A Simple Example of Localized Parametric Resonance for the Wave Equation

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

A nanoliter volume nuclear magnetic resonance (NMR) system using tunneling magneto-resistive (TMR) sensors to recognize biomolecules

The need to incorporate advanced engineering tools in biology, biochemistry and medicine is in great demand. Many of the existing instruments and tools are usually expensive and require special facilities.^ With the advent of nanotechnology in the past decade, new approaches to develop devices and tools have been generated by academia and industry. ^ One such technology, NMR spectroscopy, has been used by biochemists for more than 2 decades to study the molecular structure of chemical compounds. However, NMR spectrometers are very expensive and require special laboratory rooms for their proper operation. High magnetic fields with strengths in the order of several Tesla make these instruments unaffordable to most research groups.^ This doctoral research proposes a new technology to develop NMR spectrometers that can operate at field strengths of less than 0.5 Tesla using an inexpensive permanent magnet and spin dependent nanoscale magnetic devices. This portable NMR system is intended to analyze samples as small as a few nanoliters.^ The main problem to resolve when downscaling the variables is to obtain an NMR signal with high Signal-To-Noise-Ratio (SNR). A special Tunneling Magneto-Resistive (TMR) sensor design was developed to achieve this goal. The minimum specifications for each component of the proposed NMR system were established. A complete NMR system was designed based on these minimum requirements. The goat was always to find cost effective realistic components. The novel design of the NMR system uses technologies such as Direct Digital Synthesis (DDS), Digital Signal Processing (DSP) and a special Backpropagation Neural Network that finds the best match of the NMR spectrum. The system was designed, calculated and simulated with excellent results.^ In addition, a general method to design TMR Sensors was developed. The technique was automated and a computer program was written to help the designer perform this task interactively.^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Structure-based modeling of head -related transfer functions towards interactive customization of binaural sound systems

One of the most popular techniques for creating spatialized virtual sounds is based on the use of Head-Related Transfer Functions (HRTFs). HRTFs are signal processing models that represent the modifications undergone by the acoustic signal as it travels from a sound source to each of the listener's eardrums. These modifications are due to the interaction of the acoustic waves with the listener's torso, shoulders, head and pinnae, or outer ears. As such, HRTFs are somewhat different for each listener. For a listener to perceive synthesized 3-D sound cues correctly, the synthesized cues must be similar to the listener's own HRTFs. ^ One can measure individual HRTFs using specialized recording systems, however, these systems are prohibitively expensive and restrict the portability of the 3-D sound system. HRTF-based systems also face several computational challenges. This dissertation presents an alternative method for the synthesis of binaural spatialized sounds. The sound entering the pinna undergoes several reflective, diffractive and resonant phenomena, which determine the HRTF. Using signal processing tools, such as Prony's signal modeling method, an appropriate set of time delays and a resonant frequency were used to approximate the measured Head-Related Impulse Responses (HRIRs). Statistical analysis was used to find out empirical equations describing how the reflections and resonances are determined by the shape and size of the pinna features obtained from 3D images of 15 experimental subjects modeled in the project. These equations were used to yield “Model HRTFs” that can create elevation effects. ^ Listening tests conducted on 10 subjects show that these model HRTFs are 5% more effective than generic HRTFs when it comes to localizing sounds in the frontal plane. The number of reversals (perception of sound source above the horizontal plane when actually it is below the plane and vice versa) was also reduced by 5.7%, showing the perceptual effectiveness of this approach. The model is simple, yet versatile because it relies on easy to measure parameters to create an individualized HRTF. This low-order parameterized model also reduces the computational and storage demands, while maintaining a sufficient number of perceptually relevant spectral cues. ^

Life Among the Stars

Dr. James Webb, professor of physics at Florida International University, lectures on the humanities view of the universe.Lecture held on March 5, 2014 at the Green Library, Modesto Maidique Campus, Florida International University.

