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

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

Hypernuclear structure with the new Nijmegen potentials

Information on level density for nuclei with mass numbers A?20250 is deduced from discrete low-lying levels and neutron resonance data. The odd-mass nuclei exhibit in general 47 times the level density found for their neighboring even-even nuclei at the same excitation energy. This excess corresponds to an entropy of ?1.7kB for the odd particle. The value is approximately constant for all midshell nuclei and for all ground state spins. For these nuclei it is argued that the entropy scales with the number of particles not coupled in Cooper pairs. A simple model based on the canonical ensemble theory accounts qualitatively for the observed properties.

Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.

The diagnosis of severe thunderstorms with high-resolution WRF model

Thunderstorm, resulting from vigorous convective activity, is one of the most spectacular weather phenomena in the atmosphere. A common feature of the weather during the pre-monsoon season over the Indo-Gangetic Plain and northeast India is the outburst of severe local convective storms, commonly known as ‘Nor’westers’(as they move from northwest to southeast). The severe thunderstorms associated with thunder, squall lines, lightning and hail cause extensive losses in agricultural, damage to structure and also loss of life. In this paper, sensitivity experiments have been conducted with the Non-hydrostatic Mesoscale Model (NMM) to test the impact of three microphysical schemes in capturing the severe thunderstorm event occurred over Kolkata on 15 May 2009. The results show that the WRF-NMM model with Ferrier microphysical scheme appears to reproduce the cloud and precipitation processes more realistically than other schemes. Also, we have made an attempt to diagnose four severe thunderstorms that occurred during pre-monsoon seasons of 2006, 2007 and 2008 through the simulated radar reflectivity fields from NMM model with Ferrier microphysics scheme and validated the model results with Kolkata Doppler Weather Radar (DWR) observations. Composite radar reflectivity simulated by WRF-NMM model clearly shows the severe thunderstorm movement as observed by DWR imageries, but failed to capture the intensity as in observations. The results of these analyses demonstrated the capability of high resolution WRF-NMM model in the simulation of severe thunderstorm events and determined that the 3 km model improve upon current abilities when it comes to simulating severe thunderstorms over east Indian region

Regional climate model applications on sub-regional scales over the Indian monsoon region: The role of domain size on downscaling uncertainty

Regional climate models are becoming increasingly popular to provide high resolution climate change information for impacts assessments to inform adaptation options. Many countries and provinces requiring these assessments are as small as 200,000 km2 in size, significantly smaller than an ideal domain needed for successful applications of one-way nested regional climate models. Therefore assessments on sub-regional scales (e.g., river basins) are generally carried out using climate change simulations performed for relatively larger regions. Here we show that the seasonal mean hydrological cycle and the day-to-day precipitation variations of a sub-region within the model domain are sensitive to the domain size, even though the large scale circulation features over the region are largely insensitive. On seasonal timescales, the relatively smaller domains intensify the hydrological cycle by increasing the net transport of moisture into the study region and thereby enhancing the precipitation and local recycling of moisture. On daily timescales, the simulations run over smaller domains produce higher number of moderate precipitation days in the sub-region relative to the corresponding larger domain simulations. An assessment of daily variations of water vapor and the vertical velocity within the sub-region indicates that the smaller domains may favor more frequent moderate uplifting and subsequent precipitation in the region. The results remained largely insensitive to the horizontal resolution of the model, indicating the robustness of the domain size influence on the regional model solutions. These domain size dependent precipitation characteristics have the potential to add one more level of uncertainty to the downscaled projections.

A REVIEW OF SOIL CONSTITUTIVE MODELS FOR SOIL STRUCTURE INTEREACTION ANALYSIS

Soils are multiphase materials comprised of mineral grains, air voids and water. Soils are not linearly elastic or perfectly plastic for external loading. Various constitutive models are available to describe the various aspects of soil behaviour. But no single soil model can completely describe the behaviour of real soil under all conditions. This paper attempts to compare various soil models and suggest a suitable model for the Soil Structure Interaction analysis especially for Kochi marine clay.

Preconditioner updates applied to CFD model problems

In the present paper we concentrate on solving sequences of nonsymmetric linear systems with block structure arising from compressible flow problems. We attempt to improve the solution process by sharing part of the computational effort throughout the sequence. This is achieved by application of a cheap updating technique for preconditioners which we adapted in order to be used for our applications. Tested on three benchmark compressible flow problems, the strategy speeds up the entire computation with an acceleration being particularly pronounced in phases of instationary behavior.

Influence of the electronic shell structure on the elastic scattering of heavy ions

The interatomic potential of the system I - I at intermediate and small distances is calculated from atomic DFS electron densities within a statistical model. Structures in the potential, due to the electronic shells, are investigated. Calculations of the elastic differential scattering cross section for small angles and several keV impact energies show a detailed peak pattern which can be correlated to individual electronic shell interaction.

Numerical aspects in the data model of conceptual information systems

While most data analysis and decision support tools use numerical aspects of the data, Conceptual Information Systems focus on their conceptual structure. This paper discusses how both approaches can be combined.

