Ion acceleration in laser-excited plasma wake fields

The dynamics of the plasma ions in the wake fields of short, ultraintense laser pulses in underdense plasmas are investigated analytically and numerically. Owing to the large ion-to-electron mass ratio, the motion of plasma ions in-such wake fields has often been assumed to be neglectable. It is shown that when the laser intensity exceeds 10(20) W/cm(2), the ion motion can no longer be ignored. In this case, ion momentum peaks appear behind the laser pulse, which correspond with the ion density peaks. The laser-excited wake field appears to be effective for ion acceleration, in particular to ions with high-charge numbers. The dependence of ion acceleration on the laser intensity, pulse width, and background plasma density is discussed. (c) 2006 Optical Society of America.

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.

Earthquakes of the Nepal Himalaya : towards a physical model of the seismic cycle

Home to hundreds of millions of souls and land of excessiveness, the Himalaya is also the locus of a unique seismicity whose scope and peculiarities still remain to this day somewhat mysterious. Having claimed the lives of kings, or turned ancient timeworn cities into heaps of rubbles and ruins, earthquakes eerily inhabit Nepalese folk tales with the fatalistic message that nothing lasts forever. From a scientific point of view as much as from a human perspective, solving the mysteries of Himalayan seismicity thus represents a challenge of prime importance. Documenting geodetic strain across the Nepal Himalaya with various GPS and leveling data, we show that unlike other subduction zones that exhibit a heterogeneous and patchy coupling pattern along strike, the last hundred kilometers of the Main Himalayan Thrust fault, or MHT, appear to be uniformly locked, devoid of any of the “creeping barriers” that traditionally ward off the propagation of large events. The approximately 20 mm/yr of reckoned convergence across the Himalaya matching previously established estimates of the secular deformation at the front of the arc, the slip accumulated at depth has to somehow elastically propagate all the way to the surface at some point. And yet, neither large events from the past nor currently recorded microseismicity nearly compensate for the massive moment deficit that quietly builds up under the giant mountains. Along with this large unbalanced moment deficit, the uncommonly homogeneous coupling pattern on the MHT raises the question of whether or not the locked portion of the MHT can rupture all at once in a giant earthquake. Univocally answering this question appears contingent on the still elusive estimate of the magnitude of the largest possible earthquake in the Himalaya, and requires tight constraints on local fault properties. What makes the Himalaya enigmatic also makes it the potential source of an incredible wealth of information, and we exploit some of the oddities of Himalayan seismicity in an effort to improve the understanding of earthquake physics and cipher out the properties of the MHT. Thanks to the Himalaya, the Indo-Gangetic plain is deluged each year under a tremendous amount of water during the annual summer monsoon that collects and bears down on the Indian plate enough to pull it away from the Eurasian plate slightly, temporarily relieving a small portion of the stress mounting on the MHT. As the rainwater evaporates in the dry winter season, the plate rebounds and tension is increased back on the fault. Interestingly, the mild waggle of stress induced by the monsoon rains is about the same size as that from solid-Earth tides which gently tug at the planets solid layers, but whereas changes in earthquake frequency correspond with the annually occurring monsoon, there is no such correlation with Earth tides, which oscillate back-and-forth twice a day. We therefore investigate the general response of the creeping and seismogenic parts of MHT to periodic stresses in order to link these observations to physical parameters. First, the response of the creeping part of the MHT is analyzed with a simple spring-and-slider system bearing rate-strengthening rheology, and we show that at the transition with the locked zone, where the friction becomes near velocity neutral, the response of the slip rate may be amplified at some periods, which values are analytically related to the physical parameters of the problem. Such predictions therefore hold the potential of constraining fault properties on the MHT, but still await observational counterparts to be applied, as nothing indicates that the variations of seismicity rate on the locked part of the MHT are the direct expressions of variations of the slip rate on its creeping part, and no variations of the slip rate have been singled out from the GPS measurements to this day. When shifting to the locked seismogenic part of the MHT, spring-and-slider models with rate-weakening rheology are insufficient to explain the contrasted responses of the seismicity to the periodic loads that tides and monsoon both place on the MHT. Instead, we resort to numerical simulations using the Boundary Integral CYCLes of Earthquakes algorithm and examine the response of a 2D finite fault embedded with a rate-weakening patch to harmonic stress perturbations of various periods. We show that such simulations are able to reproduce results consistent with a gradual amplification of sensitivity as the perturbing period get larger, up to a critical period corresponding to the characteristic time of evolution of the seismicity in response to a step-like perturbation of stress. This increase of sensitivity was not reproduced by simple 1D-spring-slider systems, probably because of the complexity of the nucleation process, reproduced only by 2D-fault models. When the nucleation zone is close to its critical unstable size, its growth becomes highly sensitive to any external perturbations and the timings of produced events may therefore find themselves highly affected. A fully analytical framework has yet to be developed and further work is needed to fully describe the behavior of the fault in terms of physical parameters, which will likely provide the keys to deduce constitutive properties of the MHT from seismological observations.

