2,522 research outputs found
On the uniqueness of invariant tori in D4*S1 symmetric systems
The uniqueness of the branch of two-tori in the D4-equivariant Hopf bifurcation problem is proved in a neighbourhood of a particular limiting case where, after reduction, the Euler equations for the rotation of a free rigid body apply
Hopf bifurcation with non-semisimple 1:1 resonance
A generalised Hopf bifurcation, corresponding to non-semisimple double imaginary eigenvalues (case of 1:1 resonance), is analysed using a normal form approach. This bifurcation has linear codimension-3, and a centre subspace of dimension 4. The four-dimensional normal form is reduced to a three-dimensional system, which is normal to the group orbits of a phase-shift symmetry. There may exist 0, 1 or 2 small-amplitude periodic solutions. Invariant 2-tori of quasiperiodic solutions bifurcate from these periodic solutions. The authors locate one-dimensional varieties in the parameter space 1223 on which the system has four different codimension-2 singularities: a Bogdanov-Takens bifurcation a 1322 symmetric cusp, a Hopf/Hopf mode interaction without strong resonance, and a steady-state/Hopf mode interaction with eigenvalues (0, i,-i)
Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
We demonstrate numerically that non-Abelian quasihole excitations of the fractional quantum Hall state have some of the key properties necessary
to support quantum computation. We find that as the quasihole spacing is
increased, the unitary transformation which describes winding two quasiholes
around each other converges exponentially to its asymptotic limit and that the
two orthogonal wavefunctions describing a system with four quasiholes become
exponentially degenerate. We calculate the length scales for these two decays
to be and
respectively. Additionally we determine which fusion channel is lower in energy
when two quasiholes are brought close together.Comment: 4 pages, 3 figure
Ashkin-Teller universality in a quantum double model of Ising anyons
We study a quantum double model whose degrees of freedom are Ising anyons.
The terms of the Hamiltonian of this system give rise to a competition between
single and double topologies. By studying the energy spectra of the Hamiltonian
at different values of the coupling constants, we find extended gapless regions
which include a large number of critical points described by conformal field
theories with central charge c=1. These theories are part of the Z_2 orbifold
of the bosonic theory compactified on a circle. We observe that the Hilbert
space of our anyonic model can be associated with extended Dynkin diagrams of
affine Lie algebras which yields exact solutions at some critical points. In
certain special regimes, our model corresponds to the Hamiltonian limit of the
Ashkin-Teller model, and hence integrability over a wide range of coupling
parameters is established.Comment: 11 pages, minor revision
The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently rotating cylinders
A new turbulent Taylor-Couette system consisting of two independently
rotating cylinders has been constructed. The gap between the cylinders has a
height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius
(from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and
outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up
to 3.4 x 10^6 with water as working fluid. With this Taylor-Couette system, the
parameter space (Re_i, Re_o, {\eta}) extends to (2.0 x 10^6, {\pm}1.4 x 10^6,
0.716-0.909). The system is equipped with bubble injectors, temperature
control, skin-friction drag sensors, and several local sensors for studying
turbulent single-phase and two-phase flows. Inner cylinder load cells detect
skin-friction drag via torque measurements. The clear acrylic outer cylinder
allows the dynamics of the liquid flow and the dispersed phase (bubbles,
particles, fibers, etc.) inside the gap to be investigated with specialized
local sensors and nonintrusive optical imaging techniques. The system allows
study of both Taylor-Couette flow in a high-Reynolds-number regime, and the
mechanisms behind skin-friction drag alterations due to bubble injection,
polymer injection, and surface hydrophobicity and roughness.Comment: 13 pages, 14 figure
Measurement of angular momentum transport in turbulent flow between independently rotating cylinders
We present measurements of the angular momentum flux (torque) in
Taylor-Couette flow of water between independently rotating cylinders for all
regions of the \(\Omega_1, \Omega_2\) parameter space at high Reynolds
numbers, where \(\Omega_2\) is the inner (outer) cylinder angular
velocity. We find that the Rossby number Ro = \(\Omega_1 -
\Omega_2\)/\Omega_2 fully determines the state and torque as compared to
G(Ro = \infty) \equiv \Gi. The ratio G/\Gi is a linear function of
in four sections of the parameter space. For flows with
