A molecular dynamics study of the microscopic properties of simple dense fluids

The microscopic properties of a two-dimensional model dense fluid of Lennard-Jones disks have been studied using the so-called "molecular dynamics" method. Analyses of the computer-generated simulation data in terms of "conventional" thermodynamic and distribution functions verify the physical validity of the model and the simulation technique.

The radial distribution functions g(r) computed from the simulation data exhibit several subsidiary features rather similar to those appearing in some of the g(r) functions obtained by X-ray and thermal neutron diffraction measurements on real simple liquids. In the case of the model fluid, these "anomalous" features are thought to reflect the existence of two or more alternative configurations for local ordering.

Graphical display techniques have been used extensively to provide some intuitive insight into the various microscopic phenomena occurring in the model. For example, "snapshots" of the instantaneous system configurations for different times show that the "excess" area allotted to the fluid is collected into relatively large, irregular, and surprisingly persistent "holes". Plots of the particle trajectories over intervals of 2.0 to 6.0 x 10^-12 sec indicate that the mechanism for diffusion in the dense model fluid is "cooperative" in nature, and that extensive diffusive migration is generally restricted to groups of particles in the vicinity of a hole.

A quantitative analysis of diffusion in the model fluid shows that the cooperative mechanism is not inconsistent with the statistical predictions of existing theories of singlet, or self-diffusion in liquids. The relative diffusion of proximate particles is, however, found to be retarded by short-range dynamic correlations associated with the cooperative mechanism--a result of some importance from the standpoint of bimolecular reaction kinetics in solution.

A new, semi-empirical treatment for relative diffusion in liquids is developed, and is shown to reproduce the relative diffusion phenomena observed in the model fluid quite accurately. When incorporated into the standard Smoluchowski theory of diffusion-controlled reaction kinetics, the more exact treatment of relative diffusion is found to lower the predicted rate of reaction appreciably.

Finally, an entirely new approach to an understanding of the liquid state is suggested. Our experience in dealing with the simulation data--and especially, graphical displays of the simulation data--has led us to conclude that many of the more frustrating scientific problems involving the liquid state would be simplified considerably, were it possible to describe the microscopic structures characteristic of liquids in a concise and precise manner. To this end, we propose that the development of a formal language of partially-ordered structures be investigated.

Lattice anomalies and magnetic states in Fe_5Si_3-Mn_5Si_3 alloys

The lattice anomalies and magnetic states in the (Fe_100-xMn_x)₅Si₃ alloys have been investigated. Contrary to what was previously reported, results of x-ray diffraction show a second phase (α') present in Fe-rich alloys and therefore strictly speaking a complete solid solution does not exist. Mössbauer spectra, measured as a function of composition and temperature, indicate the presence of two inequivalent sites, namely 6(g) site (designated as site I) and 4(d) (site II). A two-site model (TSM) has been introduced to interpret the experimental findings. The compositional variation of lattice parameters a and c, determined from the x-ray analysis, exhibits anomalies at x = 22.5 and x = 50, respectively. The former can be attributed to the effect of a ferromagnetic transition; while the latter is due to the effect of preferential substitution between Fe and Mn atoms according to TSM.

The reduced magnetization of these alloys deduced from magnetic hyperfine splittings has been correlated with the magnetic transition temperatures in terms of the molecular field theory. It has been found from both the Mössbauer effect and magnetization measurements that for composition 0 ≤ x ˂ 50 both sites I and II are ferromagnetic at liquid-nitrogen temperature and possess moments parallel to each other. In the composition range 50 ˂ x ≤ 100 , the site II is antiferromagnetic whereas site I is paramagnetic even at a temperature below the bulk Néel temperatures. In the vicinity of x = 50 however, site II is in a state of transition between ferromagnetism and antiferromagnetism. The present study also suggests that only Mn in site II are responsible for the antiferromagnetism in Mn₅Si₃ contrary to a previous report.

Electrical resistance has also been measured as a function of temperature and composition. The resistive anomalies observed in the Mn-rich alloys are believed to result from the effect of the antiferromagnetic Brillouin zone on the mobility of conduction electrons.

Tsunamis - a model of their generation and propagation

A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered.

An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model.

Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of non-linear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation.

A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation.

An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally.

The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.

Properties of α-monoclinic selenium

The growth of bulky and platelet shaped α-monoclinic crystals is discussed. A simple method is devised for identifying and orienting them.

