Equivalent representation form of oscillators with elastic and damping nonlinear terms

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others

Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer

Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a beam, splitting in two "beams," single or double traces with suppressed reflection or transmission, etc.

The trouble with resonance energies: a Hückel theory topic

Resonance energies are shown to be quasithermodynamic in character. Hence, they are generally unsuitable as bases for anticipating kinetic stabilities. Examples are provided, leading to the conclusion that those who intend the word 'aromatic' to mean chemically unreactive, need to carry out full Hückel calculations in order to rank hydrocarbons using the frontier orbital energies.

Low-mass diffraction dissociation at the LHC ; role of the background

A dual model with a nonlinear proton Regge trajectory in the missing mass (M_X^2) channel is constructed. A background based on a direct-channel exotic trajectory, developed and applied earlier for the inclusive electron-proton cross section description in the nucleon resonance region, is used. The parameters of the model are determined from the extrapolations to earlier experiments. Predictions for the low-mass (2 < M_X^2 < 8GeV^2) diffraction dissociation cross sections at the LHC energies are given.

Determinação da origem biossintética de ácido acético através da técnica "Site Specific Natural Isotopic Fractionation Studied by Nuclear Magnetic Resonance (SNIF-NMR)"

The main purpose of this work is to describe the use of the technique Site-Specific Natural Isotopic Fractionation of hydrogen (SNIF-NMR), using ²H and ¹H NMR spectroscopy, to investigate the biosynthetic origin of acetic acid in commercial samples of Brazilian vinegar. This method is based on the deuterium to hydrogen ratio at a specific position (methyl group) of acetic acid obtained by fermentation, through different biosynthetic mechanisms, which result in different isotopic ratios. We measured the isotopic ratio of vinegars obtained through C3, C4, and CAM biosynthetic mechanisms, blends of C3 and C4 (agrins) and synthetic acetic acid.

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

Photomultiplier nonlinear response in time-domain laser-induced luminescence spectroscopy

A new procedure to find the limiting range of the photomultiplier linear response of a low-cost, digital oscilloscope-based time-resolved laser-induced luminescence spectrometer (TRLS), is presented. A systematic investigation on the instrument response function with different signal input terminations, and the relationship between the luminescence intensity reaching the photomultiplier and the measured decay time are described. These investigations establish that setting the maximum intensity of the luminescence signal below 0.3V guarantees, for signal input terminations equal or higher than 99.7 ohm, a linear photomultiplier response.

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

Electron paramagnetic resonance (EPR) spectral components of spin-labeled lipids in saturated phospholipid bilayers: effect of cholesterol

Electron paramagnetic resonance (EPR) spectroscopy was used to study the main structural accommodations of spin labels in bilayers of saturated phosphatidylcholines with acyl chain lengths ranging from 16 to 22 carbon atoms. EPR spectra allowed the identification of two distinct spectral components in thermodynamic equilibrium at temperatures below and above the main phase transition. An accurate analysis of EPR spectra, using two fitting programs, enabled determination of the thermodynamic profile for these major probe accommodations. Focusing the analysis on two-component EPR spectra of a spin-labeled lipid, the influence of 40 mol % cholesterol in DPPC was studied.

SIMULTANEOUS DETERMINATION OF PROTOCATECHUIC ALDEHYDE AND PROTOCATECHUIC ACID USING THE LOCALIZED SURFACE PLASMON RESONANCE PEAK OF SILVER NANOPARTICLES AND CHEMOMETRIC METHODS

A simple and sensitive spectrophotometric method is proposed for the simultaneous determination of protocatechuic acid and protocatechuic aldehyde. The method is based on the difference in the kinetic rates of the reactions of analytes with [Ag(NH3)2]+ in the presence of polyvinylpyrrolidone to produce silver nanoparticles. The data obtained were processed by chemometric methods using principal component analysis artificial neural network and partial least squares. Excellent linearity was obtained in the concentration ranges of 1.23-58.56 µg mL-1 and 0.08-30.39 µg mL-1 for PAC and PAH, respectively. The limits of detection for PAC and PAH were 0.039 and 0.025 µg mL-1, respectively.

Magnetic Resonance Experiments with Atomic Hydrogen

In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H₂ differ dramatically because atoms remain fixed in the H₂ lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H₂. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H₂ molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x10¹⁹ cm^-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.

