "Photon echo measurements in liquids using pulses longer than the electronic dephasing time." In International Conference on Ultrafast Phenomena. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/up.1996.wd.4.
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Liquid dynamics has been studied by various time-domain techniques such as photon echoes [1] and dynamic Stokes shift measurement [2], which utilize electronic absorption as a probe. Attempts to measure electronic dephasing times in solution using the standard photon echo technique have been hampered by the rapidity as well as the non-Markovian nature of the dynamics. Much emphasis has been directed toward employing shorter and shorter pulses. However, photon echoes using short pulses often simply measure the ultrafast break up of the intra-molecular vibrational wavepacket created by the large spectral bandwidth of the pulses. Recently, it has been shown that three pulse stimulated photon echo peak shift (3PEPS) measurements give accurate dynamical information on solute-solvent interaction [1,3]. In this technique, peak shifts are determined precisely by simultaneously measuring signals in the phase matching directions –k1+k2+k3 and k1−k2+k3. The peak shift reflects the ability of the system to rephase after evolving in a population state for time, T. That is, the decrease of 3PEPS mirrors the electronic transition frequency correlation function, M(t). Here we report 3PEPS studies on various polar protic and aprotic solvents using 22 fs and 90 fs pulses. It is shown the 3PEPS with pulses much longer than a typical electronic dephasing time still gives accurate information on ultrafast as well as slow dynamics in liquids. The experimental results are consistent with the numerical simulations including finite pulse duration.
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Al Enezi, D., M. AL Hajeri, S. Gholum, S. Nath, T. Ahmad, Z. Ramadan, S. Osman, et al. "Realtime Drilling Geomechanics Aids Safe Drilling through Unstable Shales and Channel Sands of Wara Formations, Minagish Field, West Kuwait." In SPE Trinidad and Tobago Section Energy Resources Conference. SPE, 2021. http://dx.doi.org/10.2118/200929-ms.
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Abstract As part of any successful development plan of any hydrocarbon field, drilling boreholes safely is a key factor to make the entire process safe, economic and environmentally friendly. One of the main factors that dictates whether a borehole is going to be drilled safely or not is to understand the geomichanical behavior of the different formation to be penetrated. A definition of geomechanics could be stated as the science that studies the relationship between each of; in-situ stresses, rock mechanics, and the drilling fluid properties. In Kuwait and during the course of efforts to develop Wara channel sands in Minagish Field to the west of the country, Kuwait Oil Company (KOC) realized that continuing to drill development wells using conventional drilling practices is not any more an easy task. Considerable non-productive time has been recorded due encountering events such as shale carvings and pack off leading to stuck pipe. In addition, partial to total lost circulation were faced while drilling through Mutriba Formation which added to the complexity of problem. This study involved gathering data from offset wells to build a mechanical earth model for the area where the new well is going to be drilled. The main objective of having the model built is to perform wellbore stability analysis (WBS) and compute the quantitative mud window values to insure stable and safe borehole drilling. As the case of any study, performing reliable WBS analysis requires accurate modeling of earth stresses and rock mechanical properties. This process is primarily based on sonic logs (compressional and shear slowness), formation bulk density and lithology distribution. The study started with an audit of the available data sets in the region to select the best offset wells and generating empirical correlations to fill- up any missing and/or poor-quality data zones. Initially,7offset wells were identified, based on the geological distribution and data availability.Out of them, only four wells were found to have compressional slowness and three with bulk density measurements. However, it is worth mentioning that no shear slowness measurements were available in any of the offset wells in the region. Due to this, a correlation based compressional-shear relationship from nearby wells was proposed for the pre-drill study. The mechanical properties were characterized using the tri-axial core test results available from Wara and Burgan Formations. Empirical correlations were developed to obtain static mechanical properties from the dynamical mechanical ones and log responses. In addition, horizontal stresses in the region were constrained with formation integrity test data to have better control on the model. Finally, after the WBS model was built,it was compared to the available caliper data from the offset wells for calibration purposes. The resulted pre-drill geomechanics model was used to advise on the drilling parameters (mud weight) to be used in drilling the new development well. Moreover, and being the first realtime drilling geomechanics (RTDG) job in in Kuwait, an LWD sonic was used while drilling to supply the pre-drill model with realtime compressional and shear slowness measurements. Having the model updated in realtime with data from the formation at the borehole location resulted in optimizing the mud weight window limits by the geomechanics engineers as the well was being drilled. Following these mud weight recommendations based on the updated pre-drill model resulted in a smooth landing and horizontal sections in which all the wiper trips until the final pull out of hole were smooth.
