305 research outputs found
Characteristics of Conservation Laws for Difference Equations
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not derivations and do not obey the chain rule for derivatives. We show how these problems may be resolved and illustrate various uses of the characteristic. In particular, we establish the converse of Noether's Theorem for difference equations, we show (without taking a continuum limit) that the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and we obtain all five-point conservation laws for the potential Lotka-Volterra equation
Electronic transport through ballistic chaotic cavities: reflection symmetry, direct processes, and symmetry breaking
We extend previous studies on transport through ballistic chaotic cavities
with spatial left-right (LR) reflection symmetry to include the presence of
direct processes. We first analyze fully LR-symmetric systems in the presence
of direct processes and compare the distribution w(T) of the transmission
coefficient T with that for an asymmetric cavity with the same "optical" S
matrix. We then study the problem of "external mixing" of the symmetry caused
by an asymmetric coupling of the cavity to the outside. We first consider the
case where symmetry breaking arises because two symmetrically positioned
waveguides are coupled to the cavity by means of asymmetric tunnel barriers.
Although this system is asymmetric with respect to the LR operation, it has a
striking memory of the symmetry of the cavity it was constructed from.
Secondly, we break LR symmetry in the absence of direct proceses by
asymmetrically positioning the two waveguides and compare the results with
those for the completely asymmetric case.Comment: 15 pages, 8 Postscript figures, submitted to Phys. Rev.
Stokes Diagnostis of 2D MHD-simulated Solar Magnetogranulation
We study the properties of solar magnetic fields on scales less than the
spatial resolution of solar telescopes. A synthetic infrared
spectropolarimetric diagnostics based on a 2D MHD simulation of
magnetoconvection is used for this. We analyze two time sequences of snapshots
that likely represent two regions of the network fields with their immediate
surrounding on the solar surface with the unsigned magnetic flux density of 300
and 140 G. In the first region we find from probability density functions of
the magnetic field strength that the most probable field strength at logtau_5=0
is equal to 250 G. Weak fields (B < 500 G) occupy about 70% of the surface,
while stronger fields (B 1000 G) occupy only 9.7% of the surface. The magnetic
flux is -28 G and its imbalance is -0.04. In the second region, these
parameters are correspondingly equal to 150 G, 93.3 %, 0.3 %, -40 G, and -0.10.
We estimate the distribution of line-of-sight velocities on the surface of log
tau_5=-1. The mean velocity is equal to 0.4 km/s in the first simulated region.
The averaged velocity in the granules is -1.2 km/s and in the intergranules is
2.5 km/s. In the second region, the corresponding values of the mean velocities
are equal to 0, -1.8, 1.5 km/s. In addition we analyze the asymmetry of
synthetic Stokes-V profiles of the Fe I 1564.8 nm line. The mean values of the
amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude
asymmetry is increased to 10% while the area asymmetry is only slightly varied.Comment: 24 pages, 12 figure
An expansion for polynomials orthogonal over an analytic Jordan curve
We consider polynomials that are orthogonal over an analytic Jordan curve L
with respect to a positive analytic weight, and show that each such polynomial
of sufficiently large degree can be expanded in a series of certain integral
transforms that converges uniformly in the whole complex plane. This expansion
yields, in particular and simultaneously, Szego's classical strong asymptotic
formula and a new integral representation for the polynomials inside L. We
further exploit such a representation to derive finer asymptotic results for
weights having finitely many singularities (all of algebraic type) on a thin
neighborhood of the orthogonality curve. Our results are a generalization of
those previously obtained in [7] for the case of L being the unit circle.Comment: 15 pages, 1 figur
Magnetic and lattice polaron in Holstein-t-J model
We investigate the interplay between the formation of lattice and magnetic
polaron in the case of a single hole in the antiferromagnetic background. We
present an exact analytical solution of the Holstein-t-J model in infinite
dimensions. Ground state energy, electron-lattice correlation function, spin
bag dimension as well as spectral properties are calculated. The magnetic and
hole-lattice correlations sustain each other, i.e. the presence of
antiferromagnetic correlations favors the formation of the lattice polaron at
lower value of the electron-phonon coupling while the polaronic effect
contributes to reduce the number of spin defects in the antiferromagnetic
background. The crossover towards a spin-lattice small polaron region of the
phase diagram becomes a discontinuous transition in the adiabatic limit.Comment: revtex, 8 eps figures included NEW version. Appendix with a full
proof include
Raman phonons as a probe of disorder, fluctuations and local structure in doped and undoped orthorhombic and rhombohedral manganites
We present a rationalization of the Raman spectra of orthorhombic and
rhombohedral, stoichiometric and doped, manganese perovskites. In particular we
study RMnO3 (R= La, Pr, Nd, Tb, Ho, Er, Y and Ca) and the different phases of
Ca or Sr doped RMnO3 compounds as well as cation deficient RMnO3. The spectra
of manganites can be understood as combinations of two kinds of spectra
corresponding to two structural configurations of MnO6 octahedra and
independently of the average structure obtained by diffraction techniques. The
main peaks of compounds with regular MnO6 octahedra, as CaMnO3, highly Ca doped
LaMnO3 or the metallic phases of Ca or Sr doped LaMnO3, are bending and tilt
MnO6 octahedra modes which correlate to R-O(1) bonds and Mn-O-Mn angles
respectively. In low and optimally doped manganites, the intensity and width of
