L'objectif de ce travail est de déterminer l'intérêt des bases de données présentant un nombre important de relevés floristiques et écologiques complets pour étudier de façon quantitative le comportement écologique des espèces végétales forestières sur de vastes territoires.<br />Les données utilisées sont celles d'EcoPlant, développée à l'Ecole Nationale du Génie Rural des Eaux et des Forêts (ENGREF, Nancy) pour stocker des milliers de relevés phytoécologiques complets (relevés floristiques et caractéristiques climatiques et édaphiques précises), réalisés dans les forêts de France. La définition de 54 courbes de réponse théoriques d'espèces végétales vis-à-vis du pH, et la création de jeux artificiels de données binaires de taille variable pour essayer de re-créer les courbes de réponse théoriques, ont permis de montrer qu'il est difficile de modéliser de manière fiable le comportement des espèces peu fréquentes avec la régression logistique. En effet, nous montrons que 50 à 100 occurrences d'une espèce représentent un seuil minimal pour déterminer précisément l'optimum, l'amplitude et la probabilité maximale de la courbe de réponse écologique des espèces avec la régression logistique, ce qui justifie la nécessité de travailler avec de larges bases de données.<br />Pour tester la stabilité du comportement écologique des espèces sur de vastes territoires, nous avons comparé la réponse au pH du sol de 46 herbacées forestières entre le nord-est et le nord-ouest de la France, et de 21 herbacées forestières entre les Vosges et le Jura. En contexte de plaine ou de montagne, la majorité des espèces étudiées n'ont pas révélé de différences régionales marquées en terme d'optimum ou d'amplitude écologiques vis-à-vis du pH de l'horizon A du sol. Les quelques différences régionales observées ont été expliquées dans les deux cas par des conditions de compétition différentes dans chaque région. Nous concluons que l'étude de la réponse écologique peut s'effectuer sur de vastes territoires tels que la France, à condition que les conditions de compétition ne soient pas trop différentes selon les régions.<br />Une caractéristique majeure de la base EcoPlant est de stocker des informations édaphiques et climatiques, couplée à des relevés floristiques effectués sur les mêmes sites. L'étude conjointe de la réponse écologique des espèces végétales vis-à-vis de facteurs climatiques et édaphiques a rarement été menée, puisque la majorité des études étudient la réponse climatique des espèces végétales. Nous illustrons l'importance de prendre en compte des variables édaphiques de nutrition dans les modèles de niche écologique et de distribution géographique des plantes terrestres, par la modélisation de l'écologie et de la distribution de l'Erable champêtre (Acer campestre L.) dans les forêts françaises.<br />L'ensemble des résultats met en évidence l'intérêt des bases de données importantes et écologiquement complètes telles qu'EcoPlant pour approfondir la connaissance des différentes dimensions de la niche écologique des espèces à l'échelle de vastes territoires.

Nous proposons dans cette recherche une solution nouvelle quant à l'existence et à la nature de la singularité initiale d'espace-temps. Dans le contexte de la supergravité N=2 et de la théorie topologique des champs, nous considérons que la singularité initiale d'espace-temps correspond à un instanton gravitationnel singulier de taille zéro caractérisé par une configuration Riemanienne de la métrique (++++) en dimension D = 4. Associée à un état topologique correspondant à l'échelle zéro de l'espace-temps, la singularité initiale n'est pas ici considérée en termes de divergences des champs physiques, mais peut être résolue dans la cadre de la théorie topologique des champs. Nous obtenons ce résultat à partir de l'observation physique selon laquelle le pré espace-temps doit être considéré en équilibre thermique à l'échelle de Planck. En conséquences, nous suggérons de manière naturelle qu'à l'échelle de Planck l'espace-temps à l'équilibre doit être soumis à la condition KMS. Dans ce contexte, l'état KMS dans lequel se trouve le pré espace-temps à l'échelle de Planck pourrait être interprété comme le résultat d'une unification entre " état physique" (métrique lorentzienne +++-) et "état topologique" (métrique riemanienne ++++). Ceci correspond à la phase d'oscillation quantique de la signature de la métrique déjà mise en évidence dans des travaux antérieurs. Nous suggérons alors que "la singularité d'échelle zéro" doit être comprise en termes d'invariants topologiques, en particulier le premier invariant de Donaldson. En conséquences, nous proposons ici un nouvel invariant topologique, asssocié à l'échelle 0 et de la forme Z = TR (-1)s, que nous appelons "invariant de singularité". Enfin, dans ce contexte, nous proposons la conjecture selon laquelle le problème de l'interaction inertielle pourrait être expliqué en termes d'amplitude topologique liée à l'instanton gravitationnel singulier caractérisant, dans notre approche, l'échelle zéro de l'espace-temps.

