Richard Bradley - US grants

The principal investigator, together with other researchers at the investigator's home institution, will work in the field of probability theory. In particular, this group will work on limit theorems for sequences of random variable, both when the random variables are independent and when they are dependent.

Electromigration failure of polycrystalline aluminum interconnects is one of the primary failure mechanisms limiting the reliability of integrated circuits. In this research, Monte Carlo simulations and analytical studies will be made of a model of electromigration failure in polycrystalline metal thin films based on percolation theory. The dependence of the average film lifetime and the distributions of lifetimes on the temperature and degree of structural disorder will be investigated. An empirical distribution for the film lifetime which is commonly employed in engineering applications will be compared to the Monte Carlo results, providing a test of this distribution for much lower failure rates than is possible experimentally. A theory of the failure kinetics will be constructed which is based on recent advances in the theory of irreversible processes in random media. As time permits, these ideas will be applied to the related problem of fatigue-induced fracture in inhomogeneous brittle materials. %%% As integrated circuits become smaller and smaller, the problem of how to connect elements within these circuits, and the circuits themselves to the outside world, becomes more critical. As these connections, or interconnects, become smaller, the probability that circuit failure may occur in the interconnect increases. Thus, an understanding of the underlying mechanisms and of the probability for interconnect failure are important for predicting lifetimes of devices. This grant is using an unconventional approach to look at this difficult problem. Percolation theory looks at conducting systems such as interconnects from a general point of view. It is not as concerned about the underlying physical details as with the more global aspects of the problem. The research proposed here will use percolation theory for the first time to try to make predictions of interconnect lifetimes and determine general parameters which affect interconnect failure.

Standard practice in animal communication studies is to define signal units subjectively. In this pilot study, the researchers will explore the feasibility of using recently developed quantitative methods to define objectively the basic signal units (notes) in the vocalizations of a monophyletic group of birds (chickadees). After assessing the performance of the computer- based SIGNAL Sound Analysis System, they will assess intra- population and inter-population variation in several common notes of representative species. They will then define the entire repertoire of a previously unstudied species in a hierarchical manner by examining clusters of similar combinations of note- types. Finally, they will assess the feasibility of using vocal data for phylogenetic reconstruction. If these preliminary studies are favorable, they will propose a follow-up project using these methods to reconstruct the evolution of vocal complexity in chickadees. This study, should it prove generally successful, will clarify hypothesized analogies between human and animal communication systems. For example, human phonemes and animal note-types function similarly as basic units of differentiable sound. Although human and animal communication systems differ quantitatively in the amount of information they can encode, they may have converged evolutionarily on a generally optimal organizational framework founded on a few dozen distinct sounds. This similarity suggests that similar constraints on perceptual processing of sound operate in both systems.

9500307 Bradley Abstract This proposal concerns the study of random sequences and random fields satisfying strong mixing conditions. A random sequence is said to satisfy a "strong mixing condition" if (according to an appropriate criterion) the amount of stochastic "dependence" between the "past" and the "future" becomes uniformly arbitrarily small as the amount of "time" between past and future becomes sufficiently large. For random fields, the notions of "strong mixing" are similar, involving the uniform asymptotic independence between sets of observations as the "distance" between them becomes large. For such random sequences and random fields, both "structural properties" and limit theorems are investigated. In particular, this proposal involves a continuation of some recent work by the principal investigator in which the central limit theorem is proved for a certain class of random fields under strong mixing assumptions considerably weaker than in earlier similar theorems by other researchers. This proposal concerns the study of probabilistic models that involve "weak dependence," in which the "past" and "present" might have considerable influence on the "near future" but much less influence on the "far future." For example, the average annual national unemployment rate is one of many phenomena which appear to fit such a model; the unemployment rate for the year 1995 could presumably have considerable effect on the rate for the year 1996 or 1997 but not much effect on the rate for the year 2050. This proposal involves an investigation into various kinds of "structural properties" of probabilistic models of weak dependence, and also various long-term "laws of averages" that such models might satisfy. In particular, part of this proposal involves a continuation of some recent work by the principal investigator which considerably enlarges the class of weak dependence models that are known to satisfy a certain important law of averages. This proposal also concerns the study of similar types of probabilistic models in which observations are separated by location instead of time.

