Mathematical development of stress-strain law for rock block contacts

The fracture behavior of rock block contacts has been studied for many years. Unfortunately, up to now, there is not a rigorous formulation or a solid theoretical foundation to support it. A mathematical development to represent the failure mechanism which occurs in the contacts between rock blocks is presented to evaluate the performance of breaking mechanism of such blocks relating it to the morphology of the contact and mechanical parameters of the material. The examined framework includes the evaluation of the surface roughness of first order in the failure mechanism of the granular particles of large size and the development of a theoretical model describing the morphology of the contact between rock blocks.

Intermolecular and Intramolecular Charge Transfer in Functional Molecular Materials

This thesis is devoted to the investigation of inter and intramolecular charge transfer (CT) in molecular functional materials and specifically organic dyes and CT crystals. An integrated approach encompassing quantum-chemical calculations, semiempirical tools, theoretical models and spectroscopic measurements is applied to understand structure-property relationships governing the low-energy physics of these materials. Four main topics were addressed: 1) Spectral properties of organic dyes. Charge-transfer dyes are constituted by electron donor (D) and electron acceptor (A) units linked through bridge(s) to form molecules with different symmetry and dimensionality. Their low-energy physics is governed by the charge resonance between D and A groups and is effectively described by a family of parametric Hamiltonians known as essential-state models. These models account for few electronic states, corresponding to the main resonance structures of the relevant dye, leading to a simple picture that is completed introducing the coupling of the electronic system to molecular vibrations, treated in a non-adiabatic way, and an effective classical coordinate, describing polar solvation. In this work a specific essential-state model was proposed and parametrized for the dye Brilliant Green. The central issue in this work has been the definition of the diabatic states, a not trivial task for a multi-branched chromophore. In a second effort, we have used essential-state models for the description of the early-stage dynamics of excited states after ultrafast excitation. Crucial to this work is the fully non-adiabatic treatment of the coupled electronic and vibrational motion, allowing for a reliable description of the dynamics of systems showing a multistable, broken-symmetry excited state. 2) Mixed-stack CT salts. Mixed-stack (MS) CT crystals are an interesting class of multifunctional molecular materials, where D and A molecules arrange themselves to form stacks, leading to delocalized electrons in one dimension. The interplay between the intermolecular CT, electrostatic interactions, lattice phonons and molecular vibrations leads to intriguing physical properties that include (photoinduced) phase transitions, multistability, antiferromagnetism, ferroelectricity and potential multiferroicity. The standard microscopic model to describe this family of materials is the Modified Hubbard model accounting for electron-phonon coupling (Peierls coupling), electron-molecular vibrations coupling (Holstein coupling) and electrostatic interactions. We adopt and validate a method, based on DFT calculations on dimeric DA structures, to extract relevant model parameters. The approach offers a powerful tool to shed light on the complex physics of MS-CT salts. 3) Charge transfer in organic radical dipolar dyes. In collaboration with the group of Prof. Jaume Veciana (ICMAB- Barcellona), we have studied spectral properties of a special class of CT dyes with D-bridge-A structure where the acceptor group is a stable radical (of the perchlorotriphenylmethyl, PTM, family), leading to an open-shell CT dyes. These materials are of interest since they associate the electronic and optical properties of CT dyes with magnetic properties from the unpaired electron. The first effort was devoted to the parametrization of the relevant essential-state model. Two strategies were adopted, one based on the calculation of the low-energy spectral properties, the other based on the variation of ground state properties with an applied electric field. 4) The spectral properties of organic nanoparticles based on radical species are investigated in collaboration with Dr. I. Ratera (ICMAB- Barcellona). Intriguing spectroscopic behavior was observed pointing to the presence of excimer states. In an attempt to rationalize these findings, extensive calculations (TD-DFT and ZINDO) were performed. The results for the isolated dyes are validated against experimental spectra in solution. To address intermolecular interactions we studied dimeric structures in the gas phase, but the preliminary results obtained do not support excimer formation.

