Physics Commons^™

Mutual Information, Strange Attractors, And The Optimal Estimation Of Dimension, J. M. Martinerie, Alfonso M. Albano, A. I. Mees, P. E. Rapp

Physics Faculty Research and Scholarship

It has been shown that the appropriate setting of data windows is crucial to a successful estimation of a time-series correlation dimension using the Grassberger-Procaccia algorithm [Physica 9D, 189 (1983); Phys. Rev. Lett. 50, 346 (1983)], and it has been proposed that the first minimum of the corresponding mutual-information function may be an appropriate window value. We have tested this hypothesis against data generated by the Rossler equations, the Lorenz equations, and a three-dimensional irrational torus. We conclude that mutual information is not consistently successful in identifying the optimal window.

Solid State Proton Spin Relaxation And T-Butyl And Methyl Group Reorientation In 1-Bromo-2,4,6-Tri-T-Butylbenzene, Anne M. Fry, Peter A. Beckmann, Albert J. Fry, Peter C. Fox, Ari Isenstadt

Physics Faculty Research and Scholarship

We have used the solid state proton spin relaxation technique to investigate the barriers for methyl and t-butyl group reorientation in polycrystalline 1-bromo-2,4,6-tri-t-butylbenzene. The barriers in the range of 15-19 kJ/mol (3-5 kcal/mol) are compared with those found in related molecules. It is shown that the neighboring ring bromine atom has an effect on the barrier for t-butyl group reorientation similar to that of a neighboring hydrogen atom despite the significantly larger van der Waals' radius of a bromine atom. This most likely occurs because of the relatively long carbon-bromine bond, the distorted ring geometry, and the relatively high polarizability …

Solid State Proton Spin Relaxation In Ethylbenzenes: Methyl Reorientation Barriers And Molecular Structure, Peter A. Beckmann, Laura Happersett, Antonia V. Herzog, William M. Tong

Physics Faculty Research and Scholarship

We have investigated the dynamics of the ethyl groups and their constituent methyl groups in polycrystalline ethylbenzene (EB), 1,2-diethylbenzene (1,2-DEB), 1,3-DEB, and 1,4-DEB using the solid state proton spin relaxation (SSPSR) technique. The temperature and Larmor frequency dependence of the Zeeman spin-lattice relaxation rate is reported and interpreted in terms of the molecular dynamics. We determine that only the methyl groups are reorienting on the nuclear magnetic resonance time scale. The observed barrier of about 12 kJ/mol for methyl group reorientation in the solid samples of EB, 1,2-DEB, and 1,3-DEB is consistent with that of the isolated molecule, implying that …

Correlation-Dimension Calculations For Broadband Intensity Fluctuations In Emission From A Heavily Saturated Source Of Amplified Spontaneous Emission, B. Das, Alfonso M. Albano, N. B. Abraham

Physics Faculty Research and Scholarship

Broadband intensity fluctuations from a heavily saturated source of amplified spontaneous emission (ASE) operating on the 3.51-μm transition of xenon show no evidence of a dynamical origin represented by a low-dimensional underlying chaotic attractor. The broadband coupled-mode fluctuations in ASE thus seem to be stochastic when contrasted with the recently reported deterministic nature of similar broadband fluctuations of single-mode lasers operating on the same transition.

Methyl Reorientation In Methylphenanthrenes. Ii. Solid-State Proton Spin-Lattice Relaxation In The 1-Ch3, 9-Ch3, And 1-Cd3, 9-Ch3 Systems, F B. Mallory, C. W. Mallory, K. G. Conn, Peter A. Beckmann

Physics Faculty Research and Scholarship

We report proton Zeeman relaxation rates R as a function of temperature T at 8.5 and 53 MHz in polycrystalline 1,9-dimethylphenanthrene (1,9-DMP) and l-trideuteriomethyl-9-methylphenanthrene (1, 9-DMP[1-d3]). The data are interpreted using a Davidson-Cole spectral density for intramolecular reorientation and the implications of this are discussed. R vs T−1data for 1,9-DMP[1-d3] are used to determine the parameters that characterize the reorientation of the 9-methyl group. By assuming that the parameters characterizing the dynamics of the 9-methyl group are the same in 1,9-DMP and 1,9-DMP[1-d3], we subtract out the R vs T−1 contribution of the 9-methyl group in 1,9-DMP to …

Thermally Activated Methyl And T-Butyl Group Reorientation In Solids, Peter A. Beckmann

