Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

The distribution and ages of regional lithologies in the lunar maria

A research program was designed (1) to map regional lithological units of the lunar surface based on measurements of spatial variations in spectral reflectance, and, (2) to establish the sequence of the formation of such lithological units from measurements of the accumulated affects of impacting bodies.

Spectral reflectance data were obtained by scanning luminance variations over the lunar surface at three wavelengths (0.4µ, 0.52µ, and 0.7µ). These luminance measurements were reduced to normalized spectral reflectance values relative to a standard area in More Serenitotis. The spectral type of each lunar area was identified from the shape of its reflectance spectrum. From these data lithological units or regions of constant color were identified. The maria fall into two major spectral classes: circular moria like More Serenitotis contain S-type or red material and thin, irregular, expansive maria like Mare Tranquillitatis contain T-type or blue material. Four distinct subtypes of S-type reflectances and two of T-type reflectances exist. As these six subtypes occur in a number of lunar regions, it is concluded that they represent specific types of material rather than some homologous set of a few end members.

The relative ages or sequence of formation of these more units were established from measurements of the accumulated impacts which have occurred since more formation. A model was developed which relates the integrated flux of particles which hove impacted a surface to the distribution of craters as functions of size and shape. Erosion of craters is caused chiefly by small bodies which produce negligible individual changes in crater shape. Hence the shape of a crater can be used to estimate the total number of small impacts that have occurred since the crater was formed. Relative ages of a surface can then be obtained from measurements of the slopes of the walls of the oldest craters formed on the surface. The results show that different maria and regions within them were emplaced at different times. An approximate absolute time scale was derived from Apollo 11 crystallization ages under an assumption of a constant rote of impacting for the last 4 x 10^9 yrs. Assuming, constant flux, the period of mare formation lasted from over 4 x 10^9 yrs to about 1.5 x 10^9 yrs ago.

A synthesis of the results of relative age measurements and of spectral reflectance mapping shows that (1) the formation of the lunar maria occurred in three stages; material of only one spectral type was deposited in each stage, (2) two distinct kinds of maria exist, each type distinguished by morphology, structure, gravity anomalies, time of formation, and spectral reflectance type, and (3) individual maria have complicated histories; they contain a variety of lithic units emplaced at different times.

Seismic reflection experiments imaging the physical nature of crustal structures in southern California

Seismic reflection methods have been extensively used to probe the Earth's crust and suggest the nature of its formative processes. The analysis of multi-offset seismic reflection data extends the technique from a reconnaissance method to a powerful scientific tool that can be applied to test specific hypotheses. The treatment of reflections at multiple offsets becomes tractable if the assumptions of high-frequency rays are valid for the problem being considered. Their validity can be tested by applying the methods of analysis to full wave synthetics.

Three studies illustrate the application of these principles to investigations of the nature of the crust in southern California. A survey shot by the COCORP consortium in 1977 across the San Andreas fault near Parkfield revealed events in the record sections whose arrival time decreased with offset. The reflectors generating these events are imaged using a multi-offset three-dimensional Kirchhoff migration. Migrations of full wave acoustic synthetics having the same limitations in geometric coverage as the field survey demonstrate the utility of this back projection process for imaging. The migrated depth sections show the locations of the major physical boundaries of the San Andreas fault zone. The zone is bounded on the southwest by a near-vertical fault juxtaposing a Tertiary sedimentary section against uplifted crystalline rocks of the fault zone block. On the northeast, the fault zone is bounded by a fault dipping into the San Andreas, which includes slices of serpentinized ultramafics, intersecting it at 3 km depth. These interpretations can be made despite complications introduced by lateral heterogeneities.

In 1985 the Calcrust consortium designed a survey in the eastern Mojave desert to image structures in both the shallow and the deep crust. Preliminary field experiments showed that the major geophysical acquisition problem to be solved was the poor penetration of seismic energy through a low-velocity surface layer. Its effects could be mitigated through special acquisition and processing techniques. Data obtained from industry showed that quality data could be obtained from areas having a deeper, older sedimentary cover, causing a re-definition of the geologic objectives. Long offset stationary arrays were designed to provide reversed, wider angle coverage of the deep crust over parts of the survey. The preliminary field tests and constant monitoring of data quality and parameter adjustment allowed 108 km of excellent crustal data to be obtained.

