A Study on the Reversed Lack of Memory Property and its Generalizations

In this thesis, the concept of reversed lack of memory property and its generalizations is studied.We we generalize this property which involves operations different than the ”addition”. In particular an associative, binary operator ” * ” is considered. The univariate reversed lack of memory property is generalized using the binary operator and a class of probability distributions which include Type 3 extreme value, power function, reflected Weibull and negative Pareto distributions are characterized (Asha and Rejeesh (2009)). We also define the almost reversed lack of memory property and considered the distributions with reversed periodic hazard rate under the binary operation. Further, we give a bivariate extension of the generalized reversed lack of memory property and characterize a class of bivariate distributions which include the characterized extension (CE) model of Roy (2002a) apart from the bivariate reflected Weibull and power function distributions. We proved the equality of local proportionality of the reversed hazard rate and generalized reversed lack of memory property. Study of uncertainty is a subject of interest common to reliability, survival analysis, actuary, economics, business and many other fields. However, in many realistic situations, uncertainty is not necessarily related to the future but can also refer to the past. Recently, Di Crescenzo and Longobardi (2009) introduced a new measure of information called dynamic cumulative entropy. Dynamic cumulative entropy is suitable to measure information when uncertainty is related to the past, a dual concept of the cumulative residual entropy which relates to uncertainty of the future lifetime of a system. We redefine this measure in the whole real line and study its properties. We also discuss the implications of generalized reversed lack of memory property on dynamic cumulative entropy and past entropy.In this study, we extend the idea of reversed lack of memory property to the discrete set up. Here we investigate the discrete class of distributions characterized by the discrete reversed lack of memory property. The concept is extended to the bivariate case and bivariate distributions characterized by this property are also presented. The implication of this property on discrete reversed hazard rate, mean past life, and discrete past entropy are also investigated.

Bidirectional communication using delay coupled chaotic directly modulated semiconductor lasers

Chaotic synchronization of two directly modulated semiconductor lasers with negative delayed optoelectronic feedback is investigated and this scheme is found to be useful for e±cient bidirectional communication between the lasers. A symmetric bidirec- tional coupling is identified as a suitable method for isochronal synchronization of such lasers. The optimum values of coupling and feedback strength that can provide maxi- mum quality of synchronization are identified. This method is successfully employed for encoding/decoding both analog and digital messages. The importance of a symmetric coupling is demonstrated by studying the variation of decoding efficiency with respect to asymmetric coupling.

Multi-user bidirectional communication using isochronal synchronisation of array of chaotic directly modulated semiconductor lasers

Isochronal synchronisation between the elements of an array of three mutually coupled directly modulated semiconductor lasers is utilized for the purpose of simultaneous bidirectional secure communication. Chaotic synchronisation is achieved by adding the coupling signal to the self feedback signal provided to each element of the array. A symmetric coupling is effective in inducing synchronisation between the elements of the array. This coupling scheme provides a direct link between every pair of elements thus making the method suitable for simultaneous bidirectional communication between them. Both analog and digital messages are successfully encrypted and decrypted simultaneously by each element of the array.

Effect of a fluctuating parameter mismatch and the associated time-scales on coupled Rossler oscillators

We study the effect of parameter fluctuations and the resultant multiplicative noise on the synchronization of coupled chaotic systems. We introduce a new quantity, the fluctuation rate Ф as the number of perturbations occurring to the parameter in unit time. It is shown that ϕ is the most significant quantity that determines the quality of synchronization. It is found that parameter fluctuations with high fluctuation rates do not destroy synchronization, irrespective of the statistical features of the fluctuations. We also present a quasi-analytic explanation to the relation between ϕ and the error in synchrony.

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.

Suppression of chaos through reverse period doubling in coupled directly modulated semiconductor lasers

The effect of coupling on two high frequency modulated semiconductor lasers is numerically studied. The phase diagrams and bifurcatio.n diagrams are drawn. As the coupling constant is increased the system goes from chaotic to periodic behavior through a reverse period doubling sequence. The Lyapunov exponent is calculated to characterize chaotic and periodic regions.

