DOE Office of Scientific and Technical Information (OSTI.GOV)

Ming, Xianshun; Liu, Xinyu; Sun, Liqun

We develop the theory of all-dielectric absorbers based on temporal coupled mode theory (TCMT), with parameters extracted from eigenfrequency simulations. An infinite square array of cylindrical resonators embedded in air is investigated, and we find that it supports two eigenmodes of opposite symmetry that are each responsible for half of the total absorption. The even and odd eigenmodes are found to be the hybrid electric (EH111) and hybrid magnetic (HE111) waveguide modes of a dielectric wire of circular cross section, respectively. The geometry of the cylindrical array is shown to be useful for individual tuning of the radiative loss ratesmore » of the eigenmodes, thus permitting frequency degeneracy. Further, by specifying the resonators’ loss tangent, the material loss rate can be made to equal the radiative loss rate, thus achieving a state of degenerate critical coupling and perfect absorption. Our results are supported by S-parameter simulations, and agree well with waveguide theory.« less

Engineered spin-spin interactions on a 2D array of trapped ions

NASA Astrophysics Data System (ADS)

Britton, Joe; Sawyer, Brian; Bollinger, John

2013-05-01

We work with laser cooled 9Be+ ions confined in a Penning trap to simulate quantum magnetic interactions. The valence electron of each ion behaves as an ideal spin- 1 / 2 particle. We recently demonstrated a uniform anti-ferromagnetic Ising interaction on a naturally occurring two-dimensional (2D) triangular crystal of 100 < N < 350 ions. The Ising interaction is generated by a spin-dependent optical dipole force (ODF). For spins separated by distance d, we show that the range can be tuned according to (d / d 0)-a, for 0 < a < 3 . For different operating parameters we can also generate an infinite range ferromagnetic Ising interaction. We also use the ODF for spectroscopy and thermometry of the normal modes of the trapped ion array. A detailed understanding of the modes is important because they mediate the spin-spin interactions. This work is supported by NIST and the DARPA OLE program.

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

Critical phenomena on k -booklets

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2017-01-01

We define a "k -booklet" to be a set of k semi-infinite planes with -∞

Stable Direct Adaptive Control of Linear Infinite-dimensional Systems Using a Command Generator Tracker Approach

NASA Technical Reports Server (NTRS)

Balas, M. J.; Kaufman, H.; Wen, J.

1985-01-01

A command generator tracker approach to model following contol of linear distributed parameter systems (DPS) whose dynamics are described on infinite dimensional Hilbert spaces is presented. This method generates finite dimensional controllers capable of exponentially stable tracking of the reference trajectories when certain ideal trajectories are known to exist for the open loop DPS; we present conditions for the existence of these ideal trajectories. An adaptive version of this type of controller is also presented and shown to achieve (in some cases, asymptotically) stable finite dimensional control of the infinite dimensional DPS.

Quantitative analysis of frequency-domain induced polarization soundings over horizontal beds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patella, D.; Schiavone, D.

1976-06-01

Following up a recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = I - rho/sub infinity//rho/sub dc/ with rho/sub infinity/ the resistivity at infinite frequency, it is shown at first how, through the Laplace transform theory, rho/sub infinity/ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, the integral expression of the apparent resistivity at infinite frequency is derived rho/sub infinity,a/ in the case of a horizontally layered earth. Finally,more » from the definition of the maximum apparent frequency-effect, analytical expressions of fe/sub a/ are obtained for both Schlumberger and dipole arrays placed on the surface of the multi-layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves.« less

Krogh-cylinder and infinite-domain models for washout of an inert diffusible solute from tissue.

PubMed

Secomb, Timothy W

2015-01-01

Models based on the Krogh-cylinder concept are developed to analyze the washout from tissue by blood flow of an inert diffusible solute that permeates blood vessel walls. During the late phase of washout, the outflowing solute concentration decays exponentially with time. This washout decay rate is predicted for a range of conditions. A single capillary is assumed to lie on the axis of a cylindrical tissue region. In the classic "Krogh-cylinder" approach, a no-flux boundary condition is applied on the outside of the cylinder. An alternative "infinite-domain" approach is proposed that allows for solute exchange across the boundary, but with zero net exchange. Both models are analyzed, using finite-element and analytical methods. The washout decay rate depends on blood flow rate, tissue diffusivity and vessel permeability of solute, and assumed boundary conditions. At low blood flow rates, the washout rate can exceed the value for a single well-mixed compartment. The infinite-domain approach predicts slower washout decay rates than the Krogh-cylinder approach. The infinite-domain approach overcomes a significant limitation of the Krogh-cylinder approach, while retaining its simplicity. It provides a basis for developing methods to deduce transport properties of inert solutes from observations of washout decay rates. © 2014 John Wiley & Sons Ltd.

On chemical distances and shape theorems in percolation models with long-range correlations

NASA Astrophysics Data System (ADS)

Drewitz, Alexander; Ráth, Balázs; Sapozhnikov, Artëm

2014-08-01

In this paper, we provide general conditions on a one parameter family of random infinite subsets of {{Z}}^d to contain a unique infinite connected component for which the chemical distances are comparable to the Euclidean distance. In addition, we show that these conditions also imply a shape theorem for the corresponding infinite connected component. By verifying these conditions for specific models, we obtain novel results about the structure of the infinite connected component of the vacant set of random interlacements and the level sets of the Gaussian free field. As a byproduct, we obtain alternative proofs to the corresponding results for random interlacements in the work of Černý and Popov ["On the internal distance in the interlacement set," Electron. J. Probab. 17(29), 1-25 (2012)], and while our main interest is in percolation models with long-range correlations, we also recover results in the spirit of the work of Antal and Pisztora ["On the chemical distance for supercritical Bernoulli percolation," Ann Probab. 24(2), 1036-1048 (1996)] for Bernoulli percolation. Finally, as a corollary, we derive new results about the (chemical) diameter of the largest connected component in the complement of the trace of the random walk on the torus.

A menu-driven software package of Bayesian nonparametric (and parametric) mixed models for regression analysis and density estimation.

PubMed

Karabatsos, George

2017-02-01

Most of applied statistics involves regression analysis of data. In practice, it is important to specify a regression model that has minimal assumptions which are not violated by data, to ensure that statistical inferences from the model are informative and not misleading. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models, constructed from MATLAB Compiler. Currently, this package gives the user a choice from 83 Bayesian models for data analysis. They include 47 Bayesian nonparametric (BNP) infinite-mixture regression models; 5 BNP infinite-mixture models for density estimation; and 31 normal random effects models (HLMs), including normal linear models. Each of the 78 regression models handles either a continuous, binary, or ordinal dependent variable, and can handle multi-level (grouped) data. All 83 Bayesian models can handle the analysis of weighted observations (e.g., for meta-analysis), and the analysis of left-censored, right-censored, and/or interval-censored data. Each BNP infinite-mixture model has a mixture distribution assigned one of various BNP prior distributions, including priors defined by either the Dirichlet process, Pitman-Yor process (including the normalized stable process), beta (two-parameter) process, normalized inverse-Gaussian process, geometric weights prior, dependent Dirichlet process, or the dependent infinite-probits prior. The software user can mouse-click to select a Bayesian model and perform data analysis via Markov chain Monte Carlo (MCMC) sampling. After the sampling completes, the software automatically opens text output that reports MCMC-based estimates of the model's posterior distribution and model predictive fit to the data. Additional text and/or graphical output can be generated by mouse-clicking other menu options. This includes output of MCMC convergence analyses, and estimates of the model's posterior predictive distribution, for selected functionals and values of covariates. The software is illustrated through the BNP regression analysis of real data.

Boundary control for a flexible manipulator based on infinite dimensional disturbance observer

NASA Astrophysics Data System (ADS)

Jiang, Tingting; Liu, Jinkun; He, Wei

2015-07-01

This paper focuses on disturbance observer and boundary control design for the flexible manipulator in presence of both boundary disturbance and spatially distributed disturbance. Taking the infinite-dimensionality of the flexural dynamics into account, this study proposes a partial differential equation (PDE) model. Since the spatially distributed disturbance is infinite dimensional, it cannot be compensated by the typical disturbance observer, which is designed by finite dimensional approach. To estimate the spatially distributed disturbance, we propose a novel infinite dimensional disturbance observer (IDDO). Applying the IDDO as a feedforward compensator, a boundary control scheme is designed to regulate the joint position and eliminate the elastic vibration simultaneously. Theoretical analysis validates the stability of both the proposed disturbance observer and the boundary controller. The performance of the closed-loop system is demonstrated by numerical simulations.

Dynamic Behavior of Engineered Lattice Materials

PubMed Central

Hawreliak, J. A.; Lind, J.; Maddox, B.; Barham, M.; Messner, M.; Barton, N.; Jensen, B. J.; Kumar, M.

2016-01-01

Additive manufacturing (AM) is enabling the fabrication of materials with engineered lattice structures at the micron scale. These mesoscopic structures fall between the length scale associated with the organization of atoms and the scale at which macroscopic structures are constructed. Dynamic compression experiments were performed to study the emergence of behavior owing to the lattice periodicity in AM materials on length scales that approach a single unit cell. For the lattice structures, both bend and stretch dominated, elastic deflection of the structure was observed ahead of the compaction of the lattice, while no elastic deformation was observed to precede the compaction in a stochastic, random structure. The material showed lattice characteristics in the elastic response of the material, while the compaction was consistent with a model for compression of porous media. The experimental observations made on arrays of 4 × 4 × 6 lattice unit cells show excellent agreement with elastic wave velocity calculations for an infinite periodic lattice, as determined by Bloch wave analysis, and finite element simulations. PMID:27321697

Pattern-induced anchoring transitions in nematic liquid crystals

NASA Astrophysics Data System (ADS)

Rojas-Gómez, Óscar A.; Romero-Enrique, José M.; Silvestre, Nuno M.; Telo da Gama, Margarida M.

2017-02-01

In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross-section sculpted on a chemically homogeneous substrate which favours local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinct far-field orientations, as well as the anchoring transitions between them, are associated with the presence of topological defects either on or close to the substrate. For the sawtooth and sinusoidal cases, we observe a homeotropic to planar anchoring transition as the substrate roughness increases. On the other hand, a homeotropic to oblique anchoring transition is observed for crenellated substrates. In this case, the anchoring phase diagram shows a complex dependence on the substrate roughness and substrate anchoring strength.

Evaluation of lattice sums by the Poisson sum formula

NASA Technical Reports Server (NTRS)

Ray, R. D.

1975-01-01

The Poisson sum formula was applied to the problem of summing pairwise interactions between an observer molecule and a semi-infinite regular array of solid state molecules. The transformed sum is often much more rapidly convergent than the original sum, and forms a Fourier series in the solid surface coordinates. The method is applicable to a variety of solid state structures and functional forms of the pairwise potential. As an illustration of the method, the electric field above the (100) face of the CsCl structure is calculated and compared to earlier results obtained by direct summation.

Lectures on the scattering of light. [by dielectric sphere

NASA Technical Reports Server (NTRS)

Saxon, D. S.

1974-01-01

The exact (Mie) theory for the scattering of a plane wave by a dielectric sphere is presented. Since this infinite series solution is computationally impractical for large spheres, another formulation is given in terms of an integral equation valid for a bounded, but otherwise general array of scatterers. This equation is applied to the scattering by a single sphere, and several methods are suggested for approximating the scattering cross section in closed form. A tensor scattering matrix is introduced, in terms of which some general scattering theorems are derived. The application of the formalism to multiple scattering is briefly considered.

Origin of Hawking radiation: firewall or atmosphere?

NASA Astrophysics Data System (ADS)

Kim, Wontae

2017-02-01

The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation is the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of superplanckian excitations at the horizon can be supported by the infinite Tolman temperature at the horizon. In an exactly soluble model, we explicitly show that the firewall necessarily emerges out of the Unruh vacuum so that the Tolman temperature in the Unruh vacuum is divergent in essence due to the infinitely blueshifted negative ingoing flux crossing the horizon rather than the outgoing flux. We also show that the outgoing Hawking radiation in the Unruh vacuum indeed originates from the atmosphere, not just at the horizon, which is of no relevance to the infinite blueshift. Consequently, the firewall from the infinite Tolman temperature and the Hawking radiation from the atmosphere turn out to be compatible, once we waive the claim that the Hawking radiation in the Unruh vacuum originates from the infinitely blueshifted outgoing excitations at the horizon.

On the coalescence-dispersion modeling of turbulent molecular mixing

NASA Technical Reports Server (NTRS)

Givi, Peyman; Kosaly, George

1987-01-01

The general coalescence-dispersion (C/D) closure provides phenomenological modeling of turbulent molecular mixing. The models of Curl and Dopazo and O'Brien appear as two limiting C/D models that bracket the range of results one can obtain by various models. This finding is used to investigate the sensitivtiy of the results to the choice of the model. Inert scalar mixing is found to be less model-sensitive than mixing accompanied by chemical reaction. Infinitely fast chemistry approximation is used to relate the C/D approach to Toor's earlier results. Pure mixing and infinite rate chemistry calculations are compared to study further a recent result of Hsieh and O'Brien who found that higher concentration moments are not sensitive to chemistry.

Sparse covariance estimation in heterogeneous samples*

PubMed Central

Rodríguez, Abel; Lenkoski, Alex; Dobra, Adrian

2015-01-01

Standard Gaussian graphical models implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected from heterogeneous populations where such an assumption is not satisfied, leading in turn to nonlinear relationships among variables. To address such situations we explore mixtures of Gaussian graphical models; in particular, we consider both infinite mixtures and infinite hidden Markov models where the emission distributions correspond to Gaussian graphical models. Such models allow us to divide a heterogeneous population into homogenous groups, with each cluster having its own conditional independence structure. As an illustration, we study the trends in foreign exchange rate fluctuations in the pre-Euro era. PMID:26925189

Computational Aspects of N-Mixture Models

PubMed Central

Dennis, Emily B; Morgan, Byron JT; Ridout, Martin S

2015-01-01

The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, Biometrics 60, 105–115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, K, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of K in computer packages should be avoided. Instead we propose a simple automatic way to choose K. The methods are illustrated by analysis of data on Hermann's tortoise Testudo hermanni. PMID:25314629

From nonfinite to finite 1D arrays of origami tiles.

PubMed

Wu, Tsai Chin; Rahman, Masudur; Norton, Michael L

2014-06-17

CONSPECTUS: DNA based nanotechnology provides a basis for high-resolution fabrication of objects almost without physical size limitations. However, the pathway to large-scale production of large objects is currently unclear. Operationally, one method forward is to use high information content, large building blocks, which can be generated with high yield and reproducibility. Although flat DNA origami naturally invites comparison to pixels in zero, one, and two dimensions and voxels in three dimensions and has provided an excellent mechanism for generating blocks of significant size and complexity and a multitude of shapes, the field is young enough that a single "brick" has not become the standard platform used by the majority of researchers in the field. In this Account, we highlight factors we considered that led to our adoption of a cross-shaped, non-space-filling origami species, designed by Dr. Liu of the Seeman laboratory, as the building block ideal for use in the fabrication of finite one-dimensional arrays. Three approaches that can be employed for uniquely coding origami-origami linkages are presented. Such coding not only provides the energetics for tethering the species but also uniquely designates the relative orientation of the origami building blocks. The strength of the coding approach implemented in our laboratory is demonstrated using examples of oligomers ranging from finite multimers composed of four, six, and eight origami structures to semi-infinite polymers (100mers). Two approaches to finite array design and the series of assembly steps that each requires are discussed. The process of AFM observation for array characterization is presented as a critical case study. For these soft species, the array images do not simply present the solution phase geometry projected onto a two-dimensional surface. There are additional perturbations associated with fluidic forces associated with sample preparation. At this time, reconstruction of the "true" or average solution structures for blocks is more readily achieved using computer models than using direct imaging methods. The development of scalable 1D-origami arrays composed of uniquely addressable components is a logical, if not necessary, step in the evolution of higher order fully addressable structures. Our research into the fabrication of arrays has led us to generate a listing of several important areas of future endeavor. Of high importance is the re-enforcement of the mechanical properties of the building blocks and the organization of multiple arrays on a surface of technological importance. While addressing this short list of barriers to progress will prove challenging, coherent development along each of these lines of inquiry will accelerate the appearance of commercial scale molecular manufacturing.

Variational optimization algorithms for uniform matrix product states

NASA Astrophysics Data System (ADS)

Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F.; Haegeman, J.

2018-01-01

We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

A Fast Method to Calculate the Spatial Impulse Response for 1-D Linear Ultrasonic Phased Array Transducers

PubMed Central

Zou, Cheng; Sun, Zhenguo; Cai, Dong; Muhammad, Salman; Zhang, Wenzeng; Chen, Qiang

2016-01-01

A method is developed to accurately determine the spatial impulse response at the specifically discretized observation points in the radiated field of 1-D linear ultrasonic phased array transducers with great efficiency. In contrast, the previously adopted solutions only optimize the calculation procedure for a single rectangular transducer and required approximation considerations or nonlinear calculation. In this research, an algorithm that follows an alternative approach to expedite the calculation of the spatial impulse response of a rectangular linear array is presented. The key assumption for this algorithm is that the transducer apertures are identical and linearly distributed on an infinite rigid plane baffled with the same pitch. Two points in the observation field, which have the same position relative to two transducer apertures, share the same spatial impulse response that contributed from corresponding transducer, respectively. The observation field is discretized specifically to meet the relationship of equality. The analytical expressions of the proposed algorithm, based on the specific selection of the observation points, are derived to remove redundant calculations. In order to measure the proposed methodology, the simulation results obtained from the proposed method and the classical summation method are compared. The outcomes demonstrate that the proposed strategy can speed up the calculation procedure since it accelerates the speed-up ratio which relies upon the number of discrete points and the number of the array transducers. This development will be valuable in the development of advanced and faster linear ultrasonic phased array systems. PMID:27834799

Automation of a Linear Accelerator Dosimetric Quality Assurance Program

NASA Astrophysics Data System (ADS)

Lebron Gonzalez, Sharon H.

According to the American Society of Radiation Oncology, two-thirds of all cancer patients will receive radiation therapy during their illness with the majority of the treatments been delivered by a linear accelerator (linac). Therefore, quality assurance (QA) procedures must be enforced in order to deliver treatments with a machine in proper conditions. The overall goal of this project is to automate the linac's dosimetric QA procedures by analyzing and accomplishing various tasks. First, the photon beam dosimetry (i.e. total scatter correction factor, infinite percentage depth dose (PDD) and profiles) were parameterized. Parameterization consists of defining the parameters necessary for the specification of a dosimetric quantity model creating a data set that is portable and easy to implement for different applications including: beam modeling data input into a treatment planning system (TPS), comparing measured and TPS modelled data, the QA of a linac's beam characteristics, and the establishment of a standard data set for comparison with other data, etcetera. Second, this parameterization model was used to develop a universal method to determine the radiation field size of flattened (FF), flattening-filter-free (FFF) and wedge beams which we termed the parameterized gradient method (PGM). Third, the parameterized model was also used to develop a profile-based method for assessing the beam quality of photon FF and FFF beams using an ionization chamber array. The PDD and PDD change was also predicted from the measured profile. Lastly, methods were created to automate the multileaf collimator (MLC) calibration and QA procedures as well as the acquisition of the parameters included in monthly and annual photon dosimetric QA. A two field technique was used for the calculation of the MLC leaf relative offsets using an electronic portal imaging device (EPID). A step-and-shoot technique was used to accurately acquire the radiation field size, flatness, symmetry, output and beam quality specifiers in a single delivery to an ionization chamber array for FF and FFF beams.

Infinite variance in fermion quantum Monte Carlo calculations.

PubMed

Shi, Hao; Zhang, Shiwei

2016-03-01

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

Thermal Conductivity in Soil: Theoretical Approach by 3D Infinite Resistance Grid Model

NASA Astrophysics Data System (ADS)

Changjan, A.; Intaravicha, N.

2018-05-01

Thermal conductivity in soil was elementary characteristic of soil that conduct heat, measured in terms of Fourier’s Law for heat conduction and useful application in many fields: such as Utilizing underground cable for transmission and distribution systems, the rate of cooling of the cable depends on the thermal properties of the soil surrounding the cable. In this paper, we investigated thermal conductivity in soil by infinite three dimensions (3D) electrical resistance circuit concept. Infinite resistance grid 3D was the grid of resistors that extends to infinity in all directions. Model of thermal conductivity in soil of this research was generated from this concept: comparison between electrical resistance and thermal resistance in soil. Finally, we investigated the analytical form of thermal conductivity in soil which helpful for engineering and science students that could exhibit education with a principle of physics that applied to real situations.

An iterative fullwave simulation approach to multiple scattering in media with randomly distributed microbubbles

NASA Astrophysics Data System (ADS)

Joshi, Aditya; Lindsey, Brooks D.; Dayton, Paul A.; Pinton, Gianmarco; Muller, Marie

2017-05-01

Ultrasound contrast agents (UCA), such as microbubbles, enhance the scattering properties of blood, which is otherwise hypoechoic. The multiple scattering interactions of the acoustic field with UCA are poorly understood due to the complexity of the multiple scattering theories and the nonlinear microbubble response. The majority of bubble models describe the behavior of UCA as single, isolated microbubbles suspended in infinite medium. Multiple scattering models such as the independent scattering approximation can approximate phase velocity and attenuation for low scatterer volume fractions. However, all current models and simulation approaches only describe multiple scattering and nonlinear bubble dynamics separately. Here we present an approach that combines two existing models: (1) a full-wave model that describes nonlinear propagation and scattering interactions in a heterogeneous attenuating medium and (2) a Paul-Sarkar model that describes the nonlinear interactions between an acoustic field and microbubbles. These two models were solved numerically and combined with an iterative approach. The convergence of this combined model was explored in silico for 0.5 × 106 microbubbles ml-1, 1% and 2% bubble concentration by volume. The backscattering predicted by our modeling approach was verified experimentally with water tank measurements performed with a 128-element linear array transducer. An excellent agreement in terms of the fundamental and harmonic acoustic fields is shown. Additionally, our model correctly predicts the phase velocity and attenuation measured using through transmission and predicted by the independent scattering approximation.

The infinite sites model of genome evolution.

PubMed

Ma, Jian; Ratan, Aakrosh; Raney, Brian J; Suh, Bernard B; Miller, Webb; Haussler, David

2008-09-23

We formalize the problem of recovering the evolutionary history of a set of genomes that are related to an unseen common ancestor genome by operations of speciation, deletion, insertion, duplication, and rearrangement of segments of bases. The problem is examined in the limit as the number of bases in each genome goes to infinity. In this limit, the chromosomes are represented by continuous circles or line segments. For such an infinite-sites model, we present a polynomial-time algorithm to find the most parsimonious evolutionary history of any set of related present-day genomes.

The Nagaoka state and its stability in the one-band Hubbard model

NASA Astrophysics Data System (ADS)

Shen, Shun-Qing; Qiu, Zhao-Ming; Tian, Guang-Shan

1993-07-01

In this article, we discuss the stability of the Nagaoka state with an infinite number of holes in the infinite- U Hubbard model. We shall rigorously show that the Nagaoka state is stable if the total number of holes Nh ≈ Nα∧ with O⩽α<2/ ( d+2) as the number of lattice sites N∧ tends to infinity. Our theorem improves greatly the previous results obtained by Barbieri et al. [Phys. Rev. B 41 (1990) 11697] and by Tian [Phys. Rev. B 44 (1991) 4444].

The Faculty of Language Integrates the Two Core Systems of Number.

PubMed

Hiraiwa, Ken

2017-01-01

Only humans possess the faculty of language that allows an infinite array of hierarchically structured expressions (Hauser et al., 2002; Berwick and Chomsky, 2015). Similarly, humans have a capacity for infinite natural numbers, while all other species seem to lack such a capacity (Gelman and Gallistel, 1978; Dehaene, 1997). Thus, the origin of this numerical capacity and its relation to language have been of much interdisciplinary interest in developmental and behavioral psychology, cognitive neuroscience, and linguistics (Dehaene, 1997; Hauser et al., 2002; Pica et al., 2004). Hauser et al. (2002) and Chomsky (2008) hypothesize that a recursive generative operation that is central to the computational system of language (called Merge ) can give rise to the successor function in a set-theoretic fashion, from which capacities for discretely infinite natural numbers may be derived. However, a careful look at two domains in language, grammatical number and numerals, reveals no trace of the successor function. Following behavioral and neuropsychological evidence that there are two core systems of number cognition innately available, a core system of representation of large, approximate numerical magnitudes and a core system of precise representation of distinct small numbers (Feigenson et al., 2004), I argue that grammatical number reflects the core system of precise representation of distinct small numbers alone. In contrast, numeral systems arise from integrating the pre-existing two core systems of number and the human language faculty. To the extent that my arguments are correct, linguistic representations of number, grammatical number, and numerals do not incorporate anything like the successor function.

The Faculty of Language Integrates the Two Core Systems of Number

PubMed Central

Hiraiwa, Ken

2017-01-01

Only humans possess the faculty of language that allows an infinite array of hierarchically structured expressions (Hauser et al., 2002; Berwick and Chomsky, 2015). Similarly, humans have a capacity for infinite natural numbers, while all other species seem to lack such a capacity (Gelman and Gallistel, 1978; Dehaene, 1997). Thus, the origin of this numerical capacity and its relation to language have been of much interdisciplinary interest in developmental and behavioral psychology, cognitive neuroscience, and linguistics (Dehaene, 1997; Hauser et al., 2002; Pica et al., 2004). Hauser et al. (2002) and Chomsky (2008) hypothesize that a recursive generative operation that is central to the computational system of language (called Merge) can give rise to the successor function in a set-theoretic fashion, from which capacities for discretely infinite natural numbers may be derived. However, a careful look at two domains in language, grammatical number and numerals, reveals no trace of the successor function. Following behavioral and neuropsychological evidence that there are two core systems of number cognition innately available, a core system of representation of large, approximate numerical magnitudes and a core system of precise representation of distinct small numbers (Feigenson et al., 2004), I argue that grammatical number reflects the core system of precise representation of distinct small numbers alone. In contrast, numeral systems arise from integrating the pre-existing two core systems of number and the human language faculty. To the extent that my arguments are correct, linguistic representations of number, grammatical number, and numerals do not incorporate anything like the successor function. PMID:28360870

Point vortex modelling of the wake dynamics behind asymmetric vortex generator arrays

NASA Astrophysics Data System (ADS)

Baldacchino, D.; Ferreira, C.; Ragni, D.; van Bussel, G. J. W.

2016-09-01

In this work, we present a simple inviscid point vortex model to study the dynamics of asymmetric vortex rows, as might appear behind misaligned vortex generator vanes. Starting from the existing solution of the infinite vortex cascade, a numerical model of four base-vortices is chosen to represent two primary counter-rotating vortex pairs and their mirror plane images, introducing the vortex strength ratio as a free parameter. The resulting system of equations is also defined in terms of the vortex row separation and the qualitative features of the ensuing motion are mapped. A translating and orbiting regime are identified for different cascade separations. The latter occurs for all unequal strength vortex pairs. Thus, the motion is further classified by studying the cyclic behaviour of the orbiting regime and it is shown that for small mismatches in vortex strength, the orbiting length and time scales are sufficiently large as to appear, in the near wake, as translational (non-orbiting). However, for larger mismatches in vortex strength, the orbiting motion approaches the order of the starting height of the vortex. Comparisons between experimental data and the potential flow model show qualitative agreement whilst viscous effects account for the major discrepancies. Despite this, the model captures the orbital mode observed in the measurements and provides an impetus for considering the impact of these complex interactions on vortex generator designs.

Stretching, twisting and supercoiling in short, single DNA molecules

NASA Astrophysics Data System (ADS)

Lam, Pui-Man; Zhen, Yi

2018-02-01

We had combined the Neukirch-Marko model that describes the extension, torque and supercoiling in single, stretched and twisted DNA of infinite contour length, with a form of the free energy suggested by Sinha and Samuels to describe short DNA, with contour length only a few times the persistence length. We find that the free energy of the stretched but untwisted DNA, is significantly modified from its infinitely length value and this in turn modifies significantly the torque and supercoiling. We show that this is consistent with short DNA being more flexible than infinitely long DNA. We hope our results will stimulate experimental investigation of torque and supercoiling in short DNA.

Density functional theory study of the conformational space of an infinitely long polypeptide chain

NASA Astrophysics Data System (ADS)

Ireta, Joel; Scheffler, Matthias

2009-08-01

The backbone conformational space of infinitely long polyalanine is investigated with density-functional theory and mapping the potential energy surface in terms of (L, θ) cylindrical coordinates. A comparison of the obtained (L, θ) Ramachandran-like plot with results from an extended set of protein structures shows excellent conformity, with the exception of the polyproline II region. It is demonstrated the usefulness of infinitely long polypeptide models for investigating the influence of hydrogen bonding and its cooperative effect on the backbone conformations. The results imply that hydrogen bonding together with long-range electrostatics is the main actuator for most of the structures assumed by protein residues.

Dynamics with infinitely many time derivatives in Friedmann-Robertson-Walker background and rolling tachyons

NASA Astrophysics Data System (ADS)

Joukovskaya, Liudmila

2009-02-01

Dynamics with infinitely many time derivatives has place in string field theory and have been profoundly investigated there. Recently there has been considerable interest in theories with infinitely many derivatives in the cosmological context in view of new features which these theories might accommodate owing to nonlocal interaction. In present work we continue investigation of such models, as a concrete example we study the dynamics of unstable D-brane in the open string theory in the Friedmann-Robertson-Walker background. We construct numerical solutions describing dynamical interpolation between the perturbative and non-perturbative vacua. The obtained solutions have several interesting properties and might be of interest from the cosmological points of view.

Quark ensembles with the infinite correlation length

NASA Astrophysics Data System (ADS)

Zinov'ev, G. M.; Molodtsov, S. V.

2015-01-01

A number of exactly integrable (quark) models of quantum field theory with the infinite correlation length have been considered. It has been shown that the standard vacuum quark ensemble—Dirac sea (in the case of the space-time dimension higher than three)—is unstable because of the strong degeneracy of a state, which is due to the character of the energy distribution. When the momentum cutoff parameter tends to infinity, the distribution becomes infinitely narrow, leading to large (unlimited) fluctuations. Various vacuum ensembles—Dirac sea, neutral ensemble, color superconductor, and BCS state—have been compared. In the case of the color interaction between quarks, the BCS state has been certainly chosen as the ground state of the quark ensemble.

On infinite-dimensional state spaces

NASA Astrophysics Data System (ADS)

Fritz, Tobias

2013-05-01

It is well known that the canonical commutation relation [x, p] = i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p] = i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context from which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V-1U2V = U3, then finite-dimensionality entails the relation UV-1UV = V-1UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V-1U2V = U3 holds only up to ɛ and then yields a lower bound on the dimension.

Extraction of diffuse correlation spectroscopy flow index by integration of Nth-order linear model with Monte Carlo simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shang, Yu; Lin, Yu; Yu, Guoqiang, E-mail: guoqiang.yu@uky.edu

2014-05-12

Conventional semi-infinite solution for extracting blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements may cause errors in estimation of BFI (αD{sub B}) in tissues with small volume and large curvature. We proposed an algorithm integrating Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in tissue for the extraction of αD{sub B}. The volume and geometry of the measured tissue were incorporated in the Monte Carlo simulation, which overcome the semi-infinite restrictions. The algorithm was tested using computer simulations on four tissue models with varied volumes/geometries and applied on an in vivo strokemore » model of mouse. Computer simulations shows that the high-order (N ≥ 5) linear algorithm was more accurate in extracting αD{sub B} (errors < ±2%) from the noise-free DCS data than the semi-infinite solution (errors: −5.3% to −18.0%) for different tissue models. Although adding random noises to DCS data resulted in αD{sub B} variations, the mean values of errors in extracting αD{sub B} were similar to those reconstructed from the noise-free DCS data. In addition, the errors in extracting the relative changes of αD{sub B} using both linear algorithm and semi-infinite solution were fairly small (errors < ±2.0%) and did not rely on the tissue volume/geometry. The experimental results from the in vivo stroke mice agreed with those in simulations, demonstrating the robustness of the linear algorithm. DCS with the high-order linear algorithm shows the potential for the inter-subject comparison and longitudinal monitoring of absolute BFI in a variety of tissues/organs with different volumes/geometries.« less

Excitation of a Parallel Plate Waveguide by an Array of Rectangular Waveguides

NASA Technical Reports Server (NTRS)

Rengarajan, Sembiam

2011-01-01

This work addresses the problem of excitation of a parallel plate waveguide by an array of rectangular waveguides that arises in applications such as the continuous transverse stub (CTS) antenna and dual-polarized parabolic cylindrical reflector antennas excited by a scanning line source. In order to design the junction region between the parallel plate waveguide and the linear array of rectangular waveguides, waveguide sizes have to be chosen so that the input match is adequate for the range of scan angles for both polarizations. Electromagnetic wave scattered by the junction of a parallel plate waveguide by an array of rectangular waveguides is analyzed by formulating coupled integral equations for the aperture electric field at the junction. The integral equations are solved by the method of moments. In order to make the computational process efficient and accurate, the method of weighted averaging was used to evaluate rapidly oscillating integrals encountered in the moment matrix. In addition, the real axis spectral integral is evaluated in a deformed contour for speed and accuracy. The MoM results for a large finite array have been validated by comparing its reflection coefficients with corresponding results for an infinite array generated by the commercial finite element code, HFSS. Once the aperture electric field is determined by MoM, the input reflection coefficients at each waveguide port, and coupling for each polarization over the range of useful scan angles, are easily obtained. Results for the input impedance and coupling characteristics for both the vertical and horizontal polarizations are presented over a range of scan angles. It is shown that the scan range is limited to about 35 for both polarizations and therefore the optimum waveguide is a square of size equal to about 0.62 free space wavelength.

On the measurement of airborne, angular-dependent sound transmission through supercritical bars.

PubMed

Shaw, Matthew D; Anderson, Brian E

2012-10-01

The coincidence effect is manifested by maximal sound transmission at angles at which trace wave number matching occurs. Coincidence effect theory is well-defined for unbounded thin plates using plane-wave excitation. However, experimental results for finite bars are known to diverge from theory near grazing angles. Prior experimental work has focused on pulse excitation. An experimental setup has been developed to observe coincidence using continuous- wave excitation and phased-array methods. Experimental results with an aluminum bar exhibit maxima at the predicted angles, showing that coincidence is observable using continuous waves. Transmission near grazing angles is seen to diverge from infinite plate theory.

Optical binding with cold atoms

NASA Astrophysics Data System (ADS)

Máximo, C. E.; Bachelard, R.; Kaiser, R.

2018-04-01

Optical binding is a form of light-mediated forces between elements of matter which emerge in response to the collective scattering of light. Such a phenomenon has been studied mainly in the context of the equilibrium stability of dielectric sphere arrays which move amid dissipative media. In this article, we demonstrate that optically bounded states of a pair of cold atoms can exist, in the absence of nonradiative damping. We study the scaling laws for the unstable-stable phase transition at negative detuning and the unstable-metastable one for positive detuning. In addition, we show that angular momentum can lead to dynamical stabilization with infinite-range scaling.

The impact of finite-area inhomogeneities on resistive and Hall measurement

NASA Astrophysics Data System (ADS)

Koon, Daniel

2013-03-01

I derive an iterative expression for the electric potential in an otherwise homogeneous thin specimen as the result of a finite-area inhomogeneity in either the direct conductance, the Hall conductance, or both. This expression extends to the finite-area regime the calculation of the effect of such inhomogeneities on the measurement error in the sheet resistance and Hall sheet resistance. I then test these results on the exactly-solvable case of a circular inhomogeneity equally distant from the four electrodes of either a square four-point-probe array on an infinitely large conducting specimen or a circular van der Pauw specimen with symmetrically-placed electrodes.

Beyond Clausius-Mossotti - Wave propagation on a polarizable point lattice and the discrete dipole approximation. [electromagnetic scattering and absorption by interstellar grains

NASA Technical Reports Server (NTRS)

Draine, B. T.; Goodman, Jeremy

1993-01-01

We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant. The discrete dipole approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities.

Auto-ignition of methane-air mixtures flowing along an array of thin catalytic plates

NASA Astrophysics Data System (ADS)

Treviño, C.

2010-12-01

In this paper, the heterogeneous ignition of a methane-air mixture flowing along an infinite array of catalytic parallel plates has been studied by inclusion of gas expansion effects and the finite heat conduction on the plates. The system of equations considers the full compressible Navier-Stokes equations coupled with the energy equations of the plates. The gas expansion effects which arise from temperature changes have been considered. The heterogeneous kinetics considers the adsorption and desorption reactions for both reactants. The limits of large and small longitudinal thermal conductance of the plate material are analyzed and the critical conditions for ignition are obtained in closed form. The governing equations are solved numerically using finite differences. The results show that ignition is more easily produced as the longitudinal wall thermal conductance increases, and the effects of the gas expansion on the catalytic ignition process are rather small due to the large value of the activation energy of the desorption reaction of adsorbed oxygen atoms.

Degenerate critical coupling in all-dielectric metasurface absorbers

DOE PAGES

Ming, Xianshun; Liu, Xinyu; Sun, Liqun; ...

2017-09-27

We develop the theory of all-dielectric absorbers based on temporal coupled mode theory (TCMT), with parameters extracted from eigenfrequency simulations. An infinite square array of cylindrical resonators embedded in air is investigated, and we find that it supports two eigenmodes of opposite symmetry that are each responsible for half of the total absorption. The even and odd eigenmodes are found to be the hybrid electric (EH111) and hybrid magnetic (HE111) waveguide modes of a dielectric wire of circular cross section, respectively. The geometry of the cylindrical array is shown to be useful for individual tuning of the radiative loss ratesmore » of the eigenmodes, thus permitting frequency degeneracy. Further, by specifying the resonators’ loss tangent, the material loss rate can be made to equal the radiative loss rate, thus achieving a state of degenerate critical coupling and perfect absorption. Our results are supported by S-parameter simulations, and agree well with waveguide theory.« less

Reports of investigations on: Derivation of an infinite-dilution activity coefficient model and application to two-component vapor/liquid equilibria data: Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roper, V.P.; Kobayashi, R.

1988-02-01

Infinite-dilution fugacity coefficients were obtained for the system fluorene/phenanthrene at thirteen temperatures by fitting total pressure across the entire mole fraction range by a computer routine. A thermodynamically consistent routine, that allowed for both positive and negative pressure deviations from the ideal values, was used to correlate data over the full mole fraction range from 0 to 1. The four-suffix Margules activity coefficient model without modification essentially served this purpose since total pressures and total pressure derivatives with respect to mole fraction were negligible compared to pressure measurement precision. The water/ethanol system and binary systems comprised of aniline, chlorobenzene, acetonitrilemore » and other polar compounds were fit for total pressure across the entire mole fraction range for binary Vapor-Liquid-Equilbria (VLE) using the rigorous, thermodynamically consistent Gibbs-Duhem Relation derived by Ibl and Dodge. Data correlation was performed using a computer least squares procedure. Infinite-dilution fugacity coefficients were obtained using a modified Margules activity coefficient model.« less

A simplified heat transfer model for predicting temperature change inside food package kept in cold room.

