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Partition Function (partition + function)
Selected AbstractsComposition of Partially Ionized Systems Using the PlanckLarkin Partition Function of Mid-Z ionsCONTRIBUTIONS TO PLASMA PHYSICS, Issue 10 2009A. Sengebusch Abstract We report on the composition of warm, dense plasmas of M-shell ions. Assuming local thermal equilibrium, the abundance of different ionization stages is given by a set of coupled Saha-equations. In order to avoid discontinuities at the Mott density, the partition functions have to account for pressure ionization due to continuum lowering consistently. The Planck-Larkin renormalization of bound and scattering states is well elaborated for hydrogenic systems. This paper shows the consistent extension to moderately ionized Mid-Z elements. We present results for solid-density polymere and titanium plasmas (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Instantons and Donaldson,Thomas invariantsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2008M. Cirafici Abstract We review some recent progress in understanding the relation between a six dimensional topological Yang,Mills theory and the enumerative geometry of Calabi,Yau threefolds. The gauge theory localizes on generalized instanton solutions and is conjecturally equivalent to Donaldson,Thomas theory. We evaluate the partition function of the U(N) theory in its Coulomb branch on flat space by employing equivariant localization techniques on its noncommutative deformation. Geometrically this corresponds to a higher dimensional generalization of the ADHM formalism. This formalism can be extended to a generic toric Calabi,Yau. [source] Strings and D-branes in holographic backgroundsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2005D. Israël Abstract We review recent progress in the study of non-rational (boundary) conformal field theories and their applications to describe exact holographic backgrounds in superstring theory. We focus mainly on the example of the supersymmetric coset SL(2, ,)/U(1), corresponding to the two-dimensional black hole, and its dual N = 2 Liouville. In particular we discuss the modular properties of their characters, their partition function as well as the exact boundary states for their various D-branes. Then these results are used to construct the corresponding quantities in the CFT of the NS5-brane background, with applications to Little String Theories. [source] Parameter estimation in Bayesian reconstruction of SPECT images: An aid in nuclear medicine diagnosisINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2004Antonio López Abstract Despite the adequacy of Bayesian methods to reconstruct nuclear medicine SPECT (single-photon emission computed tomography) images, they are rarely used in everyday medical practice. This is primarily because of their computational cost and the need to appropriately select the prior model hyperparameters. We propose a simple procedure for the estimation of these hyperparameters and the reconstruction of the original image and test the procedure on both synthetic and real SPECT images. The experimental results demonstrate that the proposed hyperparameter estimation method produces satisfactory reconstructions. Although we have used generalized Gaussian Markov random fields (GGMRF) as prior models, the proposed estimation method can be applied to any priors with convex potential and tractable partition function with respect to the scale hyperparameter. © 2004 Wiley Periodicals, Inc. Int J Imaging Syst Technol 14, 21,27, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20003 [source] Phase behavior of ionic clusters down to nanoscale.INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2010A review of recent work Abstract As finding an exact and manageable partition function for nanoclusters is a desirable but, so far, unattainable task, approximated treatments are proposed to explain and predict phase changes and phase coexistence at these size scales. In this article, a review of those approaches is presented, mainly focusing the authors work on the subject. The foundations and limitations of the proposed models are discussed and perspectives for extended treatments are given. The discussions are illustrated with new molecular dynamics simulations of unconstrained NaI and NaCl clusters. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Convenient expression of the rate constant for nonadiabatic transitionINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005Yoshishige Okuno Abstract We derived a convenient expression of the rate constant for nonadiabatic transitions, with the intention of making it possible and practical to calculate the rate constant. For this derivation, we first assume that the seam, at which the adiabatic potential energy surfaces of reactant and product electronic states exhibit an avoided crossing, corresponds to the dividing surface of the nonadiabatic transition. Second, we use the probability that a nonadiabatic transition occurs in the seam. Third, the partition function in the seam is described by the local profile of the adiabatic potential energy surfaces of both the reactant and product electronic states. The rate constant expression thus derived not only gives significant insight into understanding nonadiabatic transitions, but also makes it possible to obtain a rough estimate of the rate constant. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [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] An algorithm for computing nucleic acid base-pairing probabilities including pseudoknotsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2004Robert M. Dirks Abstract Given a nucleic acid sequence, a recent algorithm allows the calculation of the partition function over secondary structure space including a class of physically relevant pseudoknots. Here, we present a method for computing base-pairing probabilities starting from the output of this partition function algorithm. The approach relies on the calculation of recursion probabilities that are computed by backtracking through the partition function algorithm, applying a particular transformation at each step. This transformation is applicable to any partition function algorithm that follows the same basic dynamic programming paradigm. Base-pairing probabilities are useful for analyzing the equilibrium ensemble properties of natural and engineered nucleic acids, as demonstrated for a human telomerase RNA and a synthetic DNA nanostructure. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1295,1304, 2004 [source] On the noise correlation matrix for multiple radio frequency coilsMAGNETIC RESONANCE IN MEDICINE, Issue 2 2007Ryan Brown Abstract Noise correlation between multiple receiver coils is discussed using principles of statistical physics. Using the general fluctuation-dissipation theorem we derive the prototypic correlation formula originally determined by Redpath (Magn Res Med 1992;24:85,89), which states that correlation of current spectral noise depends on the real part of the inverse impedance matrix at a given frequency. A distinct correlation formula is also derived using the canonical partition function, which states that correlation of total current noise over the entire frequency spectrum depends on the inverse inductance matrix. The Kramers-Kronig relation is used to equate the inverse inductance matrix to the spectral integral of the inverse impedance matrix, implying that the total noise is equal to the summation of the spectral noise over the entire frequency spectrum. Previous conflicting arguments on noise correlation may be reconciled by differentiating between spectral and total noise correlation. These theoretical derivations are verified experimentally using two-coil arrays. Magn Reson Med 58:218,224, 2007. © 2007 Wiley-Liss, Inc. [source] One-dimensional disordered magnetic Ising systems: A new approachPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 9 2009Vladimir Gasparian Abstract We reconsider the problem of a one-dimensional Ising model with an arbitrary nearest-neighbor random exchange integral, temperature, and random magnetic field in each site. A convenient formalism is developed that reduces the partition function to a recurrence equation, which is convenient both for numerical as well as for analytical approaches. We have calculated asymptotic expressions for an ensemble averaged free energy and the averaged magnetization in the case of strong and weak couplings in external constant magnetic field. With a random magnetic field at each site in addition to nearest-neighbor random exchange integrals we also evaluated the free energy. We show that the zeros of the partition function for the Ising model in the complex external magnetic field plane formally coincide with the singularities of the real part of electron's transmission amplitude through the chain of , -function potentials. [source] Composition of Partially Ionized Systems Using the PlanckLarkin Partition Function of Mid-Z ionsCONTRIBUTIONS TO PLASMA PHYSICS, Issue 10 2009A. Sengebusch Abstract We report on the composition of warm, dense plasmas of M-shell ions. Assuming local thermal equilibrium, the abundance of different ionization stages is given by a set of coupled Saha-equations. In order to avoid discontinuities at the Mott density, the partition functions have to account for pressure ionization due to continuum lowering consistently. The Planck-Larkin renormalization of bound and scattering states is well elaborated for hydrogenic systems. This paper shows the consistent extension to moderately ionized Mid-Z elements. We present results for solid-density polymere and titanium plasmas (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Heterotic strings on homogeneous spaces,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 9 2005D. Israël Abstract We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS-NS 2-forms and gauge field fluxes. We give the general formalism and modular-invariant partition functions, then we consider some examples such as SU (2)/U (1) ~ S2 (already described in a previous paper) and the SU (3)/U(1)2 flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton. [source] Electric/magnetic deformations of S3 and AdS3, and geometric cosets,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 1 2005D. Israël We analyze asymmetric marginal deformations of SU(2)k and SL(2,,)k WZW models. These appear in heterotic string backgrounds with non-vanishing Neveu,Schwarz three-forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S3 or AdS3, include in particular geometric cosets such as S2, AdS2 or H2. Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS2 × S2 background. We also comment on potential holographic applications. [source] Asymmetrically gauged WZNW modelsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003T. Quella Many interesting exactly solvable backgrounds can be obtained by gauging WZNW models asymmetrically. These include the base of the conifold and the time dependent Nappi-Witten background in which a 3-dimensional universe passes through a series of big-bang big-crunch singularities. In this short note we review recent results on the conformal field theory description of asymmetric cosets. In particular, we present formulas for their bulk modular invariant partition functions and for a large number of D-brane boundary states. [source] Comparative study of kinetics and reactivity indices of free radical polymerization reactions,INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2005K. Van Cauter Abstract Density functional theory calculations are used to determine the kinetics and reactivity indices of the first propagation steps of the polyethylene and poly(vinyl chloride) polymerization. Transition state theory is applied to evaluate the rate coefficient from the microscopically determined energies and partition functions. A comparison with the experimental Arrhenius plots validates the level of theory. The ability of reactivity indices to predict certain aspects of the studied propagation reactions is tested. Global softnesses of the reactants give an indication of the relative energy barriers of subsequent monomer additions. The correlation between energy and hardness profiles along the reaction path confirm the principle of maximum hardness. Local indices predict the regioselectivity of the attack of the growing radical to vinyl chloride. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] The minimized dead-end elimination criterion and its application to protein redesign in a hybrid scoring and search algorithm for computing partition functions over molecular ensemblesJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2008Ivelin Georgiev Abstract One of the main challenges for protein redesign is the efficient evaluation of a combinatorial number of candidate structures. The modeling of protein flexibility, typically by using a rotamer library of commonly-observed low-energy side-chain conformations, further increases the complexity of the redesign problem. A dominant algorithm for protein redesign is dead-end elimination (DEE), which prunes the majority of candidate conformations by eliminating rigid rotamers that provably are not part of the global minimum energy conformation (GMEC). The identified GMEC consists of rigid rotamers (i.e., rotamers that have not been energy-minimized) and is thus referred to as the rigid-GMEC. As a postprocessing step, the conformations that survive DEE may be energy-minimized. When energy minimization is performed after pruning with DEE, the combined protein design process becomes heuristic, and is no longer provably accurate: a conformation that is pruned using rigid-rotamer energies may subsequently minimize to a lower energy than the rigid-GMEC. That is, the rigid-GMEC and the conformation with the lowest energy among all energy-minimized conformations (the minimized-GMEC) are likely to be different. While the traditional DEE algorithm succeeds in not pruning rotamers that are part of the rigid-GMEC, it makes no guarantees regarding the identification of the minimized-GMEC. In this paper we derive a novel, provable, and efficient DEE-like algorithm, called minimized-DEE (MinDEE), that guarantees that rotamers belonging to the minimized-GMEC will not be pruned, while still pruning a combinatorial number of conformations. We show that MinDEE is useful not only in identifying the minimized-GMEC, but also as a filter in an ensemble-based scoring and search algorithm for protein redesign that exploits energy-minimized conformations. We compare our results both to our previous computational predictions of protein designs and to biological activity assays of predicted protein mutants. Our provable and efficient minimized-DEE algorithm is applicable in protein redesign, protein-ligand binding prediction, and computer-aided drug design. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Identification and thermodynamic treatment of several types of large-amplitude motionsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 14 2005Gernot Katzer Abstract We present a partially automated method for the thermodynamic treatment of large-amplitude motions. Starting from the molecular geometry and the Hessian matrix, we evaluate anharmonic partition functions for selected vibrational degrees of freedom. Supported anharmonic vibration types are internal rotation and inversion (oscillation in a double-well potential). By heuristic algorithms, we identify internal rotations in most cases automatically from the Hessian eigenvectors, and we also estimate the parameters of anharmonic partition functions (e.g., potential barrier, periodicity, and symmetry number) with thermodynamically sufficient precision. We demonstrate the validity of our schemes by comparison to pointwise calculated ab initio potential curves. © 2005 Wiley Periodicals, Inc. J Comput Chem 14: 1438,1451, 2005 [source] | ||||||||||||||||