http://hdl.handle.net/123456789/899 2023-06-04T21:37:51Z http://hdl.handle.net/123456789/1363 Title: Emergent Patterns in Nonlinear Systems and their Applications Authors: Kohar, Vivek; Sinha, Sudeshna Abstract: Nonlinear dynamical systems exhibit many counterintuitive phenomenon and exotic spatiotemporal patterns. On one hand, phenomenon like chaos and stochastic resonance in individual nonlinear dynamical units challenge our everyday intuitions, on the other, complex systems consisting of interacting nonlinear dynamical units provide us a framework to model many physical, biological, social and engineering systems thereby enabling us to get deeper insights into wide ranging complex phenomena. The work in this thesis is divided into two broad categories. First, we explore the application of nonlinear systems in the design of computing devices. Second, we attempt to broaden our understanding of nonlinear systems in general by investigating the emergence of spatiotemporal patterns in complex networks with time-varying connections. Specifically in the first part, we study the possibility of utilizing the phenomenon of stochastic resonance in bistable or multi-stable nonlinear dynamical systems to implement memory and logic function. This phenomenon has commonly been referred to as “Logical Stochastic Resonance (LSR)”. We demonstrate how noise enables a bistable system to behave as a memory device, as well as a logic gate for sub−threshold input signals. It is shown how this system can implement memory using noise constructively to store information. Namely, in some optimal range of noise, the system can operate flexibly, both as a AND/OR gate and a Set−Reset latch, on variation of an asymmetrizing bias. Then we examine the intriguing possibility of obtaining dynamical behavior equivalent to LSR in a noise-free bistable system, subjected only to periodic forcing, such as a sinusoidal driving or rectangular pulse trains. We find that such a system, despite having no stochastic influence, also yields phenomenon analogous to LSR, in an appropriate window of frequency and amplitude of the periodic forcing. The results are corroborated by electronic circuit experiments. Next we demonstrate how width of the optimal noise window can be increased by utilizing the constructive interplay of noise and periodic forcing, namely, noise in conjunction with a periodic drive enables the system to yield consistent logic outputs for all noise strengths below a certain threshold. Thus we establish that in scenarios where noise level is below the minimum threshold required for LSR (or stochastic resonance in general), we can add a periodic forcing to obtain the desired effects. We have also ix shown that the periodic forcing results in lower latency effects and reduces the switching time, leading to faster operation of the devices. Further, if a LSR element is coupled to another LSR element with a lower potential barrier, then it is able to adapt to varying noise intensity, so that its operation remains robust even under high noise conditions. Lastly, we test these concepts in vertical-cavity surface-emitting lasers (VCSELs) which are widely used for high-bit-rate data transmission because of their various advantages over conventional edge emitting lasers like low threshold current, single-longitudinalmode operation, higher modulation bandwidth and circular output beam profile. We attempt to enhance the the operational range of VCSEL based stochastic logic gate by adding a periodic signal. The enhancement is observed in form of decrease in the minimum bit time necessary for successful operation or increase of size of the optimal noise window. In the second part of this thesis, we study the behaviour of nonlinear dynamical elements coupled with each other. Firstly, we study the impact of small heterogeneity in signals applied to globally coupled nonlinear bistable elements. In absence of coupling, the collective response is simply the average of response to all the uncorrelated signals. When the elements are coupled and a bias is applied, we find that even a very small number of heterogeneous inputs are able to drag the collective response towards the stable state of the minority inputs. In our explicit demonstration we have taken Schmitt triggers as the nonlinear bistable elements, and the inputs are encoded as voltages applied to them. The average of the output voltages of all Schmitt triggers corresponds to the output of the system. We also observe that the minimum heterogeneity that can be detected scales with the ratio of threshold voltage to the source voltage of the Schmitt triggers, and can be be brought down to the limit of single bit detection. In last two works, we focus on changes in emergent phenomenon when the underlying interaction network is dynamic and the connections evolve with time. Such time variations represent the evolution of interactions over time or any discontinuities in interactions, i.e. when the nodes interact only for limited time. These evolving interaction patterns are commonly found in social networks, communication, biological systems, spread of epidemics, computer networks, world wide web etc and have been shown