Investigating the potential magnetic origin of wind variability in OB stars

In this thesis, the origin of large-scale structures in hot star winds, believed to be responsible for the presence of discrete absorption components (DACs) in the absorption troughs of ultraviolet resonance lines, is constrained using both observations and numerical simulations. These structures are understood as arising from bright regions on the stellar surface, although their physical cause remains unknown. First, we use high quality circular spectropolarimetric observations of 13 well-studied OB stars to evaluate the potential role of dipolar magnetic fields in producing DACs. We perform longitudinal field measurements and place limits on the field strength using Bayesian inference, assuming that it is dipolar. No magnetic field was detected within this sample. The derived constraints statistically refute any significant dynamical influence from a magnetic dipole on the wind for all of these stars, ruling out such fields as a cause for DACs. Second, we perform numerical simulations using bright spots constrained by broadband optical photometric observations. We calculate hydrodynamical wind models using three sets of spot sizes and strengths. Co-rotating interaction regions are yielded in each model, and radiative transfer shows that the properties of the variations in the UV resonance lines synthesized from these models are consistent with those found in observed UV spectra, establishing the first consistent link between UV spectroscopic line profile variability and photometric variations and thus supporting the bright spot paradigm (BSP). Finally, we develop and apply a phenomenological model to quantify the measurable effects co-rotating bright spots would have on broadband optical photometry and on the profiles of photopheric lines in optical spectra. This model can be used to evaluate the existence of these spots, and, in the event of their detection, characterize them. Furthermore, a tentative spot evolution model is presented. A preliminary analysis of its output, compared to the observed photometric variations of xi Persei, suggests the possible existence of “active longitudes” on the surface of this star. Future work will expand the range of observational diagnostics that can be interpreted within the BSP, and link phenomenology (bright spots) to physical processes (magnetic spots or non-radial pulsations).

Journal of research of the National Bureau of Standards. Section B, Mathematical sciences.

Title from masthead.

Elements of theoretical physics /

Includes index.

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Damage location in structures by monitoring vibration characteristics

The aim of this work was to investigate the feasibility of detecting and locating damage in large frame structures where visual inspection would be difficult or impossible. This method is based on a vibration technique for non-destructively assessing the integrity of structures by using measurements of changes in the natural frequencies. Such measurements can be made at a single point in the structure. The method requires that initially a comprehensive theoretical vibration analysis of the structure is undertaken and from it predictions are made of changes in dynamic characteristics that will occur if each member of the structure is damaged in turn. The natural frequencies of the undamaged structure are measured, and then routinely remeasured at intervals . If a change in the natural frequencies is detected a statistical method. is used to make the best match between the measured changes in frequency and the family of theoretical predictions. This predicts the most likely damage site. The theoretical analysis was based on the finite element method. Many structures were extensively studied and a computer model was used to simulate the effect of the extent and location of the damage on natural frequencies. Only one such analysis is required for each structure to be investigated. The experimental study was conducted on small structures In the laboratory. Frequency changes were found from inertance measurements on various plane and space frames. The computational requirements of the location analysis are small and a desk-top micro computer was used. Results of this work showed that the method was successful in detecting and locating damage in the test structures.

In-fibre twist sensor based on TFBG structures

We report a novel in-fibre twist sensor utilising strong polarisation dependent coupling behaviour of fiber Bragg grating with 81° tilted structure. The demonstrated twist sensor has shown high torsion sensitivity and capability of direction recognition.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations.

Evolution of optical pulses in fiber lines with lumped nonlinear devices as a mapping problem

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations. © 2005 Springer Science+Business Media, Inc.

Role of plasma in femtosecond laser pulse propagation

This paper describes physics of nonlinear ultra-short laser pulse propagation affected by plasma created by the pulse itself. Major applications are also discussed. Nonlinear propagation of the femtosecond laser pulses in gaseous and solid transparent dielectric media is a fundamental physical phenomenon in a wide range of important applications such as laser lidars, laser micro-machining (ablation) and microfabrication etc. These applications require very high intensity of the laser field, typically 1013–1015 TW/cm2. Such high intensity leads to significant ionisation and creation of electron-ion or electron-hole plasma. The presence of plasma results into significant multiphoton and plasma absorption and plasma defocusing. Consequently, the propagation effects appear extremely complex and result from competitive counteraction of the above listed effects and Kerr effect, diffraction and dispersion. The theoretical models used for consistent description of laser-plasma interaction during femtosecond laser pulse propagation are derived and discussed. It turns out that the strongly nonlinear effects such self-focusing followed by the pulse splitting are essential. These phenomena feature extremely complex dynamics of both the electromagnetic field and plasma density with different spatio-temporal structures evolving at the same time. Some numerical approaches capable to handle all these complications are also discussed. ©2006 American Institute of Physics