On Ultrafast Time-Domain TeraHertz Spectroscopy in the Condensed Phase: Linear Spectroscopic Measurements of Hydrogen-Bond Dynamics of Astrochemical Ice Analogs and Nonlinear TeraHertz Kerr Effect Measurements of Vibrational Quantum Beats

Much of the chemistry that affects life on planet Earth occurs in the condensed phase. The TeraHertz (THz) or far-infrared (far-IR) region of the electromagnetic spectrum (from 0.1 THz to 10 THz, 3 cm^-1 to 300 cm^-1, or 3000 μm to 30 μm) has been shown to provide unique possibilities in the study of condensed-phase processes. The goal of this work is to expand the possibilities available in the THz region and undertake new investigations of fundamental interest to chemistry. Since we are fundamentally interested in condensed-phase processes, this thesis focuses on two areas where THz spectroscopy can provide new understanding: astrochemistry and solvation science. To advance these fields, we had to develop new instrumentation that would enable the experiments necessary to answer new questions in either astrochemistry or solvation science. We first developed a new experimental setup capable of studying astrochemical ice analogs in both the TeraHertz (THz), or far-Infrared (far-IR), region (0.3 - 7.5 THz; 10 - 250 cm^-1) and the mid-IR (400 - 4000 cm^-1). The importance of astrochemical ices lies in their key role in the formation of complex organic molecules, such as amino acids and sugars in space. Thus, the instruments are capable of performing variety of spectroscopic studies that can provide especially relevant laboratory data to support astronomical observations from telescopes such as the Herschel Space Telescope, the Stratospheric Observatory for Infrared Astronomy (SOFIA), and the Atacama Large Millimeter Array (ALMA). The experimental apparatus uses a THz time-domain spectrometer, with a 1750/875 nm plasma source and a GaP detector crystal, to cover the bandwidth mentioned above with ~10 GHz (~0.3 cm^-1) resolution.

Using the above instrumentation, experimental spectra of astrochemical ice analogs of water and carbon dioxide in pure, mixed, and layered ices were collected at different temperatures under high vacuum conditions with the goal of investigating the structure of the ice. We tentatively observe a new feature in both amorphous solid water and crystalline water at 33 cm^-1 (1 THz). In addition, our studies of mixed and layered ices show how it is possible to identify the location of carbon dioxide as it segregates within the ice by observing its effect on the THz spectrum of water ice. The THz spectra of mixed and layered ices are further analyzed by fitting their spectra features to those of pure amorphous solid water and crystalline water ice to quantify the effects of temperature changes on structure. From the results of this work, it appears that THz spectroscopy is potentially well suited to study thermal transformations within the ice.

To advance the study of liquids with THz spectroscopy, we developed a new ultrafast nonlinear THz spectroscopic technique: heterodyne-detected, ultrafast THz Kerr effect (TKE) spectroscopy. We implemented a heterodyne-detection scheme into a TKE spectrometer that uses a stilbazoiumbased THz emitter, 4-N,N-dimethylamino-4-N-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS), and high numerical aperture optics which generates THz electric field in excess of 300 kV/cm, in the sample. This allows us to report the first measurement of quantum beats at terahertz (THz) frequencies that result from vibrational coherences initiated by the nonlinear, dipolar interaction of a broadband, high-energy, (sub)picosecond THz pulse with the sample. Our instrument improves on both the frequency coverage, and sensitivity previously reported; it also ensures a backgroundless measurement of the THz Kerr effect in pure liquids. For liquid diiodomethane, we observe a quantum beat at 3.66 THz (122 cm^-1), in exact agreement with the fundamental transition frequency of the υ4 vibration of the molecule. This result provides new insight into dipolar vs. Raman selection rules at terahertz frequencies.

To conclude we discuss future directions for the nonlinear THz spectroscopy in the Blake lab. We report the first results from an experiment using a plasma-based THz source for nonlinear spectroscopy that has the potential to enable nonlinear THz spectra with a sub-100 fs temporal resolution, and how the optics involved in the plasma mechanism can enable THz pulse shaping. Finally, we discuss how a single-shot THz detection scheme could improve the acquisition of THz data and how such a scheme could be implemented in the Blake lab. The instruments developed herein will hopefully remain a part of the groups core competencies and serve as building blocks for the next generation of THz instrumentation that pushes the frontiers of both chemistry and the scientific enterprise as a whole.

