1,878 research outputs found
Asymptotic construction of pulses in the Hodgkin Huxley model for myelinated nerves
A quantitative description of pulses and wave trains in the spatially
discrete Hodgkin-Huxley model for myelinated nerves is given. Predictions of
the shape and speed of the waves and the thresholds for propagation failure are
obtained. Our asymptotic predictions agree quite well with numerical solutions
of the model and describe wave patterns generated by repeated firing at a
boundary.Comment: to appear in Phys. Rev.
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
Oscillatory wave fronts in chains of coupled nonlinear oscillators
Wave front pinning and propagation in damped chains of coupled oscillators
are studied. There are two important thresholds for an applied constant stress
: for (dynamic Peierls stress), wave fronts fail to propagate,
for stable static and moving wave fronts coexist, and
for (static Peierls stress) there are only stable moving wave
fronts. For piecewise linear models, extending an exact method of Atkinson and
Cabrera's to chains with damped dynamics corroborates this description. For
smooth nonlinearities, an approximate analytical description is found by means
of the active point theory. Generically for small or zero damping, stable wave
front profiles are non-monotone and become wavy (oscillatory) in one of their
tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.
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
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
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
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