Freezing of random RNA

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.     

Secondary structure formation of homopolymeric single-stranded nucleic acids including force and loop entropy: Implications for DNA hybridization

Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy —c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low-temperature/low-force compact (folded) structure and a high-temperature/high-force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c ≲ 2.479 a melting transition is possible; for c ≤ 2 the chain is always in the folded phase and for 2.479 ≲ c always in the unfolded phase. A force-induced melting transition with singular behavior is possible for all loop exponents c < 2.479 and can be observed experimentally by single-molecule force spectroscopy. These findings have implications for the hybridization or denaturation of double-stranded nucleic acids. The Poland-Scheraga model for nucleic acid duplex melting does not allow base pairing between nucleotides on the same strand in denatured regions of the double strand. If the sequence allows these intra-strand base pairs, we show that for a realistic loop exponent c ≈ 2.1 pronounced secondary structures appear inside the single strands. This leads to a lower melting temperature of the duplex than predicted by the Poland-Scheraga model. Further, these secondary structures renormalize the effective loop exponent [^(c)] \hat{{c}}, which characterizes the weight of a denatured region of the double strand, and thus affect universal aspects of the duplex melting transition.     

Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation, and Fragmentation

We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact, and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady-state mass distribution decays exponentially for large mass in one phase. In the other phase, the mass distribution decays as a power law accompanied, in addition, by the formation of an infinite aggregate. The model is solved exactly within a mean-field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time-dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.     

Glassy conformations in wrinkled membranes

Partially polymerized membranes display a striking mechanical transition at low temperature known as the wrinkling transition. Fluorescence and scanning electron microscopy as well as profile measurements using an atomic force microscope revealed the existence of three degrees of wrinkling depending on the degree of the membrane polymerization. At low polymerization the membrane undergoes a cascade of wrinkling to form a folded phase with a characteristic exponent eta equal to 3, at intermediate polymerization, the membrane is in an intermediate-wrinkled phase (similar to the crumpling of an elastic sheet) with eta approximately 2.5, while at high polymerization the membrane undergoes an abrupt "compaction" to the wrinkled-rough phase with eta approximately 2.     

Phase separation and pattern formation in a binary Bose-Einstein condensate

The miscibility-immiscibility phase transition in binary Bose-Einstein condensates (BECs) can be controlled by a coupling between the two components. Here we propose a new scheme that uses coupling-induced pattern formation to test the Kibble-Zurek mechanism (KZM) of topological-defect formation in a quantum phase transition. For a binary BEC in a ring trap we find that the number of domains forming the pattern scales as a function of the coupling quench rate with an exponent as predicted by the KZM. For a binary BEC in an elongated harmonic trap we find a different scaling law due to the transition being spatially inhomogeneous. We perform a "quantum simulation" of the harmonically trapped system in a ring trap to verify the scaling exponent.     

Localization-delocalization transition in a system of quantum kicked rotors

The quantum dynamics of atoms subjected to pairs of closely spaced delta kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the single delta-kick system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power L approximately h(-0.75) and obtain a regime of near-linear spectral variances which approximate the "critical statistics" relation summation2(L) approximately or equal to chi(L) approximately 1/2 (1-nu)L, where nu approximately 0.75 is related to the fractal classical phase-space structure. The origin of the nu approximately 0.75 exponent is analyzed.     

Impact of loop statistics on the thermodynamics of RNA folding

Loops are abundant in native RNA structures and proliferate close to the unfolding transition. By including a statistical weight approximately l(-c) for loops of length l in the recursion relation for the partition function, we show that the heat capacity depends sensitively on the presence and value of the exponent c, even for a short explicit tRNA sequence. For long homo-RNA, we analytically calculate the critical temperature and critical exponents which exhibit a nonuniversal dependence on c.     

面向自组装结构精确控制的聚集结构定量计算及表征方法

在自组装结构形成过程中,热涨落会导致出现多种无定形结构及转化路径. 这些无定型结构对应着不同的粒子聚集程度,但是目前缺乏描述它们的定量方法. 为了实现对自组装结构的精确控制,其中重要的一步是定量描述和分析在自组装结构形成过程中出现的不同聚集结构. 本文提出了一种直接计算以及定量对比不同聚集结构的方法,进一步给出了几个案例研究用来评估聚集结构如何受外界控制因素(如相互作用范围、强度、以及吸引作用的各向异性)的影响.     

