Beura, Shradhananda; Majhi, Banshidhar; Dash, Ratnakar; Roy, Susnata
2015-04-01
An efficient approach for classification of mammograms for detection of breast cancer is presented. The approach utilises the two-dimensional discrete orthonormal S-transform (DOST) to extract the coefficients from the digital mammograms. A feature selection algorithm based the on null-hypothesis test with statistical 'two-sample t-test' method has been suggested to select most significant coefficients from a large number of DOST coefficients. The selected coefficients are used as features in the classification of mammographic images as benign or malignant. This scheme utilises an AdaBoost algorithm with random forest as its base classifier. Two standard databases Mammographic Image Analysis Society (MIAS) and Digital Database for Screening Mammography (DDSM) are used for the validation of the proposed scheme. Simulation results show an optimal classification performance with respect to accuracies of 98.3 and 98.8% and AUC (receiver operating characteristic) values of 0.9985 and 0.9992 for MIAS and DDSM, respectively. Comparative analysis shows that the proposed scheme outperforms its competent schemes. PMID:26609404
Majhi, Banshidhar; Dash, Ratnakar; Roy, Susnata
2015-01-01
An efficient approach for classification of mammograms for detection of breast cancer is presented. The approach utilises the two-dimensional discrete orthonormal S-transform (DOST) to extract the coefficients from the digital mammograms. A feature selection algorithm based the on null-hypothesis test with statistical ‘two-sample t-test’ method has been suggested to select most significant coefficients from a large number of DOST coefficients. The selected coefficients are used as features in the classification of mammographic images as benign or malignant. This scheme utilises an AdaBoost algorithm with random forest as its base classifier. Two standard databases Mammographic Image Analysis Society (MIAS) and Digital Database for Screening Mammography (DDSM) are used for the validation of the proposed scheme. Simulation results show an optimal classification performance with respect to accuracies of 98.3 and 98.8% and AUC (receiver operating characteristic) values of 0.9985 and 0.9992 for MIAS and DDSM, respectively. Comparative analysis shows that the proposed scheme outperforms its competent schemes. PMID:26609404
Symmetric Discrete Orthonormal Stockwell Transform
NASA Astrophysics Data System (ADS)
Wang, Yanwei; Orchard, Jeff
2008-09-01
The Stockwell Transform (ST) is a time-frequency signal decomposition that is gaining in popularity, likely because of its direct relation with the Fourier Transform (FT). A discrete and non-redundant version of the ST, denoted the Discrete Orthonormal Stockwell Transform (DOST), has made the use of the ST more feasible. However, the matrix multiplication required by the DOST can still be a formidable computation, especially for high-dimensional data. Moreover, the symmetric property of the ST and FT is not present in the DOST. In this paper, we investigate a new Symmetric Discrete Orthonormal Stockwell Transform (SDOST) that still keeps the non-redundant multiresolution features of the DOST, while maintaining a symmetry property similar to that of the FT. First, we give a brief introduction for the ST and the DOST. Then we analyze the DOST coefficients and modify the transform to get a symmetric version. A small experiment shows that the SDOST has kept the abilities of the DOST and demonstrates the advantage of symmetry when applying the SDOST.
Local distinguishability of generic unentangled orthonormal bases
NASA Astrophysics Data System (ADS)
Lebl, Jiří; Shakeel, Asif; Wallach, Nolan
2016-01-01
An orthonormal basis consisting of unentangled (pure tensor) elements in a tensor product of Hilbert spaces is an unentangled orthonormal basis (UOB). In general, for n qubits, we prove that in its natural structure as a real variety, the space of UOB is a bouquet of products of Riemann spheres parametrized by a class of edge colorings of hypercubes. Its irreducible components of maximum dimension are products of 2n-1 two spheres. Using a theorem of Walgate and Hardy, we observe that the UOB whose elements are distinguishable by local operations and classical communication (called locally distinguishable or LOCC distinguishable UOB) are exactly those in the maximum dimensional components. Bennett et al. [Phys. Rev. A 59, 1070 (1999)., 10.1103/PhysRevA.59.1070], in their in-depth study of quantum nonlocality without entanglement, include a specific three-qubit example UOB which is not LOCC distinguishable; we construct certain generalized counterparts of this UOB in n qubits.
Approximation and compression with sparse orthonormal transforms.
Sezer, Osman Gokhan; Guleryuz, Onur G; Altunbasak, Yucel
2015-08-01
We propose a new transform design method that targets the generation of compression-optimized transforms for next-generation multimedia applications. The fundamental idea behind transform compression is to exploit regularity within signals such that redundancy is minimized subject to a fidelity cost. Multimedia signals, in particular images and video, are well known to contain a diverse set of localized structures, leading to many different types of regularity and to nonstationary signal statistics. The proposed method designs sparse orthonormal transforms (SOTs) that automatically exploit regularity over different signal structures and provides an adaptation method that determines the best representation over localized regions. Unlike earlier work that is motivated by linear approximation constructs and model-based designs that are limited to specific types of signal regularity, our work uses general nonlinear approximation ideas and a data-driven setup to significantly broaden its reach. We show that our SOT designs provide a safe and principled extension of the Karhunen-Loeve transform (KLT) by reducing to the KLT on Gaussian processes and by automatically exploiting non-Gaussian statistics to significantly improve over the KLT on more general processes. We provide an algebraic optimization framework that generates optimized designs for any desired transform structure (multiresolution, block, lapped, and so on) with significantly better n -term approximation performance. For each structure, we propose a new prototype codec and test over a database of images. Simulation results show consistent increase in compression and approximation performance compared with conventional methods. PMID:25823033
A family of orthonormal wavelet bases with dilation factor 4
NASA Astrophysics Data System (ADS)
Karoui, Abderrazek
2006-05-01
In this paper, we study a method for the construction of orthonormal wavelet bases with dilation factor 4. More precisely, for any integer M>0, we construct an orthonormal scaling filter mM([xi]) that generates a mother scaling function [phi]M, associated with the dilation factor 4. The computation of the different coefficients of mM([xi])2 is done by the use of a simple iterative method. Also, this work shows how this construction method provides us with a whole family of compactly supported orthonormal wavelet bases with arbitrary high regularity. A first estimate of [alpha](M), the asymptotic regularity of [phi]M is given by [alpha](M)~0.25M. Examples are provided to illustrate the results of this work.
Orthonormal filters for identification in active control systems
NASA Astrophysics Data System (ADS)
Mayer, Dirk
2015-12-01
Many active noise and vibration control systems require models of the control paths. When the controlled system changes slightly over time, adaptive digital filters for the identification of the models are useful. This paper aims at the investigation of a special class of adaptive digital filters: orthonormal filter banks possess the robust and simple adaptation of the widely applied finite impulse response (FIR) filters, but at a lower model order, which is important when considering implementation on embedded systems. However, the filter banks require prior knowledge about the resonance frequencies and damping of the structure. This knowledge can be supposed to be of limited precision, since in many practical systems, uncertainties in the structural parameters exist. In this work, a procedure using a number of training systems to find the fixed parameters for the filter banks is applied. The effect of uncertainties in the prior knowledge on the model error is examined both with a basic example and in an experiment. Furthermore, the possibilities to compensate for the imprecise prior knowledge by a higher filter order are investigated. Also comparisons with FIR filters are implemented in order to assess the possible advantages of the orthonormal filter banks. Numerical and experimental investigations show that significantly lower computational effort can be reached by the filter banks under certain conditions.
Zhao, Chunyu; Burge, James H
2013-12-16
Zernike polynomials are an orthonormal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. In optical testing, slope or curvature of a surface or wavefront is sometimes measured instead, from which the surface or wavefront map is obtained. Previously we derived an orthonormal set of vector polynomials that fit to slope measurement data and yield the surface or wavefront map represented by Zernike polynomials. Here we define a 3-element curvature vector used to represent the second derivatives of a continuous surface, and derive a set of orthonormal curvature basis functions that are written in terms of Zernike polynomials. We call the new curvature functions the C polynomials. Closed form relations for the complete basis set are provided, and we show how to determine Zernike surface coefficients from the curvature data as represented by the C polynomials. PMID:24514717
PAC learning using Nadaraya-Watson estimator based on orthonormal systems
Qiao, Hongzhu; Rao, N.S.V.; Protopopescu, V.
1997-08-01
Regression or function classes of Euclidean type with compact support and certain smoothness properties are shown to be PAC learnable by the Nadaraya-Watson estimator based on complete orthonormal systems. While requiring more smoothness properties than typical PAC formulations, this estimator is computationally efficient, easy to implement, and known to perform well in a number of practical applications. The sample sizes necessary for PAC learning of regressions or functions under sup norm cost are derived for a general orthonormal system. The result covers the widely used estimators based on Haar wavelets, trignometric functions, and Daubechies wavelets.
Orthonormal mode sets for the two-dimensional fractional Fourier transformation.
Alieva, Tatiana; Bastiaans, Martin J
2007-05-15
A family of orthonormal mode sets arises when Hermite-Gauss modes propagate through lossless first-order optical systems. It is shown that the modes at the output of the system are eigenfunctions for the symmetric fractional Fourier transformation if and only if the system is described by an orthosymplectic ray transformation matrix. Essentially new orthonormal mode sets can be obtained by letting helical Laguerre-Gauss modes propagate through an antisymmetric fractional Fourier transformer. The properties of these modes and their representation on the orbital Poincaré sphere are studied. PMID:17440542
Error estimates of Lagrange interpolation and orthonormal expansions for Freud weights
NASA Astrophysics Data System (ADS)
Kwon, K. H.; Lee, D. W.
2001-08-01
Let Sn[f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of Sn[f] and discuss the speed of the convergence of Sn[f] in weighted Lp space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial Ln[f], whose nodal points are the zeros of orthonormal polynomials with respect to a Freud weight. In particular, if W(x)=e-(1/2)x2 is the Hermite weight function, then we obtain sufficient conditions for the inequalities to hold:andwhere and k=0,1,2...,r.
An Automatic Orthonormalization Method for Solving Stiff Boundary-Value Problems
NASA Astrophysics Data System (ADS)
Davey, A.
1983-08-01
A new initial-value method is described, based on a remark by Drury, for solving stiff linear differential two-point cigenvalue and boundary-value problems. The method is extremely reliable, it is especially suitable for high-order differential systems, and it is capable of accommodating realms of stiffness which other methods cannot reach. The key idea behind the method is to decompose the stiff differential operator into two non-stiff operators, one of which is nonlinear. The nonlinear one is specially chosen so that it advances an orthonormal frame, indeed the method is essentially a kind of automatic orthonormalization; the second is auxiliary but it is needed to determine the required function. The usefulness of the method is demonstrated by calculating some eigenfunctions for an Orr-Sommerfeld problem when the Reynolds number is as large as 10°.
Ultrasonic flaw detection using threshold modified S-transform.
Benammar, Abdessalem; Drai, Redouane; Guessoum, Abderrezak
2014-02-01
Interference noising originating from the ultrasonic testing defect signal seriously influences the accuracy of the signal extraction and defect location. Time-frequency analysis methods are mainly used to improve the defects detection resolution. In fact, the S-transform, a hybrid of the Short time Fourier transform (STFT) and wavelet transform (WT), has a time frequency resolution which is far from ideal. In this paper, a new modified S-transform based on thresholding technique, which offers a better time frequency resolution compared to the original S-transform is proposed. The improvement is achieved by the introduction of a new scaling rule for the Gaussian window used in S-transform. Simulation results are presented and show correct time frequency information of multiple Gaussian echoes under low signal-to-noise ratio (SNR) environment. In addition, experimental results demonstrate better and reliable detection of close echoes drowned in the noise. PMID:24120270
NASA Astrophysics Data System (ADS)
Ma, Jun; Parhi, Keshab K.; Hekstra, Gerben J.; Deprettere, Ed F. A.
1998-10-01
CORDIC based IIR digital filters are orthogonal filters whose internal computations consist of orthogonal transformations. These filters possess desirable properties for VLSI implementations such as regularity, local connection, low sensitivity to finite word-length implementation, and elimination of limit cycles. Recently, fine-grain pipelined CORDIC based IIR digital filter architectures which can perform the filtering operations at arbitrarily high sample rates at the cost of linear increase in hardware complexity have been developed. These pipelined architectures consists of only Givens rotations and a few additions which can be mapped onto CORDIC arithmetic based processors. However, in practical applications, implementations of GIvens rotations using traditional CORDIC arithmetic are quite expensive. For example, for 16 bit accuracy, using floating point data format with 16 bit mantissa and 5 bit exponent, it will require approximately 20 pairs of shift-add operations for one Givens rotation. In this paper, we propose an efficient implementation of pipelined CORDIC based IIR digital filters based on fast orthonormal (mu) -rotations. Using this method, the Givens rotations are approximated by angel corresponding to orthonormal (mu) -rotations, which are based on the idea of CORDIC and can perform rotation with minimal number of shift-add operations. We present various methods of construction for such orthonormal (mu) -rotations. A significant reduction of the number of required shift-add operations is achieved. All types of fast rotations can be implemented as a cascade of only four basic types of shift-add stages. These stages can be executed on a modified floating-point CORDIC architecture, making the pipelined filter highly suitable for VLSI implementations.
Takagi-Sugeno fuzzy models in the framework of orthonormal basis functions.
Machado, Jeremias B; Campello, Ricardo J G B; Amaral, Wagner Caradori
2013-06-01
An approach to obtain Takagi-Sugeno (TS) fuzzy models of nonlinear dynamic systems using the framework of orthonormal basis functions (OBFs) is presented in this paper. This approach is based on an architecture in which local linear models with ladder-structured generalized OBFs (GOBFs) constitute the fuzzy rule consequents and the outputs of the corresponding GOBF filters are input variables for the rule antecedents. The resulting GOBF-TS model is characterized by having only real-valued parameters that do not depend on any user specification about particular types of functions to be used in the orthonormal basis. The fuzzy rules of the model are initially obtained by means of a well-known technique based on fuzzy clustering and least squares. Those rules are then simplified, and the model parameters (GOBF poles, GOBF expansion coefficients, and fuzzy membership functions) are subsequently adjusted by using a nonlinear optimization algorithm. The exact gradients of an error functional with respect to the parameters to be optimized are computed analytically. Those gradients provide exact search directions for the optimization process, which relies solely on input-output data measured from the system to be modeled. An example is presented to illustrate the performance of this approach in the modeling of a complex nonlinear dynamic system. PMID:23096073
Analytical Derivation of Row-Orthonormal Hyperspherical Harmonics for Triatomic Systems
NASA Astrophysics Data System (ADS)
Wang, Desheng; Kuppermann, Aron
2009-12-01
Hyperspherical harmonics for triatomic systems as functions of row-orthonormal hyperspherical coordinates, (also called democratic hyperspherical harmonics) are obtained explicitly in terms of Jacobi polynomials and trigonometeric functions. These harmonics are regular at the poles of the triatomic kinetic energy operator, are complete, and are not highly oscillatory. They constitute an excellent basis set for calculating the local hyperspherical surface functions in the strong interaction region of nuclear configuration space. This basis set is, in addition, numerically very efficient and should permit benchmark-quality calculations of state-to-state differential and integral cross sections for those systems. The approach used for their derivation is new and should be applicable to systems of more than three atoms.
Statistical denoising of signals in the S-transform domain
NASA Astrophysics Data System (ADS)
Weishi, Man; Jinghuai, Gao
2009-06-01
In this paper, the denoising of stochastic noise in the S-transform (ST) and generalized S-transform (GST) domains is discussed. First, the mean power spectrum (MPS) of white noise is derived in the ST and GST domains. The results show that the MPS varies linearly with the frequency in the ST and GST domains (with a Gaussian window). Second, the local power spectrum (LPS) of red noise is studied by employing the Monte Carlo method in the two domains. The results suggest that the LPS of Gaussian red noise can be transformed into a chi-square distribution with two degrees of freedom. On the basis of the difference between the LPS distribution of signals and noise, a denoising method is presented through hypothesis testing. The effectiveness of the method is confirmed by testing synthetic seismic data and a chirp signal.