This dataset, along with two others from the central and western Mojave, was used to constrain rock properties and the physical condition of the crust. The multi-offset analysis proceeded in two steps. First, an increase in reflection peak frequency with offset is indicative of a thinly layered reflector. The thickness and velocity contrast of the layering can be calculated from the spectral dispersion, to discriminate between structures resulting from broad scale or local effects. Second, the amplitude effects at different offsets of P-P scattering from weak elastic heterogeneities indicate whether the signs of the changes in density, rigidity, and Lame's parameter at the reflector agree or are opposed. The effects of reflection generation and propagation in a heterogeneous, anisotropic crust were contained by the design of the experiment and the simplicity of the observed amplitude and frequency trends. Multi-offset spectra and amplitude trend stacks of the three Mojave Desert datasets suggest that the most reflective structures in the middle crust are strong Poisson's ratio (σ) contrasts. Porous zones or the juxtaposition of units of mutually distant origin are indicated. Heterogeneities in σ increase towards the top of a basal crustal zone at ~22 km depth. The transition to the basal zone and to the mantle include increases in σ. The Moho itself includes ~400 m layering having a velocity higher than that of the uppermost mantle. The Moho maintains the same configuration across the Mojave despite 5 km of crustal thinning near the Colorado River. This indicates that Miocene extension there either thinned just the basal zone, or that the basal zone developed regionally after the extensional event.

The deuteron-deuteron reaction and the stopping cross section of D_2O ice below 600 kev

The energy loss of protons and deuterons in D_2O ice has been measured over the energy range, E_p 18 - 541 kev. The double focusing magnetic spectrometer was used to measure the energy of the particles after they had traversed a known thickness of the ice target. One method of measurement is used to determine relative values of the stopping cross section as a function of energy; another method measures absolute values. The results are in very good agreement with the values calculated from Bethe’s semi-empirical formula. Possible sources of error are considered and the accuracy of the measurements is estimated to be ± 4%.

The D(dp)H^3 cross section has been measured by two methods. For E_D = 200 - 500 kev the spectrometer was used to obtain the momentum spectrum of the protons and tritons. From the yield and stopping cross section the reaction cross section at 90° has been obtained.

For E_D = 35 – 550 kev the proton yield from a thick target was differentiated to obtain the cross section. Both thin and thick target methods were used to measure the yield at each of ten angles. The angular distribution is expressed in terms of a Legendre polynomial expansion. The various sources of experimental error are considered in detail, and the probable error of the cross section measurements is estimated to be ± 5%.

Gene enrichment using antibodies to DNA/RNA hybrids : mapping the ribosomal DNA of slime mold and rat

A novel method for gene enrichment has been developed and applied to mapping the rRNA genes of two eucaryotic organisms. The method makes use of antibodies to DNA/RNA hybrids prepared by injecting rabbits with the synthetic hybrid poly(rA)•poly(dT). Antibodies which cross-react with non-hybrid nucleic acids were removed from the purified IgG fraction by adsorption on columns of DNA-Sepharose, oligo(dT)-cellulose, and poly(rA)-Sepharose. Subsequent purification of the specific DNA/RNA hybrid antibody was carried out on a column of oligo(dT)-cellulose to which poly(rA) was hybridized. Attachment of these antibodies to CNBr-activated Sepharose produced an affinity resin which specifically binds DNA/RNA hybrids.

