Local Bifurcations in a Nonlinear Model of a Bioreactor

This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008.

Growing Neural Networks Using Nonconventional Activation Functions

In the paper, an ontogenic artificial neural network (ANNs) is proposed. The network uses orthogonal activation functions that allow significant reducing of computational complexity. Another advantage is numerical stability, because the system of activation functions is linearly independent by definition. A learning procedure for proposed ANN with guaranteed convergence to the global minimum of error function in the parameter space is developed. An algorithm for structure network structure adaptation is proposed. The algorithm allows adding or deleting a node in real-time without retraining of the network. Simulation results confirm the efficiency of the proposed approach.

Integrated optimisation of surface roughness and tool performance when face milling 416 SS

Tool life is an important factor to be considered during the optimisation of a machining process since cutting parameters can be adjusted to optimise tool changing, reducing cost and time of production. Also the performance of a tool is directly linked to the generated surface roughness and this is important in cases where there are strict surface quality requirements. The prediction of tool life and the resulting surface roughness in milling operations has attracted considerable research efforts. The research reported herein is focused on defining the influence of milling cutting parameters such as cutting speed, feed rate and axial depth of cut, on three major tool performance parameters namely, tool life, material removal and surface roughness. The research is seeking to define methods that will allow the selection of optimal parameters for best tool performance when face milling 416 stainless steel bars. For this study the Taguchi method was applied in a special design of an orthogonal array that allows studying the entire parameter space with only a number of experiments representing savings in cost and time of experiments. The findings were that the cutting speed has the most influence on tool life and surface roughness and very limited influence on material removal. By last tool life can be judged either from tool life or volume of material removal.

Parametric pattern selection in a reaction-diffusion model

We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.

Real-time intensity domain characterization of fibre lasers using spatio-temporal dynamics

Fibre lasers are light sources that are synonymous with stability. They can give rise to highly coherent continuous-wave radiation, or a stable train of mode locked pulses with well-defined characteristics. However, they can also exhibit an exceedingly diverse range of nonlinear operational regimes spanning a multi-dimensional parameter space. The complex nature of the dynamics poses significant challenges in the theoretical and experimental studies of such systems. Here, we demonstrate how the real-time experimental methodology of spatio-temporal dynamics can be used to unambiguously identify and discern between such highly complex lasing regimes. This two-dimensional representation of laser intensity allows the identification and tracking of individual features embedded in the radiation as they make round-trip circulations inside the cavity. The salient features of this methodology are highlighted by its application to the case of Raman fibre lasers and a partially mode locked ring fibre laser operating in the normal dispersion regime.

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Bayesian adaptive estimation of arbitrary points on a psychometric function

Bayesian adaptive methods have been extensively used in psychophysics to estimate the point at which performance on a task attains arbitrary percentage levels, although the statistical properties of these estimators have never been assessed. We used simulation techniques to determine the small-sample properties of Bayesian estimators of arbitrary performance points, specifically addressing the issues of bias and precision as a function of the target percentage level. The study covered three major types of psychophysical task (yes-no detection, 2AFC discrimination and 2AFC detection) and explored the entire range of target performance levels allowed for by each task. Other factors included in the study were the form and parameters of the actual psychometric function Psi, the form and parameters of the model function M assumed in the Bayesian method, and the location of Psi within the parameter space. Our results indicate that Bayesian adaptive methods render unbiased estimators of any arbitrary point on psi only when M=Psi, and otherwise they yield bias whose magnitude can be considerable as the target level moves away from the midpoint of the range of Psi. The standard error of the estimator also increases as the target level approaches extreme values whether or not M=Psi. Contrary to widespread belief, neither the performance level at which bias is null nor that at which standard error is minimal can be predicted by the sweat factor. A closed-form expression nevertheless gives a reasonable fit to data describing the dependence of standard error on number of trials and target level, which allows determination of the number of trials that must be administered to obtain estimates with prescribed precision.

Transition dynamics for multi-pulsing in mode-locked lasers

We consider experimentally and theoretically a refined parameter space in a mode-locked fiber laser near the transition to multi-pulsing. Increasing cavity energy drives the dynamics through a periodic instability to chaotic dynamics. © 2010 Optical Society of America.