Physics Faculty Research and Scholarship

We reinterpret proton spin-lattice relaxation measurements in solid 1,4-di-t-butylbenzene (1,4-DTB) [P. A. Beckmann, F. A. Fusco, and A. E. O'Neill, J. Magn. Reson. 59 63 (1984)] in light of a recent study of solid 1,3-DTB [P. A. Beckmann, A. I. Hill, E. B. Kohler, and H. Yu, Phys. Rev. B 38 11098 (1988))]. We investigate the relationship between the spectral density that characterizes the intramolecular reorientation of the t-butyl groups and their constituent methyl groups in DTB, and the t-butyl group environment which dictates the symmetry of the local electrostatic potential. For both isomers, if one assumes a sixfold potential, …

Nuclear-Spin Relaxation In Molecular Solids With Reorienting Methyl And T-Butyl Groups: The Spectral Density And The State Of The Solid, Peter A. Beckmann, Audrey I. Hill, Ellen B. Kohler, Hong Yu

Physics Faculty Research and Scholarship

There are two solid phases which either have a large hysteresis of at least 90 K, or are both stable below 200 K. The sample melts at 262 K. We interpret the high-temperature phase R-versus-T-1 data with three models. First, we adopt a one-correlation-time model using a Davidson-Cole spectral density which suggests that there is a distribution of correlation times, or, equivalently, a distribution of activation energies for t-butyl and methyl group reorientation. In this case, the methyl and t-butyl reorientation is characterized by a cutoff activation energy of 17±1 kJ/mol which is to be compared with 18±1 kJ/mol in …

Singular-Value Decomposition And The Grassberger-Procaccia Algorithm, Alfonso M. Albano, J. Muench, C. Schwartz, A. I. Mees, P. E. Rapp

Physics Faculty Research and Scholarship

A singular-value decomposition leads to a set of statistically independent variables which are used in the Grassberger-Procaccia algorithm to calculate the correlation dimension of an attractor from a scalar time series. This combination alleviates some of the difficulties associated with each technique when used alone, and can significantly reduce the computational cost of estimating correlation dimensions from a time series.

Nuclear-Spin Relaxation In Molecular Solids With Reorienting Methyl And T-Butyl Groups: The Spectral Density And The State Of The Solid, Peter A. Beckmann, Audrey I. Hill, Ellen B. Kohler, Hong Yu

Physics Faculty Research and Scholarship

We have measured the temperature T dependence of the proton Zeeman relaxation rate R in polycrystalline 1,3-di-t-butylbenzene (1,3-DTB) at Larmor frequencies of ω/(2π)=8.50, 22.5, and 53.0 MHz. The relaxation is caused by the modulation of the methyl proton dipole-dipole interactions by the reorientation of the t-butyl groups [C(CH3)3] and their three constituent methyl groups (CH3).

There are two solid phases which either have a large hysteresis of at least 90 K, or are both stable below 200 K. The sample melts at 262 K. We interpret the high-temperature phase R-versus-T−1data with three models. First, we adopt a one-correlation-time model using …

Spectral Densities And Nuclear Spin Relaxation In Solids, Peter A. Beckmann

Physics Faculty Research and Scholarship

We investigate the properties of ten spectral densities relevant for nuclear spin relaxation studies in solids. This is preceded by a brief review of nuclear spin relaxation in solids which includes a discussion of the appropriate spin-dependent interactions and the various relaxation rates which can be measured. Also, the link between nuclear spin relaxation and dielectric relaxation is discussed. Where possible and/or appropriate each of the spectral densities is expressed as a continuous distribution of Bloembergen-Purcell-Pound (or Debye) spectral densities 2ξ /(1 + ξ2 ω2) for nuclear Larmor angular frequency ω and correlation time ξ. The spectral densities are named …

Semiclassical Analysis Of A Detuned Ring Laser With A Saturable Absorber: New Results For The Steady States, D. E. Chyba, N. B. Abraham, Alfonso M. Albano

Physics Faculty Research and Scholarship

This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is …

Methyl And Tert-Butyl Reorientation And Distributions Of Activation Energies In Molecular Solids: A Nuclear Spin-Relaxation Study In 2,4- And 2,5-Di-Tert-Butylhydroxybenzene, Peter A. Beckmann, A. M. Cheung, E. E. Fisch, F. A. Fusco, R. E. Herzog, M. Narisimhan