<p>During development of type 1 and type 2 diabetes plasma insulin patterns are altered. Since the islet insulin release pattern has been implicated in this development, insulin secretion from single islets was studied and linked to the islet protein levels of uncoupling protein-2 (UCP2). Islets were isolated from NOD- and KKA^y- mice, GK- and GK-derived congenic rats, which are animal models of diabetes, and three human subjects with type 2 diabetes. At basal glucose (3 mM), insulin release from such islets was pulsatile and the amount released was comparable to that of control islets. When the glucose concentration was raised to 11 mM insulin release was essentially unchanged in islets isolated from older NOD- and KKA^y- mice, GK- and Niddm1i congenic rats, and NIDDM persons. In islets from Niddm1f congenic rats, younger NOD- and KKA^y-mice, control animals and normal human donors the secretion rate increased 2-9 fold when the glucose concentration was raised. This rise in secretion was manifested as increase of the amplitude of the insulin oscillations without affecting their frequency. Impaired glucose-induced insulin release was associated with reduction in glucose oxidation measured in NOD-islets, unaffected respiration measured in GK-islets and higher protein level of UCP2 measured in KKA^y-islets. When the UCP2 amounts in KKA^y-islets were reduced by culture to those of control islets, glucose-induced insulin secretion was essentially normalized. Our studies suggest that the deranged plasma insulin patterns observed in diabetes are related to decrease in the amplitude of insulin oscillations from the islets rather than loss of the oscillatory activity. This reduction of pulse amplitude may be related to impaired glucose metabolism and/or increased mitochondrial uncoupling. </p>

During development of type 1 and type 2 diabetes plasma insulin patterns are altered. Since the islet insulin release pattern has been implicated in this development, insulin secretion from single islets was studied and linked to the islet protein levels of uncoupling protein-2 (UCP2). Islets were isolated from NOD- and KKAy- mice, GK- and GK-derived congenic rats, which are animal models of diabetes, and three human subjects with type 2 diabetes. At basal glucose (3 mM), insulin release from such islets was pulsatile and the amount released was comparable to that of control islets. When the glucose concentration was raised to 11 mM insulin release was essentially unchanged in islets isolated from older NOD- and KKAy- mice, GK- and Niddm1i congenic rats, and NIDDM persons. In islets from Niddm1f congenic rats, younger NOD- and KKAy-mice, control animals and normal human donors the secretion rate increased 2-9 fold when the glucose concentration was raised. This rise in secretion was manifested as increase of the amplitude of the insulin oscillations without affecting their frequency. Impaired glucose-induced insulin release was associated with reduction in glucose oxidation measured in NOD-islets, unaffected respiration measured in GK-islets and higher protein level of UCP2 measured in KKAy-islets. When the UCP2 amounts in KKAy-islets were reduced by culture to those of control islets, glucose-induced insulin secretion was essentially normalized. Our studies suggest that the deranged plasma insulin patterns observed in diabetes are related to decrease in the amplitude of insulin oscillations from the islets rather than loss of the oscillatory activity. This reduction of pulse amplitude may be related to impaired glucose metabolism and/or increased mitochondrial uncoupling.

