Lecture notes on sediment transportation and channel stability

These notes have been prepared for a series of lectures on sediment transportation and channel stability given by the authors to a group of engineers and geologists of the U. S. Department of Agriculture assembled at Caltech on September 12-16,1960. The material herein is not intended to serve as a complete textbook, because it covers only subjects of the one-week sequence of lectures Due to limitation of space and time, coverage of many subjects is brief and others are omitted altogether. At the end of each chapter the reader will find a selected list of references for more detailed study

The petrogenesis of the Agamenticus complex and late Paleozoic and Mesozoic tectonics in New England

The Mesozoic opening of the Atlantic Ocean was associated with the emplacement of subalkalic to alkalic complexes along a linear trend that extends southeasterly from Montreal, Canada, into the Gulf of Maine. The portion of this trend within southwestern Maine consists of Triassic and Cretaceouscomplexes. The central complexes were emplaced within three different lithotectonic blocks or terranes and thus provide a number of unique opportunities for the investigation of Mesozoic anorogenic magmatism. Proposed terrane boundaries in southwestern Maine and adjacent regions were investigated by a detailed analysis of maps of regional aeromagnetic and gravity data. Significant aeromagnetic anomalies associated with lithologic units and fault zones onshore (i.e. the Nonesuch River, Calef, and Portsmouth faults) provide the basis for offshore fault zone indentification and the interpolation of coastal New England geology and terrane boundaries into the western and west-central portions of the Gulf of Maine. Within the western Gulf of Maine north-south aeromagnetic linears deflect westward, become segmented, and merge with the offshore extension of the Bloody Bluff and Clinton-Newbury Fault Zones. The regional pattern can be explained in terms of regional dextral transpression resulting from the late Paleozoic (Alleghanian (?)) deformation of previously accreted lithotectonic packages to the north and northwest of the Bloody Bluff and Clinton-Newbury fault zones. Early Mesozoic rift-related magmatism was investigated through a detailed petrogenetic study of the Triassic Agamenticus Complex. Least squares models suggest that the aegirine granite and, possibly, the alkalic granite can be derived by fractional crystallization from a subsolvus augite syenite parent. Trace element modeling suggests that processes other than liquid-crystal equilibrium fractionation, such as volatile fluxing and deuteric alteration, also played a role in the development of the magmas. An alkalic syenite and biotite granite cannot be modeled as either cumulate or fractionate phases from this process and are considered to be separate magmatic pulses derived by partial melting of the lower crust. The Triassic and Cretaceous felsic complexes in southwestern Maine can be separated on the basis of trace element and potential field data: eg. Triassic complexes are depleted in Sr and Ba and lack the positive aeromagnetic and gravity anomalies associated with the Cretaceous complexes. These data are interpreted to reflect the transition from dominantly crustally derived magmas in the Triassic to mantle derived melts in the Cretaceous. Significantly different petrogenetic processes operating at the beginning and end of the rifting cycle resulted in the emplacment of mantle derived melts at progressively higher levels within the crust as Mesozoic taphrogenesis evolved

High-Temperature Expansion for the Orientational Specific Heat of Solid H\u3csub\u3e2\u3c/sub\u3e and D\u3csub\u3e2\u3c/sub\u3e

Terms up to order (Γ/kBT)5 in the high-temperature expansion of the orientational specific heat of ortho-para alloys of solid H2 or D2 are evaluated. Good agreement is obtained between theory and experiment using a Padé approximant and effective values of the quadrupolar coupling constant, Γeff/Γ0=0.83 for D2 and Γeff/Γ0=0.80 for H2, where Γ0 is the value for a rigid lattice. These values agree with other determinations of Γeff, whereas the T−2 approximation for the specific heat yields anomalously small values of Γeff

Orientational Phases of Hydrogen Molecules on a Triangular Lattice

A mean-field theory for the ordering of hydrogen molecules on a triangular net is derived in terms of the quadrupole coupling constant Γ, the crystal field Vc, and the temperature T. The phase diagram consists of six regions, separated by first- and second-order transitions. For almost all values of Vc/Γ for which ordering occurs, the disordered to ordered phase transition is continuous. At T=0 K, all phases have energy gaps except for a ferrorotational phase which behaves like an XY model

Two-Libron Spectrum of Solid H\u3csub\u3e2\u3c/sub\u3e and D\u3csub\u3e2\u3c/sub\u3e

It is shown that the two-libron lines in the Raman spectrum of solid hydrogen result from the large cubic anharmonicity of the quadrupole-quadrupole Hamiltonian. A localized picture is used to describe the interaction of two librational excitations on neighboring molecules, and dynamic interactions with other molecules are treated perturbatively. In this approximation the average single-libron energy agrees with the anharmonic calculation in the accompanying paper. Using a value of the quadrupole-coupling constant obtained from the single-libron spectrum, the resulting two-libron energies and Raman transition probabilities are in excellent agreement with the observed spectrum