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Jaubert, Jean-Noe¨l, Romain Privat, and Michel Molie`re. "Ethanol and Distillate Blends: A Thermodynamic Approach to Miscibility Issues." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22126.
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In the recent years, the quest for an ever wider cluster of sustainable primary energies has prompted an increasing number of attempts to combine the emission sobriety of bio fuels with the energy density advantage of fossil fuels. A number of compositions incorporating hydrocarbons, ethanol and in some cases limited amounts of water have been proposed, especially in the forms of micro emulsions, with a variable success. Indeed due to markedly different physical and chemical properties, ethanol and gasoil are able to blend and form homogeneous solutions only in limited proportion ranges. Indeed, such mixtures often give rise to liquid-liquid equilibrium. A key parameter is thus the Minimum Miscibility Temperature (MMT), i.e. the temperature above which ethanol and gasoil become completely miscible. In fact, commercial gasoils do not constitute a monolithic product but display in the contrary a large span of compositions that influence the stability of these blends. In this context, the LRGP laboratory (Laboratoire Re´actions et Ge´nie des Proce´de´s) has undertaken an investigation program intended to understand the factors underlying the stability of ethanol/gasoil blends. The approach is based on the calculation of the liquid-liquid phase diagrams formed by anhydrous ethanol and a mixture of various hydrocarbons representative of the diesel oil pool using the group contribution concept. Indeed, for correlating thermodynamic properties, it is often convenient to regard a molecule as an aggregate of functional groups; as a result, some thermodynamic properties (heat of mixing, activity coefficients) can be calculated by summing group contributions. In this study, the universal quasichemical functional group activity coefficient (UNIFAC) method has been employed as it appears to be particularly useful for making reasonable estimates for the studied non ideal mixtures for which data are sparse or totally absent. In any group-contribution method, the basic idea is that whereas there are thousands of chemical compounds of interest in chemical technology, the number of functional groups that constitute these compounds is much smaller. Therefore, if we assume that a physical property of a fluid is the sum of contributions made by the molecule’s functional groups, we obtain a possible technique for correlating the properties of a very large number of fluids in terms of a much smaller number of parameters that characterize the contributions of individual groups. This paper shows the large influence exerted by the paraffinic, aromatic and naphthenic character of the gasoil but also the sulfur content of the fossil fraction on the shape of the liquid-liquid phase diagram and on the value of the minimum miscibility temperature.
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Stevens, Robert J., Pamela M. Norris, and Arthur W. Lichtenberger. "Experimental Determination of the Relationship Between Thermal Boundary Resistance and Non-Abrupt Interfaces and Electron-Phonon Coupling." In ASME 2004 Heat Transfer/Fluids Engineering Summer Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/ht-fed2004-56556.
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Understanding thermal boundary resistance (TBR) is becoming increasingly important for the thermal management of micro and optoelectronic devices. The current understanding of room temperature TBR is often not adequate for the thermal design of tomorrow’s complex micro and nano devices. Theories have been developed to explain the resistance to energy transport by phonons across interfaces. The acoustic mismatch model (AMM) [1, 2], which has had success at explaining low temperature TBR, does not account for the high frequency phonons and imperfect interfaces of real devices at room temperature. The diffuse mismatch model (DMM) was developed to account for real surfaces with higher energy phonons [3, 4]. DMM assumes that all phonons incident on the interface from both sides are elastically scattered and then emitted to either side of the interface. The probability that a phonon is emitted to a particular side is proportional to the phonon density of states of the two interface materials. Inherent to the DMM is that the transport is independent of the interface structure itself and is only dependent on the properties of the two materials. Recent works have shown that the DMM does not adequately capture all the energy transport mechanisms at the interface [5, 6]. In particular, the DMM under-predicts transport across interfaces between non Debye-like materials, such at Pb and diamond, by approximately an order of magnitude. The DMM also tends to over-predict transport for interfaces made with materials of similar acoustic properties, Debye-like materials. There have been several explanations and models developed to explain the discrepancies between the mismatch models and experimental data. Some of these models are based on modification of the AMM and DMM [7–9]. Other works have utilized lattice-dynamical modeling to calculate phonon transmission coefficients and