Ocean Domains and Maximum Degree of Spherical Harmonic and Orthonormal Expansions
NASA Technical Reports Server (NTRS)
Rapp, R.
1999-01-01
Ocean domains used for the orthonormal (ON) systems are studied to determine the maximum degree of spherical harmonic and orthonormal expansions that can be constructed. Although it was shown that one domain was restricted to degree 24, others were shown could be constructed to determine expansions to at least degree 36. Since 1991 the maximum degree expansion used for several Ohio State studies has been 24. In this report it is shown that the maximum degree for the ocean domain used by Wang and Rapp [1994] was 32 and 29 for the domain used by Rapp, Zhang, Yi [1996]. A modification of the former domain was developed (D1e) that enabled a solution to degree 36 to be determined. A modification of the Rapp, Zhang, Yi domain (D7d) enabled a degree 30 solution to be made. Combination coefficients were developed for domain D1e, to degree 36, and to degree 30 for domain D7d. The degree 30 spherical harmonic expansion provided by Pavlis [1998] of the POCM_4B dynamic ocean topography (DOT), and the degree 30 part of the degree 360 expansion [Rapp. 1998] of the POCM_4B model was converted to an ON expansion valid for the D7d domain. The degree 36 part of the degree 360 expansion was converted to the ON expansion for the D1e domain. The square root of the degree variances of the various solutions were compared. The root mean square value of DOT from the Pai,lis expansion, after conversion to the ON system, was + or - 66.52 cm (D7d domain). The value from the degree 30 part of the 360 expansion was + or - 66.65 cm. The value based on the actual POCM-4B data, in the D7d domain, was + or - 66.74 cm showing excellent agreement with the ON results. If the spherical harmonic coefficients had been used the implied root mean square value was + or - 60.76 cm [Pavlis] and + or -59.70 cm [Rapp].
The gradient of potential vorticity, quaternions and an orthonormal frame for fluid particles
NASA Astrophysics Data System (ADS)
Gibbon, J. D.; Holm, D. D.
2011-04-01
The gradient of potential vorticity (PV) is an important quantity because of the way PV (denoted as $q$) tends to accumulate locally in the oceans and atmospheres. Recent analysis by the authors has shown that the vector quantity $\\bdB = \\bnabla q\\times \\bnabla\\theta$ for the three-dimensional incompressible rotating Euler equations evolves according to the same stretching equation as for $\\bom$ the vorticity and $\\bB$, the magnetic field in magnetohydrodynamics (MHD). The $\\bdB$-vector therefore acts like the vorticity $\\bom$ in Euler's equations and the $\\bB$-field in MHD. For example, it allows various analogies, such as stretching dynamics, helicity, superhelicity and cross helicity. In addition, using quaternionic analysis, the dynamics of the $\\bdB$-vector naturally allow the construction of an orthonormal frame attached to fluid particles\\,; this is designated as a quaternion frame. The alignment dynamics of this frame are particularly relevant to the three-axis rotations that particles undergo as they traverse regions of a flow when the PV gradient $\\bnabla q$ is large.
On the decoding of intracranial data using sparse orthonormalized partial least squares
NASA Astrophysics Data System (ADS)
van Gerven, Marcel A. J.; Chao, Zenas C.; Heskes, Tom
2012-04-01
It has recently been shown that robust decoding of motor output from electrocorticogram signals in monkeys over prolonged periods of time has become feasible (Chao et al 2010 Front. Neuroeng. 3 1-10 ). In order to achieve these results, multivariate partial least-squares (PLS) regression was used. PLS uses a set of latent variables, referred to as components, to model the relationship between the input and the output data and is known to handle high-dimensional and possibly strongly correlated inputs and outputs well. We developed a new decoding method called sparse orthonormalized partial least squares (SOPLS) which was tested on a subset of the data used in Chao et al (2010) (freely obtainable from neurotycho.org (Nagasaka et al 2011 PLoS ONE 6 e22561)). We show that SOPLS reaches the same decoding performance as PLS using just two sparse components which can each be interpreted as encoding particular combinations of motor parameters. Furthermore, the sparse solution afforded by the SOPLS model allowed us to show the functional involvement of beta and gamma band responses in premotor and motor cortex for predicting the first component. Based on the literature, we conjecture that this first component is involved in the encoding of movement direction. Hence, the sparse and compact representation afforded by the SOPLS model facilitates interpretation of which spectral, spatial and temporal components are involved in successful decoding. These advantages make the proposed decoding method an important new tool in neuroprosthetics.
Du, Hubing; Gao, Honghong
2016-08-20
Affected by the height dependent effects, the phase-shifting shadow moiré can only be implemented in an approximate way. In the technique, a fixed phase step around π/2 rad between two adjacent frames is usually introduced by a grating translation in its own plane. So the method is not flexible in some situations. Additionally, because the shadow moiré fringes have a complex intensity distribution, computing the introduced phase shift from the existing arccosine function or arcsine function-based phase shift extraction algorithm always exhibits instability. To solve it, we developed a Gram-Schmidt orthonormalization approach based on a three-frame self-calibration phase-shifting algorithm with equal but unknown phase steps. The proposed method using the arctangent function is fast and can be implemented robustly in many applications. We also do optical experiments to demonstrate the correction of the proposed method by referring to the result of the conventional five-step phase-shifting shadow moiré. The results show the correctness of the proposed method. PMID:27556993
On the L^p_\\mu-strong property of orthonormal systems
NASA Astrophysics Data System (ADS)
Grigorian, M. G.
2003-10-01
Let \\{\\varphi_n(x)\\} be a system of bounded functions complete and orthonormal in L^2_{ \\lbrack 0,1 \\rbrack } and assume that \\Vert\\varphi_n\\Vert _{p_0}\\leqslant\\mathrm{const}, n\\geqslant 1, for some p_0>2. Then the elements of the system can be rearranged so that the resulting system has the L^p_\\mu-strong property: for each \\varepsilon>0 there exists a (measurable) subset E\\subset \\lbrack 0,1 \\rbrack of measure \\vert E\\vert>1-\\varepsilon and a measurable function \\mu(x), 0<\\mu(x)\\leqslant 1, \\mu(x)=1 on E such that for all p>2 and f(x)\\in L^p_\\mu \\lbrack 0,1 \\rbrack one can find a function g(x)\\in L^1_{ \\lbrack 0,1 \\rbrack } coinciding with f(x) on E such that its Fourier series in the system \\{\\varphi_{\\sigma(k)}(x)\\} converges to g(x) in the L^p_\\mu \\lbrack 0,1 \\rbrack -norm and the sequence of Fourier coefficients of this function belongs to all spaces l^q, q>2.
On representing rotations by Rodrigues parameters in non-orthonormal reference systems.
Morawiec, A
2016-09-01
A Rodrigues vector is a triplet of real numbers used for parameterizing rotations or orientations in three-dimensional space. Because of its properties (e.g. simplicity of fundamental regions for misorientations) this parameterization is frequently applied in analysis of orientation maps of polycrystalline materials. By conventional definition, the Rodrigues parameters are specified in orthonormal coordinate systems, whereas the bases of crystal lattices are generally non-orthogonal. Therefore, the definition of Rodrigues parameters is extended so they can be directly linked to non-Cartesian bases of a crystal. The new parameters are co- or contravariant components of vectors specified with respect to the same basis as atomic positions in a unit cell. The generalized formalism allows for redundant crystallographic axes. The formulas for rotation composition and the relationship to the rotation matrix are similar to those used in the Cartesian case, but they have a wider range of applicability: calculations can be performed with an arbitrary metric tensor of the crystal lattice. The parameterization in oblique coordinate frames of lattices is convenient for crystallographic applications because the generalized parameters are directly related to indices of rotation-invariant lattice directions and rotation-invariant lattice planes. PMID:27580203
Lu, Yuzhen; Li, Richard; Lu, Renfu
2016-09-01
Structured illumination using sinusoidal patterns has been used for optical imaging of biological tissues in biomedical research, and of horticultural products in food quality evaluation. Implementation of structured-illumination imaging relies on retrieval of amplitude images, which is conventionally achieved by a phase-shifting technique that requires collecting a minimum of three phase-shifted images. In this study, we have proposed Gram-Schmidt orthonormalization (GSO) to retrieve amplitude component (AC) images using only two phase-shifted images. We have proposed two forms of GSO implementation, and prior to GSO processing, we eliminated the direct component (DC) background by subtracting a DC image we recovered using a spiral phase function (SPF) in the Fourier space. We demonstrated the GSO methods through numerical simulations and application examples of detection of bruise defects in apples by structured-illumination reflectance imaging (SIRI). GSO performed comparably to conventional three-phase-based demodulation. It is simple, fast and effective for amplitude retrieval and requires no prior phase information, which could facilitate fast implementation of structured-illumination imaging. PMID:27607260
Homogeneous hierarchies: A discrete analogue to the wavelet-based multiresolution approximation
Mirkin, B.
1996-12-31
A correspondence between discrete binary hierarchies and some orthonormal bases of the n-dimensional Euclidean space can be applied to such problems as clustering, ordering, identifying/testing in very large data bases, or multiresolution image/signal processing. The latter issue is considered in the paper. The binary hierarchy based multiresolution theory is expected to lead to effective methods for data processing because of relaxing the regularity restrictions of the classical theory.
Distributed mean curvature on a discrete manifold for Regge calculus
NASA Astrophysics Data System (ADS)
Conboye, Rory; Miller, Warner A.; Ray, Shannon
2015-09-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of the volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as the fractional rate of change of the normal vector.
Edwards, Lloyd J.; Simpson, Sean L.
2014-01-01
Background The use of 24-hour ambulatory blood pressure monitoring (ABPM) in clinical practice and observational epidemiological studies has grown considerably in the past 25 years. ABPM is a very effective technique for assessing biological, environmental, and drug effects on blood pressure. Objectives In order to enhance the effectiveness of ABPM for clinical and observational research studies via analytical and graphical results, developing alternative data analysis approaches using modern statistical techniques are important. Methods The linear mixed model for the analysis of longitudinal data is particularly well-suited for the estimation of, inference about, and interpretation of both population (mean) and subject-specific trajectories for ABPM data. We propose using a linear mixed model with orthonormal polynomials across time in both the fixed and random effects to analyze ABPM data. Results We demonstrate the proposed analysis technique using data from the Dietary Approaches to Stop Hypertension (DASH) study, a multicenter, randomized, parallel arm feeding study that tested the effects of dietary patterns on blood pressure. Conclusions The linear mixed model is relatively easy to implement (given the complexity of the technique) using available software, allows for straight-forward testing of multiple hypotheses, and the results can be presented to research clinicians using both graphical and tabular displays. Using orthonormal polynomials provides the ability to model the nonlinear trajectories of each subject with the same complexity as the mean model (fixed effects). PMID:24667908
NASA Astrophysics Data System (ADS)
Lee, Hanshin; Hart, Michael; Hill, Gary J.; Rafal, Marc D.
2010-07-01
Wavefront sensing (WFS) is one of the key elements for active alignment of the new Wide-Field Corrector (WFC), as it tracks sidereal motion, with respect to the fixed Hobby-Eberly Telescope (HET) primary mirror. During a track, part of the 10m-pupil of the WFC can lie outside the primary periphery and be clipped off. An additional field-dependent central obscuration by the holes and baffles of the WFC leads to complex pupil geometries. The combination of these is a complicated dynamically varying non-circular telescope pupil. This unique problem to the WFS on the HET needs to be dealt with by choosing an appropriate set of orthonormal aberration polynomials during wavefront reconstruction. In this paper, three ways of computing orthonormal aberration polynomials and their coefficients are discussed. These are based on the Gram-Schmidt (GS) process, but differ in the way of computing key integrals during the GS process. The first method analytically computes the integrals, where a computer algebra program is used. The second uses the Gaussian quadrature over triangulated pupil geometries that approximate the true pupil shape. The last uses indirect numerical estimates of the integrals, which turned out to be natural by-products of the usual least-square Zernike polynomials fit. It is shown that the first method is limited to cases of simple pupil shapes, while the second can be applied to more general pupil shapes. However, when dealing with complicated dynamically varying non-circular pupils, the last method can be vastly more efficient than the second and enables the possibility of estimating orthonormal aberration coefficient on the fly. Also noticed is that the last method naturally takes into account the pixelation effect of pupil geometries due to pixel-based imaging sensors (e.g. CCDs). With these benefits, the last method can be used as a viable tool in real-time wavefront analysis over dynamically changing pupils as in the Hobby- Eberly Telescope, which is
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
2015-12-01
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
An asymptotic formula for polynomials orthonormal with respect to a varying weight. II
Komlov, A V; Suetin, S P
2014-09-30
This paper gives a proof of the theorem announced by the authors in the preceding paper with the same title. The theorem states that asymptotically the behaviour of the polynomials which are orthonormal with respect to the varying weight e{sup −2nQ(x)}p{sub g}(x)/√(∏{sub j=1}{sup 2p}(x−e{sub j})) coincides with the asymptotic behaviour of the Nuttall psi-function, which solves a special boundary-value problem on the relevant hyperelliptic Riemann surface of genus g=p−1. Here e{sub 1}
Application of S-transform profilometry in train wheel surface three dimensional measurement
NASA Astrophysics Data System (ADS)
Wang, Haiqing; Zhang, Yu; Li, Jinlong; Hu, Jiayuan
2015-12-01
A three dimensional (3D) measurement method for train wheel surface is proposed based on S-transform profilometry. This method is based on S-transform in fringe analysis. A fringe pattern with a carrier frequency component is projected onto the wheel tread, the deformed fringe patterns caused by the height distribution of wheel surface is recorded as an image, and the fundamental spectrum of S-transform spectra from the image is abstracted by use of weighting filters, then the wrapped phase is obtained by IFFT of the fundamental spectrum. 2D-SRNCP (sorting by reliability following a non-continuous path) phase unwrapping algorithm is used to unwrap phase, which can be used to reconstruct the surface distribution of wheel. Simulation and testing experiment is taken and the result shows that, comparing with light-section method, this method can realize a faster inspection and a higher accuracy measurement of 3D wheel surface.
ERIC Educational Resources Information Center
Ghezzi, Patrick M.
2007-01-01
The advantages of emphasizing discrete trials "teaching" over discrete trials "training" are presented first, followed by a discussion of discrete trials as a method of teaching that emerged historically--and as a matter of necessity for difficult learners such as those with autism--from discrete trials as a method for laboratory research. The…
NASA Astrophysics Data System (ADS)
Cheng, Z.; Chen, Y.; Liu, Y.; Liu, W.; Zhang, G.
2015-12-01
Among those hydrocarbon reservoir detection techniques, the time-frequency analysis based approach is one of the most widely used approaches because of its straightforward indication of low-frequency anomalies from the time-frequency maps, that is to say, the low-frequency bright spots usually indicate the potential hydrocarbon reservoirs. The time-frequency analysis based approach is easy to implement, and more importantly, is usually of high fidelity in reservoir prediction, compared with the state-of-the-art approaches, and thus is of great interest to petroleum geologists, geophysicists, and reservoir engineers. The S transform has been frequently used in obtaining the time-frequency maps because of its better performance in controlling the compromise between the time and frequency resolutions than the alternatives, such as the short-time Fourier transform, Gabor transform, and continuous wavelet transform. The window function used in the majority of previous S transform applications is the symmetric Gaussian window. However, one problem with the symmetric Gaussian window is the degradation of time resolution in the time-frequency map due to the long front taper. In our study, a bi-Gaussian S transform that substitutes the symmetric Gaussian window with an asymmetry bi-Gaussian window is proposed to analyze the multi-channel seismic data in order to predict hydrocarbon reservoirs. The bi-Gaussian window introduces asymmetry in the resultant time-frequency spectrum, with time resolution better in the front direction, as compared with the back direction. It is the first time that the bi-Gaussian S transform is used for analyzing multi-channel post-stack seismic data in order to predict hydrocarbon reservoirs since its invention in 2003. The superiority of the bi-Gaussian S transform over traditional S transform is tested on a real land seismic data example. The performance shows that the enhanced temporal resolution can help us depict more clearly the edge of the
Seizure detection approach using S-transform and singular value decomposition.