Characterizing the transition dynamics for multi-pulsing in mode-locked lasers

We consider experimentally and theoretically a refined parameter space near the transition to multi-pulse modelocking. Near the transition, the onset of instability is initiated by a Hopf (periodic) bifurcation. As cavity energy is increased, the band of unstable, oscillatory modes generates a chaotic behavior between single- and multi-pulse operation. Both theory and experiment are in good qualitative agreement and they suggest that the phenomenon is of a universal nature in mode-locked lasers at the onset of multi-pulsing from N to N + 1 pulses per round trip. This is the first theoretical and experimental characterization of the transition behavior, made possible by a highly refined tuning of the gain pump level. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Collective excitability, synchronization, and array-enhanced coherence resonance in a population of lasers with a saturable absorber

In this article we present a numerical study of the collective dynamics in a population of coupled semiconductor lasers with a saturable absorber, operating in the excitable regime under the action of additive noise. We demonstrate that temporal and intensity synchronization takes place in a broad region of the parameter space and for various array sizes. The synchronization is robust and occurs even for a set of nonidentical coupled lasers. The cooperative nature of the system results in a self-organization process which enhances the coherence of the single element of the population too and can have broad impact for detection purposes, for building all-optical simulators of neural networks and in the field of photonics-based computation.

Exploitation du potentiel sismique des étoiles naines blanches

Le but de cette thèse est d’explorer le potentiel sismique des étoiles naines blanches pulsantes, et en particulier celles à atmosphères riches en hydrogène, les étoiles ZZ Ceti. La technique d’astérosismologie exploite l’information contenue dans les modes normaux de vibration qui peuvent être excités lors de phases particulières de l’évolution d’une étoile. Ces modes modulent le flux émergent de l’étoile pulsante et se manifestent principalement en termes de variations lumineuses multi-périodiques. L’astérosismologie consiste donc à examiner la luminosité d’étoiles pulsantes en fonction du temps, afin d’en extraire les périodes, les amplitudes apparentes, ainsi que les phases relatives des modes de pulsation détectés, en utilisant des méthodes standards de traitement de signal, telles que des techniques de Fourier. L’étape suivante consiste à comparer les périodes de pulsation observées avec des périodes générées par un modèle stellaire en cherchant l’accord optimal avec un modèle physique reconstituant le plus fidèlement possible l’étoile pulsante. Afin d’assurer une recherche optimale dans l’espace des paramètres, il est nécessaire d’avoir de bons modèles physiques, un algorithme d’optimisation de comparaison de périodes efficace, et une puissance de calcul considérable. Les périodes des modes de pulsation de modèles stellaires de naines blanches peuvent être généralement calculées de manière précise et fiable sur la base de la théorie linéaire des pulsations stellaires dans sa version adiabatique. Afin de définir dans son ensemble un modèle statique de naine blanche propre à l’analyse astérosismologique, il est nécessaire de spécifier la gravité de surface, la température effective, ainsi que différents paramètres décrivant la disposition en couche de l’enveloppe. En utilisant parallèlement les informations obtenues de manière indépendante (température effective et gravité de surface) par la méthode spectroscopique, il devient possible de vérifier la validité de la solution obtenue et de restreindre de manière remarquable l’espace des paramètres. L’exercice astérosismologique, s’il est réussi, mène donc à la détermination précise des paramètres de la structure globale de l’étoile pulsante et fournit de l’information unique sur sa structure interne et l’état de sa phase évolutive. On présente dans cette thèse l’analyse complète réussie, de l’extraction des fréquences à la solution sismique, de quatre étoiles naines blanches pulsantes. Il a été possible de déterminer les paramètres structuraux de ces étoiles et de les comparer remarquablement à toutes les contraintes indépendantes disponibles dans la littérature, mais aussi d’inférer sur la dynamique interne et de reconstruire le profil de rotation interne. Dans un premier temps, on analyse le duo d’étoiles ZZ Ceti, GD 165 et Ross 548, afin de comprendre les différences entre leurs propriétés de pulsation, malgré le fait qu’elles soient des étoiles similaires en tout point, spectroscopiquement parlant. L’analyse sismique révèle des structures internes différentes, et dévoile la sensibilité de certains modes de pulsation à la composition interne du noyau de l’étoile. Afin de palier à cette sensibilité, nouvellement découverte, et de rivaliser avec les données de qualité exceptionnelle que nous fournissent les missions spatiales Kepler et Kepler2, on développe une nouvelle paramétrisation des profils chimiques dans le coeur, et on valide la robustesse de notre technique et de nos modèles par de nombreux tests. Avec en main la nouvelle paramétrisation du noyau, on décroche enfin le ”Saint Graal” de l’astérosismologie, en étant capable de reproduire pour la première fois les périodes observées à la précision des observations, dans le cas de l’étude sismique des étoiles KIC 08626021 et de GD 1212.