In order to map the rDNA of the slime mold Dictyostelium discoideum, R-loops were formed using unsheared nuclear DNA and the 178 and 268 rRNAs of this organism. This mixture was passed through a column containing the affinity resin, and bound molecules containing R- loops were eluted by high salt. This purified rDN A was observed directly in the electron microscope. Evidence was obtained that there is a physical end to Dictyostelium rDN A molecules approximately 10 kilobase pairs (kbp) from the region which codes for the 268 rRNA. This finding is consistent with reports of other investigators that the rRNA genes exist as inverse repeats on extra-chromosomal molecules of DNA unattached to the remainder of the nuclear DNA in this organism.

The same general procedure was used to map the rRNA genes of the rat. Molecules of DNA which contained R-loops formed with the 188 and 288 rRNAs were enriched approximately 150- fold from total genomal rat DNA by two cycles of purification on the affinity column. Electron microscopic measurements of these molecules enabled the construction of an R-loop map of rat rDNA. Eleven of the observed molecules contained three or four R-loops or else two R-loops separated by a long spacer. These observations indicated that the rat rRNA genes are arranged as tandem repeats. The mean length of the repeating units was 37.2 kbp with a standard deviation of 1.3 kbp. These eleven molecules may represent repeating units of exactly the same length within the errors of the measurements, although a certain degree of length heterogeneity cannot be ruled out. If significantly shorter or longer repeating units exist, they are probably much less common than the 37.2 kbp unit.

The last section of the thesis describes the production of antibodies to non-histone chromosomal proteins which have been exposed to the ionic detergent sodium dodecyl sulfate (SDS). The presence of low concentrations of SDS did not seem to affect either production of antibodies or their general specificity. Also, a technique is described for the in situ immunofluorescent detection of protein antigens in polyacrylamide gels.

Lock Acquisition and Sensitivity Analysis of Advanced LIGO Interferometers

Laser interferometer gravitational wave observatory (LIGO) consists of two complex large-scale laser interferometers designed for direct detection of gravitational waves from distant astrophysical sources in the frequency range 10Hz - 5kHz. Direct detection of space-time ripples will support Einstein's general theory of relativity and provide invaluable information and new insight into physics of the Universe.

Initial phase of LIGO started in 2002, and since then data was collected during six science runs. Instrument sensitivity was improving from run to run due to the effort of commissioning team. Initial LIGO has reached designed sensitivity during the last science run, which ended in October 2010.

In parallel with commissioning and data analysis with the initial detector, LIGO group worked on research and development of the next generation detectors. Major instrument upgrade from initial to advanced LIGO started in 2010 and lasted till 2014.

This thesis describes results of commissioning work done at LIGO Livingston site from 2013 until 2015 in parallel with and after the installation of the instrument. This thesis also discusses new techniques and tools developed at the 40m prototype including adaptive filtering, estimation of quantization noise in digital filters and design of isolation kits for ground seismometers.

The first part of this thesis is devoted to the description of methods for bringing interferometer to the linear regime when collection of data becomes possible. States of longitudinal and angular controls of interferometer degrees of freedom during lock acquisition process and in low noise configuration are discussed in details.

Once interferometer is locked and transitioned to low noise regime, instrument produces astrophysics data that should be calibrated to units of meters or strain. The second part of this thesis describes online calibration technique set up in both observatories to monitor the quality of the collected data in real time. Sensitivity analysis was done to understand and eliminate noise sources of the instrument.

Coupling of noise sources to gravitational wave channel can be reduced if robust feedforward and optimal feedback control loops are implemented. The last part of this thesis describes static and adaptive feedforward noise cancellation techniques applied to Advanced LIGO interferometers and tested at the 40m prototype. Applications of optimal time domain feedback control techniques and estimators to aLIGO control loops are also discussed.

Commissioning work is still ongoing at the sites. First science run of advanced LIGO is planned for September 2015 and will last for 3-4 months. This run will be followed by a set of small instrument upgrades that will be installed on a time scale of few months. Second science run will start in spring 2016 and last for about 6 months. Since current sensitivity of advanced LIGO is already more than factor of 3 higher compared to initial detectors and keeps improving on a monthly basis, upcoming science runs have a good chance for the first direct detection of gravitational waves.

