http://www.bibsonomy.org/burst/user/statphys23/integralBibSonomy BuRST Feed for /user/statphys23/integral2008-10-08T12:59:06+02:00http://www.bibsonomy.org/bibtex/200fdf2700ff5078bc27bae43980bbd31/statphys23statphys232007-06-20T10:16:09+02:00integral topic-1 configuration spheres results virial hard coefficients analytic exact statphys23 <span style="color:#555555;">I. <a href="http://www.bibsonomy.org/author/Urrutia">Urrutia</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyConfiguration Integral and Thermodynamic properties for small systems of confined Hard Spheres2007integral topic-1 configuration spheres results virial hard coefficients analytic exact statphys23 Exact results for the inhomogeneous Hard Sphere (HS) fluid systems are of great theoretical interest. In this work we analyze the configuration integral (CI) of the canonical partition function for two and three HS constrained to move on closed volumes of simple geometrical shape. We present the exact analytical expressions of such CI for some simple shaped pores. The dependence of thermodynamic properties of these systems over a wide range of pore size parameter are studied focusing on low and high density limits.http://www.bibsonomy.org/bibtex/28c054bd51e368635c9756bc1d113b895/statphys23statphys232007-06-20T10:16:09+02:00montecarlo liquid equation statphys23 methods structure theory integral topic-6 <span style="color:#555555;">D.L. <a href="http://www.bibsonomy.org/author/Cheung">Cheung</a> und L. <a href="http://www.bibsonomy.org/author/Anton">Anton</a> und M.P. <a href="http://www.bibsonomy.org/author/Allen">Allen</a> und A.J. <a href="http://www.bibsonomy.org/author/Masters">Masters</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyStructure of molecular fluids: hunting the bridge function2007montecarlo liquid equation statphys23 methods structure theory integral topic-6 The bridge function, $b(1,2)$, is an elusive quantity. It is a crucial ingredient for predicting liquid properties yet it is virtually an unknown quantity for non-spherical molecules. To remedy this situation we present novel Monte Carlo (MC) and Integral Equation Theory (IET) methodologies for its calculation [1]. We also, through Duh-Haymet (DH) scaling plots [2], test the hypothesis that $b(1,2)$ is a function of the indirect correlation function $\gamma(1,2)$. Results for a number of systems will be presented. In particular a systematic study $b(1,2)$ for hard spheroids with a range of aspect ratios will be made [1,3]. DH plots, direct comparison of $b(1,2)$ and $\gamma(1,2)$ will be used to test the universality of the hard spheroid bridge function. For most of the elongations studied, the relationship between $b(1,2)$ and $\gamma(1,2)$ resembles the hard-sphere case, but for fluids of thin hard platelets the behaviour is anomalous. Extension of previous work into mixtures and the nematic phase will also be discussed.\\ 1) D. L. Cheung, L. Anton, M. P. Allen, and A. J. Masters, Phys. Rev. E, 73, 061204, 2006 \\ 2) D. M. Duh and A. D. J. Haymet, J. Chem. Phys., 97, 7712, 1992 \\ 3) D. L. Cheung, L. Anton, M. P. Allen, and A. J. Masters, 'Structure of molecular fluids: closure relationships for hard spheriods', in preparationhttp://www.bibsonomy.org/bibtex/2d7e7daf3ad9126bff41de3d178a29f75/statphys23statphys232007-06-20T10:16:09+02:00liquid nematic topic-1 statphys23 functional correlation density equation function theory integral crystal pair <span style="color:#555555;">P. <a href="http://www.bibsonomy.org/author/Mishra">Mishra</a> und Y. <a href="http://www.bibsonomy.org/author/Singh">Singh</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyPair Correlation Functions in Nematics and the Density-Functional Theory of Freezing2007liquid nematic topic-1 statphys23 functional correlation density equation function theory integral crystal pair The freezing of a fluid of anisotropic molecules into a nematic phase is a typical example of a first-order phase transition in which the continuous symmetry of the isotropic phase is broken.In a nematic phase molecules are aligned along a particular but arbitrary direction so as to have a long range order in orientation while translational degrees of freedom remain disordered as in the isotropic fluid.It is shown that in the nematic phase there are two qualitatively different contributions to pair correlation functions;one that preserves rotational invariance and the other that breaks it and vanishes in the isotropic phase.The symmetry preserving part of the pair correlation passes smoothly without any abrupt change through the isotropic-nematic transition.We describe a method of solving the Ornstein-Zernike equation with a closure relation to get both the symmetry conserving and symmetry breaking parts of pair correlation functions.Using these correlation functions we construct