Multimode Analysis of Nanoscale Biomolecular Interactions

Biomolecular interactions, including protein-protein, protein-DNA, and protein-ligand interactions, are of special importance in all biological systems. These interactions may occer during the loading of biomolecules to interfaces, the translocation of biomolecules through transmembrane protein pores, and the movement of biomolecules in a crowded intracellular environment. The molecular interaction of a protein with its binding partners is crucial in fundamental biological processes such as electron transfer, intracellular signal transmission and regulation, neuroprotective mechanisms, and regulation of DNA topology. In this dissertation, a customized surface plasmon resonance (SPR) has been optimized and new theoretical and label free experimental methods with related analytical calculations have been developed for the analysis of biomolecular interactions. Human neuroglobin (hNgb) and cytochrome c from equine heart (Cyt c) proteins have been used to optimize the customized SPR instrument. The obtained Kd value (~13 µM), from SPR results, for Cyt c-hNgb molecular interactions is in general agreement with a previously published result. The SPR results also confirmed no significant impact of the internal disulfide bridge between Cys 46 and Cys 55 on hNgb binding to Cyt c. Using SPR, E. coli topoisomerase I enzyme turnover during plasmid DNA relaxation was found to be enhanced in the presence of Mg2+. In addition, a new theoretical approach of analyzing biphasic SPR data has been introduced based on analytical solutions of the biphasic rate equations. In order to develop a new label free method to quantitatively study protein-protein interactions, quartz nanopipettes were chemically modified. The derived Kd (~20 µM) value for the Cyt c-hNgb complex formations matched very well with SPR measurements (Kd ~16 µM). The finite element numerical simulation results were similar to the nanopipette experimental results. These results demonstrate that nanopipettes can potentially be used as a new class of a label-free analytical method to quantitatively characterize protein-protein interactions in attoliter sensing volumes, based on a charge sensing mechanism. Moreover, the molecule-based selective nature of hydrophobic and nanometer sized carbon nanotube (CNT) pores was observed. This result might be helpful to understand the selective nature of cellular transport through transmembrane protein pores.

Electroproduction of hyperons at low momentum transfer

A high resolution study of the H(e,e'K+)Λ,Σ0 reaction was performed at Hall A, TJNAF as part of the hypernuclear experiment E94-107. One important ingredient to the measurement of the hypernuclear cross section is the elementary cross section for production of hyperons, Λ and Σ0. This reaction was studied using a hydrogen (i.e. a proton) target. Data were taken at very low Q2 (∼0.07 (GeV/c)2) and W∼2.2 GeV. Kaons were detected along the direction of q, the momentum transferred by the incident electron (θCM~6°). In addition, there are few data available regarding electroproduction of hyperons at low Q2 and θCM, and the available theoretical models differ significantly in this kinematical region of W. The measurement of the elementary cross section was performed by scaling the Monte Carlo cross section (MCEEP) with the experimental-to-simulated yield ratio. The Monte Carlo cross section includes an experimental fit and extrapolation from the existing data for electroproduction of hyperons. Moreover, the estimated transverse component of the electroproduction cross section of H(e,e'K+)Λ was compared to the different predictions of the theoretical models and exisiting data curves for photoproductions of hyperons. None of the models fully describe the cross-section results over the entire angular range. Furthermore, measurements of the Σ0/Λ production ratio were performed at θCM, where data are not available. Finally, data for the measurements of the differential cross sections and the Σ0/Λ production were binned in Q2, W and θCM to understand the dependence on these variables. These results are not only a fundamental contribution to the hypernuclear spectroscopy studies but also an important experimental measurement to constrain existing theoretical models for the elementary reaction.

Investigation of particle identification methods for the analysis of the photoproduction of neutral kaons on a liquid deuterium target

The Photoproduction of neutral kaons off a deuteron target has been investigated at the Tohoku University Laboratory of Nuclear Science. The PID methods investigated incorporated a combination of momentum, velocity (β=v/c), and energy deposition per unit length (dE/dx) measurements. The analysis demonstrates that energy deposition and time of flight are exceedingly useful. A higher signal to background ratio was achieved for hard cuts in combination. A probabilistic likelihood estimation approach (LE) as a method for PID was also explored. The probability of a particle being correctly identified by this LE method and the preliminary results denote the need for highly precise limitations on the distributions from which the parameters would be extracted. It was confirmed that these PID are applicable approaches to properly identify pions for the analysis of this experiment. However, the background evident in the mass spectra points to the need for a higher level of proton identification.