A finite state model for on-line analytical processing in triadic contexts

About ten years ago, triadic contexts were presented by Lehmann and Wille as an extension of Formal Concept Analysis. However, they have rarely been used up to now, which may be due to the rather complex structure of the resulting diagrams. In this paper, we go one step back and discuss how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data. Our approach is inspired by the slice & dice paradigm of On-Line-Analytical Processing (OLAP). We recall the basic ideas of OLAP, and show how they may be transferred to triadic contexts. For modeling the navigation patterns a user might follow, we use the formalisms of finite state machines. In order to present the benefits of our model, we show how it can be used for navigating the IT Baseline Protection Manual of the German Federal Office for Information Security.

3D Simultaneous Inversion for Seismic Structure and Local Hypocenters in Germany under Consideration of Seismic Anisotropy in the Upper Mantel

The main task of this work has been to investigate the effects of anisotropy onto the propagation of seismic waves along the Upper Mantle below Germany and adjacent areas. Refraction- and reflexion seismic experiments proved the existence of Upper Mantle anisotropy and its influence onto the propagation of Pn-waves. By the 3D tomographic investigations that have been done here for the crust and the upper mantle, considering the influence of anisotropy, a gap for the investigations in Europe has been closed. These investigations have been done with the SSH-Inversionprogram of Prof. Dr. M. Koch, which is able to compute simultaneously the seismic structure and hypocenters. For the investigation, a dataset has been available with recordings between the years 1975 to 2003 with a total of 60249 P- and 54212 S-phase records of 10028 seismic events. At the beginning, a precise analysis of the residuals (RES, the difference between calculated and observed arrivaltime) has been done which confirmed the existence of anisotropy for Pn-phases. The recognized sinusoidal distribution has been compensated by an extension of the SSH-program by an ellipse with a slow and rectangular fast axis with azimuth to correct the Pn-velocities. The azimuth of the fast axis has been fixed by the application of the simultaneous inversion at 25° - 27° with a variation of the velocities at +- 2.5 about an average value at 8 km/s. This new value differs from the old one at 35°, recognized in the initial residual analysis. This depends on the new computed hypocenters together with the structure. The application of the elliptical correction has resulted in a better fit of the vertical layered 1D-Model, compared to the results of preceding seismological experiments and 1D and 2D investigations. The optimal result of the 1D-inversion has been used as initial starting model for the 3D-inversions to compute the three dimensional picture of the seismic structure of the Crust and Upper Mantle. The simultaneous inversion has showed an optimization of the relocalization of the hypocenters and the reconstruction of the seismic structure in comparison to the geology and tectonic, as described by other investigations. The investigations for the seismic structure and the relocalization have been confirmed by several different tests. First, synthetic traveltime data are computed with an anisotropic variation and inverted with and without anisotropic correction. Further, tests with randomly disturbed hypocenters and traveltime data have been proceeded to verify the influence of the initial values onto the relocalization accuracy and onto the seismic structure and to test for a further improvement by the application of the anisotropic correction. Finally, the results of the work have been applied onto the Waldkirch earthquake in 2004 to compare the isotropic and the anisotropic relocalization with the initial optimal one to verify whether there is some improvement.

Asymptotic model for shape resonance control of diatomics by intense non-resonant light

We derive a universal model for atom pairs interacting with non-resonant light via the polarizability anisotropy, based on the long range properties of the scattering. The corresponding dynamics can be obtained using a nodal line technique to solve the asymptotic Schrödinger equation. It consists of imposing physical boundary conditions at long range and vanishing the wavefunction at a position separating the inner zone and the asymptotic region. We show that nodal lines which depend on the intensity of the non-resonant light can satisfactorily account for the effect of the polarizability at short range. The approach allows to determine the resonance structure, energy, width, channel mixing and hybridization even for narrow resonances.

Hierarchical Object Recognition Using Libraries of Parameterized Model Sub-Parts

This thesis describes the development of a model-based vision system that exploits hierarchies of both object structure and object scale. The focus of the research is to use these hierarchies to achieve robust recognition based on effective organization and indexing schemes for model libraries. The goal of the system is to recognize parameterized instances of non-rigid model objects contained in a large knowledge base despite the presence of noise and occlusion. Robustness is achieved by developing a system that can recognize viewed objects that are scaled or mirror-image instances of the known models or that contain components sub-parts with different relative scaling, rotation, or translation than in models. The approach taken in this thesis is to develop an object shape representation that incorporates a component sub-part hierarchy- to allow for efficient and correct indexing into an automatically generated model library as well as for relative parameterization among sub-parts, and a scale hierarchy- to allow for a general to specific recognition procedure. After analysis of the issues and inherent tradeoffs in the recognition process, a system is implemented using a representation based on significant contour curvature changes and a recognition engine based on geometric constraints of feature properties. Examples of the system's performance are given, followed by an analysis of the results. In conclusion, the system's benefits and limitations are presented.