Estresse no trabalho e pressão arterial: reflexões metodológicas sobre linearidade e operacionalização da exposição

O modelo demanda-controle proposto por Karasek caracteriza as situações de estresse no ambiente laboral que é definido pela alta exigência no trabalho resultante da combinação do efeito da demanda psicológica no trabalho (estressores) e moderadores do estresse, especialmente a capacidade de tomar decisões (controle). Existem diversas formas de operacionalizar a exposição (alta exigência no trabalho) descritas na literatura. No entanto, não há consenso sobre qual a melhor operacionalização. Outra questão negligenciada pela maioria dos autores é a forma funcional da curva exposição-resposta ou não linearidade da associação. Entre os desfechos avaliados em estudos sobre os efeitos do estresse no trabalho, usando o modelo demanda-controle, estão as doenças cardiovasculares, como a hipertensão arterial. Contudo, os resultados relatados parecem conflitantes sobre a associação entre o estresse no trabalho e a hipertensão arterial. Os objetivos deste trabalho são estudar a associação entre o estresse no trabalho e aumento da pressão arterial/hipertensão arterial usando as diferentes formas de operacionalização do estresse no trabalho e avaliar a curva exposição-resposta quanto à linearidade. O trabalho é um estudo seccional desenvolvido na população do Estudo Pró-Saúde que é composta por servidores públicos de uma universidade no Rio de Janeiro. Modelos de regressão usando diferentes distribuições foram usados para estimar a associação entre a alta exigência no trabalho e a pressão arterial/hipertensão arterial. Funções não lineares foram utilizadas para investigar a linearidade da associação entre a exposição e os desfechos. Os resultados sugerem que a relação entre a dimensão controle e a pressão arterial seja não linear. Foram observadas associações significativas entre alta exigência no trabalho e pressão arterial sistólica e diastólica para algumas formas de operacionalização da exposição, quando analisados separadamente. No entanto, quando analisadas de forma conjunta por meio do modelo de resposta bivariada não foi encontrada associação. Também não foi encontrada associação entre a alta exigência no trabalho e hipertensão arterial para nenhuma forma de operacionalização da exposição. Os modelos estatísticos com melhor ajuste foram aqueles em que a exposição foi operacionalizada por meio de quadrantes gerados pela mediana de cada uma das dimensões e de forma dicotômica com termo de interação entre demanda psicológica e controle. Neste estudo estas foram as formas mais adequadas de operacionalização. Os resultados também mostram que a associação entre a dimensão controle e a pressão arterial é não linear. Conclui-se que não há garantia de linearidade da associação entre estresse no trabalho e pressão arterial e que essa associação pode ser influenciada pela forma de operacionalização da exposição e do desfecho ou da estratégia de modelagem.

Response of linear, viscous damped systems to excitations having time-varying frequency

The response of linear, viscous damped systems to excitations having time-varying frequency is the subject of exact and approximate analyses, which are supplemented by an analog computer study of single degree of freedom system response to excitations having frequencies depending linearly and exponentially on time.

The technique of small perturbations and the methods of stationary phase and saddle-point integration, as well as a novel bounding procedure, are utilized to derive approximate expressions characterizing the system response envelope—particularly near resonances—for the general time-varying excitation frequency.

Descriptive measurements of system resonant behavior recorded during the course of the analog study—maximum response, excitation frequency at which maximum response occurs, and the width of the response peak at the half-power level—are investigated to determine dependence upon natural frequency, damping, and the functional form of the excitation frequency.

The laboratory problem of determining the properties of a physical system from records of its response to excitations of this class is considered, and the transient phenomenon known as “ringing” is treated briefly.

It is shown that system resonant behavior, as portrayed by the above measurements and expressions, is relatively insensitive to the specifics of the excitation frequency-time relation and may be described to good order in terms of parameters combining system properties with the time derivative of excitation frequency evaluated at resonance.

One of these parameters is shown useful for predicting whether or not a given excitation having a time-varying frequency will produce strong or subtle changes in the response envelope of a given system relative to the steady-state response envelope. The parameter is shown, additionally, to be useful for predicting whether or not a particular response record will exhibit the “ringing” phenomenon.