thermal boundary conductivities for abrupt and disordered interfaces [3, 6, 10–13]. Recent efforts to better understand room temperature TBR have utilized molecular dynamics simulations to account for more realistic anharmonic materials and inelastic scattering [14–18]. Models have also been developed to account for electron-phonon scattering and its effect on the thermal boundary conductance for interfaces with one metal side [19–22]. Although there have been numerous thermal boundary resistance theoretical developments since the introduction of the AMM, there still is not an unifying theory that has been well validated for high temperature solid-solid interfaces. Most of the models attempt to explain some of the experimental outliers, such as Pb/diamond and TiN/MgO interfaces [6, 23], but have not been fully tested for a range of experimental data. Part of the problem lies in the fact that very little reliable data is available, especially data that is systematically taken to validate a particular model. To this end, preliminary measurements of TBR are being made on a series of metal on non-metal substrate interfaces using a non-destructive optical technique, transient thermal reflectance (TTR) described in Stevens et al. [5]. Initial testing examines the impact of different substrate preparation and deposition conditions on TBR for Debye-like interfaces for which TBR should be small for clean and abrupt interfaces. Variables considered include sputter etching power and duration, electron beam source clean, and substrate temperature control. The impact of alloying and non-abrupt interfaces on the TBR is examined by fabricating interfaces of both Debye-like and non Debye-like interfaces followed by systematically measuring TBR and altering the interfaces by annealing the samples to increase the diffusion depths at the interfaces. Inelastic electron scattering at the interface has been proposed by Hubermann et al. and Sergeev to decrease TBR at interfaces [19–21]. Two sets of samples are prepared to examine the electron-phonon connection to improved thermal boundary conductance. The first consists of thin Pt and Ag films on Si and sapphire substrates. Pt and Ag electron-phonon coupling factors are 60 and 3.1×1016 W/m3K respectively. Both Pt and Ag have similar Debye temperatures, so electron scattering rates can be examined without much change in acoustic effects. The second electron scattering sample series consist of multiple interfaces fabricated with Ni, Ge, and Si to separate the phonon and electron portions of thermal transport. The experimental data is compared to several of the proposed theories.
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von Spakovsky, Michael R., Charles E. Smith, and Vittorio Verda. "Quantum Thermodynamics for the Modeling of Hydrogen Storage on a Carbon Nanotube." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67424.
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A typical approach for modeling systems at a nanoscale in states of non-equilibrium undergoing an irreversible process is to use an ad hoc mixture of molecular dynamics (linear and nonlinear), i.e. classical mechanics, coupled to assumptions of stable equilibrium which allow one via analogy to incorporate equilibrium thermodynamic state information such as temperature and pressure into the modeling process. However, such an approach cannot describe the actual thermodynamic evolution in state which occurs in these systems since the equation of motion used (Newton’s second law) can only describe the evolution in state from one mechanical state to another. To capture the actual thermodynamic evolution, a more general equation of motion is needed. Such an equation has been proposed, i.e. the Beretta equation of motion, as part of a general theory, which unifies (not simply bridges as is the case in statistical thermodynamics) quantum mechanics and thermodynamics. It is called the unified quantum theory of mechanics and thermodynamics or quantum thermodynamics. This equation, which strictly satisfies all of the implications of the laws of thermodynamics, including the second law, as well as of quantum mechanics, describes the thermodynamic evolution in state of a system in non-equilibrium regardless of whether or not the system is in a state far from or close to stable equilibrium. This theory and its dynamical postulate are used here to model the storage of hydrogen in an isolated box modeled in 1D and 2D with a carbon atom at one end of the box in 1D and a carbon nanotube in the middle of the box in 2D. The system is prepared in a state with the hydrogen molecules initially far from stable equilibrium, after which the system is allowed to relax (evolve) to a state of stable equilibrium. The so-called energy eigenvalue problem is used to determine the energy eigenlevels and eigenstates of the system, while the nonlinear Beretta equation of motion is used to determine the evolution of the thermodynamic state of the system as well as the spatial distributions of the hydrogen molecules in time. The results of our initial simulations show in detail the trajectory of the state of the system as the hydrogen molecules, which are initially arranged to be far from the carbon atom or the carbon nanotube, are seen to spread out in the container and eventually become more concentrated near the carbon atom or atoms.