Xia, Yudan; Zhou, Weidong; Li, Chengcheng; Yuan, Qi; Geng, Shujuan
2015-11-01
Automatic seizure detection plays a significant role in the diagnosis of epilepsy. This paper presents a novel method based on S-transform and singular value decomposition (SVD) for seizure detection. Primarily, S-transform is performed on EEG signals, and the obtained time-frequency matrix is divided into submatrices. Then, the singular values of each submatrix are extracted using singular value decomposition (SVD). Effective features are constructed by adding the largest singular values in the same frequency band together and fed into Bayesian linear discriminant analysis (BLDA) classifier for decision. Finally, postprocessing is applied to obtain higher sensitivity and lower false detection rate. A total of 183.07 hours of intracranial EEG recordings containing 82 seizure events from 20 patients were used to evaluate the system. The proposed method had a sensitivity of 96.40% and a specificity of 99.01%, with a false detection rate of 0.16/h. PMID:26439656
Detection of near-surface cavities by generalized S-transform of Rayleigh waves
NASA Astrophysics Data System (ADS)
Shao, Guang-zhou; Tsoflias, George P.; Li, Chang-jiang
2016-06-01
The near-surface cavities can cause a huge hidden trouble for urban infrastructure construction, such as, foundation settlement and roadbed subsidence, and so on. So, it is an important task to detect the underground cavities effectively for many engineering projects. At the same time, because of the complexity of near-surface materials and the limited resolution of geophysical methods, detecting the location of the hidden cavities quantitatively is still a technical challenge which needs to be studied further. Base on the study of Xia et al. (Xia et al., 2007), we performed a little modification to the travel time equation for the Rayleigh-wave diffraction. We put forward another way to detect the shallow subsurface voids. The generalized S-transform was adopted to extract the arrival times of the diffracted Rayleigh waves from the near and far-offset boundaries of the void at a certain receiver. Then the arrival times were used to calculate the boundary locations of the void. Three half-space void models and a two-layered void model were used to demonstrate the feasibility and effect of detecting a void with the generalized S-transform. A rotated staggered-grid finite-difference method was adopted in wave field modeling to obtain the synthetic seismic record. Finally, a real world field data was used to verify the detecting effect. The theoretical models and the real world example showed that it is feasible and effective to use the generalized S-transform to detect the near-surface cavities.
Principles of Discrete Time Mechanics
NASA Astrophysics Data System (ADS)
Jaroszkiewicz, George
2014-04-01
1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.
Intelligent Power Swing Detection Scheme to Prevent False Relay Tripping Using S-Transform
NASA Astrophysics Data System (ADS)
Mohamad, Nor Z.; Abidin, Ahmad F.; Musirin, Ismail
2014-06-01
Distance relay design is equipped with out-of-step tripping scheme to ensure correct distance relay operation during power swing. The out-of-step condition is a consequence result from unstable power swing. It requires proper detection of power swing to initiate a tripping signal followed by separation of unstable part from the entire power system. The distinguishing process of unstable swing from stable swing poses a challenging task. This paper presents an intelligent approach to detect power swing based on S-Transform signal processing tool. The proposed scheme is based on the use of S-Transform feature of active power at the distance relay measurement point. It is demonstrated that the proposed scheme is able to detect and discriminate the unstable swing from stable swing occurring in the system. To ascertain validity of the proposed scheme, simulations were carried out with the IEEE 39 bus system and its performance has been compared with the wavelet transform-based power swing detection scheme.
Weighted Averaging for Calculating Azimuthal Angles and Filtering Love Waves Using S-transforms
NASA Astrophysics Data System (ADS)
Napoli, V.; Russell, D. R.
2015-12-01
The S-transform methodology is based on Stockwell transforms, which is a form of a short Fourier transform, with a time domain transform window defined by a Gaussian function. The Gaussian function has a standard deviation equal to the frequency of interest. Applying the transform to multiple frequencies of interest results in a time/frequency spectrogram, which has the advantage of being simply invertible back to the time domain. This allows for the calculation of instantaneous frequency/time phase and amplitude measurements, which makes 2D signal filtration of surface waves possible. By solving for the transverse angle of propagation of narrow band filtered Love waves at a range of periods (8-25s) we calculate a vector of possible azimuths, one at each period. We then average over all the bands of interest to determine the mean angle of propagation. To avoid using unreliable low signal-to-noise (SNR) azimuth estimates, we use a SNR weighted average to more accurately reflect the overall signal propagation azimuth. We then use the mean signal azimuth to design a 2D Love wave rejection filter that will reject off-azimuth noise and then invert this to the time domain for an improved signal on the propagation azimuth. We apply this method to the 2009 Democratic People's Republic of Korea nuclear test. After testing the weighted averaging approach, the SNR ratio increases by a factor of 2 overall, and a signal on the transverse component is identified as a Rayleigh wave that "leaked" into the transverse component. Without this method, there could have been improper Love wave signal identification for the event. Using this innovative SNR weighted averaging technique to calculate propagation angle indicates that S-transform filters can lower the noise level by a factor of 2 or more, helping with low SNR events, and remove Rayleigh "leakage" into the transverse channel.
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Carlsten, B.E.; Haynes, W.B.
1996-08-01
The authors theoretically and numerically investigate the operation and behavior of the discrete monotron oscillator, a novel high-power microwave source. The discrete monotron differs from conventional monotrons and transit time oscillators by shielding the electron beam from the monotron cavity`s RF fields except at two distinct locations. This makes the discrete monotron act more like a klystron than a distributed traveling wave device. As a result, the oscillator has higher efficiency and can operate with higher beam powers than other single cavity oscillators and has more stable operation without requiring a seed input signal than mildly relativistic, intense-beam klystron oscillators.
Dynamic deconvolution of seismic data based on generalized S-transform
NASA Astrophysics Data System (ADS)
Zhou, Huailai; Tian, Yaming; Ye, Yan
2014-09-01
The commonly used methods to improve resolution of seismic data are based on stationary convolution model that is inconsistent with the actual propagation law of seismic wavelet in inhomogeneous media. Therefore, to address this artifact, in this paper authors take seismic scattering and attenuation into integrative consideration, and propose an adaptively dynamic deconvolution method based on generalized S-transform (GST). This method introduces the favorable multi-resolution characteristics of GST into the dynamic deconvolution. Firstly, GST of nonstationary seismic trace can be approximately presented as the product of GST of the dynamic propagating wavelet and the reflectivity in time-frequency domain. We then use polynomial fitting to model the time-frequency spectra of nonstationary seismic trace to obtain the estimation of dynamic propagation wavelet and the reflectivity. This method, without calculating directly the value of Q, is applicable to the case when Q varies, and is robust in the presence of noise. Applications to synthetic and field data validate that this method can effectively enhance seismic data resolution without boosting noise, and restore the attenuated energy of nonstationary seismic signal.
Fractional S-transform-part 2: Application to reservoir prediction and fluid identification
NASA Astrophysics Data System (ADS)
Du, Zheng-Cong; Xu, De-Ping; Zhang, Jin-Ming
2016-06-01
The fractional S-transform (FRST) has good time-frequency focusing ability. The FRST can identify geological features by rotating the fractional Fourier transform frequency (FRFTfr) axis. Different seismic signals have different optimal fractional parameters which is not conducive to multichannel seismic data processing. Thus, we first decompose the common-frequency sections by the FRST and then we analyze the low-frequency shadow. Second, the combination of the FRST and blind-source separation is used to obtain the independent spectra of the various geological features. The seismic data interpretation improves without requiring to estimating the optimal fractional parameters. The top and bottom of a limestone reservoir can be clearly recognized on the common-frequency section, thus enhancing the vertical resolution of the analysis of the low-frequency shadows compared with traditional ST. Simulations suggest that the proposed method separates the independent frequency information in the time-fractional-frequency domain. We used field seismic and well data to verify the proposed method.
NASA Astrophysics Data System (ADS)
Assous, S.; Humeau, A.; Tartas, M.; Abraham, P.; L'Huillier, J. P.
2005-05-01
Conventional signal processing typically involves frequency selective techniques which are highly inadequate for nonstationary signals. In this paper, we present an approach to perform time-frequency selective processing of laser Doppler flowmetry (LDF) signals using the S-transform. The approach is motivated by the excellent localization, in both time and frequency, afforded by the wavelet basis functions. Suitably chosen Gaussian wavelet functions are used to characterize the subspace of signals that have a given localized time-frequency support, thus enabling a time-frequency partitioning of signals. In this paper, the goal is to study the influence of various pharmacological substances taken by the oral way (celecobix (Celebrex®), indomethacin (Indocid®) and placebo) on the physiological activity behaviour. The results show that no statistical differences are observed in the energy computed from the time-frequency representation of LDF signals, for the myogenic, neurogenic and endothelial related metabolic activities between Celebrex and placebo, and Indocid and placebo. The work therefore proves that these drugs do not affect these physiological activities. For future physiological studies, there will therefore be no need to exclude patients having taken cyclo-oxygenase 1 inhibitions.
ERIC Educational Resources Information Center
Peters, James V.
2004-01-01
Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.
Discretizations of axisymmetric systems
NASA Astrophysics Data System (ADS)
Frauendiener, Jörg
2002-11-01
In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.
A discrete fractional random transform
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Zhao, Haifa; Liu, Shutian
2005-11-01
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.
Discrete Newtonian cosmology: perturbations
NASA Astrophysics Data System (ADS)
Ellis, George F. R.; Gibbons, Gary W.
2015-03-01
In a previous paper (Gibbons and Ellis 2014 Discrete Newtonian cosmology Class. Quantum Grav. 31 025003), we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lemaître-Robertson-Walker cosmological models of general relativity theory, provided the distribution of particles obeys the central configuration equation. In this paper we show that one can obtain perturbed such Newtonian solutions that give the same linearized structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zel’dovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass.
Discrete breathers in crystals
NASA Astrophysics Data System (ADS)
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
ERIC Educational Resources Information Center
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Discreteness induced extinction
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira; da Silva, Linaena Méricy
2015-11-01
Two simple models based on ecological problems are discussed from the point of view of non-equilibrium statistical mechanics. It is shown how discrepant may be the results of the models that include spatial distribution with discrete interactions when compared with the continuous analogous models. In the continuous case we have, under certain circumstances, the population explosion. When we take into account the finiteness of the population, we get the opposite result, extinction. We will analyze how these results depend on the dimension d of the space and describe the phenomenon of the "Discreteness Inducing Extinction" (DIE). The results are interpreted in the context of the "paradox of sex", an old problem of evolutionary biology.
A paradigm for discrete physics
Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.
1987-01-01
An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity.
NASA Astrophysics Data System (ADS)
Kotulski, Zbigniew; Szczepaski, Janusz
In the paper we propose a new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems. We formulate the requirements for such systems to assure their safety. We also give examples of practical realisation of chaotic cryptosystems, using a generalisation of the method presented in [7]. The proposed algorithm of encryption and decryption is based on multiple iteration of a certain dynamical chaotic system. We assume that some part of the initial condition is a plain message. As the secret key we assume the system parameter(s) and additionally another part of the initial condition.
NASA Astrophysics Data System (ADS)
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2011-08-01
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞.
NASA Astrophysics Data System (ADS)
Wang, Yuqing; Peng, Zhenming
2016-06-01
As the extension of time-bandwidth product (TBP) in the fractional domain, the generalized time-bandwidth product (GTBP) provides a rotation-independent measure of compactness. A new fractional S transform (FrST) is proposed to avoid missing the physical meaning of the fractional time-frequency plane. FrST is based on the GTBP criterion and the time-frequency rotation property of fractional Fourier transform (FrFT). In addition, we introduce the normalized second-order central moment (NSOCM) calculation method to determine the optimal order. The optimal order searching process can be converted into the NSOCM calculation. Compared with TBP search algorithms, the NSOCM approach has higher computational efficiency. The qualitative advantage of the NSOCM approach in the optimal order selection is demonstrated by a series of model tests. The optimal FrST based on NSOCM (OFrST) can produce more compact time-frequency support than the S transform. The real seismic data spectral decomposition results show that the proposed algorithm can obtain single-frequency visualization with better time-frequency concentration, thereby enhancing the precision of reservoir prediction.
Fault diagnosis of rolling element bearing based on S transform and gray level co-occurrence matrix
NASA Astrophysics Data System (ADS)
Zhao, Minghang; Tang, Baoping; Tan, Qian
2015-08-01
Time-frequency analysis is an effective tool to extract machinery health information contained in non-stationary vibration signals. Various time-frequency analysis methods have been proposed and successfully applied to machinery fault diagnosis. However, little research has been done on bearing fault diagnosis using texture features extracted from time-frequency representations (TFRs), although they may contain plenty of sensitive information highly related to fault pattern. Therefore, to make full use of the textural information contained in the TFRs, this paper proposes a novel fault diagnosis method based on S transform, gray level co-occurrence matrix (GLCM) and multi-class support vector machine (Multi-SVM). Firstly, S transform is chosen to generate the TFRs due to its advantages of providing frequency-dependent resolution while keeping a direct relationship with the Fourier spectrum. Secondly, the famous GLCM-based texture features are extracted for capturing fault pattern information. Finally, as a classifier which has good discrimination and generalization abilities, Multi-SVM is used for the classification. Experimental results indicate that the GLCM-based texture features extracted from TFRs can identify bearing fault patterns accurately, and provide higher accuracies than the traditional time-domain and frequency-domain features, wavelet packet node energy or two-direction 2D linear discriminant analysis based features of the same TFRs in most cases.
Noyes, H.P. ); Starson, S. )
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields'' with the relativistic Wheeler-Feynman action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs.
Discrete Sibson interpolation.
Park, Sung W; Linsen, Lars; Kreylos, Oliver; Owens, John D; Hamann, Bernd
2006-01-01
Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds. PMID:16509383
Discrete Pearson distributions
Bowman, K.O.; Shenton, L.R.; Kastenbaum, M.A.
1991-11-01
These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.
Immigration and Prosecutorial Discretion
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
2015-01-01
Immigration has become an increasingly salient national issue in the US, and the Department of Justice recently increased federal efforts to prosecute immigration offenses. This shift, however, relies on the cooperation of US attorneys and their assistants. Traditionally federal prosecutors have enjoyed enormous discretion and have been responsive to local concerns. To consider how the centralized goal of immigration enforcement may have influenced federal prosecutors in regional offices, we review their prosecution of immigration offenses in California using over a decade's worth of data. Our findings suggest that although centralizing forces influence immigration prosecutions, individual US attorneys' offices retain distinct characteristics. Local factors influence federal prosecutors' behavior in different ways depending on the office. Contrary to expectations, unemployment rates did not affect prosecutors' willingness to pursue immigration offenses, nor did local popular opinion about illegal immigration. PMID:26146530
Discrete stability in stochastic programming
Lepp, R.
1994-12-31
In this lecture we study stability properties of stochastic programs with recourse where the probability measure is approximated by a sequence of weakly convergent discrete measures. Such discrete approximation approach gives us a possibility to analyze explicitly the behavior of the second stage correction function. The approach is based on modern functional analytical methods of an approximation of extremum problems in function spaces, especially on the notion of the discrete convergence of vectors to an essentially bounded measurable function.
Smirnov, Yu. F.; Asherova, R. M.
2011-06-15
The structure of all discrete series of unitary irreducible representations of the U{sub q}(u(3, 1)) and U{sub q}(u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g Prime ){sub q}. The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U{sub q}(u(n, 1)) Superset-Of-Or-Equal-To U{sub q}(u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) Superset-Of-Or-Equal-To u(n) classical algebra.
Discrete Mathematics and Curriculum Reform.
