Studies on some aspects of wave propagation through nonlinear media

Nonlinearity is a charming element of nature and Nonlinear Science has now become one of the most important tools for the fundamental understanding of the nature. Solitons— solutions of a class of nonlinear partial differential equations — which propagate without spreading and having particle— like properties represent one of the most striking aspects of nonlinear phenomena. The study of wave propagation through nonlinear media has wide applications in different branches of physics.Different mathematical techniques have been introduced to study nonlinear systems. The thesis deals with the study of some of the aspects of electromagnetic wave propagation through nonlinear media, viz, plasma and ferromagnets, using reductive perturbation method. The thesis contains 6 chapters

Development and Investigations of Mobile Antennas for less Radiation Hazards

Antennas, the key element in wireless communication devices had undergone amazing developments especially in the direction of compactness and safety aspects. In the last two decades, the use of the cellular phones has become the most popular mode of communication across the globe. At the same time, the concerns about the radiation effects have increased in the general public. The main concern of this thesis is to develop a mobile antenna which gives reduced RF interference to the user. The reduction of the power absorbed by the user can tremendously avoid any possible health hazards. The radiation characteristic of a monopole antenna is modified with good radiation characteristics suitable for a mobile handset. The modification is implemented by using different resonating structures which provides reduced radiation along one direction. The direction of less radiation can be changed by modifying the planar antenna structure to a ground folded antenna. This modified structure with excellent radiation characteristic is suitable for modern wireless handheld devices with less user RF interference. Specific Absorption Rate (SAR) is an important parameter for mobile handset. The SAR is estimated for the newly developed antenna for different conditions and discussed in this thesis.

Design of an Edge -coupled dual -ring Split-ring resonator

Electric permittivity and magnetic permeability control electromagnetic wave propagation th rough materials. I n naturally occu rring materials, these are positive. Artificial materials exhi b iting negative material properties have been reported : they are referred to as metamaterials. This paper concentrates on a ring-type split-ring resonator (SRR) exhibiting negative magnetic permeability. The design and synthesis of the SRR using the genetic-algorithm approach is explained in detail. A user-friendly g raphical user i nterface (G U I ) for an SRR optim izer and estimator using MATLAB TM is also presented

Flexible microwave absorbers based on barium hexaferrite, carbon black, and nitrile rubber for 2–12 GHz applications

Flexile single layer electromagnetic wave absorbers were designed by incorporating appropriate amounts of carbon black in a nitrile butadiene rubber matrix along with an optimized amount of magnetic counterpart, namely, barium hexaferrite for applications in S, C, and X-bands. Effective dielectric permittivity and magnetic permeability were measured using cavity perturbation method in the frequency range of 2–12 GHz. The microwave absorbing characteristics of the composites were studied in the S, C, and X-bands employing a model in which an electromagnetic wave is incident normally on a metal terminated single layer. Reflection loss exceeding 20 dB is obtained for all the samples in a wide frequency range of 2–12 GHz when an appropriate absorber thickness between 5 and 9mm is chosen. The impact of carbon black is clearly observed in the optimized composites on the mechanical strength, thickness, band width of absorption, dielectric properties,

Development and microwave characterization of selected biocompatible materials and conducting polymers

The 20th century witnessed the extensive use of microwaves in industrial, scientific and medical fields. The major hindrance to many developments in the ISM field is the lack of knowledge about the effect of microwaves on materials used in various applications. The study of the interaction of microwaves with materials demanded the knowledge of the dielectric properties of these materials. However, the dielectric properties of many of these materials are still unknown or less studied. This thesis is an effort to shed light into the dielectric properties of some materials which are used in medical, scientific and industrial fields. Microwave phantoms are those materials used in microwave simulation applications. Effort has been taken to develop and characterize low cost, eco-friendly phantoms from Biomaterials and Bioceramics. The interaction of microwaves with living tissues paved way to the development of materials for electromagnetic shielding. Materials with good conductivity/absorption properties could be used for EMI shielding applications. Conducting polymer materials are developed and characterized in this context. The materials which are developed and analyzed in this thesis are Biomaterials, Bioceramics and Conducting polymers. The use of materials of biological origin in scientific and medical applications provides an eco-friendly pathway. The microwave characterization of the materials were done using cavity material perturbation method. Low cost and ecofriendly biomaterial films were developed from Arrowroot and Chitosan. The developed films could be used in applications such as microwave phantom material, capsule material in pharmaceutical applications, trans-dermal patch material and eco-friendly Band-Aids. Bioceramics with better bioresorption and biocompatibility were synthesized. Bioceramics such as Hydroxyapatite, Beta tricalcium phosphate and Biphasic Calcium Phosphate were studied. The prepared bioceramics could be used as phantom material representing Collagen, Bone marrow, Human abdominal wall fat and Human chest fat. Conducting polymers- based on Polyaniline, are developed and characterized. The developed materials can be used in electromagnetic shielding applications such as in anechoic chambers, transmission cables etc

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Mid-holocene and last glacial maximum climate simulations with the IPSL model-part I: comparing IPSLCM5A to IPSLCM4

