298 research outputs found
A second order minimality condition for the Mumford-Shah functional
A new necessary minimality condition for the Mumford-Shah functional is
derived by means of second order variations. It is expressed in terms of a sign
condition for a nonlocal quadratic form on , being a
submanifold of the regular part of the discontinuity set of the critical point.
Two equivalent formulations are provided: one in terms of the first eigenvalue
of a suitable compact operator, the other involving a sort of nonlocal capacity
of . A sufficient condition for minimality is also deduced. Finally, an
explicit example is discussed, where a complete characterization of the domains
where the second variation is nonnegative can be given.Comment: 30 page
Improved Understanding of Atomic Ordering in Y4SixAl2- xO9- xNxMaterials Using a Combined Solid-State NMR and Computational Approach
Ceramics based around silicon aluminum oxynitrides are of both fundamental structural chemistry and technological interest. Certain oxynitride crystal structures allow very significant compositional variation through extensive Si/N exchange for Al/O, which implies a degree of atomic ordering. In this study, solid-state 29Si MAS NMR and variable field 1D and 2D 27Al MAS NMR measurements are combined with density functional theory calculations of both the structural and NMR interaction parameters for various points across the Y4Si2O7N2-Y4Al2O9 compositional range. This series provides numerous possibilities for significant variation of atomic ordering in the local ditetrahedral (Si,Al)2O7-xNx units. The two slightly structurally inequivalent aluminum sites in Y4Al2O9 are unambiguously assigned to the observed resonances. Computational findings on Y4Si2O7N2 demonstrate that the single observed 29Si NMR resonance covers a range of local inequivalent silicon environments. For the first time, the MAS NMR and neutron diffraction data from the Y4SiAlO8N structure have been directly reconciled, thus establishing aspects of atomic order and disorder that characterize this system. This comparison suggests that, although the diffraction data indicates long-range structural order supporting a highly crystalline character, the short-range information afforded by the solid-state NMR measurements indicates significant atomic disorder throughout the (Si,Al)2O7-xNx units
The resultant on compact Riemann surfaces
We introduce a notion of resultant of two meromorphic functions on a compact
Riemann surface and demonstrate its usefulness in several respects. For
example, we exhibit several integral formulas for the resultant, relate it to
potential theory and give explicit formulas for the algebraic dependence
between two meromorphic functions on a compact Riemann surface. As a particular
application, the exponential transform of a quadrature domain in the complex
plane is expressed in terms of the resultant of two meromorphic functions on
the Schottky double of the domain.Comment: 44 page
Critical properties of 1-D spin 1/2 antiferromagnetic Heisenberg model
We discuss numerical results for the 1-D spin 1/2 antiferromagnetic
Heisenberg model with next-to-nearest neighbour coupling and in the presence of
an uniform magnetic field. The model develops zero frequency excitations at
field dependent soft mode momenta. We compute critical quantities from finite
size dependence of static structure factors.Comment: talk given by H. Kr{\"o}ger at Heraeus Seminar Theory of Spin
Lattices and Lattice Gauge Models, Bad Honnef (1996), 20 pages, LaTeX + 18
figures, P
Understanding preventive behaviors among mid-Western African-American men: a pilot qualitative study of prostate screening
http://dx.doi.org/10.1016/j.jomh.2011.03.00
Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation
The current status of electric dipole moments of diamagnetic atoms which
involves the synergy between atomic experiments and three different theoretical
areas -- particle, nuclear and atomic is reviewed. Various models of particle
physics that predict CP violation, which is necessary for the existence of such
electric dipole moments, are presented. These include the standard model of
particle physics and various extensions of it. Effective hadron level combined
charge conjugation (C) and parity (P) symmetry violating interactions are
derived taking into consideration different ways in which a nucleon interacts
with other nucleons as well as with electrons. Nuclear structure calculations
of the CP-odd nuclear Schiff moment are discussed using the shell model and
other theoretical approaches. Results of the calculations of atomic electric
dipole moments due to the interaction of the nuclear Schiff moment with the
electrons and the P and time-reversal (T) symmetry violating
tensor-pseudotensor electron-nucleus are elucidated using different
relativistic many-body theories. The principles of the measurement of the
electric dipole moments of diamagnetic atoms are outlined. Upper limits for the
nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained
combining the results of atomic experiments and relativistic many-body
theories. The coefficients for the different sources of CP violation have been
estimated at the elementary particle level for all the diamagnetic atoms of
current experimental interest and their implications for physics beyond the
standard model is discussed. Possible improvements of the current results of
the measurements as well as quantum chromodynamics, nuclear and atomic
calculations are suggested.Comment: 46 pages, 19 tables and 16 figures. A review article accepted for
EPJ
Broadband Quantum Enhancement of the LIGO Detectors with Frequency-Dependent Squeezing
Quantum noise imposes a fundamental limitation on the sensitivity of interferometric gravitational-wave detectors like LIGO, manifesting as shot noise and quantum radiation pressure noise. Here, we present the first realization of frequency-dependent squeezing in full-scale gravitational-wave detectors, resulting in the reduction of both shot noise and quantum radiation pressure noise, with broadband detector enhancement from tens of hertz to several kilohertz. In the LIGO Hanford detector, squeezing reduced the detector noise amplitude by a factor of 1.6 (4.0 dB) near 1 kHz; in the Livingston detector, the noise reduction was a factor of 1.9 (5.8 dB). These improvements directly impact LIGO's scientific output for high-frequency sources (e.g., binary neutron star postmerger physics). The improved low-frequency sensitivity, which boosted the detector range by 15%-18% with respect to no squeezing, corresponds to an increase in the astrophysical detection rate of up to 65%. Frequency-dependent squeezing was enabled by the addition of a 300-meter-long filter cavity to each detector as part of the LIGO A+ upgrade
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