The electric field of a weakly electric fish

Freshwater fish of the genus Apteronotus (family Gymnotidae) generate a weak, high frequency electric field (< 100 mV/cm, 0.5-10 kHz) which permeates their local environment. These nocturnal fish are acutely sensitive to perturbations in their electric field caused by other electric fish, and nearby objects whose impedance is different from the surrounding water. This thesis presents high temporal and spatial resolution maps of the electric potential and field on and near Apteronotus. The fish's electric field is a complicated and highly stable function of space and time. Its characteristics, such as spectral composition, timing, and rate of attenuation, are examined in terms of physical constraints, and their possible functional roles in electroreception.

Temporal jitter of the periodic field is less than 1 µsec. However, electrocyte activity is not globally synchronous along the fish 's electric organ. The propagation of electrocyte activation down the fish's body produces a rotation of the electric field vector in the caudal part of the fish. This may assist the fish in identifying nonsymmetrical objects, and could also confuse electrosensory predators that try to locate Apteronotus by following its fieldlines. The propagation also results in a complex spatiotemporal pattern of the EOD potential near the fish. Visualizing the potential on the same and different fish over timescales of several months suggests that it is stable and could serve as a unique signature for individual fish.

Measurements of the electric field were used to calculate the effects of simple objects on the fish's electric field. The shape of the perturbation or "electric image" on the fish's skin is relatively independent of a simple object's size, conductivity, and rostrocaudal location, and therefore could unambiguously determine object distance. The range of electrolocation may depend on both the size of objects and their rostrocaudal location. Only objects with very large dielectric constants cause appreciable phase shifts, and these are strongly dependent on the water conductivity.

Mathematical study of complex networks : brain, internet, and power grid

The dissertation is concerned with the mathematical study of various network problems. First, three real-world networks are considered: (i) the human brain network (ii) communication networks, (iii) electric power networks. Although these networks perform very different tasks, they share similar mathematical foundations. The high-level goal is to analyze and/or synthesis each of these systems from a “control and optimization” point of view. After studying these three real-world networks, two abstract network problems are also explored, which are motivated by power systems. The first one is “flow optimization over a flow network” and the second one is “nonlinear optimization over a generalized weighted graph”. The results derived in this dissertation are summarized below.

Brain Networks: Neuroimaging data reveals the coordinated activity of spatially distinct brain regions, which may be represented mathematically as a network of nodes (brain regions) and links (interdependencies). To obtain the brain connectivity network, the graphs associated with the correlation matrix and the inverse covariance matrix—describing marginal and conditional dependencies between brain regions—have been proposed in the literature. A question arises as to whether any of these graphs provides useful information about the brain connectivity. Due to the electrical properties of the brain, this problem will be investigated in the context of electrical circuits. First, we consider an electric circuit model and show that the inverse covariance matrix of the node voltages reveals the topology of the circuit. Second, we study the problem of finding the topology of the circuit based on only measurement. In this case, by assuming that the circuit is hidden inside a black box and only the nodal signals are available for measurement, the aim is to find the topology of the circuit when a limited number of samples are available. For this purpose, we deploy the graphical lasso technique to estimate a sparse inverse covariance matrix. It is shown that the graphical lasso may find most of the circuit topology if the exact covariance matrix is well-conditioned. However, it may fail to work well when this matrix is ill-conditioned. To deal with ill-conditioned matrices, we propose a small modification to the graphical lasso algorithm and demonstrate its performance. Finally, the technique developed in this work will be applied to the resting-state fMRI data of a number of healthy subjects.

Communication Networks: Congestion control techniques aim to adjust the transmission rates of competing users in the Internet in such a way that the network resources are shared efficiently. Despite the progress in the analysis and synthesis of the Internet congestion control, almost all existing fluid models of congestion control assume that every link in the path of a flow observes the original source rate. To address this issue, a more accurate model is derived in this work for the behavior of the network under an arbitrary congestion controller, which takes into account of the effect of buffering (queueing) on data flows. Using this model, it is proved that the well-known Internet congestion control algorithms may no longer be stable for the common pricing schemes, unless a sufficient condition is satisfied. It is also shown that these algorithms are guaranteed to be stable if a new pricing mechanism is used.

