13 resultados para Lies

em CaltechTHESIS


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The determination of the energy levels and the probabilities of transition between them, by the formal analysis of observed electronic, vibrational, and rotational band structures, forms the direct goal of all investigations of molecular spectra, but the significance of such data lies in the possibility of relating them theoretically to more concrete properties of molecules and the radiation field. From the well developed electronic spectra of diatomic molecules, it has been possible, with the aid of the non-relativistic quantum mechanics, to obtain accurate moments of inertia, molecular potential functions, electronic structures, and detailed information concerning the coupling of spin and orbital angular monenta with the angular momentum of nuclear rotation. The silicon fluori1e molecule has been investigated in this laboratory, and is found to emit bands whose vibrational and rotational structures can be analyzed in this detailed fashion.

Like silicon fluoride, however, the great majority of diatomic molecules are formed only under the unusual conditions of electrical discharge, or in high temperature furnaces, so that although their spectra are of great theoretical interest, the chemist is eager to proceed to a study of polyatomic molecules, in the hope that their more practically interesting structures might also be determined with the accuracy and assurance which characterize the spectroscopic determinations of the constants of diatomic molecules. Some progress has been made in the determination of molecule potential functions from the vibrational term values deduced from Raman and infrared spectra, but in no case can the calculations be carried out with great generality, since the number of known term values is always small compared with the total number of potential constants in even so restricted a potential function as the simple quadratic type. For the determination of nuclear configurations and bond distances, however, a knowledge of the rotational terms is required. The spectra of about twelve of the simpler polyatomic molecules have been subjected to rotational analyses, and a number of bond distances are known with considerable accuracy, yet the number of molecules whose rotational fine structure has been resolved even with the most powerful instruments is small. Consequently, it was felt desirable to investigate the spectra of a number of other promising polyatomic molecules, with the purpose of carrying out complete rotational analyses of all resolvable bands, and ascertaining the value of the unresolved band envelopes in determining the structures of such molecules, in the cases in which resolution is no longer possible. Although many of the compounds investigated absorbed too feebly to be photographed under high dispersion with the present infrared sensitizations, the location and relative intensities of their bands, determined by low dispersion measurements, will be reported in the hope that these compounds may be reinvestigated in the future with improved techniques.

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Observations of the Galactic center region black hole candidate 1E 1740.7-2942 have been carried out using the Caltech Gamma-Ray Imaging Payload (GRIP), the Röntgensatellit (ROSAT) and the Very Large Array (VLA). These multiwavelength observations have helped to establish the association between a bright emitter of hard X-rays and soft γ-rays, the compact core of a double radio jet source, and the X-ray source, 1E 1740.7-2942. They have also provided information on the X-ray and hard X-ray spectrum.

The Galactic center region was observed by GRIP during balloon flights from Alice Springs, NT, Australia on 1988 April 12 and 1989 April 3. These observations revealed that 1E 1740.7-2942 was the strongest source of hard X-rays within ~10° of the Galactic center. The source spectrum from each flight is well fit by a single power law in the energy range 35-200 keV. The best-fit photon indices and 100 keV normalizations are: γ = (2.05 ± 0.15) and K_(100) = (8.5 ± 0.5) x 10^(-5) cm^(-2) s^(-1) keV^(-1) and γ = (2.2 ± 0.3) and K_(100) = (7.0 ± 0.7) x 10^(-5) cm^(-2) s^(-1) keV^(-1) for the 1988 and 1989 observations respectively. No flux above 200 keV was detected during either observation. These values are consistent with a constant spectrum and indicate that 1E 1740.7-2942 was in its normal hard X-ray emission state. A search on one hour time scales showed no evidence for variability.

The ROSAT HRI observed 1E 1740.7-2942 during the period 1991 March 20-24. An improved source location has been derived from this observation. The best fit coordinates (J2000) are: Right Ascension = 17^h43^m54^s.9, Declination = -29°44'45".3, with a 90% confidence error circle of radius 8".5. The PSPC observation was split between periods from 1992 September 28- October 4 and 1993 March 23-28. A thermal bremsstrahlung model fit to the data yields a column density of N_H = 1.12^(+1.51)_(0.18) x cm^(-2) , consistent with earlier X- ray measurements.

