424 research outputs found
How large can the first eigenvalue be on a surface of genus two?
Sharp upper bounds for the first eigenvalue of the Laplacian on a surface of
a fixed area are known only in genera zero and one. We investigate the genus
two case and conjecture that the first eigenvalue is maximized on a singular
surface which is realized as a double branched covering over a sphere. The six
ramification points are chosen in such a way that this surface has a complex
structure of the Bolza surface. We prove that our conjecture follows from a
lower bound on the first eigenvalue of a certain mixed Dirichlet-Neumann
boundary value problem on a half-disk. The latter can be studied numerically,
and we present conclusive evidence supporting the conjecture.Comment: 20 pages; 4 figure
Magnetocaloric effect and magnetization in a Ni-Mn-Ga Heusler alloy in the vicinity of magnetostructural transition
The magnetic and thermodynamic properties of a Ni2.19Mn0.81Ga alloy with
coupled magnetic and structural (martensitic) phase transitions were studied
experimentally and theoretically. The magnetocaloric effect was measured by a
direct method in magnetic fields 0-26 kOe at temperatures close to the
magnetostructural transition temperature. For theoretical description of the
alloy properties near the magnetostructural transition a statistical model is
suggested, that takes into account the coexistence of martensite and austenite
domains in the vicinity of martensite transformation point.Comment: presented at ICM-2003, to appear in JMM
Magnetospheric convection from Cluster EDI measurements compared with the ground-based ionospheric convection model IZMEM
Cluster/EDI electron drift observations above the Northern and Southern polar cap areas for more than seven and a half years (2001–2008) have been used to derive a statistical model of the high-latitude electric potential distribution for summer conditions. Based on potential pattern for different orientations of the interplanetary magnetic field (IMF) in the GSM y-z-plane, basic convection pattern (BCP) were derived, that represent the main characteristics of the electric potential distribution in dependence on the IMF. The BCPs comprise the IMF-independent potential distribution as well as patterns, which describe the dependence on positive and negative IMF<I>B<sub>z</sub></I> and IMF<I>B<sub>y</sub></I> variations. The full set of BCPs allows to describe the spatial and temporal variation of the high-latitude electric potential (ionospheric convection) for any solar wind IMF condition near the Earth's magnetopause within reasonable ranges. The comparison of the Cluster/EDI model with the IZMEM ionospheric convection model, which was derived from ground-based magnetometer observations, shows a good agreement of the basic patterns and its variation with the IMF. According to the statistical models, there is a two-cell antisunward convection within the polar cap for northward IMF<I>B<sub>z</sub></I>+&le;2 nT, while for increasing northward IMF<I>B<sub>z</sub></I>+ there appears a region of sunward convection within the high-latitude daytime sector, which assumes the form of two additional cells with sunward convection between them for IMF<I>B<sub>z</sub></I>+&asymp;4–5 nT. This results in a four-cell convection pattern of the high-latitude convection. In dependence of the &plusmn;IMF<I>B<sub>y</sub></I> contribution during sufficiently strong northward IMF<I>B<sub>z</sub></I> conditions, a transformation to three-cell convection patterns takes place
On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators
This paper addresses the problem of computing the eigenvalues lying in the
gaps of the essential spectrum of a periodic Schrodinger operator perturbed by
a fast decreasing potential. We use a recently developed technique, the so
called quadratic projection method, in order to achieve convergence free from
spectral pollution. We describe the theoretical foundations of the method in
detail, and illustrate its effectiveness by several examples.Comment: 17 pages, 2 tables and 2 figure
Self‐consistent modeling of the large‐scale distortions in the geomagnetic field during the 24–27 September 1998 major magnetic storm
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94715/1/jgra17531.pd
Magnetoelectric Effect and Spontaneous Polarization in HoFe(BO) and HoNdFe(BO)
The thermodynamic, magnetic, dielectric, and magnetoelectric properties of
HoFe(BO) and HoNdFe(BO) are
investigated. Both compounds show a second order Ne\'{e}l transition above 30 K
and a first order spin reorientation transition below 10 K.
HoFe(BO) develops a spontaneous electrical polarization below the
Ne\'{e}l temperature (T) which is diminished in external magnetic fields.
