Nonlinear Dynamics of Nd:YAG lasers: Hopf bifurcation, Multistability and Chaotic Synchronization

In this thesis we have presented some aspects of the nonlinear dynamics of Nd:YAG lasers including synchronization, Hopf bifurcation, chaos control and delay induced multistability.We have chosen diode pumped Nd:YAG laser with intracavity KTP crystal operating with two mode and three mode output as our model system.Different types of orientation for the laser cavity modes were considered to carry out the studies. For laser operating with two mode output we have chosen the modes as having parallel polarization and perpendicular polarization. For laser having three mode output, we have chosen them as two modes polarized parallel to each other while the third mode polarized orthogonal to them.

Isolation and Characterization of Agglutinin in the Hemolymph of Penaeus indicus H. Milne Edwards

The present study is an attempt to find out the ralation between RNA/DNA ratio, protein,percentage growth rate and specific growth rate of prawn,Penaeus indicus with respect to Nervous system, Eyestalk and Muscle tissues during ontogenesis. We have isolated and purified a natural agglutinin in the hemolymph of P.indicus with antigenecity, agglutinating, hemolytic and antibacterial properties. The influence of growth and environmental parameters on the level of agglutinin in the hemolymph was studied. Agglutinin concentration during normal growth process was compared. The agglutinin concentration in the hemolymph was quantified through developing ELISA, which is useful in health monitoring studies of individual species. Complete amino acid composition of both the subunits of P.indicus agglutinin were analysed. P.indicus agglutinin showed similarity to those proteins having antigenecity,hemolytic and agglutinating properties.Hence, agglutinin was considered as a natural defence protein in the hemolymph of P.indicus responsible for immune surveillance. The humoral defence mechanism of agglutinin was a co-operative effort with hemocytes and complement system. The composition of isolated agglutinin of P.indicus amino acids will be helpful in the synthesis of new antibacterial analogues which can be used against disease causing organisms.

Signatures of Higher Functions of Brain Dynamics in Electroencephalogram: A Nonlinear Analysis

The brain with its highly complex structure made up of simple units,imterconnected information pathways and specialized functions has always been an object of mystery and sceintific fascination for physiologists,neuroscientists and lately to mathematicians and physicists. The stream of biophysicists are engaged in building the bridge between the biological and physical sciences guided by a conviction that natural scenarios that appear extraordinarily complex may be tackled by application of principles from the realm of physical sciences. In a similar vein, this report aims to describe how nerve cells execute transmission of signals ,how these are put together and how out of this integration higher functions emerge and get reflected in the electrical signals that are produced in the brain.Viewing the E E G Signal through the looking glass of nonlinear theory, the dynamics of the underlying complex system-the brain ,is inferred and significant implications of the findings are explored.

Studies on Some Aspects of Light Beam Propagation Through Certain Nonlinear Media

This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.

Permutation entropy based real-time chatter detection using audio signal in turning process

Machine tool chatter is an unfavorable phenomenon during metal cutting, which results in heavy vibration of cutting tool. With increase in depth of cut, the cutting regime changes from chatter-free cutting to one with chatter. In this paper, we propose the use of permutation entropy (PE), a conceptually simple and computationally fast measurement to detect the onset of chatter from the time series using sound signal recorded with a unidirectional microphone. PE can efficiently distinguish the regular and complex nature of any signal and extract information about the dynamics of the process by indicating sudden change in its value. Under situations where the data sets are huge and there is no time for preprocessing and fine-tuning, PE can effectively detect dynamical changes of the system. This makes PE an ideal choice for online detection of chatter, which is not possible with other conventional nonlinear methods. In the present study, the variation of PE under two cutting conditions is analyzed. Abrupt variation in the value of PE with increase in depth of cut indicates the onset of chatter vibrations. The results are verified using frequency spectra of the signals and the nonlinear measure, normalized coarse-grained information rate (NCIR).

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.

Permutation Entropy Based Analysis of Complex Signals for Characterising Change in System Dynamics

