A trace method for directly synthesizing Liapunov functions of aperiodic systems
Liapunov functions synthesis for aperiodic linear systems by inspecting traces of state matrix and products
Chen, C. F.↗
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Optimal control of aperiodic discrete-time systems.
Optimal control and trajectory optimization in aperiodic discrete time functional systems
APERIODIC FUNCTION↗
Quasicrystal stability and nucleation kinetics from density functional theory
The aperiodic order of quasicrystals bridges the amorphous and crystalline regime, so it has remained unclear whether quasicrystals are metastable or stable phases of matter. Density functional theory is often used to evaluate thermodynamic stability, but quasicrystals are long-range aperiodic and their energies cannot be calculated using conventional ab initio methods. Here, in this work, we perform first-principles calculations on quasicrystal nanoparticles of increasing size, from which we can directly extrapolate their bulk and surface energies. Using this technique, we determine with high confidence that the icosahedral quasicrystals ScZn 7.33 and YbCd 5.7 are ground-state phases, thus revealing that translational symmetry is not a necessary condition for the zero-temperature stability of inorganic solids. Although we found the ScZn 7.33 quasicrystal to be thermodynamically stable, we show on a mixed thermodynamic and kinetic phase diagram that its solidification from the melt is limited by nucleation, which illustrates why even stable materials may be kinetically challenging to grow. Our techniques broadly open the door to first-principles investigations into the structure–bonding–stability relationships of aperiodic materials.
density functional theory↗
Construction of complementary code sequence sets, part 7.1D
A set of code sequences is a complementary code sequence set if the sum of the aperiodic autocorrelation functions for the sequences is zero everywhere except at the origin. A simple construction for sets of complementary code sequences is discussed.
Sarwate, D. V.↗
New Dimensions in the Theory of Excited States and X-ray Spectra (Final Report)
This Final Technical Report briefly summarizes the achievements during the lifetime of our DOE BES grant DE-FG02-97ER45623. The long-term goal of this project has been the development of quantitative theories of the interaction between radiation and matter, with a focus on x-ray spectroscopies. X-ray spectra have long been among the most important probes of atomic-scale structure and properties of matter, ranging from atoms and molecular systems to condensed matter and exotic states. These spectroscopies are widely used in investigations at the major DOE synchrotron x-ray facilities and related centers world-wide. In addition to fundamental theory, a major goal of our project has been the development of computational software that implements the theory for calculations of x-ray spectra of various materials throughout the periodic table. Due to the complex nature of x-ray spectra, quantitative theory is essential for its interpretation. The theory is challenging since it involves excited state electronic structure and many-body correlation effects that go beyond independent particle approximations like DFT or Hartree-Fock. Moreover, the experimental investigations typically involve a broad range of energy, time, and temperature scales, from the UV-Vis to hard x-ray energies of order 10 4 eV, and temperatures T from ambient up to the warm-dense-matter regime where the Fermi energy kBTF is of order a few eV, i.e., temperatures of order 105 Kelvin. This broad range of experimental conditions has fostered many novel theoretical approaches and computational techniques, many of which we have developed systematically over the duration of the grant. In contrast to the traditional wave-function approach of quantum theory and electronic structure methods, our theoretical approach is based on modern Green's function techniques. This approach is better suited for aperiodic structures, excited states, and broad spectral ranges, since it avoids the computational bottlenecks of sum-over-states approaches, as in the Fermi golden rule. This theoretical framework has been incorporated into efficient, user-friendly x-ray spectroscopy software which is now used routinely worldwide to simulate and analyze spectra. These theoretical tools provide an essential complement to synchrotron and next-generation light sources, which are used to investigate complex materials with ever increasing precision. Moreover, the synergism between theory, computation and experiment contributed by our research enhances scientific understanding and creates opportunities for innovations in materials and energy science and in many fields. As documented in this Report, this research grant has been remarkably successful in achieving these goals. In particular, this grant has supported the development of the x-ray spectroscopy software suite known as FEFF (named for an effective scattering amplitude f eff in the theory). The FEFF codes have become one of the premier tools for quantitative simulations of x-ray spectra as documented by many thousands of citations in the Web of Science and Google-Scholar.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The X-ray halo of Cygnus X-1
Four Einstein HRI images of Cygnus X-1 were examined for the presence of a halo due to scattering of X-rays by interstellar grains. The analysis technique exploits the intrinsic aperiodic variability of the source to map the point response function of the optics. A residual, nonvariable component to the surface brightness distribution (comprising approximately more than 12 percent of the source flux) is interpreted as a scattered halo. The halo flux does not reflect the short term time variability of the central source as it is smoothed by differential time delays of order days. The Cygnus X-1 halo is consistent with those of other sources derived in previous studies using different techniques. Comparison is made with a scattering model, and the sensitivity of the halo flux to maximal grain size is demonstrated.
