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Human Action Recognition Based on Analysis of Video Sequences
Get PDFHuman actions are defined as the coordinated movement of different body parts in a meaningful way to describe different aspects of human behavior. Recognizing human actions through computer vision is a trending research area as it has applications in both indoor and outdoor environments. Human action recognition (HAR) has a broad application area in the field of surveillance, patient’s behaviour detection, video retrieval, sports video analysis, human-computer interaction, etc. However, processing of the action videos is a challenging and complex task. This motivates to develop a good HAR algorithm with better video representation, feature extraction and classification capabilities to recognize different action classes effectively. In this regard, at first a semisupervised tree and 3D local feature based HAR paradigm (sST-3DF) is developed. Here, a motion history image (MHI) based interest point refinement is proposed to remove the noisy interest points. Histogram of oriented gradient (HOG) and histogram of optical flow (HOF) techniques are extended from spatial to spatio-temporal domain to preserve the temporal information. These local features are used to build the trees for the random forest technique. During tree building, a semi-supervised learning is proposed for better splitting of data points at each node. For recognition of an action from the video, mutual information is estimated for all the extracted interest points to each of the trained class by passing them through the random forest. Next, a two-stream sequential network is developed to leverage sequential and shape information for recognition of human actions more efficiently. In this technique, a deep bi-directional long short term memory (DBiLSTM) network is constructed to model temporal relationship between action frames through sequential learning. Action information in each frame is extracted using pre-trained convolutional neural network (CNN). During the shape learning, the knowledge of shape information for each action through depth history image (DHI) is used to train a deep pre-trained CNN network. Depth information of each action frame is estimated and projected onto the X-Y plane to create the DHI images. The major limitations of the above discussed algorithms are: first, the performance of the existing algorithms degrades comprehensively in the presence of partial loss of action data due to obstruction. Second, the performance of the existing networks is limited without exploiting the dependency relationship between different streams of a multistream network. To handle these problems, a novel double input sequential network (DISNet) is proposed with 3D obstruction model which takes care the HAR algorithm in the presence of partial loss of action data. The DISNet which learns inter-stream information, is jointly trained on the normal data and the artificially created obstructed data of a single video to provide immunity to the HAR network against obstructions. As most of the available action datasets do not have partial loss of action data, a 3D obstruction model is proposed to manually add obstructions in action videos. All the above discussed algorithms works well when training data is sufficient. However, in real time surveillance, generally it is difficult to collect a larger training dataset for rarely occurring actions. As the abnormal actions do not occur frequently, the HAR must have the ability to recognize abnormal actions from insufficient training data. To handle this challenge, a HAR technique is developed with a local maxima of difference image (LMDI) based interest point detection technique, random projection tree with overlapping split and modified voting score for better action recognition. In LMDI based interest point detection method, difference images are constructed using consecutive frame differencing technique and next, 3D peak detection is applied on these bunch of difference images to extract the required interest points. Histogram of oriented gradients and histogram of optical flow as local features are extracted around each of the interest point. These local features are then indexed by random projection trees. Overlapping split is used during tree structuring to reduce failure probability. Hough voting technique is applied on testing video to compute highest similarity matching score with individual training classes. In addition to Hough voting score, the number of matched interest points of a single query video with each training class, is considered for recognition. The effectiveness of all the proposed techniques are verified by conducting experiments on publicly available human action recognition datasets such as KTH, Weizmann, UCF sports, and JHMDB
Probing The Circumgalactic Medium With Quasar Absorption Lines
