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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6
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Publication Open 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; 49854The 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.Publication Open 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; 49854The 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.Publication Open 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 SciencesThe 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.Publication Open Access Generalized unitarity relation for linear scattering systems in one dimension(Springer, 2019) Department of Physics; Department of Mathematics; Department of Physics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; College of Sciences; 4231We derive a generalized unitarity relation for an arbitrary linear scattering system that may violate unitarity, time-reversal invariance, PT - symmetry, and transmission reciprocity.Publication Open Access Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials(American Institute of Physics (AIP) Publishing, 2013) Eden, A.; Zelik, S. V.; Department of Mathematics; Department of Mathematics; Kalantarov, Varga; Faculty Member; college of sciences; 117655We study initial boundary value problems for the unstable convective Cahn-Hilliard (CH) equation, i.e., the Cahn Hilliard equation whose energy integral is not bounded below. It is well-known that without the convective term, the solutions of the unstable CH equation ?t u + ? 4xu + ?2x(|u|pu) = 0 may blow up in ?nite time for anyp > 0. In contrast to that, we show that the presence of the convective term u?xuin the Cahn-Hilliard equation prevents blow up at least for 0 < p <49. We alsoshow that the blowing up solutions still exist if p is large enough (p ? 2). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered.Publication Open 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; 7129The 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.Publication Open 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 SciencesThe 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.Publication Open Access A note on a strongly damped wave equation with fast growing nonlinearities(American Institute of Physics (AIP) Publishing, 2015) Zelik, Sergey; Department of Mathematics; Department of Mathematics; Kalantarov, Varga; Faculty Member; College of Sciences; 117655A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the nonlinearities involved, the initial boundary value problem for the considered equation is globally well-posed in the class of sufficiently regular solutions and the semigroup generated by the problem possesses a global attractor in the corresponding phase space. These results are obtained for the nonlinearities of an arbitrary polynomial growth and without the assumption that the considered problem has a global Lyapunov function. (C) 2015 AIP Publishing LLCPublication Open Access Self-dual spectral singularities and coherent perfect absorbing lasers without PT-symmetry(Institute of Physics (IOP) Publishing, 2012) Department of Mathematics; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; College of Sciences; 4231A PT-symmetric optically active medium that lases at the threshold gain also acts as a complete perfect absorber at the laser wavelength. This is because spectral singularities of PT-symmetric complex potentials are always accompanied by their time-reversal dual. We investigate the significance of PT-symmetry for the appearance of these self-dual spectral singularities. In particular, using a realistic optical system we show that self-dual spectral singularities can emerge also for non-PT-symmetric configurations. This signifies the existence of non-PT-symmetric coherent perfect absorbing lasers.Publication Open Access Inverted Berezinskii-Kosterlitz-Thouless singularity and high-temperature algebraic order in an Ising model on a scale-free hierarchical-lattice small-world network(American Physical Society (APS), 2006) Hinczewski, Michael; Department of Physics; Department of Physics; Berker, Ahmet Nihat; Faculty Member; College of SciencesWe have obtained exact results for the Ising model on a hierarchical lattice incorporating three key features characterizing many real-world networks-a scale-free degree distribution, a high clustering coefficient, and the small-world effect. By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly clustered, small-world system is studied. Using the self-similar structure of the network, we obtain analytic expressions for the degree distribution P(k) and clustering coefficient C for all p, as well as the average path length center dot for p=0 and 1. The ferromagnetic Ising model on this network is studied through an exact renormalization-group transformation of the quenched bond probability distribution, using up to 562 500 renormalized probability bins to represent the distribution. For p < 0.494, we find power-law critical behavior of the magnetization and susceptibility, with critical exponents continuously varying with p, and exponential decay of correlations away from T-c. For p >= 0.494, in fact where the network exhibits small-world character, the critical behavior radically changes: We find a highly unusual phase transition, namely an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with nonzero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. Approaching T-c from below, the magnetization and the susceptibility, respectively, exhibit the singularities of exp(-C/root T-c-T) and exp(D/root T-c-T), with C and D positive constants. With long-range bond strengths decaying with distance, we see a phase transition with power-law critical singularities for all p, and evaluate an unusually narrow critical region and important corrections to power-law behavior that depend on the exponent characterizing the decay of long-range interactions.