No magnetoelectric effect could be observed in HoFe(BO). In
contrast, the solid solution HoNdFe(BO) exhibits
both, a spontaneous polarization below T and a magnetoelectric effect at
higher fields that extends to high temperatures. The superposition of
spontaneous polarization, induced by the internal magnetic field in the ordered
state, and the magnetoelectric polarizations due to the external field results
in a complex behavior of the total polarization measured as a function of
temperature and field.Comment: 12 pages, 15 figure
Measuring the evolution of contemporary western popular music
Popular music is a key cultural expression that has captured listeners'
attention for ages. Many of the structural regularities underlying musical
discourse are yet to be discovered and, accordingly, their historical evolution
remains formally unknown. Here we unveil a number of patterns and metrics
characterizing the generic usage of primary musical facets such as pitch,
timbre, and loudness in contemporary western popular music. Many of these
patterns and metrics have been consistently stable for a period of more than
fifty years, thus pointing towards a great degree of conventionalism.
Nonetheless, we prove important changes or trends related to the restriction of
pitch transitions, the homogenization of the timbral palette, and the growing
loudness levels. This suggests that our perception of the new would be rooted
on these changing characteristics. Hence, an old tune could perfectly sound
novel and fashionable, provided that it consisted of common harmonic
progressions, changed the instrumentation, and increased the average loudness.Comment: Supplementary materials not included. Please see the journal
reference or contact the author
Revisiting the exercise heart rate-music tempo preference relationship
In the present study, we investigated a hypothesized quartic relationship (meaning three inflection points) between exercise heart rate (HR) and preferred music tempo. Initial theoretical predictions suggested a positive linear relationship (Iwanaga, 1995a, 1995b); however, recent experimental work has shown that as exercise HR increases, step changes and plateaus that punctuate the profile of music tempo preference may occur (Karageorghis, Jones, & Stuart, 2008). Tempi bands consisted of slow (95–100 bpm), medium
(115–120 bpm), fast (135–140 bpm), and very fast (155–160 bpm) music. Twenty-eight active undergraduate students cycled at exercise intensities representing 40, 50, 60, 70, 80, and 90% of their maximal HR reserve while their music preference was assessed using a 10-point scale. The Exercise Intensity x Music Tempo interaction was significant, F(6.16, 160.05) = 7.08, p < .001, ηp 2 =.21, as was the test for both cubic and quartic trajectories in the exercise HR–preferred-music-tempo relationship (p < .001). Whereas slow tempo music was not preferred at any exercise intensity, preference for fast tempo increased, relative to medium and very fast tempo music, as exercise intensity increased. The implications for the prescription of music in exercise and physical activity contexts are discussed
Space weather and space anomalies
A large database of anomalies, registered by 220 satellites in different orbits over the period 1971-1994 has been compiled. For the first time, data from 49 Russian Kosmos satellites have been included in a statistical analysis. The database also contains a large set of daily and hourly space weather parameters. A series of statistical analyses made it possible to quantify, for different satellite orbits, space weather conditions on the days characterized by anomaly occurrences. In particular, very intense fluxes (&gt;1000 pfu at energy &gt;10 MeV) of solar protons are linked to anomalies registered by satellites in high-altitude (&gt;15000 km), near-polar (inclination &gt;55&deg;) orbits typical for navigation satellites, such as those used in the GPS network, NAVSTAR, etc. (the rate of anomalies increases by a factor ~20), and to a much smaller extent to anomalies in geostationary orbits, (they increase by a factor ~4). Direct and indirect connections between anomaly occurrence and geomagnetic perturbations are also discussed
Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs
Bound states of the Hamiltonian describing a quantum particle living on three
dimensional straight strip of width are investigated. We impose the Neumann
boundary condition on the two concentric windows of the radii and
located on the opposite walls and the Dirichlet boundary condition on the
remaining part of the boundary of the strip. We prove that such a system
exhibits discrete eigenvalues below the essential spectrum for any .
When and tend to the infinity, the asymptotic of the eigenvalue is
derived. A comparative analysis with the one-window case reveals that due to
the additional possibility of the regulating energy spectrum the anticrossing
structure builds up as a function of the inner radius with its sharpness
increasing for the larger outer radius. Mathematical and physical
interpretation of the obtained results is presented; namely, it is derived that
the anticrossings are accompanied by the drastic changes of the wave function
localization. Parallels are drawn to the other structures exhibiting similar
phenomena; in particular, it is proved that, contrary to the two-dimensional
geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure
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