ERIC Educational Resources Information Center
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Discrete Mathematics and Its Applications
ERIC Educational Resources Information Center
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
NASA Astrophysics Data System (ADS)
Zandong Sun, Sam; Sun, Xuekai; Wang, Yonggang; Xie, Huiwen
2015-10-01
Pre-stack seismic data is acknowledged to be more favorable in estimating Q values since it carries much more valuable information in traveltime and amplitude than post-stack data. However, the spectrum of reflectors can be strongly altered by nearby reflector or side lobes of the wavelet, which thereby degrades the accuracy of Q estimation based on the pre-stack spectral ratio method. To solve this problem, we propose a method based on the modified S-transform (MST) for estimating Q values from pre-stack gathers, in which Q values can be obtained with regression analysis based on the relationship between spectral ratio slope and the square of offset. Through tests on a numerical model, we first prove advantages of this pre-stack spectral ratio method compared to the traditional post-stack method. Besides, it is also shown that application of MST would lead to a much more focused intercept, which is the kernel for the pre-stack method. Therefore, the accuracy of Q estimation using MST is further improved when compared with that of conventional S-transform (ST). Based on this Q estimation method, we apply relevant processing methods (e.g. inverse Q filtering and dynamic Q migration) in practice, in order to improve imaging resolution and gathering quality with better amplitude and phase relationships. Applications on a carbonate reservoir witness remarkable enhancements of the imaging result, in which features of faults and deep strata are more clearly revealed. Moreover, pre-stack common-reflection-point (CRP) gathers obtained by dynamic Q migration well compensate the amplitude loss and correct the phase. Its ultimate pre-stack elastic inversion result better characterizes the geologic rules of complex carbonate reservoir predominated by secondary-storage-space.
Discreteness inducing coexistence
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira
2013-12-01
Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.
Huang, Z. )
1992-12-01
We examine an interesting scenario to solve the domain-wall problem recently suggested by Preskill, Trivedi, Wilczek, and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as {ital CP} and {ital Z}{sub 2} can be anomalous due to a so-called {ital K} term induced by instantons. We point out that the {ital Z}{sub 2} domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the {ital CP}-conserving one and the {ital CP}-breaking one. In the first case, there exist two {ital Z}{sub 2}-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of {ital CP} violation are discussed and shown to be well within the experimental limits in weak interactions.
Khan, M M; Varma, M P; Cleland, J; O'Kane, H O; Webb, S W; Mulholland, H C; Adgey, A A
1981-01-01
Data concerning 17 consecutive patients with discrete subaortic stenosis are recorded. Twelve patients underwent operative resection of the obstructing lesion. Of these all except one were symptomatic and all had electrocardiographic evidence of left ventricular hypertrophy or left ventricular hypertrophy with strain. They had a peak resting systolic left ventricular outflow tract gradient of greater than 50 mmHg as predicted from the combined cuff measurement of systolic blood pressure and the echocardiographically estimated left ventricular systolic pressure and/or as determined by cardiac catheterisation. The outflow tract gradient as predicted from M-mode echocardiography and peak systolic pressure showed close correlation with that measured at cardiac catheterisation or operation. During the postoperative follow-up from one month to 11 years, of 11 patients, one patient required a further operation for recurrence of the obstruction four years after the initial operation. All patients are now asymptomatic. Five patients have not had an operation. The left ventricular outflow tract gradient as assessed at the time of cardiac catheterisation was greater than 50 mmHg. One patient has been lost to follow-up. The remaining four have been followed from four to eight years and have remained asymptomatic and the electrocardiograms have remained unchanged. Careful follow-up of all patients is essential with continuing clinical assessment, electrocardiograms, M-mode and two-dimensional echocardiograms, and if necessary cardiac catheterisation. Prophylaxis against bacterial endocarditis is also essential. Images PMID:6457617
Haydock’s recursive solution of self-adjoint problems. Discrete spectrum
Moroz, Alexander
2014-12-15
Haydock’s recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber’s quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock’s recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials (p{sub n}(E)) in energy variable E. The polynomials (p{sub n}(E)) are orthonormal with respect to the density of states n{sub 0}(E) and energy eigenstate |E〉 is the generating function of (p{sub n}(E)). The generality of Haydock’s recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
The discrete variational derivative method based on discrete differential forms
NASA Astrophysics Data System (ADS)
Yaguchi, Takaharu; Matsuo, Takayasu; Sugihara, Masaaki
2012-05-01
As is well known, for PDEs that enjoy a conservation or dissipation property, numerical schemes that inherit this property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice. Lately, Furihata and Matsuo have developed the so-called “discrete variational derivative method” that automatically constructs energy preserving or dissipative finite difference schemes. Although this method was originally developed on uniform meshes, the use of non-uniform meshes is of importance for multi-dimensional problems. On the other hand, the theories of discrete differential forms have received much attention recently. These theories provide a discrete analogue of the vector calculus on general meshes. In this paper, we show that the discrete variational derivative method and the discrete differential forms by Bochev and Hyman can be combined. Applications to the Cahn-Hilliard equation and the Klein-Gordon equation on triangular meshes are provided as demonstrations. We also show that the schemes for these equations are H1-stable under some assumptions. In particular, one for the nonlinear Klein-Gordon equation is obtained by combination of the energy conservation property and the discrete Poincaré inequality, which are the temporal and spacial structures that are preserved by the above methods.
Exact discretization by Fourier transforms
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-08-01
A discretization of differential and integral operators of integer and non-integer orders is suggested. New type of differences, which are represented by infinite series, is proposed. A characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Therefore the suggested differences are considered as an exact discretization of derivatives. These differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. The suggested differences operators allows us to have difference equations whose solutions are equal to the solutions of corresponding differential equations. The exact discretization of the derivatives of integer orders is given by the suggested differences of the same integer orders. Similarly, the exact discretization of the Riesz derivatives and integrals of integer and non-integer order is given by the proposed fractional differences of the same order.
Novel approach to data discretization
NASA Astrophysics Data System (ADS)
Borowik, Grzegorz; Kowalski, Karol; Jankowski, Cezary
2015-09-01
Discretization is an important preprocessing step in data mining. The data discretization method involves determining the ranges of values for numeric attributes, which ultimately represent discrete intervals for new attributes. The ranges for the proposed set of cuts are analyzed, in order to obtain a minimal set of ranges while retaining the possibility of classification. For this purpose, a special discernibility function can be constructed as a conjunction of alternative cuts set for each pair of different objects of different decisions- cuts discern these objects. However, the data mining methods based on discernibility matrix are insufficient for large databases. The purpose of this paper is the idea of implementation of a new data discretization algorithm that is based on statistics of attribute values and that avoids building the discernibility matrix explicitly. Evaluation of time complexity has shown that the proposed method is much more efficient than currently available solutions for large data sets.
Chaos in Periodic Discrete Systems
NASA Astrophysics Data System (ADS)
Shi, Yuming; Zhang, Lijuan; Yu, Panpan; Huang, Qiuling
This paper focuses on chaos in periodic discrete systems, whose state space may vary with time. Some close relationships between some chaotic dynamical behaviors of a periodic discrete system and its autonomous induced system are given. Based on these relationships, several criteria of chaos are established and some sufficient conditions for no chaos are given for periodic discrete systems. Further, it is shown that a finite-dimensional linear periodic discrete system is not chaotic in the sense of Li-Yorke or Wiggins. In particular, an interesting problem of whether nonchaotic rules may generate a chaotic system is studied, with some examples provided, one of which surprisingly shows that a composition of globally asymptotically stable maps can be chaotic. In addition, some properties of sign pattern matrices of non-negative square matrices are given for convenience of the study.
Microscopic derivation of discrete hydrodynamics.
Español, Pep; Anero, Jesús G; Zúñiga, Ignacio
2009-12-28
By using the standard theory of coarse graining based on Zwanzig's projection operator, we derive the dynamic equations for discrete hydrodynamic variables. These hydrodynamic variables are defined in terms of the Delaunay triangulation. The resulting microscopically derived equations can be understood, a posteriori, as a discretization on an arbitrary irregular grid of the Navier-Stokes equations. The microscopic derivation provides a set of discrete equations that exactly conserves mass, momentum, and energy and the dissipative part of the dynamics produces strict entropy increase. In addition, the microscopic derivation provides a practical implementation of thermal fluctuations in a way that the fluctuation-dissipation theorem is satisfied exactly. This paper points toward a close connection between coarse-graining procedures from microscopic dynamics and discretization schemes for partial differential equations. PMID:20059064
Nie, Xinhua; Pan, Zhongming; Zhang, Dasha; Zhou, Han; Chen, Min; Zhang, Wenna
2014-01-01
Magnetic anomaly detection (MAD) is a passive approach for detection of a ferromagnetic target, and its performance is often limited by external noises. In consideration of one major noise source is the fractal noise (or called 1/f noise) with a power spectral density of 1/fa (0orthonormal wavelet decomposition can play the role of a Karhunen-Loève-type expansion to the 1/f-type signal by its decorrelation abilities, an effective energy detection method based on undecimated discrete wavelet transform (UDWT) is proposed in this paper. Firstly, the foundations of magnetic anomaly detection and UDWT are introduced in brief, while a possible detection system based on giant magneto-impedance (GMI) magnetic sensor is also given out. Then our proposed energy detection based on UDWT is described in detail, and the probabilities of false alarm and detection for given the detection threshold in theory are presented. It is noticeable that no a priori assumptions regarding the ferromagnetic target or the magnetic noise probability are necessary for our method, and different from the discrete wavelet transform (DWT), the UDWT is shift invariant. Finally, some simulations are performed and the results show that the detection performance of our proposed detector is better than that of the conventional energy detector even utilized in the Gaussian white noise, especially when the spectral parameter α is less than 1.0. In addition, a real-world experiment was done to demonstrate the advantages of the proposed method. PMID:25343484
NASA Astrophysics Data System (ADS)
Jones, J. P.; Carniel, R.; Malone, S.
2005-12-01
The time-varying properties of volcanic tremor demand advanced techniques capable of analyzing changes in both time and frequency domains. Specifically, rapid data preprocessing techniques with the ability to distinguish signal from noise are especially valuable in analyzing the temporal, spatial, and spectral properties of these signals. To this end, we use the Discrete Wavelet Packet Transform and the Best Shift Basis algorithm to select an orthonormal basis for continuous volcanic tremor data, then apply a simple statistical test to eliminate frequency bands that primarily consist of Gaussian white noise. We then use the Maximal Overlap Discrete Wavelet Packet Transform to compute and analyze features in the detail coefficients of each "signal" band. Because MODWPT detail coefficients are equivalent to a time series convolved with a zero phase filter, we apply standard polarization and amplitude-based location techniques to each frequency band's detail coefficients to analyze possible source locations and mechanisms. To demonstrate the usefulness of these techniques, we present a sample analysis of data from Erta 'Ale volcano, Ethiopia, recorded on a temporary network in November 2003. Data were sampled at 100 Hz and the DWPT was computed with the LA(16) wavelet to a maximum level of j = 7. The optimal basis for this data set consists of 54 frequency bands, but only 9 contain meaningful "signal" energy. We identify two frequency bands whose locations suggest a distributed source; three frequency bands whose signals may come from the lava lake itself; three high-frequency bands of scattered energy; and one very high frequency band of non-Gaussian instrument noise. Finally, we discuss optimization efforts, computational efficiency, and the feasibility of using similar wavelet methods to preprocess data in real time or near real time.
Analysis and design of modified window shapes for S-transform to improve time-frequency localization
NASA Astrophysics Data System (ADS)
Ma, Jianping; Jiang, Jin
2015-06-01
This paper deals with window design issues for modified S-transform (MST) to improve the performance of time-frequency analysis (TFA). After analyzing the drawbacks of existing window functions, a window design technique is proposed. The technique uses a sigmoid function to control the window width in frequency domain. By proper selection of certain tuning parameters of a sigmoid function, windows with different width profiles can be obtained for multi-component signals. It is also interesting to note that the MST algorithm can be considered as a special case of a generalized method that adds a tunable shaping function to the standard window in frequency domain to meet specific frequency localization needs. The proposed design technique has been validated on a physical vibration test system using signals with different characteristics. The results have demonstrated that the proposed MST algorithm has superior time-frequency localization capabilities over standard ST, as well as other classical TFA methods. Subsequently, the proposed MST algorithm is applied to vibration monitoring of pipes in a water supply process controlled by a diaphragm pump for fault detection purposes.
Distributed Relaxation for Conservative Discretizations
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.
2001-01-01
A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.
ERIC Educational Resources Information Center
Langley-Weber, Terri
2012-01-01
This qualitative study examined the influences of teachers' experiences on their perceptions of teaching English language learners (ELLs) framed within Mezirow's transformative learning theory. Eight teachers ranging from pre-Kindergarten to 12th grade participated in long interviews responding to a 10 item questionnaire. Each teacher…
Cheraghi-Sohi, Sudeh; Calnan, Michael
2013-11-01
There has much debate about the extent to which professional discretion has been challenged by recent organisational changes such as through the new forms of governance associated with the introduction of the principles of the New Public Management (NPM) into health systems and other public sector services. What appears to be missing from these debates is a detailed analysis of the concept of professional discretion itself. This paper attempts to fill this gap by delineating the key concepts of professional discretion evident in the literature and exploring their significance in an empirical study of the influence of the 2004 new general medical services contract (nGMS) and the introduction of the Quality and Outcomes Framework (QOF), a prescriptive pay-for-performance system designed to standardise the quality of care provision in general medical practice in the United Kingdom. The study adopted a longitudinal design using semi-structured interviews with general practitioners (GPs, N = 62) working in the English National Health Service (NHS) between 2007 and 2009. A multi-dimensional conception of discretion was used to explore how GP discretion might have been influenced by contractual changes and in particular, QOF. The findings suggest that through a complex interplay of factors, a post-QOF reduction in GP discretion was identifiable, highlighting different potential sources of constraint such as in the social, organisational and economic dimensions of discretion. The evidence also suggested the emergence of a new form of organisational medical professionalism within general practice characterised by standardisation, bureaucracy and performance management. PMID:24034951
Geometry of discrete quantum computing
NASA Astrophysics Data System (ADS)
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Reduced discretization error in HZETRN
Slaba, Tony C.; Blattnig, Steve R.; Tweed, John
2013-02-01
The deterministic particle transport code HZETRN is an efficient analysis tool for studying the effects of space radiation on humans, electronics, and shielding materials. In a previous work, numerical methods in the code were reviewed, and new methods were developed that further improved efficiency and reduced overall discretization error. It was also shown that the remaining discretization error could be attributed to low energy light ions (A < 4) with residual ranges smaller than the physical step-size taken by the code. Accurately resolving the spectrum of low energy light particles is important in assessing risk associated with astronaut radiation exposure. In this work, modifications to the light particle transport formalism are presented that accurately resolve the spectrum of low energy light ion target fragments. The modified formalism is shown to significantly reduce overall discretization error and allows a physical approximation to be removed. For typical step-sizes and energy grids used in HZETRN, discretization errors for the revised light particle transport algorithms are shown to be less than 4% for aluminum and water shielding thicknesses as large as 100 g/cm{sup 2} exposed to both solar particle event and galactic cosmic ray environments.
Some discrete multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Arvesú, J.; Coussement, J.; van Assche, W.
2003-04-01
In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
NASA Astrophysics Data System (ADS)
Varner, R. K.; Graham, K.; Bryce, J. G.; Finkel, L.; Froburg, E.; Hale, S.; Johnson, J. E.; von Damm, K.