Frequency-Domain and Wide-Pulse Time-Domain Measurements of Lanthanide Luminescence and Lanthanide-Based Resonance Energy Transfer

Resonance energy transfer (RET) is a non-radiative transfer of the excitation energy from the initially excited luminescent donor to an acceptor. The requirements for the resonance energy transfer are: i) the spectral overlap between the donor emission spectrum and the acceptor absorption spectrum, ii) the close proximity of the donor and the acceptor, and iii) the suitable relative orientations of the donor emission and the acceptor absorption transition dipoles. As a result of the RET process the donor luminescence intensity and the donor lifetime are decreased. If the acceptor is luminescent, a sensitized acceptor emission appears. The rate of RET depends strongly on the donor–acceptor distance (r) and is inversely proportional to r6. The distance dependence of RET is utilized in binding assays. The proximity requirement and the selective detection of the RET-modified emission signal allow homogeneous separation free assays. The term lanthanide-based RET is used when luminescent lanthanide compounds are used as donors. The long luminescence lifetimes, the large Stokes’ shifts and the intense, sharply-spiked emission spectra of the lanthanide donors offer advantages over the conventional organic donor molecules. Both the organic lanthanide chelates and the inorganic up-converting phosphor (UCP) particles have been used as donor labels in the RET based binding assays. In the present work lanthanide luminescence and lanthanide-based resonance energy transfer phenomena were studied. Luminescence lifetime measurements had an essential role in the research. Modular frequency-domain and time-domain luminometers were assembled and used successfully in the lifetime measurements. The frequency-domain luminometer operated in the low frequency domain ( 100 kHz) and utilized a novel dual-phase lock-in detection of the luminescence. One of the studied phenomena was the recently discovered non-overlapping fluorescence resonance energy transfer (nFRET). The studied properties were the distance and temperature dependences of nFRET. The distance dependence was found to deviate from the Förster theory and a clear temperature dependence was observed whereas conventional RET was completely independent of the temperature. Based on the experimental results two thermally activated mechanisms were proposed for the nFRET process. The work with the UCP particles involved the measurement of the luminescence properties of the UCP particles synthesized in our laboratory. The goal of the UCP particle research is to develop UCP donor labels for binding assays. In the present work the effect of the dopant concentrations and the core–shell structure on the total up-conversion luminescence intensity, the red–green emission ratio, and the luminescence lifetime was studied. Also the non-radiative nature of the energy transfer from the UCP particle donors to organic acceptors was demonstrated for the first time in aqueous environment and with a controlled donor–acceptor distance.

Detection of Pathologic Changes Following Traumatic Brain Injury Using Magnetic Resonance Imaging

Background: Approximately two percent of Finns have sequels after traumatic brain injury (TBI), and many TBI patients are young or middle-aged. The high rate of unemployment after TBI has major economic consequences for society, and traumatic brain injury often has remarkable personal consequences, as well. Structural imaging is often needed to support the clinical TBI diagnosis. Accurate early diagnosis is essential for successful rehabilition and, thus, may also influence the patient’s outcome. Traumatic axonal injury and cortical contusions constitute the majority of traumatic brain lesions. Several studies have shown magnetic resonance imaging (MRI) to be superior to computed tomography (CT) in the detection of these lesions. However, traumatic brain injury often leads to persistent symptoms even in cases with few or no findings in conventional MRI. Aims and methods: The aim of this prospective study was to clarify the role of conventional MRI in the imaging of traumatic brain injury, and to investigate how to improve the radiologic diagnostics of TBI by using more modern diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) techniques. We estimated, in a longitudinal study, the visibility of the contusions and other intraparenchymal lesions in conventional MRI at one week and one year after TBI. We used DWI-based measurements to look for changes in the diffusivity of the normal-appearing brain in a case-control study. DTI-based tractography was used in a case-control study to evaluate changes in the volume, diffusivity, and anisotropy of the long association tracts in symptomatic TBI patients with no visible signs of intracranial or intraparenchymal abnormalities on routine MRI. We further studied the reproducibility of different tools to identify and measure white-matter tracts by using a DTI sequence suitable for clinical protocols. Results: Both the number and extent of visible traumatic lesions on conventional MRI diminished significantly with time. Slightly increased diffusion in the normal-appearing brain was a common finding at one week after TBI, but it was not significantly associated with the injury severity. Fractional anisotropy values, that represent the integrity of the white-matter tracts, were significantly diminished in several tracts in TBI patients compared to the control subjects. Compared to the cross-sectional ROI method, the tract-based analyses had better reproducibility to identify and measure white-matter tracts of interest by means of DTI tractography. Conclusions: As conventional MRI is still applied in clinical practice, it should be carried out soon after the injury, at least in symptomatic patients with negative CT scan. DWI-related brain diffusivity measurements may be used to improve the documenting of TBI. DTI tractography can be used to improve radiologic diagnostics in a symptomatic TBI sub-population with no findings on conventional MRI. Reproducibility of different tools to quantify fibre tracts vary considerably, which should be taken into consideration in the clinical DTI applications.