The climates of the mid-Holocene (MH), 6,000 years ago, and of the Last Glacial Maximum (LGM), 21,000 years ago, have extensively been simulated, in particular in the framework of the Palaeoclimate Modelling Intercomparion Project. These periods are well documented by paleo-records, which can be used for evaluating model results for climates different from the present one. Here, we present new simulations of the MH and the LGM climates obtained with the IPSL_CM5A model and compare them to our previous results obtained with the IPSL_CM4 model. Compared to IPSL_CM4, IPSL_CM5A includes two new features: the interactive representation of the plant phenology and marine biogeochemistry. But one of the most important differences between these models is the latitudinal resolution and vertical domain of their atmospheric component, which have been improved in IPSL_CM5A and results in a better representation of the mid-latitude jet-streams. The Asian monsoon’s representation is also substantially improved. The global average mean annual temperature simulated for the pre-industrial (PI) period is colder in IPSL_CM5A than in IPSL_CM4 but their climate sensitivity to a CO2 doubling is similar. Here we show that these differences in the simulated PI climate have an impact on the simulated MH and LGM climatic anomalies. The larger cooling response to LGM boundary conditions in IPSL_CM5A appears to be mainly due to differences between the PMIP3 and PMIP2 boundary conditions, as shown by a short wave radiative forcing/feedback analysis based on a simplified perturbation method. It is found that the sensitivity computed from the LGM climate is lower than that computed from 2 × CO2 simulations, confirming previous studies based on different models. For the MH, the Asian monsoon, stronger in the IPSL_CM5A PI simulation, is also more sensitive to the insolation changes. The African monsoon is also further amplified in IPSL_CM5A due to the impact of the interactive phenology. Finally the changes in variability for both models and for MH and LGM are presented taking the example of the El-Niño Southern Oscillation (ENSO), which is very different in the PI simulations. ENSO variability is damped in both model versions at the MH, whereas inconsistent responses are found between the two versions for the LGM. Part 2 of this paper examines whether these differences between IPSL_CM4 and IPSL_CM5A can be distinguished when comparing those results to palaeo-climatic reconstructions and investigates new approaches for model-data comparisons made possible by the inclusion of new components in IPSL_CM5A.

Some orbital characteristics of lunar artificial satellites

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate

We use the time-dependent mean-field Cross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation managed bright soliton in a quasi-one dimensional Bose-Einstein condensate (BEC). Because of three-body recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a perturbation procedure that an alimentation of atoms from an external source to the BEC may compensate for the dissipation loss and lead to a dynamically-stabilized soliton. The result of the analytical perturbation method is in excellent agreement with mean-field numerics. It seems possible to obtain such a dynamically stabilized BEC soliton without dissipation in laboratory.

Boussinesq solitary-wave as a multiple-time solution of the Korteweg-de Vries hierarchy

We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg-de Vries hierarchy, we show that the solitary-wave of the Boussinesq equation is a solitary-wave satisfying simultaneously all equations of the Korteweg-de Vries hierarchy, each one in an appropriate slow time variable. © 1995 American Institute of Physics.

The Role of the Korteweg-de Vries Hierarchy in the N-Soliton Dynamics of the Shallow Water Wave Equation

We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the well known N-soliton dynamics of the shallow water wave equation, in the particular case of α = 2β, can be reduced to the N-soliton solution that satisfies simultaneously all equations of the Korteweg-de Vries hierarchy.

Dinâmica não linear de m Pêndula eletromecânico com excitação vertical

Pós-graduação em Matemática - IBILCE

Pertubação orbital devida a um terceiro corpo com distribuição não uniforme de massa e em órbita elíptica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Magma-Driven Multiple Dike Propagation and Fracture Toughness of Crustal Rocks

Dike swarms consisting of tens to thousands of subparallel dikes are commonly observed at Earth's surface, raising the possibility of simultaneous propagation of two or more dikes at various stages of a swarm's development. The behavior of multiple propagating dikes differs from that of a single dike owing to the interacting stress fields associated with each dike. We analyze an array of parallel, periodically spaced dikes that grow simultaneously from an overpressured source into a semi-infinite, linear elastic host rock. To simplify the analysis, we assume steady state (constant velocity) magma flow and dike propagation. We use a perturbation method to analyze the coupled, nonlinear problem of multiple dike propagation and magma transport. The stress intensity factor at the dike tips and the opening displacements of the dike surfaces are calculated. The numerical results show that dike spacing has a profound effect on the behavior of dike propagation. The stress intensity factors at the tips of parallel dikes decrease with a decrease in dike spacing and are significantly smaller than that for a single dike with the same length. The reduced stress intensity factor indicates that, compared to a single dike, propagation of parallel dikes is more likely to be arrested under otherwise the same conditions. It also implies that fracture toughness of the host rock in a high confining pressure environment may not be as high as inferred from the propagation of a single dike. Our numerical results suggest fracture toughness values on the order of 100 MPa root m. The opening displacements for parallel dikes are smaller than that for a single dike, which results in higher magma pressure gradients in parallel dikes and lower flux of magma transport.