Electrical Power Networks: Optimal power flow (OPF) has been one of the most studied problems for power systems since its introduction by Carpentier in 1962. This problem is concerned with finding an optimal operating point of a power network minimizing the total power generation cost subject to network and physical constraints. It is well known that OPF is computationally hard to solve due to the nonlinear interrelation among the optimization variables. The objective is to identify a large class of networks over which every OPF problem can be solved in polynomial time. To this end, a convex relaxation is proposed, which solves the OPF problem exactly for every radial network and every meshed network with a sufficient number of phase shifters, provided power over-delivery is allowed. The concept of “power over-delivery” is equivalent to relaxing the power balance equations to inequality constraints.

Flow Networks: In this part of the dissertation, the minimum-cost flow problem over an arbitrary flow network is considered. In this problem, each node is associated with some possibly unknown injection, each line has two unknown flows at its ends related to each other via a nonlinear function, and all injections and flows need to satisfy certain box constraints. This problem, named generalized network flow (GNF), is highly non-convex due to its nonlinear equality constraints. Under the assumption of monotonicity and convexity of the flow and cost functions, a convex relaxation is proposed, which always finds the optimal injections. A primary application of this work is in the OPF problem. The results of this work on GNF prove that the relaxation on power balance equations (i.e., load over-delivery) is not needed in practice under a very mild angle assumption.

Generalized Weighted Graphs: Motivated by power optimizations, this part aims to find a global optimization technique for a nonlinear optimization defined over a generalized weighted graph. Every edge of this type of graph is associated with a weight set corresponding to the known parameters of the optimization (e.g., the coefficients). The motivation behind this problem is to investigate how the (hidden) structure of a given real/complex valued optimization makes the problem easy to solve, and indeed the generalized weighted graph is introduced to capture the structure of an optimization. Various sufficient conditions are derived, which relate the polynomial-time solvability of different classes of optimization problems to weak properties of the generalized weighted graph such as its topology and the sign definiteness of its weight sets. As an application, it is proved that a broad class of real and complex optimizations over power networks are polynomial-time solvable due to the passivity of transmission lines and transformers.

Design, specification, and synthesis of aircraft electric power systems control logic

Cyber-physical systems integrate computation, networking, and physical processes. Substantial research challenges exist in the design and verification of such large-scale, distributed sensing, ac- tuation, and control systems. Rapidly improving technology and recent advances in control theory, networked systems, and computer science give us the opportunity to drastically improve our approach to integrated flow of information and cooperative behavior. Current systems rely on text-based spec- ifications and manual design. Using new technology advances, we can create easier, more efficient, and cheaper ways of developing these control systems. This thesis will focus on design considera- tions for system topologies, ways to formally and automatically specify requirements, and methods to synthesize reactive control protocols, all within the context of an aircraft electric power system as a representative application area.

This thesis consists of three complementary parts: synthesis, specification, and design. The first section focuses on the synthesis of central and distributed reactive controllers for an aircraft elec- tric power system. This approach incorporates methodologies from computer science and control. The resulting controllers are correct by construction with respect to system requirements, which are formulated using the specification language of linear temporal logic (LTL). The second section addresses how to formally specify requirements and introduces a domain-specific language for electric power systems. A software tool automatically converts high-level requirements into LTL and synthesizes a controller.

The final sections focus on design space exploration. A design methodology is proposed that uses mixed-integer linear programming to obtain candidate topologies, which are then used to synthesize controllers. The discrete-time control logic is then verified in real-time by two methods: hardware and simulation. Finally, the problem of partial observability and dynamic state estimation is ex- plored. Given a set placement of sensors on an electric power system, measurements from these sensors can be used in conjunction with control logic to infer the state of the system.

