On the closure and convexity of attainable sets in finite and infinite dimensions.
Closure and convexity of attainable control sets in finite and infinite dimensions, noting Liapunov theorem
OPTIMAL CONTROL↗
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Coupled hydromagnetic wave excitation and ion acceleration upstream of the earth's bow shock
A self-consistent theory is set forth for the excitation of hydromagnetic waves and the acceleration of 'diffuse' ions upstream of the earth's bow shock in the quasi-equilibrium that results when the solar wind velocity and the interplanetary magnetic field are nearly parallel. For the waves, the quasi-equilibrium derives from a balance between excitation by the ions, which stream relative to the solar wind plasma, and convective loss to the magnetosheath. For the diffuse ions, the quasi-equilibrium derives from a balance between injection at the shock front, confinement to the foreshock by pitch angle scattering on the waves, and acceleration by compression at the shock front. It also results from loss to the magnetosheath, loss due to escape upstream of the foreshock, and loss via diffusion perpendicular to the average magnetic field onto field lines that do not connect to the shock front. Diffusion equations describing the ion transport and wave kinetic equations describing the hydromagnetic wave transport are solved self-consistently to give analytical expressions. These describe (1) the differential wave intensity spectrum as a function of frequency and distance from the bow shock and (2) the ion omnidirectional distribution functions and anisotropies as functions of energy and distance from the bow shock.
Lee, M. A.↗
A beam theory for anisotropic materials
Beam theory plays an important role in structural analysis. The basic assumption is that initially plane sections remain plane after deformation, neglecting out-of-plane warpings. Predictions based on these assumptions are accurate for slender, solid, cross-sectional beams made out of isotropic materials. The beam theory derived in this paper from variational principles is based on the sole kinematic assumption that each section is infinitely rigid in its own plane, but free to warp out of plane. After a short review of the Bernoulli and Saint-Venant approaches to beam theory, a set of orthonormal eigenwarpings is derived. Improved solutions can be obtained by expanding the axial displacements or axial stress distribution in series of eigenwarpings and using energy principles to derive the governing equations. The improved Saint-Venant approach leads to fast converging solutions and accurate results are obtained considering only a few eigenwarping terms.
Bauchau, O. A.↗
Porous Media and Mixture Models for Hygrothermal Behavior of Phenolic Composites
Theoretical models are proposed to describe the interaction of water with phenolic polymer. The theoretical models involve the study of the flow of a viscous fluid through a porous media and the thermodynamic theory of mixtures. From the theory, a set of mathematical relations are developed to simulate the effect of water on the thermostructural response of phenolic composites. The expressions are applied to simulate the measured effect of water in a series of experiments conducted on carbon phenolic composites.
Sullivan, Roy M.↗
Accurate Heats of Formation for PHn, PHn+, and PHn-
Accurate heats of formation are computed for PHn and PHn+, for n=1-3, and for PHn-, for n= 1-2. The geometries and vibrational frequencies are determined at the B3LYP level of theory. The energetics are determined at the CCSD(T) level of theory. Basis set limit values are obtained by extrapolation. Spin-orbit effects are taken from experiment. The temperature dependence of the heat of formation, heat capacity, and entropy are computed for the temperature range 300 to 4000 K and fit to a polynomial.
Ricca, Alessandra↗
Heats of Formation for CF(sub n) (n = 1 - 4), CF(sup +, sub n) (n = 1 - 4), and CF(sup -, sub n) (n = 1 - 3)
Accurate heats of formation are computed for CF(sub n) (n = 1 - 4), CF(sup +, sub n) (n = 1 - 4), and CF(sup -, sub n) (n = 1 - 3). The geometries and vibrational frequencies are determined at the B3LYP level of theory. The energetics are determined at the CCSD(T) level of theory. Basis set limit values are obtained by extrapolation. In those cases where the CCSD(T) calculations become prohibitively large, the basis set extrapolation is performed at the MP2 level. The temperature dependence of the heat of formation, heat capacity, and entropy are computed for the temperature range 300 to 4000 K and fit to a polynomial.
Ricca, Alessandra↗
Heats of NF(sub n) (n= 1-3) and NF(sub n)(+)(n = 1-3)
Accurate heats of formation are computed for NF(sub n) and NF(sub n)(+), for n = 1-3. The geometries and the vibrational frequencies are determined at the B3LYP level of theory. The energetics are determined at the CCSD(T) level of theory. Basis set limit values are obtained by extrapolation. In those cases where the CCSD(T) calculations become prohibitively large, the basis set extrapolation is performed at the MP2 level. The temperature dependence of the heat of formation, heat capacity, and entropy are computed for the temperature range 300 to 4000 K and fit to a polynomial.
Ricca, Alessandra↗
The Atomization Energy of Mg4
The atomization energy of Mg4 is determined using the MP2 and CCSD(T) levels of theory. Basis set incompleteness, basis set extrapolation, and core-valence effects are discussed. Our best atomization energy, including the zero-point energy and scalar relativistic effects, is 24.6+/-1.6 kcal per mol. Our computed and extrapolated values are compared with previous results, where it is observed that our extrapolated MP2 value is good agreement with the MP2-R12 value. The CCSD(T) and MP2 core effects are found to have the opposite signs.
Bauschlicher, Charles W., Jr.↗
Confidence set interference with a prior quadratic bound
Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.