No full textQuasars (QSOs), the most distant and intrinsically luminous objects in the Universe, provide a direct probe to the history of the Universe. The quasar absorption spectroscopy has been one of the most used sensitive tools to probe the physical conditions of several different astrophysical environments. In particular, absorption lines observed in the background distance quasar spectra are unique probes of intervening gas from very high density (H ∼ 105 cm−3) outflowing gas to the extremely low density (H ∼ 10−5 cm−3) intergalactic medium (IGM). Studying them in absorption at low and high redshifts reveals a plethora of information about the nature of the gaseous environments, chemical enrichment, formation, and evolution of galaxies. This thesis examines the absorbing gas traced by double ionized carbon (C III) metal line species using archival data of high resolution optical (groundbased) and ultraviolet (UV) (spacebased) quasar spectra. In the first part of the thesis, a detailed survey of high ( > 2) C III systems has been carried out using archival spectroscopic data of ground based observations made with UVVisual Echelle Spectrograph (UVES) onboard Very Large Telescope(VLT) and the high Resolution Echelle Spectrometer (HIRES) on Keck. Out of a plethora of C III systems identified in this survey, 53 optically thin C III systems in the redshift range, 2.1 −1.2) are found when they are divided appropriately in the vs. (C III) plane. Further studies of C III absorbers in the redshift range, 1.0 ≤ ≤ 2.0 are important to map the redshift evolution of these absorbers and gain insights into the time evolution physical conditions of the circumgalactic medium. Finally, for the future direction of this work, a new PYTHON code “Quasar AbsorptionGALaxy Survey (QAGALS) is developed to automatically search for photometric/spectroscopic data of galaxies within a userdefined impact parameter around the intervening absorbers. QAGALS have also implemented the SED fitting code for modeling galaxy spectra with spectroscopic and photometric observations to compute the observed galaxy properties such as redshift, age, mass, star formation rate (SFR) and specific star formation rate (sSFR). For demonstration, QAGALS is used to search for galaxies from the SDSS DR16 catalog and compute the galaxy properties associated with the low C III sample
Post Combustion Carbon Dioxide Capture: Exploration of Prospective Solvents
No full textGlobal warming is one of the toughest challenge, humanity is currently facing. Temperature of the Earth’s surface is influenced through the process of absorption of heat radiation by greenhouse gases, like H2O, CO2, CH4 etc. In the prevailing state of technology, huge CO2 are thrown from thermal power plant installations, natural gas purification, and refinery off gases. Carbon dioxide gas being a greenhouse gas needs to be controlled in its emission from various point sources, which is under the purview of revamping current technology as a benign one. Different post-combustion CO2 capture techniques are available like, absorption (physical and chemical), adsorption (physical), membrane, and cryogenic separation. Among them, chemical absorption-desorption is the most mature and suitable technology available so far. In chemical absorption process, solvent plays most vital role, which is weighed in terms of its CO2 absorption capacity, absorption rate, energy penalty for regeneration, availability, degradation resistance, toxicity etc. Hence, selection of solvent as CO2 absorbent seeks paramount attention.
Various limitations including high regeneration energy, higher vapour pressure, limited CO2 loading capacity of common alkanolamines solvents like monoethanolamine (MEA), diethanolamine (DEA), methyldiethanolamine (MDEA), 2-amino-2-methyl propanol (AMP) and their blends, necessitated the exploration of alternative CO2 absorbing solvents. Newer solvents having different spatial arrangements have been utilized to study the effect of their molecular structure in CO2 absorbing property. Among them, 2-diethylaminoethanol (DEAE) and 1-(2-hydroxyethyl)piperidine (HEP) and their blends with piperazine (PZ) performed as better CO2 absorbents in the screening of solvent experiments followed by detail solubility studies.
Amino acid salts are very promising because of their negligible vapour pressure, lesser toxicity, high absorption capacity and rate, thermal stability etc. Pottasium salt of arginine (KArg) and lysine (KLys) revealed the highest apparent rate and capacity and potassium salt of 2-aminoisobutyric acid (KAmib) possesses moderate apparent rate and high capacity in the screening experiments among amino acid salts. KAmib, being a sterically hindered primary amino acid (similar structure like 2-amino-2-methyl-1-propanol (AMP)) salt; forms unstable carbamate thus possesses high capacity of CO2 absorption and lower regeneration energy. Due to high apparent rate constant of KArg, KLys and PZ compounds, they were used as rate promoters to enhance the CO2 absorption rate of KAmib solvent successfully.
Absorption of CO2 in amine based solvent is a regenerative and chemical absorption process. Regeneration energy varies depending upon the solvent formulation and is directly related with enthalpy of CO2 absorption of that solvent. Enthalpy of CO2 absorption is measured through calorimetric experiments. Interestingly, enthalpy of CO2 absorption could be precisely predicted from thermodynamic model using equilibrium CO2 solubility data. Since no experimental or predicted enthalpy of CO2 absorption in DEAE, HEP and their blends with PZ are available in the open literature, prediction of enthalpy from activity coefficient based model on solubility seems to be a significant contribution of this dissertation.