Timely detection of sudden change in dynamics that adversely affect the performance of systems and quality of products has great scientific relevance. This work focuses on effective detection of dynamical changes of real time signals from mechanical as well as biological systems using a fast and robust technique of permutation entropy (PE). The results are used in detecting chatter onset in machine turning and identifying vocal disorders from speech signal.Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. Here we propose the use of permutation entropy (PE), to detect the dynamical changes in two non linear processes, turning under mechanical system and speech under biological system.Effectiveness of PE in detecting the change in dynamics in turning process from the time series generated with samples of audio and current signals is studied. Experiments are carried out on a lathe machine for sudden increase in depth of cut and continuous increase in depth of cut on mild steel work pieces keeping the speed and feed rate constant. The results are applied to detect chatter onset in machining. These results are verified using frequency spectra of the signals and the non linear measure, normalized coarse-grained information rate (NCIR).PE analysis is carried out to investigate the variation in surface texture caused by chatter on the machined work piece. Statistical parameter from the optical grey level intensity histogram of laser speckle pattern recorded using a charge coupled device (CCD) camera is used to generate the time series required for PE analysis. Standard optical roughness parameter is used to confirm the results.Application of PE in identifying the vocal disorders is studied from speech signal recorded using microphone. Here analysis is carried out using speech signals of subjects with different pathological conditions and normal subjects, and the results are used for identifying vocal disorders. Standard linear technique of FFT is used to substantiate thc results.The results of PE analysis in all three cases clearly indicate that this complexity measure is sensitive to change in regularity of a signal and hence can suitably be used for detection of dynamical changes in real world systems. This work establishes the application of the simple, inexpensive and fast algorithm of PE for the benefit of advanced manufacturing process as well as clinical diagnosis in vocal disorders.

Development and Evaluation of Blind Identification Techniques for Nonlinear Systems

Identification and Control of Non‐linear dynamical systems are challenging problems to the control engineers.The topic is equally relevant in communication,weather prediction ,bio medical systems and even in social systems,where nonlinearity is an integral part of the system behavior.Most of the real world systems are nonlinear in nature and wide applications are there for nonlinear system identification/modeling.The basic approach in analyzing the nonlinear systems is to build a model from known behavior manifest in the form of system output.The problem of modeling boils down to computing a suitably parameterized model,representing the process.The parameters of the model are adjusted to optimize a performanace function,based on error between the given process output and identified process/model output.While the linear system identification is well established with many classical approaches,most of those methods cannot be directly applied for nonlinear system identification.The problem becomes more complex if the system is completely unknown but only the output time series is available.Blind recognition problem is the direct consequence of such a situation.The thesis concentrates on such problems.Capability of Artificial Neural Networks to approximate many nonlinear input-output maps makes it predominantly suitable for building a function for the identification of nonlinear systems,where only the time series is available.The literature is rich with a variety of algorithms to train the Neural Network model.A comprehensive study of the computation of the model parameters,using the different algorithms and the comparison among them to choose the best technique is still a demanding requirement from practical system designers,which is not available in a concise form in the literature.The thesis is thus an attempt to develop and evaluate some of the well known algorithms and propose some new techniques,in the context of Blind recognition of nonlinear systems.It also attempts to establish the relative merits and demerits of the different approaches.comprehensiveness is achieved in utilizing the benefits of well known evaluation techniques from statistics. The study concludes by providing the results of implementation of the currently available and modified versions and newly introduced techniques for nonlinear blind system modeling followed by a comparison of their performance.It is expected that,such comprehensive study and the comparison process can be of great relevance in many fields including chemical,electrical,biological,financial and weather data analysis.Further the results reported would be of immense help for practical system designers and analysts in selecting the most appropriate method based on the goodness of the model for the particular context.

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

Nonlinear and magneto-optical transmission studies on magnetic nanofluids of non-interacting metallic nickel nanoparticles

Oxide free stable metallic nanofluids have the potential for various applications such as in thermal management and inkjet printing apart from being a candidate system for fundamental studies. A stable suspension of nickel nanoparticles of ∼5 nm size has been realized by a modified two-step synthesis route. Structural characterization by x-ray diffraction and transmission electron microscopy shows that the nanoparticles are metallic and are phase pure. The nanoparticles exhibited superparamagnetic properties. The magneto-optical transmission properties of the nickel nanofluid (Ni-F) were investigated by linear optical dichroism measurements. The magnetic field dependent light transmission studies exhibited a polarization dependent optical absorption, known as optical dichroism, indicating that the nanoparticles suspended in the fluid are non-interacting and superparamagnetic in nature. The nonlinear optical limiting properties of Ni-F under high input optical fluence were then analyzed by an open aperture z-scan technique. The Ni-F exhibits a saturable absorption at moderate laser intensities while effective two-photon absorption is evident at higher intensities. The Ni-F appears to be a unique material for various optical devices such as field modulated gratings and optical switches which can be controlled by an external magnetic field

Provenance, Isolation and Characterisation of Organic Matter in the Cochin Estuarine Sediment-“a Diagenetic Amino Acid Marker Scenario

