3,689 research outputs found
A variational principle for volume-preserving dynamics
We provide a variational description of any Liouville (i.e. volume
preserving) autonomous vector fields on a smooth manifold. This is obtained via
a ``maximal degree'' variational principle; critical sections for this are
integral manifolds for the Liouville vector field. We work in coordinates and
provide explicit formulae
Interplane magnetic coupling effects in the multilattice compound Y_2Ba_4Cu_7O_{15}
We investigate the interplane magnetic coupling of the multilattice compound
Y_2Ba_4Cu_7O_{15} by means of a bilayer Hubbard model with inequivalent planes.
We evaluate the spin response, effective interaction and the intra- and
interplane spin-spin relaxation times within the fluctuation exchange
approximation. We show that strong in-plane antiferromagnetic fluctuations are
responsible for a magnetic coupling between the planes, which in turns leads to
a tendency of the fluctuation in the two planes to equalize.
This equalization effect grows whit increasing in-plane antiferromagnetic
fluctuations, i. e., with decreasing temperature and decreasing doping, while
it is completely absent when the in-layer correlation length becomes of the
order of one lattice spacing. Our results provide a good qualitative
description of NMR and NQR experiments in Y_2Ba_4Cu_7O_{15}.Comment: Final version, to appear. in Phys. Rev. B (Rapid Communications),
sched. Jan. 9
FÖRSTER TRANSFER CALCULATIONS BASED ON CRYSTAL STRUCTURE DATA FROM Agmenellum quadruplicatum C-PHYCOCYANIN
Excitation energy transfer in C-phycocyanin is modeled using the Forster inductive resonance mechanism. Detailed calculations are carried out using coordinates and orientations of the chromophores derived from X-ray crystallographic studies of C-phycocyanin from two different species (Schirmer et al, J. Mol. Biol. 184, 257–277 (1985) and ibid., 188, 651-677 (1986)). Spectral overlap integrals are estimated from absorption and fluorescence spectra of C-phycocyanin of Mastigocladus laminosus and its separated subunits. Calculations are carried out for the β-subunit, αβ-monomer, (αβ)3-trimer and (αβ)0-hexamer species with the following chromophore assignments: β155 = 's’(sensitizer), β84 =‘f (fluorescer) and α84 =‘m’(intermediate):]:. The calculations show that excitation transfer relaxation occurs to 3=98% within 200 ps in nearly every case; however, the rates increase as much as 10-fold for the higher aggregates. Comparison with experimental data on fluorescence decay and depolarization kinetics from the literature shows qualitative agreement with these calculations. We conclude that Forster transfer is sufficient to account for all of the observed fluorescence properties of C-phycocyanin in aggregation states up to the hexamer and in the absence of linker polypeptides
Effects of Electronic Correlations on the Thermoelectric Power of the Cuprates
We show that important anomalous features of the normal-state thermoelectric
power S of high-Tc materials can be understood as being caused by doping
dependent short-range antiferromagnetic correlations. The theory is based on
the fluctuation-exchange approximation applied to Hubbard model in the
framework of the Kubo formalism. Firstly, the characteristic maximum of S as
function of temperature can be explained by the anomalous momentum dependence
of the single-particle scattering rate. Secondly, we discuss the role of the
actual Fermi surface shape for the occurrence of a sign change of S as a
function of temperature and doping.Comment: 4 pages, with eps figure
Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds
A description of time-dependent Mechanics in terms of Lagrangian submanifolds
of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is
presented. Two new Tulczyjew triples are discussed. The first one is adapted to
the restricted Hamiltonian formalism and the second one is adapted to the
extended Hamiltonian formalism
Geometrization of Quantum Mechanics
We show that it is possible to represent various descriptions of Quantum
Mechanics in geometrical terms. In particular we start with the space of
observables and use the momentum map associated with the unitary group to
provide an unified geometrical description for the different pictures of
Quantum Mechanics. This construction provides an alternative to the usual GNS
construction for pure states.Comment: 16 pages. To appear in Theor. Math. Phys. Some typos corrected.
