5,218 research outputs found
Premicellar aggregation of amphiphilic molecules: Aggregate lifetime and polydispersity
A recently introduced thermodynamic model of amphiphilic molecules in
solution has yielded, under certain realistic conditions, a significant
presence of metastable aggregates well below the critical micelle concentration
-- a phenomenon that has been reported also experimentally. The theory is
extended in two directions pertaining to the experimental and technological
relevance of such premicellar aggregates. (a) Combining the thermodynamic model
with reaction rate theory, we calculate the lifetime of the metastable
aggregates. (b) Aggregation number fluctuations are examined. We demonstrate
that, over most of the metastable concentration range, the premicellar
aggregates should have macroscopic lifetimes and small polydispersity.Comment: 7 pages, 2 figure
Update on tests of the Cen A neutron-emission model of highest energy cosmic rays
We propose that neutron emission from Cen A dominates the cosmic ray sky at
the high end of the spectrum. Neutrons that are able to decay generate proton
diffusion fronts, whereas those that survive decay produce a spike in the
direction of the source. We use recent data reported by the Pierre Auger
Collaboration to normalize the injection spectrum and estimate the required
luminosity in cosmic rays. We find that such a luminosity, L_{CR} ~ 5 x 10^{40}
erg/s, is considerably smaller than the bolometric luminosity of Cen A, L_{bol}
~ 10^{43} erg/s. We compute the incoming current flux density as viewed by an
observer on Earth and show that the anisotropy amplitude is in agreement with
data at the 1\sigma level. Regardless of the underlying source model, our
results indicate that after a decade of data taking the Pierre Auger
Observatory will be able to test our proposal.Comment: To be published in PR
On the accuracy of solving confluent Prony systems
In this paper we consider several nonlinear systems of algebraic equations
which can be called "Prony-type". These systems arise in various reconstruction
problems in several branches of theoretical and applied mathematics, such as
frequency estimation and nonlinear Fourier inversion. Consequently, the
question of stability of solution with respect to errors in the right-hand side
becomes critical for the success of any particular application. We investigate
the question of "maximal possible accuracy" of solving Prony-type systems,
putting stress on the "local" behavior which approximates situations with low
absolute measurement error. The accuracy estimates are formulated in very
simple geometric terms, shedding some light on the structure of the problem.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
Exact Nonperturbative Unitary Amplitudes for 1->N Transitions
I present an extension to arbitrary N of a previously proposed field
theoretic model, in which unitary amplitudes for processes were
obtained. The Born amplitude in this extension has the behavior
expected in a bosonic field theory. Unitarity
is violated when , or when Numerical
solutions of the coupled Schr\"odinger equations shows that for weak coupling
and a large range of N>\ncrit, the exact unitary amplitude is reasonably fit
by a factorized expression |A(1->N)| \sim (0.73 /N) \cdot \exp{(-0.025/\g2)}.
