Ripples in a string coupled to Glauber spins

Each oscillator in a linear chain (a string) interacts with a local Ising spin in contact with a thermal bath. These spins evolve according to Glauber dynamics. Below a critical temperature, a rippled state in the string is accompanied by a nonzero spin polarization. The system is shown to form ripples in the string which, for slow spin relaxation, vibrates rapidly about quasi-stationary states described as snapshots of a coarse-grained stroboscopic map. For moderate observation times, ripples are observed irrespective of the final thermodynamically stable state (rippled or not).Comment: 5 pages, 2 figure

Depinning transitions in discrete reaction-diffusion equations

We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The critical parameter values are characterized at the depinning transition and an approximation for the front speed just beyond threshold is given.Comment: 27 pages, 12 figures, to appear in SIAM J. Appl. Mat

Theory of defect dynamics in graphene: defect groupings and their stability

We use our theory of periodized discrete elasticity to characterize defects in graphene as the cores of dislocations or groups of dislocations. Earlier numerical implementations of the theory predicted some of the simpler defect groupings observed in subsequent Transmission Electron Microscope experiments. Here we derive the more complicated defect groupings of three or four defect pairs from our theory, show that they correspond to the cores of two pairs of dislocation dipoles and ascertain their stability.Comment: 11 pages, 7 figures; replaced figure

Wavefront depinning transition in discrete one-dimensional reaction-diffusion systems

Pinning and depinning of wavefronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and controlled by constant external forces. A theory of the depinning transition for these systems, including scaling laws and asymptotics of wavefronts, is presented and confirmed by numerical calculations.Comment: 4 pages, 4 figure

Spin-oscillator model for DNA/RNA unzipping by mechanical force

We model unzipping of DNA/RNA molecules subject to an external force by a spin-oscillator system. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value $F_c$ of an applied external force $F$, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to $(F-F_c)$ as in an Arrhenius law.Comment: 9 pages, 6 figures, submitted to PR

Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins

A fast harmonic oscillator is linearly coupled with a system of Ising spins that are in contact with a thermal bath, and evolve under a slow Glauber dynamics at dimensionless temperature $\theta$. The spins have a coupling constant proportional to the oscillator position. The oscillator-spin interaction produces a second order phase transition at $\theta=1$ with the oscillator position as its order parameter: the equilibrium position is zero for $\theta>1$ and non-zero for $\theta< 1$. For $\theta<1$, the dynamics of this system is quite different from relaxation to equilibrium. For most initial conditions, the oscillator position performs modulated oscillations about one of the stable equilibrium positions with a long relaxation time. For random initial conditions and a sufficiently large spin system, the unstable zero position of the oscillator is stabilized after a relaxation time proportional to $\theta$. If the spin system is smaller, the situation is the same until the oscillator position is close to zero, then it crosses over to a neighborhood of a stable equilibrium position about which keeps oscillating for an exponentially long relaxation time. These results of stochastic simulations are predicted by modulation equations obtained from a multiple scale analysis of macroscopic equations.Comment: 30 pages, 9 figure

Wavelength selection of rippling patterns in myxobacteria

Rippling patterns of myxobacteria appear in starving colonies before they aggregate to form fruiting bodies. These periodic traveling cell density waves arise from the coordination of individual cell reversals, resulting from an internal clock regulating them, and from contact signaling during bacterial collisions. Here we revisit a mathematical model of rippling in myxobacteria due to Igoshin et al.\ [Proc. Natl. Acad. Sci. USA {\bf 98}, 14913 (2001) and Phys. Rev. E {\bf 70}, 041911 (2004)]. Bacteria in this model are phase oscillators with an extra internal phase through which they are coupled to a mean-field of oppositely moving bacteria. Previously, patterns for this model were obtained only by numerical methods and it was not possible to find their wavenumber analytically. We derive an evolution equation for the reversal point density that selects the pattern wavenumber in the weak signaling limit, show the validity of the selection rule by solving numerically the model equations and describe other stable patterns in the strong signaling limit. The nonlocal mean-field coupling tends to decohere and confine patterns. Under appropriate circumstances, it can annihilate the patterns leaving a constant density state via a nonequilibrium phase transition reminiscent of destruction of synchronization in the Kuramoto model.Comment: Revtex 26 pages, 7 figure

Protein unfolding and refolding as transitions through virtual states

Single-molecule atomic force spectroscopy probes elastic properties of titin, ubiquitin and other relevant proteins. We explain bioprotein folding dynamics under both length- and force-clamp by modeling polyprotein modules as particles in a bistable potential, weakly connected by harmonic spring linkers. Multistability of equilibrium extensions provides the characteristic sawtooth force-extension curve. We show that abrupt or stepwise unfolding and refolding under force-clamp conditions involve transitions through virtual states (which are quasi-stationary domain configurations) modified by thermal noise. These predictions agree with experimental observations.Comment: 6 pages, accepted for publication in EPL http://iopscience.iop.org/ep