Majority Rule Dynamics in Finite Dimensions

We investigate the long-time behavior of a majority rule opinion dynamics model in finite spatial dimensions. Each site of the system is endowed with a two-state spin variable that evolves by majority rule. In a single update event, a group of spins with a fixed (odd) size is specified and all members of the group adopt the local majority state. Repeated application of this update step leads to a coarsening mosaic of spin domains and ultimate consensus in a finite system. The approach to consensus is governed by two disparate time scales, with the longer time scale arising from realizations in which spins organize into coherent single-opinion bands. The consequences of this geometrical organization on the long-time kinetics are explored.Comment: 8 pages, 2-column revtex format, 11 figures. Version 2: minor changes in response to referee comments and typos corrected; final version for PR

Distribution of dwell times of a ribosome: effects of infidelity, kinetic proofreading and ribosome crowding

Ribosome is a molecular machine that polymerizes a protein where the sequence of the amino acid residues, the monomers of the protein, is dictated by the sequence of codons (triplets of nucleotides) on a messenger RNA (mRNA) that serves as the template. The ribosome is a molecular motor that utilizes the template mRNA strand also as the track. Thus, in each step the ribosome moves forward by one codon and, simultaneously, elongates the protein by one amino acid. We present a theoretical model that captures most of the main steps in the mechano-chemical cycle of a ribosome. The stochastic movement of the ribosome consists of an alternating sequence of pause and translocation; the sum of the durations of a pause and the following translocation is the time of dwell of the ribosome at the corresponding codon. We derive the analytical expression for the distribution of the dwell times of a ribosome in our model. Whereever experimental data are available, our theoretical predictions are consistent with those results. We suggest appropriate experiments to test the new predictions of our model, particularly, the effects of the quality control mechanism of the ribosome and that of their crowding on the mRNA track.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at DOI:10.1088/1478-3975/8/2/02600

Majority versus minority dynamics: Phase transition in an interacting two-state spin system

We introduce a simple model of opinion dynamics in which binary-state agents evolve due to the influence of agents in a local neighborhood. In a single update step, a fixed-size group is defined and all agents in the group adopt the state of the local majority with probability p or that of the local minority with probability 1-p. For group size G=3, there is a phase transition at p_c=2/3 in all spatial dimensions. For p>p_c, the global majority quickly predominates, while for p<p_c, the system is driven to a mixed state in which the densities of agents in each state are equal. For p=p_c, the average magnetization (the difference in the density of agents in the two states) is conserved and the system obeys classical voter model dynamics. In one dimension and within a Kirkwood decoupling scheme, the final magnetization in a finite-length system has a non-trivial dependence on the initial magnetization for all p.ne.p_c, in agreement with numerical results. At p_c, the exact 2-spin correlation functions decay algebraically toward the value 1 and the system coarsens as in the classical voter model.Comment: 11 pages, 3 figures, revtex4 2-column format; minor revisions for publication in PR

Fate of Zero-Temperature Ising Ferromagnets

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 1/4 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales, with the longer stemming from the influence of a long-lived diagonal stripe ``defect''. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically ``blinking'' metastable states.Comment: 4 pages in column format, 6 figure

Dynamic Scaling in One-Dimensional Cluster-Cluster Aggregation

We study the dynamic scaling properties of an aggregation model in which particles obey both diffusive and driven ballistic dynamics. The diffusion constant and the velocity of a cluster of size $s$ follow $D(s) \sim s^\gamma$ and $v(s) \sim s^\delta$, respectively. We determine the dynamic exponent and the phase diagram for the asymptotic aggregation behavior in one dimension in the presence of mixed dynamics. The asymptotic dynamics is dominated by the process that has the largest dynamic exponent with a crossover that is located at $\delta = \gamma - 1$. The cluster size distributions scale similarly in all cases but the scaling function depends continuously on $\gamma$ and $\delta$. For the purely diffusive case the scaling function has a transition from exponential to algebraic behavior at small argument values as $\gamma$ changes sign whereas in the drift dominated case the scaling function decays always exponentially.Comment: 6 pages, 6 figures, RevTeX, submitted to Phys. Rev.

Dynamics of Social Balance on Networks

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2. A finite network always falls into a socially-balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network does not increase in an update is imposed, then the network quickly reaches a balanced final state.Comment: 10 pages, 7 figures, 2-column revtex4 forma

Equation of State for Macromolecules of Variable Flexibility in Good Solvents: A Comparison of Techniques for Monte Carlo Simulations of Lattice Models

The osmotic equation of state for the athermal bond fluctuation model on the simple cubic lattice is obtained from extensive Monte Carlo simulations. For short macromolecules (chain length N=20) we study the influence of various choices for the chain stiffness on the equation of state. Three techniques are applied and compared in order to critically assess their efficiency and accuracy: the repulsive wall method, the thermodynamic integration method (which rests on the feasibility of simulations in the grand canonical ensemble), and the recently advocated sedimentation equilibrium method, which records the density profile in an external (e.g. gravitation-like) field and infers, via a local density approximation, the equation of state from the hydrostatic equilibrium condition. We confirm the conclusion that the latter technique is far more efficient than the repulsive wall method, but we find that the thermodynamic integration method is similarly efficient as the sedimentation equilibrium method. For very stiff chains the onset of nematic order enforces the formation of isotropic-nematic interface in the sedimentation equilibrium method leading to strong rounding effects and deviations from the true equation of state in the transition regime.Comment: 32 pages, 18 figures, submitted to Phys.Rev.E; one paragraph added to conclusions sectio

Исследование эффективности охлаждения вала печного вентилятора, оснащенного устройствами стержневого тип

The design of the air cooling device for the furnace fan’s shaft of rod type of three standard sizes is proposed. During the experiments at the experimental stand, the convective heat transfer from the surface of these devices to the environment at a different shaft rotation frequency was obtained critically. It was established that in the range of variation of the relative length of the rods from 3.3 to 6.1, a regime close to the self-similar mode takes place, where the heat transfer from their surface can be described by a universal dependence. In the range of variation of the relative length of the rods from 6.1 to 8.6, the experimental data are generalized in the form of a power law with a proportionality coefficient that depends on the ratio of the shaft diameter to the outer diameter of the device. The least coefficient of heat transfer from the external surface was found in ST-346 with the largest outside diameter and, correspondingly, the longest rods, which is apparently due to the fact that in the process of heat transfer from the shaft to the environment, the limiting heat exchange section is the heat supply by heat conduction along of the rods axis. The highest heat transfer coefficient under comparable conditions is observed in ST-286 with medium rods, where the heat supply is more balanced by thermal conductivity along the rods and its removal from their external surfaces by convection to the environment. When comparing the data obtained with CT-286 and CT-220, it was found that at the same shaft rotation frequency, the heat transfer coefficient over the surface of ST-286 is about 15–20 %, which is associated with a decrease in intensity of air blowing of shortened rods of ST-220 due to the decrease in their average linear speed of movement along the circumference. From the analysis of the obtained results, it follows that the most effective in comparable conditions is the device with a maximum diameter of 346 mm, where the dissipated thermal power in the steady state is 1.1 times higher than that of the device with a diameter of 286 mm and 2.0 times greater than for devices with a diameter of 220 mm. The obtained materials can be used in the design of heating and thermal furnaces using forced coolant circulation. © 2017 National University of Science and Technology MISIS. All rights reserved.The work was financially supported by Act 211 of the Government of the Russian Federation, contract no. 02.A03.21.0006