the broad bands are related to the amplitude of the dynamic fluctuations
produced by polaron hopping in the paramagnetic insulating regime. The
activation energy, which is proportional to the polaron binding energy, is the
measure of this amplitude. This study permits to detect and confirm the
coexistence, in several compounds, of a paramagnetic matrix with lattice
polaron together with regions without dynamic or static octahedron distortions,
identical to the ferromagnetic metallic phase. We show that Raman spectroscopy
is an excellent tool to obtain information on the local structure of the
different micro or macro-phases present simultaneously in many manganites.Comment: Submitted to PR
The Sunrise Mission
The first science flight of the balloon-borne \Sunrise telescope took place
in June 2009 from ESRANGE (near Kiruna/Sweden) to Somerset Island in northern
Canada. We describe the scientific aims and mission concept of the project and
give an overview and a description of the various hardware components: the 1-m
main telescope with its postfocus science instruments (the UV filter imager
SuFI and the imaging vector magnetograph IMaX) and support instruments (image
stabilizing and light distribution system ISLiD and correlating wavefront
sensor CWS), the optomechanical support structure and the instrument mounting
concept, the gondola structure and the power, pointing, and telemetry systems,
and the general electronics architecture. We also explain the optimization of
the structural and thermal design of the complete payload. The preparations for
the science flight are described, including AIV and ground calibration of the
instruments. The course of events during the science flight is outlined, up to
the recovery activities. Finally, the in-flight performance of the
instrumentation is briefly summarized.Comment: 35 pages, 17 figure
Phenomenological description of quantum gravity inspired modified classical electrodynamics
We discuss a large class of phenomenological models incorporating quantum
gravity motivated corrections to electrodynamics. The framework is that of
electrodynamics in a birefringent and dispersive medium with non-local
constitutive relations, which are considered up to second order in the inverse
of the energy characterizing the quantum gravity scale. The energy-momentum
tensor, Green functions and frequency dependent refraction indices are
obtained, leading to departures from standard physics. The effective character
of the theory is also emphasized by introducing a frequency cutoff. The
analysis of its effects upon the standard notion of causality is performed,
showing that in the radiation regime the expected corrections get further
suppressed by highly oscillating terms, thus forbiding causality violations to
show up in the corresponding observational effects.Comment: 14 pages, to be published in Obregon Festschrift 2006, Gen. Rel. and
Gra
Fatigue in Women with Fibromyalgia: A Gene-Physical Activity Interaction Study
Fatigue is a cardinal symptom in fibromyalgia. Fatigue is assumed to be the result of genetic susceptibility and environmental factors. We aimed at examining the role of genetic susceptibility for fatigue in southern Spanish women with fibromyalgia, by looking at single nucleotide polymorphisms in 34 fibromyalgia candidate-genes, at the interactions between genes, and at the gene-physical activity interactions. We extracted DNA from saliva of 276 fibromyalgia women to analyze gene-polymorphisms. Accelerometers registered physical activity and sedentary behavior. Fatigue was assessed with the Multidimensional Fatigue Inventory. Based on the Bonferroni's and False Discovery Rate values, we found that the genotype of the rs4453709 polymorphism (sodium channel protein type 9 subunit alpha, SCN9A, gene) was related to reduced motivation (AT carriers showed the highest reduced motivation) and reduced activity (AA carriers showed the lowest reduced activity). Carriers of the heterozygous genotype of the rs1801133 (methylene tetrahydrofolate reductase, MTHFR, gene) or rs4597545 (SCN9A gene) polymorphisms who were physically active reported lower scores on fatigue compared to their inactive counterparts. Highly sedentary carriers of the homozygous genotype of the rs7607967 polymorphism (AA/GG genotype; SCN9A gene) presented more reduced activity (a dimension of fatigue) than those with lower levels of sedentary behavior. Collectively, findings from the present study suggest that the contribution of genetics and gene-physical activity interaction to fatigue in fibromyalgia is modest
Modeling the Subsurface Structure of Sunspots
While sunspots are easily observed at the solar surface, determining their
subsurface structure is not trivial. There are two main hypotheses for the
subsurface structure of sunspots: the monolithic model and the cluster model.
Local helioseismology is the only means by which we can investigate
subphotospheric structure. However, as current linear inversion techniques do
not yet allow helioseismology to probe the internal structure with sufficient
confidence to distinguish between the monolith and cluster models, the
development of physically realistic sunspot models are a priority for
helioseismologists. This is because they are not only important indicators of
the variety of physical effects that may influence helioseismic inferences in
active regions, but they also enable detailed assessments of the validity of
helioseismic interpretations through numerical forward modeling. In this paper,
we provide a critical review of the existing sunspot models and an overview of
numerical methods employed to model wave propagation through model sunspots. We
then carry out an helioseismic analysis of the sunspot in Active Region 9787
and address the serious inconsistencies uncovered by
\citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find
that this sunspot is most probably associated with a shallow, positive
wave-speed perturbation (unlike the traditional two-layer model) and that
travel-time measurements are consistent with a horizontal outflow in the
surrounding moat.Comment: 73 pages, 19 figures, accepted by Solar Physic
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