Physics Faculty Research and Scholarship

We have measured proton Zeeman relaxation rates R in the 2,4- and 2,5-isomers of di tert-butylhydroxybenzene (DTHB) in the solid state. R was measured as a function of temperature T at proton Larmor frequencies of (j)/21T = 8.50,22.5, and 53.0 MHz. The Tranges were from 78 K to just below the melting points of 2,4- and 2,5-DTHB, 385 and 323 K, respectively. The 2,5- DTHB R vs T and (j) can be interpreted qualitatively in terms of three Bloembergen-PurcellPound (BPP) spectral densities, one for each of the three types of rotors in the molecule. The quantitative agreement is poor but …

Deuteron Zeeman Relaxation Of Cd4 In The Isotropic Liquid, The Liquid Crystalline, And The Solid State Of Several Substances, Peter A. Beckmann, Myer Bloom, E. Elliott Burnell

Physics Faculty Research and Scholarship

Measurement of deuteron Zeeman relaxation rates of CD₄ dissolved in benzene, hexane, and the liquid crystals MBBA, EBBA, and Merck ZLI‐1132 and in pure CD₄ gas as a function of temperature at 30.7 and 61.4 MHz shows that the CD₄ is uniformly dispersed in the liquid solvents but resides in gas pockets when the solvents are in the solid state. Effects of centrifugal distortion were observed in the gas phase. The relaxation rate was found to be nearly independent of solvent, temperature, and pressure for the methane–liquid mixtures. This result is explained in terms of the extended …

Nuclear Magnetic Resonance Spectroscopy And Relaxation In Molecular Solids Containing Isopropyl Groups. Part 2—The Large Two-Phase Temperature Region In 1,4-Di-Isopropylbenzene, Peter A. Beckmann

Physics Faculty Research and Scholarship

We report a proton n.m.r. study of the large, long-lived two-phase temperature region in 1,4-di-isopropylbenzene (DIB). The proton spectra are characterized by a narrow line superimposed on a 42 kHz broad line. The narrow line shows the chemical shift structure of DIB. When the sample is in the solid state the narrow lines are sharp (<30 Hz) near the melting point of 256 K and they broaden to ca.1.5 kHz at ca. 170 K where they disappear. A variety of selective and non-selective Zeeman relaxation experiments as well as a Goldman–Shen exchange experiment were performed. It is concluded that the two sets of spins do not communicate on any timescale shorter …

Low-Dimensional Chaotic Attractors For An Unstable, Inhomogeneously Broadened, Single-Mode Laser, Alfonso M. Albano, J. Abounadi, T. H. Chyba, C. E. Searle, S. Yong, R. S. Gioggia, N. B. Abraham

Physics Faculty Research and Scholarship

Quantitative characterization of the intensity pulsations from an inhomogeneously broadened laser confirm that observed irregular pulsing has its origins in deterministic chaos corresponding to motion on a strange attractor of low fractal dimensionality. The pointwise information dimension and the Grassberger-Procaccia K2 (estimators from below of the fractal dimensionality of the attractor and the Kolmogorov entropy, respectively) have been determined for digitized time series from parameter regions identified qualitatively by power spectra as representing periodic, period-doubled, quasi-periodic, and chaotic behavior. Some amount of chaos seems present for almost all operating conditions.

Nuclear-Spin-Relaxation Study Of Internal Motion In Two Organic Molecular Solids, Alfonso M. Albano, Peter A. Beckmann, M. E. Carrington, E. E. Fisch, F. A. Fusco, A. E. O'Neill, Mary E. Scott

Physics Faculty Research and Scholarship

We investigate proton spin-lattice relaxation in two powdered organic molecular solids with reorienting methyl (CH3) and tert-butyl [C(CH3)3] groups: 3,5-di-tert-butylphenol (DTBP) and 1,3,5-tri-tert-butylbenzene (TTBZ). The temperature and Larmor frequency dependence of the relaxation rate is considerably more complicated than would be expected on the basis of random reorientations of the CH3 and C(CH3)3 groups. The spectral densities describing the relaxation are broader, and show more structure, than those customarily used to interpret relaxation data. Assuming that the spectral densities may be expressed as linear superpositions of Lorentzians, we are able to obtain a single, nonexponential correlation function which leads to …

A General Nmr Spectral Density And Its Experimental Verification, A. M. Albano, Peter A. Beckmann, M. E. Carrington, F. A. Fusco, A. E. O'Neill, M. E. Scott

Physics Faculty Research and Scholarship

The authors develop a new general spectral density for use in interpreting nuclear spin-lattice relaxation measurements in molecular solids where molecular and/or intramolecular reorientation is responsible for the relaxation. They show that the simplest case of the general theory fits both the temperature and Lamor frequency dependence of some very complicated relaxation measurements which could not be previously fitted using several standard spectral densities. The relationship of the spectral density to a distribution of molecular potentials is briefly outlined.