Beyond the blur: Construction and characterization of the first autonomous AO system and An AO survey of magnetar proper motions

Adaptive optics (AO) corrects distortions created by atmospheric turbulence and delivers diffraction-limited images on ground-based telescopes. The vastly improved spatial resolution and sensitivity has been utilized for studying everything from the magnetic fields of sunspots upto the internal dynamics of high-redshift galaxies. This thesis about AO science from small and large telescopes is divided into two parts: Robo-AO and magnetar kinematics.

In the first part, I discuss the construction and performance of the world’s first fully autonomous visible light AO system, Robo-AO, at the Palomar 60-inch telescope. Robo-AO operates extremely efficiently with an overhead < 50s, typically observing about 22 targets every hour. We have performed large AO programs observing a total of over 7,500 targets since May 2012. In the visible band, the images have a Strehl ratio of about 10% and achieve a contrast of upto 6 magnitudes at a separation of 1′′. The full-width at half maximum achieved is 110–130 milli-arcsecond. I describe how Robo-AO is used to constrain the evolutionary models of low-mass pre-main-sequence stars by measuring resolved spectral energy distributions of stellar multiples in the visible band, more than doubling the current sample. I conclude this part with a discussion of possible future improvements to the Robo-AO system.

In the second part, I describe a study of magnetar kinematics using high-resolution near-infrared (NIR) AO imaging from the 10-meter Keck II telescope. Measuring the proper motions of five magnetars with a precision of upto 0.7 milli-arcsecond/yr, we have more than tripled the previously known sample of magnetar proper motions and proved that magnetar kinematics are equivalent to those of radio pulsars. We conclusively showed that SGR 1900+14 and SGR 1806-20 were ejected from the stellar clusters with which they were traditionally associated. The inferred kinematic ages of these two magnetars are 6±1.8 kyr and 650±300 yr respectively. These ages are a factor of three to four times greater than their respective characteristic ages. The calculated braking index is close to unity as compared to three for the vacuum dipole model and 2.5-2.8 as measured for young pulsars. I conclude this section by describing a search for NIR counterparts of new magnetars and a future promise of polarimetric investigation of a magnetars’ NIR emission mechanism.

Design of adjustable superresolving filters based on birefringent crystals

A two-mode adjustable superresolving filter based on a birefringent filter is proposed. This kind of filter has superresolution in two modes of adjustment. One is rotation of the binary pupil filter on the optical axis of the system and the other is the tilt of the filter away from the pupil plane on axis parallel or perpendicular to the optical axis of the crystal. The filters act as complex amplitude filters in the former mode, and as pure phase filters in the latter. By analyzing two superresolving parameters, we obtain the optimal design parameters that ensure a large field of view, a large superresolving range, and a high setting accuracy. This kind of filter can provide more flexibility in practical applications. (c) 2006 Optical Society of America.

International Support of Climate Change Policies in Developing Countries: Strategic, Moral and Fairness Aspects

33 p.

Evaluation of Two Alternative Carbon Capture and Storage Technologies: A Stochastic Model

30 p.