PubMed

Raval, A H; Solanki, S C; Yadav, Rajvir

2013-04-01

A simple analytical heat flow model for a closed rectangular food package containing fruits or vegetables is proposed for predicting time temperature distribution during transient cooling in a controlled environment cold room. It is based on the assumption of only conductive heat transfer inside a closed food package with effective thermal properties, and convective and radiative heat transfer at the outside of the package. The effective thermal conductivity of the food package is determined by evaluating its effective thermal resistance to heat conduction in the packages. Food packages both as an infinite slab and a finite slab have been investigated. The finite slab solution has been obtained as the product of three infinite slab solutions describe in ASHRAE guide and data book. Time temperature variation has been determined and is presented graphically. The cooling rate and the half cooling time were also obtained. These predicted values, are compared with the experimentally measured values for both the finite and infinite closed packages containing oranges. An excellent agreement between them validated the simple proposed model.

Floquet time crystal in the Lipkin-Meshkov-Glick model

NASA Astrophysics Data System (ADS)

Russomanno, Angelo; Iemini, Fernando; Dalmonte, Marcello; Fazio, Rosario

2017-06-01

In this work we discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under perturbations of the kicking protocol, its existence being intimately linked to the underlying Z2 symmetry breaking of the time-independent model. We show that the model being infinite range and having an extensive amount of symmetry-breaking eigenstates is essential for having the time-crystal behavior. In particular, we discuss the properties of the Floquet spectrum, and show the existence of doublets of Floquet states which are, respectively, even and odd superposition of symmetry-broken states and have quasienergies differing of half the driving frequencies, a key essence of Floquet time crystals. Remarkably, the stability of the time-crystal phase can be directly analyzed in the limit of infinite size, discussing the properties of the corresponding classical phase space. Through a detailed analysis of the robustness of the time crystal to various perturbations we are able to map the corresponding phase diagram. We finally discuss the possibility of an experimental implementation by means of trapped ions.

Quantum networks in divergence-free circuit QED

NASA Astrophysics Data System (ADS)

Parra-Rodriguez, A.; Rico, E.; Solano, E.; Egusquiza, I. L.

2018-04-01

Superconducting circuits are one of the leading quantum platforms for quantum technologies. With growing system complexity, it is of crucial importance to develop scalable circuit models that contain the minimum information required to predict the behaviour of the physical system. Based on microwave engineering methods, divergent and non-divergent Hamiltonian models in circuit quantum electrodynamics have been proposed to explain the dynamics of superconducting quantum networks coupled to infinite-dimensional systems, such as transmission lines and general impedance environments. Here, we study systematically common linear coupling configurations between networks and infinite-dimensional systems. The main result is that the simple Lagrangian models for these configurations present an intrinsic natural length that provides a natural ultraviolet cutoff. This length is due to the unavoidable dressing of the environment modes by the network. In this manner, the coupling parameters between their components correctly manifest their natural decoupling at high frequencies. Furthermore, we show the requirements to correctly separate infinite-dimensional coupled systems in local bases. We also compare our analytical results with other analytical and approximate methods available in the literature. Finally, we propose several applications of these general methods to analogue quantum simulation of multi-spin-boson models in non-perturbative coupling regimes.

The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, III: The 3-D Boltzmann equation

NASA Astrophysics Data System (ADS)

Yin, Huicheng; Zhao, Wenbin

2018-01-01

This paper is a continuation of the works in [35] and [37], where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively. In this paper, we are concerned with the global existence and large time behavior of compressible Boltzmann gases in an infinitely expanding ball. Such a problem is one of the interesting models in studying the theory of global smooth solutions to multidimensional compressible gases with time dependent boundaries and vacuum states at infinite time. Due to the conservation of mass, the fluid in the expanding ball becomes rarefied and eventually tends to a vacuum state meanwhile there are no appearances of vacuum domains in any part of the expansive ball, which is easily observed in finite time. In the present paper, we will confirm this physical phenomenon for the Boltzmann equation by obtaining the exact lower and upper bound on the macroscopic density function.

Ultrasonic measurements of the reflection coefficient at a water/polyurethane foam interface.

PubMed

Sagers, Jason D; Haberman, Michael R; Wilson, Preston S

2013-09-01

Measured ultrasonic reflection coefficients as a function of normal incidence angle are reported for several samples of polyurethane foam submerged in a water bath. Three reflection coefficient models are employed as needed in this analysis to approximate the measured data: (1) an infinite plane wave impinging on an elastic halfspace, (2) an infinite plane wave impinging on a single fluid layer overlying a fluid halfspace, and (3) a finite acoustic beam impinging on an elastic halfspace. The compressional wave speed in each sample is calculated by minimizing the sum of squared error (SSE) between the measured and modeled data.

Huygen-Fresnel Diffraction Model H-Fdm for the Simulation of Ultrasonic Time-Of Diffraction Technique in 2d Geometries

NASA Astrophysics Data System (ADS)

Reddy, K. Sanjeeva; Krishnamurthy, C. V.; Balasubramaniam, Krishnan; Balasubramanian, T.

2010-02-01

This paper discusses the evaluation of diffracted signals from cracks in 2D based on a new Huygen-Fresnel Diffraction Model (H-FDM). The model employs the frequency-domain far-field displacement expressions derived by Miller & Pursey [1] in 2D for a line source located on the free surface of a semi-infinite elastic medium. At each frequency in the bandwidth of a pulsed excitation, the complex diffracted field is obtained by summing over the unblocked virtual sources located in the section containing a vertical crack. The time-domain diffracted signal is obtained using standard FFT procedures. The effect of beam refraction from a wedge-based finite transducer has been modeled by treating the finite transducer as an array of line sources. The model has been used for predicting diffracted signals in time-of-flight from the crack like defect. The model allows the evaluation of back wall signal amplitude and lateral wave amplitude as well. Experiments have been carried out on 10 mm thick aluminum sample with surface breaking crack of lengths 2 mm and 4 mm using shear probe shoe. The simulated A-Scan results for the aluminum sample with 2 mm and 4 mm surface breaking lengths compare very well in relative amplitudes and time of arrivals with experiments. The H-FDM model offers a tool to evaluate diffraction and related phenomena quantitatively with modest computational resources.

Neural networks for continuous online learning and control.

PubMed

Choy, Min Chee; Srinivasan, Dipti; Cheu, Ruey Long

2006-11-01

This paper proposes a new hybrid neural network (NN) model that employs a multistage online learning process to solve the distributed control problem with an infinite horizon. Various techniques such as reinforcement learning and evolutionary algorithm are used to design the multistage online learning process. For this paper, the infinite horizon distributed control problem is implemented in the form of real-time distributed traffic signal control for intersections in a large-scale traffic network. The hybrid neural network model is used to design each of the local traffic signal controllers at the respective intersections. As the state of the traffic network changes due to random fluctuation of traffic volumes, the NN-based local controllers will need to adapt to the changing dynamics in order to provide effective traffic signal control and to prevent the traffic network from becoming overcongested. Such a problem is especially challenging if the local controllers are used for an infinite horizon problem where online learning has to take place continuously once the controllers are implemented into the traffic network. A comprehensive simulation model of a section of the Central Business District (CBD) of Singapore has been developed using PARAMICS microscopic simulation program. As the complexity of the simulation increases, results show that the hybrid NN model provides significant improvement in traffic conditions when evaluated against an existing traffic signal control algorithm as well as a new, continuously updated simultaneous perturbation stochastic approximation-based neural network (SPSA-NN). Using the hybrid NN model, the total mean delay of each vehicle has been reduced by 78% and the total mean stoppage time of each vehicle has been reduced by 84% compared to the existing traffic signal control algorithm. This shows the efficacy of the hybrid NN model in solving large-scale traffic signal control problem in a distributed manner. Also, it indicates the possibility of using the hybrid NN model for other applications that are similar in nature as the infinite horizon distributed control problem.

A maximally particle-hole asymmetric spectrum emanating from a semi-Dirac point.

PubMed

Quan, Yundi; Pickett, Warren E

2018-02-21

Tight binding models have proven an effective means of revealing Dirac (massless) dispersion, flat bands (infinite mass), and intermediate cases such as the semi-Dirac (sD) dispersion. This approach is extended to a three band model that yields, with chosen parameters in a two-band limit, a closed line with maximally asymmetric particle-hole dispersion: infinite mass holes, zero mass particles. The model retains the sD points for a general set of parameters. Adjacent to this limiting case, hole Fermi surfaces are tiny and needle-like. A pair of large electron Fermi surfaces at low doping merge and collapse at half filling to a flat (zero energy) closed contour with infinite mass along the contour and enclosing no carriers on either side, while the hole Fermi surface has shrunk to a point at zero energy, also containing no carriers. The tight binding model is used to study several characteristics of the dispersion and density of states. The model inspired generalization of sD dispersion to a general  ±[Formula: see text] form, for which analysis reveals that both n and m must be odd to provide a diabolical point with topological character. Evolution of the Hofstadter spectrum of this three band system with interband coupling strength is presented and discussed.

A maximally particle-hole asymmetric spectrum emanating from a semi-Dirac point

NASA Astrophysics Data System (ADS)

Quan, Yundi; Pickett, Warren E.

2018-02-01

Tight binding models have proven an effective means of revealing Dirac (massless) dispersion, flat bands (infinite mass), and intermediate cases such as the semi-Dirac (sD) dispersion. This approach is extended to a three band model that yields, with chosen parameters in a two-band limit, a closed line with maximally asymmetric particle-hole dispersion: infinite mass holes, zero mass particles. The model retains the sD points for a general set of parameters. Adjacent to this limiting case, hole Fermi surfaces are tiny and needle-like. A pair of large electron Fermi surfaces at low doping merge and collapse at half filling to a flat (zero energy) closed contour with infinite mass along the contour and enclosing no carriers on either side, while the hole Fermi surface has shrunk to a point at zero energy, also containing no carriers. The tight binding model is used to study several characteristics of the dispersion and density of states. The model inspired generalization of sD dispersion to a general  ± \\sqrt{k_x2n +k_y2m} form, for which analysis reveals that both n and m must be odd to provide a diabolical point with topological character. Evolution of the Hofstadter spectrum of this three band system with interband coupling strength is presented and discussed.

Infinite-disorder critical points of models with stretched exponential interactions

NASA Astrophysics Data System (ADS)

Juhász, Róbert

2014-09-01

We show that an interaction decaying as a stretched exponential function of distance, J(l)˜ e-cl^a , is able to alter the universality class of short-range systems having an infinite-disorder critical point. To do so, we study the low-energy properties of the random transverse-field Ising chain with the above form of interaction by a strong-disorder renormalization group (SDRG) approach. We find that the critical behavior of the model is controlled by infinite-disorder fixed points different from those of the short-range model if 0 < a < 1/2. In this range, the critical exponents calculated analytically by a simplified SDRG scheme are found to vary with a, while, for a > 1/2, the model belongs to the same universality class as its short-range variant. The entanglement entropy of a block of size L increases logarithmically with L at the critical point but, unlike the short-range model, the prefactor is dependent on disorder in the range 0 < a < 1/2. Numerical results obtained by an improved SDRG scheme are found to be in agreement with the analytical predictions. The same fixed points are expected to describe the critical behavior of, among others, the random contact process with stretched exponentially decaying activation rates.

Modeling the transport of organic chemicals between polyethylene passive samplers and water in finite and infinite bath conditions.

PubMed

Tcaciuc, A Patricia; Apell, Jennifer N; Gschwend, Philip M

2015-12-01

Understanding the transfer of chemicals between passive samplers and water is essential for their use as monitoring devices of organic contaminants in surface waters. By applying Fick's second law to diffusion through the polymer and an aqueous boundary layer, the authors derived a mathematical model for the uptake of chemicals into a passive sampler from water, in finite and infinite bath conditions. The finite bath model performed well when applied to laboratory observations of sorption into polyethylene (PE) sheets for various chemicals (polycyclic aromatic hydrocarbons, polychlorinated biphenyls [PCBs], and dichlorodiphenyltrichloroethane [DDT]) and at varying turbulence levels. The authors used the infinite bath model to infer fractional equilibration of PCB and DDT analytes in field-deployed PE, and the results were nearly identical to those obtained using the sampling rate model. However, further comparison of the model and the sampling rate model revealed that the exchange of chemicals was inconsistent with the sampling rate model for partially or fully membrane-controlled transfer, which would be expected in turbulent conditions or when targeting compounds with small polymer diffusivities and small partition coefficients (e.g., phenols, some pesticides, and others). The model can be applied to other polymers besides PE as well as other chemicals and in any transfer regime (membrane, mixed, or water boundary layer-controlled). Lastly, the authors illustrate practical applications of this model such as improving passive sampler design and understanding the kinetics of passive dosing experiments. © 2015 SETAC.

Nonlinear damping model for flexible structures. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Zang, Weijian

1990-01-01

The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.

The importance of flow history in mixed shear and extensional flows

NASA Astrophysics Data System (ADS)

Wagner, Caroline; McKinley, Gareth

2015-11-01

Many complex fluid flows of experimental and academic interest exhibit mixed kinematics with regions of shear and elongation. Examples include flows through planar hyperbolic contractions in microfluidic devices and through porous media or geometric arrays. Through the introduction of a ``flow-type parameter'' α which varies between 0 in pure shear and 1 in pure elongation, the local velocity fields of all such mixed flows can be concisely characterized. It is tempting to then consider the local stress field and interpret the local state of stress in a complex fluid in terms of shearing or extensional material functions. However, the material response of such fluids exhibit a fading memory of the entire deformation history. We consider a dilute solution of Hookean dumbbells and solve the Oldroyd-B model to obtain analytic expressions for the entire stress field in any arbitrary mixed flow of constant strain rate and flow-type parameter α. We then consider a more complex flow for which the shear rate is constant but the flow-type parameter α varies periodically in time (reminiscent of flow through a periodic array or through repeated contractions and expansions). We show that the flow history and kinematic sequencing (in terms of whether the flow was initialized as shearing or extensional) is extremely important in determining the ensuing stress field and rate of dissipated energy in the flow, and can only be ignored in the limit of infinitely slow flow variations.

Phase-field modeling of stress-induced instabilities

NASA Astrophysics Data System (ADS)

Kassner, Klaus; Misbah, Chaouqi; Müller, Judith; Kappey, Jens; Kohlert, Peter

2001-03-01

A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. Using a formulation that is independent of the state of reference chosen for the displacement field, we write down the elastic energy in an unambiguous fashion, thus obtaining an entire class of models. According to the choice of reference state, the particular model emerging from this class will become equivalent to one of the two independently constructed models on which brief accounts have been given recently [J. Müller and M. Grant, Phys. Rev. Lett. 82, 1736 (1999); K. Kassner and C. Misbah, Europhys. Lett. 46, 217 (1999)]. We show that our phase-field approach recovers the sharp-interface limit corresponding to the continuum model equations describing the Asaro-Tiller-Grinfeld instability. Moreover, we use our model to derive hitherto unknown sharp-interface equations for a situation including a field of body forces. The numerical utility of the phase-field approach is demonstrated by reproducing some known results and by comparison with a sharp-interface simulation. We then proceed to investigate the dynamics of extended systems within the phase-field model which contains an inherent lower length cutoff, thus avoiding cusp singularities. It is found that a periodic array of grooves generically evolves into a superstructure which arises from a series of imperfect period doublings. For wave numbers close to the fastest-growing mode of the linear instability, the first period doubling can be obtained analytically. Both the dynamics of an initially periodic array and a random initial structure can be described as a coarsening process with winning grooves temporarily accelerating whereas losing ones decelerate and even reverse their direction of motion. In the absence of gravity, the end state of a laterally finite system is a single groove growing at constant velocity, as long as no secondary instabilities arise (that we have not been able to see with our code). With gravity, several grooves are possible, all of which are bound to stop eventually. A laterally infinite system approaches a scaling state in the absence of gravity and probably with gravity, too.

Electronic excitations in finite and infinite polyenes

NASA Astrophysics Data System (ADS)

Tavan, Paul; Schulten, Klaus

1987-09-01

We study electronic excitations in long polyenes, i.e., in one-dimensional strongly correlated electron systems which are neither infinite nor small. The excitations are described within Hubbard and Pariser-Parr-Pople (PPP) models by means of a multiple-reference double-excitation expansion [P. Tavan and K. Schulten, J. Chem. Phys. 85, 6602 (1986)]. We find that quantized ``transition'' momenta can be assigned to electronic excitations in finite chains. These momenta link excitation energies of finite chains to dispersion relations of infinite chains, i.e., they bridge the gap between finite and infinite systems. A key result is the following: Excitation energies E in polyenes with N carbon atoms are described very accurately by the formula Eβ=ΔEβ0+αβk(N)q, q=1,2,..., where β denotes the excitation class, ΔEβ0 the energy gap in the infinite system [αβk(N)>0], and k(N) the elementary transition momentum. The parameters ΔEβ0 and αβ are determined for covalent and ionic excitations in alternating and nonalternating polyenes. The covalent excitations are combinations of triplet excitations T, i.e., T, TT, TTT, . . . . The lowest singlet excitations in the infinite polyene, e.g., in polyacetylene or polydiacetylene, are TT states. Available evidence proves that these states can dissociate into separate triplets. The bond structure of TT states is that of a neutral soliton-antisoliton pair. The level density of TT states in long polyenes is high enough to allow dissociation into separate solitons.

MARKOV: A methodology for the solution of infinite time horizon MARKOV decision processes

USGS Publications Warehouse

Williams, B.K.

1988-01-01

Algorithms are described for determining optimal policies for finite state, finite action, infinite discrete time horizon Markov decision processes. Both value-improvement and policy-improvement techniques are used in the algorithms. Computing procedures are also described. The algorithms are appropriate for processes that are either finite or infinite, deterministic or stochastic, discounted or undiscounted, in any meaningful combination of these features. Computing procedures are described in terms of initial data processing, bound improvements, process reduction, and testing and solution. Application of the methodology is illustrated with an example involving natural resource management. Management implications of certain hypothesized relationships between mallard survival and harvest rates are addressed by applying the optimality procedures to mallard population models.

Revealing infinite derivative gravity's true potential: The weak-field limit around de Sitter backgrounds

NASA Astrophysics Data System (ADS)

Edholm, James

2018-03-01

General Relativity is known to produce singularities in the potential generated by a point source. Our universe can be modeled as a de Sitter (dS) metric and we show that ghost-free infinite derivative gravity (IDG) produces a nonsingular potential around a dS background, while returning to the GR prediction at large distances. We also show that although there are an apparently infinite number of coefficients in the theory, only a finite number actually affect the predictions. By writing the linearized equations of motion in a simplified form, we find that at distances below the Hubble length scale, the difference between the IDG potential around a flat background and around a de Sitter background is negligible.

On the Genealogy of Asexual Diploids

NASA Astrophysics Data System (ADS)

Lam, Fumei; Langley, Charles H.; Song, Yun S.

Given molecular genetic data from diploid individuals that, at present, reproduce mostly or exclusively asexually without recombination, an important problem in evolutionary biology is detecting evidence of past sexual reproduction (i.e., meiosis and mating) and recombination (both meiotic and mitotic). However, currently there is a lack of computational tools for carrying out such a study. In this paper, we formulate a new problem of reconstructing diploid genealogies under the assumption of no sexual reproduction or recombination, with the ultimate goal being to devise genealogy-based tools for testing deviation from these assumptions. We first consider the infinite-sites model of mutation and develop linear-time algorithms to test the existence of an asexual diploid genealogy compatible with the infinite-sites model of mutation, and to construct one if it exists. Then, we relax the infinite-sites assumption and develop an integer linear programming formulation to reconstruct asexual diploid genealogies with the minimum number of homoplasy (back or recurrent mutation) events. We apply our algorithms on simulated data sets with sizes of biological interest.

The Effect of Finite Thickness Extent on Estimating Depth to Basement from Aeromagnetic Data

NASA Astrophysics Data System (ADS)

Blakely, R. J.; Salem, A.; Green, C. M.; Fairhead, D.; Ravat, D.

2014-12-01

Depth to basement estimation methods using various components of the spectral content of magnetic anomalies are in common use by geophysicists. Examples of these are the Tilt-Depth and SPI methods. These methods use simple models having the base of the magnetic body at infinity. Recent publications have shown that this 'infinite depth' assumption causes underestimation of the depth to the top of sources, especially in areas where the bottom of the magnetic layer is shallow, as would occur in high heat-flow regions. This error has been demonstrated in both model studies and using real data with seismic or well control. To overcome the limitation of infinite depth this contribution presents the mathematics for a finite depth contact body in the Tilt depth and SPI methods and applies it to the central Red Sea where the Curie isotherm and Moho are shallow. The difference in the depth estimation between the infinite and finite contacts is such a case is significant and can exceed 200%.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice.

PubMed

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-10-10

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic-to-paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models.

Exact low-temperature series expansion for the partition function of the zero-field Ising model on the infinite square lattice

PubMed Central

Siudem, Grzegorz; Fronczak, Agata; Fronczak, Piotr

2016-01-01

In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact determination of the number of spin configurations at a given energy. With these coefficients, we show that the ferromagnetic–to–paramagnetic phase transition in the square lattice Ising model can be explained through equivalence between the model and the perfect gas of energy clusters model, in which the passage through the critical point is related to the complete change in the thermodynamic preferences on the size of clusters. The combinatorial approach reported in this article is very general and can be easily applied to other lattice models. PMID:27721435

Analysis of the moments of the sensitivity function for resistivity over a homogeneous half-space: Rules of thumb for pseudoposition, offline sensitivity and resolution

NASA Astrophysics Data System (ADS)

Butler, S. L.

2017-08-01

It is instructive to consider the sensitivity function for a homogeneous half space for resistivity since it has a simple mathematical formula and it does not require a priori knowledge of the resistivity of the ground. Past analyses of this function have allowed visualization of the regions that contribute most to apparent resistivity measurements with given array configurations. The horizontally integrated form of this equation gives the sensitivity function for an infinitesimally thick horizontal slab with a small resistivity contrast and analysis of this function has admitted estimates of the depth of investigation for a given electrode array. Recently, it has been shown that the average of the vertical coordinate over this function yields a simple formula that can be used to estimate the depth of investigation. The sensitivity function for a vertical inline slab has also been previously calculated. In this contribution, I show that the sensitivity function for a homogeneous half-space can also be integrated so as to give sensitivity functions to semi-infinite vertical slabs that are perpendicular to the array axis. These horizontal sensitivity functions can, in turn, be integrated over the spatial coordinates to give the mean horizontal positions of the sensitivity functions. The mean horizontal positions give estimates for the centres of the regions that affect apparent resistivity measurements for arbitrary array configuration and can be used as horizontal positions when plotting pseudosections even for non-collinear arrays. The mean of the horizontal coordinate that is perpendicular to a collinear array also gives a simple formula for estimating the distance over which offline resistivity anomalies will have a significant effect. The root mean square (rms) widths of the sensitivity functions are also calculated in each of the coordinate directions as an estimate of the inverse of the resolution of a given array. For depth and in the direction perpendicular to the array, the rms thickness is shown to be very similar to the mean distance. For the direction parallel to the array, the rms thickness is shown to be proportional to the array length and similar to the array length divided by 2 for many arrays. I expect that these formulas will provide useful rules of thumb for estimating the centres and extents of regions influencing apparent resistivity measurements for survey planning and for education.

On infinite-dimensional state spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fritz, Tobias

It is well known that the canonical commutation relation [x, p]=i can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating the commutation relation, Occam's razor prefers the infinite-dimensional model in which [x, p]=i holds on the nose. This reasoning one will necessarily have to make in any approach which tries to detect the infinite-dimensionality. One drawback of using the canonical commutation relation for this purpose is that it has unclear operational meaning. Here, we identify an operationally well-defined context frommore » which an analogous conclusion can be drawn: if two unitary transformations U, V on a quantum system satisfy the relation V{sup -1}U{sup 2}V=U{sup 3}, then finite-dimensionality entails the relation UV{sup -1}UV=V{sup -1}UVU; this implication strongly fails in some infinite-dimensional realizations. This is a result from combinatorial group theory for which we give a new proof. This proof adapts to the consideration of cases where the assumed relation V{sup -1}U{sup 2}V=U{sup 3} holds only up to {epsilon} and then yields a lower bound on the dimension.« less

Autonomous control systems: applications to remote sensing and image processing

NASA Astrophysics Data System (ADS)

Jamshidi, Mohammad

2001-11-01

One of the main challenges of any control (or image processing) paradigm is being able to handle complex systems under unforeseen uncertainties. A system may be called complex here if its dimension (order) is too high and its model (if available) is nonlinear, interconnected, and information on the system is uncertain such that classical techniques cannot easily handle the problem. Examples of complex systems are power networks, space robotic colonies, national air traffic control system, and integrated manufacturing plant, the Hubble Telescope, the International Space Station, etc. Soft computing, a consortia of methodologies such as fuzzy logic, neuro-computing, genetic algorithms and genetic programming, has proven to be powerful tools for adding autonomy and semi-autonomy to many complex systems. For such systems the size of soft computing control architecture will be nearly infinite. In this paper new paradigms using soft computing approaches are utilized to design autonomous controllers and image enhancers for a number of application areas. These applications are satellite array formations for synthetic aperture radar interferometry (InSAR) and enhancement of analog and digital images.

Generating a stationary infinite range tractor force via a multimode optical fibre

NASA Astrophysics Data System (ADS)

Ebongue, C. A.; Holzmann, D.; Ostermann, S.; Ritsch, H.

2017-06-01

Optical fibres confine and guide light almost unattenuated and thus convey light forces to polarizable nano-particles over very long distances. Radiation pressure forces arise from scattering of guided photons into free space while gradient forces are based on coherent scattering between different fibre modes or propagation directions. Interestingly, even scattering between co-propagating modes induces longitudinal forces as the transverse confinement of the light modes creates mode dependent longitudinal wave-vectors and photon momenta. We generalize a proven scattering matrix based approach to calculate single as well as inter-particle forces to include several forward and backward propagating modes. We show that an injection of the higher order mode only in a two mode fibre will induce a stationary tractor force against the injection direction, when the mode coupling to the lower order mode dominates against backscattering and free space losses. Generically this arises for non-absorbing particles at the centre of a waveguide. The model also gives improved predictions for inter-particle forces in evanescent nanofibre fields as experimentally observed recently. Surprisingly strong tractor forces can also act on whole optically bound arrays.

A novel phase assignment protocol and driving system for a high-density focused ultrasound array.

PubMed

Caulfield, R Erich; Yin, Xiangtao; Juste, Jose; Hynynen, Kullervo

2007-04-01

Currently, most phased-array systems intended for therapy are one-dimensional (1-D) and use between 5 and 200 elements, with a few two-dimensional (2-D) systems using several hundred elements. The move toward lambda/2 interelement spacing, which provides complete 3-D beam steering, would require a large number of closely spaced elements (0.15 mm to 3 mm). A solution to the resulting problem of cost and cable assembly size, which this study examines, is to quantize the phases available at the array input. By connecting elements with similar phases to a single wire, a significant reduction in the number of incoming lines can be achieved while maintaining focusing and beam steering capability. This study has explored the feasibility of such an approach using computer simulations and experiments with a test circuit driving a 100-element linear array. Simulation results demonstrated that adequate focusing can be obtained with only four phase signals without large increases in the grating lobes or the dimensions of the focus. Experiments showed that the method can be implemented in practice, and adequate focusing can be achieved with four phase signals with a reduction of 20% in the peak pressure amplitude squared when compared with the infinite-phase resolution case. Results indicate that the use of this technique would make it possible to drive more than 10,000 elements with 33 input lines. The implementation of this method could have a large impact on ultrasound therapy and diagnostic devices.

A Tutorial Introduction to Bayesian Models of Cognitive Development

DTIC Science & Technology

2011-01-01

typewriter with an infinite amount of paper. There is a space of documents that it is capable of producing, which includes things like The Tempest and does...not include, say, a Vermeer painting or a poem written in Russian. This typewriter represents a means of generating the hypothesis space for a Bayesian...learner: each possible document that can be typed on it is a hypothesis, the infinite set of documents producible by the typewriter is the latent

Realizing the Potential of the Effective Area Model: Refining the Software and Incorporating Recent Advances to Maximize Usefulness on Military Installations

DTIC Science & Technology

2010-07-01

list(e0 = -0.3, Dmax = 50, D0 = 20) > d <- seq(params$Dmax * 1.1) > plot(d, sapply(d, point.edge.effect, params), type = "l", lwd = 2, + xlab...infinite.edge.effect(): > params$k = 50 > plot(d, sapply(d, infinite.edge.effect, params), type = "l", + lwd = 2, xlab = "distance", ylab = "z", main = "effect of

Spring back of infinite honeycomb sheets beyond plastic deformation

NASA Astrophysics Data System (ADS)

Bonfanti, A.; Bhaskar, A.

2015-02-01

Cellular structures are promising for applications where high stiffness and strength are required with the minimal use of material. They are often used in applications where the plastic deformation plays an important role, such as those involving crashworthiness, energy absorption, and stents. The elastic analysis of a honeycomb sheet has been carried out in the past [1]. The present analysis extends this classical work in the elasto-plastic regime. Recoil analysis due to elastic recovery is absent from the published literature. This work aims to develop an analytical model to calculate the spring back for a simplified case, that of an infinite honeycomb sheet. An elastic-perfectly plastic material model is assumed. The recoil for a clamped beam with a load and moment applied at the free edge is analytically calculated first. This is carried out by relating the stress distribution of the cross section to the final deformed shape. The part corresponding to the elastic contribution is subsequently subtracted in order to obtain the final configuration after the external load is removed. This simple elasto-plastic analysis is then incorporated into the analysis of an infinite sheet made of uniform hexagonal cells. The translational symmetry of the lattice is exploited along with the analysis of a beam under tip loading through to plastic stage and recoil. The final shape of the struts upon the removal of the remote stress is completely determined by the plastic deformation which cannot be recovered. The expression for the beam thus obtained is then used to build an analytical model for an infinite honeycomb sheet loaded in both directions.

Dry granular avalanche impact force on a rigid wall of semi-infinite height

NASA Astrophysics Data System (ADS)

Albaba, Adel; Lambert, Stéphane; Faug, Thierry

2017-06-01

The present paper tackles the problem of the impact of a dry granular avalanche-flow on a rigid wall of semi-infinite height. An analytic force model based on depth-averaged shock theory is proposed to describe the flow-wall interaction and the resulting impact force on the wall. Provided that the analytic force model is fed with the incoming flow conditions regarding thickness, velocity and density, all averaged over a certain distance downstream of the undisturbed incoming flow, it reproduces very well the time history of the impact force actually measured by detailed discrete element simulations, for a wide range of slope angles.

Numerical procedure to determine geometric view factors for surfaces occluded by cylinders

NASA Technical Reports Server (NTRS)

Sawyer, P. L.

1978-01-01

A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.

Low Temperature Analysis of Correlation Functions of the Blume-Emery-Griffiths Model at the Antiquadrupolar-Disordered Interface

NASA Astrophysics Data System (ADS)

Lima, Paulo C.

2016-11-01

We show that at low temperatures the d dimensional Blume-Emery-Griffiths model in the antiquadrupolar-disordered interface has all its infinite volume correlation functions < prod _{iin A}σ _i^{n_i}rangle _{τ }, where Asubset Z^d is finite and sum _{iin A}n_i is odd, equal zero, regardless of the boundary condition τ . In particular, the magnetization < σ _irangle _{τ } is zero, for all τ . We also show that the infinite volume mean magnetization lim _{Λ → ∞}Big < 1/|Λ |sum _{iin Λ }σ _iBig rangle _{Λ ,τ } is zero, for all τ.

The cosmological model of eternal inflation and the transition from chance to biological evolution in the history of life

PubMed Central

Koonin, Eugene V

2007-01-01

Background Recent developments in cosmology radically change the conception of the universe as well as the very notions of "probable" and "possible". The model of eternal inflation implies that all macroscopic histories permitted by laws of physics are repeated an infinite number of times in the infinite multiverse. In contrast to the traditional cosmological models of a single, finite universe, this worldview provides for the origin of an infinite number of complex systems by chance, even as the probability of complexity emerging in any given region of the multiverse is extremely low. This change in perspective has profound implications for the history of any phenomenon, and life on earth cannot be an exception. Hypothesis Origin of life is a chicken and egg problem: for biological evolution that is governed, primarily, by natural selection, to take off, efficient systems for replication and translation are required, but even barebones cores of these systems appear to be products of extensive selection. The currently favored (partial) solution is an RNA world without proteins in which replication is catalyzed by ribozymes and which serves as the cradle for the translation system. However, the RNA world faces its own hard problems as ribozyme-catalyzed RNA replication remains a hypothesis and the selective pressures behind the origin of translation remain mysterious. Eternal inflation offers a viable alternative that is untenable in a finite universe, i.e., that a coupled system of translation and replication emerged by chance, and became the breakthrough stage from which biological evolution, centered around Darwinian selection, took off. A corollary of this hypothesis is that an RNA world, as a diverse population of replicating RNA molecules, might have never existed. In this model, the stage for Darwinian selection is set by anthropic selection of complex systems that rarely but inevitably emerge by chance in the infinite universe (multiverse). Conclusion The plausibility of different models for the origin of life on earth directly depends on the adopted cosmological scenario. In an infinite universe (multiverse), emergence of highly complex systems by chance is inevitable. Therefore, under this cosmology, an entity as complex as a coupled translation-replication system should be considered a viable breakthrough stage for the onset of biological evolution. Reviewers This article was reviewed by Eric Bapteste, David Krakauer, Sergei Maslov, and Itai Yanai. PMID:17540027

The cosmological model of eternal inflation and the transition from chance to biological evolution in the history of life.

PubMed

Koonin, Eugene V

2007-05-31

Recent developments in cosmology radically change the conception of the universe as well as the very notions of "probable" and "possible". The model of eternal inflation implies that all macroscopic histories permitted by laws of physics are repeated an infinite number of times in the infinite multiverse. In contrast to the traditional cosmological models of a single, finite universe, this worldview provides for the origin of an infinite number of complex systems by chance, even as the probability of complexity emerging in any given region of the multiverse is extremely low. This change in perspective has profound implications for the history of any phenomenon, and life on earth cannot be an exception. Origin of life is a chicken and egg problem: for biological evolution that is governed, primarily, by natural selection, to take off, efficient systems for replication and translation are required, but even barebones cores of these systems appear to be products of extensive selection. The currently favored (partial) solution is an RNA world without proteins in which replication is catalyzed by ribozymes and which serves as the cradle for the translation system. However, the RNA world faces its own hard problems as ribozyme-catalyzed RNA replication remains a hypothesis and the selective pressures behind the origin of translation remain mysterious. Eternal inflation offers a viable alternative that is untenable in a finite universe, i.e., that a coupled system of translation and replication emerged by chance, and became the breakthrough stage from which biological evolution, centered around Darwinian selection, took off. A corollary of this hypothesis is that an RNA world, as a diverse population of replicating RNA molecules, might have never existed. In this model, the stage for Darwinian selection is set by anthropic selection of complex systems that rarely but inevitably emerge by chance in the infinite universe (multiverse). The plausibility of different models for the origin of life on earth directly depends on the adopted cosmological scenario. In an infinite universe (multiverse), emergence of highly complex systems by chance is inevitable. Therefore, under this cosmology, an entity as complex as a coupled translation-replication system should be considered a viable breakthrough stage for the onset of biological evolution. This article was reviewed by Eric Bapteste, David Krakauer, Sergei Maslov, and Itai Yanai.

Predictive Rate-Distortion for Infinite-Order Markov Processes

NASA Astrophysics Data System (ADS)

Marzen, Sarah E.; Crutchfield, James P.

2016-06-01

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.

Competition and the Reference Pricing Scheme for pharmaceuticals.

PubMed

Ghislandi, Simone

2011-12-01

By introducing n (>1) firms with infinite cross-price elasticity (i.e. generic drugs), we explore the effects of competition on the optimal pricing strategies under a Reference Pricing Scheme (RPS). A two-stage model repeated infinite number of times is presented. When stage 1 is competitive, the equilibrium in pure strategies exists and is efficient only if the reference price (R) does not depend on the price of the branded product. When generics collude, the way R is designed is crucial for both the stability of the cartel among generics and the collusive prices in equilibrium. An optimally designed RPS must set R as a function only of the infinitely elastic side of the market and should provide the right incentives for competition. Copyright © 2011 Elsevier B.V. All rights reserved.

Classical and quantum production of cornucopions at energies below 1018 GeV

NASA Astrophysics Data System (ADS)

Banks, T.; O'loughlin, M.

1993-01-01

We argue that the paradoxes associated with infinitely degenerate states, which plague relic particle scenarios for the end point of black hole evaporation, may be absent when the relics are horned particles. Most of our arguments are based on simple observations about the classical geometry of extremal dilaton black holes, but at a crucial point we are forced to speculate about classical solutions to string theory in which the infinite coupling singularity of the extremal dilaton solution is shielded by a condensate of massless modes propagating in its infinite horn. We use the nonsingular c=1 solution of (1+1)-dimensional string theory as a crude model for the properties of the condensate. We also present a brief discussion of more general relic scenarios based on large relics of low mass.

Random Walks in a One-Dimensional Lévy Random Environment

NASA Astrophysics Data System (ADS)

Bianchi, Alessandra; Cristadoro, Giampaolo; Lenci, Marco; Ligabò, Marilena

2016-04-01

We consider a generalization of a one-dimensional stochastic process known in the physical literature as Lévy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points, whose nearest-neighbor distances are i.i.d. and long-tailed (with finite mean but possibly infinite variance). The motion is a continuous-time, constant-speed interpolation of a symmetric random walk on the marked points. We first study the quenched random walk on the point process, proving the CLT and the convergence of all the accordingly rescaled moments. Then we derive the quenched and annealed CLTs for the continuous-time process.

Mirror Numbers and Wigner's ``Unreasonable Effectiveness''

NASA Astrophysics Data System (ADS)

Berezin, Alexander

2006-04-01

Wigner's ``unreasonable effectiveness of mathematics in physics'' can be augmented by concept of mirror number (MN). It is defined as digital string infinite in both directions. Example is ()5141327182() where first 5 digits is Pi ``spelled'' backward (``mirrored'') and last 5 digits is the beginning of decimal exp1 string. Let MN be constructed from two different transcendental (or algebraically irrational) numbers, set of such MNs is Cantor-uncountable. Most MNs have contain any finite digital sequence repeated infinitely many times. In spirit of ``Contact'' (C.Sagan) each normal MN contains ``Library of Babel'' of all possible texts and patterns (J.L.Borges). Infinite at both ends, MN do not have any numerical values and, contrary to numbers written in positional systems, all digits in MNs have equal weight -- sort of ``numerological democracy''. In Pythagorean-Platonic models (space-time and physical world originating from pure numbers) idea of MN resolves paradox of ``beginning'' (or ``end'') of time. Because in MNs all digits have equal status, (quantum) randomness leads to more uniform and fully ergodic phase trajectories (cf. F.Dyson, Infinite in All Directions) .

Constraints on black hole remnants

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giddings, S.B.

1994-01-15

One possible fate of information lost to black holes is its preservation in black hole remnants. It is argued that a type of effective field theory describes such remnants (generically referred to as informons). The general structure of such a theory is investigated and the infinite pair production problem is revisited. A toy model for remnants clarifies some of the basic issues; in particular, infinite remnant production is not suppressed simply by the large internal volumes as proposed in cornucopion scenarios. Criteria for avoiding infinite production are stated in terms of couplings in the effective theory. Such instabilities remain amore » problem barring what would be described in that theory as a strong coupling conspiracy. The relation to Euclidean calculations of cornucopion production is sketched, and potential flaws in that analysis are outlined. However, it is quite plausible that pair production of ordinary black holes (e.g., Reissner-Noerdstrom or others) is suppressed due to strong effective couplings. It also remains an open possibility that a microsopic dynamics can be found yielding an appropriate strongly coupled effective theory of neutral informons without infinite pair production.« less

A POD reduced order model for resolving angular direction in neutron/photon transport problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buchan, A.G., E-mail: andrew.buchan@imperial.ac.uk; Calloo, A.A.; Goffin, M.G.