Theoretical Analysis of Inelastic Neutron Scattering in Solid Hydrogen

The inelastic-neutron-scattering cross section of (J=1) solid hydrogen is studied and the experimental data of Stein and co-workers analyzed. The rms displacement ⟨u2⟩1/2 is deduced from the data via different methods and mutually consistent values of order 0.65 Å are obtained. The enhancement of the cross section at the libron energy due to libron-phonon interactions is found to be the same, about 40% each for both one-and two-libron processes, in agreement with the neutron scattering data. The rms splitting at the libron-phonon crossovers is found to be about 1 cm−1, somewhat smaller than found by Mertens and Biem. A sum rule for the J=1 to J=0 cross section is given which relates the average energy of this transition to the orientational internal energy. Using high-temperature expansions and experimental data for the specific heat, we obtain a qualitative fit to the neutron scattering data in the orientationally disordered phase. In the ordered phase both the sum rule and a direct calculation indicate the existence of a libron sideband above the main J=1 to J=0 line having an intensity of 10% of the main line. The energy of the main line at zero temperature is calculated including (a) tipping corrections, (b) virtual excitations with J not conserved, and (c) modified zero-point energy. The value of the electrostatic quadrupole-quadrupole coupling constant deduced from the data of Stein and co-workers using this calculation is in agreement with that obtained from other experiments

Evaluation Factors for Multi-Stakeholder Broadband Visual Communication Projects

This paper presents a summary of multifaceted evaluation factors that we have identified through our research with Broadband Visual Communication (BVC) projects involving multiple stakeholders. The main benefit of these evaluation factors is that they provide a general evaluation framework for multiple stakeholder projects. The factors are social infrastructure, technical infrastructure, physical space, interaction style and content

Possible Néel Orderings of the Kagomé Antiferromagnet

Possible Néel orderings of antiferromagnetically coupled spins on a kagomé lattice are studied using linear-spin-wave theory and high-temperature expansions. Spin-wave analysis, applied to q=0 (three spins per magnetic unit cell) and to √3 × √3 (nine spins per cell) Néel orderings yield identical excitation spectra with twofold-degenerate linear modes and a dispersionless zero-energy mode. This dispersionless mode is equivalent to an excitation localized to an arbitrary hexagon of nearest-neighbor spins. Second- (J2) and third- (J3) neighbor interactions are shown to stabilize the q=0 state for J2\u3eJ3 and the √3 × √3 state for J23. A high-temperature expansion of the spin-spin susceptibility χαβ(q) is performed to order 1/T8, for n-component, classical spins with nearest-neighbor interactions only. To order 1/T7 the largest eigenvalue of the susceptibility matrix is found to be independent of wave vector with an eigenvector that corresponds to the dispersionless mode of the ordered phase. This degeneracy is removed at order 1/T8. For n=0, the q=0 mode is favored; for n=1, the band is flat; and, for n\u3e1, the maximum susceptibility is found for a √3 × √3 excitation. Similar results are found for the three-dimensional pyrochlore lattice. The high-temperature expansion is used to interpret experimental data for the uniform susceptibility and powder-neutron-diffraction spectrum for the kagomé-lattice system SrCr8−xGa4+xO19

Effects of Librational Anharmonicity in the Solid Hydrogens

We compare the results of the recently published anharmonic theory of librons to the best available data on the libron Raman frequencies. This allows us to deduce a refined estimate of the effective value of the intermolecular quadrupolar coupling constant Γeff for solid H2 and D2. The effect on the librons of virtual transitions to the (J=3) rotational state is included with the result that Γeff is decreased. Our estimate from the optical data is then Γeff=0.72±0.04 and 0.58±0.03 cm−1 for D2(x=1) and H2(x=1), respectively, at zero pressure, where x denotes the mole fraction of J=1 molecules. We also use the anharmonic density of states to analyze specific heat and (∂P/∂T)V data from which we obtain the average libron energy as a function of x. For D2(x=1) the result is Γeff=0.70±0.04 cm−1. Measurements of the conversion-induced pressure change in H2 give Γeff=0.56±0.03 cm−1. Both these determinations are in good agreement with the results from optical data for librons. Furthermore, it is found that there is no significant difference between Γeff(x=1) and Γeff determined from pair spectra in H2 and D2 with x≪1. The anharmonic density of states is also used to interpret the infrared absorption sideband spectrum for the creation of a vibron plus libron(s). The part of the spectrum which we attribute to one-libron processes has a width in agreement with this model and as expected there are two-libron processes resulting from cubic anharmonic libron-libron interactions. Incoherent-neutron-scattering data is also consistent with the anharmonic-libron spectrum