Gain and noise spectral density in an electronic parametric amplifier with added white noise

In this paper, we discuss the behavior of a linear classical parametric amplifier (PA) in the presence of white noise and give theoretical estimates of the noise spectral density based on approximate Green's functions obtained by using averaging techniques. Furthermore, we give analytical estimates for parametric amplification bandwidth of the amplifier and for the noisy precursors to instability. To validate our theory we compare the analytical results with experimental data obtained in an analog circuit. We describe the implementation details and the setup used in the experimental study of the amplifier. Near the threshold to the first parametric instability, and in degenerate-mode amplification, the PA achieved very high gains in a very narrow bandwidth centered on its resonance frequency. In quasi-degenerate mode amplification, we obtained lower values of gain, but with a wider bandwidth that is tunable. The experimental data were accurately described by the predictions of the model. Moreover, we noticed spectral components in the output signal of the amplifier which are due to noise precursors of instability. The position, width, and magnitude of these components are in agreement with the noise spectral density obtained by the theory proposed here

Tensor coupling and pseudospin symmetry in nuclei

In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy decomposition of the pseudospin energy splittings, we show that the changes in these splittings come by mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners, and by changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.Comment: 11 pages, 5 figures, uses REVTeX macro

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

Dynamical nature of the nuclear pseudospin and its isospin asymmetry

Pseudospin symmetry in nuclei is investigated by solving the Dirac equation with Woods-Saxon scalar and vector radial potentials. We relate the pseudospin interaction with a pseudospin-orbit term in a Schroedinger-like equation for the lower component of the Dirac spinor. We show that this term gives a large contribution to the energy splittings of pseudospin partners, so that the near pseudospin degeneracy arises from a significant cancellation among the different terms in that equation. This is a manifestation of the dynamical character of this symmetry in the nucleus. We analyze the isospin dependence of the pseudospin symmetry in a nuclear isotope chain by including a vector-isovector potential V_rho and a Coulomb potential and conclude that V_rho gives the main contribution to the observed pseudospin isospin asymmetry.Comment: 4 pages, 2 figures, uses World Scientific style file. Contribution presented at the VIII International Workshop on Hadron Physics, Bento Goncalves, RS, Brazil, April 14-19, 2002. To be published by World Scientific in the proceedings of the "International Workshop on Hadron Physics 2002

Modelling interstellar extinction in stellar populations

In stellar astrophysics, the determination of the magnitude of interstellar extinction is critical, due to its effect on the observed brightness and colour of the stars. Extinction is therefore an important factor in deriving scientific information from the colour-magnitude diagrams (CMDs) of stellar populations. The treatment of extinction in standard CMD analyses is to employ constant ratios of extinction in each photometric filter relative to the visual Johnson-V filter, denoted AX/AV in a generic filter X. This work presents a theoretical analysis of the behaviour of the extinction ratios AX/AV in multiple photometric systems as the values of three stellar parameters (effective temperature, surface gravity and metallicity) are varied. The results of this analysis show significant variations in the value of AX/AV with changes in the stellar parameters. For certain ultraviolet filters and an AV value of 1.0, the fractional flux lost to extinction is up to two orders of magnitude greater between different stellar atmospheres. Analytic functions of these stellar parameters are proposed to describe these variations. Also presented is an application of these functions to generic isochrones in multiple photometric filter systems. This was followed by an application of the extinction-ratio functions to the highly-reddened star cluster NGC 6793 whose members also have accurate Gaia parallax measurements. When a proper analysis of extinction, via the AX=AV functions, is used on the cluster data, it is shown that there is a non-negligible impact on the age determination for the cluster in multiple CMD axes and in different filter systems. For NGC 6793, the observational data predicts an age of 603 Myr, an AV value of 0.843 and a metallicity of [Fe/H] = 0.0 when the extinction in each filter is held constant. When the extinction is allowed to vary according to the AX/AV functions, the predicted values for these parameters become 500 Myr, 1.1 and +0.062, respectively. The uncertainties in the observational data, the models and all other factors considered were found to be insufficiently large to render the difference between these results insignificant. It was therefore concluded that changing the method of calculating extinction in isochrones results in a significant change in cluster parameter estimates, particularly for the age and AV values

Spin and pseudospin symmetries in the antinucleon spectrum of nuclei

Spin and pseudospin symmetries in the spectra of nucleons and antinucleons are studied in a relativistic mean-field theory with scalar and vector Woods-Saxon potentials, in which the strength of the latter is allowed to change. We observe that, for nucleons and antinucleons, the spin symmetry is of perturbative nature and it is almost an exact symmetry in the physical region for antinucleons. The opposite situation is found in the pseudospin symmetry case, which is better realized for nucleons than for antinucleons, but is of dynamical nature and cannot be viewed in a perturbative way both for nucleons and antinucleons. This is shown by computing the spin-orbit and pseudospin-orbit couplings for selected spin and pseudospin partners in both spectra.Comment: 8 figures, uses revtex 4.1 macro

Flexibility of expressive timing in repeated musical performances

Performances by soloists in the Western classical tradition are normally highly prepared, yet must sound fresh and spontaneous. How do musicians manage this? We tested the hypothesis that they achieve the necessary spontaneity by varying the musical gestures that express their interpretation of a piece. We examined the tempo arches produced by final slowing at the ends of phrases in performances of J. S. Bach’s No. 6 (Prelude) for solo cello (12 performances) and the Italian Concerto (Presto) for solo piano (eight performances). The performances were given by two experienced concert soloists during a short time period (3½ months for the Prelude, 2 weeks for the Presto) after completing their preparations for public performance. We measured the tempo of each bar or half-bar, and the stability of tempo across performances (difference of the tempo of each bar/half bar from each of the other performances). There were phrase arches for both tempo and stability with slower, less stable tempi at beginnings and ends of phrases and faster, more stable tempi mid-phrase. The effects of practice were complex. Tempo decreased overall with practice, while stability increased in some bars and decreased in others. One effect of practice may be to imbue well-learned, automatic motor sequences with freshness and spontaneity through cognitive control at phrase boundaries where slower tempi and decreased stability provide opportunities for slower cognitive processes to modulate rapid automatic motor sequences

Reduced kinetic models of facilitative transport

AbstractIn spite of the highly complex structural dynamics of globular proteins, the processes mediated by them can usually be described in terms of relatively simple kinetic diagrams. How do complex proteins, characterized by undergoing transitions among a possibly very large number of intermediate states, exhibit functional properties that can be interpreted in terms of kinetic diagrams consisting of only a small number of states? One possible way of explaining this apparent contradiction is that, under some conditions, a reduction of the actual complete kinetic diagram that describes all of the macromolecular states and transitions takes place. In this work, we contribute with a formal basis to this interpretation, by generalizing the procedure of diagram reduction to the case of multicyclic kinetic diagrams. As an example, we apply the procedure to a complex kinetic model of facilitative transport. We develop Monte Carlo simulations to obtain the kinetic parameters of the complex model and we compare them with the ones analytically obtained from the reduced model. We confirm that, under some conditions, the kinetic behavior of the complex transporter is indistinguishable from the one of a four-state simple carrier model, derived from the former by diagram reduction. Besides introducing some novel methodological aspects, this work further contributes to the idea that, under many physiological and experimental conditions, a reduction occurs of the complete kinetic diagram that describes the dynamics of a globular protein

Ventilator-associated pneumonia prevention: one good turn does not always deserve another

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