Limitation of regenerative absorption process could be overcome by using some water soluble organic solvents (acetone and tetrahydrofuran (THF)) having very low dielectric constant compared to water at low temperature for solvent regeneration. Solvent regeneration by this technique is only possible when the CO2 rich solution contains only bicarbonate and carbonate ions; not carbamate ions. CO2 rich DEAE solution was used for the study of CO2 regeneration using organic solvents like acetone/THF. This is one of the directional aspects of the present dissertation, which deserves further attention.
Besides experimental study to explore a suitable solvent for gas treating process, thermodynamic modelling plays important role to complement experimental results. Deshmukh and Mather model, one of the efficient activity coefficient based models describing multi-component and multi-phase fluid phase equilibria was used to correlate the vapour-liquid equilibrium data generated in the work. Liquid phase speciation for both CO2 loaded single and blended amine solutions, and enthalpy of CO2 absorption were predicted effectively using the developed model in MATLAB platform.
For developing Thermodynamic equilibrium and kinetic rate models, physicochemical parameters of those amine based solvents are required. In view of this, physicochemical properties like density and viscosity of single and blended alkanolamines over wide range of temperature, relative amine compositions were generated and correlated using thermodynamic framework, which are useful contribution to the design database of sour gas treating process
Multicriteria based Resource Allocation Policies for Cloud based Systems
No full textModern distributed computing systems provide ubiquitous services as utilities to end-user. Major advantages of such systems are characteristics such as ease of use, flexibility, and scalability. These systems are often associated with variable traffic patterns and large scale. The objective of service providers is to earn profit by deploying minimum resources while that for end-user is to use resources for minimum time. Conflicting objectives make the problem of resource allocation in these systems NP complete thereby, creating a demand for efficient resource allocation policies. Heterogeneity in architectures and end user bases ask for multiple criteria or joint resource allocation policies that optimize multiple aspects of resource allocation. This thesis addresses some of the problems associated with resource allocation in these advanced distributed systems. Resource allocation policies are presented for cloud and fog cloud systems that optimize response time and energy consumption from the perspective of the end user. For cloud computing systems, the major concern is end user response time. Reduction in response time not only helps service providers to attract more customers but also benefits the end-user with improved cost and quality of service. In order to reduce the response time for end-user in cloud, two resource allocation policies are proposed: (i.) greedy allocation, and (ii.) ACOAHP based allocation. The greedy resource allocation policy is based on Paretooptimal joint allocation (POJA) of compute and network resources. The ACOAHP based resource allocation approach reduces the overall end user response time by Nature inspired joint allocation (NIJA) of compute and network resources. Mathematically and experimentally it is verified that the proposed approaches report superior results in comparison to existing resource allocation policies for cloud systems. For the fog cloud hybrid architecture that operate at the edge of the network, the major concern is delay sensitive execution. Two AHP based resource allocation policies are presented for the fog cloud hybrid systems with the aim to reduce the response time for end-user. These policies differ in the way they assign weights to the multiple criteria. The first policy uses the principal Eigenvector to derive predefined criteria weights. However, the second policy finds the weights of the criteria dynamically from the data using the AHP technique of Simultaneous Evaluation of Criteria and Alternatives (SECA). Experimentally, it is verified that the proposed approaches outperform state of the art resource allocation policies for fog cloud hybrid architectures. In fog cloud systems, apart from response time, another major concern is the limited battery life of the end user mobile devices. A noisy channel affects the energy consumption of end-user devices due to attenuation and distortion in the transmitted signal. The attenuation and distortion can be attributed to the multipath propagation and mobility of end-users. In order to address the issue of power consumption of end-user devices, an energy efficient resource allocation policy is presented based on Markov Decision Process. The Markovian offloading approach considers a Rayleigh fading time varying network between the end-users and the fog cloud servers. Experimentally, it is shown that the proposed approach is able to extend the battery life of end-user devices