9703712 Bradley Strong mixing conditions for random sequences and random fields have been useful in modeling phenomena in the real world in which observations that are ``far apart'' in time or location have only slight influence on each other. In this research, several questions are studied in connection with strongly mixing random sequences, and connections with random fields are discussed briefly. Question 1 deals with a possible ``trichotomy'' for the asymptotic behavior of the partial sums from a strictly stationary, strongly mixing sequence of random variables taking their values in a Banach space. Question 2 deals with the exact location of a part of the ``borderline'' of the central limit theorem under the (Rosenblatt) strong mixing condition. Question 3 deals with the spectral density of random sequences under a certain strong mixing condition. Question 4 deals with a possible connection (or lack of one) between two strong mixing conditions; the relevance of this question to an old conjecture of I.A. Ibragimov is discussed. In the real world, there are many phenomena which appear to be ``weakly dependent,'' in the sense that observations that are ``close'' in time or location may have considerable influence on each other, while observations that are ``far apart'' in time or location have only slight influence on each other. For example, the annual unemployment rate for the year 1998 may have considerable influence on the unemployment rates for the years 1999 and 2000, but will presumably have almost no influence on the employment rate in, say, the year 2050. Similarly, the fluctuations in the wind currents at a given location may be highly correlated with the (wind current) fluctuations ten miles away, but perhaps have no discernible correlation with the fluctuations 3000 miles away. For the modeling of such phenomena, much attention has been devoted in probability theory to a broad type of weak dependence known under the name ``stron g mixing conditions.'' An understanding of ``structural'' properties of strong mixing conditions can help in assessing their appropriateness for the modeling of a given real world phenomenon, and ``laws of averages'' connected with such conditions can provide the foundation for the statistical inference for the given phenomenon. This research deals with several questions concerning both ``structural'' properties and ``laws of averages'' in connection with various strong mixing conditions.

9987339
Jeffs

Unwanted radio signals block radio astronomers access to important scientific information about the universe. Man's increasing desire to be connected for communication produces a proliferation of man made RF and microwave sources. Prevention measurements through FCC regulation and ITU agreements are effective, but do not provide a viable final solution to an increasing problem.

This proposal is to develop adaptive algorithms for interference cancellation and to evaluate their ability to remove interference from radio telescopes. In addition a hardware/software prototype system, built on the principles developed in the first part of the proposal will be applied to the real-world problem of removing interference caused by Russian Federation Global Navigation Satellite System (GLONASS). This will be demonstrated without manual demonstration.
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Two radio spectrometers with frequency coverage from 10 to 800 MHz will be constructed and deployed at the National Radio Quite Zone in Green Bank, WV. This effort, (i) develops a basic research tool in solar radio astrophysics for use by the wider community, (ii) remedies the lack of an important component of the United States National Space Weather Program: the need for readily available low-frequency, broadband, radio dynamic spectra in western longitudes, and (iii) provides a platform for research and development work on broadband antennas, feeds, and receivers operating from decimeter to decameter wavelengths. This program has important applications for instrument upgrades as well as future generations of instruments such as the LOw Frequency ARray (LOFAR) and the Frequency Agile Solar Radiotelescope (FASR).

AST-0352705/Jeffs, BYU

The award will support research into the development of radio frequency interference excision techniques for applications in sensitive radio astronomical instrumentation. The work will exploit recent advances in high speed signal processing and microwave technology. The work will extend single-dish real-time excision algorithms to array feeds for medium and large radio telescopes.

This is a collaborative project, lead 0607838/Backer, non-lead 0607759/Bradley.

When the first stars formed from the densest regions of the evolving cosmic structure, their ultraviolet light stimulated hydrogen-line emission from the intergalactic medium. Although theory suggests that this radiation should be measurable, there are many uncertainties about the amplitude, angular structure, and frequency and redshift variation, of the signal. Progress in our understanding of the Epoch of Reionization (EoR) rests on detection and detailed study of this redshifted 21-cm line, and several experiments are planned or under way. This effort starts simple, with phased developments year by year, and is already deploying test elements sensitive in the 120-205 MHz range. An innovative correlator is under construction. The existing emphasis is on array calibration, wide-field imaging, and understanding how to achieve the stability needed for deep integrations. This continuation project will consolidate and expand, including deploying a larger array in Western Australia, where confounding radio frequency interference is minimal. Together, the northern and southern arrays will produce a catalog of the brightest sources at these frequencies in the entire sky, and prove key capabilities aimed at the future Precision Array to Probe the Epoch of Reionization (PAPER), investigating one of the most fascinating times in the Universe.

This project both benefits from, and helps, related projects, including (but not limited to) the Frequency Agile Solar Radiotelescope, the Allen Telescope Array, and the California Array for Millimeter Astronomy. These are contributions to low frequency radio astronomy in general, as well as to solar physics and space weather. The study is also sharply focused around graduate student and postdoc involvement in instrumentation development. PAPER will also be a pioneer in launching a Radio Astronomy Park and radio quiet zone in a unique part of the globe.

The project is continued development of the Precision Array to Probe the Epoch of Reionization, which is a sophisticated radio array designed to measure highly-redshifted spectral lines from neutral hydrogen emanating from one of the earliest epochs of the formation of the universe. This version of the array will be placed at a very remote and radio-quiet location in Western Australia.