2015-09-01

This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to a high resolution expansion of the BTE's angular dimension. In addition, the individual snapshots are not recorded through time, as in standard POD, but instead theymore » are recorded through space. In essence this work swaps the roles of the dimensions space and time in standard POD methods, with angle and space respectively. It is shown here how the POD model can be formed from the POD basis functions in a highly efficient manner. The model is then applied to two radiation problems; one involving the transport of radiation through a shield and the other through an infinite array of pins. Both problems are selected for their complex angular flux solutions in order to provide an appropriate demonstration of the model's capabilities. It is shown that the POD model can resolve these fluxes efficiently and accurately. In comparison to high resolution models this POD model can reduce the size of a problem by up to two orders of magnitude without compromising accuracy. Solving times are also reduced by similar factors.« less

Analysis of Multiple Cracks in an Infinite Functionally Graded Plate

NASA Technical Reports Server (NTRS)

Shbeeb, N. I.; Binienda, W. K.; Kreider, K. L.

1999-01-01

A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate. The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity.

Techniques for Computation of Frequency Limited H∞ Norm

NASA Astrophysics Data System (ADS)

Haider, Shafiq; Ghafoor, Abdul; Imran, Muhammad; Fahad Mumtaz, Malik

2018-01-01

Traditional H ∞ norm depicts peak system gain over infinite frequency range, but many applications like filter design, model order reduction and controller design etc. require computation of peak system gain over specific frequency interval rather than infinite range. In present work, new computationally efficient techniques for computation of H ∞ norm over frequency limited interval are proposed. Proposed techniques link norm computation with maximum singular value of the system in limited frequency interval. Numerical examples are incorporated to validate the proposed concept.

A Study of the Behavior and Micromechanical Modelling of Granular Soil. Volume 2. An Experimental Investigation of the Behavior of Granular Media Under Load

DTIC Science & Technology

1991-05-22

infinite number of possi’le crystal orientations is assumed, this infinitely sided polyhedron becomes a curved yield surface. Plastic strain in the...families, each surface of yield polyhedron mentioned above expands and shifts differently. These slip directions are all more or less parallel to the...result, only the monotonic portion of test D29 was corrected for membrane compliance and used as part of the monotonic proportional test database

An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces

NASA Astrophysics Data System (ADS)

Kochmann, D. M.; Drugan, W. J.

2016-06-01

An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis.

Effect of the heterogeneity of metamaterials on the Casimir-Lifshitz interaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azari, Arash; Golestanian, Ramin; Miri, MirFaez

2010-09-15

The Casimir-Lifshitz interaction between metamaterials is studied using a model that takes into account the structural heterogeneity of the dielectric and magnetic properties of the bodies. A recently developed perturbation theory for the Casimir-Lifshitz interaction between arbitrary material bodies is generalized to include nonuniform magnetic permeability profiles and used to study the interaction between the magneto-dielectric heterostructures within the leading order. The metamaterials are modeled as two-dimensional arrays of domains with varying permittivity and permeability. In the case of two semi-infinite bodies with flat boundaries, the patterned structure of the material properties is found to cause the normal Casimir-Lifshitz forcemore » to develop an oscillatory behavior when the distance between the two bodies is comparable to the wavelength of the patterned features in the metamaterials. The nonuniformity also leads to the emergence of lateral Casimir-Lifshitz forces, which tend to strengthen as the gap size becomes smaller. Our results suggest that the recent studies on Casimir-Lifshitz forces between metamaterials, which have been performed with the aim of examining the possibility of observing the repulsive force, should be revisited to include the effect of the patterned structure at the wavelength of several hundred nanometers that coincides with the relevant gap size in the experiments.« less

On localization and void coalescence as a precursor to ductile fracture.

PubMed

Tekoğlu, C; Hutchinson, J W; Pardoen, T

2015-03-28

Two modes of plastic flow localization commonly occur in the ductile fracture of structural metals undergoing damage and failure by the mechanism involving void nucleation, growth and coalescence. The first mode consists of a macroscopic localization, usually linked to the softening effect of void nucleation and growth, in either a normal band or a shear band where the thickness of the band is comparable to void spacing. The second mode is coalescence with plastic strain localizing to the ligaments between voids by an internal necking process. The ductility of a material is tied to the strain at macroscopic localization, as this marks the limit of uniform straining at the macroscopic scale. The question addressed is whether macroscopic localization occurs prior to void coalescence or whether the two occur simultaneously. The relation between these two modes of localization is studied quantitatively in this paper using a three-dimensional elastic-plastic computational model representing a doubly periodic array of voids within a band confined between two semi-infinite outer blocks of the same material but without voids. At sufficiently high stress triaxiality, a clear separation exists between the two modes of localization. At lower stress triaxialities, the model predicts that the onset of macroscopic localization and coalescence occur simultaneously. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Colossal terahertz nonlinearity of tunneling van der Waals gap (Conference Presentation)

NASA Astrophysics Data System (ADS)

Bahk, Young-Mi; Kang, Bong Joo; Kim, Yong Seung; Kim, Joon-Yeon; Kim, Won Tae; Kim, Tae Yun; Kang, Taehee; Rhie, Ji Yeah; Han, Sanghoon; Park, Cheol-Hwan; Rotermund, Fabian; Kim, Dai-Sik

2016-09-01

We manufactured an array of three angstrom-wide, five millimeter-long van der Waals gaps of copper-graphene-copper composite, in which unprecedented nonlinearity was observed. To probe and manipulate van der Waals gaps with long wavelength electromagnetic waves such as terahertz waves, one is required to fabricate vertically oriented van der Waals gaps sandwiched between two metal planes with an infinite length in the sense of being much larger than any of the wavelengths used. By comparison with the simple vertical stacking of metal-graphene-metal structure, in our structure, background signals are completely blocked enabling all the light to squeeze through the gap without any strays. When the angstrom-sized van der Waals gaps are irradiated with intense terahertz pulses, the transient voltage across the gap reaches up to 5 V with saturation, sufficiently strong to deform the quantum barrier of angstrom gaps. The large transient potential difference across the gap facilitates electron tunneling through the quantum barrier, blocking terahertz waves completely. This negative feedback of electron tunneling leads to colossal nonlinear optical response, a 97% decrease in the normalized transmittance. Our technology for infinitely long van der Waals gaps can be utilized for other atomically thin materials than single layer graphene, enabling linear and nonlinear angstrom optics in a broad spectral range.

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities

PubMed Central

Liu, Y. J.; Song, G.; Yin, H. M.

2015-01-01

The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles. PMID:26345084

Boundary effect on the elastic field of a semi-infinite solid containing inhomogeneities.

PubMed

Liu, Y J; Song, G; Yin, H M

2015-07-08

The boundary effect of one inhomogeneity embedded in a semi-infinite solid at different depths has firstly been investigated using the fundamental solution for Mindlin's problem. Expanding the eigenstrain in a polynomial form and using the Eshelby's equivalent inclusion method, one can calculate the eigenstrain and thus obtain the elastic field. When the inhomogeneity is far from the boundary, the solution recovers Eshelby's solution. The method has been extended to a many-particle system in a semi-infinite solid, which is first demonstrated by the cases of two spheres. The comparison of the asymptotic form solution with the finite-element results shows the accuracy and capability of this method. The solution has been used to illustrate the boundary effects on its effective material behaviour of a semi-infinite simple cubic lattice particulate composite. The local field of a semi-infinite composite has been calculated at different volume fractions. A representative unit cell has been taken with different depths to the surface. The average stress and strain of the unit cell have been calculated under uniform loading conditions of normal or shear force on the surface, respectively. The effective elastic moduli of the unit cell not only depend on the material proportion, but also on its distance to the surface. The present model can be extended to other types of particle distribution and ellipsoidal particles.

Asymptotics of the monomer-dimer model on two-dimensional semi-infinite lattices

NASA Astrophysics Data System (ADS)

Kong, Yong

2007-05-01

By using the asymptotic theory of Pemantle and Wilson [R. Pemantle and M. C. Wilson, J. Comb. Theory, Ser. AJCBTA70097-316510.1006/jcta.2001.3201 97, 129 (2002)], asymptotic expansions of the free energy of the monomer-dimer model on two-dimensional semi-infinite ∞×n lattices in terms of dimer density are obtained for small values of n , at both high- and low-dimer-density limits. In the high-dimer-density limit, the theoretical results confirm the dependence of the free energy on the parity of n , a result obtained previously by computational methods by Y. Kong [Y. Kong, Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.061102 74, 061102 (2006); Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.73.016106 73, 016106 (2006);Phys. Rev. EPLEEE81063-651X10.1103/PhysRevE.74.011102 74, 011102 (2006)]. In the low-dimer-density limit, the free energy on a cylinder ∞×n lattice strip has exactly the same first n terms in the series expansion as that of an infinite ∞×∞ lattice.

Markov chain sampling of the O(n) loop models on the infinite plane

NASA Astrophysics Data System (ADS)

Herdeiro, Victor

2017-07-01

A numerical method was recently proposed in Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016), 10.1103/PhysRevE.94.043322] showing a precise sampling of the infinite plane two-dimensional critical Ising model for finite lattice subsections. The present note extends the method to a larger class of models, namely the O(n) loop gas models for n ∈(1 ,2 ] . We argue that even though the Gibbs measure is nonlocal, it is factorizable on finite subsections when sufficient information on the loops touching the boundaries is stored. Our results attempt to show that provided an efficient Markov chain mixing algorithm and an improved discrete lattice dilation procedure the planar limit of the O(n) models can be numerically studied with efficiency similar to the Ising case. This confirms that scale invariance is the only requirement for the present numerical method to work.

Prediction of the interaction between a simple moving vehicle and an infinite periodically supported rail - Green's functions approach

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2010-09-01

This paper herein describes the interaction between a simple moving vehicle and an infinite periodically supported rail, in order to signalise the basic features of the vehicle/track vibration behaviour in general, and wheel/rail vibration, in particular. The rail is modelled as an infinite Timoshenko beam resting on semi-sleepers via three-directional rail pads and ballast. The time-domain analysis was performed applying Green's matrix of the track method. This method allows taking into account the nonlinearities of the wheel/rail contact and the Doppler effect. The numerical analysis is dedicated to the wheel/rail response due to two types of excitation: the steady-state interaction and rail irregularities. The study points out to certain aspects regarding the parametric resonance, the amplitude-modulated vibration due to corrugation and the Doppler effect.

Immersion probe arrays for rapid pipeline weld inspection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lebsack, S.; Heckhauser, H.

In 1992, F.H. Gottfeld, Herne, Germany, a member of the SGA Group (Societe Generale de Surveillance) and Krautkramer Branson, Koin, undertook production of a rapid automated ultrasonic testing (UT) system to inspect manually and machine welded pipeline girth welds. The result of the project is a system called MIPA, or multiple immersion probe array. The advantages of using UT to detect certain weld defects have been realized for many years, however for some applications the time required for UT has been a limiting factor. Where time has not been a factor, automated ultrasonic technology has advanced a reliable solution tomore » many inspection problems across a broad industrial base. The recent past has seen the entrance of automated ultrasonic technology into the harsh and demanding environment of pipelay operations, However, the use of these systems has been focused on automated welding processes. Their effectiveness for manual pipeline welding inspection is contested. This is due to the infinite variability of the joint alignment and shape that is unavoidable even when highly skilled welders are used.« less

Modeling and control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Mingori, D. L.

1988-01-01

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Systematization of a set of closure techniques.

PubMed

Hausken, Kjell; Moxnes, John F

2011-11-01

Approximations in population dynamics are gaining popularity since stochastic models in large populations are time consuming even on a computer. Stochastic modeling causes an infinite set of ordinary differential equations for the moments. Closure models are useful since they recast this infinite set into a finite set of ordinary differential equations. This paper systematizes a set of closure approximations. We develop a system, which we call a power p closure of n moments, where 0≤p≤n. Keeling's (2000a,b) approximation with third order moments is shown to be an instantiation of this system which we call a power 3 closure of 3 moments. We present an epidemiological example and evaluate the system for third and fourth moments compared with Monte Carlo simulations. Copyright © 2011 Elsevier Inc. All rights reserved.

Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2

NASA Astrophysics Data System (ADS)

Minami, Kazuhiko

2017-12-01

An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c = m / 2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.

A DPL model of photo-thermal interaction in an infinite semiconductor material containing a spherical hole

NASA Astrophysics Data System (ADS)

Hobiny, Aatef D.; Abbas, Ibrahim A.

2018-01-01

The dual phase lag (DPL) heat transfer model is applied to study the photo-thermal interaction in an infinite semiconductor medium containing a spherical hole. The inner surface of the cavity was traction free and loaded thermally by pulse heat flux. By using the eigenvalue approach methodology and Laplace's transform, the physical variable solutions are obtained analytically. The numerical computations for the silicon-like semiconductor material are obtained. The comparison among the theories, i.e., dual phase lag (DPL), Lord and Shulman's (LS) and the classically coupled thermoelastic (CT) theory is presented graphically. The results further show that the analytical scheme can overcome mathematical problems by analyzing these problems.

2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations

NASA Astrophysics Data System (ADS)

Yang, Y. B.; Hung, H. H.; Kao, J. C.

2010-05-01

The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.

Organ and effective dose rate coefficients for submersion exposure in occupational settings

DOE PAGES

Veinot, K. G.; Y-12 National Security Complex, Oak Ridge, TN; Dewji, S. A.; ...

2017-08-24

External dose coefficients for environmental exposure scenarios are often computed using assumption on infinite or semi-infinite radiation sources. For example, in the case of a person standing on contaminated ground, the source is assumed to be distributed at a given depth (or between various depths) and extending outwards to an essentially infinite distance. In the case of exposure to contaminated air, the person is modeled as standing within a cloud of infinite, or semi-infinite, source distribution. However, these scenarios do not mimic common workplace environments where scatter off walls and ceilings may significantly alter the energy spectrum and dose coefficients.more » In this study, dose rate coefficients were calculated using the International Commission on Radiological Protection (ICRP) reference voxel phantoms positioned in rooms of three sizes representing an office, laboratory, and warehouse. For each room size calculations using the reference phantoms were performed for photons, electrons, and positrons as the source particles to derive mono-energetic dose rate coefficients. Since the voxel phantoms lack the resolution to perform dose calculations at the sensitive depth for the skin, a mathematical phantom was developed and calculations were performed in each room size with the three source particle types. Coefficients for the noble gas radionuclides of ICRP Publication 107 (e.g., Ne, Ar, Kr, Xe, and Rn) were generated by folding the corresponding photon, electron, and positron emissions over the mono-energetic dose rate coefficients. Finally, results indicate that the smaller room sizes have a significant impact on the dose rate per unit air concentration compared to the semi-infinite cloud case. For example, for Kr-85 the warehouse dose rate coefficient is 7% higher than the office dose rate coefficient while it is 71% higher for Xe-133.« less

Organ and effective dose rate coefficients for submersion exposure in occupational settings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Veinot, K. G.; Y-12 National Security Complex, Oak Ridge, TN; Dewji, S. A.

External dose coefficients for environmental exposure scenarios are often computed using assumption on infinite or semi-infinite radiation sources. For example, in the case of a person standing on contaminated ground, the source is assumed to be distributed at a given depth (or between various depths) and extending outwards to an essentially infinite distance. In the case of exposure to contaminated air, the person is modeled as standing within a cloud of infinite, or semi-infinite, source distribution. However, these scenarios do not mimic common workplace environments where scatter off walls and ceilings may significantly alter the energy spectrum and dose coefficients.more » In this study, dose rate coefficients were calculated using the International Commission on Radiological Protection (ICRP) reference voxel phantoms positioned in rooms of three sizes representing an office, laboratory, and warehouse. For each room size calculations using the reference phantoms were performed for photons, electrons, and positrons as the source particles to derive mono-energetic dose rate coefficients. Since the voxel phantoms lack the resolution to perform dose calculations at the sensitive depth for the skin, a mathematical phantom was developed and calculations were performed in each room size with the three source particle types. Coefficients for the noble gas radionuclides of ICRP Publication 107 (e.g., Ne, Ar, Kr, Xe, and Rn) were generated by folding the corresponding photon, electron, and positron emissions over the mono-energetic dose rate coefficients. Finally, results indicate that the smaller room sizes have a significant impact on the dose rate per unit air concentration compared to the semi-infinite cloud case. For example, for Kr-85 the warehouse dose rate coefficient is 7% higher than the office dose rate coefficient while it is 71% higher for Xe-133.« less

Universal programmable quantum circuit schemes to emulate an operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Daskin, Anmer; Grama, Ananth; Kollias, Giorgos

Unlike fixed designs, programmable circuit designs support an infinite number of operators. The functionality of a programmable circuit can be altered by simply changing the angle values of the rotation gates in the circuit. Here, we present a new quantum circuit design technique resulting in two general programmable circuit schemes. The circuit schemes can be used to simulate any given operator by setting the angle values in the circuit. This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way. We also give both the classical and quantummore » complexity analysis for these circuits and show that the circuits require a few classical computations. For the electronic structure simulation on a quantum computer, one has to perform the following steps: prepare the initial wave function of the system; present the evolution operator U=e{sup -iHt} for a given atomic and molecular Hamiltonian H in terms of quantum gates array and apply the phase estimation algorithm to find the energy eigenvalues. Thus, in the circuit model of quantum computing for quantum chemistry, a crucial step is presenting the evolution operator for the atomic and molecular Hamiltonians in terms of quantum gate arrays. Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule.« less

On the tensionless limit of gauged WZW models

NASA Astrophysics Data System (ADS)

Bakas, I.; Sourdis, C.

2004-06-01

The tensionless limit of gauged WZW models arises when the level of the underlying Kac-Moody algebra assumes its critical value, equal to the dual Coxeter number, in which case the central charge of the Virasoro algebra becomes infinite. We examine this limit from the world-sheet and target space viewpoint and show that gravity decouples naturally from the spectrum. Using the two-dimensional black-hole coset SL(2,Bbb R)k/U(1) as illustrative example, we find for k = 2 that the world-sheet symmetry is described by a truncated version of Winfty generated by chiral fields with integer spin s geq 3, whereas the Virasoro algebra becomes abelian and it can be consistently factored out. The geometry of target space looks like an infinitely curved hyperboloid, which invalidates the effective field theory description and conformal invariance can no longer be used to yield reliable space-time interpretation. We also compare our results with the null gauging of WZW models, which correspond to infinite boost in target space and they describe the Liouville mode that decouples in the tensionless limit. A formal BRST analysis of the world-sheet symmetry suggests that the central charge of all higher spin generators should be fixed to a critical value, which is not seen by the contracted Virasoro symmetry. Generalizations to higher dimensional coset models are also briefly discussed in the tensionless limit, where similar observations are made.

The genealogy of samples in models with selection.

PubMed

Neuhauser, C; Krone, S M

1997-02-01

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman's well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman's coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models. DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case.

The Genealogy of Samples in Models with Selection

PubMed Central

Neuhauser, C.; Krone, S. M.

1997-01-01

We introduce the genealogy of a random sample of genes taken from a large haploid population that evolves according to random reproduction with selection and mutation. Without selection, the genealogy is described by Kingman's well-known coalescent process. In the selective case, the genealogy of the sample is embedded in a graph with a coalescing and branching structure. We describe this graph, called the ancestral selection graph, and point out differences and similarities with Kingman's coalescent. We present simulations for a two-allele model with symmetric mutation in which one of the alleles has a selective advantage over the other. We find that when the allele frequencies in the population are already in equilibrium, then the genealogy does not differ much from the neutral case. This is supported by rigorous results. Furthermore, we describe the ancestral selection graph for other selective models with finitely many selection classes, such as the K-allele models, infinitely-many-alleles models, DNA sequence models, and infinitely-many-sites models, and briefly discuss the diploid case. PMID:9071604

A brief compendium of correlations and analytical formulae for the thermal field generated by a heat source embedded in porous and purely-conductive media

NASA Astrophysics Data System (ADS)

Conti, P.; Testi, D.; Grassi, W.

2017-11-01

This work reviews and compares suitable models for the thermal analysis of forced convection over a heat source in a porous medium. The set of available models refers to an infinite medium in which a fluid moves over different three heat source geometries: i.e. the moving infinite line source, the moving finite line source, and the moving infinite cylindrical source. In this perspective, the present work presents a plain and handy compendium of the above-mentioned models for forced external convection in porous media; besides, we propose a dimensionless analysis to figure out the reciprocal deviation among available models, helping the selection of the most suitable one in the specific case of interest. Under specific conditions, the advection term becomes ineffective in terms of heat transfer performances, allowing the use of purely-conductive models. For that reason, available analytical and numerical solutions for purely-conductive media are also reviewed and compared, again, by dimensionless criteria. Therefore, one can choose the simplest solution, with significant benefits in terms of computational effort and interpretation of the results. The main outcomes presented in the paper are: the conditions under which the system can be considered subject to a Darcy flow, the minimal distance beyond which the finite dimension of the heat source does not affect the thermal field, and the critical fluid velocity needed to have a significant contribution of the advection term in the overall heat transfer process.

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Atkinson, Anthony C.

2016-01-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization. PMID:27330230

A Semi-Infinite Programming based algorithm for determining T-optimum designs for model discrimination.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Atkinson, Anthony C

2015-03-01

T-optimum designs for model discrimination are notoriously difficult to find because of the computational difficulty involved in solving an optimization problem that involves two layers of optimization. Only a handful of analytical T-optimal designs are available for the simplest problems; the rest in the literature are found using specialized numerical procedures for a specific problem. We propose a potentially more systematic and general way for finding T-optimal designs using a Semi-Infinite Programming (SIP) approach. The strategy requires that we first reformulate the original minimax or maximin optimization problem into an equivalent semi-infinite program and solve it using an exchange-based method where lower and upper bounds produced by solving the outer and the inner programs, are iterated to convergence. A global Nonlinear Programming (NLP) solver is used to handle the subproblems, thus finding the optimal design and the least favorable parametric configuration that minimizes the residual sum of squares from the alternative or test models. We also use a nonlinear program to check the global optimality of the SIP-generated design and automate the construction of globally optimal designs. The algorithm is successfully used to produce results that coincide with several T-optimal designs reported in the literature for various types of model discrimination problems with normally distributed errors. However, our method is more general, merely requiring that the parameters of the model be estimated by a numerical optimization.

Multi-Dimensional Shallow Landslide Stability Analysis Suitable for Application at the Watershed Scale

NASA Astrophysics Data System (ADS)

Milledge, D.; Bellugi, D.; McKean, J. A.; Dietrich, W.

2012-12-01

The infinite slope model is the basis for almost all watershed scale slope stability models. However, it assumes that a potential landslide is infinitely long and wide. As a result, it cannot represent resistance at the margins of a potential landslide (e.g. from lateral roots), and is unable to predict the size of a potential landslide. Existing three-dimensional models generally require computationally expensive numerical solutions and have previously been applied only at the hillslope scale. Here we derive an alternative analytical treatment that accounts for lateral resistance by representing the forces acting on each margin of an unstable block. We apply 'at rest' earth pressure on the lateral sides, and 'active' and 'passive' pressure using a log-spiral method on the upslope and downslope margins. We represent root reinforcement on each margin assuming that root cohesion is an exponential function of soil depth. We benchmark this treatment against other more complete approaches (Finite Element (FE) and closed form solutions) and find that our model: 1) converges on the infinite slope predictions as length / depth and width / depth ratios become large; 2) agrees with the predictions from state-of-the-art FE models to within +/- 30% error, for the specific cases in which these can be applied. We then test our model's ability to predict failure of an actual (mapped) landslide where the relevant parameters are relatively well constrained. We find that our model predicts failure at the observed location with a nearly identical shape and predicts that larger or smaller shapes conformal to the observed shape are indeed more stable. Finally, we perform a sensitivity analysis using our model to show that lateral reinforcement sets a minimum landslide size, while the additional strength at the downslope boundary means that the optimum shape for a given size is longer in a downslope direction. However, reinforcement effects cannot fully explain the size or shape distributions of observed landslides, highlighting the importance of spatial patterns of key parameters (e.g. pore water pressure) and motivating the model's watershed scale application. This watershed scale application requires an efficient method to find the least stable shapes among an almost infinite set. However, when applied in this context, it allows a more complete examination of the controls on landslide size, shape and location.

Haag duality for Kitaev’s quantum double model for abelian groups

NASA Astrophysics Data System (ADS)

Fiedler, Leander; Naaijkens, Pieter

2015-11-01

We prove Haag duality for cone-like regions in the ground state representation corresponding to the translational invariant ground state of Kitaev’s quantum double model for finite abelian groups. This property says that if an observable commutes with all observables localized outside the cone region, it actually is an element of the von Neumann algebra generated by the local observables inside the cone. This strengthens locality, which says that observables localized in disjoint regions commute. As an application, we consider the superselection structure of the quantum double model for abelian groups on an infinite lattice in the spirit of the Doplicher-Haag-Roberts program in algebraic quantum field theory. We find that, as is the case for the toric code model on an infinite lattice, the superselection structure is given by the category of irreducible representations of the quantum double.

The Thermodynamic Limit in Mean Field Spin Glass Models

NASA Astrophysics Data System (ADS)

Guerra, Francesco; Toninelli, Fabio Lucio

We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N1 and N2 sites, respectively, with N1+N2=N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site.

Stability diagram for the forced Kuramoto model.

PubMed

Childs, Lauren M; Strogatz, Steven H

2008-12-01

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

Seesaw-like polarized transmission behavior of silver nanowire arrays aligned by off-center spin-coating

NASA Astrophysics Data System (ADS)

Kang, Lu; Chen, Hui; Yang, Zhong-Jian; Yuan, Yongbo; Huang, Han; Yang, Bingchu; Gao, Yongli; Zhou, Conghua

2018-05-01

Straight silver nanowires were synthesized by accelerated oxidization and then aligned into ordered arrays by off-center spin-coating. Seesaw-like behavior was observed in the polarized transmission spectra of the arrays. With the increment of polarization angle (θP, defined as the angle between axis of nanowires and direction of electric field of light), transmission changed repeatedly with a period of 180°, but it moved to opposite directions between the two regions separated by supporting points locating at 494 nm. The behavior is ascribed to the competition between the extinction behaviors of the two modes of surface plasma polaritons on silver nanowires. One is the longitudinal mode which is excited by long wavelengths and tuned by function of cos2( θ p ) and the other is the transverse mode that is excited by short wavelengths and tuned by function of sin2( θ p ). Simulation was performed based on the finite-difference time domain method. The effect of the nanowire diameter and length (aspect ratio) on the position of the supporting point was studied. As nanowire width increased from 20 nm to 350 nm, the supporting point moved from 400 to 500 nm. While it changed slightly when the nanowire length increased from 3 μm to infinitely long (width fixed at 260 nm). In current study, the position of the supporting point is mainly determined by the nanowire width.

An Interactive Program on Digitizing Historical Seismograms

NASA Astrophysics Data System (ADS)

Xu, Y.; Xu, T.

2013-12-01

Retrieving information from historical seismograms is of great importance since they are considered the unique sources that provide quantitative information of historical earthquakes. Modern techniques of seismology require digital forms of seismograms that are essentially a sequence of time-amplitude pairs. However, the historical seismograms, after scanned into computers, are two dimensional arrays. Each element of the arrays contains the grayscale value or RGB value of the corresponding pixel. The problem of digitizing historical seismograms, referred to as converting historical seismograms to digital seismograms, can be formulated as an inverse problem that generating sequences of time-amplitude pairs from a two dimension arrays. This problem has infinite solutions. The algorithm for automatic digitization of historical seismogram presented considers several features of seismograms, including continuity, smoothness of the seismic traces as the prior information, and assumes that the amplitude is a single-valued function of time. An interactive program based on the algorithm is also presented. The program is developed using Matlab GUI and has both automatic and manual modality digitization. Users can easily switch between them, and try different combinations to get the optimal results. Several examples are given to illustrate the results of digitizing seismograms using the program, including a photographic record and a wide-angle reflection/refraction seismogram. Digitized result of the program (redrawn using Golden Software Surfer for high resolution image). (a) shows the result of automatic digitization, and (b) is the result after manual correction.

Interplay between gravity and quintessence: a set of new GR solutions

NASA Astrophysics Data System (ADS)

Chernin, Arthur D.; Santiago, David I.; Silbergleit, Alexander S.

2002-02-01

A set of new exact analytical general relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate (1) a static non-empty space-time with a horizon-type singular surface; (2) time-dependent spatially homogeneous `spheres' which are completely different in geometry from the Friedmann isotropic models; (3) infinitely strong anti-gravity at a `true' singularity where the density is infinitely large. It is also found that (4) the GR solutions allow for an extreme `density-free' form of energy that can generate regular space-time geometries.

Necessary optimality conditions for infinite dimensional state constrained control problems

NASA Astrophysics Data System (ADS)

Frankowska, H.; Marchini, E. M.; Mazzola, M.

2018-06-01

This paper is concerned with first order necessary optimality conditions for state constrained control problems in separable Banach spaces. Assuming inward pointing conditions on the constraint, we give a simple proof of Pontryagin maximum principle, relying on infinite dimensional neighboring feasible trajectories theorems proved in [20]. Further, we provide sufficient conditions guaranteeing normality of the maximum principle. We work in the abstract semigroup setting, but nevertheless we apply our results to several concrete models involving controlled PDEs. Pointwise state constraints (as positivity of the solutions) are allowed.

Self-consistent calculations for the electronic structure of a vacancy in copper. A solution of the embedding problem

NASA Astrophysics Data System (ADS)

Zeller, R.; Braspenning, P. J.

1982-06-01

The charge density and the local density of states for a vacancy in Cu and for the first shell of Cu neighbours are calculated by the KKR-Green's function technique. The muffin-tin potentials for the vacancy and the neighbour shell atoms are determined self-consistently in the local density approximation of density functional theory. By the use of the proper host Green's function the embedding of this cluster of 13 perturbed muffin-tins into the infinite array of bulk Cu muffin-tin potentials is described rigorously, thus representing a solution of the embedding problem. The calculations demonstrate a rather large charge transfer of 1.1 electrons from the first neighbour shell to the vacancy.

Development of methods for the analysis of multi-mode TFM images

NASA Astrophysics Data System (ADS)

Sy, K.; Bredif, P.; Iakovleva, E.; Roy, O.; Lesselier, D.

2018-05-01

TFM (Total Focusing Method) is an advanced post-processing imaging algorithm of ultrasonic array data that shows good potential in defect detection and characterization. It can be employed using an infinite number of paths between transducer and focusing point. Depending upon the geometry and the characteristics of the defect in a given part, there are not the same modes that are appropriate for the defect reconstruction. Furthermore, non-physical indications can be observed, prone to misinterpretation. These imaging artifacts are due to the coexistence of several contributions involving several modes of propagation and interactions with possible defects and/or the geometry of the part. Two methods for filtering artifacts and reducing the number of TFM images are developed and illustrated.

Counting statistics for genetic switches based on effective interaction approximation

NASA Astrophysics Data System (ADS)

Ohkubo, Jun

2012-09-01

Applicability of counting statistics for a system with an infinite number of states is investigated. The counting statistics has been studied a lot for a system with a finite number of states. While it is possible to use the scheme in order to count specific transitions in a system with an infinite number of states in principle, we have non-closed equations in general. A simple genetic switch can be described by a master equation with an infinite number of states, and we use the counting statistics in order to count the number of transitions from inactive to active states in the gene. To avoid having the non-closed equations, an effective interaction approximation is employed. As a result, it is shown that the switching problem can be treated as a simple two-state model approximately, which immediately indicates that the switching obeys non-Poisson statistics.

Heating in Integrable Time-Periodic Systems

NASA Astrophysics Data System (ADS)

Ishii, Takashi; Kuwahara, Tomotaka; Mori, Takashi; Hatano, Naomichi

2018-06-01

We investigate a heating phenomenon in periodically driven integrable systems that can be mapped to free-fermion models. We find that heating to the high-temperature state, which is a typical scenario in nonintegrable systems, can also appear in integrable time-periodic systems; the amount of energy absorption rises drastically near a frequency threshold where the Floquet-Magnus expansion diverges. As the driving period increases, we also observe that the effective temperatures of the generalized Gibbs ensemble for conserved quantities go to infinity. By the use of the scaling analysis, we reveal that, in the limit of infinite system size and driving period, the steady state after a long time is equivalent to the infinite-temperature state. We obtain the asymptotic behavior L-1 and T-2 as to how the steady state approaches the infinite-temperature state as the system size L and the driving period T increase.

The generalization of the Mermin-Wagner theorem and the possibility of long-range order in the isotropic discrete one-dimensional quantum Heisenberg model

NASA Astrophysics Data System (ADS)

Rudoy, Yu. G.; Kotelnikova, O. A.

2012-10-01

The problem of existence of long-range order in the isotropic quantum Heisenberg model on the D=1 lattice is reconsidered in view of the possibility of sufficiently slow decaying exchange interaction with infinite effective radius. It is shown that the macrosopic arguments given by Landau and Lifshitz and then supported microscopically by Mermin and Wagner fail for this case so that the non-zero spontaneous magnetization may yet exist. This result was anticipated by Thouless on the grounds of phenomenological analysis, and we give its microscopic foundation, which amounts to the generalization of Mermin-Wagner theorem for the case of the infinite second moment of the exchange interaction. Two well known in lattice statistics models - i.e., Kac-I and Kac-II - illustrate our results.

Highest weight representation for Sklyanin algebra sl(3)(u) with application to the Gaudin model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burdik, C., E-mail: burdik@kmlinux.fjfi.cvut.cz; Navratil, O.

2011-06-15

We study the infinite-dimensional Sklyanin algebra sl(3)(u). Specifically we construct the highest weight representation for this algebra in an explicit form. Its application to the Gaudin model is mentioned.

On some structure-turbulence interaction problems

NASA Technical Reports Server (NTRS)

Maekawa, S.; Lin, Y. K.

1976-01-01

The interactions between a turbulent flow structure; responding to its excitation were studied. The turbulence was typical of those associated with a boundary layer, having a cross-spectral density indicative of convection and statistical decay. A number of structural models were considered. Among the one-dimensional models were an unsupported infinite beam and a periodically supported infinite beam. The fuselage construction of an aircraft was then considered. For the two-dimensional case a simple membrane was used to illustrate the type of formulation applicable to most two-dimensional structures. Both the one-dimensional and two-dimensional structures studied were backed by a cavity filled with an initially quiescent fluid to simulate the acoustic environment when the structure forms one side of a cabin of a sea vessel or aircraft.

Frozen into stripes: fate of the critical Ising model after a quench.

PubMed

Blanchard, T; Picco, M

2013-09-01

In this article we study numerically the final state of the two-dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at T_{c}, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing an example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.

Interaction between moving tandem wheels and an infinite rail with periodic supports - Green's matrices of the track method in stationary reference frame

NASA Astrophysics Data System (ADS)

Mazilu, Traian

2017-08-01

This paper approaches the issue of the interaction between moving tandem wheels and an infinite periodically supported rail and points out at the basic characteristics in the steady-state interaction behaviour and in the interaction in the presence of the rail random irregularity. The rail is modelled as an infinite Timoshenko beam resting on supports which are discretely modelling the inertia of the sleepers and ballast and also the viscoelastic features of the rail pads, the ballast and the subgrade. Green‧s matrices of the track method in stationary reference frame were applied so as to conduct the time-domain analysis. This method allows to consider the nonlinearities of the wheel/rail contact and the Doppler effect. The study highlights certain aspects regarding the influence of the wheel base on the wheels/rail contact forces, particularly at the parametric resonance, due to the coincidence between the wheel/rail natural frequency and the passing frequency and also when the rail surface exhibits random irregularity. It has been shown that the wheel/rail dynamic behaviour is less intense when the wheel base equals integer multiple of the sleeper bay.

Effect of debond growth on stress-intensity factors in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

NASA Technical Reports Server (NTRS)

Bigelow, C. A.

1986-01-01

Stress-intensity factors are determined for a cracked infinite sheet adhesively bonded to a stringer, and debonding of the adhesive layer is predicted. The stringer is modeled as a semi-infinite sheet. Adhesive nonlinearity is also included. Both the sheet and stringer are treated as homogeneous, orthotropic materials. A set of integral equations is formulated and solved to obtain the adhesive shear stresses and crack-tip stress-intensity factors. Adhesive debonding is predicted using a rupture criterion based on the combined adhesive stresses. When the crack is not under the stringer, the debond extends along the edge of the stringer. When the crack tip is beneath the stringer, the debond grows to the end of the crack, then along the edge of the stringer. Stress levels required for debond initiation decrease as the crack tip is moved beneath the stringer. With a nonlinear adhesive, the debond initiates at higher applied stress levels than in linear adhesive cases. Compared with the linear adhesive solution, modeling a nonlinear adhesive causes the stress-intensity factor to increase when the bond is assumed to remain intact but causes the stress-intensity factor to decrease when debonding is included.

Characterization of undulatory locomotion in granular media

NASA Astrophysics Data System (ADS)

Peng, Zhiwei; Pak, On Shun; Elfring, Gwynn

2015-11-01

Undulatory locomotion is ubiquitous in nature, from the swimming of flagellated microorganisms in biological fluids, to the slithering of snakes on land, or the locomotion of sandfish lizards in sand. Analysis of locomotion in granular materials is relatively less developed compared with fluids partially due to a lack of validated force models but a recently proposed resistive force theory (RFT) in granular media has been shown useful in studying the locomotion of a sand-swimming lizard. Here we employ this model to investigate the swimming characteristics of an undulating slender filament of both finite and infinite length. For infinite swimmers, similar to results in viscous fluids, the sawtooth waveform is found to be optimal for propulsion speed at a given power consumption. We also compare the swimming characteristics of sinusoidal and sawtooth swimmers with swimming in viscous fluids. More complex swimming dynamics emerge when the assumption of an infinite swimmer is removed. In particular, we characterize the effects of drifting and pitching in terms of propulsion speed and efficiency for a finite sinusoidal swimmer. The results complement our understanding of undulatory locomotion and provide insights into the effective design of locomotive systems in granular media.

Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Bi, Chuan-Xing; Zhang, Chuanzeng; Gao, Hai-Feng; Chen, Hai-Bo

2018-04-01

The vibration behavior of thin elastic structures can be noticeably influenced by the surrounding water, which represents a kind of heavy fluid. Since the feedback of the acoustic pressure onto the structure cannot be neglected in this case, a strong coupled scheme between the structural and fluid domains is usually required. In this work, a coupled finite element and boundary element (FE-BE) solver is developed for the free vibration analysis of structures submerged in an infinite fluid domain or a semi-infinite fluid domain with a free water surface. The structure is modeled by the finite element method (FEM). The compressibility of the fluid is taken into account, and hence the Helmholtz equation serves as the governing equation of the fluid domain. The boundary element method (BEM) is employed to model the fluid domain, and a boundary integral formulation with a half-space fundamental solution is used to satisfy the Dirichlet boundary condition on the free water surface exactly. The resulting nonlinear eigenvalue problem (NEVP) is converted into a small linear one by using a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenfrequencies of interest. The Burton-Miller method is used to filter out the fictitious eigenfrequencies of the boundary integral formulations. Numerical examples are given to demonstrate the accuracy and applicability of the developed eigensolver, and also show that the fluid-loading effect strongly depends on both the water depth and the mode shapes.