Design, Composition Optimization, Fabrication, and Properties of Al2O3/ZrO2/SrO based Articulating Hip Prosthesis
No full textTotal hip replacement (THR) is a joint replacement surgery used to replace damaged, arthritic hip joint with an orthopedic prosthesis. Continuous research is in progress to develop new biomaterials with improved mechanical, tribological, and biological properties. The present work is focused on developing a new design and fabrication of femoral head (FH) & acetabular socket liner (ASL) through optimized SrO doped zirconia toughened alumina (ZTA) to achieve a competitive mechanical and biological response. The entire work has been divided into four major categories; ‘Designing, femoral head size and material selection through both static and dynamic Finite Element Analysis (FEA)’, ‘Process and composition optimization in consideration of grain size, mechanical properties, and tribological properties’, ‘Designing of tailor-made mold and fabrication of both FH and ASL’, ‘Surface profile and dimension stability, burst strength, and biological response of worn particles generated through articulating motion of FH-ASL’. In the proposed THR design, 30 mm FH- ZTA/ASL- ZTA bearing exhibits minimum stress, and minimum wear depth under stance and jogging activity compare to promising Ti6Al4V/UHMWPE bearing. While ZTA/ZTA ceramic bearing confirms the best performance for 15 years, SrO doped ZTA composition and their sintering profile have been optimized. Strontium (Sr) expedite to form elongated strontium hexaaluminate (SrAl12O19) that eventually enhances fracture toughness; simultaneously, strontium enhances the bone remineralization, an increase in the formation of new bone, and a decrease in the risk of bone fracture. Further competitive FEA analysis endorses the best choice of SrO-ZTA/SrO- ZTA bearing among any other combination of Ti6Al4V/SrO-ZTA, SrO-ZTA/UHMWPE, Co-CrMo/UHMWPE, SS316L/UHMWPE bearing assemblies. Tribological study of hydrothermally aged specimen estimated the critical load of 94 N is required for the transition from mild to severe wear when pre-existing flaw size of ~0.77 µm.
The SrO doped zirconia toughened alumina femoral head (FH; OD – 30 ± 0.01 mm) and acetabular socket liner (ASL; ID – 30.15 ± 0.01 mm) were fabricated through uniaxial pressing followed by sintering, machining, and polishing to develop defect-free precious dimension prototypes for THR. Tailor-made polishing followed by a 3D optical surface profilometer study ensures the surface characteristics of Ra ≈ 0.2 ± 0.01 m and Rq ≈ 0.5 ± 0.01 m for both FH and ASL. The FH and ASL geometrical analysis are measured using a coordinate measuring method to ensure circularity with a tolerance limit ± 0.01 mm. However, the burst strength of independent FH and FH-ASL assembly demands a further ~10 % improvement to fulfill the clinical standard. An impressive cytocompatibility and healthy cell growth behavior are noticed during in vitro C2C12 myoblast cell study in the presence of worn particles generated through a simulated articulating motion of FH-ASL assembly. Within a limited scope, an in vivo study in drosophila fly exhibits excellent growth behavior from larva to adult up to doze of 50 µg worn particles / 1 ml standard, as it is one of the best genetically studied species with having high homology with the human
Design and Implementation of Low Offset Sensor Interface for Differential Capacitive Sensors
No full textNowadays, due to advancement of micro fabrication technology, Micro-Electro-Mechanical-Systems (MEMS) based miniature sensors are becoming more popular. But sensing physical variables, which are analog in nature, with these sensors is a challenging task. Among different type of MEMS based sensors, capacitive sensors are preferred for the measurement of displacement, pressure, acceleration etc. in various applications ranging from bio-medical devices to automotive safety. An integrated capacitive sensor system comprises of a capacitive sensor and a signal conditioning circuit, which provides electrical output as a function of change in capacitance (ΔC). These sensors offer several advantages such as smaller size, lower power consumption, higher sensitivity, lesser temperature coefficient and compatibility for monolithic integration. But due to micrometer dimension, these micro capacitive sensors provide very small change in capacitance, in the range of few femto-farad (fF). Detection of such small capacitance in the presence of considerable parasitics is quite challenging. Moreover, non-idealities of the interfacing circuit components, such as DC offset, 1/f noise, kT/C noise etc. limit the performance of the system. Chopper modulation, Auto-zeroing, Correlated Double Sampling etc. are quite popular to improve the performance of the interfacing circuit. In this work, we have proposed five switched capacitor based interfacing circuit topologies, which reduces the non ideal effects of the circuit components. Apart from these five configurations, we