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End date: 1999Full Text: Yes

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    PublicationOpen Access
    A class of Banach algebras whose duals have the Schur property
    (TÜBİTAK, 1999) Mustafayev, H.; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences
    Call a commutative Banach algebra A a γ-algebra if it contains a bounded group Λ such that aco(Λ) contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of γ-algebras is quite rich. Then, for a γ-algebra A, we prove that A* has the Schur property iff the Gelfand spectrum Σ of A is scattered iff A* = ap(A) iff A* = Span(Σ).
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    PublicationOpen Access
    A note on weakly compact homomorphisms between uniform algebras
    (Polish Academy of Sciences, 1997) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences
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    PublicationOpen Access
    Angular-momentum-driven chaos in small clusters
    (American Physical Society (APS), 1998) Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129
    The effects of the rotational motion on the chaotic behavior of triatomic Lennard-Jones clusters are studied. A set of initial momentum distributions with tunable parameters is chosen to correspond to various rigid-body rotations around symmetry axes of the cluster. By smoothly varying the direction of the initial kicks given to the cluster, periodic transitions between regular and chaotic regimes are obtained. A study of initial conditions leading up to such transitions shows that the major factor that determines the extent of the chaotic behavior is the initial partitioning of the kinetic energy between the rotational and vibrational motion. From the analysis of the time evolution of various properties it is concluded that the basic role of this initial partitioning is to control the energy transfer between the kinetic and the potential energy.
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    PublicationOpen Access
    Chaotic behavior of triatomic clusters
    (American Physical Society (APS), 1997) Elmacı, N.; Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129
    The dynamics of triatomic clusters is investigated employing two-body Lennard-Jones and three-body Axilrod-Teller potential functions. Lyapunov exponents are calculated for the total energy range of -2.70 epsilon <E< -0.72 epsilon. The effects of the initial geometry of the cluster, its angular momentum, and the magnitude of three-body interactions are analyzed. It has been found that the dominating factor for the extent of chaotic behavior is the energy assigned to vibrational modes. The introduction of the rotational motion regularizes the dynamics in spite of a higher degree of nonlinearity. The three-body terms in the potential function affect the extent of the chaos in different manners depending on the initial geometry of the cluster. Finally, the time evolution of heterogeneous clusters generated by varying the size, mass, and the interaction strength of a single atom is observed. Their Lyapunov exponent spectra show that the additional nonlinearity reduces the chaotic behavior of the system in most of the cases.
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    PublicationOpen Access
    Comment on “Identical motion in classical and quantum mechanics”
    (American Physical Society (APS), 1999) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; Department of Physics; College of Sciences; 4231
    Makowski and Konkel [Phys. Rev. A 58, 4975 (1998)] have obtained certain classes of potentials which lead to identical classical and quantum Hamilton-Jacobi equations. We obtain the most general form of these potentials.
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    PublicationOpen Access
    Correcting for electrostatic cutoffs in free energy simulations: toward consistency between simulations with different cutoffs
    (American Institute of Physics (AIP) Publishing, 1998) McCammon, J. Andrew; Department of Physics; Reşat, Haluk; Faculty Member; Department of Physics; College of Sciences
    The use of electrostatic cutoffs in calculations of free energy differences by molecular simulations introduces errors. Even though both solute-solvent and solvent-solvent cutoffs are known to create discrepancies, past efforts have mostly been directed toward correcting for the solute-solvent cutoffs. In this work, an approach based on the generalized reaction field formalism is developed to correct for the solvent-solvent cutoff errors as well. It is shown using a series of simulations that when the cutoff lengths are significantly smaller than the half unit cell size, and the solute-solvent cutoff is not much larger than the solvent-solvent cutoff, the new algorithm is able to yield better agreement among simulations employing different truncation lengths.
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    PublicationOpen Access
    Correcting for solvent-solvent electrostatic cutoffs considerably improves the ion-pair potential of mean force
    (American Institute of Physics (AIP) Publishing, 1999) Department of Physics; Reşat, Haluk; Faculty Member; Department of Physics; College of Sciences
    A recently developed algorithm based on the continuum treatment of the solvent molecules beyond the electrostatic cutoff sphere is applied to the potential of mean force results between sodium and chloride ions to study the effects of the solute-solvent and solvent-solvent cutoff errors. The results show that although the solute-solvent correction improves the thermodynamic results slightly, physically realistic results are obtained only when the solvent-solvent correction is applied. This further supports past findings that proper treatment of solvent-solvent interactions is as important as that of the solute interactions, and should not be ignored.
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    PublicationOpen Access
    Dimerization of pyrrole
    (TÜBİTAK, 1998) Yurtsever, Mine; Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129
    Accurate ab-inito quantum mechanical calculations of pyrrole dimers are reported. The thermodynamical stabilities of dimers with alpha - alpha, alpha -beta, and beta - beta type linkages are compared in order to predict the possibilities of branching in polypyrroles. Calculations employing large basis sets and including electron correlation effects predict the alpha - alpha dimers as the most stable form. However, an alpha - beta type bonding requires only 1.5-2.0 kcal/mol, and the energy necessary to introduce a beta - beta type bond is 3.6-4.0 kcal/mol. These values show that a high degree of branching is possible even at room temperatures.
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    PublicationOpen Access
    Erratum: Geometric phase, bundle classification, and group representation
    (American Institute of Physics (AIP) Publishing, 1999) Department of Mathematics; Department of Physics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; Department of Physics; College of Sciences; 4231
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    Exact semiclassical evolutions in relativistic and non-relativistic scalar quantum mechanics and quantum cosmology
    (Elsevier, 1998) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    The necessary and sufficient conditions for the exactness of the semiclassical approximation for the solution of the Schrodinger and Klein-Gordon equations are obtained, It is shown that the existence of an exact semiclassical solution of the Schrodinger equation determines both the semiclassical wave function and the interaction potential uniquely up to the choice of the boundary conditions. This result also holds for the Klein-Gordon equation. Its implications for the solution of the Wheeler-DeWitt equation for the FRW scalar field minisuperspace models are discussed. In particular, exact semiclassical solutions of the Wheeler-DeWitt equation for the case of massless scalar field and exponential matter potentials are constructed, The existence of exact semiclassical solutions for polynomial matter potentials of the form lambda phi(2p) is also analyzed. It is shown that for p = 1, 2 and 3, right-going semiclassical solutions do not exist, A generalized semiclassical perturbation expansion is also developed which is quite different from the traditional (h) over bar and M-p(-1) expansions. (C) 1998 Published by Elsevier Science B.V.