In this thesis, we investigate in detail, certain important problems in cryptography and coding theory. In the first part of this thesis, we discuss the number field sieve and compare the two ways in which the sieving step is implemented -one method using the line sieve and the other using the lattice sieve. We discuss why the lattice sieve performs better than the line sieve in the presence of large primes -this has not been attempted before. In the second part of this thesis, we design low-correlation CDMA sequences over the Quadrature Amplitude Modulation (QAM) alphabet. The sequences proposed in this thesis have the lowest value of the maximum correlation parameter as compared to any other family in the literature. In the third part of this thesis, we design large families of optimal two-dimensional optical orthogonal codes for optical CDMA. The size of these codes is larger than any other code in the literature.

Cette thèse traite du problème à N corps dans les gaz de fermions ultra froids. La première partie est dédiée aux collisions à 3 et 4 fermions en interaction de contact dans le vide. Nous montrons comment calculer diagrammatiquement l'amplitude de diffusion dimère-fermion et la longueur de diffusion dimère-dimère. Par un développement en puissances du rapport des masses et à basse énergie, nous obtenons une expression analytique de l'amplitude de diffusion dimère-fermion en onde s dans la limite de grand rapport des masses entre deux espèces. En utilisant la même méthode, nous obtenons un développement analytique de la longueur de diffusion dimère-dimère en onde s dans la limite de grand rapport des masses entre deux espèces. Dans la seconde partie, nous considérons le problème à N corps dans la transition BEC-BCS. Nous dérivons la formule de Tan dans la limite d'interaction de contact, puis nous généralisons ce résultat à des mélanges bosoniques ainsi qu'à 2 dimensions. Nous calculons également l'équation d'état à l'unitarité dans l'approximation de la matrice T en utilisant 3 formules exactes pour l'énergie. Finalement, nous obtenons un développement de l'équation d'état en puissances de la densité dans la limite BEC. Le résultat est obtenu, dans le cas général où les deux espèces ont des masses différentes et sont présentes en quantité différente, en prenant en compte diagrammatiquement les vertex de diffusion à 3 et 4 corps exacts.

Until recent years, terahertz (THz) waves were an undiscovered, or most importantly, an unexploited area of electromagnetic spectrum. This was due to difficulties in generation and detection of THz waves. Recent advances in hardware technology have started to open up the field to new applications such as THz imaging. This non-destructive and non-contact imaging technique can penetrate through diverse materials such that internal structures, in some cases invisible to other imaging modalities, can be visualized. Today, there are variety of techniques available to generate and detect THz waves in both pulsed and continuous fashion in two different geometries; transition, and reflection modes. In this thesis continuous wave THz imaging was employed for higher spatial resolution. However, with any new technology comes its challenges; automated processing of THz images can be quite cumbersome. Low contrast and the presence of a widely unknown type of noise make the analysis of these images difficult. In this work, there is an attempt to detect defects in composite material via segmentation by using a Terahertz imaging system. According to our knowledge, this is the first time that this type of materials are being tested under Terahertz cameras to detect manufacturing defects in aerospace industry. In addition, segmentation accuracy of THz images have been investigated by using a phantom. Beyond the defect detection for composite materials, this can establish some general knowledge about Terahertz imaging, its capabilities and limitations. To be able to segment the THz images successfully, pre-processing techniques are inevitable. In this thesis, a variety of different image processing techniques, self-developed or available from literature, have been employed for image enhancement. These methods range from filtering to contrast adjustment to fusion of phase and amplitude images by using fuzzy set theory, to just name a few. The result of pre-procssing and segmentation methods demonstrates promising outcome for future work in this field.