to result in significantly different emergent phenomena in complex systems. In the first problem, we study the impact of time varying network topology in epidemic spreading. We study a simple model mimicking disease spreading on a network with dynamically varying connections, and investigate the dynamical consequences of x switching links in the network. Our central observation is that the disease cycles get more synchronized, indicating the onset of epidemics, as the underlying network changes more rapidly. This behavior is found for periodically switched links, as well as links that switch stochastically in time. We find that the influence of changing links is more pronounced in networks where the nodes have lower degree, and the disease cycle has a longer infective stage. Further, in periodically switching links, we observe finer dynamical features, such as beating patterns in the emergent oscillations and resonant enhancement of synchronization, arising from the interplay between the time-scales of the connectivity changes and that of the epidemic outbreaks. In the second problem, we study the stability of the synchronous state in evolving networks. Many earlier studies have analyzed the stability of the synchronous state by linearizing the dynamical equations. But this approach is valid only in case of small perturbations of the synchronous state. In general, the dynamical equations governing the dynamics over the nodes are nonlinear and the higher order terms no longer remain negligible in case of large perturbations. In such cases, the basin stability approach may be used to complement the linear stability analysis. The basin stability paradigm is particularly useful in case of time varying networks as it can be applied to a large class of systems whereas the linear stability analysis can be done only in some specific cases. In our study, we consider synchronization of chaotic R¨ossler oscillators over Watts−Strogatz networks. We vary the fraction of random links, p, to cover broad range of networks varying from regular ring topology for p = 0 to random networks for p = 1. We find that for sufficiently fast re-wirings, the time varying networks can be approximated by static time averaged networks. Using the basin stability framework, we are able to estimate the rewiring frequency at which the network can be approximated by the static time average. Further we are also able to get insight into how the transition from a static to a time averaged case takes place and show how the stability range changes at different rewiring timescales. We find that not only the basin stability of small world networks highest in static cases as reported earlier, but they approach the time averaged coupling case fastest. Further, we find that faster rewiring networks synchronize quickly and the impact of rewiring is maximum when the number of neighbours is less. Lastly, we show that linear stability analysis alone is not sufficient to accurately predict the stability of synchronized states in time varying networks and the basin stability analysis should also be used to complement the analysis. In the last chapter of the thesis, we conclude our findings and summarize the important results of all the chapters. We also list some possible extensions of the works presented in this thesis. 2015-07-06T00:00:00Z http://hdl.handle.net/123456789/1362 Title: Modulation of Metabotropic Glutamate Receptor 1 (mGluR1) Intracellular Trafficking Authors: Pandey, Saurabh; Bhattacharyya, Samarjit Abstract: Trafficking of G-protein coupled receptors (GPCRs) plays a crucial role in controlling the precise localization of the receptor as well as its regulation. Metabotropic glutamate receptor 1 (mGluR1) is a member of the group I mGluR family. This receptor belongs to the family of G-protein coupled receptors (GPCRs). mGluR1 plays a critical role in neuronal circuit formation and also in multiple types of synaptic plasticity including learning and memory. This receptor has also been implicated in various neuropsychiatric disorders like Fragile X-syndrome, autism etc. Although it has been reported that similar to many other GPCRs mGluR1 also gets endocytosed on ligand application but the subsequent events after the internalization of the receptor and the cellular and molecular mechanisms that govern mGluR1 trafficking in the central nervous system has not been studied. We show in this study that mGluR1 internalized on ligand application. Subsequent to endocytosis, majority of the receptors localized at the recycling compartment and no significant presence of the receptor was noticed in the lysosome. Furthermore, mGluR1 returned to the cell membrane subsequent to ligand-mediated internalization. We found that the recycling of mGluR1 was dependent on the activity of protein phosphatase 2A (PP2A). Finally, we studied the role of a scaffolding protein Tamalin in the trafficking of group I mGluRs. Our data suggested that in primary hippocampal neurons Tamalin played critical role in the ligand-mediated trafficking of group I mGluRs as well as in mGluR-dependent AMPAR trafficking which is the cellular correlate for mGluR-dependent synaptic plasticity. 