Influence of composition on the structure, electric and magnetic properties of Pd-Mn-P and Pd-Co-P amorphous alloys

The influence of composition on the structure and on the electric and magnetic properties of amorphous Pd-Mn-P and Pd-Co-P prepared by rapid quenching techniques were investigated in terms of (1) the 3d band filling of the first transition metal group, (2) the phosphorus concentration effect which acts as an electron donor and (3) the transition metal concentration.

The structure is essentially characterized by a set of polyhedra subunits essentially inverse to the packing of hard spheres in real space. Examination of computer generated distribution functions using Monte Carlo random statistical distribution of these polyhedra entities demonstrated tile reproducibility of the experimentally calculated atomic distribution function. As a result, several possible "structural parameters" are proposed such as: the number of nearest neighbors, the metal-to-metal distance, the degree of short-range order and the affinity between metal-metal and metal-metalloid. It is shown that the degree of disorder increases from Ni to Mn. Similar behavior is observed with increase in the phosphorus concentration.

The magnetic properties of Pd-Co-P alloys show that they are ferromagnetic with a Curie temperature between 272 and 399°K as the cobalt concentration increases from 15 to 50 at.%. Below 20 at.% Co the short-range exchange interactions which produce the ferromagnetism are unable to establish a long-range magnetic order and a peak in the magnetization shows up at the lowest temperature range . The electric resistivity measurements were performed from liquid helium temperatures up to the vicinity of the melting point (900°K). The thermomagnetic analysis was carried out under an applied field of 6.0 kOe. The electrical resistivity of Pd-Co-P shows the coexistence of a Kondo-like minimum with ferromagnetism. The minimum becomes less important as the transition metal concentration increases and the coefficients of ℓn T and T^2 become smaller and strongly temperature dependent. The negative magnetoresistivity is a strong indication of the existence of localized moment.

The temperature coefficient of resistivity which is positive for Pd- Fe-P, Pd-Ni-P, and Pd-Co-P becomes negative for Pd-Mn-P. It is possible to account for the negative temperature dependence by the localized spin fluctuation model and the high density of states at the Fermi energy which becomes maximum between Mn and Cr. The magnetization curves for Pd-Mn-P are typical of those resulting from the interplay of different exchange forces. The established relationship between susceptibility and resistivity confirms the localized spin fluctuation model. The magnetoresistivity of Pd-Mn-P could be interpreted in tenns of a short-range magnetic ordering that could arise from the Rudennan-Kittel type interactions.

Radiation from a short electric dipole antenna in a hot uniaxial plasma

The effects of electron temperature on the radiation fields and the resistance of a short dipole antenna embedded in a uniaxial plasma have been studied. It is found that for ω < ω_p the antenna excites two waves, a slow wave and a fast wave. These waves propagate only within a cone whose axis is parallel to the biasing magnetostatic field B_o and whose semicone angle is slightly less than sin ^(-1) (ω/ω_p). In the case of ω > ω_p the antenna excites two separate modes of radiation. One of the modes is the electromagnetic mode, while the other mode is of hot plasma origin. A characteristic interference structure is noted in the angular distribution of the field. The far fields are evaluated by asymptotic methods, while the near fields are calculated numerically. The effects of antenna length ℓ, electron thermal speed, collisional and Landau damping on the near field patterns have been studied.

The input and the radiation resistances are calculated and are shown to remain finite for nonzero electron thermal velocities. The effect of Landau damping and the antenna length on the input and radiation resistances has been considered.

The radiation condition for solving Maxwell's equations is discussed and the phase and group velocities for propagation given. It is found that for ω < ω_p in the radial direction (cylindrical coordinates) the power flow is in the opposite direction to that of the phase propagation. For ω > ω_p the hot plasma mode has similar characteristics.

Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

A study of the proposed Diamond Creek Reservoir

Politically the Colorado river is an interstate as well as an international stream. Physically the basin divides itself distinctly into three sections. The upper section from head waters to the mouth of San Juan comprises about 40 percent of the total of the basin and affords about 87 percent of the total runoff, or an average of about 15 000 000 acre feet per annum. High mountains and cold weather are found in this section. The middle section from the mouth of San Juan to the mouth of the Williams comprises about 35 percent of the total area of the basin and supplies about 7 percent of the annual runoff. Narrow canyons and mild weather prevail in this section. The lower third of the basin is composed of mainly hot arid plains of low altitude. It comprises some 25 percent of the total area of the basin and furnishes about 6 percent of the average annual runoff.

