A simple model of DNA denaturation and mutually avoiding walks statistics

Recently Garel, Monthus and Orland [Europhys. Lett. 55, 132 (2001)] considered a model of DNA denaturation in which excluded volume effects within each strand are neglected, while mutual avoidance is included. Using an approximate scheme they found a first order denaturation. We show that a first order transition for this model follows from exact results for the statistics of two mutually avoiding random walks, whose reunion exponent is c > 2, both in two and three dimensions. Analytical estimates of c due to the interactions with other denaturated loops, as well as numerical calculations, indicate that the transition is even sharper than in models where excluded volume effects are fully incorporated. The probability distribution of distances between homologous base pairs decays as a power law at the transition. Received 8 July 2002 / Received in final form 25 July 2002 Published online 17 September 2002     

Why is the DNA denaturation transition first order?

We study a model for the denaturation transition of DNA in which the molecules are considered as being composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d = 2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.     

Nature of the Peierls- to Mott-insulator transition in 1D

In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on the strengths of the electron-phonon coupling and the Hubbard interaction the transition is either first order or evolves continuously across a narrow intermediate phase with finite spin, charge, and optical excitation gaps. Received 7 July 2002 / Received in final form 21 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: holger.fehske@physik.uni-greifswald.de     

Monte Carlo simulations of the classical two-dimensional discrete frustrated model

The classical two-dimensional discrete frustrated φ ⁴ model is studied by Monte Carlo simulations. The correlation function is obtained for two values of a parameter d that determines the frustration in the model. The ground state is a ferro-phase for d = - 0.35 and a commensurate phase with period N = 6 for d = - 0.45. Mean field predicts that at higher temperature the system enters a para-phase via an incommensurate state, in both cases. Monte Carlo data for d = - 0.45 show two phase transitions with a floating-incommensurate phase between them. The phase transition at higher temperature is of the Kosterlitz-Thouless type. Analysis of the data for d = - 0.35 shows only a single phase transition between the floating-fluid phase and the ferro-phase within the numerical error. Received 16 December 2002 / Received in final form 17 January 2003 Published online 6 March 2003 RID="a" ID="a"e-mail: vladimir@shg.ru     

Polaronic behavior in single- and many-electron Holstein model: A new perturbation approach

A new perturbation approach is developed for single- and many-electron Holstein model in one-, two-, and three-dimension. The results show that this approach has a good agreement with the Migdal theory in the adiabatic regime when the coupling is moderate (λ < 1), but with the Lang-Firsov theory in the antiadiabatic regime ( ω/W≫ 1). In the intermediate region, our approach can describe the transition from a large-polaron Fermi-liquid to the small-polaron, and this transition may be discontinuous in adiabatic regime, which means a phase transition appears in many-electron system. In single-electron case, we eliminate the abrupt transition using the degenerate perturbation theory, and the calculated ground state energy and effective mass are successfully compared with those of previous authors. Besides, the method has the advantage of requiring little computational effort. Received 27 December 2001 / Received in final form 8 April 2002 Published online 31 July 2002     

Spontaneous thermal expansion of nematic elastomers

We study the monodomain (single-crystal) nematic elastomer materials, all side-chain siloxane polymers with the same mesogenic groups and crosslinking density, but differing in the type of crosslinking. Increasing the proportion of long di-functional segments of main-chain nematic polymer, acting as network crosslinking, results in dramatic changes in the uniaxial equilibrium thermal expansion on cooling from the isotropic phase. At higher concentration of main chains their behaviour dominates the elastomer properties. At low concentration of main-chain material, we detect two distinct transitions at different temperatures, one attributed to the main-chain, the other to the side-chain component. The effective uniaxial anisotropy of nematic rubber, r(T) = / proportional to the effective nematic order parameter Q(T), is given by an average of the two components and thus reflects the two-transition nature of thermal expansion. The experimental data is compared with the theoretical model of ideal nematic elastomers; applications in high-amplitude thermal actuators are discussed in the end. Received 25 June 2001 and Received in final form 29 September 2001     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

The mechanisms of recrystallization after melting in syndiotactic polypropylene and isotactic polystyrene

Several semicrystalline polymers show a recrystallization after melting during a heating scan. We have studied the mechanisms of such recrystallization processes for two different polymers, namely syndiotactic polypropylene (sPP) and isotactic polystyrene (iPS). This was done by monitoring the structure evolution during the recrystallization process and its changes during a subsequent heating scan via time- and temperature-dependent SAXS measurements, respectively. The results of this study showed that the sPP samples exhibited a recrystallization mechanism similar to the multi-stage route found upon initial crystallization of semicrystalline polymers from an entangled melt. Meanwhile, a different recrystallization mechanism was shown by the iPS samples. In this case, the recrystallization process proceeded as a direct growth into the melt in a one-step process. This is the first time we have observed such a mechanism which resembles the picture presented by the classical models for crystallization from an entangled polymer melt. The reason for such different mechanisms may be related to the initial melt state prior to crystallization. It seems as though, when crystallization sets in an entangled polymer melt, it follows the multi-stage route, whereas if the melt is locally disentangled, it proceeds by a direct growth mechanism. Received 23 July 2001 and Received in final form 4 October 2001     

Magnetism and phase separation in the ground state of the Hubbard model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Néel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed. Received 9 January 2002 Published online 25 June 2002     

Ground-state properties of the Falicov-Kimball model in one and two dimensions

A new numerical method is used to study the ground-state properties of the spinless Falicov-Kimball model in one and two dimensions. The resultant solutions are used to examine the phase diagram of the model as well as possibilities for valence and metal-insulator transitions. In one dimension a comprehensive phase diagram of the model is presented. On the base of this phase diagram, the complete picture of valence and metal-insulator transitions is discussed. In two dimensions the structure of ground-state configurations is described for intermediate interactions between f and d electrons. In this region the phase separation and metal-insulator transitions are found at low f-electron concentrations. It is shown that valence transitions exhibit a staircase structure. Received 20 October 2000     

