24,102 research outputs found
Conformal gravity: light deflection revisited and the galactic rotation curve failure
We show how Conformal Gravity (CG) has to satisfy a fine-tuning condition to
describe the rotation curves of disk galaxies without the aid of dark matter.
Interpreting CG as a gauge natural theory yields conservation laws and their
associated superpotentials without ambiguities. We consider the light
deflection of a point-like lens and impose that the two Schwarzschild-like
metrics with and without the lens are identical at infinite distances from the
lens. The energy conservation law implies that the parameter in the
linear term of the metric has to vanish, otherwise the two metrics are
physically inaccessible from each other. This linear term is responsible to
mimic the role of dark matter in disk galaxies and gravitational lensing
systems. Our analysis shows that removing the need of dark matter with CG thus
relies on a fine-tuning condition on . We also illustrate why the
results of previous investigations of gravitational lensing in CG largely
disagree. These discrepancies derive from the erroneous use of the deflection
angle definition adopted in General Relativity, where the vacuum solution is
asymptotically flat, unlike CG. In addition, the lens mass is identified with
various combinations of the metric parameters. However, these identifications
are arbitrary, because the mass is not a conformally invariant quantity, unlike
the conserved charge associated to the energy conservation law. Based on this
conservation law and by removing the fine-tuning condition on , i.e. by
setting , the energy difference between the metric with the
point-like lens and the metric without it defines a conformally invariant
quantity that can in principle be used for (1) a proper derivation of light
deflection in CG, and (2) the identification of the lens mass with a function
of the parameters and of the Schwarzschild-like metric.Comment: 16 pages, 1 figure. Revised version according to the referees
comments. The results reported in the original version remain unchange
Application and flight test of linearizing transformations using measurement feedback to the nonlinear control problem
The design of nonlinear controllers has relied on the use of detailed aerodynamic and engine models that must be associated with the control law in the flight system implementation. Many of these controllers were applied to vehicle flight path control problems and have attempted to combine both inner- and outer-loop control functions in a single controller. An approach to the nonlinear trajectory control problem is presented. This approach uses linearizing transformations with measurement feedback to eliminate the need for detailed aircraft models in outer-loop control applications. By applying this approach and separating the inner-loop and outer-loop functions two things were achieved: (1) the need for incorporating detailed aerodynamic models in the controller is obviated; and (2) the controller is more easily incorporated into existing aircraft flight control systems. An implementation of the controller is discussed, and this controller is tested on a six degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Simulation data are presented which validates this approach over a large portion of the F-15 flight envelope. Proof of this concept is provided by flight-test data that closely matches simulation results. Flight-test data are also presented
Stability Analysis of Integral Delay Systems with Multiple Delays
This note is concerned with stability analysis of integral delay systems with
multiple delays. To study this problem, the well-known Jensen inequality is
generalized to the case of multiple terms by introducing an individual slack
weighting matrix for each term, which can be optimized to reduce the
conservatism. With the help of the multiple Jensen inequalities and by
developing a novel linearizing technique, two novel Lyapunov functional based
approaches are established to obtain sufficient stability conditions expressed
by linear matrix inequalities (LMIs). It is shown that these new conditions are
always less conservative than the existing ones. Moreover, by the positive
operator theory, a single LMI based condition and a spectral radius based
condition are obtained based on an existing sufficient stability condition
expressed by coupled LMIs. A numerical example illustrates the effectiveness of
the proposed approaches.Comment: 14 page
Discrete time piecewise affine models of genetic regulatory networks
We introduce simple models of genetic regulatory networks and we proceed to
the mathematical analysis of their dynamics. The models are discrete time
dynamical systems generated by piecewise affine contracting mappings whose
variables represent gene expression levels. When compared to other models of
regulatory networks, these models have an additional parameter which is
identified as quantifying interaction delays. In spite of their simplicity,
their dynamics presents a rich variety of behaviours. This phenomenology is not
limited to piecewise affine model but extends to smooth nonlinear discrete time
models of regulatory networks. In a first step, our analysis concerns general
properties of networks on arbitrary graphs (characterisation of the attractor,
symbolic dynamics, Lyapunov stability, structural stability, symmetries, etc).