Backus, George E.↗
Queuing theory models for computer networks
A set of simple queuing theory models which can model the average response of a network of computers to a given traffic load has been implemented using a spreadsheet. The impact of variations in traffic patterns and intensities, channel capacities, and message protocols can be assessed using them because of the lack of fine detail in the network traffic rates, traffic patterns, and the hardware used to implement the networks. A sample use of the models applied to a realistic problem is included in appendix A. Appendix B provides a glossary of terms used in this paper. This Ames Research Center computer communication network is an evolving network of local area networks (LANs) connected via gateways and high-speed backbone communication channels. Intelligent planning of expansion and improvement requires understanding the behavior of the individual LANs as well as the collection of networks as a whole.
Galant, David C.↗
Kinetic theory of turbulent compressible flows and comparison with classical theory
A complete set of turbulent correlations is given in terms of expansion coefficients in a double series of Hermite polynomials of a two-particle correlation in phase space. Only two of these coefficients, corresponding to Reynolds stress and turbulent heat flux, are shown to appear in gasdynamic equations of turbulence. This is accomplished by incorporating the phase-space correlation in the collision integral of Boltzmann's equation and by deriving generalized Navier-Stokes and Fourier transport relations. In contrast to the classical formalism, the simple expression remains invariant in form whether the flow is compressible or not. Nevertheless, a bilinear transformation of fluctuating quantities shows that the two formalisms are identical with regard to terms of double correlations. The kinetic theory justifies nonexistence of the higher-order correlations characteristic of compressible-turbulence equations in the classical regime.
Tsuge, S.↗
Computational aspects of helicopter trim analysis and damping levels from Floquet theory
Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.
Gaonkar, Gopal H.↗
Thermal relaxation and the complete set of second-order transport coefficients for the unitary Fermi gas from kinetic theory
We compute the complete set of second-order transport coefficients of the unitary Fermi gas, a dilute gas of spin-1/2 particles interacting via an 𝑠 -wave interaction tuned to infinite scattering length. The calculation is based on kinetic theory and the Chapman-Enskog method at second order in the Knudsen expansion. We take into account the exact two-body collision integral. We extend previous results on second-order coefficients related to shear stress by including terms related to heat flow and gradients of the fugacity. We confirm that the thermal relaxation time is given by the simple estimate 𝜏 𝜅 = 𝜅𝑚/(𝑐 𝑃 𝑇) even if the full collision kernel is taken into account. Furthermore, 𝜅 is the thermal conductivity, 𝑚 is the mass of the particles, 𝑐𝑃 is the specific heat at constant pressure, and 𝑇 is the temperature.
Kinetic theory↗
A unified development of several techniques for the representation of random vectors and data sets
Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.
Bundick, W. T.↗
Calculation of Mg(+)-ligand relative binding energies
The calculated relative binding energies of 16 organic molecules to Mg(+) are compared with experimental results where available. The geometries of the ligands and the Mg(+)-ligand complexes arc optimized at the self-consistent field level using a 6-31G* basis set. The Mg(+) binding energies are evaluated using second-order perturbation theory and basis sets of triple-sigma quality augmented with two sets of polarization functions. This level of theory is calibrated against higher levels of theory for selected systems. The computed binding energies are accurate to about 2 kcal/mol.
Partridge, Harry↗
Solving problems by interrogating sets of knowledge systems: Toward a theory of multiple knowledge systems
The main purpose is to develop a theory for multiple knowledge systems. A knowledge system could be a sensor or an expert system, but it must specialize in one feature. The problem is that we have an exhaustive list of possible answers to some query (such as what object is it). By collecting different feature values, in principle, it should be possible to give an answer to the query, or at least narrow down the list. Since a sensor, or for that matter an expert system, does not in most cases yield a precise value for the feature, uncertainty must be built into the model. Also, researchers must have a formal mechanism to be able to put the information together. Researchers chose to use the Dempster-Shafer approach to handle the problems mentioned above. Researchers introduce the concept of a state of recognition and point out that there is a relation between receiving updates and defining a set valued Markov Chain. Also, deciding what the value of the next set valued variable is can be phrased in terms of classical decision making theory such as minimizing the maximum regret. Other related problems are examined.
Dekorvin, Andre↗
Application of vector-valued rational approximations to the matrix eigenvalue problem and connections with Krylov subspace methods
Let F(z) be a vectored-valued function F: C approaches C sup N, which is analytic at z=0 and meromorphic in a neighborhood of z=0, and let its Maclaurin series be given. We use vector-valued rational approximation procedures for F(z) that are based on its Maclaurin series in conjunction with power iterations to develop bona fide generalizations of the power method for an arbitrary N X N matrix that may be diagonalizable or not. These generalizations can be used to obtain simultaneously several of the largest distinct eigenvalues and the corresponding invariant subspaces, and present a detailed convergence theory for them. In addition, it is shown that the generalized power methods of this work are equivalent to some Krylov subspace methods, among them the methods of Arnoldi and Lanczos. Thus, the theory provides a set of completely new results and constructions for these Krylov subspace methods. This theory suggests at the same time a new mode of usage for these Krylov subspace methods that were observed to possess computational advantages over their common mode of usage.
Sidi, Avram↗
Distribution functions of probabilistic automata
Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.
Denotational semantics↗