The density, previously in disagreement with the value calculated from x-ray studies, is carefully redetermined, and found to be in good agreement with the latter.

The relative dielectric constant is determined, an effort being made to eliminate errors inherent in previous measurements, which have not been in agreement. A two parameter model is derived which explains the anisotropy in the relative dielectric constant of orthorhombic sulfur, which is also composed of 8-atom puckered ring molecules. The model works less well for α-monoclinic selenium. The relative dielectric constant anisotropy is quite noticeable, being 6.06 along the crystal b axis, and 8.52-8.93 normal to the axis.

Thin crystal platelets of α-monoclinic selenium (less than 1µ thick) are used to extend optical transmission measurements up to 4.5eV. Previously the measurements extended up to 2.1 eV, limited by the thickness of the available crystals. The absorption edge is at 2.20 eV, with changes in slope of the absorption coefficient occurring at 2.85 eV and 3.8 eV. Measurement of transmission through solutions of selenium in CS_2 and trichlorethylene yield an absorption edge of 2.75 eV. There is evidence the selenium exists in solution partly as Se_8 rings, the building block of monoclinic selenium. Transmission is measured at low temperatures (80°K and 10°K) using the platelets. The absorption edge is at 2.38 eV and 2.39 eV, respectively, for the two temperatures. Measurements at low temperatures with polarized and unpolarized light reveal interesting absorption anisotropy near 2.65 eV.

The Regulation of Sleep and Circadian Rhythms: The Role of Melatonin and Adenosine in Zebrafish

Sleep is a highly conserved behavioral state whose regulation is still unclear. In this thesis I initially briefly introduce the known sleep circuitry and regulation in vertebrates, and why zebrafish is seen as a good model to study sleep-regulation. I describe the existing two-process model of sleep regulation, which posits that the two processes C (circadian) and S (homeostatic) control timing of sleep-wake behavior. I then study the role melatonin plays in the circadian regulation of sleep using zebrafish. Firstly, we find that the absence of melatonin results in a reduction of sleep at night, establishing that endogenous melatonin is required for sleep at night. Secondly, melatonin mutants show a reduction in sleep in animals with no functional behavioral rhythms suggesting that melatonin does not require intact circadian rhythms for its effect on sleep. Thirdly, melatonin mutants do not exhibit any changes in circadian rhythms, suggesting that the circadian clock does not require melatonin for its function. Fourthly, we find that in the absence of melatonin, there is no rhythmic expression of sleep, suggesting that melatonin is the output molecule of process C. Lastly, we describe a connection between adenosine signaling (output molecules of process S), and melatonin. Following this we proceed to study the role adenosine signaling plays in sleep-wake behavior. We find that firstly, adenosine receptor A1 and A2 are involved in sleep- wake behavior in zebrafish, based on agonist/antagonist behavioral results. Secondly, we find that several brain regions such as PACAP cells in the rostral midbrain, GABAergic cells in the forebrain and hindbrain, Dopamine and serotonin cells in the caudal hypothalamus and sox2 cells lining the hindbrain ventricle are activated in response to the A1 antagonist and VMAT positive cells are activated in response to the A2A agonist, suggesting these areas are involved in adenosine signaling in zebrafish. Thirdly, we find that knocking out the zebrafish adenosine receptors has no effect on sleep architecture. Lastly, we find that while the A1 agonist phenotype requires the zfAdora1a receptor, the antagonist and the A2A agonist behavioral phenotypes are not mediated by the zfAdora1a, zfAdora1b and zfAdoraA2Aa, zfAdora2Ab receptors respectively.

Circadian clock mutants of Drosophila melanogaster

Three mutants of Drosophila melanogaster have been isolated in which the free-running period of the circadian eclosion rhythm and the adult locomotor activity rhythm is affected. One mutant is arrhythmic, another has a short period of 19 hours, and the third has a long period of 28 hours. The mutants retain their phenotypes over the temperature range 18° to 25° C. All three mutants map near the tip of the X chromosome (distal to the centromere). By deficiency mapping, the short-period mutation has been localized to the 3B1-2 region. Complementation tests show that all three mutations affect the same functional gene.

Analysis of activity rhythms of individual mosaic flies indicates that the site of action of the short-period mutation is probably located in the head of the fly. A few activity patterns of split-head and mixed-head mosaics appear to possess both mutant and heterozygous components, suggesting that the fly head may contain two complete clocks capable of maintaining their periodicities independently.

