5,379 research outputs found
Swelling of particle-encapsulating random manifolds
We study the statistical mechanics of a closed random manifold of fixed area
and fluctuating volume, encapsulating a fixed number of noninteracting
particles. Scaling analysis yields a unified description of such swollen
manifolds, according to which the mean volume gradually increases with particle
number, following a single scaling law. This is markedly different from the
swelling under fixed pressure difference, where certain models exhibit
criticality. We thereby indicate when the swelling due to encapsulated
particles is thermodynamically inequivalent to that caused by fixed pressure.
The general predictions are supported by Monte Carlo simulations of two
particle-encapsulating model systems -- a two-dimensional self-avoiding ring
and a three-dimensional self-avoiding fluid vesicle. In the former the
particle-induced swelling is thermodynamically equivalent to the
pressure-induced one whereas in the latter it is not.Comment: 8 pages, 6 figure
The Potential of Restarts for ProbSAT
This work analyses the potential of restarts for probSAT, a quite successful
algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT
instances that are close to the phase transition. We estimate an optimal
restart time from empirical data, reaching a potential speedup factor of 1.39.
Calculating restart times from fitted probability distributions reduces this
factor to a maximum of 1.30. A spin-off result is that the Weibull distribution
approximates the runtime distribution for over 93% of the used instances well.
A machine learning pipeline is presented to compute a restart time for a
fixed-cutoff strategy to exploit this potential. The main components of the
pipeline are a random forest for determining the distribution type and a neural
network for the distribution's parameters. ProbSAT performs statistically
significantly better than Luby's restart strategy and the policy without
restarts when using the presented approach. The structure is particularly
advantageous on hard problems.Comment: Eurocast 201
Stability of Quasicrystals Composed of Soft Isotropic Particles
Quasicrystals whose building blocks are of mesoscopic rather than atomic
scale have recently been discovered in several soft-matter systems. Contrary to
metallurgic quasicrystals whose source of stability remains a question of great
debate to this day, we argue that the stability of certain soft-matter
quasicrystals can be directly explained by examining a coarse-grained free
energy for a system of soft isotropic particles. We show, both theoretically
and numerically, that the stability can be attributed to the existence of two
natural length scales in the pair potential, combined with effective three-body
interactions arising from entropy. Our newly gained understanding of the
stability of soft quasicrystals allows us to point at their region of stability
in the phase diagram, and thereby may help control the self-assembly of
quasicrystals and a variety of other desired structures in future experimental
realizations.Comment: Revised abstract, more detailed explanations, and better images of
the numerical minimization of the free energ
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
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
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
Predictions for the Cosmogenic Neutrino Flux in Light of New Data from the Pierre Auger Observatory
The Pierre Auger Observatory (PAO) has measured the spectrum and composition
of the ultrahigh energy cosmic rays with unprecedented precision. We use these
measurements to constrain their spectrum and composition as injected from their
sources and, in turn, use these results to estimate the spectrum of cosmogenic
neutrinos generated in their propagation through intergalactic space. We find
that the PAO measurements can be well fit if the injected cosmic rays consist
entirely of nuclei with masses in the intermediate (C, N, O) to heavy (Fe, Si)
range. A mixture of protons and heavier species is also acceptable but (on the
basis of existing hadronic interaction models) injection of pure light nuclei
(p, He) results in unacceptable fits to the new elongation rate data. The
expected spectrum of cosmogenic neutrinos can vary considerably, depending on
the precise spectrum and chemical composition injected from the cosmic ray
sources. In the models where heavy nuclei dominate the cosmic ray spectrum and
few dissociated protons exceed GZK energies, the cosmogenic neutrino flux can
be suppressed by up to two orders of magnitude relative to the all-proton
prediction, making its detection beyond the reach of current and planned
neutrino telescopes. Other models consistent with the data, however, are
proton-dominated with only a small (1-10%) admixture of heavy nuclei and
predict an associated cosmogenic flux within the reach of upcoming experiments.
Thus a detection or non-detection of cosmogenic neutrinos can assist in
discriminating between these possibilities.Comment: 10 pages, 7 figure
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