Regulation of the fitness of Atlantic salmon (Salmo salar) by intra-specific competition amongst the juveniles

Factors affecting the fitness of juvenile salmon are discussed. Although fitness from the genetic point of view is defined as the relative capacity of carriers of a given genotype to transmit their genes to the gene pool of the following generations, growth and survival of individuals are also components of fitness, and are influenced by responses to competition, which is the major topic of this article including implications for management. In order to better understand the relationships of density-dependent survival in Newfoundland, egg depositions were manipulated experimentally in the Freshwater River. Figures demonstrate the relationship between stock (number of eggs per 100 m2 of river) and recruitment (number of smolts per l00 m2 of Atlantic salmon, and also the percentage survival from egg to smolt stage related to potential egg depositions.

Smooth sets for borel equivalence relations and the covering property for σ-ideals of compact sets

This thesis is divided into three chapters. In the first chapter we study the smooth sets with respect to a Borel equivalence realtion E on a Polish space X. The collection of smooth sets forms σ-ideal. We think of smooth sets as analogs of countable sets and we show that an analog of the perfect set theorem for Σ¹₁ sets holds in the context of smooth sets. We also show that the collection of Σ¹₁ smooth sets is ∏¹₁ on the codes. The analogs of thin sets are called sparse sets. We prove that there is a largest ∏¹₁ sparse set and we give a characterization of it. We show that in L there is a ∏¹₁ sparse set which is not smooth. These results are analogs of the results known for the ideal of countable sets, but it remains open to determine if large cardinal axioms imply that ∏¹₁ sparse sets are smooth. Some more specific results are proved for the case of a countable Borel equivalence relation. We also study I(E), the σ-ideal of closed E-smooth sets. Among other things we prove that E is smooth iff I(E) is Borel.

In chapter 2 we study σ-ideals of compact sets. We are interested in the relationship between some descriptive set theoretic properties like thinness, strong calibration and the covering property. We also study products of σ-ideals from the same point of view. In chapter 3 we show that if a σ-ideal I has the covering property (which is an abstract version of the perfect set theorem for Σ¹₁ sets), then there is a largest ∏¹₁ set in I^int (i.e., every closed subset of it is in I). For σ-ideals on 2^ω we present a characterization of this set in a similar way as for C₁, the largest thin ∏¹₁ set. As a corollary we get that if there are only countable many reals in L, then the covering property holds for Σ¹₂ sets.

Comparison of marketing policies applied by the same company in different countries and analysis of the reasons for the differences

The focus of this project is going to be, as the title indicates, on the comparison of marketing policies applied by the same company in different countries and analysis of the reasons for the differences. In order to do that, I have selected the company Nestlé to analyze the marketing decisions it makes across national boundaries to market the brand of Kit Kat and keep it as a leader snack worldwide. After having analyzed the brand in all continents, I can say the execution of the strategy used by Nestlé with Kit Kat really matches the planning of the strategy which is to think globally and act locally. Nestlé uses global brand identity but, from the internal point of view, it uses local ingredients and gives autonomy to its local branches based in different countries to make pricing and distributions decisions and therefore satisfy different consumers’ needs and preferences in local environments where changes happen very rapidly. The “glocal” approach to marketing is an effective way for Nestlé Kit Kat to stay focused on the consumer in worldwide markets.

Instrumentation for Kinetic-Inductance-Detector-Based Submillimeter Radio Astronomy

A substantial amount of important scientific information is contained within astronomical data at the submillimeter and far-infrared (FIR) wavelengths, including information regarding dusty galaxies, galaxy clusters, and star-forming regions; however, these wavelengths are among the least-explored fields in astronomy because of the technological difficulties involved in such research. Over the past 20 years, considerable efforts have been devoted to developing submillimeter- and millimeter-wavelength astronomical instruments and telescopes.

The number of detectors is an important property of such instruments and is the subject of the current study. Future telescopes will require as many as hundreds of thousands of detectors to meet the necessary requirements in terms of the field of view, scan speed, and resolution. A large pixel count is one benefit of the development of multiplexable detectors that use kinetic inductance detector (KID) technology.