Superconductor-insulator transition of Josephson-junction arrays on a honeycomb lattice in a magnetic field

We study the superconductor to insulator transition at zero temperature in aJosephson-junction array model on a honeycomb lattice with f flux quantum perplaquette. The path integral representation of the model corresponds to a (2 + 1)-dimensional classical model, which isused to investigate the critical behavior by extensive Monte Carlo simulations on largesystem sizes. In contrast to the model on a square lattice, the transition is found to befirst order for f = 1 /3 and continuous for f = 1 / 2 but in a different universality class.The correlation-length critical exponent is estimated from finite-size scaling of vortexcorrelations. The estimated universal conductivity at the transition is approximately fourtimes its value for f =0. The results are compared with experimental observations on ultrathinsuperconducting films with a triangular lattice of nanoholes in a transverse magneticfield.     

Statistical models of diffusion and aggregation for coke formation in a catalyst pore

We simulated models of diffusion and aggregation in long pores of small widths in order to represent the basic mechanisms of coke deposition in catalysts’ pores. Coke precursors are represented by particles injected at the pore entrance. Knudsen diffusion, which is usually expected inside the pores, is modeled by ballistic motion of those particles. The regime of molecular diffusion is also analyzed via models of lattice random walks biased along the pores. The aggregation at the surface or near previously aggregated particles was modeled by different probabilistic rules, accounting for the possibilities of more compact or more ramified deposits. In the model of Knudsen diffusion and in some cases of molecular diffusion, there is an initial regime of uniform deposition along the pore, after which the deposits acquire an approximately wedge shape, with the pore plugging near its entrance. After the regime of uniform deposition and before that of critical pore plugging, the average aggregation position slowly decreases with the number N of deposited particles approximately as N^-0.25. The apparently universal features of deposits generated by microscopic models are compared with those currently adopted in continuum models.     

Bose-Einstein condensation of magnons in Cs2CuCl4

We report on results of specific heat measurements on single crystals of the frustrated quasi-2D spin-1/2 antiferromagnet Cs2CuCl4 (T(N)=0.595 K) in external magnetic fields B<12 T and for temperatures T>30 mK. Decreasing B from high fields leads to the closure of the field-induced gap in the magnon spectrum at a critical field Bc approximately = 8.51 T and a magnetic phase transition is clearly seen below Bc. In the vicinity of Bc, the phase transition boundary is well described by the power law Tc(B) proportional, variant (Bc-B)(1/phi), with the measured critical exponent phi approximately =1.5. These findings are interpreted as a Bose-Einstein condensation of magnons.     

Stability analysis of a noise-induced Hopf bifurcation

We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic bifurcation occurs when the Lyapunov exponent of the linearised system becomes positive. We deduce from a simple formula for the Lyapunov exponent the phase diagram of the stochastic Duffing oscillator. The behaviour of physical observables, such as the oscillators mean energy, is studied both close to and far from the bifurcation.Received: 8 August 2003, Published online: 19 November 2003PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.) - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Localization-induced Griffiths phase of disordered Anderson lattices

We demonstrate that local density of states fluctuations in disordered Anderson lattice models universally lead to the emergence of non-Fermi liquid (NFL) behavior. The NFL regime appears at moderate disorder ( W = Wc) and is characterized by power-law anomalies, e.g., C/T approximately 1/T((1-alpha)), where the exponent alpha varies continuously with disorder, as in other Griffiths phases. This Griffiths phase is not associated with the proximity to any magnetic ordering, but reflects the approach to a disorder-driven metal-insulator transition (MIT). Remarkably, the MIT takes place only at much larger disorder W(MIT) approximately 12Wc, resulting in an extraordinarily robust NFL metallic phase.     

半刚性高分子链螺旋结构诱导纳米棒的有序结构

在自然界中, 螺旋结构广泛存在. 在熵的驱动下, 高分子链能在某些特殊情形下形成螺旋结构. 采用分子动力学方法研究了高分子链诱导纳米棒的自组装行为, 发现纳米棒/高分子链体系的构象与纳米棒的数量、高分子链的刚性等密切相关. 当纳米棒与高分子链之间存在适度吸附能时, 纳米棒能够形成三种完全不同的构象, 特别是在半刚性高分子链诱导下纳米棒能够形成线型排列. 研究结果对新型材料制备具有一定指导意义.     

Low temperature disordered phase of alpha-Pb/Ge(111)

A new structural phase transition has been observed at low temperature for the one-third of a monolayer (alpha phase) of Pb on Ge(111) using a variable-temperature scanning tunneling microscope. The well-known (sqrt[3] x sqrt[3])R30 degrees to (3 x 3) transition is accompanied by a new structural phase transition from (3 x 3) to a disordered phase at approximately 76 K. The formation of this "glasslike" phase is a consequence of competing interactions on different length scales.     

