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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6

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Quartile: search.filters.quartile.Q1Subject: search.filters.subject.Mathematical physics

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Now showing 1 - 10 of 26
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    PublicationOpen Access
    Macroscopic loop formation in circular DNA denaturation
    (American Physical Society (APS), 2012) Bar, Amir; Mukamel, David; Department of Physics; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; College of Sciences; 49854
    The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed at the expense of (i) overtwist or (ii) supercoils. Recent work has shown that the supercoiling mechanism results in a picture similar to Bose-Einstein condensation where a macroscopic loop appears at T-c and grows steadily with temperature, while the nature of the denatured phase for the overtwisting case has not been studied. By extending an earlier result, we show here that a macroscopic loop appears in the overtwisting scenario as well. We calculate its size as a function of temperature and show that the fraction of the total sum of microscopic loops decreases above T-c, with a cusp at the critical point.
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    PublicationOpen Access
    Buckling of stiff polymers: influence of thermal fluctuations
    (American Physical Society (APS), 2007) Emanuel, Marc; Mohrbach, Herve; Schiessel, Helmut; Kulic, Igor M.; Department of Mechanical Engineering; Department of Mechanical Engineering; Sayar, Mehmet; Faculty Member; College of Engineering; 109820
    The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.
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    PublicationOpen Access
    Denaturation of circular DNA: supercoil mechanism 2011
    (American Physical Society (APS), 2011) Bar, Amir; Mukamel, David; Department of Physics; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; College of Sciences; 49854
    The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga (PS) model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double-stranded helix, released by a loop denaturation, is absorbed by supercoils. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent c. However the first-order transition displayed by the PS model for c > 2 in linear DNA is replaced by a continuous transition with arbitrarily high order as c approaches 2, while the second-order transition found in the linear case in the regime 1 < c <= 2 disappears. In addition, our analysis reveals that melting under fixed linking number is a condensation transition, where the condensate is a macroscopic loop which appears above the critical temperature.
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    PublicationOpen Access
    High-precision thermodynamic and critical properties from tensor renormalization-group flows
    (American Physical Society (APS), 2008) Hinczewski, Michael; Department of Physics; Department of Physics; Berker, Ahmet Nihat; Faculty Member; College of Sciences
    The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10(-5) along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D=24, corresponding to 4624-dimensional renormalization-group flows.
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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; Department of Chemistry; Yurtsever, İsmail Ersin; Faculty Member; 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
    Interface-roughening phase diagram of the three-dimensional Ising model for all interaction anisotropies from hard-spin mean-field theory
    (American Physical Society (APS), 2011) Department of Physics; Department of Physics; Berker, Ahmet Nihat; Faculty Member; College of Sciences
    The roughening phase diagram of the d = 3 Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, from decoupled planes to the isotropic model to the solid-on-solid model, using hard-spin mean-field theory. The phase diagram contains the line of ordering phase transitions and, at lower temperatures, the line of roughening phase transitions, where the interface between ordered domains roughens. Upon increasing the anisotropy, roughening transition temperatures settle after the isotropic case, whereas the ordering transition temperature increases to infinity. The calculation is repeated for the d = 2 Ising model for the full range of anisotropy, yielding no roughening transition.
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    PublicationOpen Access
    Lyapunov exponents for classical-quantum mixed-mode dynamics
    (American Physical Society (APS), 1996) Department of Chemistry; Department of Chemistry; Yurtsever, İsmail Ersin; Researcher; 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
    Quantum correlated heat engine with spin squeezing
    (American Physical Society (APS), 2014) Altıntaş, Ferdi; Department of Physics; Department of Physics; Hardal, Ali Ümit Cemal; Müstecaplıoğlu, Özgür Esat; Faculty Member; Graduate School of Sciences and Engineering; College of Sciences; N/A; 1674
    We propose a four-level quantum heat engine in an Otto cycle with a working substance of two spins subject to an external magnetic field and coupled to each other by a one-axis twisting spin squeezing nonlinear interaction. We calculate the positive work and the efficiency of the engine for different parameter regimes. In particular, we investigate the effects of quantum correlations at the end of the two isochoric processes of the Otto cycle, as measured by the entanglement of formation and quantum discord, on the work extraction and efficiency. The regimes where the quantum correlations could enhance the efficiency and work extraction are characterized.
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    PublicationOpen Access
    Calculating the local solvent chemical potential in crystal hydrates
    (American Physical Society (APS), 2000) Mezei, M.; Department of Chemical and Biological Engineering; Department of Chemical and Biological Engineering; Reşat, Haluk; Faculty Member; College of Engineering
    Determining solvation patterns in biological systems is crucial in investigating the functional role water may play in structural stabilization and molecular recognition. Determining whether a particular position would be occupied by a solvent molecule requires the local thermodynamics to be known. In this work we introduce a simple and inexpensive approach based on grand canonical molecular simulations to determine the occupancy factors of the cavities. The method is applied to the test case of the sodium salt of hyaluronic acid. The results agree very well with experimental results and demonstrate the success of the method.
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    PublicationOpen Access
    Solution of the quantum fluid dynamical equations with radial basis function interpolation
    (American Physical Society (APS), 2000) Hu, X. G.; Ho, T. S.; Rabitz, H.; Department of Mathematics; Department of Mathematics; Aşkar, Attila; Faculty Member; College of Sciences; 178822
    The paper proposes a numerical technique within the Lagrangian description for propagating the quantum fluid dynamical (QFD) equations in terms of the Madelung field variables R and S, which are connected to the wave function via the transformation Psi= exp{(R + iS)/(h) over bar}. The technique rests on the QFD equations depending only on the form, not the magnitude, of the probability density rho = \psi\(2) and on the structure of R = (h) over bar/2 In rho generally being simpler and smoother than rho. The spatially smooth functions R and S are especially suitable for multivariate radial basis function interpolation to enable the implementation of a robust numerical scheme. Examples of two-dimensional model systems show that the method rivals, in both efficiency and accuracy, the split-operator and Chebychev expansion methods. The results on a three-dimensional model system indicates that the present method is superior to the existing ones, especially, for its low storage requirement and its uniform accuracy. The advantage of the new algorithm is expected to increase fur higher dimensional systems to provide a practical computational tool.