have also proposed an auto-calibration method to reduce the offset from sensor mismatch which can be implemented fully on-chip. These interfacing circuits are analysed theoretically and simulated using spectre simulator in Cadence Virtuoso environment. Among five interfacing circuits, four are designed and fabricated in UMC 180 nm CMOS process technology and the fifth one is designed in SCL 180 nm CMOS process technology. The fabricated UMC IC is integrated with a SOI MEMS capacitive acceleration sensor and measurement is carried out. Static characterization of the fabricated IC is carried out with the help of on-chip capacitors and the dynamic testing of the integrated system is done by a custom-made vibration setup with a sub-woofer system. The static and dynamic measurement results along with the merits and demerits of the proposed interfaces are reported in this thesis
Thermo-Hydrodynamics of Single-Phase and Two-Phase Flow Boiling in a Novel Design Recharging Microchannel Heat Sink
No full textAs the world is shifting towards a digital era with advances in technology, demand for high-performance electronic devices is ever increasing. Every electronic device consists of many integrated circuits, which are the soul of such devices. According to Moore’s law, every two years, the number of transistors doubles in an integrated circuit. This indicates that the performance of electronic devices is directly proportional to the number of transistors. Though these electronic devices' performance increases, the size, and weight of these devices are decreasing due to the compact packaging of miniaturized transistors. Due to the presence of many transistors in integrated circuits, more heat is generated in these high-performance electronic devices. Thus, requiring removal of high heat flux generated in these devices continuously for maintaining the temperature below a certain threshold temperature called safe operating temperature. Non-compliance with this will lead to higher component failure and a reduced average life of these electronic devices. Due to its compact size, lightweight, and higher surface area to volume ratio, the microchannel heat sink (MCHS) is one of the most promising cooling techniques for thermal management of high-performance electronic devices. Though traditional straight MCHSs extract heat at a better rate from high-performance electronic devices, they are not fully suitable for ever-increasing high heat flux cooling applications. Therefore, several researchers developed various heat transfer enhancement techniques (i.e., passive techniques) to augment the heat transfer performance of MCHSs using the concept of breaking and redeveloping thermal and hydrodynamic boundary layers by incorporating flow obstructions like ribs, cavities, obstacles, dimples, and protrusions, etc. Still, new techniques/methods can be proposed and explored that can provide higher thermal performance without using ribs and cavities. In this background, this thesis proposed a novel approach/method, “recharging microchannel” for heat transfer enhancement in microchannel heat sinks. The proposed design divides a simple/straight microchannel into multiple divisions by placing transverse walls at equal intervals, and each division will have an individual inlet and outlet through the top cover-plate. In this design, coolant at inlet temperature enters multiple times through the total length of a conventional microchannel or the substrate; thus, making the system equivalent to multiple smaller length microchannels placed end to end and fresh fluid (at ambient temperature) supplied to every channel simultaneously. Due to independent inlet and outlet, both thermal and hydrodynamic boundary layers develop in each smaller channel. The flow remains mostly developing in nature across the substrate length, thus carrying more heat out of the system and maintaining almost uniform temperature distribution on the substrate bottom surface. The main objective of this work is to investigate or explore the overall performance of the proposed design recharging microchannel (RMC) compared to simple/straight microchannel (SMC) by considering both single-phase and two-phase (i.e., flow boiling) approach. The results of this study are covered in the following chapters:
Chapter 2 compares the thermo-hydrodynamic performance of recharging microchannel and simple microchannel to investigate the advantages of the proposed microchannel over referenced microchannel. The effects of geometrical and thermo-physical parameters on the thermo-hydrodynamic performance of recharging microchannel are also discussed in this chapter by considering a wide range of geometrical and thermo-physical parameters. Additionally, the effect of axial wall conduction is also investigated in both recharging and simple microchannels.
Chapter 3 discusses and compares entropy generation in recharging microchannel and simple microchannel. This chapter also discusses the effects of geometrical and thermophysical parameters on entropy generation in recharging microchannel.