The proposed Diamond Creek reservoir is located in the middle section and is wholly within the boundary of Arizona. The site is at the mouth of Diamond Creek and is only 16 m. from Beach Spring, a station on the Santa Fe railroad. It is solely a power project with a limited storage capacity. The dam which creats the reservoir is of the gravity type to be constructed across the river. The walls and foundation are of granite. For a dam of 290 feet in height, the back water will be about 25 m. up the river.

The power house will be placed right below the dam perpendicular to the axis of the river. It is entirely a concrete structure. The power installation would consist of eighteen 37 500 H.P. vertical, variable head turbines, directly connected to 28 000 kwa. 110 000 v. 3 phase, 60 cycle generators with necessary switching and auxiliary apparatus. Each unit is to be fed by a separate penstock wholly embedded into the masonry.

Concerning the power market, the main electric transmission lines would extend to Prescott, Phoenix, Mesa, Florence etc. The mining regions of the mountains of Arizona would be the most adequate market. The demand of power in the above named places might not be large at present. It will, from the observation of the writer, rapidly increase with the wonderful advancement of all kinds of industrial development.

All these things being comparatively feasible, there is one difficult problem: that is the silt. At the Diamond Creek dam site the average annual silt discharge is about 82 650 acre feet. The geographical conditions, however, will not permit silt deposites right in the reservoir. So this design will be made under the assumption given in Section 4.

The silt condition and the change of lower course of the Colorado are much like those of the Yellow River in China. But one thing is different. On the Colorado most of the canyon walls are of granite, while those on the Yellow are of alluvial loess: so it is very hard, if not impossible, to get a favorable dam site on the lower part. As a visitor to this country, I should like to see the full development of the Colorado: but how about THE YELLOW!

A comparison of the costs of operation of the motor bus, Birney safety car, and trolley bus on the local transportation routes in Pasadena

With the installation by the Pacific Electric Railway of a bus system in Pasadena to supplant most of its trolley lines, the problem of the comparison of the costs of the two systems naturally presented itself. The study here undertaken was originally started as just a comparison of the motor bus and Birney Safety Car, but as the work progressed it seemed advisable to include the trolley bus as well - a method of transportation that is comparatively new as far as development is concerned, but which seems to be finding increasing favor in the East.

Part I. Electric birefringence studies of deoxyribonucleic acids. Part II. Selective dissociation of nucleohistone complexes

Part I

The electric birefringence of dilute DNA solutions has been studied in considerable detail and on a large number of samples, but no new and reliable information was discovered concerning the tertiary structure of DNA. The large number of variables which effect the birefringence results is discussed and suggestions are made for further work on the subject.

The DNA molecules have been aligned in a rapidly alternating (10 to 20 kc/sec) square wave field confirming that the orientation mechanism is that of counterion polarization. A simple empirical relation between the steady state birefringence, Δn_st, and the square of the electric field, E, has been found: Δn_st = E²/(a E² + b), where a = 1/Δn_s and b = (E²/Δn_st)_E→o. Δn_s is the birefringence extrapolated to infinite field strength.

The molecules show a distribution of relaxation times from 10^-4 to 0.2 sec, which is consistent with expectations for flexible coil molecules. The birefringence and the relaxation times decrease with increasing salt concentrations. They also depend on the field strength and pulse duration in a rather non-reproducible manner, which may be due in part to changes in the composition of the solution or in the molecular structure of the DNA (other than denaturation). Further progress depends on the development of some control over these effects.