Solute effects on the helix-coil transition

We discuss the effects of the solvent composition on the helix-coil transition of a polypeptide chain. We use a simple model to demonstrate that improving the hydrogen-bonding ability of the solvent can make the transition less cooperative, without affecting the transition temperature. This effect is very different from other solvent effects which primarily influence the melting transition rather than the cooperativity. Received 10 December 2001 and Received in final form 22 March 2002     

Optical and electrical properties of hydrogenated yttrium nanoparticles

We studied the effect of hydrogen in yttrium nanoparticles on a quartz substrate, using optical spectroscopy and electrical resistance measurements. Pulsed laser deposition is used to obtain the Y clusters in an UHV environment. We show, that these clusters are highly sensitive to monoatomic H₁ produced from ambient hydrogen gas pressures, ranging from 10^-5 to 50 mbar with our experimental arrangement. The changes of optical and electrical properties due to the chemical reaction within the particles are sufficient to consider this material as a possible sensor for low concentrations of hydrogen. Received 29 November 2000     

Incommensurate modulated magnetic structure in orthorhombic EuPdSb

Orthorhombic EuPdSb is known to undergo two magnetic transitions, at 12 K and at T _N≃ 18 K, and in phase III (T < 12 K), single crystal magnetisation data have shown that the spin structure is collinear antiferromagnetic, with magnetic moments along the crystal a axis. From a ¹⁵¹Eu M?ssbauer absorption study, we show that, at any temperature within phase III, all the moments have equal sizes, and that in phase II (12 K< T <18 K) the magnetic structure is modulated and incommensurate with the lattice spacings. The modulation is close to a pure sine-wave just below T _N = 18 K, and it squares up as temperature is lowered. We measured the thermal variations of the first and third harmonics of the moment modulation, and we could determine the first and third harmonics of the exchange coupling. We furthermore show that the antiferromagnetic-incommensurate transition at 12 K is strongly first order, with a hysteresis of 0.05 K, and that the incommensurate-paramagnetic transition at 18 K is weakly first order. Finally, we present an explanation of the spin-flop transition observed in the single crystal magnetisation data in phase III when || in terms of an anisotropic molecular field tensor. Received 17 January 2001 and Received in final form 20 March 2001     

The secondary structure of RNA under tension

We study the force-induced unfolding of random disordered RNA or single-stranded DNA polymers. The system undergoes a second-order phase transition from a collapsed globular phase at low forces to an extensive necklace phase with a macroscopic end-to-end distance at high forces. At low temperatures, the sequence inhomogeneities modify the critical behaviour. We provide numerical evidence for the universality of the critical exponents which, by extrapolation of the scaling laws to zero force, contain useful information on the ground-state (f = 0) properties. This provides a good method for quantitative studies of scaling exponents characterizing the collapsed globule. In order to get rid of the blurring effect of thermal fluctuations, we restrict ourselves to the ground state at fixed external force. We analyze the statistics of rearrangements, in particular below the critical force, and point out its implications for force-extension experiments on single molecules. Received 18 June 2002 and Received in final form 23 September 2002 RID="a" ID="a"e-mail: muller@ipno.in2p3.fr     

Are changes in morphology clear indicators for the glass transition in thin polymer films? Tentative ideas

I present some tentative ideas on the possibility of plastic deformation which might be relevant in ultra-thin polymer films at temperatures close but below the glass transition temperature. Several possible sources for sufficiently strong forces are discussed. The relevance of such forces in experiments aiming at determining thin-film properties like the glass transition temperature, thermal expansion or surface morphology is discussed. Received 19 September 2001 and Received in final form 5 December 2001     

From the melt via mesomorphic and granular crystalline layers to lamellar crystallites: A major route followed in polymer crystallization?

Based on broad and detailed evidence from a large variety of experiments on several polymer systems carried out by other authors and ourselves, a novel concept for understanding the crystallization of polymers from the melt is developed. The experiments generally indicate that the formation and growth of the lamellar crystallites is a multi-step process passing over intermediate states. We suggest a specific route which is compatible with the observations. It is proposed that the initial step is always the creation of a mesomorphic layer which spontaneously thickens, up to a critical value, where it solidifies through a cooperative structural transition. The transition produces a granular crystalline layer, which transforms in the last step into homogeneous lamellar crystallites. The model leads to predictions about the temperature dependencies of the crystal thickness and the growth rate which are at variance with conventional views but in agreement with findings in recent experiments. Received 17 February 2000 and Received in final form 30 March 2000     

Metal-insulator transition in two-dimensional systems with long-range correlated disorder

We study the localization properties of electrons in a two-dimensional model with on-site energies exhibiting long-range correlated disorder. The localization length and conductance of the system are calculated by using the finite size scaling method combined with transfer matrix technique. In the presence of long-range correlations, we find that there is a continuous line of fixed points indicating that the system undergoes a disorder driven Kosterlitz-Thouless-type metal-insulator transition. Received 6 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: wsliu@sjtu.edu.cn     

Localization properties of two interacting particles in a quasi-periodic potential with a metal-insulator transition

We study the influence of many-particle interactions on a metal-insulator transition. We consider the two-interacting-particle problem for onsite interacting particles on a one-dimensional quasiperiodic chain, the so-called Aubry-André model. We show numerically by the decimation method and finite-size scaling that the interaction does not modify the critical parameters such as the transition point and the localization-length exponent. We compare our results to the case of finite density systems studied by means of the density-matrix renormalization scheme. Received 28 June 2001     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002