Contact discontinuities in a cold collision-free two-beam plasma

NASA Technical Reports Server (NTRS)

Kirkland, K. B.; Sonnerup, B. U. O.

1982-01-01

The structure of contact discontinuities in a collision-free plasma is examined using a model of a plasma which consists of two oppositely directed cold ion beams and a background of cold massless electrons such that exact charge neutrality is maintained and that the electric field is zero. The basic equations describing self-consistent equilibria are obtained for the more general situation where a net flow across the layer takes place and where the magnetic field has two nonzero tangential components but where the electric field remains zero. These equations are then specialized to the case of no net plasma flow where one of the tangential components is zero, and four different classes of sheets are obtained, all having thickness the order of the ion inertial length. The first class is for layers separating two identical plasma and magnetic field regions, the second is for an infinite array of parallel layers producing an undulated magnetic field, the third is for layers containing trapped ions in closed orbits which separate two vacuum regions with uniform identical magnetic fields, and the fourth is for layers which reflect a single plasma beam, leaving a vacuum with a reversed and compressed tangential field on the other side.

Poroelastic Trailing Edge Noise and the Silent Flight of the Owl

NASA Astrophysics Data System (ADS)

Jaworski, Justin; Peake, Nigel

2012-11-01

Many species of owl rely on specialised plummage to reduce their self-noise levels and enable hunting in acoustic stealth. One such plummage arrangement, a compliant array of feathers at the wing trailing edge, is believed to mitigate the scattering of boundary layer turbulence which is the predominant source of airframe noise. The owl noise problem is modelled analytically by the diffraction of a quadrupole source by a semi-infinite porous and elastic edge, and the resulting set of equations is solved exactly using the Wiener-Hopf technique to identify important dimensionless parameters and their scaling behaviour with respect to the aerodynamic noise produced. Special attention is paid to the limiting cases of elastic-impermeable as well as rigid-porous plate conditions, the latter of which is compared against available experimental measurements in the literature. Results from this analysis and comparison seek to validate the weaker sixth-power dependence of far-field acoustic power on flow velocity for porous trailing edges, develop a rigorous basis for the aeroacoustic tailoring of poroelastic edges to reduce airframe noise, and help explain one of the mechanisms of aerodynamic noise suppression by owls.

Analysis of the sound field in finite length infinite baffled cylindrical ducts with vibrating walls of finite impedance.

PubMed

Shao, Wei; Mechefske, Chris K

2005-04-01

This paper describes an analytical model of finite cylindrical ducts with infinite flanges. This model is used to investigate the sound radiation characteristics of the gradient coil system of a magnetic resonance imaging (MRI) scanner. The sound field in the duct satisfies both the boundary conditions at the wall and at the open ends. The vibrating cylindrical wall of the duct is assumed to be the only sound source. Different acoustic conditions for the wall (rigid and absorptive) are used in the simulations. The wave reflection phenomenon at the open ends of the finite duct is described by general radiation impedance. The analytical model is validated by the comparison with its counterpart in a commercial code based on the boundary element method (BEM). The analytical model shows significant advantages over the BEM model with better numerical efficiency and a direct relation between the design parameters and the sound field inside the duct.

Generating Models of Infinite-State Communication Protocols Using Regular Inference with Abstraction

NASA Astrophysics Data System (ADS)

Aarts, Fides; Jonsson, Bengt; Uijen, Johan

In order to facilitate model-based verification and validation, effort is underway to develop techniques for generating models of communication system components from observations of their external behavior. Most previous such work has employed regular inference techniques which generate modest-size finite-state models. They typically suppress parameters of messages, although these have a significant impact on control flow in many communication protocols. We present a framework, which adapts regular inference to include data parameters in messages and states for generating components with large or infinite message alphabets. A main idea is to adapt the framework of predicate abstraction, successfully used in formal verification. Since we are in a black-box setting, the abstraction must be supplied externally, using information about how the component manages data parameters. We have implemented our techniques by connecting the LearnLib tool for regular inference with the protocol simulator ns-2, and generated a model of the SIP component as implemented in ns-2.

Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges

NASA Astrophysics Data System (ADS)

Blas, Harold; Callisaya, Hector Flores

2018-02-01

We have studied the space-reflection symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal and opposite velocities, split into two infinite towers of conserved and asymptotically conserved charges. For two-solitons without definite parity under space-reflection symmetry (kink-kink and kink-antikink scatterings with unequal and opposite velocities) our numerical results show the existence of the asymptotically conserved charges only. However, we show that in the center-of-mass reference frame of the two solitons the parity symmetries and their associated set of exactly conserved charges can be restored. Moreover, the positive parity breather-like (kink-antikink bound state) solution exhibits a tower of exactly conserved charges and a subset of charges which are periodic in time. We back up our results with extensive numerical simulations which also demonstrate the existence of long lived breather-like states in these models. The time evolution has been simulated by the 4th order Runge-Kutta method supplied with non-reflecting boundary conditions.

Comparison principle for impulsive functional differential equations with infinite delays and applications

NASA Astrophysics Data System (ADS)

Li, Xiaodi; Shen, Jianhua; Akca, Haydar; Rakkiyappan, R.

2018-04-01

We introduce the Razumikhin technique to comparison principle and establish some comparison results for impulsive functional differential equations (IFDEs) with infinite delays, where the infinite delays may be infinite time-varying delays or infinite distributed delays. The idea is, under the help of Razumikhin technique, to reduce the study of IFDEs with infinite delays to the study of scalar impulsive differential equations (IDEs) in which the solutions are easy to deal with. Based on the comparison principle, we study the qualitative properties of IFDEs with infinite delays , which include stability, asymptotic stability, exponential stability, practical stability, boundedness, etc. It should be mentioned that the developed results in this paper can be applied to IFDEs with not only infinite delays but also persistent impulsive perturbations. Moreover, even for the special cases of non-impulsive effects or/and finite delays, the criteria prove to be simpler and less conservative than some existing results. Finally, two examples are given to illustrate the effectiveness and advantages of the proposed results.

On Kronecker-Capelli type theorems for infinite systems

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.; Potapova, Sargylana V.

2017-11-01

On the basis of the new concept of the decrement of an infinite matrices and determinants, we studied the inconsistency of a general infinite systems of linear algebraic equations. We proved the theorem on inconsistency of a infinite system when the decrement of its matrix is nonzero.

Hard-sphere mixture excess free energy at infinite size ratio

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tukur, N.M.; Hamad, E.Z.; Mansoori, G.A.

1999-02-01

This article presents the exact limiting value of the derivative of the excess Helmholtz energy, A{sup E}, with respect to molecular size at constant temperature, density and composition for a binary mixture of hard spheres with an infinite size ratio ({sigma}{sub 11}/{sigma}{sub 22}{r_arrow}{infinity}); i.e., lim{sub {sigma}{sub 22}{r_arrow}0}[({partial_derivative}A{sub hs}{sup E}/RT)/{partial_derivative}{sigma}{sub 22}]{sub T,{rho},x,{sigma}{sub 11}}=({pi}/2){rho}x{sub 1}x{sub 2}{sigma}{sub 11}{sup 2}/(1{minus}({pi}/6){rho}x{sub 1}{sigma}{sub 11}{sup 3}). This limiting value is compared with the Mansoori{endash}Carnahan{endash}Starling{endash}Leland (MCSL) and also used to test the limits of some commonly used models in estimating the excess free energy of solvents in mixtures or polymer solutions. The models evaluated include the van Laar,more » Wilson, Edmond{endash}Ogston, Flory{endash}Huggins, Lacome{endash}Sanchez, Scott{endash}Magat, and Chen {ital et al.} It is shown that while the MCSL equation of state produces the same limiting value as the exact value reported here the other mixture models deviate from the exact value. This expression may be utilized to correct the mixture theories at their infinite size ratio limits. {copyright} {ital 1999 American Institute of Physics.}« less

Improved Modeling of Open Waveguide Aperture Radiators for use in Conformal Antenna Arrays

NASA Astrophysics Data System (ADS)

Nelson, Gregory James

Open waveguide apertures have been used as radiating elements in conformal arrays. Individual radiating element model patterns are used in constructing overall array models. The existing models for these aperture radiating elements may not accurately predict the array pattern for TEM waves which are not on boresight for each radiating element. In particular, surrounding structures can affect the far field patterns of these apertures, which ultimately affects the overall array pattern. New models of open waveguide apertures are developed here with the goal of accounting for the surrounding structure effects on the aperture far field patterns such that the new models make accurate pattern predictions. These aperture patterns (both E plane and H plane) are measured in an anechoic chamber and the manner in which they deviate from existing model patterns are studied. Using these measurements as a basis, existing models for both E and H planes are updated with new factors and terms which allow the prediction of far field open waveguide aperture patterns with improved accuracy. These new and improved individual radiator models are then used to predict overall conformal array patterns. Arrays of open waveguide apertures are constructed and measured in a similar fashion to the individual aperture measurements. These measured array patterns are compared with the newly modeled array patterns to verify the improved accuracy of the new models as compared with the performance of existing models in making array far field pattern predictions. The array pattern lobe characteristics are then studied for predicting fully circularly conformal arrays of varying radii. The lobe metrics that are tracked are angular location and magnitude as the radii of the conformal arrays are varied. A constructed, measured array that is close to conforming to a circular surface is compared with a fully circularly conformal modeled array pattern prediction, with the predicted lobe angular locations and magnitudes tracked, plotted and tabulated. The close match between the patterns of the measured array and the modeled circularly conformal array verifies the validity of the modeled circularly conformal array pattern predictions.

A two-field modified Lagrangian formulation for robust simulations of extrinsic cohesive zone models

NASA Astrophysics Data System (ADS)

Cazes, F.; Coret, M.; Combescure, A.

2013-06-01

This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field Lagrangian weak formulation in which cohesive tractions are chosen as the field variables along the crack's path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading-unloading change of state at the integration points of the cohesive elements. Therefore, a modified Lagrangian formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.

Inflation of Unreefed and Reefed Extraction Parachutes

NASA Technical Reports Server (NTRS)

Ray, Eric S.; Varela, Jose G.

2015-01-01

Data from the Orion and several other test programs have been used to reconstruct inflation parameters for 28 ft Do extraction parachutes as well as the parent aircraft pitch response during extraction. The inflation force generated by extraction parachutes is recorded directly during tow tests but is usually inferred from the payload accelerometer during Low Velocity Airdrop Delivery (LVAD) flight test extractions. Inflation parameters are dependent on the type of parent aircraft, number of canopies, and standard vs. high altitude extraction conditions. For standard altitudes, single canopy inflations are modeled as infinite mass, but the non-symmetric inflations in a cluster are modeled as finite mass. High altitude extractions have necessitated reefing the extraction parachutes, which are best modeled as infinite mass for those conditions. Distributions of aircraft pitch profiles and inflation parameters have been generated for use in Monte Carlo simulations of payload extractions.

Quantum Black Hole Model and HAWKING’S Radiation

NASA Astrophysics Data System (ADS)

Berezin, Victor

The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appeared to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking’s radiation in the limit of low temperatures both for large and nearly extreme Reissner-Nordstrom black holes. The above mentioned infinite degeneracy of the mass (energy) eigenvalues may appeared helpful in resolving the well known information paradox in the black hole physics.

Analysis of transitional separation bubbles on infinite swept wings

NASA Technical Reports Server (NTRS)

Davis, R. L.; Carter, J. E.

1986-01-01

A previously developed two-dimensional local inviscid-viscous interaction technique for the analysis of airfoil transitional separation bubbles, ALESEP (Airfoil Leading Edge Separation), has been extended for the calculation of transitional separation bubbles over infinite swept wings. As part of this effort, Roberts' empirical correlation, which is interpreted as a separated flow empirical extension of Mack's stability theory for attached flows, has been incorporated into the ALESEP procedure for the prediction of the transition location within the separation bubble. In addition, the viscous procedure used in the ALESEP techniques has been modified to allow for wall suction. A series of two-dimensional calculations is presented as a verification of the prediction capability of the interaction techniques with the Roberts' transition model. Numerical tests have shown that this two-dimensional natural transition correlation may also be applied to transitional separation bubbles over infinite swept wings. Results of the interaction procedure are compared with Horton's detailed experimental data for separated flow over a swept plate which demonstrates the accuracy of the present technique. Wall suction has been applied to a similar interaction calculation to demonstrate its effect on the separation bubble. The principal conclusion of this paper is that the prediction of transitional separation bubbles over two-dimensional or infinite swept geometries is now possible using the present interacting boundary layer approach.

Topological Constraints in Directed Polymer Melts.

PubMed

Serna, Pablo; Bunin, Guy; Nahum, Adam

2015-11-27

Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length L wander in the transverse direction only by a distance of order (lnL)^{ζ} with ζ≃1.5. This is strongly suppressed in comparison with the Brownian L^{1/2} scaling which holds in the absence of the topological constraint. It is also much smaller than the predictions of standard heuristic approaches-in particular the L^{1/4} of a mean-field-like "array of obstacles" model-so our results present a sharp challenge to theory. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion in the transverse direction. To cast light on the suppression of the strands' wandering, we analyze the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and nondirected.

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

Transition probabilities for non self-adjoint Hamiltonians in infinite dimensional Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagarello, F., E-mail: fabio.bagarello@unipa.it

In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite dimensional Hilbert spaces. This is useful, but quite restrictive since many physically relevant quantum systems live in infinite dimensional Hilbert spaces. In this paper we consider this situation, and we discuss some applications to well known models, introduced in the literature in recent years: the extended harmonic oscillator, the Swanson model and a generalized version of the Landau levels Hamiltonian. Not surprisingly we willmore » find new interesting features not previously found in finite dimensional Hilbert spaces, useful for a deeper comprehension of this kind of physical systems.« less

Fluctuation instability of the Dirac Sea in quark models of strong interactions

NASA Astrophysics Data System (ADS)

Zinovjev, G. M.; Molodtsov, S. V.

2016-03-01

A number of exactly integrable (quark) models of quantum field theory that feature an infinite correlation length are considered. An instability of the standard vacuum quark ensemble, a Dirac sea (in spacetimes of dimension higher than three), is highlighted. It is due to a strong ground-state degeneracy, which, in turn, stems from a special character of the energy distribution. In the case where the momentumcutoff parameter tends to infinity, this distribution becomes infinitely narrow and leads to large (unlimited) fluctuations. A comparison of the results for various vacuum ensembles, including a Dirac sea, a neutral ensemble, a color superconductor, and a Bardeen-Cooper-Schrieffer (BCS) state, was performed. In the presence of color quark interaction, a BCS state is unambiguously chosen as the ground state of the quark ensemble.

Many roads to synchrony: natural time scales and their algorithms.

PubMed

James, Ryan G; Mahoney, John R; Ellison, Christopher J; Crutchfield, James P

2014-04-01

We consider two important time scales-the Markov and cryptic orders-that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the ε-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the ε-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.

Combustion Of Interacting Droplet Arrays In Microgravity

NASA Technical Reports Server (NTRS)

Dietrich, D. L.; Struk, P. M.; Ikegami, M.; Xu, G.

2003-01-01

Theory and experiments involving single droplet combustion date back to 1953, with the first microgravity work appearing in 1956. The problem of a spherical droplet burning in an infinite, quiescent microgravity environment is a classical problem in combustion research with the classical solution appearing in nearly every textbook on combustion. The microgravity environment offered by ground-based facilities such as drop towers and space-based facilities is ideal for studying the problem experimentally. A recent review by Choi and Dryer shows significant advances in droplet combustion have been made by studying the problem experimentally in microgravity and comparing the results to one dimensional theoretical and numerical treatments of the problem. Studying small numbers of interacting droplets in a well-controlled geometry represents a logical step in extending single droplet investigations to more practical spray configurations. Studies of droplet interactions date back to Rex and co-workers, and were recently summarized by Annamalai and Ryan. All previous studies determined the change in the burning rate constant, k, or the flame characteristics as a result of interactions. There exists almost no information on how droplet interactions a effect extinction limits, and if the extinction limits change if the array is in the diffusive or the radiative extinction regime. Thus, this study examined experimentally the effect that droplet interactions have on the extinction process by investigating the simplest array configuration, a binary droplet array. The studies were both in normal gravity, reduced pressure ambients and microgravity facilities. The microgravity facilities were the 2.2 and 5.2 second drop towers at the NASA Glenn Research Center and the 10 second drop tower at the Japan Microgravity Center. The experimental apparatus and the data analysis techniques are discussed in detail elsewhere.

Avian photoreceptor patterns represent a disordered hyperuniform solution to a multiscale packing problem

NASA Astrophysics Data System (ADS)

Jiao, Yang; Lau, Timothy; Hatzikirou, Haralampos; Meyer-Hermann, Michael; Corbo, Joseph C.; Torquato, Salvatore

2014-02-01

Optimal spatial sampling of light rigorously requires that identical photoreceptors be arranged in perfectly regular arrays in two dimensions. Examples of such perfect arrays in nature include the compound eyes of insects and the nearly crystalline photoreceptor patterns of some fish and reptiles. Birds are highly visual animals with five different cone photoreceptor subtypes, yet their photoreceptor patterns are not perfectly regular. By analyzing the chicken cone photoreceptor system consisting of five different cell types using a variety of sensitive microstructural descriptors, we find that the disordered photoreceptor patterns are "hyperuniform" (exhibiting vanishing infinite-wavelength density fluctuations), a property that had heretofore been identified in a unique subset of physical systems, but had never been observed in any living organism. Remarkably, the patterns of both the total population and the individual cell types are simultaneously hyperuniform. We term such patterns "multihyperuniform" because multiple distinct subsets of the overall point pattern are themselves hyperuniform. We have devised a unique multiscale cell packing model in two dimensions that suggests that photoreceptor types interact with both short- and long-ranged repulsive forces and that the resultant competition between the types gives rise to the aforementioned singular spatial features characterizing the system, including multihyperuniformity. These findings suggest that a disordered hyperuniform pattern may represent the most uniform sampling arrangement attainable in the avian system, given intrinsic packing constraints within the photoreceptor epithelium. In addition, they show how fundamental physical constraints can change the course of a biological optimization process. Our results suggest that multihyperuniform disordered structures have implications for the design of materials with novel physical properties and therefore may represent a fruitful area for future research.

Modality, Infinitives, and Finite Bare Verbs in Dutch and English Child Language

ERIC Educational Resources Information Center

Blom, Elma

2007-01-01

This article focuses on the meaning of nonfinite clauses ("root infinitives") in Dutch and English child language. I present experimental and naturalistic data confirming the claim that Dutch root infinitives are more often modal than English root infinitives. This cross-linguistic difference is significantly smaller than previously assumed,…

Large-scale detection of repetitions

PubMed Central

Smyth, W. F.

2014-01-01

Combinatorics on words began more than a century ago with a demonstration that an infinitely long string with no repetitions could be constructed on an alphabet of only three letters. Computing all the repetitions (such as ⋯TTT⋯ or ⋯CGACGA⋯ ) in a given string x of length n is one of the oldest and most important problems of computational stringology, requiring time in the worst case. About a dozen years ago, it was discovered that repetitions can be computed as a by-product of the Θ(n)-time computation of all the maximal periodicities or runs in x. However, even though the computation is linear, it is also brute force: global data structures, such as the suffix array, the longest common prefix array and the Lempel–Ziv factorization, need to be computed in a preprocessing phase. Furthermore, all of this effort is required despite the fact that the expected number of runs in a string is generally a small fraction of the string length. In this paper, I explore the possibility that repetitions (perhaps also other regularities in strings) can be computed in a manner commensurate with the size of the output. PMID:24751872

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillion, D.

This code enables one to display, take line-outs on, and perform various transformations on an image created by an array of integer*2 data. Uncompressed eight-bit TIFF files created on either the Macintosh or the IBM PC may also be read in and converted to a 16 bit signed integer image. This code is designed to handle all the formats used for PDS (photo-densitometer) files at the Lawrence Livermore National Laboratory. These formats are all explained by the application code. The image may be zoomed infinitely and the gray scale mapping can be easily changed. Line-outs may be horizontal or verticalmore » with arbitrary width, angled with arbitrary end points, or taken along any path. This code is usually used to examine spectrograph data. Spectral lines may be identified and a polynomial fit from position to wavelength may be found. The image array can be remapped so that the pixels all have the same change of lambda width. It is not necessary to do this, however. Lineouts may be printed, saved as Cricket tab-delimited files, or saved as PICT2 files. The plots may be linear, semilog, or logarithmic with nice values and proper scientific notation. Typically, spectral lines are curved.« less

Scalable L-infinite coding of meshes.

PubMed

Munteanu, Adrian; Cernea, Dan C; Alecu, Alin; Cornelis, Jan; Schelkens, Peter

2010-01-01

The paper investigates the novel concept of local-error control in mesh geometry encoding. In contrast to traditional mesh-coding systems that use the mean-square error as target distortion metric, this paper proposes a new L-infinite mesh-coding approach, for which the target distortion metric is the L-infinite distortion. In this context, a novel wavelet-based L-infinite-constrained coding approach for meshes is proposed, which ensures that the maximum error between the vertex positions in the original and decoded meshes is lower than a given upper bound. Furthermore, the proposed system achieves scalability in L-infinite sense, that is, any decoding of the input stream will correspond to a perfectly predictable L-infinite distortion upper bound. An instantiation of the proposed L-infinite-coding approach is demonstrated for MESHGRID, which is a scalable 3D object encoding system, part of MPEG-4 AFX. In this context, the advantages of scalable L-infinite coding over L-2-oriented coding are experimentally demonstrated. One concludes that the proposed L-infinite mesh-coding approach guarantees an upper bound on the local error in the decoded mesh, it enables a fast real-time implementation of the rate allocation, and it preserves all the scalability features and animation capabilities of the employed scalable mesh codec.

Nonlinear response of GaAs gratings in the extraordinary transmission regime.

PubMed

Vincenti, Maria Antonietta; de Ceglia, Domenico; Scalora, Michael

2011-12-01

We theoretically describe a way to enhance harmonic generation from subwavelength slits milled on semiconductor substrates in strongly absorptive regimes. The metal-like response typical of semiconductors, like GaAs and GaP, triggers enhanced transmission and nonlinear optical phenomena in the deep UV range. We numerically study correlations between linear and nonlinear responses and their intricacies in infinite arrays, and highlight differences between nonlinear surface and magnetic sources, and intrinsic χ((2)) and χ((3)) contributions to harmonic generation. The results show promising efficiencies at wavelengths below 120 nm, and reveal coupling of TE and TM polarizations for pump and harmonic signals. A downconversion process that can regenerate pump photons with polarization orthogonal to the incident pump is also discussed. © 2011 Optical Society of America

Interpenetrating and non-interpenetrating 3-dimensional coordination polymer frameworks from multiple building blocks

NASA Astrophysics Data System (ADS)

Bradshaw, Darren; Rosseinsky, Matthew J.

2005-12-01

Reaction of Co(NO3)2ṡ6H2O with the multidentate ligands benzene-1,3,5-tricarboxylate (btc) and the flexible bipyridyl ligand 1,2-bis(4-pyridyl)ethane (bpe) affords the 3-dimensional coordination polymers [Co3(btc)2(bpe)3(eg)2]ṡ(guests) 1, where eg = ethylene glycol, and [Co2(Hbtc)2(bpe)2]ṡ(bpe) 2. Both phases are comprised of infinite metal-carboxylate dimer chains, linked into 2-dimensional sheets by the bpe ligands. These sheets are further linked to adjacent sheets through covalent interactions, 1, or through hydrogen-bonding interactions, 2, to yield the 3-dimensional structures. Phase 1 exhibits solvent filled 1-dimensional pores, whereas 2 is triply-interpenetrated to form a dense solid array.

CHOOSING A CHEMICAL MECHANISM FOR REGULATORY AND RESEARCH AIR QUALITY MODELING APPLICATIONS

EPA Science Inventory

There are numerous, different chemical mechanisms currently available for use in air quality models, and new mechanisms and versions of mechanisms are continually being developed. The development of Morphecule-type mechanisms will add a near-infinite number of additional mecha...

Infinite hidden conditional random fields for human behavior analysis.

PubMed

Bousmalis, Konstantinos; Zafeiriou, Stefanos; Morency, Louis-Philippe; Pantic, Maja

2013-01-01

Hidden conditional random fields (HCRFs) are discriminative latent variable models that have been shown to successfully learn the hidden structure of a given classification problem (provided an appropriate validation of the number of hidden states). In this brief, we present the infinite HCRF (iHCRF), which is a nonparametric model based on hierarchical Dirichlet processes and is capable of automatically learning the optimal number of hidden states for a classification task. We show how we learn the model hyperparameters with an effective Markov-chain Monte Carlo sampling technique, and we explain the process that underlines our iHCRF model with the Restaurant Franchise Rating Agencies analogy. We show that the iHCRF is able to converge to a correct number of represented hidden states, and outperforms the best finite HCRFs--chosen via cross-validation--for the difficult tasks of recognizing instances of agreement, disagreement, and pain. Moreover, the iHCRF manages to achieve this performance in significantly less total training, validation, and testing time.

Adaptive and nonadaptive feedback control of global instabilities with application to a heated 2-D jet

NASA Astrophysics Data System (ADS)

Monkewitz, Peter A.; Mingori, D. L.

1992-04-01

Close to the onset of self-excited fluid oscillations the generic complex Ginzburg-Landau is proposed as the lowest order model for the plant. Its linear part which provides the stability boundaries is derived from first principles for both doubly-infinite and semi-infinite flow domains. Concentrating on a single global mode, the model is further simplified to the Stuart-Landau equation. For this latter model, a methodology is developed for the design of single-input single-output controllers. The so designed controllers have been implemented on a self-excited, heated two-dimensional jet with one hot wire as sensor and an acoustic speaker as actuator, and are shown to be effective within their limitations in suppressing or enhancing limit-cycle oscillations. Finally, the effect of of a controller designed to suppress the most unstable global mode on other modes is investigated experimentally in the wake of a cylinder at low Reynolds number, where an encouraging semi-quantitative correspondence to the Ginzburg-Landau model is found.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Finite Feedback Cycling in Structural Equation Models

ERIC Educational Resources Information Center

Hayduk, Leslie A.

2009-01-01

In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few…

Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions

NASA Astrophysics Data System (ADS)

Barnett, William A.; Duzhak, Evgeniya Aleksandrovna

2008-06-01

Grandmont [J.M. Grandmont, On endogenous competitive business cycles, Econometrica 53 (1985) 995-1045] found that the parameter space of the most classical dynamic models is stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with many forms of multiperiodic dynamics in between. The econometric implications of Grandmont’s findings are particularly important, if bifurcation boundaries cross the confidence regions surrounding parameter estimates in policy-relevant models. Stratification of a confidence region into bifurcated subsets seriously damages robustness of dynamical inferences. Recently, interest in policy in some circles has moved to New-Keynesian models. As a result, in this paper we explore bifurcation within the class of New-Keynesian models. We develop the econometric theory needed to locate bifurcation boundaries in log-linearized New-Keynesian models with Taylor policy rules or inflation-targeting policy rules. Central results needed in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the cases that we consider.

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

DOE PAGES

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.; ...

2017-01-13

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Electromagnetic pulse excitation of finite- and infinitely-long lossy conductors over a lossy ground plane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campione, Salvatore; Warne, Larry K.; Basilio, Lorena I.

This study details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG – Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reportedmore » method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.« less

Pattern Formation and Complexity Emergence

NASA Astrophysics Data System (ADS)

Berezin, Alexander A.

2001-03-01

Success of nonlinear modelling of pattern formation and self-organization encourages speculations on informational and number theoretical foundations of complexity emergence. Pythagorean "unreasonable effectiveness of integers" in natural processes is perhaps extrapolatable even to universal emergence "out-of-nothing" (Leibniz, Wheeler). Because rational numbers (R = M/N) are everywhere dense on real axis, any digital string (hence any "book" from "Library of Babel" of J.L.Borges) is "recorded" infinitely many times in arbitrary many rationals. Furthermore, within any arbitrary small interval there are infinitely many Rs for which (either or both) integers (Ms and Ns) "carry" any given string of any given length. Because any iterational process (such as generation of fractal features of Mandelbrot Set) is arbitrary closely approximatable with rational numbers, the infinite pattern of integers expresses itself in generation of complexity of the world, as well as in emergence of the world itself. This "tunnelling" from Platonic World ("Platonia" of J.Barbour) to a real (physical) world is modern recast of Leibniz's motto ("for deriving all from nothing there suffices a single principle").

Infinite Multiplets

DOE R&D Accomplishments Database

Nambu, Y.

1967-01-01

The main ingredients of the method of infinite multiplets consist of: 1) the use of wave functions with an infinite number of components for describing an infinite tower of discrete states of an isolated system (such as an atom, a nucleus, or a hadron), 2) the use of group theory, instead of dynamical considerations, in determining the properties of the wave functions.

Boundary Conditions for Infinite Conservation Laws

NASA Astrophysics Data System (ADS)

Rosenhaus, V.; Bruzón, M. S.; Gandarias, M. L.

2016-12-01

Regular soliton equations (KdV, sine-Gordon, NLS) are known to possess infinite sets of local conservation laws. Some other classes of nonlinear PDE possess infinite-dimensional symmetries parametrized by arbitrary functions of independent or dependent variables; among them are Zabolotskaya-Khokhlov, Kadomtsev-Petviashvili, Davey-Stewartson equations and Born-Infeld equation. Boundary conditions were shown to play an important role for the existence of local conservation laws associated with infinite-dimensional symmetries. In this paper, we analyze boundary conditions for the infinite conserved densities of regular soliton equations: KdV, potential KdV, Sine-Gordon equation, and nonlinear Schrödinger equation, and compare them with boundary conditions for the conserved densities obtained from infinite-dimensional symmetries with arbitrary functions of independent and dependent variables.

Effective-Medium Models for Marine Gas Hydrates, Mallik Revisited

NASA Astrophysics Data System (ADS)

Terry, D. A.; Knapp, C. C.; Knapp, J. H.

2011-12-01

Hertz-Mindlin type effective-medium dry-rock elastic models have been commonly used for more than three decades in rock physics analysis, and recently have been applied to assessment of marine gas hydrate resources. Comparisons of several effective-medium models with derivative well-log data from the Mackenzie River Valley, Northwest Territories, Canada (i.e. Mallik 2L-38 and 5L-38) were made several years ago as part of a marine gas hydrate joint industry project in the Gulf of Mexico. The matrix/grain supporting model (one of the five models compared) was clearly a better representation of the Mallik data than the other four models (2 cemented sand models; a pore-filling model; and an inclusion model). Even though the matrix/grain supporting model was clearly better, reservations were noted that the compressional velocity of the model was higher than the compressional velocity measured via the sonic logs, and that the shear velocities showed an even greater discrepancy. Over more than thirty years, variations of Hertz-Mindlin type effective medium models have evolved for unconsolidated sediments and here, we briefly review their development. In the past few years, the perfectly smooth grain version of the Hertz-Mindlin type effective-medium model has been favored over the infinitely rough grain version compared in the Gulf of Mexico study. We revisit the data from the Mallik wells to review assertions that effective-medium models with perfectly smooth grains are a better predictor than models with infinitely rough grains. We briefly review three Hertz-Mindlin type effective-medium models, and standardize nomenclature and notation. To calibrate the extended effective-medium model in gas hydrates, we use a well accepted framework for unconsolidated sediments through Hashin-Shtrikman bounds. We implement the previously discussed effective-medium models for saturated sediments with gas hydrates and compute theoretical curves of seismic velocities versus gas hydrate saturation to compare with well log data available from the Canadian gas hydrates research site. By directly comparing the infinitely rough and perfectly smooth grain versions of the Hertz-Mindlin type effective-medium model, we provide additional insight to the discrepancies noted in the Gulf of Mexico study.

Ab initio optimization principle for the ground states of translationally invariant strongly correlated quantum lattice models.

PubMed

Ran, Shi-Ju

2016-05-01

In this work, a simple and fundamental numeric scheme dubbed as ab initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly correlated quantum lattice models. The idea is to transform a nondeterministic-polynomial-hard ground-state simulation with infinite degrees of freedom into a single optimization problem of a local function with finite number of physical and ancillary degrees of freedom. This work contributes mainly in the following aspects: (1) AOP provides a simple and efficient scheme to simulate the ground state by solving a local optimization problem. Its solution contains two kinds of boundary states, one of which play the role of the entanglement bath that mimics the interactions between a supercell and the infinite environment, and the other gives the ground state in a tensor network (TN) form. (2) In the sense of TN, a novel decomposition named as tensor ring decomposition (TRD) is proposed to implement AOP. Instead of following the contraction-truncation scheme used by many existing TN-based algorithms, TRD solves the contraction of a uniform TN in an opposite way by encoding the contraction in a set of self-consistent equations that automatically reconstruct the whole TN, making the simulation simple and unified; (3) AOP inherits and develops the ideas of different well-established methods, including the density matrix renormalization group (DMRG), infinite time-evolving block decimation (iTEBD), network contractor dynamics, density matrix embedding theory, etc., providing a unified perspective that is previously missing in this fields. (4) AOP as well as TRD give novel implications to existing TN-based algorithms: A modified iTEBD is suggested and the two-dimensional (2D) AOP is argued to be an intrinsic 2D extension of DMRG that is based on infinite projected entangled pair state. This paper is focused on one-dimensional quantum models to present AOP. The benchmark is given on a transverse Ising chain and 2D classical Ising model, showing the remarkable efficiency and accuracy of the AOP.

Blow-up in nonlinear models of extended particles with confined constituents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alvarez, A.; Ranada, A.F.

1988-11-15

It is shown that the indefinite character of the charge in classical models of extended particles with confined constituents is a serious handicap since infinite amounts of positive and negative charge can be emitted in some solutions, causing a blow-up in finite time.

Quasiopen inflation

NASA Astrophysics Data System (ADS)

García-Bellido, Juan; Garriga, Jaume; Montes, Xavier

1998-04-01

We show that a large class of two-field models of single-bubble open inflation does not lead to infinite open universes, as was previously thought, but to an ensemble of very large but finite inflating ``islands.'' The reason is that the quantum tunneling responsible for the nucleation of the bubble does not occur simultaneously along both field directions and equal-time hypersurfaces in the open universe are not synchronized with equal-density or fixed-field hypersurfaces. The most probable tunneling trajectory corresponds to a zero value of the inflaton field; large values, necessary for the second period of inflation inside the bubble, only arise as localized fluctuations. The interior of each nucleated bubble will contain an infinite number of such inflating regions of comoving size of order γ-1, where γ is the supercurvature eigenvalue, which depends on the parameters of the model. Each one of these islands will be a quasi-open universe. Since the volume of the hyperboloid is infinite, inflating islands with all possible values of the field at their center will be realized inside of a single bubble. We may happen to live in one of those patches of comoving size d<~γ-1, where the universe appears to be open. In particular, we consider the ``supernatural'' model proposed by Linde and Mezhlumian. There, an approximate U(1) symmetry is broken by a tunneling field in a first order phase transition, and slow-roll inflation inside the nucleated bubble is driven by the pseudo Goldstone field. We find that the excitations of the pseudo Goldstone field produced by the nucleation and subsequent expansion of the bubble place severe constraints on this model. We also discuss the coupled and uncoupled two-field models.

Multiple scattering by infinitely long cylindrical glass inclusions in a saturated Biot porous medium of glass beads.

PubMed

Trabelsi, W; Franklin, H; Tinel, A

2016-05-01

The resonance spectrum of sets of two to five infinitely long parallel cylindrical glass inclusions in a fluid saturated porous matrix of unconsolidated glass beads is investigated. The ratio of bead diameters to inclusion diameters is 1/5. The far field form functions and the related phase derivatives are calculated by using an exact multiple scattering formalism and by assuming that the porous medium obeys Biot's model. In order to validate this hypothesis, comparisons between theory and experiments are done in the special case of a fast incident wave on a set of two and three inclusions.

Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type

NASA Astrophysics Data System (ADS)

Hermann, Robert

1982-07-01

Recent work by Morrison, Marsden, and Weinstein has drawn attention to the possibility of utilizing the cosymplectic structure of the dual of the Lie algebra of certain infinite dimensional Lie groups to study hydrodynamical and plasma systems. This paper treats certain models arising in elementary particle physics, considered by Lee, Weinberg, and Zumino; Sugawara; Bardacki, Halpern, and Frishman; Hermann; and Dolan. The lie algebras involved are associated with the ''current algebras'' of Gell-Mann. This class of Lie algebras contains certain of the algebras that are called ''Kac-Moody algebras'' in the recent mathematics and mathematical physics literature.

Generalized Heisenberg Algebras, SUSYQM and Degeneracies: Infinite Well and Morse Potential

NASA Astrophysics Data System (ADS)

Hussin, Véronique; Marquette, Ian

2011-03-01

We consider classical and quantum one and two-dimensional systems with ladder operators that satisfy generalized Heisenberg algebras. In the classical case, this construction is related to the existence of closed trajectories. In particular, we apply these results to the infinite well and Morse potentials. We discuss how the degeneracies of the permutation symmetry of quantum two-dimensional systems can be explained using products of ladder operators. These products satisfy interesting commutation relations. The two-dimensional Morse quantum system is also related to a generalized two-dimensional Morse supersymmetric model. Arithmetical or accidental degeneracies of such system are shown to be associated to additional supersymmetry.

Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

NASA Astrophysics Data System (ADS)

Vercher, Enriqueta

2008-08-01

This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example.

Grid-free density functional calculations on periodic systems.

PubMed

Varga, Stefan

2007-09-21

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xalpha exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.

Grid-free density functional calculations on periodic systems

NASA Astrophysics Data System (ADS)

Varga, Štefan

2007-09-01

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xα exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.

On some properties of force-free magnetic fields in infinite regions of space

NASA Technical Reports Server (NTRS)

Aly, J. J.

1984-01-01

Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.

Polarimetría de las atmósferas de Urano y Neptuno

NASA Astrophysics Data System (ADS)

López Sisterna, C.; Gil-Hutton, R.

2015-08-01

We present imaging polarimetry for Uranus and Neptune, the observations were taken with the 2.15 m telescope at CASLEO. The patterns observed for both planets turn to be centro-symmetric; unlike the observations on Jupiter and Saturn. However, the Stokes parameters introduce large errors on the degree of polarization, and the radial Stokes parameters are used instead. We obtain that the radial limb polarization is about 0.20. Further, we corrected the parameters for seeing, and compared the results with analytical models of semi-infinite and finite Rayleigh scattering atmospheres. From this comparison we conclude the polarization agrees with the semi-infinite Rayleigh scattering atmosphere.

A Functional Central Limit Theorem for the Becker-Döring Model

NASA Astrophysics Data System (ADS)

Sun, Wen

2018-04-01

We investigate the fluctuations of the stochastic Becker-Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.

An infinite swampland of U(1) charge spectra in 6D supergravity theories

NASA Astrophysics Data System (ADS)

Taylor, Washington; Turner, Andrew P.

2018-06-01

We analyze the anomaly constraints on 6D supergravity theories with a single abelian U(1) gauge factor. For theories with charges restricted to q = ±1 , ±2 and no tensor multiplets, anomaly-free models match those models that can be realized from F-theory compactifications almost perfectly. For theories with tensor multiplets or with larger charges, the F-theory constraints are less well understood. We show, however, that there is an infinite class of distinct massless charge spectra in the "swampland" of theories that satisfy all known quantum consistency conditions but do not admit a realization through F-theory or any other known approach to string compactification. We also compare the spectra of charged matter in abelian theories with those that can be realized from breaking nonabelian SU(2) and higher rank gauge symmetries.