Bode, M. F.↗
Search for scattered X-ray halos around variable sources - The X-ray halo of Cygnus X-1
The results of a program to search for the presence of halos due to X-ray scattering by interstellar grains in the line-of-sight to variable X-ray sources are reported. As part of this program, four Einstein HRI images of Cyg X-1 were examined. The analysis technique exploits the intrinsic aperiodic variability of this source to map the point response function of the optics. Any scattered halo present will not reflect short-term central source time variability, since such variability is smoothed by differential time delays of order days. Thus, a residual, nonvariable component to the surface brightness distribution (comprising about 12 percent or more of the source flux) is interpreted as a scattered halo. The Cyg X-1 halo is consistent with those of other sources found in previous studies using different techniques. Comparison is also made with a scattering model and, despite uncertainties in source spectrum and distance, reasonable agreement with the observatons is found using a standard interstellar grain model. The potential of X-ray scattering as a probe of the properties of interstellar grains is demonstrated.
Bode, M. F.↗
Steady, periodic, and aperiodic atmospheric flows
Atmospheric weather patterns usually occur on scales of a 1000 km or 5000 km and greater, and quasisteady situations can be caused by the appearance of high pressure, blocking zones. Attention is given to the wave-wave interactions and their effects on atmospheric flows on the large scale. The discussion is performed with the beta-plane model for a spherical geometry and a large number of degrees of freedom. The barotropic potential vorticity equation is defined, and discretization of the topography of the sphere results in a spectral truncation with 25 components. The solutions are generated as a function of a forcing and a dissipative parameter. The model yields steady, periodic, and aperiodic solutions, which are shown to be analogous to zonal and blocked atmospheric flows.
Legras, B.↗
Sulfated Zirconium Metal–Organic Frameworks as Well-Defined Supports for Enhancing Organometallic Catalysis
Understanding heterogeneous catalysts is a challenging pursuit due to surface site nonuniformity and aperiodicity in traditionally-used materials. One example is sulfated metal oxides, which function as highly-active catalysts and as supports for organometallic complexes. These applications are due to traits such as acidity, ability to act as a weakly coordinating ligand, and aptitude for promoting transformations via radical cation intermediates. Research is ongoing about the structural features of sulfated metal oxides that imbue the aforementioned properties, such as sulfate geometry and coordination. To better understand these materials, metal–organic frameworks (MOFs) have been targeted as structurally-defined analogs. Composed of inorganic nodes and organic linkers, MOFs possess features such as high porosity and crystallinity, which make them attractive for mechanistic studies of heterogeneous catalysts. In this work, a Zr 6 -based MOF NU-1000 is sulfated and characterized using atomically-precise techniques such as single crystal X-ray diffraction (SCXRD) in addition to diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). Here, the dynamic nature of the sulfate binding motif is found to transition from monodentate, to bidentate, to tridentate depending on the degree of hydration, as supported by density functional theory (DFT) calculations. Heightened Brønsted acidity compared to the parent MOF was observed upon sulfation, and probed through trimethylphosphine oxide (TMPO) physisorption, ammonia sorption, in-situ ammonia DRIFTS, and DFT studies. With the support structure benchmarked, an organoiridium complex was chemisorbed onto the sulfated MOF node and the efficacy of this supported catalyst was demonstrated for stoichiometric and catalytic activation of benzene-d6 and toluene with structure-activity relationships derived.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quasiaperiodic grain boundary phases of Σ5 tilt grain boundaries in refractory metals
We report ground-state structures and phase transitions in Σ5[001] tilt grain boundaries (GBs) in body-centered-cubic (bcc) refractory metals Nb, Ta, Mo, and W. Σ5 tilt GBs have been extensively investigated over the past several decades, with their ground-state structure—composed of kite-shaped structural units—previously thought to be well understood. By performing a rigorous GB structure search that optimizes the number of atoms in the boundary core, we predict different quasiaperiodic “split kite” phases analogous to those previously found in GBs in face-centered-cubic metals. Furthermore, our results suggest that complex aperiodic phases of GBs appear to be a general phenomenon, as validated through density functional theory calculations. Moreover, the atoms in the split kite phase demonstrate distinct collective diffusion dynamics. Phase-contrast image simulations of split kites show better agreement with experimental observations, offering an alternative explanation for previous microscopy results and motivating future atomically resolved imaging of the GB structure.