Chapter 4 highlights the effects of working fluid on thermo-hydrodynamic performance and entropy generation in recharging microchannel by considering water-based graphenesilver (Gr-Ag) hybrid nanofluid as the working fluid.
Chapter 5 investigates the thermo-hydrodynamic performance of two-phase flow boiling in a recharging microchannel and compares it with a simple microchannel.
Chapter 6 concentrated on the effect of inlet/outlet manifold configurations on thermohydrodynamic performance of recharging microchannel heat sink by considering different types of inlet/outlet manifold designs. The author believes that the proposed design recharging microchannel can be beneficial for high heat flux removal applications as it shows better thermo-hydrodynamic performance and reduced entropy generation compared to simple/straight microchannel
Compressed Domain Video Zoom Motion Analysis and Saliency Estimation
No full textThe work presented in the thesis is broadly in the domain of compressed domain video analysis. The thesis investigates the camera zoom motion analysis problem, the mixed camera classification problem, and one of the important video applications, namely saliency estimation. The work is motivated by the fact that the zoom motion analysis and the mixed camera classification are relatively less established since the major focus in the video processing community was on investigating the translational motions (pan and tilt) of the camera. Additionally, the saliency estimation in compressed videos is also an open problem that needed attention. The contributions of the thesis begin by investigating the zoom motion analysis problem, which comprises camera zoom motion detection and camera zoom motion classification sub¬problems. In zoom motion detection, the zooming frames are separated from the non¬zooming frames, while zoom motion classification deals with further separation of the zooming frames into zoom¬in and zoom¬out camera types. Towards this goal, the compressed domain block motion vector orientation is modeled utilizing traditional image texture descriptors. Two methods are proposed, the first in which the local ternary patterns are explored for both the zoom motion detection and classification problems and the second in which the local tetra patterns are utilized for the zoom motion detection problem. Such modeling is novel in the sense that the image texture descriptors, which found applications in face recognition and content¬based image retrieval applications, are being explored for the video zoom analysis research problem. Experimental results utilizing block motion vectors extracted from ESME and H.264 compressed videos showed good performance for both methods with a slight advantage to the local tetra patterns. However, the texture descriptors under¬performed when the input block motion vectors were noisy, calling for exploring other localized methods capable of countering motion vector noise. Zoom motion analysis problem is re¬looked by partitioning the inter¬frame block motion vector field into four representative quadrants, which enabled more localized analysis. Two methods are proposed, the first where histogram¬based features, specifically histogram intersection between quadrant histograms for the zoom motion detection problem and KL divergence between quadrant cumulative histograms for the zoom motion classification problem. The second method is on exploring the vector CURL to theoretically model the block motion vector orientation values, followed by extracting features like CURL magnitude for zoom vii motion detection and CURL direction for zoom motion classification problem. Experimental validation showed superior accuracy of detection for the two methods even in the presence of noise, with the CURL method achieving the best results compared to the texture descriptors. The focus in the latter part of the thesis shifted towards exploring the mixed camera motion problem, which consisted of recognizing complex motions, namely panning with tilting, which had not been explored earlier in literature. Inferences drawn from previous methods had suggested that the feature analysis could be improved if some representation scheme could be explored for the block motion vectors instead of directly utilizing the motion vector orientation values. It led to modeling both the orientation and the magnitude of the block motion vectors using the HSI color model. The premise was to pose the camera motion classification problem as a color recognizing task, which was carried out by assigning motion vector orientation to Hue, motion vector magnitude to Saturation while keeping Intensity unchanged. The HSI representation was converted to RGB images. These images were utilized for training a convolutional neural network to classify eleven camera patterns containing seven pure patterns and four mixed camera patterns. Experimental validation along with ablation study demonstrated good accuracy of recognition for the eleven camera patterns even in the presence of noise. The last part of the thesis looked into the compressed domain video saliency problem. Since the texture descriptors were successfully utilized earlier to model the motion vector orientation for the zoom motion analysis problem, an attempt was made to explore if such modeling could also aid in saliency determination. This premise led to exploring two texture descriptors, dual cross patterns and local derivative patterns, for saliency estimation. Two methods are investigated, the first utilizing the dual cross patterns while the second utilizing the local derivative patterns for temporal saliency determination. The spatial saliency was estimated in both methods by modeling the transform residuals using the lifting wavelet transform. The fusion of spatial and temporal saliency maps in both methods was carried out using the Dempster¬Shafer combination rule. Extensive experimental testing using eye tracking data¬set was carried out to benchmark the two proposed methods with state¬of¬the¬art method