Ablation of Steel by Microsecond Pulse Trains

Laser micromachining is an important material processing technique used in industry and medicine to produce parts with high precision. Control of the material removal process is imperative to obtain the desired part with minimal thermal damage to the surrounding material. Longer pulsed lasers, with pulse durations of milli- and microseconds, are used primarily for laser through-cutting and welding. In this work, a two-pulse sequence using microsecond pulse durations is demonstrated to achieve consistent material removal during percussion drilling when the delay between the pulses is properly defined. The light-matter interaction moves from a regime of surface morphology changes to melt and vapour ejection. Inline coherent imaging (ICI), a broadband, spatially-coherent imaging technique, is used to monitor the ablation process. The pulse parameter space is explored and the key regimes are determined. Material removal is observed when the pulse delay is on the order of the pulse duration. ICI is also used to directly observe the ablation process. Melt dynamics are characterized by monitoring surface changes during and after laser processing at several positions in and around the interaction region. Ablation is enhanced when the melt has time to flow back into the hole before the interaction with the second pulse begins. A phenomenological model is developed to understand the relationship between material removal and pulse delay. Based on melt refilling the interaction region, described by logistic growth, and heat loss, described by exponential decay, the model is fit to several datasets. The fit parameters reflect the pulse energies and durations used in the ablation experiments. For pulse durations of 50 us with pulse energies of 7.32 mJ +/- 0.09 mJ, the logisitic growth component of the model reaches half maximum after 8.3 us +/- 1.1 us and the exponential decays with a rate of 64 us +/- 15 us. The phenomenological model offers an interpretation of the material removal process.

Type Ia supernovae from violent mergers of carbon-oxygen white dwarfs: polarization signatures

The violent merger of two carbon-oxygen white dwarfs has been proposed as a viable progenitor for some Type Ia supernovae. However, it has been argued that the strong ejecta asymmetries produced by this model might be inconsistent with the low degree of polarization typically observed in Type Ia supernova explosions. Here, we test this claim by carrying out a spectropolarimetric analysis for the model proposed by Pakmor et al. for an explosion triggered during the merger of a 1.1 and 0.9 M⊙ carbon-oxygen white dwarf binary system. Owing to the asymmetries of the ejecta, the polarization signal varies significantly with viewing angle. We find that polarization levels for observers in the equatorial plane are modest (≲1 per cent) and show clear evidence for a dominant axis, as a consequence of the ejecta symmetry about the orbital plane. In contrast, orientations out of the plane are associated with higher degrees of polarization and departures from a dominant axis. While the particular model studied here gives a good match to highly polarized events such as SN 2004dt, it has difficulties in reproducing the low polarization levels commonly observed in normal Type Ia supernovae. Specifically, we find that significant asymmetries in the element distribution result in a wealth of strong polarization features that are not observed in the majority of currently available spectropolarimetric data of Type Ia supernovae. Future studies will map out the parameter space of the merger scenario to investigate if alternative models can provide better agreement with observations.

Mode locking in a periodically forced "ghostbursting" neuron model

We study a minimal integrate-and-fire based model of a "ghostbursting" neuron under periodic stimulation. These neurons are involved in sensory processing in weakly electric fish. There exist regions in parameter space in which the model neuron is mode-locked to the stimulation. We analyse this locked behavior and examine the bifurcations that define the boundaries of these regions. Due to the discontinuous nature of the flow, some of these bifurcations are nonsmooth. This exact analysis is in excellent agreement with numerical simulations, and can be used to understand the response of such a model neuron to biologically realistic input.

Towards a gravitational wave observatory designer: sensitivity limits of spaceborne detectors

The most promising concept for low frequency (millihertz to hertz) gravitational wave observatories are laser interferometric detectors in space. It is usually assumed that the noise floor for such a detector is dominated by optical shot noise in the signal readout. For this to be true, a careful balance of mission parameters is crucial to keep all other parasitic disturbances below shot noise. We developed a web application that uses over 30 input parameters and considers many important technical noise sources and noise suppression techniques to derive a realistic position noise budget. It optimizes free parameters automatically and generates a detailed report on all individual noise contributions. Thus one can easily explore the entire parameter space and design a realistic gravitational wave observatory. In this document we describe the different parameters, present all underlying calculations, and compare the final observatory's sensitivity with astrophysical sources of gravitational waves. We use as an example parameters currently assumed to be likely applied to a space mission proposed to be launched in 2034 by the European Space Agency. The web application itself is publicly available on the Internet at http://spacegravity.org/designer. Future versions of the web application will incorporate the frequency dependence of different noise sources and include a more detailed model of the observatory's residual acceleration noise.