High energy three-body breakup of three-nucleon systems

The main goal of this dissertation was to study two- and three-nucleon Short Range Correlations (SRCs) in high energy three-body breakup of 3He nucleus in 3He(e, e'NN)N reaction. SRCs are characterized by quantum fluctuations in nuclei during which constituent nucleons partially overlap with each other. A theoretical framework is developed within the Generalized Eikonal Approximation (GEA) which upgrades existing medium-energy methods that are inapplicable for high momentum and energy transfer reactions. High momentum and energy transfer is required to provide sufficient resolution for probing SRCs. GEA is a covariant theory which is formulated through the effective Feynman diagrammatic rules. It allows self-consistent calculation of single and double re-scatterings amplitudes which are present in three-body breakup processes. The calculations were carried out in detail and the analytical result for the differential cross section of 3He(e, e'NN)Nreaction was derived in a form applicable for programming and numerical calculations. The corresponding computer code has been developed and the results of computation were compared to the published experimental data, showing satisfactory agreement for a wide range of values of missing momenta. In addition to the high energy approximation this study exploited the exclusive nature of the process under investigation to gain more information about the SRCs. The description of the exclusive 3He(e, e'NN)N reaction has been done using the formalism of the nuclear decay function, which is a practically unexplored quantity and is related to the conventional spectral function through the integration of the phase space of the recoil nucleons. Detailed investigation showed that the decay function clearly exhibits the main features of two- and three-nucleon correlations. Four highly practical types of SRCs in 3He nucleus were discussed in great detail for different orders of the final state re-interactions using the decay function as an unique identifying tool. The overall conclusion in this dissertation suggests that the investigation of the decay function opens up a completely new venue in studies of short range nuclear properties.

Exclusive electrodisintegration of three-nucleon systems

The purpose of this research was to develop a theory of high-energy exclusive electrodisintegration of three-nucleon systems on the example of 3He(e, e'NN)N reaction with knocked-out nucleon in the final state. The scattering amplitudes and differential cross section of the reaction were calculated in details within the Generalized Eikonal Approximation(GEA). The manifestly covariant nature of Feynman diagrams derived in GEA allowed us to preserve both the relativistic dynamics and kinematics of the scattering while identifying the low momentum nuclear part of the amplitude with a nonrelativistic nuclear wave function. Numerical calculations of the residual system's total and relative momentum distribution were performed which show reasonable agreement with available experimental data. The theoretical framework of GEA, which was applied previously only for the case of two-body (deuteron) high energy break up reactions, has been practically implemented and shown to provide a valid description for more complex A = 3 systems.

Laser cooling of a metastable argon atomic beam

A production of low velocity and monoenergetic atomic beams would increase the resolution in spectroscopic studies and many other experiments in atomic physics. Laser Cooling uses the radiation pressure to decelerate and cool atoms. The effusing from a glow discharge metastable argon atomic beam is affected by a counterpropagating laser light tuned to the cycling transition in argon. The Zeeman shift caused by a spatially varying magnetic field compensates for the changing Doppler shift that takes the atoms out of resonance as they decelerated. Deceleration and velocity bunching of atoms to a final velocity that depends on the detuning of the laser relative to a frequency of the transition have been observed. Time-of-Flight (TOF) spectroscopy is used to examine the velocity distribution of the cooled atomic beam. These TOF studies of the laser cooled atomic beam demonstrate the utility of laser deceleration for atomic-beam "velocity selection".

Molecular detection using metallic nanowires with quantized conductance

This thesis studies the adsorption of molecules with different binding strengths onto copper nanowires with prestabilized conductance values fabricated by an electrochemical method. Since the diameters of these wires are comparable to the wavelength of conduction electrons the conductance of the nanowires is quantized, and the adsorption of even a few molecules onto atomically thin wires changes the conductance from integer values to fractional ones. These changes are proportional to the binding strength of the adsorbed molecules. The decrease in conductance is hypothesized to be caused by the scattering of the conduction electrons by the adsorbed molecules. The sensitivity of molecular adsorption-induced conductance change can be used for the development of a chemical sensor. The stabilized copper nanowires obtained in this thesis may also be used for other purposes, such as interconnecting conductors between nanodevices and digital switches in functional nanoelectronic circuitry.