The very small size of the coefficient 1/\g2 , indicative of a very weak
exponential suppression, is not in accord with standard discussions based on
saddle point analysis, which give a coefficient The weak dependence
on could have experimental implications in theories where the exponential
suppression is weak (as in this model). Non-perturbative contributions to
few-point correlation functions in this theory would arise at order $K\ \simeq\
\left((0.05/\g2)+ 2\ ln{N}\right)/ \ ln{(1/\g2)}\g2.$Comment: 11 pages, 3 figures (not included
Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials
The mean first passage time (MFPT) for photoexcitations diffusion in a
funneling potential of artificial tree-like light-harvesting antennae
(phenylacetylene dendrimers with generation-dependent segment lengths) is
computed. Effects of the non-linearity of the realistic funneling potential and
slow random solvent fluctuations considerably slow down the center-bound
diffusion beyond a temperature-dependent optimal size. Diffusion on a
disordered Cayley tree with a linear potential is investigated analytically. At
low temperatures we predict a phase in which the MFPT is dominated by a few
paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let
Nitrogen-vacancy singlet manifold ionization energy
The singlet states of the negatively-charged nitrogen-vacancy centers in
diamond play a key role in its optical spin control and readout. In this work,
the hitherto unknown ionization energy of the singlet is measured
experimentally and found to be between 1.91-2.25 eV. This is obtained by
analyzing photoluminescence measurements incorporating spin control and NV
charge state differentiation, along with simulations based on the
nitrogen-vacancy's master equation. This work establishes a protocol for a more
accurate estimate of this ionization energy, which can possibly lead to
improved read-out methods
Don't know, can't know: Embracing deeper uncertainties when analysing risks
This article is available open access through the publisher’s website at the link below. Copyright @ 2011 The Royal Society.Numerous types of uncertainty arise when using formal models in the analysis of risks. Uncertainty is best seen as a relation, allowing a clear separation of the object, source and ‘owner’ of the uncertainty, and we argue that all expressions of uncertainty are constructed from judgements based on possibly inadequate assumptions, and are therefore contingent. We consider a five-level structure for assessing and communicating uncertainties, distinguishing three within-model levels—event, parameter and model uncertainty—and two extra-model levels concerning acknowledged and unknown inadequacies in the modelling process, including possible disagreements about the framing of the problem. We consider the forms of expression of uncertainty within the five levels, providing numerous examples of the way in which inadequacies in understanding are handled, and examining criticisms of the attempts taken by the Intergovernmental Panel on Climate Change to separate the likelihood of events from the confidence in the science. Expressing our confidence in the adequacy of the modelling process requires an assessment of the quality of the underlying evidence, and we draw on a scale that is widely used within evidence-based medicine. We conclude that the contingent nature of risk-modelling needs to be explicitly acknowledged in advice given to policy-makers, and that unconditional expressions of uncertainty remain an aspiration
Evolution of constrained layer damping using a cellular automaton algorithm
Constrained layer damping (CLD) is a highly effective passive vibration control strategy if optimized adequately. Factors controlling CLD performance are well documented for the flexural modes of beams but not for more complicated mode shapes or structures. The current paper introduces an approach that is suitable for locating CLD on any type of structure. It follows the cellular automaton (CA) principle and relies on the use of finite element models to describe the vibration properties of the structure. The ability of the algorithm to reach the best solution is demonstrated by applying it to the bending and torsion modes of a plate. Configurations that give the most weight-efficient coverage for each type of mode are first obtained by adapting the existing 'optimum length' principle used for treated beams. Next, a CA algorithm is developed, which grows CLD patches one at a time on the surface of the plate according to a simple set of rules. The effectiveness of the algorithm is then assessed by comparing the generated configurations with the known optimum ones
Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers
The center-bound excitonic diffusion on dendrimers subjected to several types
of non-homogeneous funneling potentials, is considered. We first study the
mean-first passage time (MFPT) for diffusion in a linear potential with
different types of correlated and uncorrelated random perturbations. Increasing
the funneling force, there is a transition from a phase in which the MFPT grows
exponentially with the number of generations , to one in which it does so
linearly. Overall the disorder slows down the diffusion, but the effect is much
more pronounced in the exponential compared to the linear phase. When the
disorder gives rise to uncorrelated random forces there is, in addition, a
transition as the temperature is lowered. This is a transition from a
high- regime in which all paths contribute to the MFPT to a low- regime
in which only a few of them do. We further explore the funneling within a
realistic non-linear potential for extended dendrimers in which the dependence
of the lowest excitonic energy level on the segment length was derived using
the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT
grows initially linearly with but crosses-over, beyond a molecular-specific
and -dependent optimal size, to an exponential increase. Finally we consider
geometrical disorder in the form of a small concentration of long connections
as in the {\it small world} model. Beyond a critical concentration of
connections the MFPT decreases significantly and it changes to a power-law or
to a logarithmic scaling with , depending on the strength of the funneling
force.Comment: 13 pages, 9 figure
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