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Department: search.filters.department.Department of ChemistrySubject: search.filters.subject.Mathematical physics

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Now showing 1 - 3 of 3
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    PublicationOpen Access
    Finite-size effects in the dynamics and thermodynamics of two-dimensional Coulomb clusters
    (American Physical Society (APS), 2005) Calvo, F.; Wales, D. J.; Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129
    The dynamics and thermodynamics of melting in two-dimensional Coulomb clusters is revisited using molecular dynamics and Monte Carlo simulations. Several parameters are considered, including the Lindemann index, the largest Lyapunov exponent, and the diffusion constant. In addition to the orientational and radial melting processes, isomerizations and complex size effects are seen to occur in a very similar way to atomic and molecular clusters. The results are discussed in terms of the energy landscape represented through disconnectivity graphs, with proper attention paid to the broken ergodicity problems in simulations. Clusters bound by 1/r(3) and e(-kappa r)/r forces, and heterogeneous clusters made of singly and doubly charged species, are also studied, as well as the evolution toward larger systems.
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    PublicationOpen Access
    Lyapunov exponents for classical-quantum mixed-mode dynamics
    (American Physical Society (APS), 1996) Department of Chemistry; Yurtsever, İsmail Ersin; Researcher; Department of Chemistry; College of Sciences; 7129
    The mixed-mode philosophy of combining classical and quantum degrees of freedom under a single umbrella is employed to study chaotic behavior under quantization. The quantal wave packet is expanded in terms of a set of basis functions. The Jacobi-Hamilton formalism of the time-dependent Schrodinger equation allows the treatment of real and imaginary components of the time-dependent expansion coefficients as coordinates and momenta so that Lyapunov exponents can be calculated. Under the mixed-mode formalism, a two-dimensional nonlinearly coupled oscillator system is partially quantized by letting one of the modes obey classical and the other quantal dynamics. The Lyapunov exponent spectrum of the complete system is obtained and the results are compared with the fully classical ones.
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    PublicationOpen Access
    Rotationally induced transitions in small clusters
    (American Physical Society (APS), 2001) Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; Department of Chemistry; College of Sciences; 7129
    The dynamics of an Ar-6 cluster held together by Lennard-Jones forces is studied classically. The development of chaotic dynamics is mainly followed by a calculation of the maximum Lyapunov exponent (MLE). Initial momentum vectors are chosen from the eigenvectors of the Hessian of the potential energy so that rotating and nonrotating clusters can be studied systematically. It is found that the dependence of MLE on the total energy is considerably different for rotational and vibrational excitations. As the magnitude of the angular momentum increases, sharp transitions in MLE are observed. These transitions are explained in terms of the changes of the topology of the effective rovibrational potential energy surface and the dynamic equilibration between the global and local minima.