Solid State Phase Transitions And Molecular Reorientation In Ortho-Carborane And Para-Carborane: An Isomer Effect, Peter A. Beckmann, Amos J. Leffler

Physics Faculty Research and Scholarship

The proton nuclear spin-lattice relaxation times at 30 MHz have been measured for ortho- and paracarborane between 170 and 310 K and between 210 and 320 K, respectively. Para-carborane undergoes solid-solid transitions at about 300 and 238 K while the ortho isomer shows only one transition at about 265 K. The details of the phase transitions are discussed and molecular reorientation in the isomers is compared.

Proton Spin-Lattice Relaxation In Meta-Carborane, Peter A. Beckmann, Armin Wendel

Physics Faculty Research and Scholarship

No abstract provided.

A Deuterium Nuclear Magnetic Resonance Study Of Chain Disorder In Lamellar Potassium Palmitate: The Effect Of Long And Short Chain Guests, Peter A. Beckmann, E. E. Burnell, M. A. Heldman, K. R. Northey, T. P. Higgs

Physics Faculty Research and Scholarship

The deuterium magnetic resonance spectra of lamellar phases of host perdeuterated potassium palmitate mixed with varying amounts of guest protiated potassium octanoate and behenate and 86.3 mol% D₂O are reported. At higher temperatures, the short chain guests give rise to more fluidity and the long chain guests give rise to less fluidity towards the end of the host chain. At low temperatures there are changes in the interaction between the polar head group and the water which depend on sample composition. The transition from the lamellar phase to the low temperature gel phase is investigated and in some …

Proton Spin Relaxation And Methyl And Hydroxy Group Motion, Peter A. Beckmann

Physics Faculty Research and Scholarship

Proton spin-lattice relaxation rates R = T1−1 have been measured in powdered samples of 4-methyl-2,6-di-tertiarybutyl phenol between 77 and 170 K. Deuteration of the hydroxy proton leads to a large change in R in the vicinity of the 120-K R maximum and in the high-temperature region. The data are successfully, although probably not uniquely, fitted and the interpretation suggests that in addition to the motion of the hydroxy proton playing a significant role in the relaxation, the two pairs of t-butyl methyl groups also contributing are inequivalent. The departure, at low temperatures, from an ω−2dependence of R where …

Electron Spin Relaxation And Tunnelling Methyl Groups, Peter A. Beckmann, S. Clough

Physics Faculty Research and Scholarship

The energy transfer has been studied between free radicals and nearby tunnelling methyl groups near the resonant condition that the electron Larmor frequency and the methyl tunnelling frequency are equal. The measurements were made in a gamma -irradiated single crystal of 4-methyl-2,6-ditertiarybutylphenol (MDBP) at 4.2K and consisted of saturating the ESR signal and observing its return to equilibrium. This has been done at eleven ESR frequencies in the range 8.97< nu s<0.63 GHz and for saturation times of 5, 50 and 200 s. A theoretical model has been developed for the non-exponential recovery which assumes that all the 4-methyl groups of the molecules surrounding a free radical have the same tunnelling rotation frequency nu t and that the only coupling between the electrons and the methyl groups is the intermolecular dipole-dipole interaction.

Proton Spin-Lattice Relaxation And Methyl Group Rotation, Peter A. Beckmann, C. I. Ratcliffe, B. A. Dunell

Physics Faculty Research and Scholarship

Proton spin-lattice relaxation times have been measured at 16, 31, and 59 MHz in 4-methyl-2,6-ditertiarybutyl phenol between 80 K and its melting point, 340 K. The variation of T1 with temperature shows too distinct minima. The lower-temperature minimum has been analyzed in terms of relaxation by reorientation of four of the six t-butyl methyl groups with an average apparent activation energy of about 2.4 kcal mole−1 (104 meV molecule−1). The higher-temperature minimum has been analyzed in terms of relaxation by reorientation of the t-butyl groups about their C3 axes with four of the six t-butyl methyl groups reorienting …