radially-increasing angular momentum, our measured torques greatly exceed those
of previous experiments [Ji \textit{et al.}, Nature, \textbf{444}, 343 (2006)],
but agree with the analysis of Richard and Zahn [Astron. Astrophys.,
\textbf{347}, 734 (1999)].Comment: 4 pages, 4 figures, to appear in Physical Review Letter
On the reduction of the degree of linear differential operators
Let L be a linear differential operator with coefficients in some
differential field k of characteristic zero with algebraically closed field of
constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we
determine the linear differential operator of minimal degree M and coefficients
in k^a, such that My=0. This result is then applied to some Picard-Fuchs
equations which appear in the study of perturbations of plane polynomial vector
fields of Lotka-Volterra type
Stimulation induced variability of pulse plethysmography does not discriminate responsiveness to intubation
Background. Hypnotic depth but not haemodynamic response to painful stimulation can be measured with various EEG-based anaesthesia monitors. We evaluated the variation of pulse plethysmography amplitude induced by an electrical tetanic stimulus (PPG variation) as a potential measure for analgesia and predictor of haemodynamic responsiveness during general anaesthesia. Methods. Ninety-five patients, ASA I or II, were randomly assigned to five groups [Group 1: bispectral index (BIS) (range) 40-50, effect site remifentanil concentration 1 ng ml−1;Group 2: BIS 40-50, remifentanil 2 ng ml−1; Group 3: BIS 40-50, remifentanil 4 ng ml−1; Group 4: BIS 25-35, remifentanil 2 ng ml−1; Group 5: BIS 55-65, remifentanil 2 ng ml−1]. A 60 mA tetanic stimulus was applied for 5 s on the ulnar nerve. From the digitized pulse oximeter wave recorded on a laptop computer, linear and non-linear parameters of PPG variation during the 60 s period after stimulation were computed. The haemodynamic response to subsequent orotracheal intubation was recorded. The PPG variation was compared between groups and between responders and non-responders to intubation (anova). Variables independently predicting the response were determined by logistic regression. Results. The probability of a response to tracheal intubation was 0.77, 0.47, 0.05, 0.18 and 0.52 in Groups 1-5, respectively (P<0.03). The PPG variability was significantly higher in responders than in non-responders but it did not improve the prediction of the response to tracheal intubation based on BIS level and effect site remifentanil concentration. Conclusion. Tetanic stimulation induced PPG variation does not reflect the analgesic state in a wide clinical range of surgical anaesthesi
Optimal Taylor-Couette flow: Radius ratio dependence
Taylor-Couette flow with independently rotating inner (i) and outer (o)
cylinders is explored numerically and experimentally to determine the effects
of the radius ratio {\eta} on the system response. Numerical simulations reach
Reynolds numbers of up to Re_i=9.5 x 10^3 and Re_o=5x10^3, corresponding to
Taylor numbers of up to Ta=10^8 for four different radius ratios {\eta}=r_i/r_o
between 0.5 and 0.909. The experiments, performed in the Twente Turbulent
Taylor-Couette (T^3C) setup, reach Reynolds numbers of up to Re_i=2x10^6$ and
Re_o=1.5x10^6, corresponding to Ta=5x10^{12} for {\eta}=0.714-0.909. Effective
scaling laws for the torque J^{\omega}(Ta) are found, which for sufficiently
large driving Ta are independent of the radius ratio {\eta}. As previously
reported for {\eta}=0.714, optimum transport at a non-zero Rossby number
Ro=r_i|{\omega}_i-{\omega}_o|/[2(r_o-r_i){\omega}_o] is found in both
experiments and numerics. Ro_opt is found to depend on the radius ratio and the
driving of the system. At a driving in the range between {Ta\sim3\cdot10^8} and
{Ta\sim10^{10}}, Ro_opt saturates to an asymptotic {\eta}-dependent value.
Theoretical predictions for the asymptotic value of Ro_{opt} are compared to
the experimental results, and found to differ notably. Furthermore, the local
angular velocity profiles from experiments and numerics are compared, and a
link between a flat bulk profile and optimum transport for all radius ratios is
reported.Comment: Submitted to JFM, 28 pages, 17 figure
Absence of a structural glass phase in a monoatomic model liquid predicted to undergo an ideal glass transition
We study numerically a monodisperse model of interacting classical particles
predicted to exhibit a static liquid-glass transition. Using a dynamical Monte
Carlo method we show that the model does not freeze into a glassy phase at low
temperatures. Instead, depending on the choice of the hard-core radius for the
particles the system either collapses trivially or a polycrystalline hexagonal
structure emerges.Comment: 4 pages, 4 figures, minor changes in introduction and conclusions,
additional reference
- …