Definition 2 in page 5 rewritte
Emergence of good conduct, scaling and Zipf laws in human behavioral sequences in an online world
We study behavioral action sequences of players in a massive multiplayer
online game. In their virtual life players use eight basic actions which allow
them to interact with each other. These actions are communication, trade,
establishing or breaking friendships and enmities, attack, and punishment. We
measure the probabilities for these actions conditional on previous taken and
received actions and find a dramatic increase of negative behavior immediately
after receiving negative actions. Similarly, positive behavior is intensified
by receiving positive actions. We observe a tendency towards anti-persistence
in communication sequences. Classifying actions as positive (good) and negative
(bad) allows us to define binary 'world lines' of lives of individuals.
Positive and negative actions are persistent and occur in clusters, indicated
by large scaling exponents alpha~0.87 of the mean square displacement of the
world lines. For all eight action types we find strong signs for high levels of
repetitiveness, especially for negative actions. We partition behavioral
sequences into segments of length n (behavioral `words' and 'motifs') and study
their statistical properties. We find two approximate power laws in the word
ranking distribution, one with an exponent of kappa-1 for the ranks up to 100,
and another with a lower exponent for higher ranks. The Shannon n-tuple
redundancy yields large values and increases in terms of word length, further
underscoring the non-trivial statistical properties of behavioral sequences. On
the collective, societal level the timeseries of particular actions per day can
be understood by a simple mean-reverting log-normal model.Comment: 6 pages, 5 figure
Role of the Wnt receptor Frizzled-1 in presynaptic differentiation and function
<p>Abstract</p> <p>Background</p> <p>The <it>Wnt </it>signaling pathway regulates several fundamental developmental processes and recently has been shown to be involved in different aspects of synaptic differentiation and plasticity. Some <it>Wnt </it>signaling components are localized at central synapses, and it is thus possible that this pathway could be activated at the synapse.</p> <p>Results</p> <p>We examined the distribution of the <it>Wnt </it>receptor Frizzled-1 in cultured hippocampal neurons and determined that this receptor is located at synaptic contacts co-localizing with presynaptic proteins. Frizzled-1 was found in functional synapses detected with FM1-43 staining and in synaptic terminals from adult rat brain. Interestingly, overexpression of Frizzled-1 increased the number of clusters of Bassoon, a component of the active zone, while treatment with the extracellular cysteine-rich domain (CRD) of Frizzled-1 decreased Bassoon clustering, suggesting a role for this receptor in presynaptic differentiation. Consistent with this, treatment with the Frizzled-1 ligand <it>Wnt-3a </it>induced presynaptic protein clustering and increased functional presynaptic recycling sites, and these effects were prevented by co-treatment with the CRD of Frizzled-1. Moreover, in synaptically mature neurons <it>Wnt-3a </it>was able to modulate the kinetics of neurotransmitter release.</p> <p>Conclusion</p> <p>Our results indicate that the activation of the <it>Wnt </it>pathway through Frizzled-1 occurs at the presynaptic level, and suggest that the synaptic effects of the <it>Wnt </it>signaling pathway could be modulated by local activation through synaptic Frizzled receptors.</p
On higher analogues of Courant algebroids
In this paper, we study the algebraic properties of the higher analogues of
Courant algebroid structures on the direct sum bundle
for an -dimensional manifold. As an application, we revisit Nambu-Poisson
structures and multisymplectic structures. We prove that the graph of an
-vector field is closed under the higher-order Dorfman bracket iff
is a Nambu-Poisson structure. Consequently, there is an induced Leibniz
algebroid structure on . The graph of an -form is
closed under the higher-order Dorfman bracket iff is a
premultisymplectic structure of order , i.e. \dM\omega=0. Furthermore,
there is a Lie algebroid structure on the admissible bundle
. In particular, for a 2-plectic structure, it induces
the Lie 2-algebra structure given in \cite{baez:classicalstring}.Comment: 13 page
Geometric Integration of Hamiltonian Systems Perturbed by Rayleigh Damping
Explicit and semi-explicit geometric integration schemes for dissipative
perturbations of Hamiltonian systems are analyzed. The dissipation is
characterized by a small parameter , and the schemes under study
preserve the symplectic structure in the case . In the case
the energy dissipation rate is shown to be asymptotically
correct by backward error analysis. Theoretical results on monotone decrease of
the modified Hamiltonian function for small enough step sizes are given.
Further, an analysis proving near conservation of relative equilibria for small
enough step sizes is conducted.
Numerical examples, verifying the analyses, are given for a planar pendulum
and an elastic 3--D pendulum. The results are superior in comparison with a
conventional explicit Runge-Kutta method of the same order
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