arXiv subjects

Chao Tang

Publications and source records attributed to Chao Tang.

125 records · Page 7Linked to original sources

arXiv2000

Exact solution of stochastic directed sandpile model

We introduce and analytically solve a directed sandpile model with stochastic toppling rules. The model clearly belongs to a different universality class from its counterpart with deterministic toppling rules, previously solved by Dhar and Ramaswamy. The critical exponents are D_||=7/4, τ=10/7 in two dimensions and D_||=3/2, τ=4/3 in one dimension. The upper critical dimension of the model is three, at which the exponents apart from logarithmic corrections reach their mean-field values D_||=2, τ=3/2.

cond-mat.stat-mech↗

arXiv1999

Simple Models of the Protein Folding Problem

The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I will give an introduction to the problem, and then focus on some recent work concerning the so-called ``designability principle''. The designability of a structure is measured by the number of sequences that have that structure as their unique ground state. Structures differ drastically in terms of their designability; highly designable structures emerge with a number of associated sequences much larger than the average. These highly designable structures 1) possess ``proteinlike'' secondary structures and motifs, 2) are thermodynamically more stable, and 3) fold faster than other structures. These results suggest that protein structures are selected in nature because they are readily designed and stable against mutations, and that such selection simultaneously leads to thermodynamic stability and foldability. According to this picture, a key to the protein folding problem is to understand the emergence and the properties of the highly designable structures.

cond-mat.stat-mech↗

arXiv1999

1/f Noise and Long Configuration Memory in Bak-Tang-Wiesenfeld Models on Narrow Stripes

We report our findings of an 1/f power spectrum for the total amount of sand in directed and undirected Bak-Tang-Wiesenfeld models confined on narrow stripes and driven locally. The underlying mechanism for the 1/f noise in these systems is an exponentially long configuration memory giving rise to a very broad distribution of time scales. Both models are solved analytically with the help of an operator algebra to explicitly show the appearance of the long configuration memory.

cond-mat.stat-mech↗

arXiv1998

Designability, thermodynamic stability, and dynamics in protein folding: a lattice model study

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against mutating the amino-acid sequence, and must be fast folders. We find two criteria which, together, guarantee that a sequence will be ``protein like'': i) the ground state is a highly designable stucture, i. e. the native structure is the ground state of a large number of sequences, and ii) the sequence has a large $Δ/Γ$ ratio, $Δ$ being the average energy separation between the ground state and the excited compact conformations, and $Γ$ the dispersion in energy of excited compact conformations. These two criteria are not incompatible since, on average, sequences whose ground states are highly designable structures have large $Δ/Γ$ values. These two criteria require knowledge only of the compact-state spectrum. These claims are substantiated by the study of 45 sequences, with various values of $Δ/Γ$ and various degrees of designability, by means of a Borst-Kalos-Lebowitz algorithm, and the Ferrenberg-Swendsen histogram optimization method. Finally, we report on the reasons for slow folding. A comparison between a very slow folding sequence, an average folding one and a fast folding one suggests that slow folding originates from a proliferation of nearly compact low-energy conformations, not present for fast folders.

cond-mat.stat-mech↗

arXiv1998

Fractal Dimension of Julia Set for Non-analytic Maps

The Hausdorff dimensions of the Julia sets for non-analytic maps: f(z) = z^2 + epsilon z^* and f(z) = {z^*}^2 + epsilon are calculated perturbatively for small epsilon. It is shown that Ruelle's formula for Hausdorff dimensions of analytic maps can not be generalized to non-analytic maps.

cond-mat.stat-mech↗

arXiv1997

Low Energy Excitations and Phase Transitions in the Frustrated Two-Dimensional XY Model

We study the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with filling factors f=1/3 and 2/5. To obtain a comparison with recent experiments, we investigate the effect of weak quenched bond disorder for f=2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f=1/3 and for f=2/5 with disorder are those of the pure 2D Ising model. The relevant low energy excitations are domain walls, and we show that their properties determine the nature of the phase transition.

cond-mat.stat-mech↗

arXiv1997

Commensurability in One Dimension and the Josephson Junction Ladder

We study a Josephson junction ladder in a magnetic field in the absence of charging effects via a transfer matrix formalism. The eigenvalues of the transfer matrix are found numerically, giving a determination of the different phases of the ladder. The spatial periodicity of the ground state exhibits a devil's staircase as a function of the magnetic flux filling factor f. If the transverse Josephson coupling is varied a continuous superconducting-normal transition in the transverse direction is observed, analogous to the breakdown of the KAM trajectories in dynamical systems. We also examine how these properties may be affected by a current injected along the ladder.

cond-mat.stat-mech↗

arXiv1997

Incommensurability in the Frustrated Two-Dimensional XY Model

To examine the properties of the frustrated XY model at an incommensurate field we have examined a sequence of magnetic filling factors f which approach the irrational value of one minus the golden mean. At all f studied, the system undergoes a finite-temperature weak first-order transition involving the freezing out of Ising-like domain walls. As one approaches incommensurability, the low temperature phase of the system changes from the staircase states found by Halsey to a striped phase consisting of a superlattice of parallel shift (Pott's-like) domain walls.

cond-mat.stat-mech↗

arXiv1997

Are Protein Folds Atypical?