Until recent years, terahertz (THz) waves were an undiscovered, or most importantly, an unexploited area of electromagnetic spectrum. This was due to difficulties in generation and detection of THz waves. Recent advances in hardware technology have started to open up the field to new applications such as THz imaging. This non-destructive and non-contact imaging technique can penetrate through diverse materials such that internal structures, in some cases invisible to other imaging modalities, can be visualized. Today, there are variety of techniques available to generate and detect THz waves in both pulsed and continuous fashion in two different geometries; transition, and reflection modes. In this thesis continuous wave THz imaging was employed for higher spatial resolution. However, with any new technology comes its challenges; automated processing of THz images can be quite cumbersome. Low contrast and the presence of a widely unknown type of noise make the analysis of these images difficult. In this work, there is an attempt to detect defects in composite material via segmentation by using a Terahertz imaging system. According to our knowledge, this is the first time that this type of materials are being tested under Terahertz cameras to detect manufacturing defects in aerospace industry. In addition, segmentation accuracy of THz images have been investigated by using a phantom. Beyond the defect detection for composite materials, this can establish some general knowledge about Terahertz imaging, its capabilities and limitations. To be able to segment the THz images successfully, pre-processing techniques are inevitable. In this thesis, a variety of different image processing techniques, self-developed or available from literature, have been employed for image enhancement. These methods range from filtering to contrast adjustment to fusion of phase and amplitude images by using fuzzy set theory, to just name a few. The result of pre-procssing and segmentation methods demonstrates promising outcome for future work in this field.

The structure and dynamics of the smectic-A liquid crystal 8CB (4 cyano-4 octylbiphenyl) when sheared and confined to mesoscale gaps (with crossed cylindrical geometry and mica confining surfaces) were studied using a Surface Forces Apparatus (SFA). Triangular shear patterns with frequencies of 0.01, 0.1, 1.0 and 10 Hz, and amplitudes of 62.5 nm, 625 nm and 6.25 m were applied to samples at gap sizes of 0.5 and 5.0 m. The study was performed at room temperature (20.5C) and at two higher temperatures (22C and 27C). In order to minimize the thermal fluctuations within the test chamber and hence to allow for the rapid re-initialization of test runs, the SFA was modified to allow for quick, precise and remote control of the confining surfaces. The procedure maximized the number of tests that could be undertaken with a single pair of surfaces so that a single gap geometry could be maintained for the duration of the test run. In order to run the SFA remotely, scripts written with a commercial software package, LabVIEW, were used to control of the SFA components, its FECO-monitoring camera and all its peripheral electronic equipment as well. Samples were agitated to disrupt any shear-induced liquid crystal domain alignment from previous testing following each shear test, and methodologies were developed to ascertain the extent of confinement quickly and remotely following agitation. Separate methods were developed for gap sizes at each extreme of the mesoscale regime, where the transition from bulklike structure and dynamics to nano-confinement occurs (between 1 and 10 microns for smectic-A 8CB). The results revealed that the greater amplitude-gap aspect ratio and surface-to-domain contact associated with smaller gaps facilitated reorientation of the domains in the shear direction. Evidence was also presented of domains at the higher end or outside of the mesoscale regime that, while straining and accreting, were unable to reorient and thereby led to an overall increase of viscoelastic response. The effective viscosity was found to obey a simple power law with respect to shear rate, , and the flow behaviour indices, n, slightly in excess of unity indicate shear thickening occurs with large enough shear amplitude, and that the viscosity reached a plateau near unity over shear rates of 0.005 to 500 s-1 within the mesoscale regime. Different K and n values were observed depending on the shear amplitude used. Unlike bulk smectic 8CB, whose domains do not align well in the shear direction with large shear-strain amplitude, at mesoscale levels of confinement large amplitude shearing (up to 12.5 shear strain amplitude) was found to be very effective at aligning domains. In general domain reorientation is found to be much more rapid within the mesoscale regime than has been reported in bulk. Aggressive shearing was found to result in a complete drop in viscoelastic response within seconds, while gentler shearing is found to produce a very gradual increase that persists for more than six hours, with individual shear periods exhibiting frequent and significant deviations from the expected smooth shear path that may be a product of discrete domain reorientations. From these findings, certain traits of the smectic 8CB domain structures under mesoscale confinement were deduced, including how they respond to shear depending on the level of confinement, and how their reorientation due to shear varies not only with shear rate but also independently with shear amplitude. An equation describing the viscosity change as a function of both shear rate and shear amplitude is proposed. The shear amplitude dependence introduces the notion of shearing beyond the proposed smectic 8CB “viscoelastic limit”, which was shown to exhibit behaviour in accordance with Large Amplitude Oscillatory Shear (LAOS) techniques developed for Fourier Transform rheology. The findings provided an understanding of the behavioural changes that occur as one reduces the level of confinement of smectic materials from bulk to nanoconfinement.

