8,391 research outputs found
Restoring a fluctuation-dissipation theorem in a nonequilibrium steady state
In a nonequilibrium steady state, the violation of the
fluctuation-dissipation theorem (FDT) is connected to breaking detailed
balance. For the velocity correlations of a driven colloidal particle we
calculate an explicit expression of the FDT violation. The equilibrium form of
the FDT can be restored by measuring the velocity with respect to the local
mean velocity.Comment: streamlined derivation and minor change
Nonparametric regression penalizing deviations from additivity
Due to the curse of dimensionality, estimation in a multidimensional
nonparametric regression model is in general not feasible. Hence, additional
restrictions are introduced, and the additive model takes a prominent place.
The restrictions imposed can lead to serious bias. Here, a new estimator is
proposed which allows penalizing the nonadditive part of a regression function.
This offers a smooth choice between the full and the additive model. As a
byproduct, this penalty leads to a regularization in sparse regions. If the
additive model does not hold, a small penalty introduces an additional bias
compared to the full model which is compensated by the reduced bias due to
using smaller bandwidths. For increasing penalties, this estimator converges to
the additive smooth backfitting estimator of Mammen, Linton and Nielsen [Ann.
Statist. 27 (1999) 1443-1490]. The structure of the estimator is investigated
and two algorithms are provided. A proposal for selection of tuning parameters
is made and the respective properties are studied. Finally, a finite sample
evaluation is performed for simulated and ozone data.Comment: Published at http://dx.doi.org/10.1214/009053604000001246 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Reversibility Parameter for a Markovian Stepper
Recent experimental studies on the stepwize motion of biological molecular
motors have revealed that the ``characteristic distance'' of a step is usually
less than the actual step size. This observation implies that the
detailed-balance condition for kinetic rates of steps is violated in these
motors. In this letter, in order to clarify the significance of the
characteristic distance, we study a Langevin model of a molecular motor with a
hidden degree of freedom. We find that the ratio of the characteristic distance
to the step size is equal to unity if the dominant paths in the state space are
one dimensional, while it deviates from unity if the dominant paths are
branched. Therefore, this parameter can be utilized to determine the
reversibility of a motor even under a restricted observation.Comment: 6 pages, 2 figures - minor revision
Efficiency of autonomous soft nano-machines at maximum power
We consider nano-sized artificial or biological machines working in steady
state enforced by imposing non-equilibrium concentrations of solutes or by
applying external forces, torques or electric fields. For unicyclic and
strongly coupled multicyclic machines, efficiency at maximum power is not
bounded by the linear response value 1/2. For strong driving, it can even
approach the thermodynamic limit 1. Quite generally, such machines fall in
three different classes characterized, respectively, as "strong and efficient",
"strong and inefficient", and "balanced". For weakly coupled multicyclic
machines, efficiency at maximum power has lost any universality even in the
linear response regime
Front Propagation in the Pearling Instability of Tubular Vesicles
Recently Bar-Ziv and Moses discovered a dynamical shape transformation
induced in cylindrical lipid bilayer vesicles by the action of laser tweezers.
We develop a hydrodynamic theory of fluid bilayers in interaction with the
surrounding water and argue that the effect of the laser is to induce a sudden
tension in the membrane. We refine our previous analysis to account for the
fact that the shape transformation is not uniform but propagates outward from
the laser trap. Applying the marginal stability criterion to this situation
gives us an improved prediction for the selected initial wavelength and a new
prediction for the propagation velocity, both in rough agreement with the
experimental values. For example, a tubule of initial radius 0.7\micron\ has a
predicted initial sinusoidal perturbation in its diameter with wavelength
5.5\micron, as observed. The perturbation propagates as a front with the
qualitatively correct front velocity a bit less than 100\micron/sec. In
particular we show why this velocity is initially constant, as observed, and so
much smaller than the natural scale set by the tension. We also predict that
the front velocity should increase linearly with laser power. Finally we
introduce an approximate hydrodynamic model applicable to the fully nonlinear
regime. This model exhibits propagating fronts as well as fully-developed
``pearled" vesicles similar to those seen in the experiments.Comment: 42 pages, 6 eps figures included with text in uuencoded file, ps file
available from ftp://dept.physics.upenn.edu/pub/Nelson/pearl_propagation.ps
submitted to Journal de Physiqu
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