We observed the region of the Einstein IPC error circle for 1E 1740.7-2942 with the VLA at 1.5 and 4.9 GHz on 1989 March 2. The 4.9 GHz observation revealed two sources. Source 'A', which is the core of a double aligned radio jet source (Mirabel et al. 1992), lies within our ROSAT error circle, further strengthening its identification with 1E 1740.7-2942.

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The condensation of phenanthroline-5,6-dione (phendione) with polyamines is a versatile synthetic route to a wide variety of chelating ligands. Condensation with 2,3- napthalene diamine gives benzo[i]dipyrido[3,2-a:2',3'-c]phenazine (bdppz) a ligand containing weakly-coupled orbitals of benzophenazine (bpz) and 2,2' -bipyridinde(bpy) character. The bpy character gives Re and Ru complexes excited-state redox properties; intramolecular electron transfer (ET) takes place to the bpz portion of the ligand. The charge-separated state so produced has an extraordinarily-long 50 µs lifetime. The slow rate of charge recombination arises from a combination of extremely weak coupling between the metal center and the bpz acceptor orbital and Marcus "inverted region" behavior. Molecular orbital calculations show that only 3% the electron density in the lowest unoccupied molecular orbital lies on the bpy atoms of bdppz, effectively trapping the transferred electron on the bpz portion. The rate of charge recombination decreases with increasing driving force, showing that these rates lie in the inverted region. Comparison of forward and back ET rates shows that donor-acceptor coupling is four orders of magnitude greater for photoinduced electron transfer than it is for thermal charge recombination.

Condensation of phendione with itself or tetramines gives a series of binucleating tetrapyridophenazine ligands of incrementally-varying coordination-site separation. When a photoredox-active metal center is attached, excited-state energy and electron transfer to an acceptor metal center at the other coordination site can be studied as a function of distance. A variety of monometallic and homo- and heterodimetallic tetrapyridophenazine complexes has been synthesized. Electro- and magnetochemistry show that no ground-state interaction exists between the metals in bimetallic complexes. Excited-state energy and electron transfer, however, takes place at rates which are invariant with increasing donor-acceptor separation, indicating that a very efficient coupling mechanism is at work. Theory and experiment have suggested that such behavior might exist in extended π-systems like those presented by these ligands.

Condensation of three equivalents of 4,5-dimethyl-1,2-phenylenediamine with hexaketocyclohexane gives the trinucleating ligand hexaazahexamethyltrinapthalene (hhtn). Attaching two photredox-active metal centers and a third catalytic center to hhtn provides means by which multielectron photocatalyzed reactions might be carried out. The coordination properties of hhtn have been examined; X-ray crystallographic structure determination shows that the ligand's constricted coordination pocket leads to distorted geometries in its mono- and dimetallic derivatives.

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In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.

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One of the greatest challenges in science lies in disentangling causality in complex, coupled systems. This is illustrated no better than in the dynamic interplay between the Earth and life. The early evolution and diversification of animals occurred within a backdrop of global change, yet reconstructing the potential role of the environment in this evolutionary transition is challenging. In the 200 million years from the end-Cryogenian to the Ordovician, enigmatic Ediacaran fauna explored body plans, animals diversified and began to biomineralize, forever changing the ocean's chemical cycles, and the biological community in shallow marine ecosystems transitioned from a microbial one to an animal one.

In the following dissertation, a multi-faceted approach combining macro- and micro-scale analyses is presented that draws on the sedimentology, geochemistry and paleontology of the rocks that span this transition to better constrain the potential environmental changes during this interval.

In Chapter 1, the potential of clumped isotope thermometry in deep time is explored by assessing the importance of burial and diagenesis on the thermometer. Eocene- to Precambrian-aged carbonates from the Sultanate of Oman were analyzed from current burial depths of 350-5850 meters. Two end-member styles of diagenesis independent of burial depth were observed.

Chapters 2, 3 and 4 explore the fallibility of the Ediacaran carbon isotope record and aspects of the sedimentology and geochemistry of the rocks preserving the largest negative carbon isotope excursion on record---the Shuram Excursion. Chapter 2 documents the importance of temperature, fluid composition and mineralogy on the delta 18-O min record and interrogates the bulk trace metal signal. Chapter 3 explores the spatial variability in delta 13-C recorded in the transgressive Johnnie Oolite and finds a north-to-south trend recording the onset of the excursion. Chapter 4 investigates the nature of seafloor precipitation during this excursion and more broadly. We document the potential importance of microbial respiratory reactions on the carbonate chemistry of the sediment-water interface through time.