This award is for continuation of the development of the Precision Array to Probe the Epoch of Reionization (PAPER). The focus of PAPER is the statistical detection of HI 21-cm signals from the neutral intergalactic medium (IGM) during cosmic reionization, an event corresponding to the transition from a fully neutral IGM to a highly ionized IGM caused by the UV radiation from the first stars and supermassive black holes. Probing this last unexplored phase of cosmic evolution has been called out by the Astro2010 Decade Survey as the primary area with extraordinary discovery potential in the study of cosmic structure formation, and this constitutes the main intellectual impact of this research.

During the previous award period, under AST-0804508 and AST-0804523, PAPER established observing sites with 32 antenna elements at both NRAO Green Bank and in the Karoo Desert of South Africa. The current proposal will expand the SA deployment of PAPER to 128 elements and will support on-going observations and analysis using both the GB and SA deployments.

Broader impacts of the program include advancement of techniques in low frequency radio astronomy, and a strong educational emphasis through training of graduate students and postdocs. The project is a major stepping stone toward a future Hydrogen Epoch of Reionization Array (HERA), as recommended by A2010. PAPER has directed fabrication funds where possible to local small businesses, thus providing economic stimulus in the US. Outreach activities have included a number of public talks on the project by graduate students.

TECHNICAL SUMMARY
The Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and educational activities focused on advancing understanding of how self-assembled nanoscale patterns are produced by bombarding a solid surface with a broad ion beam. The spontaneous emergence of these patterns is not just fascinating in its own right; ion bombardment has the potential to become a cost-effective method to rapidly fabricate large-area nanostructures at length scales beyond the limits of conventional optical lithography. This project will yield insight into how these patterns form, and so will aid in the optimization of this tool.

In the sponsored research, the PIs will pioneer the application of the mathematical theory of pattern formation to the ion bombardment of solids. They will determine whether well-ordered hexagonal arrays of nanodots can be formed by bombarding an elemental solid while concurrently depositing impurities, and develop a theory that explains why nearly regular hexagonal arrays of nanorods form during ion-assisted deposition of some binary materials. Methods that may reduce or prevent the formation of defects in the patterns produced by ion bombardment will be developed and evaluated.

Outreach to K-12 students and the education of undergraduate and graduate students are important aspects of the project. High school students in AP Physics will study a macroscopic analog of pattern formation induced by ion bombardment, patterns formed by sandblasting. Demonstrations of pattern formation will be developed that will be used by Little Shop of Physics, a nationally-recognized outreach program that brings hands-on physics demonstrations to K-12 students and to the general public. The graduate student supported by the award will receive interdisciplinary training in the physics of ion bombardment and the mathematics of pattern formation.

NONTECHNICAL SUMMARY
The Division of Mathematical Sciences and the Division of Materials Research contribute funds to this award. It supports theoretical research and educational activities focused on advancing our understanding of the nanoscale patterns that emerge when a solid surface is bombarded with a broad ion beam. These nanoscale patterns have features on small length scales some million times smaller than the head of a pin. A plethora of patterns can be produced, including nanoscale mounds arranged in hexagonal arrays of remarkable and unforeseen regularity. The spontaneous emergence of these patterns is not just fascinating in its own right: ion bombardment has the potential to become a cost-effective method to rapidly fabricate large-area nanostructures. This project will yield insight into how these patterns form, and so will aid in the optimization of this tool. The sponsored research will therefore contribute to the burgeoning field of nanotechnology, which promises to transform fields as diverse as medicine, energy, and electronics.

Outreach to K-12 student and the education of undergraduate and graduate students are important aspects of the project. High school physics students will study an analog of pattern formation induced by ion bombardment, patterns formed by sandblasting. Demonstrations of pattern formation will be developed that will be used by Little Shop of Physics, a nationally-recognized outreach program that brings hands-on physics demonstrations to K-12 students and to the general public. The graduate student to be supported by the award will receive interdisciplinary training in the physics of ion bombardment and the mathematics of pattern formation.

This project is jointly funded by the Electronic and Photonic Materials Program (EPM) in the Division of Materials Research (DMR), and by the Electronics, Photonics, and Magnetic Devices Program (EPMD) in the Division of Electrical, Communications and Cyber Systems (ECCS).