In a second step, focus is made on simple circuits for which the attractor and
its changes with parameters are described. In the negative circuit of 2 genes,
a thorough study is presented which concern stable (quasi-)periodic
oscillations governed by rotations on the unit circle -- with a rotation number
depending continuously and monotonically on threshold parameters. These regular
oscillations exist in negative circuits with arbitrary number of genes where
they are most likely to be observed in genetic systems with non-negligible
delay effects.Comment: 34 page
Measures of Analysis of Time Series (MATS): A MATLAB Toolkit for Computation of Multiple Measures on Time Series Data Bases
In many applications, such as physiology and finance, large time series data
bases are to be analyzed requiring the computation of linear, nonlinear and
other measures. Such measures have been developed and implemented in commercial
and freeware softwares rather selectively and independently. The Measures of
Analysis of Time Series ({\tt MATS}) {\tt MATLAB} toolkit is designed to handle
an arbitrary large set of scalar time series and compute a large variety of
measures on them, allowing for the specification of varying measure parameters
as well. The variety of options with added facilities for visualization of the
results support different settings of time series analysis, such as the
detection of dynamics changes in long data records, resampling (surrogate or
bootstrap) tests for independence and linearity with various test statistics,
and discrimination power of different measures and for different combinations
of their parameters. The basic features of {\tt MATS} are presented and the
implemented measures are briefly described. The usefulness of {\tt MATS} is
illustrated on some empirical examples along with screenshots.Comment: 25 pages, 9 figures, two tables, the software can be downloaded at
http://eeganalysis.web.auth.gr/indexen.ht
Theory on the Dynamics of Oscillatory Loops in the Transcription Factor Networks
We develop a detailed theoretical framework for various types of
transcription factor gene oscillators. We further demonstrate that one can
build genetic-oscillators which are tunable and robust against perturbations in
the critical control parameters by coupling two or more independent
Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of
the coupled oscillators constructed in the literature so far seem to be of -OR-
type. When there are transient perturbations in one of the -OR- type
coupled-oscillators, then the overall period of the system remains constant
(period-buffering) whereas in case of -AND- type coupling the overall period of
the system moves towards the perturbed oscillator. Though there is a
period-buffering, the amplitudes of oscillators coupled through -OR- type logic
are more sensitive to perturbations in the parameters associated with the
promoter state dynamics than -AND- type. Further analysis shows that the period
of -AND- type coupled dual-feedback oscillators can be tuned without conceding
on the amplitudes. Using these results we derive the basic design principles
governing the robust and tunable synthetic gene oscillators without
compromising on their amplitudes.Comment: 37 pages, 13 figures, 2 table
Locally optimal control of continuous variable entanglement
We consider a system of two bosonic modes each subject to the dynamics
induced by a thermal Markovian environment and we identify instantaneous, local
symplectic controls that minimise the loss of entanglement in the Gaussian
regime. By minimising the decrease of the logarithmic negativity at every
instant in time, it will be shown that a non-trivial, finite amount of local
squeezing helps to counter the effect of decoherence during the evolution. We
also determine optimal control routines in the more restrictive scenario where
the control operations are applied on only one of the two modes. We find that
applying an instantaneous control only at the beginning of the dynamics, i.e.
preparing an appropriate initial state, is the optimal strategy for states with
symmetric correlations and when the dynamics is the same on both modes. More
generally, even in asymmetric cases, the delayed decay of entanglement
resulting from the optimal preparation of the initial state with no further
action turns out to be always very close to the optimised control where
multiple operations are applied during the evolution. Our study extends
directly to mono-symmetric systems of any number of modes, i.e. to systems that
are invariant under any local permutation of the modes within any one
partition, as they are locally equivalent to two-mode systems.Comment: 10 pages, 6 figures, still no joke
Dynamics of a Limit Cycle Oscillator under Time Delayed Linear and Nonlinear Feedbacks
We study the effects of time delayed linear and nonlinear feedbacks on the
dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic
investigations reveal a host of complex temporal phenomena such as phase slips,
frequency suppression, multiple periodic states and chaos. Such phenomena are
frequently observed in the collective behavior of a large number of coupled
limit cycle oscillators. Our time delayed feedback model offers a simple
paradigm for obtaining and investigating these temporal states in a single
oscillator.We construct a detailed bifurcation diagram of the oscillator as a
function of the time delay parameter and the driving strengths of the feedback
terms. We find some new states in the presence of the quadratic nonlinear
feedback term with interesting characteristics like birhythmicity, phase
reversals, radial trapping, phase jumps and spiraling patterns in the amplitude
space. Our results may find useful applications in physical, chemical or
biological systems.Comment: VERSION 4: Fig. 10(d) added, an uncited reference removed; (To appear
in Physica D) (17 pages, 21 figures, two column, aps RevTeX); VERSION 3:
Revised. In Section 2, small tau approximation added; Section 3 is divided
into subsections; periodic solution discussed in detail; Figs. 7 and 11
discarded; Figs. 12 and 14 altered; three new figures (now Figs. 10, 11 and
21) added. VERSION 2: Figs. 1 and 2 replace
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