Chapter 5 investigates the latest Precambrian sedimentary record in carbonates from the Sultanate of Oman, including how delta 13-C and delta 34-S CAS vary across depositional and depth gradients. A new model for the correlation of the Buah and Ara formations across Oman is presented. Isotopic results indicate delta 13-C varies with relative eustatic change and delta 34-S CAS may vary in absolute magnitude across Oman.

Chapter 6 investigates the secular rise in delta 18-Omin in the early Paleozoic by using clumped isotope geochemistry on calcitic and phosphatic fossils from the Cambrian and Ordovician. Results do not indicate extreme delta 18-O seawater depletion and instead suggest warmer equatorial temperatures across the early Paleozoic.

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Part 1 of this thesis is about the 24 November, 1987, Superstition Hills earthquakes. The Superstition Hills earthquakes occurred in the western Imperial Valley in southern California. The earthquakes took place on a conjugate fault system consisting of the northwest-striking right-lateral Superstition Hills fault and a previously unknown Elmore Ranch fault, a northeast-striking left-lateral structure defined by surface rupture and a lineation of hypocenters. The earthquake sequence consisted of foreshocks, the M_s 6.2 first main shock, and aftershocks on the Elmore Ranch fault followed by the M_s 6.6 second main shock and aftershocks on the Superstition Hills fault. There was dramatic surface rupture along the Superstition Hills fault in three segments: the northern segment, the southern segment, and the Wienert fault.

In Chapter 2, M_L≥4.0 earthquakes from 1945 to 1971 that have Caltech catalog locations near the 1987 sequence are relocated. It is found that none of the relocated earthquakes occur on the southern segment of the Superstition Hills fault and many occur at the intersection of the Superstition Hills and Elmore Ranch faults. Also, some other northeast-striking faults may have been active during that time.

Chapter 3 discusses the Superstition Hills earthquake sequence using data from the Caltech-U.S.G.S. southern California seismic array. The earthquakes are relocated and their distribution correlated to the type and arrangement of the basement rocks. The larger earthquakes occur only where continental crystalline basement rocks are present. The northern segment of the Superstition Hills fault has more aftershocks than the southern segment.

An inversion of long period teleseismic data of the second mainshock of the 1987 sequence, along the Superstition Hills fault, is done in Chapter 4. Most of the long period seismic energy seen teleseismically is radiated from the southern segment of the Superstition Hills fault. The fault dip is near vertical along the northern segment of the fault and steeply southwest dipping along the southern segment of the fault.

Chapter 5 is a field study of slip and afterslip measurements made along the Superstition Hills fault following the second mainshock. Slip and afterslip measurements were started only two hours after the earthquake. In some locations, afterslip more than doubled the coseismic slip. The northern and southern segments of the Superstition Hills fault differ in the proportion of coseismic and postseismic slip to the total slip.

The northern segment of the Superstition Hills fault had more aftershocks, more historic earthquakes, released less teleseismic energy, and had a smaller proportion of afterslip to total slip than the southern segment. The boundary between the two segments lies at a step in the basement that separates a deeper metasedimentary basement to the south from a shallower crystalline basement to the north.

Part 2 of the thesis deals with the three-dimensional velocity structure of southern California. In Chapter 7, an a priori three-dimensional crustal velocity model is constructed by partitioning southern California into geologic provinces, with each province having a consistent one-dimensional velocity structure. The one-dimensional velocity structures of each region were then assembled into a three-dimensional model. The three-dimension model was calibrated by forward modeling of explosion travel times.

In Chapter 8, the three-dimensional velocity model is used to locate earthquakes. For about 1000 earthquakes relocated in the Los Angeles basin, the three-dimensional model has a variance of the the travel time residuals 47 per cent less than the catalog locations found using a standard one-dimensional velocity model. Other than the 1987 Whittier earthquake sequence, little correspondence is seen between these earthquake locations and elements of a recent structural cross section of the Los Angeles basin. The Whittier sequence involved rupture of a north dipping thrust fault bounded on at least one side by a strike-slip fault. The 1988 Pasadena earthquake was deep left-lateral event on the Raymond fault. The 1989 Montebello earthquake was a thrust event on a structure similar to that on which the Whittier earthquake occurred. The 1989 Malibu earthquake was a thrust or oblique slip event adjacent to the 1979 Malibu earthquake.