The short-period mutation affects both the duration of the light-insensitive part of the oscillation and the degree to which the clock can be reset during the light-sensitive part of the oscillation.

Both the short-period and long-period mutant eclosion rhythms can be entrained to a period of 24 hours by a 12:12 light-dark cycle having a light intensity at least two orders of magnitude greater than that required to entrain the normal rhythm. The arrhythmic mutant does not entrain under these conditions. In the presence of a temperature cycle, however, the arrhythmic mutant does entrain, but its rhythm damps out when the temperature cycle is removed.

Evidence is presented that Pittendrigh's two-oscillator model for the clock in D. pseudoobscura applies to D. melanogaster as well. The three clock mutations primarily affect the light- sensitive driving oscillator. The arrhythmic mutation appears to have eliminated the driving oscillator while leaving the temperature-sensitive driven oscillator relatively intact.

Experimental studies of weak superconductivity

Experimental investigations were made of the nature of weak superconductivity in a structure having well-defined, controllable characteristics and geometry. Controlled experiments were made possible by using a thin-film structure which was entirely metallic and consisted of a superconducting film with a localized section that was weak in the sense that its transition temperature was depressed relative to the rest of the film. The depression of transition temperature was brought about by underlaying the superconductor with a normal metal.

The DC and AC electrical characteristics of this structure were studied. It was found that this structure exhibited a non-zero, time-average supercurrent at finite voltage to at least .2 mV, and generated an oscillating electric potential at a frequency given by the Josephson relation. The DC V-I characteristic and the amplitude of the AC oscillation were found to be consistent with a two- fluid (normal current-supercurrent) model of weak super-conductivity based on e thermodynamically irreversible process of repetitive phase-slip, and featuring a periodic time dependence in the amplitude of the superconducting order parameter.

The observed linewidth of the AC oscillation could be accounted for by incorporating Johnson noise in the two-fluid model.

Experimentally it was found that the behavior of a short (length on the order of the coherence distance) weak superconductor could be characterized by its critical current and normal-state resistance, and an empirical expression was obtained for the time dependence of the super-current and voltage.

It was found that the results could not be explained on the basis of the theory of the Josephson junction.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Investigations of charge-carrier dynamics at semiconductor/liquid interfaces

Theoretical and experimental investigations of charge-carrier dynamics at semiconductor/liquid interfaces, specifically with respect to interfacial electron transfer and surface recombination, are presented.

Fermi's golden rule has been used to formulate rate expressions for charge transfer of delocalized carriers in a nondegenerately doped semiconducting electrode to localized, outer-sphere redox acceptors in an electrolyte phase. The treatment allows comparison between charge-transfer kinetic data at metallic, semimetallic, and semiconducting electrodes in terms of parameters such as the electronic coupling to the electrode, the attenuation of coupling with distance into the electrolyte, and the reorganization energy of the charge-transfer event. Within this framework, rate constant values expected at representative semiconducting electrodes have been determined from experimental data for charge transfer at metallic electrodes. The maximum rate constant (i.e., at optimal exoergicity) for outer-sphere processes at semiconducting electrodes is computed to be in the range 10^-17-10^-16 cm⁴ s^-1, which is in excellent agreement with prior theoretical models and experimental results for charge-transfer kinetics at semiconductor/liquid interfaces.

Double-layer corrections have been evaluated for semiconductor electrodes in both depletion and accumulation conditions. In conjuction with the Gouy-Chapman-Stern model, a finite difference approach has been used to calculate potential drops at a representative solid/liquid interface. Under all conditions that were simulated, the correction to the driving force used to evaluate the interfacial rate constant was determined to be less than 2% of the uncorrected interfacial rate constant.

Photoconductivity decay lifetimes have been obtained for Si(111) in contact with solutions of CH₃OH or tetrahydrofuran containing one-electron oxidants. Silicon surfaces in contact with electrolyte solutions having Nernstian redox potentials > 0 V vs. SCE exhibited low effective surface recombination velocities regardless of the different surface chemistries. The formation of an inversion layer, and not a reduced density of electrical trap sites on the surface, is shown to be responsible for the long charge-carrier lifetimes observed for these systems. In addition, a method for preparing an air-stable, low surface recombination velocity Si surface through a two-step, chlorination/alkylation reaction is described.