3,986 research outputs found
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
Supporting material for co-researchers
This pack has been designed to be used alongside the Peer Research Training Resource (https://doi.org/10.25561/94819) and includes: • Skills, experience, and training reviews for Advisory Group Members and Peer Researchers • Zoom Interviews: Guide for Peer Researchers • Useful COVID-19 resources for people living with HIV The pack is suitable for academics and public involvement practitioners who are involving people with lived experience as co-researchers in research. The material presented here was developed for a participatory research study on COVID-19 experiences among people living with HIV where interviews were conducted online
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
Insight Report: COVID-19 Community Involvement - “Let’s Talk About…HIV Care”
This informal session led by the Patient Experience Research Centre (PERC), in collaboration with Positively UK, invited people living with, affected by, or working in HIV to share their experience, views, questions and concerns on accessing HIV care during COVID-19. The aim of the call was to gather feedback on specific areas to help guide a proposed qualitative (interview-based study) looking to explore experiences, specifically on: 1. Challenges and concerns in managing HIV care during COVID-19 2. Challenges in the provision of HIV care during COVID-19 3. Opportunities presented for HIV care during COVID-19 We also wished to inspire new ways to rapidly engage and involve communities remotely during a public health emergency, through strengthening partnerships with existing groups (in this case, Positively UK)
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
Linear quadrilateral lattice equations and multidimensional consistency
It is shown that every scalar linear quadrilateral lattice equation lies
within a family of similar equations, members of which are compatible between
one another on a higher dimensional lattice. There turn out to be two such
families, a natural parametrisation is given for each.Comment: 7 pages, 1 figur
Hungry Volterra equation, multi boson KP hierarchy and Two Matrix Models
We consider the hungry Volterra hierarchy from the view point of the multi
boson KP hierarchy. We construct the hungry Volterra equation as the
B\"{a}cklund transformations (BT) which are not the ordinary ones. We call them
``fractional '' BT. We also study the relations between the (discrete time)
hungry Volterra equation and two matrix models. From this point of view we
study the reduction from (discrete time) 2d Toda lattice to the (discrete time)
hungry Volterra equation.Comment: 13 pages, LaTe
Discrete analogues of the Liouville equation
The notion of Laplace invariants is transferred to the lattices and discrete
equations which are difference analogs of hyperbolic PDE's with two independent
variables. The sequence of Laplace invariants satisfy the discrete analog of
twodimensional Toda lattice. The terminating of this sequence by zeroes is
proved to be the necessary condition for existence of the integrals of the
equation under consideration. The formulae are presented for the higher
symmetries of the equations possessing integrals. The general theory is
illustrated by examples of difference analogs of Liouville equation.Comment: LaTeX, 15 pages, submitted to Teor. i Mat. Fi
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