At least two of the largest recent thrust earthquakes (San Fernando and Whittier) in the Los Angeles basin have had the extent of their thrust plane ruptures limited by strike-slip faults. This suggests that the buried thrust faults underlying the Los Angeles basin are segmented by strike-slip faults.

Earthquake and explosion travel times are inverted for the three-dimensional velocity structure of southern California in Chapter 9. The inversion reduced the variance of the travel time residuals by 47 per cent compared to the starting model, a reparameterized version of the forward model of Chapter 7. The Los Angeles basin is well resolved, with seismically slow sediments atop a crust of granitic velocities. Moho depth is between 26 and 32 km.

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Nicotinic acetylcholine receptors are pentameric ligand-gated ion channels mediating fast synaptic transmission throughout the peripheral and central nervous systems. They have been implicated in various processes related to cognitive functions, learning and memory, arousal, reward, motor control and analgesia. Therefore, these receptors present alluring potential therapeutic targets for the treatment of pain, epilepsy, Alzheimer’s disease, Parkinson’s disease, Tourette’s syndrome, schizophrenia, anxiety, depression and nicotine addiction. The work detailed in this thesis focuses on binding studies of neuronal nicotinic receptors and aims to further our knowledge of subtype specific functional and structural information.

Chapter 1 is an introductory chapter describing the structure and function of nicotinic acetylcholine receptors as well as the methodologies used for the dissertation work described herein. There are several different subtypes of nicotinic acetylcholine receptors known to date and the subtle variations in their structure and function present a challenging area of study. The work presented in this thesis deals specifically with the α4β2 subtype of nicotinic acetylcholine receptor. This subtype assembles into 2 closely related stoichiometries, termed throughout this thesis as A3B2 and A2B3 after their respective subunit composition. Chapter 2 describes binding studies of select nicotinic agonists on A3B2 and A2B3 receptors determined by whole-cell recording. Three key binding interactions, a cation-π and two hydrogen bonds, were probed for four nicotinic agonists, acetylcholine, nicotine, smoking cessation drug varenicline (Chantix®) and the related natural product cytisine.

Results from the binding studies presented in Chapter 2 show that the major difference in binding of these four agonists to A3B2 and A2B3 receptors lies in one of the two hydrogen bond interactions where the agonist acts as the hydrogen bond acceptor and the backbone NH of a conserved leucine residue in the receptor acts as the hydrogen bond donor. Chapter 3 focuses on studying the effect of modulating the hydrogen bond acceptor ability of nicotine and epibatidine on A3B2 receptor function determined by whole-cell recording. Finally, Chapter 4 describes single-channel recording studies of varenicline binding to A2B3 and A3B2 receptors.

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More than thirty years after the discovery that Human Immunodeficiency Virus (HIV) was the causative agent of Acquired Immunodeficiency Syndrome (AIDS), the disease remains pandemic as long as no effective universal vaccine is found. Over 34 million individuals in the world are infected with the virus, and the vast majority of them have no access to the antiretroviral therapies that have largely reduced HIV to a chronic disease in the developed world. The first chapter of this thesis introduces the history of the virus. The key to the infectious mechanism of the virus lies in its envelope glycoprotein (Env), a trimeric spike on the viral surface that utilizes host T cell receptors for entry. Though HIV-1 Env is immunogenic, most infected patients do not mount an effective neutralizing antibody response against it. Broadly-neutralizing anti-Env antibodies (bNAbs) present in the serum of a minority of infected individuals are usually sufficient to prevent the progression to full blown AIDS. Thus, the molecular details of these bNAbs as well as the antibody-antigen interface are of prime interest for structural studies, as insight gained would contribute to the design of a more effective immunogen and potential vaccine candidate. The second chapter of this thesis describes the low-resolution crystal structure of one such antibody, 2G12 dimer, which targets a high mannose epitope on the surface of Env. Patients infected with HIV-2, a related virus with ~35% sequence identity in the Env region, can generally mount a robust antibody response sufficient for viral control for reasons still unknown. The final two chapters of this thesis focus on the first reported structural studies of HIV-2 Env, the molecular details of which may inform HIV-1 therapy and immunogen design.