2017-07-19T00:00:00Z http://hdl.handle.net/123456789/1361 Title: Discovering New Organocatalytic Organic Transformations Using N-heterocyclic Carbene as a Catalyst Authors: Arde, Panjab Bhagwatrao; Anand, R.V. Abstract: The research work carried out in this thesis involves the development of new synthetic methodologies using N-heterocyclic carbene (NHC) as an organocatalyst. This thesis is divided into four chapters. Chapter 1: General introduction to N-heterocyclic carbene (NHC) catalysis. In recent years, persistent carbene chemistry has become one of the fascinating areas in organic chemistry. Among these, N-heterocyclic carbenes (NHCs) have found an important role in organocatalytic transformations, mainly in carbon–carbon, carbon–heteroatom bond formation and annulation reactions. The utility of NHCs has also been explored in other organic transformations such as; oxidation reactions, transesterification and silyl activation. The versatility of N-heterocyclic carbenes is due to their different modes of activation towards different functional groups . In this chapter, the applications of NHC as an organocatalyst for various types of organic reactions are highlighted. Chapter 2: N-Heterocyclic carbene as a Brønsted base catalyst This chapter is sub-divided into two parts namely Part A and Part B. PART A: N-heterocyclic carbene catalyzed access to diaryl- and triarylmethyl phosphonates through the 1,6-conjugate addition of dialkylphosphites to p-quinone methides and fuchsones. Organophosphorous derivatives are found to be an imperative class of organic compounds due to their widespread applications in many areas including organometallic chemistry, medicinal chemistry and pharmaceutical industries. These are also used as metal extractants and flame retardants. Their utility has been further extended in organic synthesis as starting materials in the synthesis of olefin derivatives. Among the organophosphorous compounds, the diaryl- and triarylmethyl phosphonate derivatives have been realized as vital derivatives due to their remarkable applications in medicinal chemistry. The classical methods for the synthesis of arylated methyl phosphonates involve the Arbuzov reaction and Friedel−Crafts type of reactions. However, harsh reaction conditions and narrow substrate scope limit the applications of this protocol. In order to overcome these shortcomings, recently, many strategies have emerged for the synthesis of diaryl- and triarylmethyl phosphonates which involve FeCl3-mediated Friedel-Crafts reaction and transition metal catalyzed coupling reactions. Although these methods involve relatively mild conditions and good regioselectivity, utilization of stoichiometric amount of FeCl3 and metal catalysts remains challenging. Despite their extensive applications, very limited number of reports are available for the synthesis of arylated methyl phosphonates, particularly diaryl- and triarylmethyl phosphonates. Therefore, developing an alternative and more efficient method for the synthesis of these compounds remains a demanding task, especially under organocatalytic conditions. In this part of Chapter 2, we disclose NHC catalyzed atom economical 1,6-conjugate addition of dialkylphosphites to p-quinone methides and fuchsones to access diaryl- and triarylmethyl phosphonates. Optimization studies have been carried out by using NHC-CO2 adducts as pre-catalyst for the NHC catalyzed 1,6-conjugate addition of dialkylphosphites to p-quinone methides and fuchsones. After screening different reaction conditions, IMes.CO2 was found to be the best precatalyst for this transformation. Having optimal reaction conditions in hand, the scope and limitations of this methodology were explored by using a wide range of p-quinone methides and dialkylphosphites. Irrespective of the nature of substituents on p-quinone methides and dialkylphosphites, the corresponding diaryl phosphonates were obtained in good to excellent yields. Triarylmethyl phosphonates were obtained in low to moderate yields at 80 °C. PART B: N-heterocyclic carbene catalyzed 1,6-conjugate addition of 2-naphthol to pquinone methides: Expedient access to unsymmetrical triarylmethanes. While working on NHC catalyzed 1,6-conjugate addition of dialkylphosphites to pquinone methides we envisioned that it is possible to access unsymmetrical triarylmethane derivatives through 1,6-conjugate addition of 2-naphthol to p-quinone methides using NHC as a Brønsted base catalyst. Unsymmetrical triarylmethanes and their derivatives are remarkable synthetic targets, due to their widespread utility as building blocks in many natural products, biologically active compounds and dyes. Few of the biologically active triarylmethanes. Although numerous methods have been developed for the synthesis of unsymmetrical triarylmethanes, traditionally triarylmethanes are accessed through Friedel-Crafts type reactions of diarylmethanols or reductive dehydroxylation of triarylmethanols. Though these methods are simple and widely used the utilization of electron-rich arenes and harsh reaction conditions limit the efficacy of these protocols. To address these issues, recently, the transition metal catalyzed reactions have been developed. Ever