Fluctuation instability of the Dirac Sea in quark models of strong interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zinovjev, G. M., E-mail: Gennady.Zinovjev@cern.ch; Molodtsov, S. V.

A number of exactly integrable (quark) models of quantum field theory that feature an infinite correlation length are considered. An instability of the standard vacuum quark ensemble, a Dirac sea (in spacetimes of dimension higher than three), is highlighted. It is due to a strong ground-state degeneracy, which, in turn, stems from a special character of the energy distribution. In the case where the momentumcutoff parameter tends to infinity, this distribution becomes infinitely narrow and leads to large (unlimited) fluctuations. A comparison of the results for various vacuum ensembles, including a Dirac sea, a neutral ensemble, a color superconductor, andmore » a Bardeen–Cooper–Schrieffer (BCS) state, was performed. In the presence of color quark interaction, a BCS state is unambiguously chosen as the ground state of the quark ensemble.« less

On Discontinuous Piecewise Linear Models for Memristor Oscillators

NASA Astrophysics Data System (ADS)

Amador, Andrés; Freire, Emilio; Ponce, Enrique; Ros, Javier

2017-06-01

In this paper, we provide for the first time rigorous mathematical results regarding the rich dynamics of piecewise linear memristor oscillators. In particular, for each nonlinear oscillator given in [Itoh & Chua, 2008], we show the existence of an infinite family of invariant manifolds and that the dynamics on such manifolds can be modeled without resorting to discontinuous models. Our approach provides topologically equivalent continuous models with one dimension less but with one extra parameter associated to the initial conditions. It is possible to justify the periodic behavior exhibited by three-dimensional memristor oscillators, by taking advantage of known results for planar continuous piecewise linear systems. The analysis developed not only confirms the numerical results contained in previous works [Messias et al., 2010; Scarabello & Messias, 2014] but also goes much further by showing the existence of closed surfaces in the state space which are foliated by periodic orbits. The important role of initial conditions that justify the infinite number of periodic orbits exhibited by these models, is stressed. The possibility of unsuspected bistable regimes under specific configurations of parameters is also emphasized.

On the symmetries of integrability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellon, M.; Maillard, J.M.; Viallet, C.

1992-06-01

In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiatemore » the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.« less

Threshold thickness for applying diffusion equation in thin tissue optical imaging

NASA Astrophysics Data System (ADS)

Zhang, Yunyao; Zhu, Jingping; Cui, Weiwen; Nie, Wei; Li, Jie; Xu, Zhenghong

2014-08-01

We investigated the suitability of the semi-infinite model of the diffusion equation when using diffuse optical imaging (DOI) to image thin tissues with double boundaries. Both diffuse approximation and Monte Carlo methods were applied to simulate light propagation in the thin tissue model with variable optical parameters and tissue thicknesses. A threshold value of the tissue thickness was defined as the minimum thickness in which the semi-infinite model exhibits the same reflected intensity as that from the double-boundary model and was generated as the final result. In contrast to our initial hypothesis that all optical properties would affect the threshold thickness, our results show that only absorption coefficient is the dominant parameter and the others are negligible. The threshold thickness decreases from 1 cm to 4 mm as the absorption coefficient grows from 0.01 mm-1 to 0.2 mm-1. A look-up curve was derived to guide the selection of the appropriate model during the optical diagnosis of thin tissue cancers. These results are useful in guiding the development of the endoscopic DOI for esophageal, cervical and colorectal cancers, among others.

Modelling dishes and exploring culinary 'precisions': the two issues of molecular gastronomy.

PubMed

This, Hervé

2005-04-01

The scientific strategy of molecular gastronomy includes modelling 'culinary definitions' and experimental explorations of 'culinary precisions'. A formalism that describes complex dispersed systems leads to a physical classification of classical sauces, as well as to the invention of an infinite number of new dishes.

Mathematical model of a smoldering log.

Treesearch

Fernando de Souza Costa; David Sandberg

2004-01-01

A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts...

Acquisition of Irregular Past Tense by Children with Specific Language Impairment.

ERIC Educational Resources Information Center

Rice, Mabel L.; Wexler, Kenneth; Marquis, Janet; Hershberger, Scott

2000-01-01

This study explored the acquisition of regular and irregular past tense in 21 children with specific language impairment. The findings support a morphosyntactic rather than morphophonological learning model, such as the extended optional infinitive model, with regard to the limitations in finiteness marking and for affected children. (Contains…

Modeling Array Stations in SIG-VISA

NASA Astrophysics Data System (ADS)

Ding, N.; Moore, D.; Russell, S.

2013-12-01

We add support for array stations to SIG-VISA, a system for nuclear monitoring using probabilistic inference on seismic signals. Array stations comprise a large portion of the IMS network; they can provide increased sensitivity and more accurate directional information compared to single-component stations. Our existing model assumed that signals were independent at each station, which is false when lots of stations are close together, as in an array. The new model removes that assumption by jointly modeling signals across array elements. This is done by extending our existing Gaussian process (GP) regression models, also known as kriging, from a 3-dimensional single-component space of events to a 6-dimensional space of station-event pairs. For each array and each event attribute (including coda decay, coda height, amplitude transfer and travel time), we model the joint distribution across array elements using a Gaussian process that learns the correlation lengthscale across the array, thereby incorporating information of array stations into the probabilistic inference framework. To evaluate the effectiveness of our model, we perform ';probabilistic beamforming' on new events using our GP model, i.e., we compute the event azimuth having highest posterior probability under the model, conditioned on the signals at array elements. We compare the results from our probabilistic inference model to the beamforming currently performed by IMS station processing.

Coexistence of stable stationary behavior and partial synchrony in an all-to-all coupled spiking neural network

NASA Astrophysics Data System (ADS)

de Smet, Filip; Aeyels, Dirk

2010-12-01

We consider the stationary and the partially synchronous regimes in an all-to-all coupled neural network consisting of an infinite number of leaky integrate-and-fire neurons. Using analytical tools as well as simulation results, we show that two threshold values for the coupling strength may be distinguished. Below the lower threshold, no synchronization is possible; above the upper threshold, the stationary regime is unstable and partial synchrony prevails. In between there is a range of values for the coupling strength where both regimes may be observed. The assumption of an infinite number of neurons is crucial: simulations with a finite number of neurons indicate that above the lower threshold partial synchrony always prevails—but with a transient time that may be unbounded with increasing system size. For values of the coupling strength in a neighborhood of the lower threshold, the finite model repeatedly builds up toward synchronous behavior, followed by a sudden breakdown, after which the synchronization is slowly built up again. The “transient” time needed to build up synchronization again increases with increasing system size, and in the limit of an infinite number of neurons we retrieve stationary behavior. Similarly, within some range for the coupling strength in this neighborhood, a stable synchronous solution may exist for an infinite number of neurons.

Models of cylindrical bubble pulsation

PubMed Central

Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hay, Todd A.; Hamilton, Mark F.

2012-01-01

Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation. It reveals that radiation is the dominant loss mechanism, and that it is 22 times greater than for a spherical bubble of the same radius. The predicted resonance frequency provides a basis of comparison for limiting forms of other models. The second model considered is a commonly used equation in Rayleigh-Plesset form that requires an incompressible liquid to be finite in extent in order for bubble pulsation to occur. The radial extent of the liquid becomes a fitting parameter, and it is found that considerably different values of the parameter are required for modeling inertial motion versus acoustical oscillations. The third model was developed by V. K. Kedrinskii [Hydrodynamics of Explosion (Springer, New York, 2005), pp. 23–26] in the form of the Gilmore equation for compressible liquids of infinite extent. While the correct resonance frequency and loss factor are not recovered from this model in the linear approximation, it provides reasonable agreement with observations of inertial motion. PMID:22978863

Comparison and analysis of theoretical models for diffusion-controlled dissolution.

PubMed

Wang, Yanxing; Abrahamsson, Bertil; Lindfors, Lennart; Brasseur, James G

2012-05-07

Dissolution models require, at their core, an accurate diffusion model. The accuracy of the model for diffusion-dominated dissolution is particularly important with the trend toward micro- and nanoscale drug particles. Often such models are based on the concept of a "diffusion layer." Here a framework is developed for diffusion-dominated dissolution models, and we discuss the inadequacy of classical models that are based on an unphysical constant diffusion layer thickness assumption, or do not correctly modify dissolution rate due to "confinement effects": (1) the increase in bulk concentration from confinement of the dissolution process, (2) the modification of the flux model (the Sherwood number) by confinement. We derive the exact mathematical solution for a spherical particle in a confined fluid with impermeable boundaries. Using this solution, we analyze the accuracy of a time-dependent "infinite domain model" (IDM) and "quasi steady-state model" (QSM), both formally derived for infinite domains but which can be applied in approximate fashion to confined dissolution with proper adjustment of a concentration parameter. We show that dissolution rate is sensitive to the degree of confinement or, equivalently, to the total concentration C(tot). The most practical model, the QSM, is shown to be very accurate for most applications and, consequently, can be used with confidence in design-level dissolution models so long as confinement is accurately treated. The QSM predicts the ratio of diffusion layer thickness to particle radius (the Sherwood number) as a constant plus a correction that depends on the degree of confinement. The QSM also predicts that the time required for complete saturation or dissolution in diffusion-controlled dissolution experiments is singular (i.e., infinite) when total concentration equals the solubility. Using the QSM, we show that measured differences in dissolution rate in a diffusion-controlled dissolution experiment are a result of differences in the degree of confinement on the increase in bulk concentration independent of container geometry and polydisperse vs single particle dissolution. We conclude that the constant diffusion-layer thickness assumption is incorrect in principle and should be replaced by the QSM with accurate treatment of confinement in models of diffusion-controlled dissolution.

Focusing light in a bianisotropic slab with negatively refracting materials.

PubMed

Liu, Yan; Guenneau, Sebastien; Gralak, Boris; Ramakrishna, S Anantha

2013-04-03

We investigate the electromagnetic response of a pair of complementary bianisotropic media, which consist of a medium with positive refractive index (+ε, +μ, +ξ) and a medium with negative refractive index(-ε, -μ, -ξ). We show that this idealized system has peculiar imaging properties in that it reproduces images of a source, in principle, with unlimited resolution. We then consider an infinite array of line sources regularly spaced in a 1D photonic crystal (PC) consisting of 2n layers of bianisotropic complementary media. Using coordinate transformations, we map this system into 2D corner chiral lenses of 2n heterogeneous anisotropic complementary media sharing a vertex, within which light circles around closed trajectories. Alternatively, one can consider corner lenses with homogeneous isotropic media and map them into 1D PCs with heterogeneous bianisotropic layers. Interestingly, such complementary media are described by scalar, or matrix valued, sign-shifting parameters, which satisfy a new version of the generalized lens theorem of Pendry and Ramakrishna. This theorem can be derived using Fourier series solutions of the Maxwell-Tellegen equations, or from space-time symmetry arguments. Also of interest are 2D periodic checkerboards consisting of alternating rectangular cells of complementary media which are such that one point source in one cell gives rise to an infinite set of images with an image in every other cell. Such checkerboards can themselves be mapped into a class of 3D corner lenses of complementary bianisotropic media. These theoretical results are illustrated by finite element computations.

Geospatial Data Stream Processing in Python Using FOSS4G Components

NASA Astrophysics Data System (ADS)

McFerren, G.; van Zyl, T.

2016-06-01

One viewpoint of current and future IT systems holds that there is an increase in the scale and velocity at which data are acquired and analysed from heterogeneous, dynamic sources. In the earth observation and geoinformatics domains, this process is driven by the increase in number and types of devices that report location and the proliferation of assorted sensors, from satellite constellations to oceanic buoy arrays. Much of these data will be encountered as self-contained messages on data streams - continuous, infinite flows of data. Spatial analytics over data streams concerns the search for spatial and spatio-temporal relationships within and amongst data "on the move". In spatial databases, queries can assess a store of data to unpack spatial relationships; this is not the case on streams, where spatial relationships need to be established with the incomplete data available. Methods for spatially-based indexing, filtering, joining and transforming of streaming data need to be established and implemented in software components. This article describes the usage patterns and performance metrics of a number of well known FOSS4G Python software libraries within the data stream processing paradigm. In particular, we consider the RTree library for spatial indexing, the Shapely library for geometric processing and transformation and the PyProj library for projection and geodesic calculations over streams of geospatial data. We introduce a message oriented Python-based geospatial data streaming framework called Swordfish, which provides data stream processing primitives, functions, transports and a common data model for describing messages, based on the Open Geospatial Consortium Observations and Measurements (O&M) and Unidata Common Data Model (CDM) standards. We illustrate how the geospatial software components are integrated with the Swordfish framework. Furthermore, we describe the tight temporal constraints under which geospatial functionality can be invoked when processing high velocity, potentially infinite geospatial data streams. The article discusses the performance of these libraries under simulated streaming loads (size, complexity and volume of messages) and how they can be deployed and utilised with Swordfish under real load scenarios, illustrated by a set of Vessel Automatic Identification System (AIS) use cases. We conclude that the described software libraries are able to perform adequately under geospatial data stream processing scenarios - many real application use cases will be handled sufficiently by the software.

Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Um, Jaegon; Yi, Su Do; Kim, Beom Jun

2011-11-01

In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional lattices, however, one can also consider infinite-dimensional structures, and the question is whether this mean-field character extends to quantum-mechanical cases as well. We therefore investigate the transverse-field quantum Ising model on the globally coupled network and on the Watts-Strogatz small-world network by means of quantum Monte Carlo simulations and the finite-size scaling analysis. We confirm that both of the structures exhibit critical behavior consistent with the mean-field description. In particular, we show that the existing cumulant method has difficulty in estimating the correct dynamic critical exponent and suggest that an order parameter based on the quantum-mechanical expectation value can be a practically useful numerical observable to determine critical behavior when there is no well-defined dimensionality.

Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags

NASA Astrophysics Data System (ADS)

Karmakar, R.; Sur, A.; Kanoria, M.

2016-07-01

The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord-Shulman and dual-phase-lag models.

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium

NASA Astrophysics Data System (ADS)

Chernomordik, Victor; Gandjbakhche, Amir H.; Hassan, Moinuddin; Pajevic, Sinisa; Weiss, George H.

2010-12-01

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the objective being to estimate the position and lifetime of the fluorophore. This can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.

Softened gravity and the extension of the standard model up to infinite energy

NASA Astrophysics Data System (ADS)

Giudice, Gian F.; Isidori, Gino; Salvio, Alberto; Strumia, Alessandro

2015-02-01

Attempts to solve naturalness by having the weak scale as the only breaking of classical scale invariance have to deal with two severe difficulties: gravity and the absence of Landau poles. We show that solutions to the first problem require premature modifications of gravity at scales no larger than 1011 GeV, while the second problem calls for many new particles at the weak scale. To build models that fulfill these properties, we classify 4- dimensional Quantum Field Theories that satisfy Total Asymptotic Freedom (TAF): the theory holds up to infinite energy, where all coupling constants flow to zero. We develop a technique to identify such theories and determine their low-energy predictions. Since the Standard Model turns out to be asymptotically free only under the unphysical conditions g 1 = 0, M t = 186 GeV, M τ = 0, M h = 163 GeV, we explore some of its weak-scale extensions that satisfy the requirements for TAF.

Cosmic Topology

NASA Astrophysics Data System (ADS)

Luminet, Jean-Pierre

2015-08-01

Cosmic Topology is the name given to the study of the overall shape of the universe, which involves both global topological features and more local geometrical properties such as curvature. Whether space is finite or infinite, simply-connected or multi-connected like a torus, smaller or greater than the portion of the universe that we can directly observe, are questions that refer to topology rather than curvature. A striking feature of some relativistic, multi-connected "small" universe models is to create multiples images of faraway cosmic sources. While the most recent cosmological data fit the simplest model of a zero-curvature, infinite space model, they are also consistent with compact topologies of the three homogeneous and isotropic geometries of constant curvature, such as, for instance, the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn. After a "dark age" period, the field of Cosmic Topology has recently become one of the major concerns in cosmology, not only for theorists but also for observational astronomers, leaving open a number of unsolved issues.

An Airborne Radar Model For Non-Uniformly Spaced Antenna Arrays

DTIC Science & Technology

2006-03-01

Department of Defense, or the United States Government . AFIT-GE-ENG-06-58 An Airborne Radar Model For Non-Uniformly Spaced Antenna Arrays THESIS Presented...different circular arrays, one containing 24 elements and one containing 15 elements. The circular array per- formance is compared to that of a 6 × 6...model and compared to the radar model of [5, 6, 13]. The two models are mathematically equivalent when the uniformly spaced array is linear. The two

Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane

DTIC Science & Technology

2014-07-01

Electromagnetic Scattering by Multiple Cavities Embedded in the Infinite 2D Ground Plane Peijun Li 1 and Aihua W. Wood 2 1 Department of...of the electromagnetic wave scattering by multiple open cavities, which are embedded in an infinite two-dimensional ground plane . By introducing a...equation, variational formulation. I. INTRODUCTION A cavity is referred to as a local perturbation of the infinite ground plane . Given the cavity

Recent advances in the biomimicry of structural colours.

PubMed

Dumanli, Ahu Gümrah; Savin, Thierry

2016-12-21

Nature has mastered the construction of nanostructures with well-defined macroscopic effects and purposes. Structural colouration is a visible consequence of the particular patterning of a reflecting surface with regular structures at submicron length scales. Structural colours usually appear bright, shiny, iridescent or with a metallic look, as a result of physical processes such as diffraction, interference, or scattering with a typically small dissipative loss. These features have recently attracted much research effort in materials science, chemistry, engineering and physics, in order to understand and produce structural colours. In these early stages of photonics, researchers facing an infinite array of possible colour-producing structures are heavily inspired by the elaborate architectures they find in nature. We review here the recent technological strategies employed to artificially mimic the structural colours found in nature, as well as some of their current and potential applications.

Measurement of toroidal vessel eddy current during plasma disruption on J-TEXT.

PubMed

Liu, L J; Yu, K X; Zhang, M; Zhuang, G; Li, X; Yuan, T; Rao, B; Zhao, Q

2016-01-01

In this paper, we have employed a thin, printed circuit board eddy current array in order to determine the radial distribution of the azimuthal component of the eddy current density at the surface of a steel plate. The eddy current in the steel plate can be calculated by analytical methods under the simplifying assumptions that the steel plate is infinitely large and the exciting current is of uniform distribution. The measurement on the steel plate shows that this method has high spatial resolution. Then, we extended this methodology to a toroidal geometry with the objective of determining the poloidal distribution of the toroidal component of the eddy current density associated with plasma disruption in a fusion reactor called J-TEXT. The preliminary measured result is consistent with the analysis and calculation results on the J-TEXT vacuum vessel.

Modeling interface exchange coupling: Effect on switching of granular FePt films

NASA Astrophysics Data System (ADS)

Abugri, Joseph B.; Visscher, P. B.; Su, Hao; Gupta, Subhadra

2015-07-01

To raise the areal density of magnetic recording to ˜1 Tbit/in2, there has been much recent work on the use of FePt granular films, because their high perpendicular anisotropy allows small grains to be stable. However, their coercivity may be higher than available write-head fields. One approach to reduce the coercivity is to heat the grain (heat assisted magnetic recording). Another strategy is to add a soft capping layer to help nucleate switching via exchange coupling with the hard FePt grains. We have simulated a model of such a capped medium and have studied the effect of the strength of the interface exchange and thickness of hard layer and soft layer on the overall coercivity. Although the magnetization variation within such boundary layers may be complex, the net effect of the boundary can often be modeled as an infinitely thin interface characterized by an interface exchange energy density—we show how to do this consistently in a micromagnetic simulation. Although the switching behavior in the presence of exchange, magnetostatic, and external fields is quite complex, we show that by adding these fields one at a time, the main features of the M-H loop can be understood. In particular, we find that even without hard-soft interface exchange, magnetostatic coupling eliminates the zero-field kink in the loop, so that the absence of the kink does not (as has sometimes been assumed) imply exchange coupling. The computations have been done with a public-domain micromagnetics simulator that has been adapted to easily simulate arrays of grains.

Kinematic Cosmology & a new ``Steady State'' Model of Continued Creation

NASA Astrophysics Data System (ADS)

Wegener, Mogens

2006-03-01

Only a new "steady state" model justifies the observations of fully mature galaxies at ever increasing distances. The basic idea behind the world model presented here, which is a synthesis of the cosmologies of Parmenides and Herakleitos, is that the invariant structure of the infinite contents of a universe in flux may be depicted as a finite hyperbolic pseudo-sphere.

Effect of membrane microheterogeneity and domain size on fluorescence resonance energy transfer.

PubMed

Towles, Kevin B; Brown, Angela C; Wrenn, Steven P; Dan, Nily

2007-07-15

Studies of multicomponent membranes suggest lateral inhomogeneity in the form of membrane domains, but the size of small (nanoscale) domains in situ cannot be determined with current techniques. In this article, we present a model that enables extraction of membrane domain size from time-resolved fluorescence resonance energy transfer (FRET) data. We expand upon a classic approach to the infinite phase separation limit and formulate a model that accounts for the presence of disklike domains of finite dimensions within a two-dimensional infinite planar bilayer. The model was tested against off-lattice Monte Carlo calculations of a model membrane in the liquid-disordered (l(d)) and liquid-ordered (l(o)) coexistence regime. Simulated domain size was varied from 5 to 50 nm, and two fluorophores, preferentially partitioning into opposite phases, were randomly mixed to obtain the simulated time-resolved FRET data. The Monte Carlo data show clear differences in the efficiency of energy transfer as a function of domain size. The model fit of the data yielded good agreement for the domain size, especially in cases where the domain diameter is <20 nm. Thus, data analysis using the proposed model enables measurement of nanoscale membrane domains using time-resolved FRET.

Magneto-elastic modeling of composites containing chain-structured magnetostrictive particles

NASA Astrophysics Data System (ADS)

Yin, H. M.; Sun, L. Z.; Chen, J. S.

2006-05-01

Magneto-elastic behavior is investigated for two-phase composites containing chain-structured magnetostrictive particles under both magnetic and mechanical loading. To derive the local magnetic and elastic fields, three modified Green's functions are derived and explicitly integrated for the infinite domain containing a spherical inclusion with a prescribed magnetization, body force, and eigenstrain. A representative volume element containing a chain of infinite particles is introduced to solve averaged magnetic and elastic fields in the particles and the matrix. Effective magnetostriction of composites is derived by considering the particle's magnetostriction and the magnetic interaction force. It is shown that there exists an optimal choice of the Young's modulus of the matrix and the volume fraction of the particles to achieve the maximum effective magnetostriction. A transversely isotropic effective elasticity is derived at the infinitesimal deformation. Disregarding the interaction term, this model provides the same effective elasticity as Mori-Tanaka's model. Comparisons of model results with the experimental data and other models show the efficacy of the model and suggest that the particle interactions have a considerable effect on the effective magneto-elastic properties of composites even for a low particle volume fraction.

Analytic models of ducted turbomachinery tone noise sources. Volume 2: Subprogram documentation

NASA Technical Reports Server (NTRS)

Clark, T. L.; Ganz, U. W.; Graf, G. A.; Westall, J. S.

1974-01-01

Analytical models were developed for computing the periodic sound pressures of subsonic fans in an infinite hardwall annular duct with uniform flow. The computer programs are described which are used for numerical computations of sound pressure mode amplitudes. The data are applied to the acoustic properties of turbomachinery.

Opinion dynamics on an adaptive random network

NASA Astrophysics Data System (ADS)

Benczik, I. J.; Benczik, S. Z.; Schmittmann, B.; Zia, R. K. P.

2009-04-01

We revisit the classical model for voter dynamics in a two-party system with two basic modifications. In contrast to the original voter model studied in regular lattices, we implement the opinion formation process in a random network of agents in which interactions are no longer restricted by geographical distance. In addition, we incorporate the rapidly changing nature of the interpersonal relations in the model. At each time step, agents can update their relationships. This update is determined by their own opinion, and by their preference to make connections with individuals sharing the same opinion, or rather with opponents. In this way, the network is built in an adaptive manner, in the sense that its structure is correlated and evolves with the dynamics of the agents. The simplicity of the model allows us to examine several issues analytically. We establish criteria to determine whether consensus or polarization will be the outcome of the dynamics and on what time scales these states will be reached. In finite systems consensus is typical, while in infinite systems a disordered metastable state can emerge and persist for infinitely long time before consensus is reached.

Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background.

PubMed

Luminet, Jean-Pierre; Weeks, Jeffrey R; Riazuelo, Alain; Lehoucq, Roland; Uzan, Jean-Philippe

2003-10-09

The current 'standard model' of cosmology posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the largest scales. Temperature correlations across the microwave sky match expectations on angular scales narrower than 60 degrees but, contrary to predictions, vanish on scales wider than 60 degrees. Several explanations have been proposed. One natural approach questions the underlying geometry of space--namely, its curvature and topology. In an infinite flat space, waves from the Big Bang would fill the universe on all length scales. The observed lack of temperature correlations on scales beyond 60 degrees means that the broadest waves are missing, perhaps because space itself is not big enough to support them. Here we present a simple geometrical model of a finite space--the Poincaré dodecahedral space--which accounts for WMAP's observations with no fine-tuning required. The predicted density is Omega(0) approximately 1.013 > 1, and the model also predicts temperature correlations in matching circles on the sky.

Standard, Random, and Optimum Array conversions from Two-Pole resistance data

DOE PAGES

Rucker, D. F.; Glaser, Danney R.

2014-09-01

We present an array evaluation of standard and nonstandard arrays over a hydrogeological target. We develop the arrays by linearly combining data from the pole-pole (or 2-pole) array. The first test shows that reconstructed resistances for the standard Schlumberger and dipoledipole arrays are equivalent or superior to the measured arrays in terms of noise, especially at large geometric factors. The inverse models for the standard arrays also confirm what others have presented in terms of target resolvability, namely the dipole-dipole array has the highest resolution. In the second test, we reconstruct random electrode combinations from the 2-pole data segregated intomore » inner, outer, and overlapping dipoles. The resistance data and inverse models from these randomized arrays show those with inner dipoles to be superior in terms of noise and resolution and that overlapping dipoles can cause model instability and low resolution. Finally, we use the 2-pole data to create an optimized array that maximizes the model resolution matrix for a given electrode geometry. The optimized array produces the highest resolution and target detail. Thus, the tests demonstrate that high quality data and high model resolution can be achieved by acquiring field data from the pole-pole array.« less

Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping

NASA Astrophysics Data System (ADS)

Lu, Jianfeng; Zhou, Zhennan

2018-02-01

To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limit, the ring polymer evolves according to an averaged Hamiltonian with respect to all possible surface index configurations of the ring polymer and thus connects the surface hopping approach to the mean-field path-integral molecular dynamics. A multiscale integrator for the infinite swapping limit is also proposed to enable efficient sampling based on the limiting dynamics. Numerical results demonstrate the huge improvement of sampling efficiency of the infinite swapping compared with the direct simulation of path-integral molecular dynamics with surface hopping.

The infinite limit as an eliminable approximation for phase transitions

NASA Astrophysics Data System (ADS)

Ardourel, Vincent

2018-05-01

It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al., 2000). Based on this theory, I argue for the plausibility for eliminating the infinite limit for studying phase transitions. I offer a new account for phase transitions in finite systems, and I argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.

Propagation of high frequency electrostatic surface waves along the planar interface between plasma and dusty plasma

NASA Astrophysics Data System (ADS)

Mishra, Rinku; Dey, M.

2018-04-01

An analytical model is developed that explains the propagation of a high frequency electrostatic surface wave along the interface of a plasma system where semi-infinite electron-ion plasma is interfaced with semi-infinite dusty plasma. The model emphasizes that the source of such high frequency waves is inherent in the presence of ion acoustic and dust ion acoustic/dust acoustic volume waves in electron-ion plasma and dusty plasma region. Wave dispersion relation is obtained for two distinct cases and the role of plasma parameters on wave dispersion is analyzed in short and long wavelength limits. The normalized surface wave frequency is seen to grow linearly for lower wave number but becomes constant for higher wave numbers in both the cases. It is observed that the normalized frequency depends on ion plasma frequencies when dust oscillation frequency is neglected.

Probability distribution of the entanglement across a cut at an infinite-randomness fixed point

NASA Astrophysics Data System (ADS)

Devakul, Trithep; Majumdar, Satya N.; Huse, David A.

2017-03-01

We calculate the probability distribution of entanglement entropy S across a cut of a finite one-dimensional spin chain of length L at an infinite-randomness fixed point using Fisher's strong randomness renormalization group (RG). Using the random transverse-field Ising model as an example, the distribution is shown to take the form p (S |L ) ˜L-ψ (k ) , where k ≡S /ln[L /L0] , the large deviation function ψ (k ) is found explicitly, and L0 is a nonuniversal microscopic length. We discuss the implications of such a distribution on numerical techniques that rely on entanglement, such as matrix-product-state-based techniques. Our results are verified with numerical RG simulations, as well as the actual entanglement entropy distribution for the random transverse-field Ising model which we calculate for large L via a mapping to Majorana fermions.

Infinite coherence time of edge spins in finite-length chains

NASA Astrophysics Data System (ADS)

Maceira, Ivo A.; Mila, Frédéric

2018-02-01

Motivated by the recent observation that exponentially long coherence times can be achieved for edge spins in models with strong zero modes, we study the impact of level crossings in finite-length spin chains on the dynamics of the edge spins. Focusing on the X Y spin-1 /2 chain with a transverse or longitudinal magnetic field, two models relevant to understanding recent experimental results on cobalt adatoms, we show that the edge spins can remain coherent for an infinite time even for a finite-length chain if the magnetic field is tuned to a value at which there is a level crossing. Furthermore, we show that the edge spins remain coherent for any initial state for the integrable case of a transverse field because all states have level crossings at the same value of the field, while the coherence time is increasingly large for lower temperatures in the case of a longitudinal field, which is nonintegrable.

Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume

DOE PAGES

Briceno, Raul A.; Hansen, Maxwell T.

2016-07-13

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

On the Magnetic Shield for a Vlasov-Poisson Plasma

NASA Astrophysics Data System (ADS)

Caprino, Silvia; Cavallaro, Guido; Marchioro, Carlo

2017-12-01

We study the screening of a bounded body Γ against the effect of a wind of charged particles, by means of a shield produced by a magnetic field which becomes infinite on the border of Γ . The charged wind is modeled by a Vlasov-Poisson plasma, the bounded body by a torus, and the external magnetic field is taken close to the border of Γ . We study two models: a plasma composed by different species with positive or negative charges, and finite total mass of each species, and another made of many species of the same sign, each having infinite mass. We investigate the time evolution of both systems, showing in particular that the plasma particles cannot reach the body. Finally we discuss possible extensions to more general initial data. We show also that when the magnetic lines are straight lines, (that imposes an unbounded body), the previous results can be improved.

An infinite set of Ward identities for adiabatic modes in cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hinterbichler, Kurt; Hui, Lam; Khoury, Justin, E-mail: khinterbichler@perimeterinstitute.ca, E-mail: lh399@columbia.edu, E-mail: jkhoury@sas.upenn.edu

2014-01-01

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N+1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain — completely for n = 0,1, and partially for n ≥ 2 — themore » q{sup n} behavior of the soft limits. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ≥ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.« less

Infinite family of three-dimensional Floquet topological paramagnets

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Vishwanath, Ashvin; Fidkowski, Lukasz

2018-06-01

We uncover an infinite family of time-reversal symmetric 3 d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium and are governed by an infinite set of Z2-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3 d FTPMs are not captured by group cohomology methods and cannot be obtained from equilibrium classifications simply by treating the discrete time translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous Z2 (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2 d system without breaking time reversal symmetry.

Infinite densities for Lévy walks.

PubMed

Rebenshtok, A; Denisov, S; Hänggi, P; Barkai, E

2014-12-01

Motion of particles in many systems exhibits a mixture between periods of random diffusive-like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous diffusion, where low-order moments 〈|x(t)|(q)〉 with q below a critical value q(c) exhibit diffusive scaling while for q>q(c) a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α, and the diffusion coefficient K(α). We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.

Edge effect on a vacancy state in semi-infinite graphene

NASA Astrophysics Data System (ADS)

Deng, Hai-Yao; Wakabayashi, Katsunori

2014-09-01

The edge effect on a single vacancy state of semi-infinite graphene (SIG) has been studied using Green's function method within the tight-binding model. In the case of infinite graphene, it is known that a vacancy induces a zero-energy resonance state, whose wave function decays inversely with distance (R) from the vacancy and is not normalizable. However, for SIG with an armchair edge, we find that the corresponding wave function decays as R-2 and hence becomes normalizable owing to the intervalley interference caused by the armchair edge. For SIG with a zigzag edge, the vacancy state depends on the sublattice of the vacancy. When the vacancy and the edge belong to different sublattices, the vacancy has no effect on the zero-energy vacancy state. In contrast, when the vacancy is located on the same sublattice as the edge, the resonance state disappears but the wave function at zero energy is strongly distorted near the vacancy. Our results reveal that the presence of edges crucially changes the vacancy state in graphene, and thus such a state can be used to probe the edge structure.

Fault-tolerant control of large space structures using the stable factorization approach

NASA Technical Reports Server (NTRS)

Razavi, H. C.; Mehra, R. K.; Vidyasagar, M.

1986-01-01

Large space structures are characterized by the following features: they are in general infinite-dimensional systems, and have large numbers of undamped or lightly damped poles. Any attempt to apply linear control theory to large space structures must therefore take into account these features. Phase I consisted of an attempt to apply the recently developed Stable Factorization (SF) design philosophy to problems of large space structures, with particular attention to the aspects of robustness and fault tolerance. The final report on the Phase I effort consists of four sections, each devoted to one task. The first three sections report theoretical results, while the last consists of a design example. Significant results were obtained in all four tasks of the project. More specifically, an innovative approach to order reduction was obtained, stabilizing controller structures for plants with an infinite number of unstable poles were determined under some conditions, conditions for simultaneous stabilizability of an infinite number of plants were explored, and a fault tolerance controller design that stabilizes a flexible structure model was obtained which is robust against one failure condition.

Experimental Identification and Simulation of Time and/or Rate Dependent Reversible and Irreversible Deformation Regions for both a Titanium and Nickel Alloy

NASA Technical Reports Server (NTRS)

Arnold, Steven M.; Lerch, Bradley A.; Sellers, Cory

2013-01-01

In this paper time and/or rate dependent deformation regions are experimentally mapped out as a function of temperature. It is clearly demonstrated that the concept of a threshold stress (a stress that delineate reversible and irreversible behavior) is valid and necessary at elevated temperatures and corresponds to the classical yield stress at lower temperatures. Also the infinitely slow modulus, (Es) i.e. the elastic modulus of the material if it was loaded at an infinitely slow strain rate, and the "dynamic modulus", modulus, Ed, which represents the modulus of the material if it is loaded at an infinitely fast rate are used to delineate rate dependent from rate independent regions. As demonstrated at elevated temperatures there is a significant difference between the two modulus values, thus indicating both significant time-dependence and rate dependence. In the case of the nickel-based super alloy, ME3, this behavior is also shown to be grain size specific. Consequently, at higher temperatures viscoelastic behavior exist below k (i.e., the threshold stress) and at stresses above k the behavior is viscoplastic. Finally a multi-mechanism, stress partitioned viscoelastic model, capable of being consistently coupled to a viscoplastic model is characterized over the full temperature range investigated for Ti-6-4 and ME3.

Asymmetrical effects of mesophyll conductance on fundamental photosynthetic parameters and their relationships estimated from leaf gas exchange measurements.

PubMed

Sun, Ying; Gu, Lianhong; Dickinson, Robert E; Pallardy, Stephen G; Baker, John; Cao, Yonghui; DaMatta, Fábio Murilo; Dong, Xuejun; Ellsworth, David; Van Goethem, Davina; Jensen, Anna M; Law, Beverly E; Loos, Rodolfo; Martins, Samuel C Vitor; Norby, Richard J; Warren, Jeffrey; Weston, David; Winter, Klaus

2014-04-01

Worldwide measurements of nearly 130 C3 species covering all major plant functional types are analysed in conjunction with model simulations to determine the effects of mesophyll conductance (g(m)) on photosynthetic parameters and their relationships estimated from A/Ci curves. We find that an assumption of infinite g(m) results in up to 75% underestimation for maximum carboxylation rate V(cmax), 60% for maximum electron transport rate J(max), and 40% for triose phosphate utilization rate T(u) . V(cmax) is most sensitive, J(max) is less sensitive, and T(u) has the least sensitivity to the variation of g(m). Because of this asymmetrical effect of g(m), the ratios of J(max) to V(cmax), T(u) to V(cmax) and T(u) to J(max) are all overestimated. An infinite g(m) assumption also limits the freedom of variation of estimated parameters and artificially constrains parameter relationships to stronger shapes. These findings suggest the importance of quantifying g(m) for understanding in situ photosynthetic machinery functioning. We show that a nonzero resistance to CO2 movement in chloroplasts has small effects on estimated parameters. A non-linear function with gm as input is developed to convert the parameters estimated under an assumption of infinite gm to proper values. This function will facilitate gm representation in global carbon cycle models. © 2013 John Wiley & Sons Ltd.

Finite horizon optimum control with and without a scrap value

NASA Astrophysics Data System (ADS)

Neck, R.; Blueschke-Nikolaeva, V.; Blueschke, D.

2017-06-01

In this paper, we study the effects of scrap values on the solutions of optimal control problems with finite time horizon. We show how to include a scrap value, either for the state variables or for the state and the control variables, in the OPTCON2 algorithm for the optimal control of dynamic economic systems. We ask whether the introduction of a scrap value can serve as a substitute for an infinite horizon in economic policy optimization problems where the latter option is not available. Using a simple numerical macroeconomic model, we demonstrate that the introduction of a scrap value cannot induce control policies which can be expected for problems with an infinite time horizon.

Influence of the geomembrane on time-lapse ERT measurements for leachate injection monitoring.

PubMed

Audebert, M; Clément, R; Grossin-Debattista, J; Günther, T; Touze-Foltz, N; Moreau, S

2014-04-01

Leachate recirculation is a key process in the operation of municipal waste landfills as bioreactors. To quantify the water content and to evaluate the leachate injection system, in situ methods are required to obtain spatially distributed information, usually electrical resistivity tomography (ERT). However, this method can present false variations in the observations due to several parameters. This study investigates the impact of the geomembrane on ERT measurements. Indeed, the geomembrane tends to be ignored in the inversion process in most previously conducted studies. The presence of the geomembrane can change the boundary conditions of the inversion models, which have classically infinite boundary conditions. Using a numerical modelling approach, the authors demonstrate that a minimum distance is required between the electrode line and the geomembrane to satisfy the good conditions of use of the classical inversion tools. This distance is a function of the electrode line length (i.e. of the unit electrode spacing) used, the array type and the orientation of the electrode line. Moreover, this study shows that if this criterion on the minimum distance is not satisfied, it is possible to significantly improve the inversion process by introducing the complex geometry and the geomembrane location into the inversion tools. These results are finally validated on a field data set gathered on a small municipal solid waste landfill cell where this minimum distance criterion cannot be satisfied. Copyright © 2014 Elsevier Ltd. All rights reserved.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Phillion, D.