Materials when subjected to deformation exhibit unstable plastic flow beyond the elastic limit. In certain range of temperature and strain rates many solid state solutions, both interstitial as well as substitutional, exhibit the phenomenon of serrated yielding which also goes by the name, the Portevin - Le Chatelier (PLC) effect. The origin of this plastic instability is due to the interaction of dislocations with solute atoms. The objective of the thesis is to provide a dynamical systems approach to the study of this plastic flow instability. The thesis work discusses, within the framework of a model, the connection between microscopic dislocation mechanisms and macroscopic mechanical response of the specimen as stress drops in stress-strain curves. An extension of the model to the associated deformation bands is also considered. The emphasis is on the dynamical aspects of the instability. The methods of nonlinear dynamics like geometrical slow manifold and Poincare map formalism are applied for the first time to study the PLC effect. However, the approach and techniques transcend this particular application as the techniques are equally well applicable for many other physical systems as well, in particular, systems involving multiple time scales. The material covered should be of interest to investigators in the materials science, in particular, those, involved in the dislocation patterning and self organization of dislocations. Many theoretical models for the PLC effect exist in literature. Although the physical phenomenon is inherently dynamic, the conventional theoretical models do not involve any dynamical aspect. A dynamical model for this effect, due to Ananthakrishna, Sahoo and Valsakumar provides an explanation in terms of the dynamic interactions between different dislocation species and evolution of densities of these dislocation species. This model is known to reproduce several of the experimental results. It is within the perspective of this model and its extensions we analyze the PLC effect. The macroscopic manifestation of the PLC effect is the repeated load drops or serration in stress-strain curves (beyond the yield point). Each of the load drop is associated with the formation of a spatial dislocation band and its subsequent propagation. From the perspective of a dynamical system, the changeover from the stress-strain curve with single yield drop to repeated yield drops (the PLC effect) corresponds to a Hopf bifurcation wherein equilibrium state changes over to a periodic steady state. These repeated load drops correspond to auto oscillations of the applied stress (in the absence of any periodic driving force). In particular, as implied by the slow loading and sudden load drops, these oscillations are classified as relaxation oscillations. Relaxation oscillations are a result of disparate time scales of dynamics of the participating modes. Within the context of the model, this refers to very different time scales of evolution of densities of mobile (fast), immobile (slow) dislocations and those with a cloud of solute atoms (not too slow). The focus of attention in the thesis work is on these auto relaxation oscillations. There are several methodologies in nonlinear dynamical systems to study the oscillatory behavior of multidimensional systems with multiple time scales. An effective way is to study the reduced dynamical system in an appropriate space without sacrificing the required dynamical information. To this end, we discuss two techniques which compliment each other. 1.Slow manifold approach: This method utilizes the presence of multiple time scales dynamics. Advantage is that the information on the nature of evolution of the periodic orbit is retained. The limitation is that the transition from one stable state to another as parameter is varied cannot be dealt with. 2.Poincare maps:This approach utilizes the recurrent behavior of the period orbit. This is a convenient methodology to study the nature of stability of periodic orbits. However, in this, the information about the nature of evolution is lost. Both the above techniques provide good description in the presence of high dissipation or larger separation of time scales of the participating modes. For slow manifold analysis, this leads to exact slow manifold structure while in the case of Poincare maps, it leads to simpler, lower dimensional attractors. Specific issues that are dealt with using these approaches and others in this thesis are the following. To start with, we first provide a comprehensive overview of the dynamical behavior as envisaged by the model system in physically relevant two parameter space. The existence of relaxation oscillations bounded by back-to-back Hopf bifurcation is a good representation of the fact that the PLC effect manifests only in a window of strain rates. Within this boundary of Hopf bifurcations relaxation oscillations destabilize to give rise to new states of order, including the chaotic states. The changes in the nature of these