2009-12-01
The University of New Hampshire’s Transforming Earth System Science Education (TESSE) project is designed to enrich the education and professional development of in-service and pre-service teachers who currently teach or plan to teach Earth science curricula. A key TESSE program goal is to foster the development of middle and high school students’ Earth System Science (ESS) literacy by engaging teachers in authentic research experiences. As part of TESSE, pre-service teachers are engaged in a research immersion experience (RIE), during which they work alongside a faculty research mentor for an intensive eight week period. The chief goal of this component of the program is to provide these pre-service teachers with authentic research experiences that will sharpen their research skills by providing guidance in designing projects and in gathering and interpreting data. The RIE also includes weekly discussions on pedagogical approaches to research with students, providing a catalyst for taking these research experiences into the classroom. For in-service teachers we have developed a course: “Research Techniques in the Earth System Sciences for Teachers.” Teachers enroll in an intensive ten-day research experience during which they participate in a research cruise on the Great Bay Estuary and collect gas and water samples, measure parameters in the water column, and collect sediment cores in order to answer questions they have posed about the estuary environment. Onshore, teacher teams analyze the water and core samples for gas and trace metal content, grain size, and other sedimentological characteristics. The research experience culminates with a public poster presentation of each team's results. Throughout the experience, teachers are engaged in a variety of discussions about transferring what they have learned about doing research to their classrooms. The integration of authentic research is a key mechanism that the TESSE program uses to help teachers
Discrete implementations of scale transform
NASA Astrophysics Data System (ADS)
Djurdjanovic, Dragan; Williams, William J.; Koh, Christopher K.
1999-11-01
Scale as a physical quantity is a recently developed concept. The scale transform can be viewed as a special case of the more general Mellin transform and its mathematical properties are very applicable in the analysis and interpretation of the signals subject to scale changes. A number of single-dimensional applications of scale concept have been made in speech analysis, processing of biological signals, machine vibration analysis and other areas. Recently, the scale transform was also applied in multi-dimensional signal processing and used for image filtering and denoising. Discrete implementation of the scale transform can be carried out using logarithmic sampling and the well-known fast Fourier transform. Nevertheless, in the case of the uniformly sampled signals, this implementation involves resampling. An algorithm not involving resampling of the uniformly sampled signals has been derived too. In this paper, a modification of the later algorithm for discrete implementation of the direct scale transform is presented. In addition, similar concept was used to improve a recently introduced discrete implementation of the inverse scale transform. Estimation of the absolute discretization errors showed that the modified algorithms have a desirable property of yielding a smaller region of possible error magnitudes. Experimental results are obtained using artificial signals as well as signals evoked from the temporomandibular joint. In addition, discrete implementations for the separable two-dimensional direct and inverse scale transforms are derived. Experiments with image restoration and scaling through two-dimensional scale domain using the novel implementation of the separable two-dimensional scale transform pair are presented.
NASA Astrophysics Data System (ADS)
Guo, Jiming; Zhou, Mingduan; Wang, Chao; Mei, Lianhui
2012-11-01
Based on the model of coordinate S-transformation, a novel method of stability analysis of datum points in high-precision GPS deformation monitoring networks is proposed. The model of coordinate S-transformation is used to calculate seven transformation parameters in adjacent two measurement stages, in order to confirm the stability of stations by coordinate differences. To judge the stability of stations, in comparison to the traditional method by a fixed the same datum point, the "threshold approach" and "statistical test approach" have been developed and applied to evaluate the stability of datum points of a first-order GPS deformation monitoring network of a hydropower station located in the West Region of China.
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Class of discrete Gabor expansion
NASA Astrophysics Data System (ADS)
Li, Shidong; Healy, Dennis M., Jr.
1994-03-01
We present a new approach to studying a discrete Gabor expansion (DGE). We show that, in general, DGE is not the usual biorthogonal decomposition, but belongs to a larger and looser decomposition scheme which we call pseudo frame decomposition. It includes the DGE scheme proposed as a special case. The standard dual frame decomposition is also a special case. We derive algorithms using techniques for Gabor sequences to compute 'biorthogonal' sequences through proper matrix representation. Our algorithms involve solutions to a linear system to obtain the 'biorthogonal' windows. This approach provides a much broader mathematical view of the DGE, and therefore, establishes a wider mathematical foundation towards the theory of DGE. The general algorithm derived also provides a whole class of discrete Gabor expansions, among which 'good' ones can be generated. Simulation results are also provided.
Systoles in discrete dynamical systems
NASA Astrophysics Data System (ADS)
Fernandes, Sara; Grácio, Clara; Ramos, Carlos Correia
2013-01-01
The fruitful relationship between Geometry and Graph Theory has been explored by several authors benefiting also the Theory of discrete dynamical systems seen as Markov chains in graphs. In this work we will further explore the relation between these areas, giving a geometrical interpretation of notions from dynamical systems. In particular, we relate the topological entropy with the systole, here defined in the context of discrete dynamical systems. We show that for continuous interval maps the systole is trivial; however, for the class of interval maps with one discontinuity point the systole acquires relevance from the point of view of the dynamical behavior. Moreover, we define the geodesic length spectrum associated to a Markov interval map and we compute the referred spectrum in several examples.
Dark Energy from Discrete Spacetime
Trout, Aaron D.
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
A FORTRAN Program for Discrete Discriminant Analysis
ERIC Educational Resources Information Center
Boone, James O.; Brewer, James K.
1976-01-01
A Fortran program is presented for discriminant analysis of discrete variables. The program assumes discrete, nominal data with no distributional, variance-covariance assumptions. The program handles a maximum of fifty predictor variables and twelve outcome groups. (Author/JKS)
Efficient genetic algorithms using discretization scheduling.
McLay, Laura A; Goldberg, David E
2005-01-01
In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling. PMID:16156928
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
Discrete vortex representation of magnetohydrodynamics
Kinney, R.; Tajima, T.; Petviashvili, N.; McWilliams, J.C.
1993-02-01
We present an alternative approach to statistical analysis of an intermittent ideal MHD fluid in two dimensions, based on the hydrodynamical discrete vortex model applied to the Elsasser variables. The model contains negative temperature states which predict the formation of magnetic islands, but also includes a natural limit under which the equilibrium states revert to the familiar twin-vortex states predicted by hydrodynamical turbulence theories. Numerical dynamical calculations yield equilibrium spectra in agreement with the theoretical predictions.
Discrete-contact nanowire photovoltaics
NASA Astrophysics Data System (ADS)
Chitambar, Michelle J.; Wen, Wen; Maldonado, Stephen
2013-11-01
A series of finite-element simulations have been performed to assess the operational characteristics of a new semiconductor nanowire solar cell design operating under high-level injection conditions. Specifically, the steady-state current-voltage behavior of a cylindrical silicon (Si) nanowire with a series of discrete, ohmic-selective contacts under intense sunlight illumination was investigated. The scope of the analysis was limited to only the factors that impact the net internal quantum yield for solar to electricity conversion. No evaluations were performed with regards to optical light trapping in the modeled structures. Several aspects in a discrete-contact nanowire device that could impact operation were explored, including the size and density of ohmic-selective contacts, the size of the nanowire, the electronic quality and conductivity of the nanowire, the surface defect density of the nanowire, and the type of ohmic selectivity employed at each contact. The analysis showed that there were ranges of values for each parameter that supported good to excellent photoresponses, with certain combinations of experimentally attainable material properties yielding internal energy conversion efficiencies at the thermodynamic limit for a single junction cell. The merits of the discrete-contact nanowire cell were contrasted with "conventional" nanowire photovoltaic cells featuring a uniform conformal contact and also with planar point-contact solar cells. The unique capacity of the discrete-contact nanowire solar cell design to operate at useful energy conversion efficiencies with low quality semiconductor nanowires (i.e., possessing short charge-carrier lifetimes) with only light doping is discussed. This work thus defines the impetus for future experimental work aimed at developing this photovoltaic architecture.
Interference in discrete Wigner functions
Cormick, Cecilia; Paz, Juan Pablo
2006-12-15
We analyze some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to represent quantum states of systems with power-of-prime dimensional Hilbert spaces. We consider ''cat'' states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase space (including the regions where the two interfering states are localized). This is a generic property, which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this by analyzing the phase-space representation of the five-qubit error-correcting code.
Observability of discretized partial differential equations
NASA Technical Reports Server (NTRS)
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
Driven discrete time quantum walks
NASA Astrophysics Data System (ADS)
Hamilton, Craig S.; Barkhofen, Sonja; Sansoni, Linda; Jex, Igor; Silberhorn, Christine
2016-07-01
We introduce the driven discrete time quantum walk (QW), where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original QW. These dynamics have two regimes, which we illustrate using the one-dimensional line. Then, we explore a search application which has certain advantages over current search protocols, namely that it does not require a complicated initial state nor a specific measurement time to observe the marked state. Finally, we describe a potential experimental implementation using existing technology.
Discreteness effects in population dynamics
NASA Astrophysics Data System (ADS)
Guevara Hidalgo, Esteban; Lecomte, Vivien
2016-05-01
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of additive observables for stochastic processes. A method commonly used in order to determine such functions is the so-called cloning algorithm which in its non-constant population version essentially reduces to the determination of the growth rate of a population, averaged over many realizations of the dynamics. However, the averaging of populations is highly dependent not only on the number of realizations of the population dynamics, and on the initial population size but also on the cut-off time (or population) considered to stop their numerical evolution. This may result in an over-influence of discreteness effects at initial times, caused by small population size. We overcome these effects by introducing a (realization-dependent) time delay in the evolution of populations, additional to the discarding of the initial transient regime of the population growth where these discreteness effects are strong. We show that the improvement in the estimation of the large deviation function comes precisely from these two main contributions.
Observers for discrete-time nonlinear systems
NASA Astrophysics Data System (ADS)
Grossman, Walter D.
Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.
Multigrid methods for isogeometric discretization.
Gahalaut, K P S; Kraus, J K; Tomar, S K
2013-01-01
We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels [Formula: see text], whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order [Formula: see text], and for [Formula: see text] and [Formula: see text] smoothness. PMID:24511168
Discrete modelling of drapery systems
NASA Astrophysics Data System (ADS)
Thoeni, Klaus; Giacomini, Anna
2016-04-01
Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R
Multigrid methods for isogeometric discretization
Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.
2013-01-01
We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168
Classicality in discrete Wigner functions
Cormick, Cecilia; Galvao, Ernesto F.; Gottesman, Daniel; Paz, Juan Pablo; Pittenger, Arthur O.
2006-01-15
Gibbons et al., [Phys. Rev. A 70, 062101 (2004)] have recently defined discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that such a class of Wigner functions W can be defined so that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by Galvao, [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W in the class form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.
Determinant Expressions for Discrete Integrable Maps
NASA Astrophysics Data System (ADS)
Sogo, Kiyoshi
2006-08-01
Explicit formulas for several discrete integrable maps with periodic boundary condition are obtained, which give the sequential time developments in a form of the quotient of successive determinants of tri-diagonal matrices. We can expect that such formulas make the corresponding numerical simulations simple and stable. The cases of discrete Lotka-Volterra and discrete KdV equations are demonstrated by using the common algorithm computing determinants of tri-diagonal matrices.
A discrete event method for wave simulation
Nutaro, James J
2006-01-01
This article describes a discrete event interpretation of the finite difference time domain (FDTD) and digital wave guide network (DWN) wave simulation schemes. The discrete event method is formalized using the discrete event system specification (DEVS). The scheme is shown to have errors that are proportional to the resolution of the spatial grid. A numerical example demonstrates the relative efficiency of the scheme with respect to FDTD and DWN schemes. The potential for the discrete event scheme to reduce numerical dispersion and attenuation errors is discussed.
Scalar discrete nonlinear multipoint boundary value problems
NASA Astrophysics Data System (ADS)
Rodriguez, Jesus; Taylor, Padraic
2007-06-01
In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].
Peña, J; Solano, E; Mendoza, A; Casals, J; Planell, J A; Gil, F J
2005-01-01
The main objective of this work has been the characterisation and correlation of the wear behaviour of the NiTi shape memory alloys in their different phases. The weight losses for the different alloys in function of the present phase, and of the M(s) transformation temperature are studied. Adhesive wear tests, Pin-on-Disk, according to the ASTM-G99 standard have been carried out. The thermoelastic martensitic transformations that cause the super-elastic effect, the reorientation and coalescence of martensitic plates and the damping effect promotes a high ability to accommodate large deformations without generating permanent damages that causes the wear. The resulting plastic deformation may be accumulated during wear process without generating fracture. The results show that the wear resistance is mainly dependent of the M(s) transformation temperature for both alloys. For the NiTi alloys also the Ni atomic percentage and the hardness of the alloys are important parameters in the wear behavior. PMID:16010037
Discretization vs. Rounding Error in Euler's Method
ERIC Educational Resources Information Center
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Discrete/PWM Ballast-Resistor Controller
NASA Technical Reports Server (NTRS)
King, Roger J.
1994-01-01
Circuit offers low switching loss and automatic compensation for failure of ballast resistor. Discrete/PWM ballast-resistor controller improved shunt voltage-regulator circuit designed to supply power from high-resistance source to low-impedance bus. Provides both coarse discrete voltage levels (by switching of ballast resistors) and continuous fine control of voltage via pulse-width modulation.
Discreteness and Gradience in Intonational Contrasts.
ERIC Educational Resources Information Center
Gussenhoven, Carlos
1999-01-01
Three experimental techniques that can be used to investigate the gradient of discrete nature of intonational differences, the semantic task, the imitation task, and the pitch range task are discussed and evaluated. It is pointed out that categorical perception is a sufficient but not a necessary, property of phonological discreteness. (Author/VWL)
Current Density and Continuity in Discretized Models
ERIC Educational Resources Information Center
Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…
Discrete Fractional Diffusion Equation of Chaotic Order
NASA Astrophysics Data System (ADS)
Wu, Guo-Cheng; Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da
Discrete fractional calculus is suggested in diffusion modeling in porous media. A variable-order fractional diffusion equation is proposed on discrete time scales. A function of the variable order is constructed by a chaotic map. The model shows some new random behaviors in comparison with other variable-order cases.
Discrete elements method of neutral particle transport
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method.
Active control of turbomachine discrete tones
NASA Astrophysics Data System (ADS)
Fleeter, Sanford
This paper was directed at active control of discrete frequency noise generated by subsonic blade rows through cancellation of the blade row interaction generated propagating acoustic waves. First discrete frequency noise generated by a rotor and stator in a duct was analyzed to determine the propagating acoustic pressure waves. Then a mathematical model was developed to analyze and predict the active control of discrete frequency noise generated by subsonic blade rows through cancellation of the propagating acoustic waves, accomplished by utilizing oscillating airfoil surfaces to generate additional control propagating pressure waves. These control waves interact with the propagating acoustic waves, thereby, in principle, canceling the acoustic waves and thus, the far field discrete frequency tones. This model was then applied to a fan exit guide vane to investigate active airfoil surface techniques for control of the propagating acoustic waves, and thus the far field discrete frequency tones, generated by blade row interactions.
Discrete breathers in graphane: Effect of temperature
NASA Astrophysics Data System (ADS)
Baimova, J. A.; Murzaev, R. T.; Lobzenko, I. P.; Dmitriev, S. V.; Zhou, Kun
2016-05-01
The discrete breathers in graphane in thermodynamic equilibrium in the temperature range 50-600 K are studied by molecular dynamics simulation. A discrete breather is a hydrogen atom vibrating along the normal to a sheet of graphane at a high amplitude. As was found earlier, the lifetime of a discrete breather at zero temperature corresponds to several tens of thousands of vibrations. The effect of temperature on the decay time of discrete breathers and the probability of their detachment from a sheet of graphane are studied in this work. It is shown that closely spaced breathers can exchange energy with each other at zero temperature. The data obtained suggest that thermally activated discrete breathers can be involved in the dehydrogenation of graphane, which is important for hydrogen energetics.
MULTISCALE DISCRETIZATION OF SHAPE CONTOURS
Prasad, L.; Rao, R.
