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

Single-turn Coils for Magnetic Pulse Welding of High-strength Steel Parts

Magnetic pulse welding provides high quality joining of fuel pin cladding for fast nuclear reactors. The tool coil there operates under the most stressful conditions: 40 T magnetic fields with tens of microseconds duration. This requires minimal coil inductance and affects the capabilities and lifetime of the coils. Two approaches are being practiced to enhance the coil durability: material research and construction optimization. The first approach considers the use of high strength steels or composite materials for the coil working area. The present work is aimed to realize the second approach – the use of multi position coils in order to maximize the number of parts welded in one coil. Experiments and finite element modeling were carried out for two designs of two- and four-position single-turn coils, which were made to process several workpieces in one current pulse. The main parameters measured and calculated were the magnetic field between the coil and the workpiece, and the ratio of its amplitude to the discharge current, Bm/Im. The currents flowing through the coils were about 700 kA, which correspond to the magnetic fields of 40–45 T. The FEM modeling revealed a 17–19% drop of the magnetic induction near the insulated slit, which, however, did not prevent the helium-tight joining of the tubes to the end plugs

Phase separation of the Potts model in que square lattice

When the two dimensional q-color Potts model in the square lattice is quenched at zero temperature with Glauber dynamics, the energy decreases in time following an Allen-Cahn power law, and the system converges to a phase with energy higher than the ground state energy after an arbitrary large time when q>4. At low but finite temperature, it cesses to obey the power-law regime and orders after a very long time, which increases with q, and before which it performs a domain growth process which tends to be slower as q increases. We briefly present and comment numerical results on the ordering at nonzero temperature.Comment: 3 pages, 1 figure, proceedings of the "International Workshop on Complex sytems", June 2006 in Santander (Spain

Temperature-driven single-valley Dirac fermions in HgTe quantum wells

We report on temperature-dependent magnetospectroscopy of two HgTe/CdHgTe quantum wells below and above the critical well thickness $d_c$. Our results, obtained in magnetic fields up to 16 T and temperature range from 2 K to 150 K, clearly indicate a change of the band-gap energy with temperature. The quantum well wider than $d_c$ evidences a temperature-driven transition from topological insulator to semiconductor phases. At the critical temperature of 90 K, the merging of inter- and intra-band transitions in weak magnetic fields clearly specifies the formation of gapless state, revealing the appearance of single-valley massless Dirac fermions with velocity of $5.6\times10^5$ m$\times$s$^{-1}$. For both quantum wells, the energies extracted from experimental data are in good agreement with calculations on the basis of the 8-band Kane Hamiltonian with temperature-dependent parameters.Comment: 5 pages, 3 figures and Supplemental Materials (4 pages

Stochastic kinetics of ribosomes: single motor properties and collective behavior

Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an {\it exact} analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a ``Michaelis-Menten-like'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in 3-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.Comment: Final published versio

Expert system of diagnostics blast furnace process

The expert system of diagnostics blast furnace process is presented. It is based on a logical-mathematical model for assessing the progress of blast furnace smelting. The model provides an opportunity to evaluate the normal operation mode of blast furnace and further deviations from this mode such as overdeveloped gas flows (peripheral and central), violation of thermal melting conditions (hot and cold course of melt), violation of smooth descent of burned materials in the furnace (tight furnace operation, higher and lower suspension of burden). The functional capabilities of developed software are represented. © Published under licence by IOP Publishing Ltd

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

Particles Sliding on a Fluctuating Surface: Phase Separation and Power Laws

We study a system of hard-core particles sliding downwards on a fluctuating one-dimensional surface which is characterized by a dynamical exponent $z$. In numerical simulations, an initially random particle density is found to coarsen and obey scaling with a growing length scale $\sim t^{1/z}$. The structure factor deviates from the Porod law in some cases. The steady state is unusual in that the density-segregation order parameter shows strong fluctuations. The two-point correlation function has a scaling form with a cusp at small argument which we relate to a power law distribution of particle cluster sizes. Exact results on a related model of surface depths provides insight into the origin of this behaviour.Comment: 5 pages, 5 Postscript figure