3,539 research outputs found
Effect of Bilayer Thickness on Membrane Bending Rigidity
The bending rigidity of bilayer vesicles self-assembled from
amphiphilic diblock copolymers has been measured using single and
dual-micropipet techniques. These copolymers are nearly a factor of 5 greater
in hydrophobic membrane thickness than their lipid counterparts, and an
order of magnitude larger in molecular weight . The macromolecular
structure of these amphiphiles lends insight into and extends relationships for
traditional surfactant behavior. We find the scaling of with thickness to
be nearly quadratic, in agreement with existing theories for bilayer membranes.
The results here are key to understanding and designing soft interfaces such as
biomembrane mimetics
Optimal conditions for the numerical calculation of the largest Lyapunov exponent for systems of ordinary differential equations
A general indicator of the presence of chaos in a dynamical system is the
largest Lyapunov exponent. This quantity provides a measure of the mean
exponential rate of divergence of nearby orbits. In this paper, we show that
the so-called two-particle method introduced by Benettin et al. could lead to
spurious estimations of the largest Lyapunov exponent. As a comparator method,
the maximum Lyapunov exponent is computed from the solution of the variational
equations of the system. We show that the incorrect estimation of the largest
Lyapunov exponent is based on the setting of the renormalization time and the
initial distance between trajectories. Unlike previously published works, we
here present three criteria that could help to determine correctly these
parameters so that the maximum Lyapunov exponent is close to the expected
value. The results have been tested with four well known dynamical systems:
Ueda, Duffing, R\"ossler and Lorenz.Comment: 12 pages, 8 figures. Accepted in the International Journal of Modern
Physics
Competing many-body interactions in systems of trapped ions
We propose and theoretically analyse an experimental configuration in which
lasers induce 3-spin interactions between trapped ions.By properly choosing the
intensities and frequencies of the lasers, 3-spin couplings may be dominant or
comparable to 2-spin terms and magnetic fields. In this way, trapped ions can
be used to study exotic quantum phases which do not have a counterpart in
nature. We study the conditions for the validity of the effective 3-spin
Hamiltonian, and predict qualitatively the quantum phase diagram of the system.Comment: RevTex4 file, color figure
Short Range Interactions in the Hydrogen Atom
In calculating the energy corrections to the hydrogen levels we can identify
two different types of modifications of the Coulomb potential , with one
of them being the standard quantum electrodynamics corrections, ,
satisfying over the whole range of
the radial variable . The other possible addition to is a potential
arising due to the finite size of the atomic nucleus and as a matter of fact,
can be larger than in a very short range. We focus here on the latter
and show that the electric potential of the proton displays some undesirable
features. Among others, the energy content of the electric field associated
with this potential is very close to the threshold of pair production.
We contrast this large electric field of the Maxwell theory with one emerging
from the non-linear Euler-Heisenberg theory and show how in this theory the
short range electric field becomes smaller and is well below the pair
production threshold
Topology induced anomalous defect production by crossing a quantum critical point
We study the influence of topology on the quench dynamics of a system driven
across a quantum critical point. We show how the appearance of certain edge
states, which fully characterise the topology of the system, dramatically
modifies the process of defect production during the crossing of the critical
point. Interestingly enough, the density of defects is no longer described by
the Kibble-Zurek scaling, but determined instead by the non-universal
topological features of the system. Edge states are shown to be robust against
defect production, which highlights their topological nature.Comment: Phys. Rev. Lett. (to be published
Dynamical properties of a dissipative discontinuous map: A scaling investigation
The effects of dissipation on the scaling properties of nonlinear
discontinuous maps are investigated by analyzing the behavior of the average
squared action \left as a function of the -th iteration of
the map as well as the parameters and , controlling nonlinearity
and dissipation, respectively. We concentrate our efforts to study the case
where the nonlinearity is large; i.e., . In this regime and for large
initial action , we prove that dissipation produces an exponential
decay for the average action \left. Also, for , we
describe the behavior of \left using a scaling function and
analytically obtain critical exponents which are used to overlap different
curves of \left onto an universal plot. We complete our study
with the analysis of the scaling properties of the deviation around the average
action .Comment: 20 pages, 7 figure
Stochastic Behavior Analysis of the Gaussian Kernel Least-Mean-Square Algorithm
The kernel least-mean-square (KLMS) algorithm is a popular algorithm in nonlinear adaptive filtering due to its
simplicity and robustness. In kernel adaptive filters, the statistics of the input to the linear filter depends on the parameters of the kernel employed. Moreover, practical implementations require a finite nonlinearity model order. A Gaussian KLMS has two design parameters, the step size and the Gaussian kernel bandwidth. Thus, its design requires analytical models for the algorithm behavior as a function of these two parameters. This paper studies the steady-state behavior and the transient behavior of the
Gaussian KLMS algorithm for Gaussian inputs and a finite order nonlinearity model. In particular, we derive recursive expressions for the mean-weight-error vector and the mean-square-error. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady state. This allows the explicit analytical determination of stability limits, and gives opportunity
to choose the algorithm parameters a priori in order to achieve prescribed convergence speed and quality of the estimate. Design examples are presented which validate the theoretical analysis and illustrates its application
Topology induced anomalous defect production by crossing a quantum critical point
We study the influence of topology on the quench dynamics of a system driven
across a quantum critical point. We show how the appearance of certain edge
states, which fully characterise the topology of the system, dramatically
modifies the process of defect production during the crossing of the critical
point. Interestingly enough, the density of defects is no longer described by
the Kibble-Zurek scaling, but determined instead by the non-universal
topological features of the system. Edge states are shown to be robust against
defect production, which highlights their topological nature.Comment: Phys. Rev. Lett. (to be published
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