a free energy functional to study the freezing transition and other properties of the ordered phase.The theory predicts accurately the isotropic-nematic transition in a system of anisotropic molecules and can be extended to study other ordred phases such as smectics and crystalline solids.http://www.bibsonomy.org/bibtex/2d974e36389db93c02fbb6308ddaa9b87/statphys23statphys232007-06-20T10:16:09+02:00nested gaudin integrable equation gas systems integral statphys23 yang one-dimensional topic-1 <span style="color:#555555;">T. <a href="http://www.bibsonomy.org/author/Iida">Iida</a> und M. <a href="http://www.bibsonomy.org/author/Wadati">Wadati</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyOne-Dimensional $\delta$-Function Fermi Gases with Imbalanced Spin Populations2007nested gaudin integrable equation gas systems integral statphys23 yang one-dimensional topic-1 The possibility to access the predicted crossover between Bardeen-Cooper-Schrieffer (BCS) superfluidity of momentum pairs and Bose-Einstein condensation (BEC) of molecules has been exploited in the ultra cold atom systems with tunable inter-atomic interaction via Feshbach resonance. More recently, experimental studies of an atomic Fermi gas with unequal numbers of two components have attracted much attention of physicists related to many fundamental problems in quantum physics. In this presentation, we would like to report an exact analysis of one-dimensional integrable two-component Fermi gas with arbitrary spin polarization at zero temperature. Rigorously speaking, neither the BCS state nor the BEC state occurs in one-dimension. However, the quasi-one dimensional experimental settings are possible and realized in laboratory, and for integrable models we have a theoretical advantage of analyzing the physical properties by using the Bethe ansatz method. We discuss a one-dimensional integrable systems of $N$ spin-$1/2$ Fermi gas with either attractive or repulsive $\delta$-function interaction at zero temperature. The ground state with arbitrary spin polarization (i.e., for all $0\le S\le N/2$, where $S$ is the total spin) is characterized by the sets of integral equations; the Gaudin integral equation for the attractive case and the Yang integral equation for the repulsive case. They determine the distribution of quasi-momenta and that of spin rapidities. We analytically investigate these integral equations with arbitrary spin polarization. The first few terms of the asymptotic expansions of the distribution functions are calculated explicitly for both strong and weak coupling cases. In the weakly attractive case, BCS-like paired fermions and unpaired separate in the quasi-momentum space. This property remains with a weakly repulsive interaction. On the other hand, in the strongly attractive case, bound pairs of fermions behave like hard core bosons. We further study some physical quantities, such as the ground state energy and the chemical potentials, as functions of the coupling constant and the polarization. These expressions are valid for all values of $S$. The method of solution and the detail of the results are found in [1] and [2]. \\ References\\ 1) T. Iida and M. Wadati, J. Phys. Soc. Jpn. \textbf{74} 1724 (2005). \\ \phantom{[1]}\ M. Wadati and T. Iida, Phys. Lett. A \textbf{360} 423 (2007). 2) T. Iida and M. Wadati, J. Low. Temp. Phys., in press. \\ \phantom{[2]}\ T. Iida and M. Wadati, in preparation.http://www.bibsonomy.org/bibtex/2aeb3988f92ab6280be364c67e7940b93/statphys23statphys232007-06-20T10:16:09+02:00equation theory sticky statphys23 hard anisotropic topic-1 spheres patches integral <span style="color:#555555;">R. <a href="http://www.bibsonomy.org/author/Fantoni">Fantoni</a> und D. <a href="http://www.bibsonomy.org/author/Gazzillo">Gazzillo</a> und A. <a href="http://www.bibsonomy.org/author/Giacometti">Giacometti</a> und M. <a href="http://www.bibsonomy.org/author/Miller">Miller</a> und G. <a href="http://www.bibsonomy.org/author/Pastore">Pastore</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyPatchy particles with adhesion: analytically solvable models2007equation theory sticky statphys23 hard anisotropic topic-1 spheres patches integral Anisotropy of molecular interactions plays an important role in many physical, chemical, and biological processes. In the framework of complex fluids (colloidal suspensions, proteins solutions, ...) an important role is played by short-ranged anisotropic attractions and repulsions. In this work we study two different models of anisotropic Sticky Hard Spheres (SHS), made up of spherical molecules with one, two , or many sticky patches: (i) the dipolar patch [1, 2] and (ii) the uniform circular patch [3]. For model (i), we study the structure within the Percus-Yevick integral equation theory with weak orientational linearization. For model (ii), we study the structure, the percolation threshold, and the gas-liquid coexistence curve within the C1 integral equation theory with strong orientational linearization and compare our results with Monte Carlo simulations. 