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n-heptane/air premixed turbulent flames in the high-Karlovitz portion of the thin reaction zone regime are characterized and modeled in this thesis using Direct Numerical Simulations (DNS) with detailed chemistry. In order to perform these simulations, a time-integration scheme that can efficiently handle the stiffness of the equations solved is developed first. A first simulation with unity Lewis number is considered in order to assess the effect of turbulence on the flame in the absence of differential diffusion. A second simulation with non-unity Lewis numbers is considered to study how turbulence affects differential diffusion. In the absence of differential diffusion, minimal departure from the 1D unstretched flame structure (species vs. temperature profiles) is observed. In the non-unity Lewis number case, the flame structure lies between that of 1D unstretched flames with "laminar" non-unity Lewis numbers and unity Lewis number. This is attributed to effective Lewis numbers resulting from intense turbulent mixing and a first model is proposed. The reaction zone is shown to be thin for both flames, yet large chemical source term fluctuations are observed. The fuel consumption rate is found to be only weakly correlated with stretch, although local extinctions in the non-unity Lewis number case are well correlated with high curvature. These results explain the apparent turbulent flame speeds. Other variables that better correlate with this fuel burning rate are identified through a coordinate transformation. It is shown that the unity Lewis number turbulent flames can be accurately described by a set of 1D (in progress variable space) flamelet equations parameterized by the dissipation rate of the progress variable. In the non-unity Lewis number flames, the flamelet equations suggest a dependence on a second parameter, the diffusion of the progress variable. A new tabulation approach is proposed for the simulation of such flames with these dimensionally-reduced manifolds.

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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.

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The region treated in the following report is a small area of about one square mile near Pacoima, California. It consists of a group of small hills that that form the western abutment of the Hansen Dam. It is underlain by a section of intrusives, sediments, and extrusives, which may be subdivided into four groups.

The oldest rocks form the Dimebere complex of Jurassic (?) plutonic rocks, pegmatites, and schists. Lying uncomformably on this is a series of alternating terrestrial sandstones and bassalts of Tertiary age. These are unconformably overlain in turn by the Hansen Dam formation, a series of marine shales and sandstone correlated with the Temblor by the fossil contact. Finally into these strata was intruded the Munglish andesite.

These strata form a shallow, plunging anticline, whose axis trends slightly east of north and lies in the center of the hills. The unconformities have been offset in several places by a series of faults apparently related to the anticline.

A complete outline of the geologic history is included in the report.

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The effect of metal atoms on photochemical transformations has been investigated by studies of the cis-trans isomerization of β-styrylferrocene.

The photostationary state lies entirely on the side of the trans isomer in the cases of direct irradiation at 3130 Å or at 3660 Å. The quantum yield at 3130 Å is 0.00650 and does not vary with concentration. In the presence of benzophenon as sensitizer the quantum yield is 0.00540. On the other hand, the quantum yield for direct irradiation at 3660 Å decreases with increasing concentration of cis β- styrylferrocene varying from 0.00365 to 0.00198.

These results lead to the suggestion that the isomerization takes place from a triplet state of β-styrylferrocene which probably has higher energy than the lowest triplet; reaction from the third triplet seems most likely.

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Experimental measurements of rate of energy loss were made for protons of energy .5 to 1.6 MeV channeling through 1 μm thick silicon targets along the <110>, <111>, and <211> axial directions, and the {100}, {110}, {111}, and {211} planar directions. A .05% resolution automatically controlled magnetic spectrometer was used. The data are presented graphically along with an extensive summary of data in the literature. The data taken cover a wider range of channels than has previously been examined, and are in agreement with the data of F. Eisen, et al., Radd. Eff. 13, 93 (1972).

The theory in the literature for channeling energy loss due to interaction with local electrons, core electrons, and distant valence electrons of the crystal atoms is summarized. Straggling is analyzed, and a computer program which calculates energy loss and straggling using this theory and the Moliere approximation to the Thomas Fermi potential, VTF, and the detailed silicon crystal structure is described. Values for the local electron density Zloc in each of the channels listed above are extracted from the data by graphical matching of the experimental and computer results.

Zeroth and second order contributions to Zloc as a function of distance from the center of the channel were computed from ∇2VTF = 4πρ for various channels in silicon. For data taken in this work and data of F. Eisen, et al., Rad. Eff. 13, 93 (1972), the calculated zeroth order contribution to Zloc lies between the experimentally extracted Zloc values obtained by using the peak and the leading edge of the transmission spectra, suggesting that the observed straggling is due both to statistical fluctuations and to path variation.