2000-09-01
We present an efficient multi-scale scheme to adaptively approximate the continuous (or densely sampled) contour of a planar shape at varying resolutions. The notion of shape is intimately related to the notion of contour, and the efficient representation of the contour of a shape is vital to a computational understanding of the shape. Any polygonal approximation of a planar smooth curve is equivalent to a piecewise constant approximation of the parameterized X and Y coordinate functions of a discrete point set obtained by densely sampling the curve. Using the Haar wavelet transform for the piecewise approximation yields a hierarchical scheme in which the size of the approximating point set is traded off against the morphological accuracy of the approximation. Our algorithm compresses the representation of the initial shape contour to a sparse sequence of points in the plane defining the vertices of the shape's polygonal approximation. Furthermore, it is possible to control the overall resolution of the approximation by a single, scale-independent parameter.
Seipin Is a Discrete Homooligomer†
Binns, Derk; Lee, SungKyung; Hilton, Christopher L.; Jiang, Qiu-Xing; Goodman, Joel M.
2011-01-01
Seipin is a transmembrane protein that resides in the endoplasmic reticulum and concentrates at junctions between the ER and cytosolic lipid droplets. Mutations in the human seipin gene, including the missense mutation A212P, lead to congenital generalized lipodystrophy (CGL), characterized by the lack of normal adipose tissue and accumulation of fat in liver and muscles. In both yeast and CGL patient fibroblasts, seipin is required for normal lipid droplet morphology; in its absence droplets appear to bud abnormally from the ER. Here we report the first purification and physical characterization of seipin. Yeast seipin is in a large discrete protein complex. Affinity purification demonstrated that seipin is the main if not exclusive protein in the complex. Detergent sucrose gradients in H2O, and D2O and gel filtration were used to determine the size of the seipin complex and account for detergent binding. Both seipin-myc13 (seipin fused to 13 tandem copies of the myc epitope) expressed from the endogenous promoter and overexpressed seipin-mCherry form ~500 kDa proteins consisting of about 9 copies of seipin. The yeast orthologue of the human A212P allele forms only smaller complexes and is unstable; we hypothesize that this accounts for its null phenotype in humans. Seipin appears as a toroid by negative staining electron microscopy. We speculate that seipin plays at least a structural role in organizing droplets or in communication between droplets and ER. PMID:21062080
Compatible Spatial Discretizations for Partial Differential Equations
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
NASA Astrophysics Data System (ADS)
Hoffmann, Tim
2000-01-01
The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schrödinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izgerin and Korepin. Moreover a doubly discrete IHM is presented that is equivalent to Ablowitz' and Ladiks doubly discrete NLSE.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Discrete flavour symmetries from the Heisenberg group
NASA Astrophysics Data System (ADS)
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
High-accuracy discrete positioning device
NASA Technical Reports Server (NTRS)
Brooks, John J. (Inventor)
1994-01-01
An article (30) is controllably and precisely positioned at one of three discrete locations defined by a linkage. The positioning apparatus includes two independently driven cranks (34, 42), with a link (50) pivotably connected between the two cranks (34, 42). Another connector (44) is pivotably connected between one of the cranks (34 or 42) and the article (30) to be positioned. The cranks (34, 42) are rotationally adjusted so that the pivot points (52, 54) of the link (50) are collinear with the axes of rotation of the cranks (40, 48), thereby defining one of the three discrete locations. Additional cranks and links can be provided to define additional discrete locations.
The discrete-time compensated Kalman filter
NASA Technical Reports Server (NTRS)
Lee, W. H.; Athans, M.
1978-01-01
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
Running Parallel Discrete Event Simulators on Sierra
Barnes, P. D.; Jefferson, D. R.
2015-12-03
In this proposal we consider porting the ROSS/Charm++ simulator and the discrete event models that run under its control so that they run on the Sierra architecture and make efficient use of the Volta GPUs.
Motion of Discrete Interfaces Through Mushy Layers
NASA Astrophysics Data System (ADS)
Braides, Andrea; Solci, Margherita
2016-04-01
We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a `bulky' part and an external `mushy region' composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.
A discrete control model of PLANT
NASA Technical Reports Server (NTRS)
Mitchell, C. M.
1985-01-01
A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.
Motion of Discrete Interfaces Through Mushy Layers
NASA Astrophysics Data System (ADS)
Braides, Andrea; Solci, Margherita
2016-08-01
We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a `bulky' part and an external `mushy region' composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.
Discrete Element Modeling of Drop Tests
NASA Astrophysics Data System (ADS)
Wang, Yuannian; Tonon, Fulvio
2012-09-01
A discrete element code with impact model has been developed and calibrated to simulate the dynamic behavior of rock materials, with special regard to rock fragmentation upon impact during rock-fall analysis. The paper summarizes the discrete element code, the calibration algorithms developed to identify the model microparameters, and the impact model. Experimental work on drop tests is then used to validate the code on modeling impact fragmentation. It has been found that the developed discrete element code and impact model can reasonably simulate rock fragmentation in drop tests. The use of the discrete element code and impact model can provide good reference results in evaluating impact fragmentation in rock-fall analysis.
Comparing the Discrete and Continuous Logistic Models
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2008-01-01
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Reducing Neuronal Networks to Discrete Dynamics
Terman, David; Ahn, Sungwoo; Wang, Xueying; Just, Winfried
2008-01-01
We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [1], we analyze the discrete model. PMID:18443649
Dynamic discretization method for solving Kepler's equation
NASA Astrophysics Data System (ADS)
Feinstein, Scott A.; McLaughlin, Craig A.
2006-09-01
Kepler’s equation needs to be solved many times for a variety of problems in Celestial Mechanics. Therefore, computing the solution to Kepler’s equation in an efficient manner is of great importance to that community. There are some historical and many modern methods that address this problem. Of the methods known to the authors, Fukushima’s discretization technique performs the best. By taking more of a system approach and combining the use of discretization with the standard computer science technique known as dynamic programming, we were able to achieve even better performance than Fukushima. We begin by defining Kepler’s equation for the elliptical case and describe existing solution methods. We then present our dynamic discretization method and show the results of a comparative analysis. This analysis will demonstrate that, for the conditions of our tests, dynamic discretization performs the best.
Eigenforms, Discrete Processes and Quantum Processes
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.
2012-05-01
This essay is a discussion of the concept of eigenform, due to Heinz von Foerster, and its relationship with discrete physics and quantum mechanics. We interpret the square root of minus one as a simple oscillatory process - a clock, and as an eigenform. By taking a generalization of this identification of i as a clock and eigenform, we show how quantum mechanics emerges from discrete physics.
Separable two-dimensional discrete Hartley transform
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Poirson, Allen
1986-01-01
Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.
`t Hooft anomaly matching for discrete symmetries
Csaki, C.; Murayama, Hitoshi |
1998-05-01
The authors show how to extend the `t Hooft anomaly matching conditions to discrete symmetries. They check these discrete anomally matching conditions on several proposed low-energy spectra of certain strongly interacting gauge theories. The excluded examples include the proposed chirally symmetric vacuum of pure N = 1 supersymmetric yang-Mills theories, certain non-supersymmetric confining theories and some self-dual N = 1 supersymmetric theories based on exceptional groups.
Terminal Dynamics Approach to Discrete Event Systems
NASA Technical Reports Server (NTRS)
Zak, Michail; Meyers, Ronald
1995-01-01
This paper presents and discusses a mathematical formalism for simulation of discrete event dynamic (DED)-a special type of 'man-made' systems to serve specific purposes of information processing. The main objective of this work is to demonstrate that the mathematical formalism for DED can be based upon a terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.!.
Discrete wavelet analysis of power system transients
Wilkinson, W.A.; Cox, M.D.
1996-11-01
Wavelet analysis is a new method for studying power system transients. Through wavelet analysis, transients are decomposed into a series of wavelet components, each of which is a time-domain signal that covers a specific octave frequency band. This paper presents the basic ideas of discrete wavelet analysis. A variety of actual and simulated transient signals are then analyzed using the discrete wavelet transform that help demonstrate the power of wavelet analysis.
NASA Astrophysics Data System (ADS)
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Quantum walks and discrete gauge theories
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Debbasch, Fabrice
2016-05-01
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E ×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.
Discrete differential geometry: The nonplanar quadrilateral mesh
NASA Astrophysics Data System (ADS)
Twining, Carole J.; Marsland, Stephen
2012-06-01
We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.
Discrete differential geometry: the nonplanar quadrilateral mesh.
Twining, Carole J; Marsland, Stephen
2012-06-01
We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids. PMID:23005244
Liu, Yushun; Zhou, Wenjun; Li, Pengfei; Yang, Shuai; Tian, Yan
2016-01-01
Due to electromagnetic interference in power substations, the partial discharge (PD) signals detected by ultrahigh frequency (UHF) antenna sensors often contain various background noises, which may hamper high voltage apparatus fault diagnosis and localization. This paper proposes a novel de-noising method based on the generalized S-transform and module time-frequency matrix to suppress noise in UHF PD signals. The sub-matrix maximum module value method is employed to calculate the frequencies and amplitudes of periodic narrowband noise, and suppress noise through the reverse phase cancellation technique. In addition, a singular value decomposition de-noising method is employed to suppress Gaussian white noise in UHF PD signals. Effective singular values are selected by employing the fuzzy c-means clustering method to recover the PD signals. De-noising results of simulated and field detected UHF PD signals prove the feasibility of the proposed method. Compared with four conventional de-noising methods, the results show that the proposed method can suppress background noise in the UHF PD signal effectively, with higher signal-to-noise ratio and less waveform distortion. PMID:27338409
Liu, Yushun; Zhou, Wenjun; Li, Pengfei; Yang, Shuai; Tian, Yan
2016-01-01
Due to electromagnetic interference in power substations, the partial discharge (PD) signals detected by ultrahigh frequency (UHF) antenna sensors often contain various background noises, which may hamper high voltage apparatus fault diagnosis and localization. This paper proposes a novel de-noising method based on the generalized S-transform and module time-frequency matrix to suppress noise in UHF PD signals. The sub-matrix maximum module value method is employed to calculate the frequencies and amplitudes of periodic narrowband noise, and suppress noise through the reverse phase cancellation technique. In addition, a singular value decomposition de-noising method is employed to suppress Gaussian white noise in UHF PD signals. Effective singular values are selected by employing the fuzzy c-means clustering method to recover the PD signals. De-noising results of simulated and field detected UHF PD signals prove the feasibility of the proposed method. Compared with four conventional de-noising methods, the results show that the proposed method can suppress background noise in the UHF PD signal effectively, with higher signal-to-noise ratio and less waveform distortion. PMID:27338409
Seleson, Pablo; Du, Qiang; Parks, Michael L.
2016-08-16
The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest
PREFACE: 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014)
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Mavromatos, Nick E.; Mitsou, Vasiliki A.; Skliros, Dimitri P.
2015-07-01
The DISCRETE 2014: Fourth Symposium in the Physics of Discrete Symmetries took place at King's College London, Strand Campus, London WC2R 2LS, from Tuesday, December 2 2014 till Saturday, December 6 2014. This is the fourth Edition of the DISCRETE conference series, which is a biannual event, having been held previously in Valencia (Discrete'08), Rome (Discrete2010) and Lisbon (Discrete2012). The topics covered at the DISCRETE series of conferences are: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence and entangled states, Lorentz symmetry breaking (phenomenology and current bounds); neutrino mass and mixing; implications for cosmology and astroparticle physics, dark matter searches; experimental prospects at LHC, new facilities. In DISCRETE 2014 we have also introduced two new topics: cosmological aspects of non-commutative space-times as well as PT symmetric Hamiltonians (non-Hermitian but with real eigenvalues), a topic that has wide applications in particle physics and beyond. The conference was opened by the King's College London Vice Principal on Research and Innovation, Mr Chris Mottershead, followed by a welcome address by the Chair of DISCRETE 2014 (Professor Nick E. Mavromatos). After these introductory talks, the scientific programme of the DISCRETE 2014 symposium started. Following the tradition of DISCRETE series of conferences, the talks (138 in total) were divided into plenary-review talks (25), invited research talks (50) and shorter presentations (63) — selected by the conveners of each session in consultation with the organisers — from the submitted abstracts. We have been fortunate to have very high-quality, thought stimulating and interesting talks at all levels, which, together with the discussions among the participants, made the conference quite enjoyable. There were 152 registered participants for the event.
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
NASA Astrophysics Data System (ADS)
Iglesias, David; Marrero, Juan C.; de Diego, David Martín; Martínez, Eduardo
2008-06-01
This paper studies the construction of geometric integrators for nonholonomic systems. We develop a formalism for nonholonomic discrete Euler Lagrange equations in a setting that permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).
ERIC Educational Resources Information Center
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major effort now underway to…
Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.
Jason, Peter; Johansson, Magnus
2016-01-01
We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers. PMID:26871085
The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis
NASA Astrophysics Data System (ADS)
De Ridder, H.; De Schepper, H.; Sommen, F.
2010-09-01
Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discrete monogenic functions defined on the grid Zhm of m-tuples of integer multiples of a variable mesh width h. Convergence to the continuous case is investigated. As illustrative examples we explicitly construct the Cauchy-Kovalevskaya extensions of the discrete delta function and of a discretized exponential.
The ultimatum game: Discrete vs. continuous offers
NASA Astrophysics Data System (ADS)
Dishon-Berkovits, Miriam; Berkovits, Richard
2014-09-01
In many experimental setups in social-sciences, psychology and economy the subjects are requested to accept or dispense monetary compensation which is usually given in discrete units. Using computer and mathematical modeling we show that in the framework of studying the dynamics of acceptance of proposals in the ultimatum game, the long time dynamics of acceptance of offers in the game are completely different for discrete vs. continuous offers. For discrete values the dynamics follow an exponential behavior. However, for continuous offers the dynamics are described by a power-law. This is shown using an agent based computer simulation as well as by utilizing an analytical solution of a mean-field equation describing the model. These findings have implications to the design and interpretation of socio-economical experiments beyond the ultimatum game.
Numerical discretization for nonlinear diffusion filter
NASA Astrophysics Data System (ADS)
Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.
2015-05-01
Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.
Discrete photon statistics from continuous microwave measurements
NASA Astrophysics Data System (ADS)
Virally, Stéphane; Simoneau, Jean Olivier; Lupien, Christian; Reulet, Bertrand
2016-04-01
Photocount statistics are an important tool for the characterization of electromagnetic fields, especially for fields with an irrelevant phase. In the microwave domain, continuous rather than discrete measurements are the norm. Using a different approach, we recover discrete photon statistics from the cumulants of a continuous distribution of field quadrature measurements. The use of cumulants allows the separation between the signal of interest and experimental noise. Using a parametric amplifier as the first stage of the amplification chain, we extract useful data from up to the sixth cumulant of the continuous distribution of a coherent field, hence recovering up to the third moment of the discrete statistics associated with a signal with much less than one average photon.
Discrete breathers in hexagonal dusty plasma lattices
Koukouloyannis, V.; Kourakis, I.
2009-08-15
The occurrence of single-site or multisite localized vibrational modes, also called discrete breathers, in two-dimensional hexagonal dusty plasma lattices is investigated. The system is described by a Klein-Gordon hexagonal lattice characterized by a negative coupling parameter epsilon in account of its inverse dispersive behavior. A theoretical analysis is performed in order to establish the possibility of existence of single as well as three-site discrete breathers in such systems. The study is complemented by a numerical investigation based on experimentally provided potential forms. This investigation shows that a dusty plasma lattice can support single-site discrete breathers, while three-site in phase breathers could exist if specific conditions, about the intergrain interaction strength, would hold. On the other hand, out of phase and vortex three-site breathers cannot be supported since they are highly unstable.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Discrete Roughness Transition for Hypersonic Flight Vehicles
NASA Technical Reports Server (NTRS)
Berry, Scott A.; Horvath, Thomas J.
2007-01-01
The importance of discrete roughness and the correlations developed to predict the onset of boundary layer transition on hypersonic flight vehicles are discussed. The paper is organized by hypersonic vehicle applications characterized in a general sense by the boundary layer: slender with hypersonic conditions at the edge of the boundary layer, moderately blunt with supersonic, and blunt with subsonic. This paper is intended to be a review of recent discrete roughness transition work completed at NASA Langley Research Center in support of agency flight test programs. First, a review is provided of discrete roughness wind tunnel data and the resulting correlations that were developed. Then, results obtained from flight vehicles, in particular the recently flown Hyper-X and Shuttle missions, are discussed and compared to the ground-based correlations.