Nuclear Spin-Lattice Relaxation And Activation Energies Of Tunnelling Methyl Groups, Peter A. Beckmann, S. Clough

Physics Faculty Research and Scholarship

The coupling of lattice vibrations with the rotational motion of hindered methyl groups is considered. It is shown that the apparent activation energy for methyl group rotation is determined at relatively high temperatures by the methyl group torsional energy splittings, but at low temperatures it depends on the frequencies of short-wavelength lattice modes which couple relatively strongly with methyl-group rotation. The temperature dependence of the proton spin lattice relaxation time from 6 to 50K is reported for three samples containing methyl groups whose tunnelling frequencies have previously been measured very precisely. They are 4-methyl-2,6-ditertiarybutylphenol (MDBP) and two deuterated derivatives. The …

The Haupt Effect: Coupled Rotational And Dipolar Relaxation Of Methyl Groups, Peter A. Beckmann, S. Clough, J. W. Hennel, J. R. Hill

Physics Faculty Research and Scholarship

A theory is described for the dynamic proton dipolar polarization observed by Haupt (1972) in 4-methylpyridine following a sudden temperature change. The theory differs from that of Haupt in assuming that transitions which change the rotational quantum number of the 4-methyl group by +or-3 occur very rapidly, maintaining thermal equilibrium within each of the three subsets of rotational levels corresponding to the three methyl group proton spin symmetry species A, Ea and Eb. The difference of A and E species populations approaches the new equilibrium value slowly and exponentially, following the temperature jump, and generates dipolar polarization in the process. …

The Electron-Methyl Group Spin-Spin Interaction, Peter A. Beckmann

Physics Faculty Research and Scholarship

The nuclear spin symmetry conversion transition, whereby a methyl group changes tunnelling state (A↔E) and total nuclear spin (ΔI = ± 1), is made resonant by the flip of an unpaired electron spin (Δms = ± 1). The coupling between an unpaired electron in a free radical and a methyl group in a nearby molecule is via the inter-molecular spin-spin interaction. The matrix elements and transition probabilities for this transition are calculated explicitly. The motivation behind the calculation is to aid in the interpretation of electron spin relaxation experiments in γ-irradiated 4-methyl-2,6-t …

Nuclear Spin Relaxation And Centrifugal Distortion Effects In Dilute Silane Gas, Peter A. Beckmann, E. E. Burnell

Physics Faculty Research and Scholarship

We have measured the proton longitudinal spin relaxation rate in dilute gaseous silane (SiH₄) between 10⁻² and 1 amagats and are able to observe the influence of rotational Q branch centrifugal distortion transitions.

Proton Spin Relaxation In Dilute Methane Gas: A Symmetrized Theory And Its Experimental Verification, Peter A. Beckmann, M. Bloom, I. Ozier

Physics Faculty Research and Scholarship

Nuclear spin relaxation in low density methane gas is investigated theoretically and experimentally. A theory is developed in which full account is taken of the tetrahedral symmetry of the molecule. For a nuclear Larmor frequency of 30 MHz, the time evolution of the nonequilibrium magnetization is measured as a function of density between approximately 0.005 and 17 amagats at temperatures of 110, 150, and 295 K. In all cases, exponential relaxation is observed. By using the theory in conjunction with the known spin rotation constants and rotational energy levels of CH₄, the measured values of the relaxation rate …

Nuclear Spin Relaxation By Intramolecular Interactions In Gases Of Homonuclear Diatomic Molecules, Myer Bloom, Peter A. Beckmann, B C. Sanctuary

Physics Faculty Research and Scholarship

The differential equations which describe the relaxation of macroscopic observables associated with nuclear spins in homonuclear diatomic molecules are derived using an expansion of the nuclear spin density matrix in terms of irreducible tensors. It is shown, using an intramolecular quadrupole mechanism, that the only difference between nuclear spin relaxation of the ortho- and para-species arises from the rotational states being restricted to odd and even values. This difference is vanishingly small at high temperatures so that the relaxation equations for nuclear magnetization become identical for both species. A previous paper predicting a difference even at high temperatures is …

Nuclear-Spin Relaxation In Low-Density Molecular Hydrogen At Room Temperature, Peter A. Beckmann, E. Elliott Burnell, Krovvidi Lalita, Robin L. Armstrong, Kenneth E. Kisman, F. R. Mccourt

Physics Faculty Research and Scholarship

No abstract provided.