1) L. Blum, P. T. Cummings, and D. Bratko, J. Chem. Phys. 92, 3741 (1990).\\ 2) M. S. Wertheim, J. Chem. Phys. 55, 4291 (1971).\\ 3) N. Kern and D. Frenkel, J. Chem. Phys. 118, 9882 (2003).http://www.bibsonomy.org/bibtex/2d35aa4fb093584da79540f607a23f7e1/statphys23statphys232007-06-20T10:16:09+02:00geometry energy solvation integral statphys23 hard-sphere topic-10 fluid free bio-molecules <span style="color:#555555;">H. <a href="http://www.bibsonomy.org/author/Hansen Goos">Hansen Goos</a> und R. <a href="http://www.bibsonomy.org/author/Roth">Roth</a> und K. <a href="http://www.bibsonomy.org/author/Mecke">Mecke</a> und S. <a href="http://www.bibsonomy.org/author/Dietrich">Dietrich</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulySolvation free energies of bio-molecules from a geometry-based approach2007geometry energy solvation integral statphys23 hard-sphere topic-10 fluid free bio-molecules Inspired by Hadwiger's theorem from integral geometry we develop a method for the calculation of solvation free energies of bio-molecules in various types of solvent. Special attention is paid to effects due to solvent {\em entropy} which we investigate by using recent accurate density functional theory (DFT) results for the hard-sphere fluid [1]. When chain-like molecules are considered, we find regimes where, depending on the state of the solvent, either a tightly packed helical or a $\beta$-sheet structure is favored. The approach is extended to more realistic solvents which exhibit intermolecular attraction and experience specific interactions with the solute molecule, allowing for studying the effect of hydrophobicity and hydrophilicity. The high computational efficiency of our method allows us to scan a large range of solvent as well as solute configurations. We confirm the accuracy of the method by comparison with full DFT calculations for fluids under confinement. 1) H. Hansen-Goos and R. Roth, J. Phys.: Condens. Matter {\bf 18}, 8413 (2006).http://www.bibsonomy.org/bibtex/246b92da17ccd5c7f136be79add8eede3/statphys23statphys232007-06-20T10:16:09+02:00broken spontaneously ordered topic-6 theory equation orientationally problem statphys23 symmetry integral fluids <span style="color:#555555;">F. <a href="http://www.bibsonomy.org/author/Holovko Myroslav">Holovko Myroslav</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyIntegral equation theory for orientationally ordered fluids2007broken spontaneously ordered topic-6 theory equation orientationally problem statphys23 symmetry integral fluids We present the integral equation study of equilibrium properties of orientationally ordered fluids in the presence of external field.The theory is built on the self-consistent solution of Ornstein-Zernike(OZ) and Lovett-Mou-Buff-Wertheim(LMBW) equations.It was shown by M.F.Holovko and T.G.Sokolovska (J.Mol.Liq.82(1999),161)that in the zero field limit the problem of spontaneously broken symmetry appears.This property is connected with the presence of Goldstone modes in ordered phase and leads to the long-range correlations of the director transverse fluctuations and to divergence in the corresponding susceptibility.The Ward identity was formulated. It gives the exact relation between the singlet distribution function and pair direct correlation function which plays the role of some sum rule at the limit of zero external field. In this report we consider some new aspects of the application of the integral equation approach in the theory of orientationally ordered fluids.Between them the influence of a different type of association and clusterization effects on the structural and thermodynamic properties.The special attention will be focused on the effects of dimerization and chain formation in orientationally ordered fluids.For this aim we combine the multidensity integral approach with corresponding LMBW equation.Some results are illustrated by the analytical solutions of mean spherical and associative mean spherical approximations for the hard sphere Maier-Saupe nematogenic system. The second aspect considered here is connected with the influence of porous materials on the equilibrium properties of orientationally ordered fluids.For this aim the replica OZ integral equation approach is combine with LMBW equation.It is shown that LMBW type equation can be used also for the solution of replica broken symmetry problem in orientationally ordered fluids. Finally the connectedness properties of orientationally ordered fluids will be discussed.For this aim the OZ integral equation for connectedness correlation functions is combine with the LMBW equation.