since the extensive utility of unsymmetrical triarylmethanes, developing a simple and atom economical approach for the synthesis of unsymmetrical triarylmethanes, especially under organocatalytic conditions is always in high demand. In this part of Chapter 2, we unveiled NHC as a Brønsted base for the 1,6-conjugate addition of 2- naphthol to p-quinone methides for obtaining unsymmetrical triarylmethane derivatives. After screening different reaction conditions, IPr.HCl was found to be the best precatalyst and dichloromethane was found to be the most appropriate solvent. Having optimized reaction conditions in hand, the scope and limitations of this methodology were further elaborated using variety of p-quinone methides as well as 2-naphthols. Regardless of the nature of substrates, the corresponding triarylmethanes were isolated in good to excellent yields. 100% atom economy and simple reaction condition are the significant features of this protocol. Chapter 3: N-heterocyclic carbene catalyzed trimethylsilylation of terminal acetylenes and indoles using Ruppert’s reagent as a silyl source under solvent free conditions. Alkynylsilicon reagents are considered important synthetic targets due to their wideranging utility in many organic transformations, such as, metal catalyzed cross-coupling reactions, alkynylation reactions and metathesis reactions. Conventionally, alkynylsilicon compounds are synthesized by deprotonation of terminal acetylenes by using strong bases such as organolithium and Grignard reagents followed by quenching with silyl electrophiles. Some other metal catalyzed or mediated protocols have also been developed to avoid some of the limitations of the traditional methods, such as utilization of strong bases and quantitative production of inorganic salts as by-products. Thence, developing an efficient and fluoride free synthetic route for the synthesis of alkynylsilicon compounds is a desirable task. It is well known in the literature that NHCs could form hypervalent complexes with silicon compounds. This concept has been applied to activate Ruppert’s reagent for the trifluoromethylation of different electrophiles. Herein we report NHC-catalyzed trimethylsilylation of terminal acetylenes using CF3 anion as a traceless base under solvent free conditions. The reaction conditions were optimized by treating phenyl acetylene and Ruppert’s reagent under different conditions; to our surprise, the reaction worked pretty well under solvent free condition to produce trimethylsilylated acetylenes in excellent yields. Encouraged by the above results, we applied this strategy for indoles as well to access Nsilylated indoles. N-silylatedindoles are found to be fascinating intermediates in synthetic organic chemistry, as indoles are vital synthons in many natural product syntheses. Traditionally, Nsilylated indoles are synthesized by deprotonation of indoles by using strong bases followed by quenching with a silyl electrophile. Recently, metal catalyzed dehydrogenative Si–N coupling methods21 have also been developed. Under optimized conditions, most of the substituted indoles were converted to their N-silylatedindoles . Solvent free conditions, high yield of products, less reaction time, simple work-up procedure are the key features of this methodology. Chapter 4: N-heterocyclic carbene catalyzed oxidative esterification of aldehydes with aryl boronic acids. Aryl benzoate derivatives have served as significant building blocks in many natural products and active pharmaceutical ingredients (APIs). Numerous approaches have been reported for the construction of ester functionality. Traditionally, aryl benzoate derivatives are synthesized either by acid catalyzed esterification or by transesterification reactions. Apart from these strategies, Baeyer-Villiger oxidation, organocatalytic esterification and transition metal catalyzed coupling reactions are the additional alternatives. While working on N-heterocyclic carbene catalyzed organic transformations, we envisioned that aryl benzoates could be directly accessed through NHC catalyzed aerobic oxidation of aryl aldehydes using boronic acids, especially in the absence of metal catalyst. In this chapter, the NHC-catalyzed oxidative esterification of aldehydes with aryl boronic acids are discussed. The extensive optimization studies revealed that the NHC derived from SIPr.HCl worked exceptionally well for NHC-catalyzed oxidative esterification of aldehydes with aryl boronic acids. Having the optimal reaction conditions in hand, scope and limitations of this transformation were screened by using diverse range of aldehydes and aryl boronic acids and in most of the cases the esters were obtained in excellent yields. Unfortunately, this methodology was not suitable for aliphatic aldehydes and boronic acids. Mechanistic details have been thoroughly investigated through the isotopic labelling experiment. 2017-07-19T00:00:00Z http://hdl.handle.net/123456789/1360 Title: Studies on The Synthesis of New Classes of Crown Ether-Type/Polyether Macrocycles and Optically Active Aza-Oxo-Thia Polyether Macrocycles Authors: Naveen; Babu, S.A. Abstract: There is no abstract 2017-07-19T00:00:00Z