420 research outputs found
Simulation of beam-beam induced emittance growth in the HL-LHC with crab cavities
The emittance growth in the HL-LHC due to beam-beam effects is examined by
virtue of strong-strong computer simulations. A model of the transverse damper
and the noise level have been tuned to simulate the emittance growth in the
present LHC. Simulations with projected HL-LHC beam parameters and crab
cavities are discussed. It is shown that with the nominal working point, the
large beam-beam tune shift moves the beam into a resonance that causes
substantial emittance growth. Increasing the working point slightly is
demonstrated to be very beneficial.Comment: 6 pages, contribution to the ICFA Mini-Workshop on Beam-Beam Effects
in Hadron Colliders, CERN, Geneva, Switzerland, 18-22 Mar 201
Vorticity statistics in the two-dimensional enstrophy cascade
We report the first extensive experimental observation of the two-dimensional
enstrophy cascade, along with the determination of the high order vorticity
statistics. The energy spectra we obtain are remarkably close to the Kraichnan
Batchelor expectation. The distributions of the vorticity increments, in the
inertial range, deviate only little from gaussianity and the corresponding
structure functions exponents are indistinguishable from zero. It is thus shown
that there is no sizeable small scale intermittency in the enstrophy cascade,
in agreement with recent theoretical analyses.Comment: 5 pages, 7 Figure
The numerical solution of forward–backward differential equations: Decomposition and related issues
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of computational and applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of computational and applied mathematics, 234,(2010), doi: 10.1016/j.cam.2010.01.039This journal article discusses the decomposition, by numerical methods, of solutions to mixed-type functional differential equations (MFDEs) into sums of “forward” solutions and “backward” solutions
Experimental study of Taylor's hypothesis in a turbulent soap film
An experimental study of Taylor's hypothesis in a quasi-two-dimensional
turbulent soap film is presented. A two probe laser Doppler velocimeter enables
a non-intrusive simultaneous measurement of the velocity at spatially separated
points. The breakdown of Taylor's hypothesis is quantified using the cross
correlation between two points displaced in both space and time; correlation is
better than 90% for scales less than the integral scale. A quantitative study
of the decorrelation beyond the integral scale is presented, including an
analysis of the failure of Taylor's hypothesis using techniques from
predictability studies of turbulent flows. Our results are compared with
similar studies of 3D turbulence.Comment: 27 pages, + 19 figure
Global Hopf bifurcation in the ZIP regulatory system
Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been
modeled by a system of ordinary differential equations based on the uptake of
zinc, expression of a transporter protein and the interaction between an
activator and inhibitor. For certain parameter choices the steady state of this
model becomes unstable upon variation in the external zinc concentration.
Numerical results show periodic orbits emerging between two critical values of
the external zinc concentration. Here we show the existence of a global Hopf
bifurcation with a continuous family of stable periodic orbits between two Hopf
bifurcation points. The stability of the orbits in a neighborhood of the
bifurcation points is analyzed by deriving the normal form, while the stability
of the orbits in the global continuation is shown by calculation of the Floquet
multipliers. From a biological point of view, stable periodic orbits lead to
potentially toxic zinc peaks in plant cells. Buffering is believed to be an
efficient way to deal with strong transient variations in zinc supply. We
extend the model by a buffer reaction and analyze the stability of the steady
state in dependence of the properties of this reaction. We find that a large
enough equilibrium constant of the buffering reaction stabilizes the steady
state and prevents the development of oscillations. Hence, our results suggest
that buffering has a key role in the dynamics of zinc homeostasis in plant
cells.Comment: 22 pages, 5 figures, uses svjour3.cl
Tropical polyhedra are equivalent to mean payoff games
We show that several decision problems originating from max-plus or tropical
convexity are equivalent to zero-sum two player game problems. In particular,
we set up an equivalence between the external representation of tropical convex
sets and zero-sum stochastic games, in which tropical polyhedra correspond to
deterministic games with finite action spaces. Then, we show that the winning
initial positions can be determined from the associated tropical polyhedron. We
obtain as a corollary a game theoretical proof of the fact that the tropical
rank of a matrix, defined as the maximal size of a submatrix for which the
optimal assignment problem has a unique solution, coincides with the maximal
number of rows (or columns) of the matrix which are linearly independent in the
tropical sense. Our proofs rely on techniques from non-linear Perron-Frobenius
theory.Comment: 28 pages, 5 figures; v2: updated references, added background
materials and illustrations; v3: minor improvements, references update
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