This code enables one to display, take line-outs on, and perform various transformations on an image created by an array of integer*2 data. Uncompressed eight-bit TIFF files created on either the Macintosh or the IBM PC may also be read in and converted to a 16 bit signed integer image. This code is designed to handle all the formates used for PDS (photo-densitometer) files at the Lawrence Livermore National Laboratory. These formats are all explained by the application code. The image may be zoomed infinitely and the gray scale mapping can be easily changed. Line-outs may be horizontal or verticalmore » with arbitrary width, angled with arbitrary end points, or taken along any path. This code is usually used to examine spectrograph data. Spectral lines may be identified and a polynomial fit from position to wavelength may be found. The image array can be remapped so that the pixels all have the same change of lambda width. It is not necessary to do this, however. Lineouts may be printed, saved as Cricket tab-delimited files, or saved as PICT2 files. The plots may be linear, semilog, or logarithmic with nice values and proper scientific notation. Typically, spectral lines are curved. By identifying points on these lines and fitting their shapes by polyn.« less

Modeling the Distribution of Fingerprint Characteristics. Revision 1.

DTIC Science & Technology

1980-09-19

the details of the print. The ridge-line details are termed Galton characteristics since Sir Francis Galton was among the first to study them...U.S.A. CONTENTS Abstract 1. Introduction 2. Background Information on Fingerprints 2.1. Types 2.2. Ridge counts 2.3. The Galton details 3. Data...The Multinomial Markov Model 7. The Poisson Markov Model 8. The Infinitely Divisible Model Acknowledgements References Appendices A The Galton

Explaining Quantitative Variation in the Rate of Optional Infinitive Errors across Languages: A Comparison of MOSAIC and the Variational Learning Model

ERIC Educational Resources Information Center

Freudenthal, Daniel: Pine, Julian; Gobet, Fernando

2010-01-01

In this study, we use corpus analysis and computational modelling techniques to compare two recent accounts of the OI stage: Legate & Yang's (2007) Variational Learning Model and Freudenthal, Pine & Gobet's (2006) Model of Syntax Acquisition in Children. We first assess the extent to which each of these accounts can explain the level of OI errors…

Full-Potential Modeling of Blade-Vortex Interactions. Degree awarded by George Washington Univ., Feb. 1987

NASA Technical Reports Server (NTRS)

Jones, Henry E.

1997-01-01

A study of the full-potential modeling of a blade-vortex interaction was made. A primary goal of this study was to investigate the effectiveness of the various methods of modeling the vortex. The model problem restricts the interaction to that of an infinite wing with an infinite line vortex moving parallel to its leading edge. This problem provides a convenient testing ground for the various methods of modeling the vortex while retaining the essential physics of the full three-dimensional interaction. A full-potential algorithm specifically tailored to solve the blade-vortex interaction (BVI) was developed to solve this problem. The basic algorithm was modified to include the effect of a vortex passing near the airfoil. Four different methods of modeling the vortex were used: (1) the angle-of-attack method, (2) the lifting-surface method, (3) the branch-cut method, and (4) the split-potential method. A side-by-side comparison of the four models was conducted. These comparisons included comparing generated velocity fields, a subcritical interaction, and a critical interaction. The subcritical and critical interactions are compared with experimentally generated results. The split-potential model was used to make a survey of some of the more critical parameters which affect the BVI.

Maintenance of genetic variation with a frequency-dependent selection model as compared to the overdominant model.

PubMed

Hedrick, P W

1972-12-01

A frequency-dependent selection model proposed by Huang, Singh and Kojima (1971) was found to be more effective at maintaining genetic variation in a finite population than the overdominant model. The fourth moment parameter of the distribution of unfixed states showed that there was a more platykurtic distribution for the frequency-dependent model. This agreed well with the expected gene frequency change found for an infinite population.

NATURALIST'S APPLICATION OF A PROMISING TURBULENCE MODEL

EPA Science Inventory

Turbulence has infinite applications to the biological sciences, affecting distributions, transport, feeding, mating, and other biological processes. The topic is like the universe for which five successive magnefications are required to finally focus on a topic that can be grasp...

Infinity: The Twilight Zone of Mathematics.

ERIC Educational Resources Information Center

Love, William P.

1989-01-01

The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)

A model for the distributed storage and processing of large arrays

NASA Technical Reports Server (NTRS)

Mehrota, P.; Pratt, T. W.

1983-01-01

A conceptual model for parallel computations on large arrays is developed. The model provides a set of language concepts appropriate for processing arrays which are generally too large to fit in the primary memories of a multiprocessor system. The semantic model is used to represent arrays on a concurrent architecture in such a way that the performance realities inherent in the distributed storage and processing can be adequately represented. An implementation of the large array concept as an Ada package is also described.

Bayesian structural inference for hidden processes.

PubMed

Strelioff, Christopher C; Crutchfield, James P

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Bayesian structural inference for hidden processes

NASA Astrophysics Data System (ADS)

Strelioff, Christopher C.; Crutchfield, James P.

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Modelling of Rail Vehicles and Track for Calculation of Ground-Vibration Transmission Into Buildings

NASA Astrophysics Data System (ADS)

Hunt, H. E. M.

1996-05-01

A methodology for the calculation of vibration transmission from railways into buildings is presented. The method permits existing models of railway vehicles and track to be incorporated and it has application to any model of vibration transmission through the ground. Special attention is paid to the relative phasing between adjacent axle-force inputs to the rail, so that vibration transmission may be calculated as a random process. The vehicle-track model is used in conjunction with a building model of infinite length. The tracking and building are infinite and parallel to each other and forces applied are statistically stationary in space so that vibration levels at any two points along the building are the same. The methodology is two-dimensional for the purpose of application of random process theory, but fully three-dimensional for calculation of vibration transmission from the track and through the ground into the foundations of the building. The computational efficiency of the method will interest engineers faced with the task of reducing vibration levels in buildings. It is possible to assess the relative merits of using rail pads, under-sleeper pads, ballast mats, floating-slab track or base isolation for particular applications.

The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics

NASA Astrophysics Data System (ADS)

Belloni, M.; Robinett, R. W.

2014-07-01

The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems. For the ISW and the attractive DDF potentials, Eq. (4) implies, as expected, that energy eigenfunctions will have a kink-a discontinuous first derivative at the location of the infinite jump(s) in the potentials. However, the large |p| behavior of the momentum-space energy eigenfunction given by Eq. (5) will be |ϕ(p)|∝1/p2. Therefore for the ISW and the attractive DDF potentials, expectation value of p will be finite, but even powers of p higher than 2 will not lead to convergent integrals. This analysis proves that despite the kinks in the ISW and attractive DDF eigenfunctions, is finite, and therefore yield appropriate solutions to the Schrödinger equation.The existence of power-law ‘tails’ of a momentum distribution as indicated in Eq. (5) in the case of ‘less than perfect’ potentials [41], including a 1/p2 power-law dependence for a singular potential (such as the DDF form) may seem a mathematical artifact, but we note two explicit realizations of exactly this type of behavior in well-studied quantum systems.As noted below (in Section 6.2) the momentum-space energy eigenfunction of the ground state of one of the most familiar (and singular) potentials, namely that of the Coulomb problem, is given by ϕ1,0,0(p)=√{8p0/π}p0/2 where p0=ħ/a0 with a0 the Bohr radius. This prediction for the p-dependence of the hydrogen ground state momentum-space distribution was verified by Weigold [42] and collaborators with measurements taken out to p-values beyond 1.4p0; well out onto the power-law ‘tail’.More recently, Tan [43] and others [44,45] have noted that for condensed matter or atomic systems with a large scattering length, so that the short-range interactions can actually be modeled as singular δ-functions, the momentum distribution also exhibits a large momentum ‘tail’ which falls off as C/k4. The constant of proportionality, C (or contact as it has come to be known), encodes important information on the microscopic physics, in much the way that the constants in Eq. (5) are related to the details of the 1D potential. In fact, in one review [46] of these developments, this connection has been described as “How the tail wags the dog in ultracold atomic gases”. Just as with the H-atom momentum distribution, experiments have verified this power-law behavior for both fermion [47,48] and more recently Bose systems [49].It is these connections, namely of exemplary results derived in simpler one-dimensional systems such as the ISW and DDF potentials which find parallels in more fundamental physical realizations, that motivate us to review many of the basic mathematical and physical results of these two ‘benchmark’ model potentials. We hope that both students and instructors alike involved in advanced undergraduate and graduate courses in quantum mechanics will find this survey useful. We trust that it will aid readers in exploring a wide array of physical effects, using rigorous mathematical methods, in the context of familiar one-dimensional systems, making use of otherwise hard-to-find results.

Analytic models of ducted turbomachinery tone noise sources. Volume 1: Analysis

NASA Technical Reports Server (NTRS)

Clark, T. L.; Ganz, U. W.; Graf, G. A.; Westall, J. S.

1974-01-01

The analytic models developed for computing the periodic sound pressure of subsonic fans and compressors in an infinite, hardwall annular duct with uniform flow are described. The basic sound-generating mechanism is the scattering into sound waves of velocity disturbances appearing to the rotor or stator blades as a series of harmonic gusts. The models include component interactions and rotor alone.

Simulation Studies of the Dielectric Grating as an Accelerating and Focusing Structure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Soong, Ken; Peralta, E.A.; Byer, R.L.

A grating-based design is a promising candidate for a laser-driven dielectric accelerator. Through simulations, we show the merits of a readily fabricated grating structure as an accelerating component. Additionally, we show that with a small design perturbation, the accelerating component can be converted into a focusing structure. The understanding of these two components is critical in the successful development of any complete accelerator. The concept of accelerating electrons with the tremendous electric fields found in lasers has been proposed for decades. However, until recently the realization of such an accelerator was not technologically feasible. Recent advances in the semiconductor industry,more » as well as advances in laser technology, have now made laser-driven dielectric accelerators imminent. The grating-based accelerator is one proposed design for a dielectric laser-driven accelerator. This design, which was introduced by Plettner, consists of a pair of opposing transparent binary gratings, illustrated in Fig. 1. The teeth of the gratings serve as a phase mask, ensuring a phase synchronicity between the electromagnetic field and the moving particles. The current grating accelerator design has the drive laser incident perpendicular to the substrate, which poses a laser-structure alignment complication. The next iteration of grating structure fabrication seeks to monolithically create an array of grating structures by etching the grating's vacuum channel into a fused silica wafer. With this method it is possible to have the drive laser confined to the plane of the wafer, thus ensuring alignment of the laser-and-structure, the two grating halves, and subsequent accelerator components. There has been previous work using 2-dimensional finite difference time domain (2D-FDTD) calculations to evaluate the performance of the grating accelerator structure. However, this work approximates the grating as an infinite structure and does not accurately model a realizable structure. In this paper, we will present a 3-dimensional frequency-domain simulation of both the infinite and the finite grating accelerator structure. Additionally, we will present a new scheme for a focusing structure based on a perturbation of the accelerating structure. We will present simulations of this proposed focusing structure and quantify the quality of the focusing fields.« less

An analytic performance model of disk arrays and its application

NASA Technical Reports Server (NTRS)

Lee, Edward K.; Katz, Randy H.

1991-01-01

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

Improving the Instruction of Infinite Series

ERIC Educational Resources Information Center

Lindaman, Brian; Gay, A. Susan

2012-01-01

Calculus instructors struggle to teach infinite series, and students have difficulty understanding series and related concepts. Four instructional strategies, prominently used during the calculus reform movement, were implemented during a 3-week unit on infinite series in one class of second-semester calculus students. A description of each…

Generalization of Faustmann's Formula for Stochastic Forest Growth and Prices with Markov Decision Process Models

Treesearch

Joseph Buongiorno

2001-01-01

Faustmann's formula gives the land value, or the forest value of land with trees, under deterministic assumptions regarding future stand growth and prices, over an infinite horizon. Markov decision process (MDP) models generalize Faustmann's approach by recognizing that future stand states and prices are known only as probabilistic distributions. The...

Lieb-Thirring inequality for a model of particles with point interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frank, Rupert L.; Seiringer, Robert

2012-09-15

We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power (5/3).

Phylogenetic mixtures and linear invariants for equal input models.

PubMed

Casanellas, Marta; Steel, Mike

2017-04-01

The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies becoming indistinguishable from the data, even for infinitely long sequences. However, when the underlying Markov process supports linear phylogenetic invariants, then provided these are sufficiently informative, the identifiability of the tree topology can be restored. In this paper, we investigate a class of processes that support linear invariants once the stationary distribution is fixed, the 'equal input model'. This model generalizes the 'Felsenstein 1981' model (and thereby the Jukes-Cantor model) from four states to an arbitrary number of states (finite or infinite), and it can also be described by a 'random cluster' process. We describe the structure and dimension of the vector spaces of phylogenetic mixtures and of linear invariants for any fixed phylogenetic tree (and for all trees-the so called 'model invariants'), on any number n of leaves. We also provide a precise description of the space of mixtures and linear invariants for the special case of [Formula: see text] leaves. By combining techniques from discrete random processes and (multi-) linear algebra, our results build on a classic result that was first established by James Lake (Mol Biol Evol 4:167-191, 1987).

Envisioning the Infinite by Projecting Finite Properties

ERIC Educational Resources Information Center

Ely, Robert

2011-01-01

We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which…

Understanding the Behaviour of Infinite Ladder Circuits

ERIC Educational Resources Information Center

Ucak, C.; Yegin, K.

2008-01-01

Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…

Torsional Buckling Tests of a Simulated Solar Array

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1996-01-01

Spacecraft solar arrays are typically large structures supported by long, thin deployable booms. As such, they may be particularly susceptible to abnormal structural behavior induced by mechanical and thermal loading. One example is the Hubble Space Telescope solar arrays which consist of two split tubes fit one inside the other called BiSTEMs. The original solar arrays on the Hubble Space Telescope were found to be severely twisted following deployment and later telemetry data showed the arrays were vibrating during daylight to night and night to daylight transition. The solar array twist however can force the BiSTEM booms to change in cross-section and cause tile solar arrays to react unpredictably to future loading. The solar arrays were redesigned to correct for tile vibration, however, upon redeployment they again twisted. To assess the influence of boom cross-sectional configuration, experiments were conducted on two types of booms, (1)booms with closed cross-sections, and (2) booms with open cross-sections. Both models were subjected to compressive loading and imposed tip deflections. An existing analytical model by Chung and Thornton was used to define the individual load ranges for each model solar array configuration. The load range for the model solar array using closed cross-section booms was 0-120 Newtons and 0-160 Newtons for the model solar array using open cross-section booms. The results indicate the model solar array with closed cross-section booms buckled only in flexure. However, the results of the experiment with open cross-section booms indicate the model solar array buckled only in torsion and with imposed tip deflections the cross section can degrade by rotation of the inner relative to the outer STEM. For tile Hubble Space Telescope solar arrays the results of these experiments indicate the twisting resulted from the initial mechanical loading of the open cross-section booms.

Nanoengineering Testbed for Nanosolar Cell and Piezoelectric Compounds

DTIC Science & Technology

2012-02-29

element mesh. The third model was a 3D finite element mesh that included complete geometric representation of Berkovich tip. This model allows for a...height of the specimen. These simulations suggest the proper specimen size to approximate a body of semi-infinite extent for a given indentation depth...tip nanoindentation model was the third and final finite element mesh created for analysis and comparison. The material model and the finite element

[Generalization of the Lotka-Volterra equation].

PubMed

Nazarenko, V G

1976-01-01

A complete qualitative study of Lotka--Volterra model with cooperative interactions in the system predator-prey is carried out. The model is as follows: (see abstract). The character of all possible stationary states is investigated in the first quadrant of the phase plane of the model variables depending on the system parameters. It is shown that for the generalized model considered unstable and stable limit cycles only of the infinite amplitude are possible in the first quadrant.

Maintenance of Genetic Variation with a Frequency-Dependent Selection Model as Compared to the Overdominant Model

PubMed Central

Hedrick, Philip W.

1972-01-01

A frequency-dependent selection model proposed by Huang, Singh and Kojima (1971) was found to be more effective at maintaining genetic variation in a finite population than the overdominant model. The fourth moment parameter of the distribution of unfixed states showed that there was a more platykurtic distribution for the frequency-dependent model. This agreed well with the expected gene frequency change found for an infinite population. PMID:4652882

Periodic Inclusion—Matrix Microstructures with Constant Field Inclusions

NASA Astrophysics Data System (ADS)

Liu, Liping; James, Richard D.; Leo, Perry H.

2007-04-01

We find a class of special microstructures consisting of a periodic array of inclusions, with the special property that constant magnetization (or eigenstrain) of the inclusion implies constant magnetic field (or strain) in the inclusion. The resulting inclusions, which we term E-inclusions, have the same property in a finite periodic domain as ellipsoids have in infinite space. The E-inclusions are found by mapping the magnetostatic or elasticity equations to a constrained minimization problem known as a free-boundary obstacle problem. By solving this minimization problem, we can construct families of E-inclusions with any prescribed volume fraction between zero and one. In two dimensions, our results coincide with the microstructures first introduced by Vigdergauz,[1,2] while in three dimensions, we introduce a numerical method to calculate E-inclusions. E-inclusions extend the important role of ellipsoids in calculations concerning phase transformations and composite materials.

Measuring optical phase digitally in coherent metrology systems

NASA Astrophysics Data System (ADS)

Kelly, Damien P.; Ryle, James; Zhao, Liang; Sheridan, John T.

2017-05-01

The accurate measurement of optical phase has many applications in metrology. For biological samples, which appear transparent, the phase data provides information about the refractive index of the sample. In speckle metrology, the phase can be used to estimate stress and strains of a rough surface with high sensitivity. In this theoretical manuscript we compare and contrast the properties of two techniques for estimating the phase distribution of a wave field under the paraxial approximation: (I) A digital holographic system, and (II) An idealized phase retrieval system. Both systems use a CCD or CMOS array to measure the intensities of the wave fields that are reflected from or transmitted through the sample of interest. This introduces a numerical aspect to the problem. For the two systems above we examine how numerical calculations can limit the performance of these systems leading to a near-infinite number of possible solutions.

Measurement of toroidal vessel eddy current during plasma disruption on J-TEXT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, L. J.; Yu, K. X.; Zhang, M., E-mail: zhangming@hust.edu.cn

2016-01-15

In this paper, we have employed a thin, printed circuit board eddy current array in order to determine the radial distribution of the azimuthal component of the eddy current density at the surface of a steel plate. The eddy current in the steel plate can be calculated by analytical methods under the simplifying assumptions that the steel plate is infinitely large and the exciting current is of uniform distribution. The measurement on the steel plate shows that this method has high spatial resolution. Then, we extended this methodology to a toroidal geometry with the objective of determining the poloidal distributionmore » of the toroidal component of the eddy current density associated with plasma disruption in a fusion reactor called J-TEXT. The preliminary measured result is consistent with the analysis and calculation results on the J-TEXT vacuum vessel.« less

Quantizing and sampling considerations in digital phased-locked loops

NASA Technical Reports Server (NTRS)

Hurst, G. T.; Gupta, S. C.

1974-01-01

The quantizer problem is first considered. The conditions under which the uniform white sequence model for the quantizer error is valid are established independent of the sampling rate. An equivalent spectral density is defined for the quantizer error resulting in an effective SNR value. This effective SNR may be used to determine quantized performance from infinitely fine quantized results. Attention is given to sampling rate considerations. Sampling rate characteristics of the digital phase-locked loop (DPLL) structure are investigated for the infinitely fine quantized system. The predicted phase error variance equation is examined as a function of the sampling rate. Simulation results are presented and a method is described which enables the minimum required sampling rate to be determined from the predicted phase error variance equations.

Diversity of Poissonian populations.

PubMed

Eliazar, Iddo I; Sokolov, Igor M

2010-01-01

Populations represented by collections of points scattered randomly on the real line are ubiquitous in science and engineering. The statistical modeling of such populations leads naturally to Poissonian populations-Poisson processes on the real line with a distinguished maximal point. Poissonian populations are infinite objects underlying key issues in statistical physics, probability theory, and random fractals. Due to their infiniteness, measuring the diversity of Poissonian populations depends on the lower-bound cut-off applied. This research characterizes the classes of Poissonian populations whose diversities are invariant with respect to the cut-off level applied and establishes an elemental connection between these classes and extreme-value theory. The measures of diversity considered are variance and dispersion, Simpson's index and inverse participation ratio, Shannon's entropy and Rényi's entropy, and Gini's index.

Evidence of infinite and finite jump processes in commodity futures prices: Crude oil and natural gas

NASA Astrophysics Data System (ADS)

Cao, Wenbin; Guernsey, Scott B.; Linn, Scott C.

2018-07-01

We examine the frequency and character of price jumps in front month oil and natural gas futures prices. Prices are sampled every five seconds over the period 2006-2014. Our test results indicate that jumps in crude oil and natural gas futures prices can be decomposed into an infinite activity jump diffusion process and a less frequent but larger jump process. We also find that we cannot reject the hypothesis that Brownian motion is also present in both return series. The results are based on a battery of tests that are "model free". We further find that jumps account for respectively 36 and 41 percent of the realized variances of the crude oil and the natural gas returns.

A nomogram for interpreting slope stability of fine-grained deposits in modern and ancient-marine environments.

USGS Publications Warehouse

Booth, J.S.; Sangrey, D.A.; Fugate, J.K.

1985-01-01

This nomogram was designed to aid in interpreting the causes of mass movement in modern and ancient settings, to provide a basis for evaluating and predicting slope stability under given conditions and to further the understanding of the relationships among the several key factors that control slope stability. Design of the nomogram is based on effective stress and combines consolidation theory as applicable to depositional environments with the infinite-slope model of slope-stability analysis. If infinite-slope conditions are assumed to exist, the effective overburden stress can be used to derive a factor of safety against static slope failure by using the angle of internal friction and the slope angle. -from Authors

A boundary element model of the transport of a semi-infinite bubble through a microvessel bifurcation

NASA Astrophysics Data System (ADS)

Calderon, Andres J.; Eshpuniyani, Brijesh; Fowlkes, J. Brian; Bull, Joseph L.

2010-06-01

Motivated by a developmental gas embolotherapy technique for selective occlusion of blood flow to tumors, we examined the transport of a pressure-driven semi-infinite bubble through a liquid-filled bifurcating channel. Homogeneity of bubble splitting as the bubble passes through a vessel bifurcation affects the degree to which the vascular network near the tumor can be uniformly occluded. The homogeneity of bubble splitting was found to increase with bubble driving pressure and to decrease with increased bifurcation angle. Viscous losses at the bifurcation were observed to affect the bubble speed significantly. The potential for oscillating bubble interfaces to induce flow recirculation and impart high stresses on the vessel endothelium was also observed.

Deciding Full Branching Time Logic by Program Transformation

NASA Astrophysics Data System (ADS)

Pettorossi, Alberto; Proietti, Maurizio; Senni, Valerio

We present a method based on logic program transformation, for verifying Computation Tree Logic (CTL*) properties of finite state reactive systems. The finite state systems and the CTL* properties we want to verify, are encoded as logic programs on infinite lists. Our verification method consists of two steps. In the first step we transform the logic program that encodes the given system and the given property, into a monadic ω -program, that is, a stratified program defining nullary or unary predicates on infinite lists. This transformation is performed by applying unfold/fold rules that preserve the perfect model of the initial program. In the second step we verify the property of interest by using a proof method for monadic ω-programs.

An input-to-state stability approach to verify almost global stability of a synchronous-machine-infinite-bus system.

PubMed

Schiffer, Johannes; Efimov, Denis; Ortega, Romeo; Barabanov, Nikita

2017-08-13

Conditions for almost global stability of an operating point of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. The analysis is conducted by employing the recently proposed concept of input-to-state stability (ISS)-Leonov functions, which is an extension of the powerful cell structure principle developed by Leonov and Noldus to the ISS framework. Compared with the original ideas of Leonov and Noldus, the ISS-Leonov approach has the advantage of providing additional robustness guarantees. The efficiency of the derived sufficient conditions is illustrated via numerical experiments.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

A correlation method to predict the surface pressure distribution on an infinite plate from which a jet is issuing. [effects of a lifting jet

NASA Technical Reports Server (NTRS)

Perkins, S. C., Jr.; Menhall, M. R.

1978-01-01

A correlation method to predict pressures induced on an infinite plate by a jet issuing from the plate into a subsonic free stream was developed. The complete method consists of an analytical method which models the blockage and entrainment properties of the jet and a correlation which accounts for the effects of separation. The method was developed for jet velocity ratios up to ten and for radial distances up to five diameters from the jet. Correlation curves and data comparisons are presented for jets issuing normally from a flat plate with velocity ratios one to twelve. Also, a list of references which deal with jets in a crossflow is presented.

Eastern Renewable Generation Integration Study: Flexibility and High Penetrations of Wind and Solar; NREL (National Renewable Energy Laboratory)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bloom, Aaron; Townsend, Aaron; Palchak, David

Balancing wind and solar in a model is relatively easy. All you need to do is assume a very large system with infinite flexibility! But what if you don't have an infinitely flexible system? What if there are thousands of generators nestled in a handful of regions that are unlikely to change their operational practices? Would you still have enough flexibility to balance hundreds of gigawatts of wind and solar at a 5 minute level? At NREL, we think we can, and our industry partners agree. This presentation was presented at the IEEE Power and Energy Society General Meeting bymore » Aaron Bloom, highlighting results of the Eastern Renewable Generation Integration Study.« less

Analytic theory of photoacoustic wave generation from a spheroidal droplet.

PubMed

Li, Yong; Fang, Hui; Min, Changjun; Yuan, Xiaocong

2014-08-25

In this paper, we develop an analytic theory for describing the photoacoustic wave generation from a spheroidal droplet and derive the first complete analytic solution. Our derivation is based on solving the photoacoustic Helmholtz equation in spheroidal coordinates with the separation-of-variables method. As the verification, besides carrying out the asymptotic analyses which recover the standard solutions for a sphere, an infinite cylinder and an infinite layer, we also confirm that the partial transmission and reflection model previously demonstrated for these three geometries still stands. We expect that this analytic solution will find broad practical uses in interpreting experiment results, considering that its building blocks, the spheroidal wave functions (SWFs), can be numerically calculated by the existing computer programs.

Modeling of a VMJ PV array under Gaussian high intensity laser power beam condition

NASA Astrophysics Data System (ADS)

Eom, Jeongsook; Kim, Gunzung; Park, Yongwan

2018-02-01

The high intensity laser power beaming (HILPB) system is one of the most promising systems in the long-rang wireless power transfer field. The vertical multi-junction photovoltaic (VMJ PV) array converts the HILPB into electricity to power the load or charges a battery. The output power of a VMJ PV array depends mainly on irradiance values of each VMJ PV cells. For simulating an entire VMJ PV array, the irradiance profile of the Gaussian HILPB and the irradiance level of the VMJ PV cell are mathematically modeled first. The VMJ PV array is modeled as a network with dimension m*n, where m represents the number of VMJ PV cells in a column, and n represents the number of VMJ PV cells in a row. In order to validate the results obtained in modeling and simulation, a laboratory setup was developed using 55 VMJ PV array. By using the output power model of VMJ PV array, we can establish an optimal power transmission path by the receiver based on the received signal strength. When the laser beam from multiple transmitters aimed at a VMJ PV array at the same time, the received power is the sum of all energy at a VMJ PV array. The transmitter sends its power characteristics as optically coded laser pulses and powers as HILPB. Using the attenuated power model and output power model of VMJ PV array, the receiver can estimate the maximum receivable powers from the transmitters and select optimal transmitters.

CWG - MUTUAL COUPLING PROGRAM FOR CIRCULAR WAVEGUIDE-FED APERTURE ARRAY (IBM PC VERSION)

NASA Technical Reports Server (NTRS)

Bailey, M. C.

1994-01-01

Mutual Coupling Program for Circular Waveguide-fed Aperture Array (CWG) was developed to calculate the electromagnetic interaction between elements of an antenna array of circular apertures with specified aperture field distributions. The field distributions were assumed to be a superposition of the modes which could exist in a circular waveguide. Various external media were included to provide flexibility of use, for example, the flexibility to determine the effects of dielectric covers (i.e., thermal protection system tiles) upon the impedance of aperture type antennas. The impedance and radiation characteristics of planar array antennas depend upon the mutual interaction between all the elements of the array. These interactions are influenced by several parameters (e.g., the array grid geometry, the geometry and excitation of each array element, the medium outside the array, and the internal network feeding the array.) For the class of array antenna whose radiating elements consist of small holes in a flat conducting plate, the electromagnetic problem can be divided into two parts, the internal and the external. In solving the external problem for an array of circular apertures, CWG will compute the mutual interaction between various combinations of circular modal distributions and apertures. CWG computes the mutual coupling between various modes assumed to exist in circular apertures that are located in a flat conducting plane of infinite dimensions. The apertures can radiate into free space, a homogeneous medium, a multilayered region or a reflecting surface. These apertures are assumed to be excited by one or more modes corresponding to the modal distributions in circular waveguides of the same cross sections as the apertures. The apertures may be of different sizes and also of different polarizations. However, the program assumes that each aperture field contains the same modal distributions, and calculates the complex scattering matrix between all mode and aperture combinations. The scattering matrix can then be used to determine the complex modal field amplitudes for each aperture with a specified array excitation. CWG is written in VAX FORTRAN for DEC VAX series computers running VMS (LAR-15236) and IBM PC series and compatible computers running MS-DOS (LAR-15226). It requires 360K of RAM for execution. To compile the source code for the PC version, the NDP Fortran compiler and linker will be required; however, the distribution medium for the PC version of CWG includes a sample MS-DOS executable which was created using NDP Fortran with the -vms compiler option. The standard distribution medium for the PC version of CWG is a 3.5 inch 1.44Mb MS-DOS format diskette. The standard distribution medium for the VAX version of CWG is a 1600 BPI 9track magnetic tape in DEC VAX BACKUP format. The VAX version is also available on a TK50 tape cartridge in DEC VAX BACKUP format. Both machine versions of CWG include an electronic version of the documentation in Microsoft Word for Windows format. CWG was developed in 1993 and is a copyrighted work with all copyright vested in NASA.

CWG - MUTUAL COUPLING PROGRAM FOR CIRCULAR WAVEGUIDE-FED APERTURE ARRAY (VAX VMS VERSION)

NASA Technical Reports Server (NTRS)

Bailey, M. C.

1994-01-01

Mutual Coupling Program for Circular Waveguide-fed Aperture Array (CWG) was developed to calculate the electromagnetic interaction between elements of an antenna array of circular apertures with specified aperture field distributions. The field distributions were assumed to be a superposition of the modes which could exist in a circular waveguide. Various external media were included to provide flexibility of use, for example, the flexibility to determine the effects of dielectric covers (i.e., thermal protection system tiles) upon the impedance of aperture type antennas. The impedance and radiation characteristics of planar array antennas depend upon the mutual interaction between all the elements of the array. These interactions are influenced by several parameters (e.g., the array grid geometry, the geometry and excitation of each array element, the medium outside the array, and the internal network feeding the array.) For the class of array antenna whose radiating elements consist of small holes in a flat conducting plate, the electromagnetic problem can be divided into two parts, the internal and the external. In solving the external problem for an array of circular apertures, CWG will compute the mutual interaction between various combinations of circular modal distributions and apertures. CWG computes the mutual coupling between various modes assumed to exist in circular apertures that are located in a flat conducting plane of infinite dimensions. The apertures can radiate into free space, a homogeneous medium, a multilayered region or a reflecting surface. These apertures are assumed to be excited by one or more modes corresponding to the modal distributions in circular waveguides of the same cross sections as the apertures. The apertures may be of different sizes and also of different polarizations. However, the program assumes that each aperture field contains the same modal distributions, and calculates the complex scattering matrix between all mode and aperture combinations. The scattering matrix can then be used to determine the complex modal field amplitudes for each aperture with a specified array excitation. CWG is written in VAX FORTRAN for DEC VAX series computers running VMS (LAR-15236) and IBM PC series and compatible computers running MS-DOS (LAR-15226). It requires 360K of RAM for execution. To compile the source code for the PC version, the NDP Fortran compiler and linker will be required; however, the distribution medium for the PC version of CWG includes a sample MS-DOS executable which was created using NDP Fortran with the -vms compiler option. The standard distribution medium for the PC version of CWG is a 3.5 inch 1.44Mb MS-DOS format diskette. The standard distribution medium for the VAX version of CWG is a 1600 BPI 9track magnetic tape in DEC VAX BACKUP format. The VAX version is also available on a TK50 tape cartridge in DEC VAX BACKUP format. Both machine versions of CWG include an electronic version of the documentation in Microsoft Word for Windows format. CWG was developed in 1993 and is a copyrighted work with all copyright vested in NASA.

Students' Conception of Infinite Series

ERIC Educational Resources Information Center

Martinez-Planell, Rafael; Gonzalez, Ana Carmen; DiCristina, Gladys; Acevedo, Vanessa

2012-01-01

This is a report of a study of students' understanding of infinite series. It has a three-fold purpose: to show that students may construct two essentially different notions of infinite series, to show that one of the constructions is particularly difficult for students, and to examine the way in which these two different constructions may be…

A Methodology for Phased Array Radar Threshold Modeling Using the Advanced Propagation Model (APM)

DTIC Science & Technology

2017-10-01

TECHNICAL REPORT 3079 October 2017 A Methodology for Phased Array Radar Threshold Modeling Using the Advanced Propagation Model (APM...Head 55190 Networks Division iii EXECUTIVE SUMMARY This report summarizes the methodology developed to improve the radar threshold modeling...PHASED ARRAY RADAR CONFIGURATION ..................................................................... 1 3. METHODOLOGY

Fluctuations around equilibrium laws in ergodic continuous-time random walks.

PubMed

Schulz, Johannes H P; Barkai, Eli

2015-06-01

We study occupation time statistics in ergodic continuous-time random walks. Under thermal detailed balance conditions, the average occupation time is given by the Boltzmann-Gibbs canonical law. But close to the nonergodic phase, the finite-time fluctuations around this mean are large and nontrivial. They exhibit dual time scaling and distribution laws: the infinite density of large fluctuations complements the Lévy-stable density of bulk fluctuations. Neither of the two should be interpreted as a stand-alone limiting law, as each has its own deficiency: the infinite density has an infinite norm (despite particle conservation), while the stable distribution has an infinite variance (although occupation times are bounded). These unphysical divergences are remedied by consistent use and interpretation of both formulas. Interestingly, while the system's canonical equilibrium laws naturally determine the mean occupation time of the ergodic motion, they also control the infinite and Lévy-stable densities of fluctuations. The duality of stable and infinite densities is in fact ubiquitous for these dynamics, as it concerns the time averages of general physical observables.

Solving three-body-breakup problems with outgoing-flux asymptotic conditions

NASA Astrophysics Data System (ADS)

Randazzo, J. M.; Buezas, F.; Frapiccini, A. L.; Colavecchia, F. D.; Gasaneo, G.

2011-11-01

An analytically solvable three-body collision system (s wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys.JPAPEH0953-407510.1088/0953-4075/43/10/101001 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.

Aeroacoustic theory for noncompact wing-gust interaction

NASA Technical Reports Server (NTRS)

Martinez, R.; Widnall, S. E.

1981-01-01

Three aeroacoustic models for noncompact wing-gust interaction were developed for subsonic flow. The first is that for a two dimensional (infinite span) wing passing through an oblique gust. The unsteady pressure field was obtained by the Wiener-Hopf technique; the airfoil loading and the associated acoustic field were calculated, respectively, by allowing the field point down on the airfoil surface, or by letting it go to infinity. The second model is a simple spanwise superposition of two dimensional solutions to account for three dimensional acoustic effects of wing rotation (for a helicopter blade, or some other rotating planform) and of finiteness of wing span. A three dimensional theory for a single gust was applied to calculate the acoustic signature in closed form due to blade vortex interaction in helicopters. The third model is that of a quarter infinite plate with side edge through a gust at high subsonic speed. An approximate solution for the three dimensional loading and the associated three dimensional acoustic field in closed form was obtained. The results reflected the acoustic effect of satisfying the correct loading condition at the side edge.

ALESEP. Part 2: A computer program for the analysis of leading edge separation bubbles on infinite swept wings

NASA Technical Reports Server (NTRS)

Davis, R. L.

1986-01-01

A program called ALESEP is presented for the analysis of the inviscid-viscous interaction which occurs due to the presence of a closed laminar-transitional separation bubble on an airfoil or infinite swept wing. The ALESEP code provides an iterative solution of the boundary layer equations expressed in an inverse formulation coupled to a Cauchy integral representation of the inviscid flow. This interaction analysis is treated as a local perturbation to a known solution obtained from a global airfoil analysis; hence, part of the required input to the ALESEP code are the reference displacement thickness and tangential velocity distributions. Special windward differencing may be used in the reversed flow regions of the separation bubble to accurately account for the flow direction in the discretization of the streamwise convection of momentum. The ALESEP code contains a forced transition model based on a streamwise intermittency function, a natural transition model based on a solution of the integral form of the turbulent kinetic energy equation, and an empirical natural transition model.

Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice

NASA Astrophysics Data System (ADS)

Saadatmand, S. N.; Bartlett, S. D.; McCulloch, I. P.

2018-04-01

Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional lattices can be efficiently obtained using state-of-the-art translation-invariant variants of matrix product states and density-matrix renormalization-group algorithms. We use these methods to calculate the fully-quantitative ground-state phase diagram of the long-range interacting triangular Ising model with a transverse field on six-leg infinite-length cylinders and scrutinize the properties of the detected phases. We compare these results with those of the corresponding nearest neighbor model. Our results suggest that, for such long-range Hamiltonians, the long-range quantum fluctuations always lead to long-range correlations, where correlators exhibit power-law decays instead of the conventional exponential drops observed for short-range correlated gapped phases. Our results are relevant for comparisons with recent ion-trap quantum simulator experiments that demonstrate highly-controllable long-range spin couplings for several hundred ions.

The Green's functions for peridynamic non-local diffusion.

PubMed

Wang, L J; Xu, J F; Wang, J X

2016-09-01

In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.

The effective theory of shift-symmetric cosmologies

NASA Astrophysics Data System (ADS)

Finelli, Bernardo; Goon, Garrett; Pajer, Enrico; Santoni, Luca

2018-05-01

A shift symmetry is a ubiquitous ingredient in inflationary models, both in effective constructions and in UV-finite embeddings such as string theory. It has also been proposed to play a key role in certain Dark Energy and Dark Matter models. Despite the crucial role it plays in cosmology, the observable, model independent consequences of a shift symmetry are yet unknown. Here, assuming an exact shift symmetry, we derive these consequences for single-clock cosmologies within the framework of the Effective Field Theory of Inflation. We find an infinite set of relations among the otherwise arbitrary effective coefficients, which relate non-Gaussianity to their time dependence. For example, to leading order in derivatives, these relations reduce the infinitely many free functions in the theory to just a single one. Our Effective Theory of shift-symmetric cosmologies describes, among other systems, perfect and imperfect superfluids coupled to gravity and driven superfluids in the decoupling limit. Our results are the first step to determine observationally whether a shift symmetry is at play in the laws of nature and whether it is broken by quantum gravity effects.

A-priori testing of sub-grid models for chemically reacting nonpremixed turbulent shear flows

NASA Technical Reports Server (NTRS)

Jimenez, J.; Linan, A.; Rogers, M. M.; Higuera, F. J.

1996-01-01

The beta-assumed-pdf approximation of (Cook & Riley 1994) is tested as a subgrid model for the LES computation of nonpremixed turbulent reacting flows, in the limit of cold infinitely fast chemistry, for two plane turbulent mixing layers with different degrees of intermittency. Excellent results are obtained for the computation of integrals properties such as product mass fraction, and the model is applied to other quantities such as powers of the temperature and the pdf of the scalar itself. Even in these cases the errors are small enough to be useful in practical applications. The analysis is extended to slightly out of equilibrium problems such as the generation of radicals, and formulated in terms of the pdf of the scalar gradients. It is shown that the conditional gradient distribution is universal in a wide range of cases whose limits are established. Within those limits, engineering approximations to the radical concentration are also possible. It is argued that the experiments in this paper are essentially in the limit of infinite Reynolds number.