Desenvolvimento profissional de futuros professores: travessias que se entrecruzam em contextos formativos

This study aimed to understand how the educational context contributes to the professional development of future teachers on introduction to teaching practice. To this end, we seek to characterize what the learning and the difficulties experienced in training contexts by future teachers, as well as the intrinsic elements to the training contexts that enable professional development. The investigated contexts were the Institutional Program Initiation Grant to Teaching (Programa Institucional de Bolsa de Iniciação à Docência – PIBID), specifically the sub-projects of Chemistry and Physics of the Federal University of Rio Grande do Norte (Universidade Federal do Rio Grande do Norte – UFRN) and Masters in Teaching of Physics and Chemistry of the University of Lisbon (MEFQ ). In both contexts, the future teachers are in contact with the school in a systematic way. The methodology used in our study is rooted in qualitative research with interpretative guidance and the design in the study of multiple cases with instrumental purpose. Participated in this study as the main subject, 40 future teachers PIBID of Physics, 24 PIBID future teachers of Chemistry and 5 future Master Teachers in Teaching Chemistry and Physics. As supporting subjects, participated in 3 PIBID Area Coordinators, the teacher of Introduction to Professional Practice of MEFQ, and 8 teachers who teach chemistry and / or physics in public schools. Multiple data collection tools were used: naturalistic observation, descriptive questionnaire, individual interviews, focus groups, reading of written records and official documents. In analyzing the data, we used the method of questioning and constant comparison. The results showed that the main learning of future teachers are related to the strategy employed in class, the change in the understanding of the role of teacher and student in the classroom, the construction of the professional profile and the development of collaborative practices. The main difficulties were related to the development of activities, the management of time and group, the dynamics of the classroom and the material conditions of work. The characteristics inherent in training contexts investigated for professional development are: the practice itself of the research, the collaboration, the focused reflection on practice, focus on student learning and the improving public schools. From the results, it is evidenced that the training contexts centered at school have the capability to resize the practice based on the analysis of actions, in a collaborative work as well as create opportunities for awareness of the concepts, the acting and the way to understand the profession. It is needed for effective mediation trainers, so that future teachers undertake their own practice and, therefore, they can build teaching strategies that promote learning which, in addition to increase the quality of education, favor the professional development throughout life.

Identidade pessoal em Hume e em Kant

The issue of this dissertation is the problem of personal identity. More specifically, the objective of this work is to investigate and compare how Hume and Kant construct, within their own philosophical systems, their theories of personal identity (of the self), so that these theories can set the grounds for the construction of theoretical knowledge. Hume’s theory of personal identity is closely connected to his empirical model of investigation, according to which no metaphysical conclusion can be accepted. This implies a very specific limitation to the humean description of personal identity. Because he can’t find a safe empirical reference for the self, Hume is obliged to describe it as a mere fiction, which the imagination creates to try to give unity to the set of perceptions that composes the mind. Kant, on the other hand, constructs his theory of the self with the aim of explaining the possibility of the a priori knowledge in Mathematics and in Physics. Kant tries to find which attributes must necessarily belong to the self so that this self can be, at the same time, the a priori transcendental condition of a subjectivity in general and the equally a priori transcendental condition for the construction of objective knowledge. Moreover, Kant shows the impossibility of objectively knowing, as intuition, the self, and limits himself to the description of the self as a mere subjective consciousness of the synthetic capacities of the understanding. Several disparities, thus, can be perceived between the theories of personal identity of these two authors. Based on these differences, the present work also examines the possibility of making an interpretation of the humean theory of the self by using elements of the kantian philosophy. The purpose of this kind of interpretation is to propose a solution to the difficulties faced by Hume in the description of his theory of personal identity.