2,056 research outputs found
Cayley--Klein Contractions of Quantum Orthogonal Groups in Cartesian Basis
Spaces of constant curvature and their motion groups are described most
naturally in Cartesian basis. All these motion groups also known as CK groups
are obtained from orthogonal group by contractions and analytical
continuations. On the other hand quantum deformation of orthogonal group is most easily performed in so-called symplectic basis. We reformulate its
standard quantum deformation to Cartesian basis and obtain all possible
contractions of quantum orthogonal group both for untouched and
transformed deformation parameter. It turned out, that similar to undeformed
case all CK contractions of are realized. An algorithm for obtaining
nonequivalent (as Hopf algebra) contracted quantum groups is suggested.
Contractions of are regarded as an examples.Comment: The statement of the basic theorem have correct. 30 pages, Latex.
Report given at X International Conference on Symmetry Methods in Physics,
August 13-19, 2003, Yerevan, Armenia. Submitted in Journal Physics of Atomic
Nucle
Flow induced ultrasound scattering: experimental studies
Sound scattering by a finite width beam on a single rigid body rotation
vortex flow is detected by a linear array of transducers (both smaller than a
flow cell), and analyzed using a revised scattering theory. Both the phase and
amplitude of the scattered signal are obtained on 64 elements of the detector
array and used for the analysis of velocity and vorticity fields. Due to
averaging on many pulses the signal-to-noise ratio of the phases difference in
the scattered sound signal can be amplified drastically, and the resolution of
the method in the detection of circulation, vortex radius, vorticity, and
vortex location becomes comparable with that obtained earlier by time-reversal
mirror (TRM) method (P. Roux, J. de Rosny, M. Tanter, and M. Fink, {\sl Phys.
Rev. Lett.} {\bf 79}, 3170 (1997)). The revised scattering theory includes two
crucial steps, which allow overcoming limitations of the existing theories.
First, the Huygens construction of a far field scattering signal is carried out
from a signal obtained at any intermediate plane. Second, a beam function that
describes a finite width beam is introduced, which allows using a theory
developed for an infinite width beam for the relation between a scattering
amplitude and the vorticity structure function. Structure functions of the
velocity and vorticity fields deduced from the sound scattering signal are
compared with those obtained from simultaneous particle image velocimetry (PIV)
measurements. Good quantitative agreement is found.Comment: 14 pages, 23 figures. accepted for publication in Phys. Fluids(June
issue
On contractions of classical basic superalgebras
We define a class of orthosymplectic and unitary
superalgebras which may be obtained from and
by contractions and analytic continuations in a similar way as the
special linear, orthogonal and the symplectic Cayley-Klein algebras are
obtained from the corresponding classical ones. Casimir operators of
Cayley-Klein superalgebras are obtained from the corresponding operators of the
basic superalgebras. Contractions of and are regarded as
an examples.Comment: 15 pages, Late
A Radiation hard bandgap reference circuit in a standard 0.13um CMOS Technology
With ongoing CMOS evolution, the gate-oxide thickness steadily decreases, resulting in an increased radiation tolerance of MOS transistors. Combined with special layout techniques, this yields circuits with a high inherent robustness against X-rays and other ionizing radiation. In bandgap voltage references, the dominant radiation-susceptibility is then no longer associated with the MOS transistors, but is dominated by the diodes. This paper gives an analysis of radiation effects in both MOSdevices and diodes and presents a solution to realize a radiation-hard voltage reference circuit in a standard CMOS technology. A demonstrator circuit was implemented in a standard 0.13 m CMOS technology. Measurements show correct operation with supply voltages in the range from 1.4 V down to 0.85 V, a reference voltage of 405 mV 7.5 mV ( = 6mVchip-to-chip statistical spread), and a reference voltage shift of only 1.5 mV (around 0.8%) under irradiation up to 44 Mrad (Si)
On the Fermionic Frequencies of Circular Strings
We revisit the semiclassical computation of the fluctuation spectrum around
different circular string solutions in AdS_5xS^5 and AdS_4xCP^3, starting from
the Green-Schwarz action. It has been known that the results for these
frequencies obtained from the algebraic curve and from the worldsheet
computations sometimes do not agree. In particular, different methods give
different results for the half-integer shifts in the mode numbers of the
frequencies. We find that these discrepancies can be removed if one carefully
takes into account the transition matrices in the spin bundle over the target
space.Comment: 13 pages, 1 figur
The main peculiarities of the processes of the deformation and destruction of lunar soil
The main results of study of the physical and mechanical properties of lunar soil, obtained by laboratory study of samples returned from the moon by Luna 16 and Luna 20, as well as by operation of the self-propelled Lunokhod 1 and Lunokhod 2 on the surface of the moon, are analyzed in the report. All studies were carried out by single methods and by means of unified instruments, allowing a confident comparison of the results obtained. The investigations conducted allowed the following values of the main physical-mechanical properties of lunar soil to be determined: in the natural condition the solid density corresponds to the porosity of 0.8; the modal value of the carrying capacity is 0.4 kg/square cm; adhesion is 0.04 to 0.06 kg/square cm; and the internal angle of friction is 20 to 25 degree. The main mechanisms of deformation and destruction of the soil are analyzed in the report, and the relationships between the mechanical properties and physical parameters of the soil are presented
Quark--anti-quark potential in N=4 SYM
We construct a closed system of equations describing the quark--anti-quark
potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is
based on the Quantum Spectral Curve method supplemented with a novel type of
asymptotics. We present a high precision numerical solution reproducing the
classical and one-loop string predictions very accurately. We also analytically
compute the first 7 nontrivial orders of the weak coupling expansion.
Moreover, we study analytically the generalized quark--anti-quark potential
in the limit of large imaginary twist to all orders in perturbation theory. We
demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger
equation. In the process we establish a link between the Q-functions and the
solution of the Bethe-Salpeter equation.Comment: 31 pages, 1 figure; v2: minor correcton
The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
We derive a set of integral equations of the TBA type for the generalized
cusp anomalous dimension, or the quark antiquark potential on the three sphere,
as a function of the angles. We do this by considering a family of local
operators on a Wilson loop with charge L. In the large L limit the problem can
be solved in terms of a certain boundary reflection matrix. We determine this
reflection matrix by using the symmetries and the boundary crossing equation.
The cusp is introduced through a relative rotation between the two boundaries.
Then the TBA trick of exchanging space and time leads to an exact equation for
all values of L. The L=0 case corresponds to the cusped Wilson loop with no
operators inserted. We then derive a slightly simplified integral equation
which describes the small angle limit. We solve this equation up to three loops
in perturbation theory and match the results that were obtained with more
direct approaches.Comment: 63 pages, 12 figures. v2: references added, typos correcte
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