Tree Ensembles on the Induced Discrete Space.
Yildiz, Olcay Taner
2016-05-01
Decision trees are widely used predictive models in machine learning. Recently, K -tree is proposed, where the original discrete feature space is expanded by generating all orderings of values of k discrete attributes and these orderings are used as the new attributes in decision tree induction. Although K -tree performs significantly better than the proper one, their exponential time complexity can prohibit their use. In this brief, we propose K -forest, an extension of random forest, where a subset of features is selected randomly from the induced discrete space. Simulation results on 17 data sets show that the novel ensemble classifier has significantly lower error rate compared with the random forest based on the original feature space. PMID:26011897
An algebra of discrete event processes
NASA Technical Reports Server (NTRS)
Heymann, Michael; Meyer, George
1991-01-01
This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Discrete-time Markovian stochastic Petri nets
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco
1995-01-01
We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a 'defective discrete phase distribution'. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.
Uncertainty relation for the discrete Fourier transform.
Massar, Serge; Spindel, Philippe
2008-05-16
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation. PMID:18518426
The discrete regime of flame propagation
NASA Astrophysics Data System (ADS)
Tang, Francois-David; Goroshin, Samuel; Higgins, Andrew
The propagation of laminar dust flames in iron dust clouds was studied in a low-gravity envi-ronment on-board a parabolic flight aircraft. The elimination of buoyancy-induced convection and particle settling permitted measurements of fundamental combustion parameters such as the burning velocity and the flame quenching distance over a wide range of particle sizes and in different gaseous mixtures. The discrete regime of flame propagation was observed by substitut-ing nitrogen present in air with xenon, an inert gas with a significantly lower heat conductivity. Flame propagation in the discrete regime is controlled by the heat transfer between neighbor-ing particles, rather than by the particle burning rate used by traditional continuum models of heterogeneous flames. The propagation mechanism of discrete flames depends on the spa-tial distribution of particles, and thus such flames are strongly influenced by local fluctuations in the fuel concentration. Constant pressure laminar dust flames were observed inside 70 cm long, 5 cm diameter Pyrex tubes. Equally-spaced plate assemblies forming rectangular chan-nels were placed inside each tube to determine the quenching distance defined as the minimum channel width through which a flame can successfully propagate. High-speed video cameras were used to measure the flame speed and a fiber optic spectrometer was used to measure the flame temperature. Experimental results were compared with predictions obtained from a numerical model of a three-dimensional flame developed to capture both the discrete nature and the random distribution of particles in the flame. Though good qualitative agreement was obtained between model predictions and experimental observations, residual g-jitters and the short reduced-gravity periods prevented further investigations of propagation limits in the dis-crete regime. The full exploration of the discrete flame phenomenon would require high-quality, long duration reduced gravity environment
Model reduction for discrete bilinear systems
NASA Technical Reports Server (NTRS)
King, A. M.; Skelton, R. E.
1987-01-01
A model reduction method for discrete bilinear systems is developed which matches q sets of Volterra and covariance parameters. These parameters are shown to represent both deterministic and stochastic attributes of the discrete bilinear system. A reduced order model which matches these q sets of parameters is defined to be a q-Volterra covariance equivalent realization (q-Volterra COVER). An algorithm is presented which constructs a class of q-Volterra COVERs parameterized by solutions to a Hermitian, quadratic, matrix equation. The algorithm is applied to a bilinear model of a robot manipulator.
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
Discrete Gabor Filters For Binocular Disparity Measurement
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1995-01-01
Discrete Gabor filters proposed for use in determining binocular disparity - difference between positions of same feature or object depicted in stereoscopic images produced by two side-by-side cameras aimed in parallel. Magnitude of binocular disparity used to estimate distance from cameras to feature or object. In one potential application, cameras charge-coupled-device video cameras in robotic vision system, and binocular disparities and distance estimates used as control inputs - for example, to control approaches to objects manipulated or to maintain safe distances from obstacles. Binocular disparities determined from phases of discretized Gabor transforms.
Hybrid Discrete-Continuous Markov Decision Processes
NASA Technical Reports Server (NTRS)
Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich
2003-01-01
This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.
Electrolytic plating apparatus for discrete microsized particles
Mayer, Anton
1976-11-30
Method and apparatus are disclosed for electrolytically producing very uniform coatings of a desired material on discrete microsized particles. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with a powered cathode for a time sufficient for such to occur.
Electroless plating apparatus for discrete microsized particles
Mayer, Anton
1978-01-01
Method and apparatus are disclosed for producing very uniform coatings of a desired material on discrete microsized particles by electroless techniques. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with each other for a time sufficient for such to occur.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Kinematics of foldable discrete space cranes
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.
1985-01-01
Exact kinematic description of a NASA proposed prototype foldable-deployable discrete space crane are presented. A computer program is developed which maps the geometry of the crane once controlling parameters are specified. The program uses a building block type approach in which it calculates the local coordinates of each repeating cell and then combines them with respect to a global coordinates system.
Neutrino mass and mixing with discrete symmetry
NASA Astrophysics Data System (ADS)
King, Stephen F.; Luhn, Christoph
2013-05-01
This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Δ(96).
Discrete Gust Model for Launch Vehicle Assessments
NASA Technical Reports Server (NTRS)
Leahy, Frank B.
2008-01-01
Analysis of spacecraft vehicle responses to atmospheric wind gusts during flight is important in the establishment of vehicle design structural requirements and operational capability. Typically, wind gust models can be either a spectral type determined by a random process having a wide range of wavelengths, or a discrete type having a single gust of predetermined magnitude and shape. Classical discrete models used by NASA during the Apollo and Space Shuttle Programs included a 9 m/sec quasi-square-wave gust with variable wavelength from 60 to 300 m. A later study derived discrete gust from a military specification (MIL-SPEC) document that used a "1-cosine" shape. The MIL-SPEC document contains a curve of non-dimensional gust magnitude as a function of non-dimensional gust half-wavelength based on the Dryden spectral model, but fails to list the equation necessary to reproduce the curve. Therefore, previous studies could only estimate a value of gust magnitude from the curve, or attempt to fit a function to it. This paper presents the development of the MIL-SPEC curve, and provides the necessary information to calculate discrete gust magnitudes as a function of both gust half-wavelength and the desired probability level of exceeding a specified gust magnitude.
Fast mix table construction for material discretization
Johnson, S. R.
2013-07-01
An effective hybrid Monte Carlo-deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a 'mix table,' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mix table in O(number of voxels x log number of mixtures) time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation. (authors)
Analysis hierarchical model for discrete event systems
NASA Astrophysics Data System (ADS)
Ciortea, E. M.
2015-11-01
The This paper presents the hierarchical model based on discrete event network for robotic systems. Based on the hierarchical approach, Petri network is analysed as a network of the highest conceptual level and the lowest level of local control. For modelling and control of complex robotic systems using extended Petri nets. Such a system is structured, controlled and analysed in this paper by using Visual Object Net ++ package that is relatively simple and easy to use, and the results are shown as representations easy to interpret. The hierarchical structure of the robotic system is implemented on computers analysed using specialized programs. Implementation of hierarchical model discrete event systems, as a real-time operating system on a computer network connected via a serial bus is possible, where each computer is dedicated to local and Petri model of a subsystem global robotic system. Since Petri models are simplified to apply general computers, analysis, modelling, complex manufacturing systems control can be achieved using Petri nets. Discrete event systems is a pragmatic tool for modelling industrial systems. For system modelling using Petri nets because we have our system where discrete event. To highlight the auxiliary time Petri model using transport stream divided into hierarchical levels and sections are analysed successively. Proposed robotic system simulation using timed Petri, offers the opportunity to view the robotic time. Application of goods or robotic and transmission times obtained by measuring spot is obtained graphics showing the average time for transport activity, using the parameters sets of finished products. individually.
Dimensionality Problem in Discrete Discriminant Analysis
NASA Astrophysics Data System (ADS)
Ferreira, Ana Sousa
2011-09-01
A high dimensional problem is very often in Discrete Discriminant Analysis (DDA) due to the fact that the number of parameters estimated in DDA models is very frequently too large. Then, the main problem is sparseness, in which some of the multinomial cells may have no data in the training sets (for one or several classes). Furthermore, there aren't truly reliable methods for selecting the most discrete discriminative features and often we deal with small sample sizes with classes not well separated. This dimensional DDA problem is often known as the "curse of dimensionality". In this context, a combining models approach seems to be promising since it is known that different DDA models perform differently on different subjects. This approach currently appears in an increasing number of papers aiming to obtain more robust and stable models. Thus, in discrete problems we propose new forms of modeling the conditional probability functions based on linear combinations of reference models (e.g. the Full Multinomial Model (FMM) and the First-order Independence Model (FOIM)). Recently, since class separability is another fundamental problem in discrete supervised problems we have focused in exploring measures for analyzing class separability. We investigate the performance of the present approaches on real and simulated data.
Conjugacy classes in discrete Heisenberg groups
Budylin, R Ya
2014-08-01
We study an extension of a discrete Heisenberg group coming from the theory of loop groups and find invariants of conjugacy classes in this group. In some cases, including the case of the integer Heisenberg group, we make these invariants more explicit. Bibliography: 4 titles.
Bayesian approach to global discrete optimization
Mockus, J.; Mockus, A.; Mockus, L.
1994-12-31
We discuss advantages and disadvantages of the Bayesian approach (average case analysis). We present the portable interactive version of software for continuous global optimization. We consider practical multidimensional problems of continuous global optimization, such as optimization of VLSI yield, optimization of composite laminates, estimation of unknown parameters of bilinear time series. We extend Bayesian approach to discrete optimization. We regard the discrete optimization as a multi-stage decision problem. We assume that there exists some simple heuristic function which roughly predicts the consequences of the decisions. We suppose randomized decisions. We define the probability of the decision by the randomized decision function depending on heuristics. We fix this function with exception of some parameters. We repeat the randomized decision several times at the fixed values of those parameters and accept the best decision as the result. We optimize the parameters of the randomized decision function to make the search more efficient. Thus we reduce the discrete optimization problem to the continuous problem of global stochastic optimization. We solve this problem by the Bayesian methods of continuous global optimization. We describe the applications to some well known An problems of discrete programming, such as knapsack, traveling salesman, and scheduling.
A deterministic discrete ordinates transport proxy application
Energy Science and Technology Software Center (ESTSC)
2014-06-03
Kripke is a simple 3D deterministic discrete ordinates (Sn) particle transport code that maintains the computational load and communications pattern of a real transport code. It is intended to be a research tool to explore different data layouts, new programming paradigms and computer architectures.
Discrete Events as Units of Perceived Time
ERIC Educational Resources Information Center
Liverence, Brandon M.; Scholl, Brian J.
2012-01-01
In visual images, we perceive both space (as a continuous visual medium) and objects (that inhabit space). Similarly, in dynamic visual experience, we perceive both continuous time and discrete events. What is the relationship between these units of experience? The most intuitive answer may be similar to the spatial case: time is perceived as an…
Applied Behavior Analysis: Beyond Discrete Trial Teaching
ERIC Educational Resources Information Center
Steege, Mark W.; Mace, F. Charles; Perry, Lora; Longenecker, Harold
2007-01-01
We discuss the problem of autism-specific special education programs representing themselves as Applied Behavior Analysis (ABA) programs when the only ABA intervention employed is Discrete Trial Teaching (DTT), and often for limited portions of the school day. Although DTT has many advantages to recommend its use, it is not well suited to teach…
Teaching Discrete Mathematics with Graphing Calculators.
ERIC Educational Resources Information Center
Masat, Francis E.
Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and…
Core-Generating Discretization for Rough Set Feature Selection
NASA Astrophysics Data System (ADS)
Tian, David; Zeng, Xiao-Jun; Keane, John
Rough set feature selection (RSFS) can be used to improve classifier performance. RSFS removes redundant attributes whilst keeping important ones that preserve the classification power of the original dataset. The feature subsets selected by RSFS are called reducts. The intersection of all reducts is called core. However, RSFS handles discrete attributes only. To process datasets consisting of real attributes, they are discretized before applying RSFS. Discretization controls core of the discrete dataset. Moreover, core may critically affect the classification performance of reducts. This paper defines core-generating discretization, a type of discretization method; analyzes the properties of core-generating discretization; models core-generating discretization using constraint satisfaction; defines core-generating approximate minimum entropy (C-GAME) discretization; models C-GAME using constraint satisfaction and evaluates the performance of C-GAME as a pre-processor of RSFS using ten datasets from the UCI Machine Learning Repository.
Discrete ordinates methods in xy geometry with spatially varying angular discretization
Bal, G.; Warin, X.
1997-10-01
The efficiency of a new quadrature rule adapted to the numerical resolution of a neutron transport problem in xy geometry is presented based on the use of the discrete ordinates method for the angular variable. The purpose of introducing this quadrature rule is to couple two different angular discretizations used on two nonoverlapping subdomains, which is useful for performing local refinement. This coupling and some numerical results of source problems are presented.
Semi-Discrete Ingham-Type Inequalities
Komornik, Vilmos Loreti, Paola
2007-03-15
One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently. Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process.
Degeneracy and discreteness in cosmological model fitting
NASA Astrophysics Data System (ADS)
Teng, Huan-Yu; Huang, Yuan; Zhang, Tong-Jie
2016-03-01
We explore the problems of degeneracy and discreteness in the standard cosmological model (ΛCDM). We use the Observational Hubble Data (OHD) and the type Ia supernovae (SNe Ia) data to study this issue. In order to describe the discreteness in fitting of data, we define a factor G to test the influence from each single data point and analyze the goodness of G. Our results indicate that a higher absolute value of G shows a better capability of distinguishing models, which means the parameters are restricted into smaller confidence intervals with a larger figure of merit evaluation. Consequently, we claim that the factor G is an effective way of model differentiation when using different models to fit the observational data.
Hydraulically controlled discrete sampling from open boreholes
Harte, Philip T.
2013-01-01
Groundwater sampling from open boreholes in fractured-rock aquifers is particularly challenging because of mixing and dilution of fluid within the borehole from multiple fractures. This note presents an alternative to traditional sampling in open boreholes with packer assemblies. The alternative system called ZONFLO (zonal flow) is based on hydraulic control of borehole flow conditions. Fluid from discrete fractures zones are hydraulically isolated allowing for the collection of representative samples. In rough-faced open boreholes and formations with less competent rock, hydraulic containment may offer an attractive alternative to physical containment with packers. Preliminary test results indicate a discrete zone can be effectively hydraulically isolated from other zones within a borehole for the purpose of groundwater sampling using this new method.
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.
Multiple Autonomous Discrete Event Controllers for Constellations
NASA Technical Reports Server (NTRS)
Esposito, Timothy C.
2003-01-01
The Multiple Autonomous Discrete Event Controllers for Constellations (MADECC) project is an effort within the National Aeronautics and Space Administration Goddard Space Flight Center's (NASA/GSFC) Information Systems Division to develop autonomous positioning and attitude control for constellation satellites. It will be accomplished using traditional control theory and advanced coordination algorithms developed by the Johns Hopkins University Applied Physics Laboratory (JHU/APL). This capability will be demonstrated in the discrete event control test-bed located at JHU/APL. This project will be modeled for the Leonardo constellation mission, but is intended to be adaptable to any constellation mission. To develop a common software architecture. the controllers will only model very high-level responses. For instance, after determining that a maneuver must be made. the MADECC system will output B (Delta)V (velocity change) value. Lower level systems must then decide which thrusters to fire and for how long to achieve that (Delta)V.
