2,238 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)
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
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
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
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
A Comprehensive User Modeling Framework and a Recommender System for Personalizing Well-Being Related Behavior Change Interventions: Development and Evaluation
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Ultrasonic Blind Stick with GPS Tracking System
This paper proposes an efficient electronic system for guidance of a blind person. It is based on the design and developments of a smart stick for visually impaired people to provide them with ease, confidence and to gain independence in an efficient and cost-effective way. This report presents the concept of the system, its theoretical and practical model for providing an electronic aid to visually impaired people. The system covers obstacle detection, light sensing, water detection, location detection and emergency messaging. The device is based on a small circuit mounted on the white cane and a small circuit serving as a control unit. A microcontroller-based circuit is used to handle the entire system functioning. The detection of obstacles is based on ultrasonic sensors giving a beeping sound, light sensing system detects the darkness and light in the surrounding to alert the user, the water sensor detects ground water to alert the user. In addition, a GPS with GSM connection sends the approximate location of the stick to the caretaker phone. The system aims to provide visually impaired people with artificial vision by giving them information on the surrounding environment
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