Dynamics, Synchronization and Pattern Formation in Coupled Thomas Oscillators
No full textThis thesis work is mainly about dynamics, synchronization and pattern formation in coupled Thomas oscillators in the chaotic regime. Two mutually coupled identical oscillators as well as oscillators in a network are considered. The synchronizability of Thomas oscillators on various networks are established via master stability function formalism under linear coupling scheme for identical setting of oscillators. For pattern formation, local, nonlocal, global coupling schemes on a ring are considered. The special nature of Thomas oscillators and its connection to active Brownian particles are established via numerical simulations. The study of dynamics and synchronization of two mutually coupled oscillators are based on the calculations of Lyapunov exponents, Bifurcation diagram, phase portrait, Transverse Lyapunov exponents, Pearson coefficients, Transverse distance and similarity index. Two different values of system parameter are used in the chaotic regime under linear and nonlinear coupling schemes. In both cases the coupled system undergoes a period of transient chaos. Three different types of initial conditions are used to study the transients and synchronization. For low value of coupling strength, the system shows weak forms of synchronization. For linear coupling, the nature of synchronization agrees with the predictions of the general observation found in prototypical Rössler system and Lorenz system. The nature of synchronization is much more complex in the case of nonlinear coupling. The system bifurcates to lag or anti-lag synchronization even after achieving complete synchronization. It also shows space-lag(swarming) and multistability with nonlinear coupling. The emergence of lag or anti-lag is confirmed with similarity index calculation. Our calculation of largest transverse Lyapunov exponent for nonlinear coupling exactly matches with the predictions of Pearson coefficient and Transverse distance which would have been lost on any linearization of the transverse perturbation equation for the coupled system. The variables in our system are components of velocity of a particle moving in a force field and indeed, there are velocity-velocity correlations like in coupled active Brownian particles. Therefore, we claim that the stochastic dynamics of active Brownian particles can be modeled by chaotic dynamics of Thomas system. We found the important results that lag / anti-lag and space lag(swarming) synchronization within the regime of complete synchronization. The synchronization properties of Thomas oscillators in a network is studied for identical oscillators with linear coupling scheme via master stability function formulation. For the set of system parameters in the chaotic regime, they show type-I and type-II behavior of MSF. The synchronizability for various network architectures are also studied. For the study of pattern formation, we considered hundred Thomas oscillators on a
ring with nonlocal coupling with nonlinear coupling function. We could achieve chimera states for a certain range of intermediate coupling constants. The Chimera states are quantified by means of strength of incoherence and discontinuity measure calculation. The system shows cluster, chimera, multi-chimera as the coupling is increased. We could also achieve chimera states for nearly local coupling with nonlinear coupling functions. The global coupling shows complete synchronization of oscillators. The obtained result of pattern formation in the network is useful to understand the dynamics of active Brownian particles. For active Brownian particles, the probability distribution of velocities resembles the present observation of the chimera states. The discontinuous jump observed in the case of zero system parameter corresponds to a first order phase transition and matches with the statistical model of self-propelled particles
A Study on The Existence And Multiplicity Of Solutions To Some Elliptic PDEs Involving Singularity
No full textThis thesis illuminates on the study of some elliptic partial differential equations (PDEs) involving singularity and measure data or a power non-linearity. The thesis emphasises mostly on the non-local PDEs. The main objective is to obtain the existence, multiplicity and regularity of solutions to the problems considered in the thesis prescribed with certain Dirichlet boundary conditions. Some of the key techniques employed in the thesis to guarantee the existence of solutions are the weak convergence method, Schauder fixed point theorem, Brouwer degree theory, different variants of mountain pass theorem, concentration compactness lemma etc. The existence of infinitely many solutions is accomplished by applying the symmetric mountain pass theorem. The regularity of the solutions is established mostly by the Moser iteration techniques