Part II

The specificity of the dissociation of reconstituted and native deoxyribonucleohistones (DNH) by monovalent salt solutions has been investigated. A novel zone ultracentrifugation method is used in which the DNH is sedimented as a zone through a preformed salt gradient, superimposed on a stabilizing D₂O (sucrose) density gradient. The results, obtained by scanning the quartz sedimentation tubes in a spectrophotometer, were verified by the conventional, preparative sedimentation technique. Procedures are discussed for the detection of microgram quantities of histones, since low concentrations must be used to prevent excessive aggregation of the DNH.

The data show that major histone fractions are selectively dissociated from DNH by increasing salt concentrations: Lysine rich histone (H I) dissociates gradually between 0.1 and 0.3 F, slightly lysine rich histone (H II) dissociates as a narrow band between 0.35 and 0.5 F, and arginine rich histone (H III, H IV) dissociates gradually above 0.5 F NaClO₄.

The activity of the partially dissociated, native DNH in sustaining RNA synthesis, their mobility and their unusual heat denaturation and renaturation behavior are described. The two-step melting behavior of the material indicates that the histones are non-randomly distributed along the DNA, but the implications are that the uncovered regions are not of gene-size length.

Anomalous electric dipole internal conversion

Electric dipole internal conversion has been experimentally studied for several nuclei in the rare earth region. Anomalies in the conversion process have been interpreted in terms of nuclear structure effects. It was found that all the experimental results could be interpreted in terms of the j ∙ r type of penetration matrix element; the j ∙ ∇ type of penetration matrix element was not important. The ratio λ of the El j ∙ r penetration matrix element to the El gamma-ray matrix element was determined from the experiments to be:

Lu¹⁷⁵,396 keV, λ = - 1000 ± 100;

282 keV, λ = 500 ± 100;

144 keV, λ = 500 ± 250;

Hf¹⁷⁷, 321 keV λ = - 1400 ± 200;

208 keV λ = - 90 ± 40;

72 keV |λ| ≤ 650;

Gd¹⁵⁵, 86 keV λ = - 150 ± 100;

Tm¹⁶⁹, 63 keV λ = - 100 ± 100;

W¹⁸², 152 keV, λ = - 160 ±80;

67 keV, λ = - 100 ± 100.

Predictions for λ are made using the unified nuclear model.

I. Electronic processes in α-sulfur. II. Polaron motion in a D.C. electric field

Part I: The mobilities of photo-generated electrons and holes in orthorhombic sulfur are determined by drift mobility techniques. At room temperature electron mobilities between 0.4 cm²/V-sec and 4.8 cm²/V-sec and hole mobilities of about 5.0 cm²/V-sec are reported. The temperature dependence of the electron mobility is attributed to a level of traps whose effective depth is about 0.12 eV. This value is further supported by both the voltage dependence of the space-charge-limited, D.C. photocurrents and the photocurrent versus photon energy measurements.

As the field is increased from 10 kV/cm to 30 kV/cm a second mechanism for electron transport becomes appreciable and eventually dominates. Evidence that this is due to impurity band conduction at an appreciably lower mobility (4.10^-4 cm²/V-sec) is presented. No low mobility hole current could be detected. When fields exceeding 30 kV/cm for electron transport and 35 kV/cm for hole transport are applied, avalanche phenomena are observed. The results obtained are consistent with recent energy gap studies in sulfur.

The theory of the transport of photo-generated carriers is modified to include the case of appreciable thermos-regeneration from the traps in one transit time.

Part II: An explicit formula for the electric field E necessary to accelerate an electron to a steady-state velocity v in a polarizable crystal at arbitrary temperature is determined via two methods utilizing Feynman Path Integrals. No approximation is made regarding the magnitude of the velocity or the strength of the field. However, the actual electron-lattice Coulombic interaction is approximated by a distribution of harmonic oscillator potentials. One may be able to find the “best possible” distribution of oscillators using a variational principle, but we have not been able to find the expected criterion. However, our result is relatively insensitive to the actual distribution of oscillators used, and our E-v relationship exhibits the physical behavior expected for the polaron. Threshold fields for ejecting the electron for the polaron state are calculated for several substances using numerical results for a simple oscillator distribution.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.