Stability of periodic orbits of coupled-map lattices

We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in terms of those for smaller orbits.

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

Bifurcation structure and Lyapunov exponents of a modulated logistic map

We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.

Metastable States and Irregular Behaviour in a Josephson Junction with Nonlinear Resistance

We consider a resistively shunted Josephson junction with a resistance that depends inversely on voltage. It is shown that such a junction in the underdamped case can give rise to extremely long-lived metastable states even in the absence of external noise. We investigate numerically this metastable state and its transition to a chaotic state. The junction voltages corresponding to these states are studied.

Enhancement of Microwave Properties of Planar Filters and Antennas using Photonic Bandgap (PBG) Structures

In this thesis, we explore the design, computation, and experimental analysis of photonic crystals, with a special emphasis on structures and devices that make a connection with practically realizable systems. First, we analyze the propenies of photonic-crystal: periodic dielectric structures that have a band gap for propagation. The band gap of periodically loaded air column on a dielectric substrate is computed using Eigen solvers in a plane wave basis. Then this idea is extended to planar filters and antennas at microwave regime. The main objectives covered in this thesis are:• Computation of Band Gap origin in Photonic crystal with the abet of Maxwell's equation and Bloch-Floquet's theorem • Extension of Band Gap to Planar structures at microwave regime • Predict the dielectric constant - synthesized dieletric cmstant of the substrates when loaded with Photonic Band Gap (PBG) structures in a microstrip transmission line • Identify the resonant characteristic of the PBG cell and extract the equivalent circuit based on PBG cell and substrate parameters for microstrip transmission line • Miniaturize PBG as Defected Ground Structures (DGS) and use the property to be implemented in planar filters with microstrip transmission line • Extended the band stop effect of PBG / DGS to coplanar waveguide and asymmetric coplanar waveguide. • Formulate design equations for the PBG / DGS filters • Use these PBG / DGS ground plane as ground plane of microstrip antennas • Analysis of filters and antennas using FDID method

Recurrence Quantification Analysis of System Signals for Detecting Tool and Chatter in Turning

In this thesis, the applications of the recurrence quantification analysis in metal cutting operation in a lathe, with specific objective to detect tool wear and chatter, are presented.This study is based on the discovery that process dynamics in a lathe is low dimensional chaotic. It implies that the machine dynamics is controllable using principles of chaos theory. This understanding is to revolutionize the feature extraction methodologies used in condition monitoring systems as conventional linear methods or models are incapable of capturing the critical and strange behaviors associated with the metal cutting process.As sensor based approaches provide an automated and cost effective way to monitor and control, an efficient feature extraction methodology based on nonlinear time series analysis is much more demanding. The task here is more complex when the information has to be deduced solely from sensor signals since traditional methods do not address the issue of how to treat noise present in real-world processes and its non-stationarity. In an effort to get over these two issues to the maximum possible, this thesis adopts the recurrence quantification analysis methodology in the study since this feature extraction technique is found to be robust against noise and stationarity in the signals.The work consists of two different sets of experiments in a lathe; set-I and set-2. The experiment, set-I, study the influence of tool wear on the RQA variables whereas the set-2 is carried out to identify the sensitive RQA variables to machine tool chatter followed by its validation in actual cutting. To obtain the bounds of the spectrum of the significant RQA variable values, in set-i, a fresh tool and a worn tool are used for cutting. The first part of the set-2 experiments uses a stepped shaft in order to create chatter at a known location. And the second part uses a conical section having a uniform taper along the axis for creating chatter to onset at some distance from the smaller end by gradually increasing the depth of cut while keeping the spindle speed and feed rate constant.The study concludes by revealing the dependence of certain RQA variables; percent determinism, percent recurrence and entropy, to tool wear and chatter unambiguously. The performances of the results establish this methodology to be viable for detection of tool wear and chatter in metal cutting operation in a lathe. The key reason is that the dynamics of the system under study have been nonlinear and the recurrence quantification analysis can characterize them adequately.This work establishes that principles and practice of machining can be considerably benefited and advanced from using nonlinear dynamics and chaos theory.