Body-centered cubic↗
Static aeroelasticity and the flying wing, revisited
The roll dynamic behavior of some wing configurations is examined. Analysis shows that the static divergence instability which occurs for symmetrical or clamped sweptforward wings is modified by roll freedom. The instability found in the present highly idealized analysis is still of an aperiodic nature, but at a speed above the conventional divergence speed. The magnitude of this difference is seen to be a function of the ratio of the wing roll mass moment of inertia to the mass moment of inertia of the wing about the roll axis, and this difference may be quite significant.
Weisshaar, T. A.↗
Chaos in a spatially-developing plane mixing layer
A spatially-developing plane mixing layer was analyzed for chaotic behavior. A direct numerical simulation of the Navier-Stokes equations in a 2-D domain infinite in y and having inflow-outflow boundary conditions in x was used for data. Spectra, correlation dimension and the largest Lyapunov exponent were computed as functions of downstream distance x. When forced at a single (fundamental) frequency with maximum amplitude, the flow is periodic at the inflow but becomes aperiodic with increasing x. The aperiodic behavior is caused by the presence of a noisy subharmonic caused by the feedback between the necessarily nonphysical inflow and outflow boundary conditions. In order to overshadow this noise the flow was also studied with the same fundamental forcing and added random forcing of amplitude upsilon prime sub R/delta U = 0.01 at the inlet. Results were qualitatively the same in both cases: for small x, spectral peaks were sharp and dimension was nearly 1, but as x increased a narrowband spectral peak grew, spectra decayed exponentially at high frequencies and dimension increased to greater than 3. Based on these results, the flow appears to exhibit deterministic chaos. However, at no location was the largest Lyapunov exponent found to be significantly greater than zero.
Broze, J. G.↗
Alpha: A real-time decentralized operating system for mission-oriented system integration and operation
Alpha is a new kind of operating system that is unique in two highly significant ways. First, it is decentralized transparently providing reliable resource management across physically dispersed nodes, so that distributed applications programming can be done largely as though it were centralized. And second, it provides comprehensive, high technology support for real-time system integration and operation, an application area which consists predominately of aperiodic activities having critical time constraints such as deadlines. Alpha is extremely adaptable so that it can be easily optimized for a wide range of problem-specific functionality, performance, and cost. Alpha is the first systems effort of the Archons Project, and the prototype was created at Carnegie-Mellon University directly on modified Sun multiprocessor workstation hardware. It has been demonstrated with a real-time C(sup 2) application. Continuing research is leading to a series of enhanced follow-ons to Alpha; these are portable but initially hosted on Concurrent's MASSCOMP line of multiprocessor products.
Jensen, E. Douglas↗
Ultra Low Power, Radiation Tolerant UHF Radio Technologies for In Situ Communication Applications
For future deep space missions, significant reductions in the mass and power requirements for short-range telecommunication systems will be critical in enabling a wide variety of new mission concepts. These possibilities include penetrators, gliders, miniature rovers, and sensor networks. Under joint funding from NASA's Cross Enterprise and JPL's Telecommunications and Mission technology programs, recent development activity has focused on the design of ultralow mass and power transceiver systems and subsystems suitable for operation in a flight environment. For these efforts, the functionality of the transceiver has been targeted towards a specific Mars communications scenario. However, the overall architecture is well suited to any short or medium range application where a remote probe will aperiodically communicate with a base station, possibly an orbiter, for the eventual purpose of relaying science information back to Earth. In 2001, these sponsors have been augmented with collaborative expertise and funding from JPL's Center for Integrated Space Microsystems in order to migrate existing concepts and designs to a System on a Chip (SOAC) solution. Additional information is contained in the original extended abstract.