This dissertation presents the development of a KID-based instrument including a portion of the millimeter-wave bandpass filters and all aspects of the readout electronics, which together enabled one of the largest detector counts achieved to date in submillimeter-/millimeter-wavelength imaging arrays: a total of 2304 detectors. The work presented in this dissertation has been implemented in the MUltiwavelength Submillimeter Inductance Camera (MUSIC), a new instrument for the Caltech Submillimeter Observatory (CSO).

Conserved quantities and the formation of black holes in the Brans-Dicke theory of gravitation

In Part I, we construct a symmetric stress-energy-momentum pseudo-tensor for the gravitational fields of Brans-Dicke theory, and use this to establish rigorously conserved integral expressions for energy-momentum Pⁱ and angular momentum J^ik. Application of the two-dimensional surface integrals to the exact static spherical vacuum solution of Brans leads to an identification of our conserved mass with the active gravitational mass. Application to the distant fields of an arbitrary stationary source reveals that Pⁱ and J^ik have the same physical interpretation as in general relativity. For gravitational waves whose wavelength is small on the scale of the background radius of curvature, averaging over several wavelengths in the Brill-Hartle-Isaacson manner produces a stress-energy-momentum tensor for gravitational radiation which may be used to calculate the changes in Pⁱ and J^ik of their source.

In Part II, we develop strong evidence in favor of a conjecture by Penrose--that, in the Brans-Dicke theory, relativistic gravitational collapse in three dimensions produce black holes identical to those of general relativity. After pointing out that any black hole solution of general relativity also satisfies Brans-Dicke theory, we establish the Schwarzschild and Kerr geometries as the only possible spherical and axially symmetric black hole exteriors, respectively. Also, we show that a Schwarzschild geometry is necessarily formed in the collapse of an uncharged sphere.

Appendices discuss relationships among relativistic gravity theories and an example of a theory in which black holes do not exist.

A contribution to the knowledge of the skin albuminose cells of Torpedo ocellata Raf [Riv.Istochim.norm.pat. 8 411-416, 1962]

Glandular cells, other than the mucous cells, have been described in the skin of various groups of fish (Teleosts, Ganoids, Selachii) and they have been called 'albuminose' by various authors. The authors propose to study the albuminose cells in the skin of Torpedo ocellata Raf. from a histochemical point of view. The albuminose cells have a complex morphological structure and a correspondingly complicated histochemical make-up. One must treat them as an example of cell with secretions of a particular type, which must and will be better incorporated when more is known of characteristics existent in other species.

The astrophysics of strongly interacting systems

This thesis presents investigations in four areas of theoretical astrophysics: the production of sterile neutrino dark matter in the early Universe, the evolution of small-scale baryon perturbations during the epoch of cosmological recombination, the effect of primordial magnetic fields on the redshifted 21-cm emission from the pre-reionization era, and the nonlinear stability of tidally deformed neutron stars.

In the first part of the thesis, we study the asymmetry-driven resonant production of 7 keV-scale sterile neutrino dark matter in the primordial Universe at temperatures T >~ 100 MeV. We report final DM phase space densities that are robust to uncertainties in the nature of the quark-hadron transition. We give transfer functions for cosmological density fluctuations that are useful for N-body simulations. We also provide a public code for the production calculation.

In the second part of the thesis, we study the instability of small-scale baryon pressure sound waves during cosmological recombination. We show that for relevant wavenumbers, inhomogenous recombination is driven by the transport of ionizing continuum and Lyman-alpha photons. We find a maximum growth factor less than ≈ 1.2 in 10⁷ random realizations of initial conditions. The low growth factors are due to the relatively short duration of the recombination epoch.

In the third part of the thesis, we propose a method of measuring weak magnetic fields, of order 10^-19 G (or 10^-21 G if scaled to the present day), with large coherence lengths in the inter galactic medium prior to and during the epoch of cosmic reionization. The method utilizes the Larmor precession of spin-polarized neutral hydrogen in the triplet state of the hyperfine transition. We perform detailed calculations of the microphysics behind this effect, and take into account all the processes that affect the hyperfine transition, including radiative decays, collisions, and optical pumping by Lyman-alpha photons.

