1,145 research outputs found
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
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
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 . The spins have a coupling
constant proportional to the oscillator position. The oscillator-spin
interaction produces a second order phase transition at with the
oscillator position as its order parameter: the equilibrium position is zero
for and non-zero for . For , 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 . 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
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 of
an applied external force , 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 as
in an Arrhenius law.Comment: 9 pages, 6 figures, submitted to PR
Statics and dynamics of a harmonic oscillator coupled to a one-dimensional Ising system
We investigate an oscillator linearly coupled with a one-dimensional Ising
system. The coupling gives rise to drastic changes both in the oscillator
statics and dynamics. Firstly, there appears a second order phase transition,
with the oscillator stable rest position as its order parameter. Secondly, for
fast spins, the oscillator dynamics is described by an effective equation with
a nonlinear friction term that drives the oscillator towards the stable
equilibrium state.Comment: Proceedings of the 2010 Granada Semina
Self-sustained current oscillations in the kinetic theory of semiconductor superlattices
We present the first numerical solutions of a kinetic theory description of
self-sustained current oscillations in n-doped semiconductor superlattices. The
governing equation is a single-miniband Boltzmann-Poisson transport equation
with a BGK (Bhatnagar-Gross-Krook) collision term. Appropriate boundary
conditions for the distribution function describe electron injection in the
contact regions. These conditions seamlessly become Ohm's law at the injecting
contact and the zero charge boundary condition at the receiving contact when
integrated over the wave vector. The time-dependent model is numerically solved
for the distribution function by using the deterministic Weighted Particle
Method. Numerical simulations are used to ascertain the convergence of the
method. The numerical results confirm the validity of the Chapman-Enskog
perturbation method used previously to derive generalized drift-diffusion
equations for high electric fields because they agree very well with numerical
solutions thereof.Comment: 26 pages, 16 figures, to appear in J. Comput. Phy
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
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