Cochin estuarine system is among the most productive aquatic environment along the Southwest coast of India, exhibits unique ecological features and possess greater socioeconomic relevance. Serious investigations carried out during the past decades on the hydro biogeochemical variables pointed out variations in the health and ecological functioning of this ecosystem. Characterisation of organic matter in the estuary has been attempted in many investigations. But detailed studies covering the degradation state of organic matter using molecular level approach is not attempted. The thesis entitled Provenance, Isolation and Characterisation of Organic Matter in the Cochin Estuarine Sediment-“ A Diagenetic Amino Acid Marker Scenario” is an integrated approach to evaluate the source, quantity, quality, and degradation state of the organic matter in the surface sediments of Cochin estuarine system with the combined application of bulk and molecular level tools. Sediment and water samples from nine stations situated at Cochin estuary were collected in five seasonal sampling campaigns, for the biogeochemical assessment and their distribution pattern of sedimentary organic matter. The sampling seasons were described and abbreviated as follows: April- 2009 (pre monsoon: PRM09), August-2009 (monsoon: MON09), January-2010 (post monsoon: POM09), April-2010 (pre monsoon: PRM10) and September- 2012 (monsoon: MON12). In order to evaluate the general environmental conditions of the estuary, water samples were analysed for water quality parameters, chlorophyll pigments and nutrients by standard methods. Investigations suggested the fact that hydrographical variables and nutrients in Cochin estuary supports diverse species of flora and fauna. Moreover the sedimentary variables such as pH, Eh, texture, TOC, fractions of nitrogen and phosphorous were determined to assess the general geochemical setting as well as redox status. The periodically fluctuating oxic/ anoxic conditions and texture serve as the most significant variables controlling other variables of the aquatic environment. The organic matter in estuary comprise of a complex mixture of autochthonous as well as allochthonous materials. Autochthonous input is limited or enhanced by the nutrient elements like N and P (in their various fractions), used as a tool to evaluate their bioavailability. Bulk parameter approach like biochemical composition, stoichiometric elemental ratios and stable carbon isotope ratio was also employed to assess the quality and quantity of sedimentary organic matter in the study area. Molecular level charactersation of free sugars and amino acids were carried out by liquid chromatographic techniques. Carbohydrates are the products of primary production and their occurrence in sediments as free sugars can provide information on the estuarine productivity. Amino acid biogeochemistry provided implications on the system productivity, nature of organic matter as well as degradation status of the sedimentary organic matter in the study area. The predominance of carbohydrates over protein indicated faster mineralisation of proteinaceous organic matter in sediments and the estuary behaves as a detrital trap for the accumulation of aged organic matter. The higher lipid content and LPD/CHO ratio pointed towards the better food quality that supports benthic fauna and better accumulation of lipid compounds in the sedimentary environment. Allochthonous addition of carbohydrates via terrestrial run off was responsible for the lower PRT/CHO ratio estimated in thesediments and the lower ratios also denoted a detrital heterotrophic environment. Biopolymeric carbon and the algal contribution to BPC provided important information on the better understanding the trophic state of the estuarine system and the higher values of chlorophyll-a to phaeophytin ratio indicated deposition of phytoplankton to sediment at a rapid rate. The estimated TOC/TN ratios implied the combined input of both terrestrial and autochthonous organic matter to sedimentsAmong the free sugars, depleted levels of glucose in sediments in most of the stations and abundance of mannose at station S5 was observed during the present investigation. Among aldohexoses, concentration of galactose was found to be higher in most of the stationsRelative abundance of AAs in the estuarine sediments based on seasons followed the trend: PRM09-Leucine > Phenylalanine > Argine > Lysine, MON09-Lysine > Aspartic acid > Histidine > Tyrosine > Phenylalanine, POM09-Lysine > Histadine > Phenyalanine > Leucine > Methionine > Serine > Proline > Aspartic acid, PRM10-Valine > Aspartic acid > Histidine > Phenylalanine > Serine > Proline, MON12-Lysine > Phenylalanine > Aspartic acid > Histidine > Valine > Tyrsine > MethionineThe classification of study area into three zones based on salinity was employed in the present study for the sake of simplicity and generalized interpretations. The distribution of AAs in the three zones followed the trend: Fresh water zone (S1, S2):- Phenylalanine > Lysine > Aspartic acid > Methionine > Valine ῀ Leucine > Proline > Histidine > Glycine > Serine > Glutamic acid > Tyrosine > Arginine > Alanine > Threonine > Cysteine > Isoleucine. Estuarine zone (S3, S4, S5, S6):- Lysine > Aspartic acid > Phenylalanine > Leucine > Valine > Histidine > Methionine > Tyrosine > Serine > Glutamic acid > Proline > Glycine > Arginine > Alanine > Isoleucine > Cysteine > Threonine. Riverine /Industrial zone (S7, S8, S9):- Phenylalanine > Lysine > Aspartic acid > Histidine > Serine > Arginine > Tyrosine > Leucine > Methionine > Glutamic acid > Alanine > Glycine > Cysteine > Proline > Isoleucine > Threonine > Valine. The abundance of AAs like glutamic acid, aspartic acid, isoleucine, valine, tyrosine, and phenylalanine in sediments of the study area indicated freshly derived organic matter.