In the final part of the thesis, we study the non-linear effects of tidal deformations of neutron stars (NS) in a compact binary. We compute the largest three- and four-mode couplings among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We demonstrate the near-exact cancellation of their effects, and resolve the question of the stability of the tidally deformed NS to leading order. This result is significant for the extraction of binary parameters from gravitational wave observations.

A Multiwavelength Study of the Intracluster Medium and the Characterization of the Multiwavelength Sub/millimeter Inductance Camera

The first part of this thesis combines Bolocam observations of the thermal Sunyaev-Zel’dovich (SZ) effect at 140 GHz with X-ray observations from Chandra, strong lensing data from the Hubble Space Telescope (HST), and weak lensing data from HST and Subaru to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive, dynamically relaxed galaxy clusters. For five of the six clusters, the full multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The multiwavelength analysis yields considerably better constraints on the total mass and concentration compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulent and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95% confidence, where r500c refers to radius at which the average enclosed density is 500 times the critical density of the Universe. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for the clusters in this sample.

The second part of this thesis focuses on the characterization of the Multiwavelength Sub/millimeter Inductance Camera (MUSIC), a photometric imaging camera that was commissioned at the Caltech Submillimeter Observatory (CSO) in 2012. MUSIC is designed to have a 14 arcminute, diffraction-limited field of view populated with 576 spatial pixels that are simultaneously sensitive to four bands at 150, 220, 290, and 350 GHz. It is well-suited for studies of dusty star forming galaxies, galaxy clusters via the SZ Effect, and galactic star formation. MUSIC employs a number of novel detector technologies: broadband phased-arrays of slot dipole antennas for beam formation, on-chip lumped element filters for band definition, and Microwave Kinetic Inductance Detectors (MKIDs) for transduction of incoming light to electric signal. MKIDs are superconducting micro-resonators coupled to a feedline. Incoming light breaks apart Cooper pairs in the superconductor, causing a change in the quality factor and frequency of the resonator. This is read out as amplitude and phase modulation of a microwave probe signal centered on the resonant frequency. By tuning each resonator to a slightly different frequency and sending out a superposition of probe signals, hundreds of detectors can be read out on a single feedline. This natural capability for large scale, frequency domain multiplexing combined with relatively simple fabrication makes MKIDs a promising low temperature detector for future kilopixel sub/millimeter instruments. There is also considerable interest in using MKIDs for optical through near-infrared spectrophotometry due to their fast microsecond response time and modest energy resolution. In order to optimize the MKID design to obtain suitable performance for any particular application, it is critical to have a well-understood physical model for the detectors and the sources of noise to which they are susceptible. MUSIC has collected many hours of on-sky data with over 1000 MKIDs. This work studies the performance of the detectors in the context of one such physical model. Chapter 2 describes the theoretical model for the responsivity and noise of MKIDs. Chapter 3 outlines the set of measurements used to calibrate this model for the MUSIC detectors. Chapter 4 presents the resulting estimates of the spectral response, optical efficiency, and on-sky loading. The measured detector response to Uranus is compared to the calibrated model prediction in order to determine how well the model describes the propagation of signal through the full instrument. Chapter 5 examines the noise present in the detector timestreams during recent science observations. Noise due to fluctuations in atmospheric emission dominate at long timescales (less than 0.5 Hz). Fluctuations in the amplitude and phase of the microwave probe signal due to the readout electronics contribute significant 1/f and drift-type noise at shorter timescales. The atmospheric noise is removed by creating a template for the fluctuations in atmospheric emission from weighted averages of the detector timestreams. The electronics noise is removed by using probe signals centered off-resonance to construct templates for the amplitude and phase fluctuations. The algorithms that perform the atmospheric and electronic noise removal are described. After removal, we find good agreement between the observed residual noise and our expectation for intrinsic detector noise over a significant fraction of the signal bandwidth.