Regulation of GABA(A) and glutamate receptor expression, synaptic facilitation and long-term potentiation in the hippocampus of prion mutant mice

Background: Prionopathies are characterized by spongiform brain degeneration, myoclonia, dementia, and periodic electroencephalographic (EEG) disturbances. The hallmark of prioniopathies is the presence of an abnormal conformational isoform (PrP(sc)) of the natural cellular prion protein (PrP(c)) encoded by the Prnp gene. Although several roles have been attributed to PrP(c), its putative functions in neuronal excitability are unknown. Although early studies of the behavior of Prnp knockout mice described minor changes, later studies report altered behavior. To date, most functional PrP(c) studies on synaptic plasticity have been performed in vitro. To our knowledge, only one electrophysiological study has been performed in vivo in anesthetized mice, by Curtis and coworkers. They reported no significant differences in paired-pulse facilitation or LTP in the CA1 region after Schaffer collateral/commissural pathway stimulation. Principal Findings: Here we explore the role of PrP(c) expression in neurotransmission and neural excitability using wild-type, Prnp -/- and PrP(c)-overexpressing mice (Tg20 strain). By correlating histopathology with electrophysiology in living behaving mice, we demonstrate that both Prnp -/- mice but, more relevantly Tg20 mice show increased susceptibility to KA, leading to significant cell death in the hippocampus. This finding correlates with enhanced synaptic facilitation in paired-pulse experiments and hippocampal LTP in living behaving mutant mice. Gene expression profiling using Illumina microarrays and Ingenuity pathways analysis showed that 129 genes involved in canonical pathways such as Ubiquitination or Neurotransmission were co-regulated in Prnp -/- and Tg20 mice. Lastly, RT-qPCR of neurotransmission-related genes indicated that subunits of GABA(A) and AMPA-kainate receptors are co-regulated in both Prnp -/- and Tg20 mice. Conclusions/Significance: Present results demonstrate that PrP(c) is necessary for the proper homeostatic functioning of hippocampal circuits, because of its relationships with GABA(A) and AMPA-Kainate neurotransmission. New PrP(c) functions have recently been described, which point to PrP(c) as a target for putative therapies in Alzheimer's disease. However, our results indicate that a "gain of function" strategy in Alzheimer's disease, or a "loss of function" in prionopathies, may impair PrP(c) function, with devastating effects. In conclusion, we believe that present data should be taken into account in the development of future therapies.

Dynamics of coupled Josephson junctions under the influence of applied fields

We investigate the effect of the phase difference of appliedfields on the dynamics of mutually coupledJosephsonjunctions. A phase difference between the appliedfields desynchronizes the system. It is found that though the amplitudes of the output voltage values are uncorrelated, a phase correlation is found to exist for small values of applied phase difference. The dynamics of the system is found to change from chaotic to periodic for certain values of phase difference. We report that by keeping the value of phase difference as π, the system continues to be in periodic motion for a wide range of values of system parameters. This result may find applications in devices like voltage standards, detectors, SQUIDS, etc., where chaos is least desired.

Creation and Annihilation of Fluxons in ac‐driven Semi-annular Josephson Junction

A new geometry (semiannular) for Josephson junction has been proposed and theoretical studies have shown that the new geometry is useful for electronic applications [1, 2]. In this work we study the voltage‐current response of the junction with a periodic modulation. The fluxon experiences an oscillating potential in the presence of the ac‐bias which increases the depinning current value. We show that in a system with periodic boundary conditions, average progressive motion of fluxon commences after the amplitude of the ac drive exceeds a certain threshold value. The analytic studies are justified by simulating the equation using finite‐difference method. We observe creation and annihilation of fluxons in semiannular Josephson junction with an ac‐bias in the presence of an external magnetic field.