513 research outputs found
Lie systems and integrability conditions for t-dependent frequency harmonic oscillators
Time-dependent frequency harmonic oscillators (TDFHO's) are studied through
the theory of Lie systems. We show that they are related to a certain kind of
equations in the Lie group SL(2,R). Some integrability conditions appear as
conditions to be able to transform such equations into simpler ones in a very
specific way. As a particular application of our results we find t-dependent
constants of the motion for certain one-dimensional TDFHO's. Our approach
provides an unifying framework which allows us to apply our developments to all
Lie systems associated with equations in SL(2,R) and to generalise our methods
to study any Lie system
Analysis of signalling pathways using continuous time Markov chains
We describe a quantitative modelling and analysis approach for signal transduction networks.
We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable
Generalizing the autonomous Kepler Ermakov system in a Riemannian space
We generalize the two dimensional autonomous Hamiltonian Kepler Ermakov
dynamical system to three dimensions using the sl(2,R) invariance of Noether
symmetries and determine all three dimensional autonomous Hamiltonian Kepler
Ermakov dynamical systems which are Liouville integrable via Noether
symmetries. Subsequently we generalize the autonomous Kepler Ermakov system in
a Riemannian space which admits a gradient homothetic vector by the
requirements (a) that it admits a first integral (the Riemannian Ermakov
invariant) and (b) it has sl(2,R) invariance. We consider both the
non-Hamiltonian and the Hamiltonian systems. In each case we compute the
Riemannian Ermakov invariant and the equations defining the dynamical system.
We apply the results in General Relativity and determine the autonomous
Hamiltonian Riemannian Kepler Ermakov system in the spatially flat Friedman
Robertson Walker spacetime. We consider a locally rotational symmetric (LRS)
spacetime of class A and discuss two cosmological models. The first
cosmological model consists of a scalar field with exponential potential and a
perfect fluid with a stiff equation of state. The second cosmological model is
the f(R) modified gravity model of {\Lambda}_{bc}CDM. It is shown that in both
applications the gravitational field equations reduce to those of the
generalized autonomous Riemannian Kepler Ermakov dynamical system which is
Liouville integrable via Noether integrals.Comment: Reference [25] update, 21 page
Solutions to Maxwell's Equations using Spheroidal Coordinates
Analytical solutions to the wave equation in spheroidal coordinates in the
short wavelength limit are considered. The asymptotic solutions for the radial
function are significantly simplified, allowing scalar spheroidal wave
functions to be defined in a form which is directly reminiscent of the
Laguerre-Gaussian solutions to the paraxial wave equation in optics.
Expressions for the Cartesian derivatives of the scalar spheroidal wave
functions are derived, leading to a new set of vector solutions to Maxwell's
equations. The results are an ideal starting point for calculations of
corrections to the paraxial approximation
Unified Treatment of Heterodyne Detection: the Shapiro-Wagner and Caves Frameworks
A comparative study is performed on two heterodyne systems of photon
detectors expressed in terms of a signal annihilation operator and an image
band creation operator called Shapiro-Wagner and Caves' frame, respectively.
This approach is based on the introduction of a convenient operator
which allows a unified formulation of both cases. For the Shapiro-Wagner
scheme, where , quantum phase and amplitude
are exactly defined in the context of relative number state (RNS)
representation, while a procedure is devised to handle suitably and in a
consistent way Caves' framework, characterized by , within the approximate simultaneous measurements of
noncommuting variables. In such a case RNS phase and amplitude make sense only
approximately.Comment: 25 pages. Just very minor editorial cosmetic change
Symmetry, singularities and integrability in complex dynamics III: approximate symmetries and invariants
The different natures of approximate symmetries and their corresponding first
integrals/invariants are delineated in the contexts of both Lie symmetries of
ordinary differential equations and Noether symmetries of the Action Integral.
Particular note is taken of the effect of taking higher orders of the
perturbation parameter. Approximate symmetries of approximate first
integrals/invariants and the problems of calculating them using the Lie method
are considered
How two neutrino superbeam experiments do better than one
We examine the use of two superbeam neutrino oscillation experiments with
baselines \lsim 1000 km to resolve parameter degeneracies inherent in the
three-neutrino analysis of such experiments. We find that with appropriate
choices of neutrino energies and baselines two experiments with different
baselines can provide a much better determination of the neutrino mass ordering
than a single experiment alone. Two baselines are especially beneficial when
the mass scale for solar neutrino oscillations is \gsim
5\times10^{-5} eV. We also examine CP violation sensitivity and the
resolution of other parameter degeneracies. We find that the combined data of
superbeam experiments with baselines of 295 and 900 km can provide sensitivity
to both the neutrino mass ordering and CP violation for
down to 0.03 for eV. It
would be highly advantageous to have a 10% determination of before the beam energies and baselines are finalized, although if
is not that well known, the neutrino energies and
baselines can be chosen to give fairly good sensitivity for a range of .Comment: 18 pages, 6 PS figures, added references and revised discussio
PathwayBooster:a tool to support the curation of metabolic pathways
BACKGROUND: Despite several recent advances in the automated generation of draft metabolic reconstructions, the manual curation of these networks to produce high quality genome-scale metabolic models remains a labour-intensive and challenging task. RESULTS: We present PathwayBooster, an open-source software tool to support the manual comparison and curation of metabolic models. It combines gene annotations from GenBank files and other sources with information retrieved from the metabolic databases BRENDA and KEGG to produce a set of pathway diagrams and reports summarising the evidence for the presence of a reaction in a given organism’s metabolic network. By comparing multiple sources of evidence within a common framework, PathwayBooster assists the curator in the identification of likely false positive (misannotated enzyme) and false negative (pathway hole) reactions. Reaction evidence may be taken from alternative annotations of the same genome and/or a set of closely related organisms. CONCLUSIONS: By integrating and visualising evidence from multiple sources, PathwayBooster reduces the manual effort required in the curation of a metabolic model. The software is available online at http://www.theosysbio.bio.ic.ac.uk/resources/pathwaybooster/. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12859-014-0447-2) contains supplementary material, which is available to authorized users
Frequencies and Damping rates of a 2D Deformed Trapped Bose gas above the Critical Temperature
We derive the equation of motion for the velocity fluctuations of a 2D
deformed trapped Bose gas above the critical temperature in the hydrodynamical
regime. From this equation, we calculate the eigenfrequencies for a few
low-lying excitation modes. Using the method of averages, we derive a
dispersion relation in a deformed trap that interpolates between the
collisionless and hydrodynamic regimes. We make use of this dispersion relation
to calculate the frequencies and the damping rates for monopole and quadrupole
mode in both the regimes. We also discuss the time evolution of the wave packet
width of a Bose gas in a time dependent as well as time independent trap.Comment: 13 pages, latex fil
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