oscillations with control parameters is projected through the bifurcation diagrams and analyzed using techniques like Floquet multipliers, Lyapunovs exponents etc. After the identification of the relevant parameter space for the monoperiodic relaxation oscillations, we focus our attention on the time scales involved in these relaxation oscillations and its connection to the time scales apparent in serrations of the stress-strain curve of the PLC effect. This characteristic feature of the PLC effect, the stick-slip nature of stress-strain curves, is believed to result from the negative strain rate dependence of the flow stress. The latter is assumed to arise from a competition of the relevant time scales involved in the phenomenon. However, in the previous works, the identification and the role of the time scales in the dynamical phenomenon is not clear. The motivation of this part of the work is to identify the time scales involved in the stress drops of the time series and their origin. Since the dynamics involves distinct time scales, in the long time limit, the evolution is controlled only by the slow modes. Hence, the adiabatic elimination or quasi-steady state approximation of the fast modes leads to an invariant manifold, the slow manifold which is useful for the analysis of time scales. The geometry of the slow manifold which is atypical with two connected pieces is shown to be at the root of the relaxation oscillations. The analysis of the slow manifold structure helps to understand the time scales of the dynamics operating in different regions of the slow manifold. The analysis also helps us to provide a proper dynamical interpretation for the negative branch of the strain rate sensitivity of the flow stress. The slow-fast dynamical nature manifests itself through multiperiodic oscillations also, in the form of mixed mode oscillations (MMOs), which are oscillations with both large amplitude excursions as well as small amplitude loops. In MMOs, the small amplitude oscillatory loops are confined to one part of the slow manifold (around the fixed point) and the large amplitude excursions arise as jumps from one piece of the slow manifold to the other. More generally, MMOs are a characteristic feature of a family of dynamical systems which also exhibit alternate periodic-chaotic sequences in bifurcation portraits. Usually, the origin of these features is explained in terms of either the approach to a homoclinic bifurcation duo to a saddle fixed point (Shilnikov scenario) or a saddle orbit (Gavrilov-Shilnikov scenario). However, the dynamical model exhibits features from both the above scenarios. The emphasis of this study is on explaining the origin of the incomplete approach to a global bifurcation in the dynamical model. Apart from attempting to understand the complex bifurcation sequences, an additional motivation for this study is the apparent lack of systematic investigation into the incomplete approach to global bifurcation exhibited by a variety of physical systems. The method of the analysis is general and applicable to the family of MMO systems. In the model, using the structure of the bifurcation sequences, and the equilibrium fixed point, a local analysis shows that the approach to homoclinicity is asymptotic at best, and is a result of the ‘softening' of eigenvalues of the saddle equilibrium point. This softening, in turn, is a consequence of back-to-back Hopf bifurcation which reflects the constraint of the physical phenomenon, namely, the occurrence of the multiple stress drops only in an interval of the strain rates. The characteristic features, namely, MMOs, alternate periodic-chaotic sequences, and incomplete approach to homoclinicity are related to each other and arise as a consequence of the atypical slow manifold structure. The slow manifold structure analysis assumes that the evolution of the system is constrained within the neighborhood of the slow manifold which also implies that the dynamical system involves high dissipation. Hence, the dimension of the effective dynamics in the long time limit is reduced. The analysis reveals information regarding the structure of the periodic orbit for a given set of parameter values but does not provide any information regarding the nature of stability of the periodic orbits. However, any insight into the mechanism of the instability of the periodic orbits in the model may lead to a better understanding of the underlying physical phenomenon. Poincare maps and equivalent discrete dynamical systems provide a convenient means to obtain such an insight on the nature of the periodic solutions of the dynamical system. This methodology compliments the invariant slow manifold analysis, since in Poincare maps, the nature of the stability information is preserved at the expense of the structure of the periodic orbit. However, these two methodologies are not exclusive to each other, since the slow manifold structure as well as Poincare maps may be constructed using a common factor, namely, extremal