Some generalizations of commutativity for linear transformations on a finite dimensional vector space

Let L be the algebra of all linear transformations on an n-dimensional vector space V over a field F and let A, B, ƐL. Let A_i+1 = A_iB - BA_i, i = 0, 1, 2,…, with A = A_o. Let f_k (A, B; σ) = A_2K+1 - ^σ1^A2K-1 ^{+ σ}2^A2K-3 -… +(-1)^Kσ_KA₁ where σ = (σ₁, σ₂,…, σ_K), σ_i belong to F and K = k(k-1)/2. Taussky and Wielandt [Proc. Amer. Math. Soc., 13(1962), 732-735] showed that f_n(A, B; σ) = 0 if σ_i is the i^th elementary symmetric function of (β₄- β_s)², 1 ≤ r ˂ s ≤ n, i = 1, 2, …, N, with N = n(n-1)/2, where β₄ are the characteristic roots of B. In this thesis we discuss relations involving f_k(X, Y; σ) where X, Y Ɛ L and 1 ≤ k ˂ n. We show: 1. If F is infinite and if for each X Ɛ L there exists σ so that f_k(A, X; σ) = 0 where 1 ≤ k ˂ n, then A is a scalar transformation. 2. If F is algebraically closed, a necessary and sufficient condition that there exists a basis of V with respect to which the matrices of A and B are both in block upper triangular form, where the blocks on the diagonals are either one- or two-dimensional, is that certain products X₁, X₂…X_r belong to the radical of the algebra generated by A and B over F, where X_i has the form f₂(A, P(A,B); σ), for all polynomials P(x, y). We partially generalize this to the case where the blocks have dimensions ≤ k. 3. If A and B generate L, if the characteristic of F does not divide n and if there exists σ so that f_k(A, B; σ) = 0, for some k with 1 ≤ k ˂ n, then the characteristic roots of B belong to the splitting field of g_k(w; σ) = w^2K+1 - σ₁w^2K-1 + σ₂w^2K-3 - …. +(-1)^K σ_Kw over F. We use this result to prove a theorem involving a generalized form of property L [cf. Motzkin and Taussky, Trans. Amer. Math. Soc., 73(1952), 108-114]. 4. Also we give mild generalizations of results of McCoy [Amer. Math. Soc. Bull., 42(1936), 592-600] and Drazin [Proc. London Math. Soc., 1(1951), 222-231].

Optimum linear coding for additive noise systems using information feedback

The feedback coding problem for Gaussian systems in which the noise is neither white nor statistically independent between channels is formulated in terms of arbitrary linear codes at the transmitter and at the receiver. This new formulation is used to determine a number of feedback communication systems. In particular, the optimum linear code that satisfies an average power constraint on the transmitted signals is derived for a system with noiseless feedback and forward noise of arbitrary covariance. The noisy feedback problem is considered and signal sets for the forward and feedback channels are obtained with an average power constraint on each. The general formulation and results are valid for non-Gaussian systems in which the second order statistics are known, the results being applicable to the determination of error bounds via the Chebychev inequality.

Spectral density of first order Piecewise linear systems excited by white noise

The Fokker-Planck (FP) equation is used to develop a general method for finding the spectral density for a class of randomly excited first order systems. This class consists of systems satisfying stochastic differential equations of form ẋ + f(x) = m/Ʃ/j = 1 h_j(x)n_j(t) where f and the h_j are piecewise linear functions (not necessarily continuous), and the n_j are stationary Gaussian white noise. For such systems, it is shown how the Laplace-transformed FP equation can be solved for the transformed transition probability density. By manipulation of the FP equation and its adjoint, a formula is derived for the transformed autocorrelation function in terms of the transformed transition density. From this, the spectral density is readily obtained. The method generalizes that of Caughey and Dienes, J. Appl. Phys., 32.11.

This method is applied to 4 subclasses: (1) m = 1, h₁ = const. (forcing function excitation); (2) m = 1, h₁ = f (parametric excitation); (3) m = 2, h₁ = const., h₂ = f, n₁ and n₂ correlated; (4) the same, uncorrelated. Many special cases, especially in subclass (1), are worked through to obtain explicit formulas for the spectral density, most of which have not been obtained before. Some results are graphed.

Dealing with parametrically excited first order systems leads to two complications. There is some controversy concerning the form of the FP equation involved (see Gray and Caughey, J. Math. Phys., 44.3); and the conditions which apply at irregular points, where the second order coefficient of the FP equation vanishes, are not obvious but require use of the mathematical theory of diffusion processes developed by Feller and others. These points are discussed in the first chapter, relevant results from various sources being summarized and applied. Also discussed is the steady-state density (the limit of the transition density as t → ∞).

Cálculo de parámetros cinéticos con técnicas termogravimétricas usando métodos no isotermos de ajuste a modelos y libres de modelos

Estudio cinético de la reacción de combustión del coque mediante el cálculo de los parámetros cinéticos de la reacción, empleando diferentes métodos de cálculo. Idioma: castellano.