Protein structures are a very special class among all possible structures. It was suggested that a ``designability principle'' plays a crucial role in nature's selection of protein sequences and structures. Here we provide a theoretical base for such a selection principle, using a novel formulation of the protein folding problem based on hydrophobic interactions. A structure is reduced to a string of 0's and 1's which represent the surface and core sites, respectively, as the backbone is traced. Each structure is therefore associated with one point in a high dimensional space. Sequences are represented by strings of their hydrophobicities and thus can be mapped into the same space. A sequence which lies closer to a particular structure in this space than to any other structures will have that structure as its ground state. Atypical structures, namely those far away from other structures in the high dimensional space, have more sequences which fold into them, and are thermodynamically more stable. We argue that the most common folds of proteins are the most atypical in the space of possible structures.

cond-mat.stat-mech↗

arXiv1997

Domain Walls and Phase Transitions in the Frustrated Two-Dimensional XY Model

We study and compare the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with magnetic filling factors f=1/3 and f=2/5. In addition to the spin waves, the low energy excitations of the system consist of various domain walls between degenerate ground states. The lowest energy domain wall has a similar structure for both f=1/3 and f=2/5 and its properties dictate the nature of the phase transition. For f=2/5 these lowest energy walls have a negative energy for binding to each other, giving rise to a branching domain-wall structure and leading to a first order phase transition. For f=1/3 this binding energy is positive, resulting in a linear critical interface. In order to make a comparison to recent experiments, we investigate the effect of small quenched bond disorder for f=2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f=1/3, and for f=2/5 with disorder, fall into the universality class of the two-dimensional Ising model.

cond-mat.stat-mech↗

arXiv1997

Nature of Driving Force for Protein Folding -- A Result From Analyzing the Statistical Potential

In a statistical approach to protein structure analysis, Miyazawa and Jernigan (MJ) derived a $20\times 20$ matrix of inter-residue contact energies between different types of amino acids. Using the method of eigenvalue decomposition, we find that the MJ matrix can be accurately reconstructed from its first two principal component vectors as $M_{ij}=C_0+C_1(q_i+q_j)+C_2 q_i q_j$, with constant $C$'s, and 20 $q$ values associated with the 20 amino acids. This regularity is due to hydrophobic interactions and a force of demixing, the latter obeying Hildebrand's solubility theory of simple liquids.

cond-mat.stat-mech↗

arXiv1996

Why Do Proteins Look Like Proteins?

Protein structures in nature often exhibit a high degree of regularity (secondary structures, tertiary symmetries, etc.) absent in random compact conformations. We demonstrate in a simple lattice model of protein folding that structural regularities are related to high designability and evolutionary stability. We measure the designability of each compact structure by the number of sequences which can design the structure, i.e., which possess the structure as their nondegenerate ground state. We find that compact structures are drastically different in terms of their designability; highly designable structures emerge with a number of associated sequences much larger than the average. These structures are found to have ``protein like'' secondary structure and even tertiary symmetries. In addition, they are also thermodynamically more stable than ordinary structures. These results suggest that protein structures are selected because they are easy to design and stable against mutations, and that such a selection simutaneously leads to thermodynamic stability.

cond-mat↗

arXiv1995

Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

We study $I$-$V$ characteristics of periodic square Nb wire networks as a function of temperature in a transverse magnetic field, with a focus on three fillings 2/5, 1/2, and 0.618 that represent very different levels of incommensurability. For all three fillings, a scaling behavior of $I$-$V$ characteristics is found, suggesting a finite temperature continuous superconducting phase transition. The low-temperature $I$-$V$ characteristics are found to have an exponential form, indicative of the domain-wall excitations.

cond-mat↗

arXiv1995

Phases of Josephson Junction Ladders

We study a Josephson junction ladder in a magnetic field in the absence of charging effects via a transfer matrix formalism. The eigenvalues of the transfer matrix are found numerically, giving a determination of the different phases of the ladder. The spatial periodicity of the ground state exhibits a devil's staircase as a function of the magnetic flux filling factor $f$. If the transverse Josephson coupling is varied a continuous superconducting-normal transition in the transverse direction is observed, analogous to the breakdown of the KAM trajectories in dynamical systems.

cond-mat↗

arXiv1995

Peak Effect in Superconductors: Melting of Larkin Domains

Motivated by the recent observations of the peak effect in high-$T_c$ YBCO superconductors, we reexamine the origin of this unusual phenomenon. We show that the mechanism based on the $k$-dependence (nonlocality) of the vortex-lattice tilt modulus $C_{44}({\bf k})$ cannot account for the essential feature of the peak effect. We propose a scenario in which the peak effect is related to the melting of Larkin domains. In our model, the rise of critical current with increasing temperature is a result of a crossover from the Larkin pinning length to the length scale set by thermally excited free dislocations.

cond-mat↗

arXiv1994

Dynamics of a Driven Single Flux Line in Superconductors

We study the low temperature dynamics of a single flux line in a bulk type-II superconductor, driven by a surface current, both near and above the onset of an instability which sets in at a critical driving. We found that above the critical driving, the velocity profile of the flux line develops a discontinuity.

cond-mat↗

arXiv1994

Self-Organized Criticality in Non-conserved Systems

The origin of self-organized criticality in a model without conservation law (Olami, Feder, and Christensen, Phys. Rev. Lett. {\bf 68}, 1244 (1992)) is studied. The homogeneous system with periodic boundary condition is found to be periodic and neutrally stable. A change to open boundaries results in the invasion of the interior by a ``self-organized'' region. The mechanism for the self-organization is closely related to the synchronization or phase-locking of the individual elements with each other. A simplified model of marginal oscillator locking on a directed lattice is used to explain many of the features in the non-conserved model: in particular, the dependence of the avalanche-distribution exponent on the conservation parameter $α$ is examined.

cond-mat↗