3,999 research outputs found
Poisson Yang-Baxter maps with binomial Lax matrices
A construction of multidimensional parametric Yang-Baxter maps is presented.
The corresponding Lax matrices are the symplectic leaves of first degree matrix
polynomials equipped with the Sklyanin bracket. These maps are symplectic with
respect to the reduced symplectic structure on these leaves and provide
examples of integrable mappings. An interesting family of quadrirational
symplectic YB maps on with Lax
matrices is also presented.Comment: 22 pages, 3 figure
On Quadrirational Yang-Baxter Maps
We use the classification of the quadrirational maps given by Adler, Bobenko
and Suris to describe when such maps satisfy the Yang-Baxter relation. We show
that the corresponding maps can be characterized by certain singularity
invariance condition. This leads to some new families of Yang-Baxter maps
corresponding to the geometric symmetries of pencils of quadrics.Comment: Proceedings of the workshop "Geometric Aspects of Discrete and
Ultra-Discrete Integrable Systems" (Glasgow, March-April 2009
Yang-Baxter maps and multi-field integrable lattice equations
A variety of Yang-Baxter maps are obtained from integrable multi-field
equations on quad-graphs. A systematic framework for investigating this
connection relies on the symmetry groups of the equations. The method is
applied to lattice equations introduced by Adler and Yamilov and which are
related to the nonlinear superposition formulae for the B\"acklund
transformations of the nonlinear Schr\"odinger system and specific
ferromagnetic models.Comment: 16 pages, 4 figures, corrected versio
Yang Baxter maps with first degree polynomial 2 by 2 Lax matrices
A family of nonparametric Yang Baxter (YB) maps is constructed by
refactorization of the product of two 2 by 2 matrix polynomials of first
degree. These maps are Poisson with respect to the Sklyanin bracket. For each
Casimir function a parametric Poisson YB map is generated by reduction on the
corresponding level set. By considering a complete set of Casimir functions
symplectic multiparametric YB maps are derived. These maps are quadrirational
with explicit formulae in terms of matrix operations. Their Lax matrices are,
by construction, 2 by 2 first degree polynomial in the spectral parameter and
are classified by Jordan normal form of the leading term. Nonquadrirational
parametric YB maps constructed as limits of the quadrirational ones are
connected to known integrable systems on quad graphs
A -anaolg of the sixth Painlev\'e equation
A -difference analog of the sixth Painlev\'e equation is presented. It
arises as the condition for preserving the connection matrix of linear
-difference equations, in close analogy with the monodromy preserving
deformation of linear differential equations. The continuous limit and special
solutions in terms of -hypergeometric functions are also discussed.Comment: 8 pages, LaTeX file (Two misprints corrected
Fabrication of integrated planar gunn diode and micro-cooler on GaAs substrate
We demonstrate fabrication of an integrated
micro cooler with the planar Gunn diode and characterise
its performance. First experimental results have shown a
small cooling at the surface of the micro cooler. This is first
demonstration of an integrated micro-cooler with a planar
Gunn diode
Space very long baseline interferometry observations of polarization in the jet of 3C 380
A comparison between low-frequency space very long baseline interferometry (VLBI) and high-frequency ground-based VLBI images can, in principle, be used to detect small variations in rotation measure (RM) on fine angular scales inaccessible to ground arrays alone. This paper reports an attempt to perform such a comparison using the jet in the quasar 3C 380. Observations made with the VSOP antenna HALCA together with a ground array at wavelength 1.6 GHz provide total intensity and polarization images of comparable resolution to those from the ground array alone at 5 GHz. The results provide an image showing derotated magnetic vector position angle of somewhat higher resolution than that available earlier. The results show variations in an RM around component A of the order of 10 rad m(-2) that could not have been detected with the ground array alone. It is concluded that satellite VLBI observations provide a promising means to study the distribution of matter and magnetic fields around parsec-scale jets. The ground observations used here follow the steady outward drift of component A, which has approximately doubled its distance from the core since the first observations in 1982. They also reveal total intensity and polarization structure associated with a bright knot 0.7 arcsec from the core which is reminiscent of that expected for a conical shock wave
Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem
We study chaotic orbits of conservative low--dimensional maps and present
numerical results showing that the probability density functions (pdfs) of the
sum of iterates in the large limit exhibit very interesting
time-evolving statistics. In some cases where the chaotic layers are thin and
the (positive) maximal Lyapunov exponent is small, long--lasting
quasi--stationary states (QSS) are found, whose pdfs appear to converge to
--Gaussians associated with nonextensive statistical mechanics. More
generally, however, as increases, the pdfs describe a sequence of QSS that
pass from a --Gaussian to an exponential shape and ultimately tend to a true
Gaussian, as orbits diffuse to larger chaotic domains and the phase space
dynamics becomes more uniformly ergodic.Comment: 15 pages, 14 figures, accepted for publication as a Regular Paper in
the International Journal of Bifurcation and Chaos, on Jun 21, 201
Microwave saturation of the Rydberg states of electrons on helium
We present measurements of the resonant microwave excitation of the Rydberg
energy levels of surface state electrons on superfluid helium. The temperature
dependent linewidth agrees well with theoretical predictions and is very small
below 300 mK. Absorption saturation and power broadening were observed as the
fraction of electrons in the first excited state was increased to 0.49, close
to the thermal excitation limit of 0.5. The Rabi frequency was determined as a
function of microwave power. The high values of the ratio of the Rabi frequency
to linewidth confirm this system as an excellent candidate for creating qubits.Comment: 4 pages, 4 figure
Planar gunn diode characterisation and resonators elements to realise oscillator circuits
The paper describes the planar Gunn diode, which is well suited to providing milli-metric and tera hertz sources using microwave monolithic integrated circuit (MMIC) technologies. Different planar Gunn electrode geometries are described along with DC, RF and thermal characterisation. To realize the planar high frequency sources there is requirement for high frequency planar resonators, the paper will describe both the radial and new diamond shaped geometries
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