Fluctuation conductivity in layered d-wave superconductors near critical disorder

We consider the fluctuation conductivity in the critical region of a disorder induced quantum phase transition in layered d-wave superconductors. We specifically address the fluctuation contribution to the systems conductivity in the limit of large (quasi-two-dimensional system) and small (quasi-three-dimensional system) separation between adjacent layers of the system. Both in-plane and c-axis conductivities were discussed near the point of insulator-superconductor phase transition. The value of the dynamical critical exponent, z = 2, permits a perturbative treatment of this quantum phase transition under the renormalization group approach. We discuss our results for the system conductivities in the critical region as function of temperature and disorder.Received: 10 October 2003, Published online: 23 December 2003PACS: 74.40. + k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.) - 73.43.Nq Quantum phase transitions     

Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions

We compute the Lyapunov exponent, the generalized Lyapunov exponents, and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than periodic orbits, are used in order to avoid the convergence problems of cycle expansions. The emphasis is on the relation between the analytic structure of the zeta function, where a branch cut plays an important role, and the asymptotic dynamics of the system. The Lyapunov exponent for the corresponding map agrees with the conjectured limit _map = -2 log(R) + C + O(R) and we derive an approximate value for the constantC in good agreement with numerical simulations. We also find a diverging diffusion constantD(t)logt and a phase transition for the generalized Lyapunov exponents.     

Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space

In this paper, we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space. It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity, the charged AdS black hole also admits a van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume. Based on this, we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework. On the one hand, we give the phase diagram structures of the charged AdS black hole accurately and analytically, which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity. On the other hand, we analyse the thermodynamic curvature of the black hole in two coordinate spaces. The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive. Based on an empirical conclusion under the framework of thermodynamic geometry, we speculate that when the square of charge is treated as an independent thermodynamic quantity, the charged AdS black hole is likely to present a repulsive between its molecules. More importantly, based on the thermodynamic curvature, we obtain a universal exponent at the critical point of phase transition.     

Aggregation ofNaja nigricollis cardiotoxin: Characterization and quantitative estimate by time-resolved polarized fluorescence

After purification to homogeneity by Bio-Rex 70 ion exchange chromatography, micromolar solutions ofNaja nigricollis cardiotoxin were found to contain significant amounts of aggregates, as detected by time-resolved polarized fluorescence of its single tryptophan residue. The level of cardiotoxin aggregation depends strongly and reversibly on the protein concentration and pH. However, supplementary reverse-phase HPLC completely suppresses this aggregation, resulting in all cases in fluorescence anisotropy decays characteristic of the pure cardiotoxin monomer. The self-association properties of cardiotoxin, in the presence of a possible cofactor eliminated by the HPLC step, may be functionally relevant, and would deserve further investigation. The physical heterogeneity of the cardiotoxin samples required an appropriate model for the analysis of fluorescence depolarization, which was iteratively improved by comparison with experimental results. In this way, an approximate molar fraction of 10–15% aggregated cardiotoxin at a 90M total protein concentration, pH 7, was determined. The fluorescence of the partly aggregated samples is significantly perturbed as compared to the HPLC-treated monomer, indicating that the cardiotoxin aggregate must have an increased average fluorescence lifetime and a strongly decreased initial anisotropy. The decrease in initial anisotropy suggests either an increased mobility of the tryptophan residue upon aggregation or fast energy transfers between residues of different cardiotoxin molecules brought within a short distance in the aggregate. This study illustrates the high sensitivity of the time-resolved fluorescence technique, through both total fluorescence and anisotropy parameters, to low levels of physical or chemical heterogeneity in a protein sample.     

Phase Diagram of 2 × 2 Adsorbates at Surfaces with Hexagonal Symmetry

The phase diagram of a lattice-gas model for 2 2 2 adsorbates at surfaces with hexagonal symmetry has been investigated by Monte Carlo simulations. The model relies on repulsive interactions between the particles for distances up to second nearest neighbor sites. It is shown that first- or second-order phase transitions take place depending on the strength of the interactions. Strong first- or second-neighbor interactions are responsible for a first-order transition while for intermediate interaction strength a second-order transition is possible. The critical exponent for the susceptibility shows the expected value of the four-states Potts model in case of a second-order transition. The value of the critical exponent is reduced when the transition changes from first to second order.