The Universe and Life: Deductions from the Weak Anthropic Principle

NASA Astrophysics Data System (ADS)

Hoyle, Fred; Wickramasinghe, Chandra

The existence of life in the Universe is interpreted in terms of the "Weak Anthropic Principle". It is shown that cosmological models are constrained to a class that involves an open timescale and access to infinite quantities of carbonaceous material.

Data-Adaptive Bias-Reduced Doubly Robust Estimation.

PubMed

Vermeulen, Karel; Vansteelandt, Stijn

2016-05-01

Doubly robust estimators have now been proposed for a variety of target parameters in the causal inference and missing data literature. These consistently estimate the parameter of interest under a semiparametric model when one of two nuisance working models is correctly specified, regardless of which. The recently proposed bias-reduced doubly robust estimation procedure aims to partially retain this robustness in more realistic settings where both working models are misspecified. These so-called bias-reduced doubly robust estimators make use of special (finite-dimensional) nuisance parameter estimators that are designed to locally minimize the squared asymptotic bias of the doubly robust estimator in certain directions of these finite-dimensional nuisance parameters under misspecification of both parametric working models. In this article, we extend this idea to incorporate the use of data-adaptive estimators (infinite-dimensional nuisance parameters), by exploiting the bias reduction estimation principle in the direction of only one nuisance parameter. We additionally provide an asymptotic linearity theorem which gives the influence function of the proposed doubly robust estimator under correct specification of a parametric nuisance working model for the missingness mechanism/propensity score but a possibly misspecified (finite- or infinite-dimensional) outcome working model. Simulation studies confirm the desirable finite-sample performance of the proposed estimators relative to a variety of other doubly robust estimators.

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Adamian, A.

1988-01-01

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Solvable Model of a Generic Trapped Mixture of Interacting Bosons: Many-Body and Mean-Field Properties

NASA Astrophysics Data System (ADS)

Klaiman, S.; Streltsov, A. I.; Alon, O. E.

2018-04-01

A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 ‑ 1), λ 2(N 2 ‑ 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.

Mechanical behaviour of synthetic surgical meshes: finite element simulation of the herniated abdominal wall.

PubMed

Hernández-Gascón, B; Peña, E; Melero, H; Pascual, G; Doblaré, M; Ginebra, M P; Bellón, J M; Calvo, B

2011-11-01

The material properties of meshes used in hernia surgery contribute to the overall mechanical behaviour of the repaired abdominal wall. The mechanical response of a surgical mesh has to be defined since the haphazard orientation of an anisotropic mesh can lead to inconsistent surgical outcomes. This study was designed to characterize the mechanical behaviour of three surgical meshes (Surgipro®, Optilene® and Infinit®) and to describe a mechanical constitutive law that accurately reproduces the experimental results. Finally, through finite element simulation, the behaviour of the abdominal wall was modelled before and after surgical mesh implant. Uniaxial loading of mesh samples in two perpendicular directions revealed the isotropic response of Surgipro® and the anisotropic behaviour of Optilene® and Infinit®. A phenomenological constitutive law was used to reproduce the measured experimental curves. To analyze the mechanical effect of the meshes once implanted in the abdomen, finite element simulation of the healthy and partially herniated repaired rabbit abdominal wall served to reproduce wall behaviour before and after mesh implant. In all cases, maximal displacements were lower and maximal principal stresses higher in the implanted abdomen than the intact wall model. Despite the fact that no mesh showed a behaviour that perfectly matched that of abdominal muscle, the Infinit® mesh was able to best comply with the biomechanics of the abdominal wall. Copyright © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Determination of thermodynamic properties of isotactic poly(1-butene) at infinite dilution using density and inverse gas chromatography.

PubMed

Kozłowska, Marta Karolina; Domańska, Urszula; Lempert, Małgorzata; Rogalski, Marek

2005-03-18

The partial molar volumes, V1(M), and the molar volume of isotactic crystalline low-molecular-weight poly(1-butene), iPBu-1, V1, have been calculated from the measured density of {iPBu-1 + solvent (n-hexane, n-heptane, n-nonane, n-decane, p-xylene, cyclohexane and chloroform)} systems. Some of the thermodynamic quantities were also obtained for the iPBu-1 with eight hydrocarbons (n-octane, n-decane, n-undecane, n-dodecane, n-tridecane, o-xylene, m-xylene, p-xylene) by the method of inverse gas chromatography at various temperatures. The weight fraction activity coefficients of the solvent at infinite dilution, omega2(infinity) and the Flory-Huggins thermodynamic interaction parameters, chi21(infinity), between polymer and solvents were determined. The partial molar free energy, deltaG2(infinity), the partial molar heat of mixing, deltaH2(infinity), at infinite dilution and the polymer solubility parameter, delta1, were calculated. Additionally, the (solid + liquid) binary mixtures equilibria, SLE, of iPBu-1 with three hydrocarbons (n-octane, n-decane and m-xylene) were studied by a dynamic method. By performing these experiments over a large concentration range, the T-x phase diagrams of the polymer-solvent systems were constructed. The excess Gibbs energy models were used to describe the nonideal behaviour of the liquid phase. The omega2(infinity) were determined from the solubility measurements and were predicted by using the UNIFAC FV model.

a Study of Ultrasonic Wave Propagation Through Parallel Arrays of Immersed Tubes

NASA Astrophysics Data System (ADS)

Cocker, R. P.; Challis, R. E.

1996-06-01

Tubular array structures are a very common component in industrial heat exchanging plant and the non-destructive testing of these arrays is essential. Acoustic methods using microphones or ultrasound are attractive but require a thorough understanding of the acoustic properties of tube arrays. This paper details the development and testing of a small-scale physical model of a tube array to verify the predictions of a theoretical model for acoustic propagation through tube arrays developed by Heckl, Mulholland, and Huang [1-5] as a basis for the consideration of small-scale physical models in the development of non-destructive testing procedures for tube arrays. Their model predicts transmission spectra for plane waves incident on an array of tubes arranged in straight rows. Relative transmission is frequency dependent with bands of high and low attenuation caused by resonances within individual tubes and between tubes in the array. As the number of rows in the array increases the relative transmission spectrum becomes more complex, with increasingly well-defined bands of high and low attenuation. Diffraction of acoustic waves with wavelengths less than the tube spacing is predicted and appears as step reductions in the transmission spectrum at frequencies corresponding to integer multiples of the tube spacing. Experiments with the physical model confirm the principle features of the theoretical treatment.

Lyapunov exponents for infinite dimensional dynamical systems

NASA Technical Reports Server (NTRS)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

Mass predictions of atomic nuclei in the infinite nuclear matter model

NASA Astrophysics Data System (ADS)

Nayak, R. C.; Satpathy, L.

2012-07-01

We present here the mass excesses, binding energies, one- and two-neutron, one- and two-proton and α-particle separation energies of 6727 nuclei in the ranges 4≤Z≤120 and 8≤A≤303 calculated in the infinite nuclear matter model. Compared to our predictions of 1999 mass table, the present ones are obtained using larger data base of 2003 mass table of Wapstra and Audi and resorting to higher accuracy in the solutions of the η-differential equations of the INM model. The local energy η's supposed to carry signature of the characteristic properties of nuclei are found to possess the predictive capability. In fact η-systematics reveal new magic numbers in the drip-line regions giving rise to new islands of stability supported by relativistic mean field theoretic calculations. This is a manifestation of a new phenomenon where shell-effect overcomes the instability due to repulsive components of the nucleon-nucleon force broadening the stability peninsula. The two-neutron separation energy-systematics derived from the present mass predictions reveal a general new feature for the existence of islands of inversion in the exotic neutron-rich regions of nuclear landscape, apart from supporting the presently known islands around 31Na and 62Ti. The five global parameters representing the properties of infinite nuclear matter, the surface, the Coulomb and the pairing terms are retained as per our 1999 mass table. The root-mean-square deviation of the present mass-fit to 2198 known masses is 342 keV, while the mean deviation is 1.3 keV, reminiscent of no left-over systematic effects. This is a substantive improvement over our 1999 mass table having rms deviation of 401 keV and mean deviation of 9 keV for 1884 data nuclei.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shang, Yu; Yu, Guoqiang, E-mail: guoqiang.yu@uky.edu

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD{sub B}). The purpose of this study is to extend the capability of the Nth-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different typesmore » of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD{sub B} in the brain layer with a step decrement of 10% while maintaining αD{sub B} values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order (N ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The Nth-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.« less

A Nth-order linear algorithm for extracting diffuse correlation spectroscopy blood flow indices in heterogeneous tissues.

PubMed

Shang, Yu; Yu, Guoqiang

2014-09-29

Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a N th-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD B ). The purpose of this study is to extend the capability of the N th-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD B in the brain layer with a step decrement of 10% while maintaining αD B values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order ( N  ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The N th-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.

Stochastic Online Learning in Dynamic Networks under Unknown Models

DTIC Science & Technology

2016-08-02

Repeated Game with Incomplete Information, IEEE International Conference on Acoustics, Speech, and Signal Processing. 20-MAR-16, Shanghai, China...in a game theoretic framework for the application of multi-seller dynamic pricing with unknown demand models. We formulated the problem as an...infinitely repeated game with incomplete information and developed a dynamic pricing strategy referred to as Competitive and Cooperative Demand Learning

A study of buried pipeline response to fault movement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiou, Y.J.; Chi, S.Y.; Chang, H.Y.

1994-02-01

This study investigates the buried pipeline response to strike slip fault movement. The large deflection pipe crossing the fault zone is modeled as an elastica, while the remaining portion of small deflection pipe is modeled as a semi-infinite beam on elastic foundation. The finite difference method is applied for the numerical solution and the results agree qualitatively with the earlier works.

Exactly solvable model of the two-dimensional electrical double layer.

PubMed

Samaj, L; Bajnok, Z

2005-12-01

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0< or = beta < 2. If there is a potential difference between the bulk interior of the electrolyte and the grounded electrode, the electrolyte region close to the electrode (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.

Fast computation of the electrolyte-concentration transfer function of a lithium-ion cell model

NASA Astrophysics Data System (ADS)

Rodríguez, Albert; Plett, Gregory L.; Trimboli, M. Scott

2017-08-01

One approach to creating physics-based reduced-order models (ROMs) of battery-cell dynamics requires first generating linearized Laplace-domain transfer functions of all cell internal electrochemical variables of interest. Then, the resulting infinite-dimensional transfer functions can be reduced by various means in order to find an approximate low-dimensional model. These methods include Padé approximation or the Discrete-Time Realization algorithm. In a previous article, Lee and colleagues developed a transfer function of the electrolyte concentration for a porous-electrode pseudo-two-dimensional lithium-ion cell model. Their approach used separation of variables and Sturm-Liouville theory to compute an infinite-series solution to the transfer function, which they then truncated to a finite number of terms for reasons of practicality. Here, we instead use a variation-of-parameters approach to arrive at a different representation of the identical solution that does not require a series expansion. The primary benefits of the new approach are speed of computation of the transfer function and the removal of the requirement to approximate the transfer function by truncating the number of terms evaluated. Results show that the speedup of the new method can be more than 3800.

Surface electromagnetic waves in Fibonacci superlattices: Theoretical and experimental results

NASA Astrophysics Data System (ADS)

El Hassouani, Y.; Aynaou, H.; El Boudouti, E. H.; Djafari-Rouhani, B.; Akjouj, A.; Velasco, V. R.

2006-07-01

We study theoretically and experimentally the existence and behavior of the localized surface modes in one-dimensional (1D) quasiperiodic photonic band gap structures. These structures are made of segments and loops arranged according to a Fibonacci sequence. The experiments are carried out by using coaxial cables in the frequency region of a few tens of MHz. We consider 1D periodic structures (superlattice) where each cell is a well-defined Fibonacci generation. In these structures, we generalize a theoretical rule on the surface modes, namely when one considers two semi-infinite superlattices obtained by the cleavage of an infinite superlattice, it exists exactly one surface mode in each gap. This mode is localized on the surface either of one or the other semi-infinite superlattice. We discuss the existence of various types of surface modes and their spatial localization. The experimental observation of these modes is carried out by measuring the transmission through a guide along which a finite superlattice (i.e., constituted of a finite number of quasiperiodic cells) is grafted vertically. The surface modes appear as maxima of the transmission spectrum. These experiments are in good agreement with the theoretical model based on the formalism of the Green function.

Field-incidence noise transmission loss of general aviation aircraft double wall configurations

NASA Astrophysics Data System (ADS)

Grosveld, F. W.

1984-01-01

Theoretical formulations have been developed to describe the transmission of reverberant sound through an infinite, semi-infinite and a finite double panel structure. The model incorporates the fundamental resonance frequencies of each of the panels, the mass-air-mass resonances of the structure, the standing wave resonances in the cavity between the panels and finally the coincidence resonance regions, where the exciting sound pressure wave and flexural waves of each of the panels coincide. It is shown that phase cancellation effects of pressure waves reflected from the cavity boundaries back into the cavity allows the transmission loss of a finite double panel structure to be approximated by a finite double panel mounted in an infinite baffle having no cavity boundaries. Comparison of the theory with high quality transmission loss data yields good agreement in the mass-controlled frequency region. It is shown that the application of acoustic blankets to the double panel structure does not eliminate the mass-air-mass resonances if those occur at low frequencies. It is concluded that this frequency region of low noise transmission loss is a potential interior noise problem area for propeller driven aircraft having a double panel fuselage construction.

Geometric MCMC for infinite-dimensional inverse problems

NASA Astrophysics Data System (ADS)

Beskos, Alexandros; Girolami, Mark; Lan, Shiwei; Farrell, Patrick E.; Stuart, Andrew M.

2017-04-01

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned Crank-Nicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method.

Tensor network simulation of QED on infinite lattices: Learning from (1 +1 ) d , and prospects for (2 +1 ) d

NASA Astrophysics Data System (ADS)

Zapp, Kai; Orús, Román

2017-06-01

The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in (3 +1 ) dimensions in regimes difficult for other methods. So far, however, TN methods have mostly simulated lattice gauge theories in (1 +1 ) dimensions. The aim of this paper is to explore the simulation of quantum electrodynamics (QED) on infinite lattices with TNs, i.e., fermionic matter fields coupled to a U (1 ) gauge field, directly in the thermodynamic limit. With this idea in mind we first consider a gauge-invariant infinite density matrix renormalization group simulation of the Schwinger model—i.e., QED in (1 +1 ) d . After giving a precise description of the numerical method, we benchmark our simulations by computing the subtracted chiral condensate in the continuum, in good agreement with other approaches. Our simulations of the Schwinger model allow us to build intuition about how a simulation should proceed in (2 +1 ) dimensions. Based on this, we propose a variational ansatz using infinite projected entangled pair states (PEPS) to describe the ground state of (2 +1 ) d QED. The ansatz includes U (1 ) gauge symmetry at the level of the tensors, as well as fermionic (matter) and bosonic (gauge) degrees of freedom both at the physical and virtual levels. We argue that all the necessary ingredients for the simulation of (2 +1 ) d QED are, a priori, already in place, paving the way for future upcoming results.

The University as an Infinite Game: Revitalising Activism in the Academy

ERIC Educational Resources Information Center

Harré, Niki; Grant, Barbara M.; Locke, Kirsten; Sturm, Sean

2017-01-01

We offer here a metaphor of the university as an "infinite game" in which we bring to life insight, imagination, and radical inclusion; and resist the "finite games" that can lead us astray. We suggest that keeping the infinite game alive within universities is a much-needed form of academic activism. We offer four vignettes…

Orthogonality preserving infinite dimensional quadratic stochastic operators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akın, Hasan; Mukhamedov, Farrukh

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

Inspiring Examples in Rearrangements of Infinite Products

ERIC Educational Resources Information Center

Ramasinghe, W.

2007-01-01

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

The Transition from Comparison of Finite to the Comparison of Infinite Sets: Teaching Prospective Teachers.

ERIC Educational Resources Information Center

Tsamir, Pessia

1999-01-01

Describes a course in Cantorian Set Theory relating to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. Indicates that when comparing the number of elements in infinite sets, teachers who took the course were more successful and more consistent in their use of single method than those who…

Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

NASA Astrophysics Data System (ADS)

Platonov, S. S.

2018-02-01

We consider some questions about the approximation of functions on the infinite-dimensional torus by trigonometric polynomials. Our main results are analogues of the direct and inverse theorems in the classical theory of approximation of periodic functions and a description of the Lipschitz spaces on the infinite-dimensional torus in terms of the best approximation.

Sculpting Computational-Level Models.

PubMed

Blokpoel, Mark

2017-06-27

In this commentary, I advocate for strict relations between Marr's levels of analysis. Under a strict relationship, each level is exactly implemented by the subordinate level. This yields two benefits. First, it brings consistency for multilevel explanations. Second, similar to how a sculptor chisels away superfluous marble, a modeler can chisel a computational-level model by applying constraints. By sculpting the model, one restricts the (potentially infinitely large) set of possible algorithmic- and implementational-level theories. Copyright © 2017 Cognitive Science Society, Inc.

Decoherence in models for hard-core bosons coupled to optical phonons

NASA Astrophysics Data System (ADS)

Dey, A.; Lone, M. Q.; Yarlagadda, S.

2015-09-01

Understanding coherent dynamics of excitons, spins, or hard-core bosons (HCBs) has tremendous scientific and technological implications for quantum computation. Here, we study decay of excited-state population and decoherence in two models for HCBs, namely, a two-site HCB model with site-dependent strong potentials and subject to non-Markovian dynamics and an infinite-range HCB model governed by Markovian dynamics. Both models are investigated in the regimes of antiadiabaticity and strong HCB-phonon coupling with each site providing a different local optical phonon environment; furthermore, the HCB systems in both models are taken to be initially uncorrelated with the environment in the polaronic frame of reference. In the case of the two-site HCB model, we show clearly that the degree of decoherence and decay of excited state are enhanced by the proximity of the site-energy difference to the eigenenergy of phonons and are most pronounced when the site-energy difference is at resonance with twice the polaronic energy; additionally, the decoherence and the decay effects are reduced when the strength of HCB-phonon coupling is increased. For the infinite-range model, when the site energies are the same, we derive an effective many-body Hamiltonian that commutes with the long-range system Hamiltonian and thus has the same set of eigenstates; consequently, a quantum-master-equation approach shows that the quantum states of the system do not decohere.

Modeling Charge Collection in Detector Arrays

NASA Technical Reports Server (NTRS)

Hardage, Donna (Technical Monitor); Pickel, J. C.

2003-01-01

A detector array charge collection model has been developed for use as an engineering tool to aid in the design of optical sensor missions for operation in the space radiation environment. This model is an enhancement of the prototype array charge collection model that was developed for the Next Generation Space Telescope (NGST) program. The primary enhancements were accounting for drift-assisted diffusion by Monte Carlo modeling techniques and implementing the modeling approaches in a windows-based code. The modeling is concerned with integrated charge collection within discrete pixels in the focal plane array (FPA), with high fidelity spatial resolution. It is applicable to all detector geometries including monolithc charge coupled devices (CCDs), Active Pixel Sensors (APS) and hybrid FPA geometries based on a detector array bump-bonded to a readout integrated circuit (ROIC).

Reliability model of disk arrays RAID-5 with data striping

NASA Astrophysics Data System (ADS)

Rahman, P. A.; D'K Novikova Freyre Shavier, G.

2018-03-01

Within the scope of the this scientific paper, the simplified reliability model of disk arrays RAID-5 (redundant arrays of inexpensive disks) and an advanced reliability model offered by the authors taking into the consideration nonzero time of the faulty disk replacement and different failure rates of disks in normal state of the disk array and in degraded and rebuild states are discussed. The formula obtained by the authors for calculation of the mean time to data loss (MTTDL) of the RAID-5 disk arrays on basis of the advanced model is also presented. Finally, the technique of estimation of the initial reliability parameters, which are used in the reliability model, and the calculation examples of the mean time to data loss of the RAID-5 disk arrays for the different number of disks are also given.

An Infinite Mixture Model for Coreference Resolution in Clinical Notes

PubMed Central

Liu, Sijia; Liu, Hongfang; Chaudhary, Vipin; Li, Dingcheng

2016-01-01

It is widely acknowledged that natural language processing is indispensable to process electronic health records (EHRs). However, poor performance in relation detection tasks, such as coreference (linguistic expressions pertaining to the same entity/event) may affect the quality of EHR processing. Hence, there is a critical need to advance the research for relation detection from EHRs. Most of the clinical coreference resolution systems are based on either supervised machine learning or rule-based methods. The need for manually annotated corpus hampers the use of such system in large scale. In this paper, we present an infinite mixture model method using definite sampling to resolve coreferent relations among mentions in clinical notes. A similarity measure function is proposed to determine the coreferent relations. Our system achieved a 0.847 F-measure for i2b2 2011 coreference corpus. This promising results and the unsupervised nature make it possible to apply the system in big-data clinical setting. PMID:27595047

Kantowski-Sachs Einstein-æther perfect fluid models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Latta, Joey; Leon, Genly; Paliathanasis, Andronikos, E-mail: lattaj@mathstat.dal.ca, E-mail: genly.leon@pucv.cl, E-mail: anpaliat@phys.uoa.gr

We investigate Kantowski-Sachs models in Einstein-æ ther theory with a perfect fluid source using the singularity analysis to prove the integrability of the field equations and dynamical system tools to study the evolution. We find an inflationary source at early times, and an inflationary sink at late times, for a wide region in the parameter space. The results by A.A. Coley, G. Leon, P. Sandin and J. Latta ( JCAP 12 (2015) 010), are then re-obtained as particular cases. Additionally, we select other values for the non-GR parameters which are consistent with current constraints, getting a very rich phenomenology. Inmore » particular, we find solutions with infinite shear, zero curvature, and infinite matter energy density in comparison with the Hubble scalar. We also have stiff-like future attractors, anisotropic late-time attractors, or both, in some special cases. Such results are developed analytically, and then verified by numerics. Finally, the physical interpretation of the new critical points is discussed.« less

Consideration of some factors affecting low-frequency fuselage noise transmission for propeller aircraft

NASA Technical Reports Server (NTRS)

Mixson, J. S.; Roussos, L. A.

1986-01-01

Possible reasons for disagreement between measured and predicted trends of sidewall noise transmission at low frequency are investigated using simplified analysis methods. An analytical model combining incident plane acoustic waves with an infinite flat panel is used to study the effects of sound incidence angle, plate structural properties, frequency, absorption, and the difference between noise reduction and transmission loss. Analysis shows that these factors have significant effects on noise transmission but they do not account for the differences between measured and predicted trends at low frequencies. An analytical model combining an infinite flat plate with a normally incident acoustic wave having exponentially decaying magnitude along one coordinate is used to study the effect of a localized source distribution such as is associated with propeller noise. Results show that the localization brings the predicted low-frequency trend of noise transmission into better agreement with measured propeller results. This effect is independent of low-frequency stiffness effects that have been previously reported to be associated with boundary conditions.

Analytical and experimental investigation on transmission loss of clamped double panels: implication of boundary effects.

PubMed

Xin, F X; Lu, T J

2009-03-01

The air-borne sound insulation performance of a rectangular double-panel partition clamp mounted on an infinite acoustic rigid baffle is investigated both analytically and experimentally and compared with that of a simply supported one. With the clamped (or simply supported) boundary accounted for by using the method of modal function, a double series solution for the sound transmission loss (STL) of the structure is obtained by employing the weighted residual (Galerkin) method. Experimental measurements with Al double-panel partitions having air cavity are subsequently carried out to validate the theoretical model for both types of the boundary condition, and good overall agreement is achieved. A consistency check of the two different models (based separately on clamped modal function and simply supported modal function) is performed by extending the panel dimensions to infinite where no boundaries exist. The significant discrepancies between the two different boundary conditions are demonstrated in terms of the STL versus frequency plots as well as the panel deflection mode shapes.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

An IBM PC-based math model for space station solar array simulation

NASA Technical Reports Server (NTRS)

Emanuel, E. M.

1986-01-01

This report discusses and documents the design, development, and verification of a microcomputer-based solar cell math model for simulating the Space Station's solar array Initial Operational Capability (IOC) reference configuration. The array model is developed utilizing a linear solar cell dc math model requiring only five input parameters: short circuit current, open circuit voltage, maximum power voltage, maximum power current, and orbit inclination. The accuracy of this model is investigated using actual solar array on orbit electrical data derived from the Solar Array Flight Experiment/Dynamic Augmentation Experiment (SAFE/DAE), conducted during the STS-41D mission. This simulator provides real-time simulated performance data during the steady state portion of the Space Station orbit (i.e., array fully exposed to sunlight). Eclipse to sunlight transients and shadowing effects are not included in the analysis, but are discussed briefly. Integrating the Solar Array Simulator (SAS) into the Power Management and Distribution (PMAD) subsystem is also discussed.

Control of single-photon routing in a T-shaped waveguide by another atom

NASA Astrophysics Data System (ADS)

Huang, Jin-Song; Wang, Jing-Wen; Wang, Yan; Li, Yan-Ling; Huang, You-Wen

2018-04-01

Quantum routers with a high routing rate of much more than 0.5 are of great importance for quantum networks. We provide a scheme to perform bidirectional high routing-rate transfer in a T-shaped coupled-resonator waveguide (CRW), which extends a recent unidirectional scheme proposed by Lu et al. (Opt Express 23:22955, 2015). By locating an extra two-level atom in the infinite CRW channel of the T-shaped CRW with a three-level system, an effective potential is generated. Our numerical results show that high routing capability from the infinite CRW channel to the semi-infinite channel can be achieved, and routing capability from the semi-infinite CRW channel to the infinite channel can also be significantly enhanced, with the help of the effective potential. Therefore, the proposed double-atom configuration could be utilized as a bidirectional quantum routing controller to implement high transfer rate routing of single photons.

Infinite index extensions of local nets and defects

NASA Astrophysics Data System (ADS)

Del Vecchio, Simone; Giorgetti, Luca

The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [62] to the case of extensions with infinite Jones index. This case naturally arises in physics, the canonical examples are given by global gauge theories with respect to a compact (non-finite) group of internal symmetries. Building on the works of Izumi-Longo-Popa [44] and Fidaleo-Isola [30], we consider generalized Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite von Neumann algebras, which generalize ordinary Q-systems introduced by Longo [58] to the infinite index case. We characterize inclusions which admit generalized Q-systems of intertwiners and define a braided product among the latter, hence we construct examples of QFTs with defects (phase boundaries) of infinite index, extending the family of boundaries in the grasp of [7].

Design and Use of Microphone Directional Arrays for Aeroacoustic Measurements

NASA Technical Reports Server (NTRS)

Humphreys, William M., Jr.; Brooks, Thomas F.; Hunter, William W., Jr.; Meadows, Kristine R.

1998-01-01

An overview of the development of two microphone directional arrays for aeroacoustic testing is presented. These arrays were specifically developed to measure airframe noise in the NASA Langley Quiet Flow Facility. A large aperture directional array using 35 flush-mounted microphones was constructed to obtain high resolution noise localization maps around airframe models. This array possesses a maximum diagonal aperture size of 34 inches. A unique logarithmic spiral layout design was chosen for the targeted frequency range of 2-30 kHz. Complementing the large array is a small aperture directional array, constructed to obtain spectra and directivity information from regions on the model. This array, possessing 33 microphones with a maximum diagonal aperture size of 7.76 inches, is easily moved about the model in elevation and azimuth. Custom microphone shading algorithms have been developed to provide a frequency- and position-invariant sensing area from 10-40 kHz with an overall targeted frequency range for the array of 5-60 kHz. Both arrays are employed in acoustic measurements of a 6 percent of full scale airframe model consisting of a main element NACA 632-215 wing section with a 30 percent chord half-span flap. Representative data obtained from these measurements is presented, along with details of the array calibration and data post-processing procedures.

A simplified solar cell array modelling program

NASA Technical Reports Server (NTRS)

Hughes, R. D.

1982-01-01

As part of the energy conversion/self sufficiency efforts of DSN engineering, it was necessary to have a simplified computer model of a solar photovoltaic (PV) system. This article describes the analysis and simplifications employed in the development of a PV cell array computer model. The analysis of the incident solar radiation, steady state cell temperature and the current-voltage characteristics of a cell array are discussed. A sample cell array was modelled and the results are presented.

Effect of embedded dexamethasone in cochlear implant array on insertion forces in an artificial model of scala tympani.

PubMed

Nguyen, Yann; Bernardeschi, Daniele; Kazmitcheff, Guillaume; Miroir, Mathieu; Vauchel, Thomas; Ferrary, Evelyne; Sterkers, Olivier

2015-02-01

Loading otoprotective drug into cochlear implant might change its mechanical properties, thus compromising atraumatic insertion. This study evaluated the effect of incorporation of dexamethasone (DXM) in the silicone of cochlear implant arrays on insertion forces. Local administration of DXM with embedded array can potentially reduce inflammation and fibrosis after cochlear implantation procedure to improve hearing preservation and reduce long-term impedances. Four models of arrays have been tested: 0.5-mm distal diameter array (n = 5) used as a control, drug-free 0.4-mm distal diameter array (n = 5), 0.4-mm distal diameter array with 1% eluded DXM silicone (n = 5), and 0.4-mm distal diameter array with 10% eluded DXM silicone (n = 5). Via a motorized insertion bench, each array has been inserted into an artificial scala tympani model. The forces were recorded by a 6-axis force sensor. Each array was tested seven times for a total number of 140 insertions. During the first 10-mm insertion, no difference between the four models was observed. From 10- to 24-mm insertion, the 0.5-mm distal diameter array presented higher insertion forces than the drug-free 0.4-mm distal diameter arrays, with or without DXM. Friction forces for drug-free 0.4-mm distal diameter array and 0.4-mm distal diameter DXM eluded arrays were similar on all insertion lengths. Incorporation of DXM in silicone for cochlear implant design does not change electrode array insertion forces. It does not raise the risk of trauma during array insertion, making it suitable for long-term in situ administration to the cochlea.

Growing hair on the extremal BTZ black hole

NASA Astrophysics Data System (ADS)

Harms, B.; Stern, A.

2017-06-01

We show that the nonlinear σ-model in an asymptotically AdS3 space-time admits a novel local symmetry. The field action is assumed to be quartic in the nonlinear σ-model fields and minimally coupled to gravity. The local symmetry transformation simultaneously twists the nonlinear σ-model fields and changes the space-time metric, and it can be used to map the extremal BTZ black hole to infinitely many hairy black hole solutions.

Information, Consistent Estimation and Dynamic System Identification.

DTIC Science & Technology

1976-11-01

Washington,DC 232129 Tj-CUOSITORING AGENCY NAMIE 6 AOORESS(lI dittevmet Itroo CuooottaaII Offics) IS.- SECURITY CLASS. (of this *.part) SCHEDULE ’B...representative model from a given model set, applicable to infinite and even non-compact model sets. S-UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAOrj(*whe...ergodicity. For a thorough development of ergodic theory the reader is referred to, e.g., Doob [1953], Halmos [1956] and Chacon and Ornstein [1959

Including Thermal Fluctuations in Actomyosin Stable States Increases the Predicted Force per Motor and Macroscopic Efficiency in Muscle Modelling

PubMed Central

2016-01-01

Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges. PMID:27626630

Introduction to the theory of infinite systems. Theory and practices

NASA Astrophysics Data System (ADS)

Fedorov, Foma M.

2017-11-01

A review of the author's work is given, which formed the basis for a new theory of general infinite systems. The Gaussian elimination and Cramer's rule have been extended to infinite systems. A special particular solution is obtained, it is called a strictly particular solution. Necessary and sufficient conditions for existence of the nontrivial solutions of homogeneous systems are given.

Confusing Aspects in the Calculation of the Electrostatic Potential of an Infinite Line of Charge

ERIC Educational Resources Information Center

Jimenez, J. L.; Campos, I.; Roa-Neri, J. A. E.

2012-01-01

In this work we discuss the trick of eliminating infinite potential of reference arguing that it corresponds to a constant of integration, in the problem of determining the electrostatic potential of an infinite line of charge with uniform density, and show how the problem must be tackled properly. The usual procedure is confusing for most…

Functors of White Noise Associated to Characters of the Infinite Symmetric Group

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Guţă, Mădălin

The characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to Veršik and Kerov. The von Neumann algebra generated by the fields with f in an infinite dimensional real Hilbert space is infinite and the vacuum vector is not separating. For a family depending on an integer N< - 1 an ``exclusion principle'' is found allowing at most ``identical particles'' on the same state: The algebras are type factors. Functors of white noise are constructed and proved to be non-equivalent for different values of N.

ARRAY OPTIMIZATION FOR TIDAL ENERGY EXTRACTION IN A TIDAL CHANNEL – A NUMERICAL MODELING ANALYSIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Zhaoqing; Wang, Taiping; Copping, Andrea

This paper presents an application of a hydrodynamic model to simulate tidal energy extraction in a tidal dominated estuary in the Pacific Northwest coast. A series of numerical experiments were carried out to simulate tidal energy extraction with different turbine array configurations, including location, spacing and array size. Preliminary model results suggest that array optimization for tidal energy extraction in a real-world site is a very complex process that requires consideration of multiple factors. Numerical models can be used effectively to assist turbine siting and array arrangement in a tidal turbine farm for tidal energy extraction.

Multi-cut solutions in Chern-Simons matrix models

NASA Astrophysics Data System (ADS)

Morita, Takeshi; Sugiyama, Kento

2018-04-01

We elaborate the Chern-Simons (CS) matrix models at large N. The saddle point equations of these matrix models have a curious structure which cannot be seen in the ordinary one matrix models. Thanks to this structure, an infinite number of multi-cut solutions exist in the CS matrix models. Particularly we exactly derive the two-cut solutions at finite 't Hooft coupling in the pure CS matrix model. In the ABJM matrix model, we argue that some of multi-cut solutions might be interpreted as a condensation of the D2-brane instantons.

Efficient Analysis of Systems Biology Markup Language Models of Cellular Populations Using Arrays.

PubMed

Watanabe, Leandro; Myers, Chris J

2016-08-19

The Systems Biology Markup Language (SBML) has been widely used for modeling biological systems. Although SBML has been successful in representing a wide variety of biochemical models, the core standard lacks the structure for representing large complex regular systems in a standard way, such as whole-cell and cellular population models. These models require a large number of variables to represent certain aspects of these types of models, such as the chromosome in the whole-cell model and the many identical cell models in a cellular population. While SBML core is not designed to handle these types of models efficiently, the proposed SBML arrays package can represent such regular structures more easily. However, in order to take full advantage of the package, analysis needs to be aware of the arrays structure. When expanding the array constructs within a model, some of the advantages of using arrays are lost. This paper describes a more efficient way to simulate arrayed models. To illustrate the proposed method, this paper uses a population of repressilator and genetic toggle switch circuits as examples. Results show that there are memory benefits using this approach with a modest cost in runtime.

On extreme events for non-spatial and spatial branching Brownian motions

NASA Astrophysics Data System (ADS)

Avan, Jean; Grosjean, Nicolas; Huillet, Thierry

2015-04-01

We study the impact of having a non-spatial branching mechanism with infinite variance on some parameters (height, width and first hitting time) of an underlying Bienaymé-Galton-Watson branching process. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then consider spatial branching processes in dimension d, not necessarily integer. The underlying branching mechanism is either a binary branching model or one presenting infinite variance. In particular we evaluate the chance p(x) of being hit if the epidemics started away at distance x. We compute the large x tail probabilities of this event, both when the branching mechanism is regular and when it exhibits very large fluctuations.

Observation of a Relaxed Plasma State in a Quasi-Infinite Cylinder

NASA Astrophysics Data System (ADS)

Gray, T.; Brown, M. R.; Dandurand, D.

2013-02-01

A helical relaxed plasma state is observed in a long cylindrical volume. The cylinder is long enough so that the predicted minimum energy state is a close approximation to the infinite cylinder solution. The plasma is injected at v≥50km/s by a coaxial magnetized plasma gun located at one end of the cylindrical volume. The relaxed state is rapidly attained in 1-2 axial Alfvén times after initiation of the plasma. Magnetic data are favorably compared with an analytical model. Magnetic data exhibit broadband fluctuations of the measured axial modes during the formation period. The broadband activity rapidly decays as the energy condenses into the lowest energy mode, which is in agreement with the minimum energy eigenstate of ∇×B=λB.

Observation of a relaxed plasma state in a quasi-infinite cylinder.

PubMed

Gray, T; Brown, M R; Dandurand, D

2013-02-22

A helical relaxed plasma state is observed in a long cylindrical volume. The cylinder is long enough so that the predicted minimum energy state is a close approximation to the infinite cylinder solution. The plasma is injected at v ≥ 50 km/s by a coaxial magnetized plasma gun located at one end of the cylindrical volume. The relaxed state is rapidly attained in 1-2 axial Alfvén times after initiation of the plasma. Magnetic data are favorably compared with an analytical model. Magnetic data exhibit broadband fluctuations of the measured axial modes during the formation period. The broadband activity rapidly decays as the energy condenses into the lowest energy mode, which is in agreement with the minimum energy eigenstate of [Symbol: see text] × B = λB.

Science for the Public Through Collaboration and Humor

NASA Astrophysics Data System (ADS)

Wargo, Richard

2013-03-01

The transformation of all things media and information into a dynamic environment of user access has created what seems infinite possibilities to inform the public in many different ways - as well as seemingly infinite possibilities to confuse. This talk will describe a rather non-conventional collaboration between two different creative cultures and its significance to maintaining scientific accuracy and devising strategies important to audience engagement - among them humor. While focusing on the award-winning effort ``When Things Get Small'' created by University of California Television producer R. Wargo in collaboration with condensed matter physicist I.K. Schuller and actor Adam J. Smith, with both NSF and private support, the case study provides insight into a model and modes which can be used successfully by other scientists to engage the public in what they do.

Science For The Public: Collaboration and Humor

NASA Astrophysics Data System (ADS)

Wargo, Richard

2013-04-01

The transformation of all things media and information into a dynamic environment of user access has created what seems infinite possibilities to inform the public in many different ways - as well as seemingly infinite possibilities to confuse. This talk will describe a rather non-conventional collaboration between two different creative cultures and its significance to maintaining scientific accuracy and devising strategies important to audience engagement - among them, humor. While focusing on the award-winning effort ``When Things Get Small'' created by University of California Television producer R. Wargo in collaboration with condensed matter physicist I.K. Schuller and actor Adam J. Smith, with both NSF and private support, the case study provides insight into a model and modes which can be used successfully by other scientists to engage the public in what they do.

Calculation of surface enthalpy of solids from an ab initio electronegativity based model: case of ice.

PubMed

Douillard, J M; Henry, M

2003-07-15

A very simple route to calculation of the surface energy of solids is proposed because this value is very difficult to determine experimentally. The first step is the calculation of the attractive part of the electrostatic energy of crystals. The partial charges used in this calculation are obtained by using electronegativity equalization and scales of electronegativity and hardness deduced from physical characteristics of the atom. The lattice energies of the infinite crystal and of semi-infinite layers are then compared. The difference is related to the energy of cohesion and then to the surface energy. Very good results are obtained with ice, if one compares with the surface energy of liquid water, which is generally considered a good approximation of the surface energy of ice.