values of the fast variable of the dynamical system. The methodologies adopted for the analysis assumes large dissipation arising out of the multiple time scale behavior such that the next maximal amplitude (NMA) maps can be modeled by one dimensional discrete dynamical systems. The dynamical portrait of the model shows differing nature of dynamics and consequently Poincare maps with different geometrical shapes in the {m,c) plane. Within the framework of one dimensional maps, these shapes can be schematically reconstructed using minimal information regarding the principal periodic orbit embedded in higher dimension and its nature of stability. This suggests that one dimensional maps might be sufficient to represent the higher dimensional dynamical system. For most of the parameter space, the NMA maps of the dynamical model possess characteristic features of a locally smooth maximum and asymptotically long tail. These features have been observed in many other physical systems, both experimental and model systems. Hence, this analysis is focused on a broader issue of Poincare maps in a family of dynamical systems with multiple time scale dynamics and mixed mode oscillations. Here, the dynamical model has been used as a representative dynamical system for this family. The scope of the study is to understand the dynamical features of the MMO systems within the framework of one dimensional systems. Specifically, by using some general constraints on the one dimensional map, we first analyze the basic mechanism that is responsible for the reversal of periodic sequences of RLk type which corresponds to the dominant periodic states of the MMO systems. This in turn allows us to understand the period adding sequences as well. The analysis also helps to demonstrate that the width of the periodic states contained within the chaotic regions bounded by two successive periodic states of the form RLk is smaller than that for RLk .To this end, we first construct a model map which mimics the dominant bifurcation sequences of MMO systems. This map is utilized to verify the analytical results for the parameter width of the periodic windows. This analysis also throws light on the origin of the ordered structure of the isolas of RLk periodic orbits, in MMO systems, which was shown to be the result of a back-to-back Hopf bifurcation. The results indicate the ubiquity in the qualitative dynamical features of physical systems from widely differing origin, exhibiting alternate periodic-chaotic sequences. Although the model for the PLC effect is successful in describing the features of the phenomenon, a shortcoming of the dynamical model has been the absence of the spatial aspect. A dominant process in the PLC effect is the movement of dislocations (mainly through cross glide) which is essentially nonlocal. This feature has been incorporated into the dynamical model through a 'diffusive' term for the mobile dislocations. Preliminary results indicate that various types of band propagation, as seen in experiments, are recovered. It is known that the solute atmosphere aggregation occurs primarily during the waiting time of the mobile dislocations after its arrest. As another extension, the present model has been revised to incorporate these aging effects also. An outline of the thesis is as follows. Focus of this thesis work is on the dynamical aspects of the PLC effect. The phenomenology and few techniques in nonlinear dynamics are introduced in Chapters 1 and 2. Chapter 3 provides a comprehensive tour of dynamical behavior of the model in physically relevant two-parameter space. The rest of the work is presented in three parts (six chapters). In the first part of the thesis, the structure of the relaxation oscillations in the phase space is analyzed using the topology of the slow manifold. A connection between the slow manifold structure and the negative strain rate sensitivity of the flow stress is attempted using this analysis (Chapter 4). As a natural extension, the approach is utilized for the analysis of multiperiodic relaxation oscillations also. The emphasis is on the connection between the dynamical behavior of the model and incomplete approach to a global bifurcation (Chapter 5). In the second part of the thesis, the stability properties of periodic orbits are analyzed in detail using the Poincare map formalism, complimenting the study on the structure of periodic orbits using slow manifold. The structure and gross features of the Poincare map are reproduced utilizing only minimum information regarding the principal periodic orbit in the multidimensional space (Chapter 6). Within the framework of one dimensional systems, we analyze the mechanisms responsible for the structure of bifurcation portraits of MMO systems (Chapter 7). Third and the last part, of work focuses on modeling the spatial aspect of the PLC effect and refinement of the dynamical model (Chapters). The last chapter, Chapter9, is devoted for discussion of the results and scope for future work.