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Register a new userNonequilibrium Critical Dynamics of a Three Species Monomer-Monomer Model
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We study a three species monomer-monomer catalytic surface reaction model with a reactive steady state bordered by three equivalent unreactive phases where the surface is saturated with one species. The transition from the reactive to a saturated phase shows directed percolation critical behavior. Each pair of these reactive-saturated phase boundaries join at a bicritical point where the universal behavior is in the even branching annihilating random walk class. We find the crossover exponent from bicritical to critical behavior and a new exponent associated with the bicritical interface dynamics.
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We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known method of a Temperley bijection of solving single-monomer problems cannot be used. In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value $c=-2$.
We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs) of stiff chains growing like t^{3/4} with time due to bending motions, and the Rouse-like regime t^{2 u / (1+ 2 u)} where u is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the prefactors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l^2_p (at a time proportional to l^3_p). A second crossover (to diffusive motion) occurs when the MSD is of order R^2. Large scale Molecular Dynamics simulations of a bead-spring model with a bond bending potential (allowing to vary l_p from 1 to 200 Lennard-Jones units) provide compelling evidence for the theory, in D=2 dimensions where u=3/4. Our results should be valuable for understanding the dynamics of DNA (and other semiflexible biopolymers) adsorbed on substrates.
We study the number of dimer-monomers $M_d(n)$ on the Tower of Hanoi graphs $TH_d(n)$ at stage $n$ with dimension $d$ equal to 3 and 4. The entropy per site is defined as $z_{TH_d}=lim_{v to infty} ln M_d(n)/v$, where $v$ is the number of vertices on $TH_d(n)$. We obtain the lower and upper bounds of the entropy per site, and the convergence of these bounds approaches to zero rapidly when the calculated stage increases. The numerical value of $z_{TH_d}$ is evaluated to more than a hundred digits correct. Using the results with $d$ less than or equal to 4, we predict the general form of the lower and upper bounds for $z_{TH_d}$ with arbitrary $d$.
Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the intrachain subchain size distribution. Irrespective of the density sufficiently long chains are found to consist of compact packings of blobs of fractal perimeter dimension dp = 5/4.
Protein assembly plays an important role throughout all phyla of life, both physiologically and pathologically. In particular, aggregation and polymerization of proteins are key-strategies that regulate cellular function. In recent years, methods to experimentally study the assembly process on a single-molecule level have been developed. This progress concomitantly has triggered the question of how to analyze this type of single-filament data adequately and what experimental conditions are necessary to allow a meaningful interpretation of the analysis. Here, we developed two analysis methods for single-filament data: the visitation analysis and the average-rate analysis. We benchmarked and compared both approaches with the classic dwell-time-analysis frequently used to study microscopic association and dissociation rates. In particular, we tested the limitations of each analysis method along the lines of the signal-to-noise ratio, the sampling rate, and the labeling efficiency and bleaching rate of the fluorescent dyes used in single-molecule fluorescence experiments. Finally, we applied our newly developed methods to study the monomer assembly of actin at the single-molecule-level in the presence of the class II nucleator Cappuccino and the WH2 repeats of Spire. For Cappuccino, our data indicated fast elongation circumventing a nucleation phase whereas, for spire, we found that the four WH2 motifs are not sufficient to promote de novo nucleation of actin.
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