382 research outputs found
Visualizing the logistic map with a microcontroller
The logistic map is one of the simplest nonlinear dynamical systems that
clearly exhibit the route to chaos. In this paper, we explored the evolution of
the logistic map using an open-source microcontroller connected to an array of
light emitting diodes (LEDs). We divided the one-dimensional interval
into ten equal parts, and associated and LED to each segment. Every time an
iteration took place a corresponding LED turned on indicating the value
returned by the logistic map. By changing some initial conditions of the
system, we observed the transition from order to chaos exhibited by the map.Comment: LaTeX, 6 pages, 3 figures, 1 listin
Records and sequences of records from random variables with a linear trend
We consider records and sequences of records drawn from discrete time series
of the form , where the are independent and identically
distributed random variables and is a constant drift. For very small and
very large drift velocities, we investigate the asymptotic behavior of the
probability of a record occurring in the th step and the
probability that all entries are records, i.e. that . Our work is motivated by the analysis of temperature time series in
climatology, and by the study of mutational pathways in evolutionary biology.Comment: 21 pages, 7 figure
A critical analysis of the hydrino model
Recently, spectroscopic and calorimetric observations of hydrogen plasmas and
chemical reactions with them have been interpreted as evidence for the
existence of electronic states of the hydrogen atom with a binding energy of
more than 13.6 eV. The theoretical basis for such states, that have been dubbed
hydrinos, is investigated. We discuss both, the novel deterministic model of
the hydrogen atom, in which the existence of hydrinos was predicted, and
standard quantum mechanics. Severe inconsistencies in the deterministic model
are pointed out and the incompatibility of hydrino states with quantum
mechanics is reviewed.Comment: 9 page
On the terms violating the custodial symmetry in multi-Higgs-doublet models
We prove that a generic multi-Higgs-doublet model (NHDM) generally must
contain terms in the potential that violate the custodial symmetry. This is
done by showing that the O(4) violating terms of the NHDM potential cannot be
excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect
higher-order corrections to necessarily introduce such terms. We also note, in
the case of custodially symmetric Higgs-quark couplings, that vacuum alignment
will lead to up-down mass degeneration; this is not true if the vacua are not
aligned.Comment: 16 pages, 1 figure. Title and abstract are modified, conclusions
remain the same. Section on Yukawa couplings is extended. Published versio
Shuffling cards, factoring numbers, and the quantum baker's map
It is pointed out that an exactly solvable permutation operator, viewed as
the quantization of cyclic shifts, is useful in constructing a basis in which
to study the quantum baker's map, a paradigm system of quantum chaos. In the
basis of this operator the eigenfunctions of the quantum baker's map are
compressed by factors of around five or more. We show explicitly its connection
to an operator that is closely related to the usual quantum baker's map. This
permutation operator has interesting connections to the art of shuffling cards
as well as to the quantum factoring algorithm of Shor via the quantum order
finding one. Hence we point out that this well-known quantum algorithm makes
crucial use of a quantum chaotic operator, or at least one that is close to the
quantization of the left-shift, a closeness that we also explore
quantitatively.Comment: 12 pgs. Substantially elaborated version, including a new route to
the quantum bakers map. To appear in J. Phys.
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
We examine the effect of accuracy of high-order spectral element methods,
with or without adaptive mesh refinement (AMR), in the context of a classical
configuration of magnetic reconnection in two space dimensions, the so-called
Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point
of the velocity. A recently developed spectral-element adaptive refinement
incompressible magnetohydrodynamic (MHD) code is applied to simulate this
problem. The MHD solver is explicit, and uses the Elsasser formulation on
high-order elements. It automatically takes advantage of the adaptive grid
mechanics that have been described elsewhere in the fluid context [Rosenberg,
Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows
both statically refined and dynamically refined grids. Tests of the algorithm
using analytic solutions are described, and comparisons of the Orszag-Tang
solutions with pseudo-spectral computations are performed. We demonstrate for
moderate Reynolds numbers that the algorithms using both static and refined
grids reproduce the pseudo--spectral solutions quite well. We show that
low-order truncation--even with a comparable number of global degrees of
freedom--fails to correctly model some strong (sup--norm) quantities in this
problem, even though it satisfies adequately the weak (integrated) balance
diagnostics.Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physic
Dobinski-type relations and the Log-normal distribution
We consider sequences of generalized Bell numbers B(n), n=0,1,... for which
there exist Dobinski-type summation formulas; that is, where B(n) is
represented as an infinite sum over k of terms P(k)^n/D(k). These include the
standard Bell numbers and their generalizations appearing in the normal
ordering of powers of boson monomials, as well as variants of the "ordered"
Bell numbers. For any such B we demonstrate that every positive integral power
of B(m(n)), where m(n) is a quadratic function of n with positive integral
coefficients, is the n-th moment of a positive function on the positive real
axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure
Tentative detection of phosphine in IRC+10216
The J,K = 1,0-0,0 rotational transition of phosphine (PH3) at 267 GHz has
been tentatively identified with a T_MB = 40 mK spectral line observed with the
IRAM 30-m telescope in the C-star envelope IRC+10216. A radiative transfer
model has been used to fit the observed line profile. The derived PH3 abundance
relative to H2 is 6 x 10^(-9), although it may have a large uncertainty due to
the lack of knowledge about the spatial distribution of this species. If our
identification is correct, it implies that PH3 has a similar abundance to that
reported for HCP in this source, and that these two molecules (HCP and PH3)
together take up about 5 % of phosphorus in IRC+10216. The abundance of PH3, as
that of other hydrides in this source, is not well explained by conventional
gas phase LTE and non-LTE chemical models, and may imply formation on grain
surfaces.Comment: 4 pages, 2 figures; accepted for publication in A&A Letter
Computing welfare losses from data under imperfect competition with heterogeneous goods
We study the percentage of welfare losses (PWL) yielded by imperfect competition under
product differentiation. When demand is linear, if prices, outputs, costs and the number of firms
can be observed, PWL is arbitrary in both Cournot and Bertrand equilibria. If in addition, the
elasticity of demand (resp. cross elasticity of demand) is known, we can calculate PWL in
Cournot (resp. Bertrand) equilibrium. When demand is isoelastic and there are many firms, PWL
can be computed from prices, outputs, costs and the number of .rms. In all these cases we find
that price-marginal cost margins and demand elasticities may influence PWL in a
counterintuitive way. We also provide conditions under which PWL increases or decreases with
concentration
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