1,491 research outputs found
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
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
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
Bifurcation analysis and phase diagram of a spin-string model with buckled states
We analyze a one-dimensional spin-string model, in which string oscillators
are linearly coupled to their two nearest neighbors and to Ising spins
representing internal degrees of freedom. String-spin coupling induces a
long-range ferromagnetic interaction among spins that competes with a spin-spin
antiferromagnetic coupling. As a consequence, the complex phase diagram of the
system exhibits different flat rippled and buckled states, with first or second
order transition lines between states. The two-dimensional version of the model
has a similar phase diagram, which has been recently used to explain the
rippled to buckled transition observed in scanning tunnelling microscopy
experiments with suspended graphene sheets. Here we describe in detail the
phase diagram of the simpler one-dimensional model and phase stability using
bifurcation theory. This gives additional insight into the physical mechanisms
underlying the different phases and the behavior observed in experiments.Comment: 15 pages, 7 figure
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
Theory of force-extension curves for modular proteins and DNA hairpins
We study a model describing the force-extension curves of modular proteins, nucleic acids, and other
biomolecules made out of several single units or modules. At a mesoscopic level of description, the configuration
of the system is given by the elongations of each of the units. The system free energy includes a double-well
potential for each unit and an elastic nearest-neighbor interaction between them. Minimizing the free energy
yields the system equilibrium properties whereas its dynamics is given by (overdamped) Langevin equations for
the elongations, in which friction and noise amplitude are related by the fluctuation-dissipation theorem. Our
results, both for the equilibrium and the dynamical situations, include analytical and numerical descriptions of
the system force-extension curves under force or length control and agree very well with actual experiments in
biomolecules. Our conclusions also apply to other physical systems comprising a number of metastable units,
such as storage systems or semiconductor superlattices
- …