Love-type wave propagation in a pre-stressed viscoelastic medium influenced by smooth moving punch

NASA Astrophysics Data System (ADS)

Singh, A. K.; Parween, Z.; Chatterjee, M.; Chattopadhyay, A.

2015-04-01

In the present paper, a mathematical model studying the effect of smooth moving semi-infinite punch on the propagation of Love-type wave in an initially stressed viscoelastic strip is developed. The dynamic stress concentration due to the punch for the force of a constant intensity has been obtained in the closed form. Method based on Weiner-hopf technique which is indicated by Matczynski has been employed. The study manifests the significant effect of various affecting parameters viz. speed of moving punch associated with Love-type wave speed, horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, frequency parameter, and viscoelastic parameter on dynamic stress concentration due to semi-infinite punch. Moreover, some important peculiarities have been traced out and depicted by means of graphs.

Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media

NASA Astrophysics Data System (ADS)

Gupta, Shishir; Ahmed, Mostaid; Pramanik, Abhijit

2017-03-01

The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.

Photon escape probabilities in a semi-infinite plane-parallel medium. [from electron plasma surrounding galactic X-ray sources

NASA Technical Reports Server (NTRS)

Williams, A. C.; Elsner, R. F.; Weisskopf, M. C.; Darbro, W.

1984-01-01

It is shown in this work how to obtain the probabilities of photons escaping from a cold electron plasma environment after having undergone an arbitrary number of scatterings. This is done by retaining the exact differential cross section for Thomson scattering as opposed to using its polarization and angle averaged form. The results are given in the form of recursion relations. The geometry used is the semi-infinite plane-parallel geometry witlh a photon source located on a plane at an arbitrary optical depth below the surface. Analytical expressions are given for the probabilities which are accurate over a wide range of initial optical depth. These results can be used to model compact X-ray galactic sources which are surrounded by an electron-rich plasma.

Quasi-integrable non-linear Schrödinger models, infinite towers of exactly conserved charges and bright solitons

NASA Astrophysics Data System (ADS)

Blas, H.; do Bonfim, A. C. R.; Vilela, A. M.

2017-05-01

Deformations of the focusing non-linear Schrödinger model (NLS) are considered in the context of the quasi-integrability concept. We strengthen the results of JHEP 09 (2012) 103 for bright soliton collisions. We addressed the focusing NLS as a complement to the one in JHEP 03 (2016) 005 , in which the modified defocusing NLS models with dark solitons were shown to exhibit an infinite tower of exactly conserved charges. We show, by means of analytical and numerical methods, that for certain two-bright-soliton solutions, in which the modulus and phase of the complex modified NLS field exhibit even parities under a space-reflection symmetry, the first four and the sequence of even order charges are exactly conserved during the scattering process of the solitons. We perform extensive numerical simulations and consider the bright solitons with deformed potential V=2η /2+\\upepsilon{({|ψ |}^2)}^{2+\\upepsilon},\\upepsilon \\in \\mathbb{R},η <0 . However, for two-soliton field components without definite parity we also show numerically the vanishing of the first non-trivial anomaly and the exact conservation of the relevant charge. So, the parity symmetry seems to be a sufficient but not a necessary condition for the existence of the infinite tower of conserved charges. The model supports elastic scattering of solitons for a wide range of values of the amplitudes and velocities and the set { η, ɛ}. Since the NLS equation is ubiquitous, our results may find potential applications in several areas of non-linear science.

Generative Perspectives on Language Acquisition: Empirical Findings, Theoretical Considerations, and Crosslinguistic Comparisons.

ERIC Educational Resources Information Center

Clahsen, Harald, Ed.

The collection of essays and studies concerning generative grammar and first and second language acquisition includes: "The Optional-Infinitive Stage in Child English: Evidence from Negation" (Tony Harris, Ken Wexler); "Towards a Structure-Building Model of Acquisition" (Andrew Radford); "The Underspecification of…

Topological Constraints in Directed Polymer Melts

NASA Astrophysics Data System (ADS)

Serna, Pablo; Bunin, Guy; Nahum, Adam

2015-11-01

Polymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length L wander in the transverse direction only by a distance of order (ln L )ζ with ζ ≃1.5 . This is strongly suppressed in comparison with the Brownian L1 /2 scaling which holds in the absence of the topological constraint. It is also much smaller than the predictions of standard heuristic approaches—in particular the L1 /4 of a mean-field-like "array of obstacles" model—so our results present a sharp challenge to theory. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion in the transverse direction. To cast light on the suppression of the strands' wandering, we analyze the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and nondirected.

Comparing the energy landscapes for native folding and aggregation of PrP

PubMed Central

Dee, Derek R.; Woodside, Michael T.

2016-01-01

ABSTRACT Protein sequences are evolved to encode generally one folded structure, out of a nearly infinite array of possible folds. Underlying this code is a funneled free energy landscape that guides folding to the native conformation. Protein misfolding and aggregation are also a manifestation of free-energy landscapes. The detailed mechanisms of these processes are poorly understood, but often involve rare, transient species and a variety of different pathways. The inherent complexity of misfolding has hampered efforts to measure aggregation pathways and the underlying energy landscape, especially using traditional methods where ensemble averaging obscures important rare and transient events. We recently studied the misfolding and aggregation of prion protein by examining 2 monomers tethered in close proximity as a dimer, showing how the steps leading to the formation of a stable aggregated state can be resolved in the single-molecule limit and the underlying energy landscape thereby reconstructed. This approach allows a more quantitative comparison of native folding versus misfolding, including fundamental differences in the dynamics for misfolding. By identifying key steps and interactions leading to misfolding, it should help to identify potential drug targets. Here we describe the importance of characterizing free-energy landscapes for aggregation and the challenges involved in doing so, and we discuss how single-molecule studies can help test proposed structural models for PrP aggregates. PMID:27191683

Drop pattern resulting from the breakup of a bidimensional grid of liquid filaments

NASA Astrophysics Data System (ADS)

Cuellar, Ingrith; Ravazzoli, Pablo D.; Diez, Javier A.; González, Alejandro G.

2017-10-01

A rectangular grid formed by liquid filaments on a partially wetting substrate evolves in a series of breakups leading to arrays of drops with different shapes distributed in a rather regular bidimensional pattern. Our study is focused on the configuration produced when two long parallel filaments of silicone oil, which are placed upon a glass substrate previously coated with a fluorinated solution, are crossed perpendicularly by another pair of long parallel filaments. A remarkable feature of this kind of grids is that there are two qualitatively different types of drops. While one set is formed at the crossing points, the rest are consequence of the breakup of shorter filaments formed between the crossings. Here, we analyze the main geometric features of all types of drops, such as shape of the footprint and contact angle distribution along the drop periphery. The formation of a series of short filaments with similar geometric and physical properties allows us to have simultaneously quasi identical experiments to study the subsequent breakups. We develop a simple hydrodynamic model to predict the number of drops that results from a filament of given initial length and width. This model is able to yield the length intervals corresponding to a small number of drops, and its predictions are successfully compared with the experimental data as well as with numerical simulations of the full Navier-Stokes equation that provide a detailed time evolution of the dewetting motion of the filament till the breakup into drops. Finally, the prediction for finite filaments is contrasted with the existing theories for infinite ones.

Dynamic analysis of periodic vibration suppressors with multiple secondary oscillators

NASA Astrophysics Data System (ADS)

Ma, Jiangang; Sheng, Meiping; Guo, Zhiwei; Qin, Qi

2018-06-01

A periodic vibration suppressor with multiple secondary oscillators is examined in this paper to reduce the low-frequency vibration. The band-gap properties of infinite periodic structure and vibration transmission properties of finite periodic structure attached with secondary oscillators with arbitrary degree of freedom are thoroughly analyzed by the plane-wave-expansion method. A simply supported plate with a periodic rectangular array of vibration suppressors is considered. The dynamic model of this periodic structure is established and the equation of harmonic vibration response is theoretically derived and numerically examined. Compared with the simply supported plate without attached suppressors, the proposed plate can obtain better vibration control, and the vibration response can be effectively reduced in several frequency bands owing to the multiple band-gap property. By analyzing the modal properties of the periodic vibration suppressors, the relationship between modal frequencies and the parameters of spring stiffness and mass is established. With the numerical results, the design guidance of the locally resonant structure with multiple secondary oscillators is proposed to provide practical guidance for application. Finally, a practical periodic specimen is designed and fabricated, and then an experiment is carried out to validate the effectiveness of periodic suppressors in the reality. The results show that the experimental band gaps have a good coincidence with those in the theoretical model, and the low-frequency vibration of the plate with periodic suppressors can be effectively reduced in the tuned band gaps. Both the theoretical results and experimental results prove that the design method is effective and the structure with periodic suppressors has a promising application in engineering.

Thin-film-transistor array: an exploratory attempt for high throughput cell manipulation using electrowetting principle

NASA Astrophysics Data System (ADS)

Shaik, F. Azam; Cathcart, G.; Ihida, S.; Lereau-Bernier, M.; Leclerc, E.; Sakai, Y.; Toshiyoshi, H.; Tixier-Mita, A.

2017-05-01

In lab-on-a-chip (LoC) devices, microfluidic displacement of liquids is a key component. electrowetting on dielectric (EWOD) is a technique to move fluids, with the advantage of not requiring channels, pumps or valves. Fluids are discretized into droplets on microelectrodes and moved by applying an electric field via the electrodes to manipulate the contact angle. Micro-objects, such as biological cells, can be transported inside of these droplets. However, the design of conventional microelectrodes, made by standard micro-fabrication techniques, fixes the path of the droplets, and limits the reconfigurability of paths and thus limits the parallel processing of droplets. In that respect, thin film transistor (TFT) technology presents a great opportunity as it allows infinitely reconfigurable paths, with high parallelizability. We propose here to investigate the possibility of using TFT array devices for high throughput cell manipulation using EWOD. A COMSOL based 2D simulation coupled with a MATLAB algorithm was used to simulate the contact angle modulation, displacement and mixing of droplets. These simulations were confirmed by experimental results. The EWOD technique was applied to a droplet of culture medium containing HepG2 carcinoma cells and demonstrated no negative effects on the viability of the cells. This confirms the possibility of applying EWOD techniques to cellular applications, such as parallel cell analysis.

Preliminary numerical analysis of improved gas chromatograph model

NASA Technical Reports Server (NTRS)

Woodrow, P. T.

1973-01-01

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Modeling Hofmeister Effects

PubMed Central

Hribar-Lee, Barbara; Vlachy, Vojko; Dill, Ken A.

2009-01-01

A two dimensional model of water, so-called Mercedes-Benz model, was used to study effects of the size of hydrophobic solute on the insertion thermodynamics in electrolyte solutions. The model was examined by the constant pressure Monte Carlo computer simulation. The results were compared with the experimental data for noble gasses and methane in water and electrolyte solution. The influence of different ions at infinite dilution on the free energy of transfer was explored. Qualitative agreement with the experimental results was obtained. The mechanism of Hofmeister effects was proposed. PMID:20161468

Modeling Hofmeister Effects.

PubMed

Hribar-Lee, Barbara; Vlachy, Vojko; Dill, Ken A

2009-03-11

A two dimensional model of water, so-called Mercedes-Benz model, was used to study effects of the size of hydrophobic solute on the insertion thermodynamics in electrolyte solutions. The model was examined by the constant pressure Monte Carlo computer simulation. The results were compared with the experimental data for noble gasses and methane in water and electrolyte solution. The influence of different ions at infinite dilution on the free energy of transfer was explored. Qualitative agreement with the experimental results was obtained. The mechanism of Hofmeister effects was proposed.

Exactly solvable relativistic model with the anomalous interaction

NASA Astrophysics Data System (ADS)

Ferraro, Elena; Messina, Antonino; Nikitin, A. G.

2010-04-01

A special class of Dirac-Pauli equations with time-like vector potentials of an external field is investigated. An exactly solvable relativistic model describing the anomalous interaction of a neutral Dirac fermion with a cylindrically symmetric external electromagnetic field is presented. The related external field is a superposition of the electric field generated by a charged infinite filament and the magnetic field generated by a straight line current. In the nonrelativistic approximation the considered model is reduced to the integrable Pron’ko-Stroganov model.

Comparative Performance and Model Agreement of Three Common Photovoltaic Array Configurations.

PubMed

Boyd, Matthew T

2018-02-01

Three grid-connected monocrystalline silicon arrays on the National Institute of Standards and Technology (NIST) campus in Gaithersburg, MD have been instrumented and monitored for 1 yr, with only minimal gaps in the data sets. These arrays range from 73 kW to 271 kW, and all use the same module, but have different tilts, orientations, and configurations. One array is installed facing east and west over a parking lot, one in an open field, and one on a flat roof. Various measured relationships and calculated standard metrics have been used to compare the relative performance of these arrays in their different configurations. Comprehensive performance models have also been created in the modeling software pvsyst for each array, and its predictions using measured on-site weather data are compared to the arrays' measured outputs. The comparisons show that all three arrays typically have monthly performance ratios (PRs) above 0.75, but differ significantly in their relative output, strongly correlating to their operating temperature and to a lesser extent their orientation. The model predictions are within 5% of the monthly delivered energy values except during the winter months, when there was intermittent snow on the arrays, and during maintenance and other outages.

A conceptual approach to approximate tree root architecture in infinite slope models

NASA Astrophysics Data System (ADS)

Schmaltz, Elmar; Glade, Thomas

2016-04-01

Vegetation-related properties - particularly tree root distribution and coherent hydrologic and mechanical effects on the underlying soil mantle - are commonly not considered in infinite slope models. Indeed, from a geotechnical point of view, these effects appear to be difficult to be reproduced reliably in a physically-based modelling approach. The growth of a tree and the expansion of its root architecture are directly connected with both intrinsic properties such as species and age, and extrinsic factors like topography, availability of nutrients, climate and soil type. These parameters control four main issues of the tree root architecture: 1) Type of rooting; 2) maximum growing distance to the tree stem (radius r); 3) maximum growing depth (height h); and 4) potential deformation of the root system. Geometric solids are able to approximate the distribution of a tree root system. The objective of this paper is to investigate whether it is possible to implement root systems and the connected hydrological and mechanical attributes sufficiently in a 3-dimensional slope stability model. Hereby, a spatio-dynamic vegetation module should cope with the demands of performance, computation time and significance. However, in this presentation, we focus only on the distribution of roots. The assumption is that the horizontal root distribution around a tree stem on a 2-dimensional plane can be described by a circle with the stem located at the centroid and a distinct radius r that is dependent on age and species. We classified three main types of tree root systems and reproduced the species-age-related root distribution with three respective mathematical solids in a synthetic 3-dimensional hillslope ambience. Thus, two solids in an Euclidian space were distinguished to represent the three root systems: i) cylinders with radius r and height h, whilst the dimension of latter defines the shape of a taproot-system or a shallow-root-system respectively; ii) elliptic paraboloids represent a cordate-root-system with radius r, height h and a constant, species-independent curvature. This procedure simplifies the classification of tree species into the three defined geometric solids. In this study we introduce a conceptual approach to estimate the 2- and 3-dimensional distribution of different tree root systems, and to implement it in a raster environment, as it is used in infinite slope models. Hereto we used the PCRaster extension in a python framework. The results show that root distribution and root growth are spatially reproducible in a simple raster framework. The outputs exhibit significant effects for a synthetically generated slope on local scale for equal time-steps. The preliminary results depict an initial step to develop a vegetation module that can be coupled with hydro-mechanical slope stability models. This approach is expected to yield a valuable contribution to the implementation of vegetation-related properties, in particular effects of root-reinforcement, into physically-based approaches using infinite slope models.

Comparison and validation of acoustic response models for wind noise reduction pipe arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marty, Julien; Denis, Stéphane; Gabrielson, Thomas

The detection capability of the infrasound component of the International Monitoring System (IMS) is tightly linked to the performance of its wind noise reduction systems. The wind noise reduction solution implemented at all IMS infrasound measurement systems consists of a spatial distribution of air inlets connected to the infrasound sensor through a network of pipes. This system, usually referred to as “pipe array,” has proven its efficiency in operational conditions. The objective of this paper is to present the results of the comparison and validation of three distinct acoustic response models for pipe arrays. The characteristics of the models andmore » the results obtained for a defined set of pipe array configurations are described. A field experiment using a newly developed infrasound generator, dedicated to the validation of these models, is then presented. The comparison between the modeled and empirical acoustic responses shows that two of the three models can be confidently used to estimate pipe array acoustic responses. Lastly, this study paves the way to the deconvolution of IMS infrasound data from pipe array responses and to the optimization of pipe array design to IMS applications.« less

Comparison and validation of acoustic response models for wind noise reduction pipe arrays

DOE PAGES

Marty, Julien; Denis, Stéphane; Gabrielson, Thomas; ...

2017-02-13

The detection capability of the infrasound component of the International Monitoring System (IMS) is tightly linked to the performance of its wind noise reduction systems. The wind noise reduction solution implemented at all IMS infrasound measurement systems consists of a spatial distribution of air inlets connected to the infrasound sensor through a network of pipes. This system, usually referred to as “pipe array,” has proven its efficiency in operational conditions. The objective of this paper is to present the results of the comparison and validation of three distinct acoustic response models for pipe arrays. The characteristics of the models andmore » the results obtained for a defined set of pipe array configurations are described. A field experiment using a newly developed infrasound generator, dedicated to the validation of these models, is then presented. The comparison between the modeled and empirical acoustic responses shows that two of the three models can be confidently used to estimate pipe array acoustic responses. Lastly, this study paves the way to the deconvolution of IMS infrasound data from pipe array responses and to the optimization of pipe array design to IMS applications.« less

Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams

NASA Astrophysics Data System (ADS)

Lim, C. W.; Wang, C. M.

2007-03-01

This article presents a complete and asymptotic representation of the one-dimensional nanobeam model with nonlocal stress via an exact variational principle approach. An asymptotic governing differential equation of infinite-order strain gradient model and the corresponding infinite number of boundary conditions are derived and discussed. For practical applications, it explores and presents a reduced higher-order solution to the asymptotic nonlocal model. It is also identified here and explained at length that most publications on this subject have inaccurately employed an excessively simplified lower-order model which furnishes intriguing solutions under certain loading and boundary conditions where the results become identical to the classical solution, i.e., without the small-scale effect at all. Various nanobeam examples are solved to demonstrate the difference between using the simplified lower-order nonlocal model and the asymptotic higher-order strain gradient nonlocal stress model. An important conclusion is the discovery of significant over- or underestimation of stress levels using the lower-order model, particularly at the vicinity of the clamped end of a cantilevered nanobeam under a tip point load. The consequence is that the design of a nanobeam based on the lower-order strain gradient model could be flawed in predicting the nonlocal stress at the clamped end where it could, depending on the magnitude of the small-scale parameter, significantly over- or underestimate the failure criteria of a nanobeam which are governed by the level of stress.

Landslide model performance in a high resolution small-scale landscape

NASA Astrophysics Data System (ADS)

De Sy, V.; Schoorl, J. M.; Keesstra, S. D.; Jones, K. E.; Claessens, L.

2013-05-01

The frequency and severity of shallow landslides in New Zealand threatens life and property, both on- and off-site. The physically-based shallow landslide model LAPSUS-LS is tested for its performance in simulating shallow landslide locations induced by a high intensity rain event in a small-scale landscape. Furthermore, the effect of high resolution digital elevation models on the performance was tested. The performance of the model was optimised by calibrating different parameter values. A satisfactory result was achieved with a high resolution (1 m) DEM. Landslides, however, were generally predicted lower on the slope than mapped erosion scars. This discrepancy could be due to i) inaccuracies in the DEM or in other model input data such as soil strength properties; ii) relevant processes for this environmental context that are not included in the model; or iii) the limited validity of the infinite length assumption in the infinite slope stability model embedded in the LAPSUS-LS. The trade-off between a correct prediction of landslides versus stable cells becomes increasingly worse with coarser resolutions; and model performance decreases mainly due to altering slope characteristics. The optimal parameter combinations differ per resolution. In this environmental context the 1 m resolution topography resembles actual topography most closely and landslide locations are better distinguished from stable areas than for coarser resolutions. More gain in model performance could be achieved by adding landslide process complexities and parameter heterogeneity of the catchment.

The Crystalline Dynamics of Spiral-Shaped Curves

NASA Astrophysics Data System (ADS)

Dudziński, Marcin; Górka, Przemysław

2015-07-01

We study the motion of spiral-shaped polygonal curves by crystalline curvature. We describe this dynamics by the corresponding infinitely dimensional system of ordinary differential equations and show that the considered model is uniquely solvable. Banach's Contraction Mapping Theorem and the Bellman-Gronwall inequality are the main tools applied in our proof.

Probabilistic Graphical Models for the Analysis and Synthesis of Musical Audio

DTIC Science & Technology

2010-11-01

Abbreviation for the names Griffiths, Engen , and McCloskey. Often used to de- note the stick-breaking distribution over infinite vectors whose elements...of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087–1092, 1953. [65] R. Miotto, L. Barrington, and G. Lanckriet

The Artist's View of Points and Lines.

ERIC Educational Resources Information Center

Millman, Richard S.; Speranza, Ramona R.

1991-01-01

Presented is the idea that art can be used to present early concepts of geometry, including the notion of the infinite. Discussed is the symbiosis that exists between the artistic and mathematical views of points, lines, and planes. Geometric models in art and using art in the classroom are discussed. (KR)

Online Video Games and Young People

ERIC Educational Resources Information Center

Ružic-Baf, Maja; Strnak, Hrvoje; Debeljuh, Andrea

2016-01-01

The availability of new information and communication technologies to an increasingly younger population, the constant availability of the Internet and the opportunity to search information, to create new types and models of communication, types of acceptance and ways of accepting and coping with the infinite amount of information, the velocity…

Electrophoresis of fd-virus particles: experiments and an analysis of the effect of finite rod lengths.

PubMed

Buitenhuis, Johan

2012-09-18

The electrophoretic mobility of rodlike fd viruses is measured and compared to theory, with the theoretical calculations performed according to Stigter (Stigter, D. Charged Colloidal Cylinder with a Gouy Double-Layer. J. Colloid Interface Sci. 1975, 53, 296-306. Stigter, D. Electrophoresis of Highly Charged Colloidal Cylinders in Univalent Salt- Solutions. 1. Mobility in Transverse Field. J. Phys. Chem. 1978, 82, 1417-1423. Stigter, D. Electrophoresis of Highly Charged Colloidal Cylinders in Univalent Salt Solutions. 2. Random Orientation in External Field and Application to Polyelectrolytes. J. Phys. Chem. 1978, 82, 1424-1429. Stigter, D. Theory of Conductance of Colloidal Electrolytes in Univalent Salt Solutions. J. Phys. Chem. 1979, 83, 1663-1670), who describes the electrophoretic mobility of infinite cylinders including relaxation effects. Using the dissociation constants of the ionizable groups on the surfaces of the fd viruses, we can calculate the mobility without any adjustable parameter (apart from the possible Stern layer thickness). In addition, the approximation in the theoretical description of Stigter (and others) of using a model of infinitely long cylinders, which consequently is independent of the aspect ratio, is examined by performing more elaborate numerical calculations for finite cylinders. It is shown that, although the electrophoretic mobility of cylindrical particles in the limit of low ionic strength depends on the aspect ratio much more than "end effects", at moderate and high ionic strengths the finite and infinite cylinder models differ only to a degree that can be attributed to end effects. Furthermore, the range of validity of the Stokes regime is systematically calculated.

Geometrical and quantum mechanical aspects in observers' mathematics

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2013-10-01

When we create mathematical models for Quantum Mechanics we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We prove that Euclidean Geometry works in sufficiently small neighborhood of the given line, but when we enlarge the neighborhood, non-euclidean Geometry takes over. We prove that the physical speed is a random variable, cannot exceed some constant, and this constant does not depend on an inertial coordinate system. We proved the following theorems: Theorem A (Lagrangian). Let L be a Lagrange function of free material point with mass m and speed v. Then the probability P of L = m 2 v2 is less than 1: P(L = m 2 v2) < 1. Theorem B (Nadezhda effect). On the plane (x, y) on every line y = kx there is a point (x0, y0) with no existing Euclidean distance between origin (0, 0) and this point. Conjecture (Black Hole). Our space-time nature is a black hole: light cannot go out infinitely far from origin.

A model of a fishery with fish stock involving delay equations.

PubMed

Auger, P; Ducrot, Arnaud

2009-12-13

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

AE8/AP8 Implementations in AE9/AP9, IRBEM, and SPENVIS

DTIC Science & Technology

2014-02-18

period applies to orbit generation only; AE8/AP8 utilizes geomagnetic field models from other epochs as specified in the table below.) SHIELDOSE2 model...finite and semi- infinite slab data tables for Bremsstrahlung have been reversed [Heynderickx, private communication, May 2013]. This correction is...Cain, J. C., S. J. Hendricks, R. A. Langel, and W. V. Hudson (1967), A proposed model for the international geomagnetic reference field, 1965, J

Complete devil's staircase and crystal-superfluid transitions in a dipolar XXZ spin chain: a trapped ion quantum simulation

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Cucchietti, Fernando M.; Müller-Hermes, Alexander; Bañuls, Mari-Carmen; Cirac, J. Ignacio; Lewenstein, Maciej

2010-11-01

Systems with long-range interactions show a variety of intriguing properties: they typically accommodate many metastable states, they can give rise to spontaneous formation of supersolids, and they can lead to counterintuitive thermodynamic behavior. However, the increased complexity that comes with long-range interactions strongly hinders theoretical studies. This makes a quantum simulator for long-range models highly desirable. Here, we show that a chain of trapped ions can be used to quantum simulate a one-dimensional (1D) model of hard-core bosons with dipolar off-site interaction and tunneling, equivalent to a dipolar XXZ spin-1/2 chain. We explore the rich phase diagram of this model in detail, employing perturbative mean-field theory, exact diagonalization and quasi-exact numerical techniques (density-matrix renormalization group and infinite time-evolving block decimation). We find that the complete devil's staircase—an infinite sequence of crystal states existing at vanishing tunneling—spreads to a succession of lobes similar to the Mott lobes found in Bose-Hubbard models. Investigating the melting of these crystal states at increased tunneling, we do not find (contrary to similar 2D models) clear indications of supersolid behavior in the region around the melting transition. However, we find that inside the insulating lobes there are quasi-long-range (algebraic) correlations, as opposed to models with nearest-neighbor tunneling, that show exponential decay of correlations.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM- FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein

2014-11-15

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less

Symmetries and Boundary Conditions with a Twist

NASA Astrophysics Data System (ADS)

Zawadzki, Krissia; D'Amico, Irene; Oliveira, Luiz N.

2017-10-01

Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here, we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. In the interest of clarity, we develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that, as a rule, boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion Θ = πL/2, where L is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for L = 2-7 show how the breaking of symmetry affects the convergence to the L → ∞ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as L = 7, the numerical results for twisted condition are very close to the L → ∞ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.

Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications

NASA Technical Reports Server (NTRS)

Chaki, Sagar; Gurfinkel, Arie

2010-01-01

We develop a learning-based automated Assume-Guarantee (AG) reasoning framework for verifying omega-regular properties of concurrent systems. We study the applicability of non-circular (AGNC) and circular (AG-C) AG proof rules in the context of systems with infinite behaviors. In particular, we show that AG-NC is incomplete when assumptions are restricted to strictly infinite behaviors, while AG-C remains complete. We present a general formalization, called LAG, of the learning based automated AG paradigm. We show how existing approaches for automated AG reasoning are special instances of LAG.We develop two learning algorithms for a class of systems, called infinite regular systems, that combine finite and infinite behaviors. We show that for infinity-regular systems, both AG-NC and AG-C are sound and complete. Finally, we show how to instantiate LAG to do automated AG reasoning for infinite regular, and omega-regular, systems using both AG-NC and AG-C as proof rules

Modelling spatiotemporal change using multidimensional arrays Meng

NASA Astrophysics Data System (ADS)

Lu, Meng; Appel, Marius; Pebesma, Edzer

2017-04-01

The large variety of remote sensors, model simulations, and in-situ records provide great opportunities to model environmental change. The massive amount of high-dimensional data calls for methods to integrate data from various sources and to analyse spatiotemporal and thematic information jointly. An array is a collection of elements ordered and indexed in arbitrary dimensions, which naturally represent spatiotemporal phenomena that are identified by their geographic locations and recording time. In addition, array regridding (e.g., resampling, down-/up-scaling), dimension reduction, and spatiotemporal statistical algorithms are readily applicable to arrays. However, the role of arrays in big geoscientific data analysis has not been systematically studied: How can arrays discretise continuous spatiotemporal phenomena? How can arrays facilitate the extraction of multidimensional information? How can arrays provide a clean, scalable and reproducible change modelling process that is communicable between mathematicians, computer scientist, Earth system scientist and stakeholders? This study emphasises on detecting spatiotemporal change using satellite image time series. Current change detection methods using satellite image time series commonly analyse data in separate steps: 1) forming a vegetation index, 2) conducting time series analysis on each pixel, and 3) post-processing and mapping time series analysis results, which does not consider spatiotemporal correlations and ignores much of the spectral information. Multidimensional information can be better extracted by jointly considering spatial, spectral, and temporal information. To approach this goal, we use principal component analysis to extract multispectral information and spatial autoregressive models to account for spatial correlation in residual based time series structural change modelling. We also discuss the potential of multivariate non-parametric time series structural change methods, hierarchical modelling, and extreme event detection methods to model spatiotemporal change. We show how array operations can facilitate expressing these methods, and how the open-source array data management and analytics software SciDB and R can be used to scale the process and make it easily reproducible.

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

NASA Technical Reports Server (NTRS)

Banks, H. T.; Wang, C.

1989-01-01

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Identities of Finitely Generated Algebras Over AN Infinite Field

NASA Astrophysics Data System (ADS)

Kemer, A. R.

1991-02-01

It is proved that for each finitely generated associative PI-algebra U over an infinite field F, there is a finite-dimensional F-algebra C such that the ideals of identities of the algebras U and C coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for T-ideals.

Transient Infiltration Analysis for Infinite Slopes using the Modified Function of Unsaturated Hydraulic Conductivity

NASA Astrophysics Data System (ADS)

Oh, Seboong; Achmad Zaky, Fauzi; Mog Park, Young

2016-04-01

The hydraulic behaviors in the soil layer are crucial to the transient infiltration analysis into natural slopes, in which unsaturated hydraulic conductivity (HC) can be evaluated theoretically from soil water retention curves (SWRC) by Mualem's equation. In the nonlinear infiltration analysis, the solution by some of smooth SWRCs is not converge for heavy rainfall condition, since the gradient of HCs is extremely steep near saturation. The van Genuchten's SWRC model has been modified near saturation and subsequently an analytical HC function was proposed to improve the van Genuchten-Mualem HC. Using the examples on 1-D infiltration analysis by the modified HC model, it is validated that any solutions can be converged for various rainfall conditions to keep numerical stability. Stability analysis based on unsaturated effective stress could simulate the infinite slope failure by the proposed HC model. The pore water pressure and the ratio of saturation increased from the surface to shallow depth (˜1m) and the factor of safety decreased gradually due to infiltration. Acknowledgements This research is supported by grants from Korean NRF (2012M3A2A1050974 and 2015R1A2A2A01), which are greatly appreciated.

Turbulent scaling laws as solutions of the multi-point correlation equation using statistical symmetries

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Rosteck, Andreas; Avsarkisov, Victor

2013-11-01

Text-book knowledge proclaims that Lie symmetries such as Galilean transformation lie at the heart of fluid dynamics. These important properties also carry over to the statistical description of turbulence, i.e. to the Reynolds stress transport equations and its generalization, the multi-point correlation equations (MPCE). Interesting enough, the MPCE admit a much larger set of symmetries, in fact infinite dimensional, subsequently named statistical symmetries. Most important, theses new symmetries have important consequences for our understanding of turbulent scaling laws. The symmetries form the essential foundation to construct exact solutions to the infinite set of MPCE, which in turn are identified as classical and new turbulent scaling laws. Examples on various classical and new shear flow scaling laws including higher order moments will be presented. Even new scaling have been forecasted from these symmetries and in turn validated by DNS. Turbulence modellers have implicitly recognized at least one of the statistical symmetries as this is the basis for the usual log-law which has been employed for calibrating essentially all engineering turbulence models. An obvious conclusion is to generally make turbulence models consistent with the new statistical symmetries.

The Effects of Accretion Disk Geometry on AGN Reflection Spectra

NASA Astrophysics Data System (ADS)

Taylor, Corbin James; Reynolds, Christopher S.

2017-08-01

Despite being the gravitational engines that power galactic-scale winds and mega parsec-scale jets in active galaxies, black holes are remarkably simple objects, typically being fully described by their angular momenta (spin) and masses. The modelling of AGN X-ray reflection spectra has proven fruitful in estimating the spin of AGN, as well as giving insight into their accretion histories and the properties of plasmas in the strong gravity regime. However, current models make simplifying assumptions about the geometry of the reflecting material in the accretion disk and the irradiating X-ray corona, approximating the disk as an optically thick, infinitely thin disk of material in the orbital plane. We present results from the new relativistic raytracing suite, Fenrir, that explore the effects that disk thickness may have on the reflection spectrum and the accompanying reverberation signatures. Approximating the accretion disk as an optically thick, geometrically thin, radiation pressure dominated disk (Shakura & Sunyaev 1973), one finds that the disk geometry is non-negligible in many cases, with significant changes in the broad Fe K line profile. Finally, we explore the systematic errors inherent in approximating the disk as being infinitely thin when modeling reflection spectrum, potentially biasing determinations of black hole and corona properties.

Correlation and nonlocality measures as indicators of quantum phase transitions in several critical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Altintas, Ferdi, E-mail: ferdialtintas@ibu.edu.tr; Eryigit, Resul, E-mail: resul@ibu.edu.tr

2012-12-15

We have investigated the quantum phase transitions in the ground states of several critical systems, including transverse field Ising and XY models as well as XY with multiple spin interactions, XXZ and the collective system Lipkin-Meshkov-Glick models, by using different quantumness measures, such as entanglement of formation, quantum discord, as well as its classical counterpart, measurement-induced disturbance and the Clauser-Horne-Shimony-Holt-Bell function. Measurement-induced disturbance is found to detect the first and second order phase transitions present in these critical systems, while, surprisingly, it is found to fail to signal the infinite-order phase transition present in the XXZ model. Remarkably, the Clauser-Horne-Shimony-Holt-Bellmore » function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state. - Highlights: Black-Right-Pointing-Pointer The ability of correlation measures to detect quantum phase transitions has been studied. Black-Right-Pointing-Pointer Measurement induced disturbance fails to detect the infinite order phase transition. Black-Right-Pointing-Pointer CHSH-Bell function detects all phase transitions even when the bipartite density matrix is uncorrelated.« less

A paradox of cumulative culture.

PubMed

Kobayashi, Yutaka; Wakano, Joe Yuichiro; Ohtsuki, Hisashi

2015-08-21

Culture can grow cumulatively if socially learnt behaviors are improved by individual learning before being passed on to the next generation. Previous authors showed that this kind of learning strategy is unlikely to be evolutionarily stable in the presence of a trade-off between learning and reproduction. This is because culture is a public good that is freely exploited by any member of the population in their model (cultural social dilemma). In this paper, we investigate the effect of vertical transmission (transmission from parents to offspring), which decreases the publicness of culture, on the evolution of cumulative culture in both infinite and finite population models. In the infinite population model, we confirm that culture accumulates largely as long as transmission is purely vertical. It turns out, however, that introduction of even slight oblique transmission drastically reduces the equilibrium level of culture. Even more surprisingly, if the population size is finite, culture hardly accumulates even under purely vertical transmission. This occurs because stochastic extinction due to random genetic drift prevents a learning strategy from accumulating enough culture. Overall, our theoretical results suggest that introducing vertical transmission alone does not really help solve the cultural social dilemma problem. Copyright © 2015 Elsevier Ltd. All rights reserved.

The Green’s functions for peridynamic non-local diffusion

PubMed Central

Wang, L. J.; Xu, J. F.

2016-01-01

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

Tree-Structured Infinite Sparse Factor Model

PubMed Central

Zhang, XianXing; Dunson, David B.; Carin, Lawrence

2013-01-01

A tree-structured multiplicative gamma process (TMGP) is developed, for inferring the depth of a tree-based factor-analysis model. This new model is coupled with the nested Chinese restaurant process, to nonparametrically infer the depth and width (structure) of the tree. In addition to developing the model, theoretical properties of the TMGP are addressed, and a novel MCMC sampler is developed. The structure of the inferred tree is used to learn relationships between high-dimensional data, and the model is also applied to compressive sensing and interpolation of incomplete images. PMID:25279389

Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous-variable systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adesso, Gerardo; CNR-INFM Coherentia , Naples; Grup d'Informacio Quantica, Universitat Autonoma de Barcelona, E-08193 Bellaterra

2007-08-15

Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e., simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N{>=}4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding, and potential exploitation of shared quantummore » correlations in continuous variable systems. We discuss how promiscuity gradually arises when considering simple families of discrete variable states, with increasing Hilbert space dimension towards the continuous variable limit. Such models are somehow analogous to Gaussian states with asymptotically diverging, but finite, squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states) exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.« less

Measuring acoustic impedances using a semi-infinite waveguide reference: Applications to wind instruments and vocal tracts

NASA Astrophysics Data System (ADS)

Wolfe, Joe; Smith, John; Tann, John; France, Ryan

2002-11-01

Acoustic pressures may generally be measured with much greater sensitivity, dynamic range, and frequency response than acoustic currents. Consequently, most measurements of acoustic impedance consist of comparison with standard impedances. The method reported here uses a semi-infinite waveguide as the reference because its impedance is purely resistive, frequency independent and accurately known, independent of theories of the boundary layer. Waveguides are effectively infinite for pulses shorter than the echo return time, or if the attenuation due to wall losses (typically 80 dB) exceeds the dynamic range of the experiment. The measurement signal from a high output impedance source is calibrated to have Fourier components proportional to fn, where n may be 1 for convenience or chosen to improve the signal:noise ratio. The method has been used on diverse systems over the range 50 Hz to 13 kHz. When applied to systems with simple geometries, the technique yields results with a little higher wall losses than those expected from the calculations of Rayleigh and Benade. Discontinuities introduce further losses as well as the expected departures from simple one-dimensional models. Measurements on musical wind instruments and on the human vocal tract are reported. [Work supported by the Australian Research Council.

Error Estimates of the Ares I Computed Turbulent Ascent Longitudinal Aerodynamic Analysis

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Ghaffari, Farhad

2012-01-01

Numerical predictions of the longitudinal aerodynamic characteristics for the Ares I class of vehicles, along with the associated error estimate derived from an iterative convergence grid refinement, are presented. Computational results are based on an unstructured grid, Reynolds-averaged Navier-Stokes analysis. The validity of the approach to compute the associated error estimates, derived from a base grid to an extrapolated infinite-size grid, was first demonstrated on a sub-scaled wind tunnel model at representative ascent flow conditions for which the experimental data existed. Such analysis at the transonic flow conditions revealed a maximum deviation of about 23% between the computed longitudinal aerodynamic coefficients with the base grid and the measured data across the entire roll angles. This maximum deviation from the wind tunnel data was associated with the computed normal force coefficient at the transonic flow condition and was reduced to approximately 16% based on the infinite-size grid. However, all the computed aerodynamic coefficients with the base grid at the supersonic flow conditions showed a maximum deviation of only about 8% with that level being improved to approximately 5% for the infinite-size grid. The results and the error estimates based on the established procedure are also presented for the flight flow conditions.