Geology of the Pacoima Area, Los Angeles County, California

The Pacoima area is located on an isolated hill in the northeast section of the San Fernando, the northeast portion of the Pacoima Quadrangle, Los Angeles County, California. Within it are exposed more than 2300 feet of Tertiary rocks, which comprise three units of Middle Miocene (?) age, and approximately 950 feet of Jurassic (?) granite basement. The formations are characterized by their mode of occurrence, marine and terrestial origin, diverse lithology, and structural features.

The basement complex is composed of intrusive granite, small masses of granodiorite and a granodiorite gneiss with the development of schistosity in sections. During the long period of erosion of the metamorphics, the granitic rocks were exposed and may have provided clastic constituents for the overlying formations.

As a result of rapid sedimentation in a transitional environment, the Middle Miocene Twin Peaks formation was laid down unconformably on the granite. This formation is essentially a large thinning bed of gray to buff pebble and cobble conglomerate grading to coarse yellow sandstone. The contact of conglomerate and granite is characterized by its faulted and depositional nature.

Beds of extrusive andesite, basalt porphyry, compact vesicular amygdaloidal basalts, andesite breccia, interbedded feldspathic sands and clays of terrestial origin, and mudflow breccia comprise the Pacoima formation which overlies the Twin Peaks formation unconformably. A transgressing shallow sea accompanied settling of the region and initiated deposition of fine clastic sediments.

The marine Topanga (?) formation is composed of brown to gray coarse sandstone grading into interbedded buff sandstones and gray shales. Intrusions of rhyolitedacite and ash beds mark continued but sporatic volcanism during this period.

The area mapped represents an arch in the Tertiary sediments. Forces that produced the uplift of the granite structural high created stresses that were relieved by jointing and faulting. Vertical and horizontal movement along these faults has displaced beds, offset contacts and complicated their structure. Uplift and erosion have exposed the present sequence of beds which dip gently to the northeast. The isolated hill is believed to be in an early stage of maturity.

A study of the ^9 Be nucleus

The reaction ⁷Li(³He, p)⁹Be has been used to measure excitations and intrinsic widths of levels in ⁹Be below the ⁷Li + d threshold. Previously unreported levels have been found at excitations of (13.78 ± .03) MeV and (16.671 ± .008) MeV with widths of (590 ± 60) keV and (41 ± 4) keV respectively. Two overlapping levels have been found at (11.81 ± .02) MeV and (11.29 ± .03) MeV with widths of (400 ± 30) keV and (620 ± 70) keV respectively. Branching ratios from ⁹Be levels populated in this reaction to the ground and first excited states of ⁸Be have been measured by observing the associated protons in coincidence with the decay neutrons. Branching ratios were found to be:

Excitation in ⁹Be .... Branching Ratio.......... Final Nucleus.........

(MeV) .......................... (percent) .....................................

.. 2.43 ........................... 7.5 ± 1.5 .............. ⁸Be(g.s.)

.. 3.03 ........................... 87 ± 13......................................

.. 4.65 ........................... 13 ± 4.......................................

.. 6.76 .............................. ≤ 2 ......................................

.. 11.29 ...............................≤ 2 ......................................

.. 11.81 ...............................≤ 3 ......................................

.. 6.76 ........................... .41 ≤ B.R. ≤ .69 ....... ⁸Be(2⁺)

.. 11.29 ........................... 14 ± 4 .......................................

.. 11.81 ........................... 12 ± 4 .......................................

Corresponding reduced widths for neutron emission are calculated and a comparison of the results with the expectations of current nuclear models is made. In particular the measured branching ratio to ⁸Be(g.s.) from ⁹Be(2.43 MeV) corresponds to an f-wave reduced with θ²_f = 2.1 x 10^-2, in units of ħ²/mR², with R = 4.35 fm. A comparison of this value with that predicted by a Nilsson model calculation, in which ⁹Be is taken to be a deformed nucleus, is discussed. The measured value for θ²_f is found to be consistent with that expected on the basis of measured E2-transition rates between rotational levels in ⁹Be.