Nontechnical Description: With wavelengths of tens of nanometers, bright beams of extreme ultraviolet and soft x-ray light in combination with specialized optics are enabling applications such as nano-imaging and the lithography of advanced semiconductor chips. Extreme ultraviolet and soft x-ray applications require optical components, such as mirrors, lenses, and gratings, capable of guiding, focusing, and dispersing or filtering the light, respectively. There are, however, enormous challenges in the engineering of these optical components, from both the materials and design standpoints. In this project, directed ion beams interacting with the sample's surface create periodic patterns with a sawtooth form. By depositing stacks of nanometer-thick metal layers on these surfaces, it is possible to significantly enhance the efficiency of the multilayers and to produce advanced optics such as blazed diffraction gratings. Such gratings can generate highly directional beams that are necessary in important applications such as interference imaging, resonant inelastic x-ray scattering, and spectroscopy. This exciting new line of research offers ample opportunities for graduate and undergraduate students to work on a cutting-edge scientific and technological problem in a truly interdisciplinary environment. The breath of the outreach efforts of this project ensures participation of a diverse group of students at all levels.

Technical Description: "Ion sculpting," i.e., bombarding a solid with a broad ion beam, can produce a remarkable variety of self-assembled nanoscale patterns on a solid surface. This project combines experiments and theoretical investigations with the goal of demonstrating a novel "ion sculpting" method to fabricate multilayer blazed gratings. This method has the potential to produce gratings of unprecedented efficiency for use at extreme ultraviolet and soft x-ray wavelengths. The project encompasses fundamental research aimed at understanding the interaction of highly directional ion beams with surfaces through experiments and modeling. The theoretical work facilitates the optimization of the ion-sculpting process and guides the experiments. State-of-the-art deposition equipment and at-wavelength metrology provide the infrastructure to fabricate and test the multilayer metal-dielectric gratings.

Diverse phenomena in nature and the laboratory give rise to patterns such as ripples, squares, or hexagons. Examples range from laboratory models of climate in which a fluid is heated from below to hexagonal arrays of firing neurons in the region of the brain responsible for spatial memory. Two classes of pattern-forming systems motivate the work of this project. The first involves nanoscale patterns produced by bombarding a solid surface with a broad ion beam. This can produce a wide variety of self-organized nanoscale patterns. The self-assembly of nanoscale patterns that occurs when solids are irradiated is not just fascinating: in the future, ion bombardment may prove to be an important tool in the fabrication of nanostructures. It is widely believed that the burgeoning field of nanotechnology will lead to advances that will transform fields as disparate as energy, electronics, and medicine. The second class of patterns involves color changes in chemical systems in which a vapor reacts with a solid or liquid. For example, a colored pattern may appear in a solution of an important class of plant pigments called anthocyanins as it is exposed to common atmospheric pollutants. These patterns are a part of the sponsored outreach to elementary and high school students. In both of these systems, the patterns vary from highly ordered ripples or lattices with a few defects to patterns so dominated by defects that a lattice structure may not be easily recognized. These defects limit the utility of nanostructures produced by ion bombardment. They are also indicative of the underlying chemical or physical mechanism by which the patterns form, and therefore help the investigators to understand those mechanisms. In this work, the investigators develop mathematical tools to understand the formation of defects. The tools are also applied to help propose experimental methods to eliminate defects in nanopatterns produced by ion bombardment. The tools also provide insight into the mechanisms driving pattern formation. The research involves undergraduate and graduate students in integrated theoretical and experimental work.

Defects are often prevalent in patterns produced in nature and the laboratory, so that the patterns are far from ideal ripples or hexagonal lattices. These defects can be interpreted as data sets that have topological characteristics. In this project, the investigators apply methods of topological data analysis (TDA) to patterns modeled by nonlinear partial differential equations. In particular, the investigators and their colleagues develop methods to quantify the order in a pattern using the output of various TDA methods. Experiments and simulations suggest that long-wavelength deformations (i.e., the zero mode) can play a significant role in the persistence of defects in a developing pattern. The investigators test this hypothesis using a multidimensional extension of TDA methods. The stability of defects is probed by deriving equations for the amplitude and phase of the patterns. Methods of predicting where defects will form as a pattern evolves are developed using TDA. Finally, combining TDA with machine learning tools, the team determines parameters in models of pattern formation from experimental data. The methods are applicable to any pattern-forming system. However, two classes of systems provide focus for this work. The first is the formation of nanoscale patterns when a solid surface is bombarded by a broad ion beam. Using TDA, the investigators determine the nature of the instability that leads to the formation of a hexagonal array of nanodots when the surface of a binary material is bombarded, a subject of considerable debate. The second class is a set of reaction-diffusion systems that we call vaporchromatic experiments. In these experiments, vapor interacts with a solution containing a polymer or pigment that changes color upon interaction with the vapor. The team develops mathematical reaction-diffusion-convection models for the formation of vaporchromatic patterns. The methods of analyzing patterns using TDA are motivated by and tested on patterns produced both by experiments and by numerical simulations of partial differential equation models. Graduate and REU undergraduate students participate in the research.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.