Lay, N. E.↗
Toward a quantitative description of solvation structure: a framework for differential solution scattering measurements
Appreciating that the role of the solute–solvent and other outer-sphere interactions is essential for understanding chemistry and chemical dynamics in solution, experimental approaches are needed to address the structural consequences of these interactions, complementing condensed-matter simulations and coarse-grained theories. High-energy X-ray scattering (HEXS) combined with pair distribution function analysis presents the opportunity to probe these structures directly and to develop quantitative, atomistic models of molecular systems in situ in the solution phase. However, at concentrations relevant to solution-phase chemistry, the total scattering signal is dominated by the bulk solvent, prompting researchers to adopt a differential approach to eliminate this unwanted background. Though similar approaches are well established in quantitative structural studies of macromolecules in solution by small- and wide-angle X-ray scattering (SAXS/WAXS), analogous studies in the HEXS regime—where sub-ångström spatial resolution is achieved—remain underdeveloped, in part due to the lack of a rigorous theoretical description of the experiment. To address this, herein we develop a framework for differential solution scattering experiments conducted at high energies, which includes concepts of the solvent-excluded volume introduced to describe SAXS/WAXS data, as well as concepts from the time-resolved X-ray scattering community. Our theory is supported by numerical simulations and experiment and paves the way for establishing quantitative methods to determine the atomic structures of small molecules in solution with resolution approaching that of crystallography.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium
The amorphous iron-germanium system ( a - Fe x Ge 1 - x ) lacks long-range structural order and hence lacks a significant Brillouin zone. The magnetization of a - Fe x Ge 1 - x is well explained by the Stoner model for Fe concentrations x above the onset of magnetic order around x = 0.4 , indicating that the local order of the amorphous structure preserves the spin-split density of states of the Fe- 3 d states sufficiently to polarize the electronic structure despite k being a bad quantum number. Measurements reveal an enhanced anomalous Hall resistivity ρ x y AH relative to crystalline FeGe; this ρ x y AH is compared to density-functional theory calculations of the anomalous Hall conductivity to resolve its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied k states but shown here to be equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of a - Fe x Ge 1 - x ( 0.38 ≤ x ≤ 0.61 ). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to k space. This effect and the accompanying Stoner-like model for the intrinsic anomalous Hall conductivity establish a unified understanding of the underlying physics of the anomalous Hall effect in both crystalline and disordered systems.
36 MATERIALS SCIENCE↗
Investigation of Aperiodic Time Processes with Autocorrelation and Fourier Analysis
Autocorrelation and frequency analyses of a series of aperiodic time events, in particular, filtered noises and sibilant sounds, were made. The position and band width of the frequency ranges are best obtained from the frequency analysis, but the energies contained in the several bands are most easily obtained from the autocorrelation function. The mean number of zero crossings of the time function was determined from the curvature of the latter function in the vicinity of the zero crossing, and also with the aid of a decimal counter. The second method was found to be more exact.
Exner, Marie Luise↗
Fuzzy operators and cyclic behavior in formal neuronal networks
Formal neuronal networks (FNN), which are comprised of threshold gates, make use of the unit step function. It is regarded as a degenerated distribution function (DDF) and will be referred to here as a non-fuzzy threshold operator (nFTO). Special networks of this kind generating long cycles of states are modified by introduction of fuzzy threshold operators (FTO), i.e., non-degenerated distribution functions (nDDF). The cyclic behavior of the new nets is compared with the original ones. The interconnection matrix and threshold values are not modified. It is concluded that the original long cycles change the fixed points and short cycles, and as the computer simulations demonstrate, the aperiodic motion that is associated with chaotic behavior appears. The emergence of the above changes depend on the steepness of the threshold operators.
Labos, E.↗