Discrete dislocation dynamics simulations in a cylinder
NASA Astrophysics Data System (ADS)
Li, Maosheng; Gao, Chan; Xu, Jianing
2015-02-01
Mechanical properties of material are closely related to the motion of dislocations, and predicting the interactions and resulting collective motion of dislocations is a major task in understanding and modelling plastically deforming materials. A discrete dislocation dynamics model is used to describe the orientation substructure within the microstructure. Discrete dislocation dynamics simulations in three dimensions have been used to examine the role of dislocation multiplication and mobility on the plasticity in small samples under uniaxial compression. In this paper we describe the application of the dislocation dynamics simulations in a cylindrical geometry. The boundary conditions for the simulation were estimated from the distribution of the geometrically necessary dislocation density which was obtained from the orientation map. Numerical studies benchmark could validate the accuracy of the algorithms and the importance of handling the singularity correctly. The results of the simulation explain the formation of the experimentally observed substructure.
Numerical valuation of discrete double barrier options
NASA Astrophysics Data System (ADS)
Milev, Mariyan; Tagliani, Aldo
2010-03-01
In the present paper we explore the problem for pricing discrete barrier options utilizing the Black-Scholes model for the random movement of the asset price. We postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number of the monitoring dates. We propose a fast and accurate numerical algorithm for its valuation. Our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in Finance and literature. A desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers. The method has a simple computer implementation and it permits observing the entire life of the option.
Computational frameworks for discrete Gabor analysis
NASA Astrophysics Data System (ADS)
Strohmer, Thomas
1997-10-01
The Gabor transform yields a discrete representation of a signal in the phase space. Since the Gabor transform is non-orthogonal, efficient reconstruction of a signal from its phase space samples is not straightforward and involves the computation of the so- called dual Gabor function. We present a unifying approach to the derivation of numerical algorithms for discrete Gabor analysis, based on unitary matrix factorization. The factorization point of view is notably useful for the design of efficient numerical algorithms. This presentation is the first systematic account of its kind. In particular, it is shown that different algorithms for the computation of the dual window correspond to different factorizations of the frame operator. Simple number theoretic conditions on the time-frequency lattice parameters imply additional structural properties of the frame operator.
Discrete scale invariance in supercritical percolation
NASA Astrophysics Data System (ADS)
Schröder, Malte; Chen, Wei; Nagler, Jan
2016-01-01
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order parameter (Chen et al 2014 Phys. Rev. Lett. 112 155701). Here we report the discovery of macrotransition cascades which follow percolation. The order parameter grows in discrete macroscopic steps with positions that can be randomly distributed even in the thermodynamic limit. These transition positions are, however, correlated and follow scaling laws which arise from discrete scale invariance (DSI) and non self-averaging, both traditionally unrelated to percolation. We reveal the DSI in ensemble measurements of these non self-averaging systems by rescaling of the individual realizations before averaging.
Optimal Discretization Resolution in Algebraic Image Reconstruction
NASA Astrophysics Data System (ADS)
Sharif, Behzad; Kamalabadi, Farzad
2005-11-01
In this paper, we focus on data-limited tomographic imaging problems where the underlying linear inverse problem is ill-posed. A typical regularized reconstruction algorithm uses algebraic formulation with a predetermined discretization resolution. If the selected resolution is too low, we may loose useful details of the underlying image and if it is too high, the reconstruction will be unstable and the representation will fit irrelevant features. In this work, two approaches are introduced to address this issue. The first approach is using Mallow's CL method or generalized cross-validation. For each of the two methods, a joint estimator of regularization parameter and discretization resolution is proposed and their asymptotic optimality is investigated. The second approach is a Bayesian estimator of the model order using a complexity-penalizing prior. Numerical experiments focus on a space imaging application from a set of limited-angle tomographic observations.
Quantum RLC circuits: Charge discreteness and resonance
NASA Astrophysics Data System (ADS)
Utreras-Díaz, Constantino A.
2008-10-01
In a recent article [C.A. Utreras-Díaz, Phys. Lett. A 372 (2008) 5059], we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance inductive circuit, we obtain the Stark ladder energies in yet another way; for the circuit driven by a combination d.c. plus a.c. electromotive force (emf) we generalize earlier results by Chandía et al. [K. Chandía, J.C. Flores, E. Lazo, Phys. Lett. A 359 (2006) 693]. As a second application, we investigate the effect of electrical resistance and charge discreteness, in the resonance conditions of a series RLC quantum circuit.
Discrete shaped strain sensors for intelligent structures
NASA Technical Reports Server (NTRS)
Andersson, Mark S.; Crawley, Edward F.
1992-01-01
Design of discrete, highly distributed sensor systems for intelligent structures has been studied. Data obtained indicate that discrete strain-averaging sensors satisfy the functional requirements for distributed sensing of intelligent structures. Bartlett and Gauss-Hanning sensors, in particular, provide good wavenumber characteristics while meeting the functional requirements. They are characterized by good rolloff rates and positive Fourier transforms for all wavenumbers. For the numerical integration schemes, Simpson's rule is considered to be very simple to implement and consistently provides accurate results for five sensors or more. It is shown that a sensor system that satisfies the functional requirements can be applied to a structure that supports mode shapes with purely sinusoidal curvature.
Discrete instability in the DNA double helix.
Tabi, Conrad Bertrand; Mohamadou, Alidou; Kofané, Timoléon Crépin
2009-12-01
Modulational instability (MI) is explored in the framework of the base-rotor model of DNA dynamics. We show, in fact, that the helicoidal coupling introduced in the spin model of DNA reduces the system to a modified discrete sine-Gordon (sG) equation. The MI criterion is thus modified and displays interesting features because of the helicoidal coupling. In the simulations, we have found that a train of pulses is generated when the lattice is subjected to MI, in agreement with analytical results obtained in a modified discrete sG equation. Also, the competitive effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. In the same way, it is shown that MI can lead to energy localization which becomes high for some values of the helicoidal coupling constant. PMID:20059197
On Discrete Lotka-Volterra Type Models
NASA Astrophysics Data System (ADS)
Mukhamedov, Farrukh; Saburov, Mansoor
The Lotka-Volterra (in short LV) model is a second order nonlinear differential equation frequently used to describe the dynamics of biological systems in which two groups of species, predators and their preys interact. One of the basic results of the LV model is that under suitable conditions the LV model can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors. The discrete analogy of LV model has been considered by many researchers and has been called a quadratic LV model. In a discrete case, one of the unexpected results is that a quadratic LV model cannot exhibit a periodic cycle. In this paper we study nonlinear LV type models which include quadratic LV as a particular case. Unlike quadratic LV models, LV type models can exhibit any asymptotical behavior such as equilibrium states, periodic cycles, and attractors.
A new model for discrete character evolution.
Grafen, A; Ridley, M
1997-01-01
The paper provides an explicit justification for the principle that a uniform taxon should contribute only one datapoint in comparative analyses with discrete variables. The justification is that phylogenetic patterns in variables unincluded in the proposed test vitiate the assumption of independence, both at the level of species and at the level of branch segments. The consequence is that a uniform taxon cannot safely be counted as more than one datapoint. The arguments use a branching discrete Markov process in continuous time, with the new feature that the tested variables are only a subset of the evolving characters. This model is proposed as a useful criterion for measuring the merit of proposed tests, and illustrates the necessity for models in evaluating comparative methods. PMID:9039396
A discrete formulation of the Wigner transport equation
NASA Astrophysics Data System (ADS)
Kim, Kyoung-Youm
2007-12-01
A discrete formulation of the Wigner distribution function (WDF) and the Wigner transport equation (WTE) is proposed, where the "discreteness" of the WDF and WTE is not just a practical, mathematical feature of discretization for the possible computations, but reveals a fundamental physics regarding the maximum correlation length of potentials (an essential quantum-mechanical feature of the WTE): it is set by the positional uncertainty due to the discrete values of momentum in evaluating the discrete WDF. Our formulation also shows that the weighting function to the potential-correlation term can be derived naturally from a mathematical necessity related to the antiperiodicity of the discrete density operator. In addition, we propose a mutually independent discretization scheme for the diagonal and cross-diagonal coordinates of the density operator, which results in a numerically effective discrete WTE in that it requires much less computational resources without significant loss in accuracy.
Discrete Bimodal Probes for Thrombus Imaging
Uppal, Ritika; Ciesienski, Kate L.; Chonde, Daniel B.; Loving, Galen S.; Caravan, Peter
2012-01-01
Here we report a generalizable solid/solution phase strategy for the synthesis of discrete bimodal fibrin-targeted imaging probes. A fibrin-specific peptide was conjugated with two distinct imaging reporters at the C- and N-terminus. In vitro studies demonstrated retention of fibrin affinity and specificity. Imaging studies showed that these probes could detect fibrin over a wide range of probe concentrations by optical, magnetic resonance, and positron emission tomography imaging. PMID:22698259
Continuous limit of discrete quantum walks
NASA Astrophysics Data System (ADS)
M N, Dheeraj; Brun, Todd A.
2015-06-01
Quantum walks can be defined in two quite distinct ways: discrete-time and continuous-time quantum walks (DTQWs and CTQWs). For classical random walks, there is a natural sense in which continuous-time walks are a limit of discrete-time walks. Quantum mechanically, in the discrete-time case, an additional "coin space" must be appended for the walk to have nontrivial time evolution. Continuous-time quantum walks, however, have no such constraints. This means that there is no completely straightforward way to treat a CTQW as a limit of a DTQW, as can be done in the classical case. Various approaches to this problem have been taken in the past. We give a construction for walks on d -regular, d -colorable graphs when the coin flip operator is Hermitian: from a standard DTQW we construct a family of discrete-time walks with a well-defined continuous-time limit on a related graph. One can think of this limit as a "coined" continuous-time walk. We show that these CTQWs share some properties with coined DTQWs. In particular, we look at a spatial search by a DTQW over the two-dimensional (2D) torus (a grid with periodic boundary conditions) of size √{N }×√{N } , where it was shown that a coined DTQW can search in time O (√{N }logN ) , but a standard CTQW takes Ω (N ) time to search for a marked element. The continuous limit of the DTQW search over the 2D torus exhibits the O (√{N }logN ) scaling, like the coined walk it is derived from. We also look at the effects of graph symmetry on the limiting walk, and show that the properties are similar to those of the DTQW as shown in Krovi and Brun, Phys. Rev. A 75, 062332 (2007), 10.1103/PhysRevA.75.062332.
DOS: the discrete-ordinates system. [LMFBR
Rhoades, W. A.; Emmett, M. B.
1982-09-01
The Discrete Ordinates System determines the flux of neutrons or photons due either to fixed sources specified by the user or to sources generated by particle interaction with the problem materials. It also determines numerous secondary results which depend upon flux. Criticality searches can be performed. Numerous input, output, and file manipulation facilities are provided. The DOS driver program reads the problem specification from an input file and calls various program modules into execution as specified by the input file.
Discrete sequence prediction and its applications
NASA Technical Reports Server (NTRS)
Laird, Philip
1992-01-01
Learning from experience to predict sequences of discrete symbols is a fundamental problem in machine learning with many applications. We apply sequence prediction using a simple and practical sequence-prediction algorithm, called TDAG. The TDAG algorithm is first tested by comparing its performance with some common data compression algorithms. Then it is adapted to the detailed requirements of dynamic program optimization, with excellent results.
Additive discrete 1D linear canonical transform
NASA Astrophysics Data System (ADS)
Zhao, Liang; Healy, John J.; Guo, Chang-liang; Sheridan, John T.
2015-09-01
The continuous linear canonical transforms (LCT) can describe a wide variety of wave field propagations through paraxial (first order) optical systems. Digital algorithms to numerically calculate the LCT are therefore important in modelling scalar wave field propagations and are also of interest for many digital signal processing applications. The continuous LCT is additive, but discretization can remove this property. In this paper we discuss three special cases of the LCT for which constraints can be identified to ensure the DLCT is additive.
Computational requirements for a discrete Kalman filter.
NASA Technical Reports Server (NTRS)
Mendel, J. M.
1971-01-01
Computational requirements - i.e., computing time per cycle (iteration) and required storage - which determine minimum sampling rates and computer memory size, were obtained as functions of the dimensions of the important system matrices for a discrete Kalman filter. Two types of measurement processing are discussed: simultaneous and sequential. It is shown that it is often better to process statistically independent measurements in more than one batch and then use sequential processing than to process them together via simultaneous processing.
High dimensional cohomology of discrete groups.
Brown, K S
1976-06-01
For a large class of discrete groups Gamma, relations are established between the high dimensional cohomology of Gamma and the cohomology of the normalizers of the finite subgroups of Gamma. The results are stated in terms of a generalization of Tate cohomology recently constructed by F. T. Farrell. As an illustration of these results, it is shown that one can recover a cohomology calculation of Lee and Szczarba, which they used to calculate the odd torsion in K(3)(Z). PMID:16592322
High dimensional cohomology of discrete groups
Brown, Kenneth S.
1976-01-01
For a large class of discrete groups Γ, relations are established between the high dimensional cohomology of Γ and the cohomology of the normalizers of the finite subgroups of Γ. The results are stated in terms of a generalization of Tate cohomology recently constructed by F. T. Farrell. As an illustration of these results, it is shown that one can recover a cohomology calculation of Lee and Szczarba, which they used to calculate the odd torsion in K3(Z). PMID:16592322
Performance of the discrete electrode railgun
Usuba, S.; Kakudate, Y.; Yoshida, M.; Aoki, K.; Yamawaki, H.; Fujiwara, S. ); Miyamoto, M. ); Kubota, A. ); Den, M. )
1991-01-01
In this paper a concept of Discrete Electrode (DE) railgun is presented. Plasma acceleration experiments using small DE railguns showed that the DE railgun could regulate the armature current distribution by means of fuses and a velocity of the armature current propagation was significantly higher than that in a normal type railgun. A mechanism of the armature current propagation in the DE railgun was discussed.
Joint discrete universality of Hurwitz zeta functions
NASA Astrophysics Data System (ADS)
Laurinčikas, A.
2014-11-01
We obtain a joint discrete universality theorem for Hurwitz zeta functions. Here the parameters of zeta functions and the step of shifts of these functions approximating a given family of analytic functions are connected by some condition of linear independence. Nesterenko's theorem gives an example satisfying this condition. The universality theorem is applied to estimate the number of zeros of a linear combination of Hurwitz zeta functions. Bibliography: 20 titles.
Discrete Atomic Layers at the Molecular Level
NASA Astrophysics Data System (ADS)
Yorimitsu, Hideki; Bhanuchandra, M.
2015-12-01
In this review, we deal with the syntheses of large discrete atomic layers at the molecular level. Spectroscopic measurements as well as X-ray crystallographic analyses lead to unambiguous characterizations of these layers. The molecular atomic layers can be considered to be parts of graphenes and related atomic layers, thereby helping to understand such indefinitely huge atomic layers or serving as seeds for the controlled synthesis of nanocarbons.
Police investigations: discretion denied yet undeniably exercised
Belur, J.; Tilley, N.; Osrin, D.; Daruwalla, N.; Kumar, M.; Tiwari, V.
2014-01-01
Police investigations involve determining whether a crime has been committed, and if so what type of crime, who has committed it and whether there is the evidence to charge the perpetrators. Drawing on fieldwork in Delhi and Mumbai, this paper explores how police investigations unfolded in the specific context of women’s deaths by burning in India. In particular, it focuses on the use of discretion despite its denial by those exercising it. In India, there are distinctive statutes relating to women’s suspicious deaths, reflecting the widespread expectation that the bride’s family will pay a dowry to the groom’s family and the tensions to which this may on occasion give rise in the early years of a marriage. Often, there are conflicting claims influencing how the woman’s death is classified. These in turn affect police investigation. The nature and direction of police discretion in investigating women’s deaths by burning reflect in part the unique nature of the legislation and the particular sensitivities in relation to these types of death. They also highlight processes that are liable to be at work in any crime investigation. It was found that police officers exercised unacknowledged discretion at seven specific points in the investigative process, with potentially significant consequences for the achievement of just outcomes: first response, recording the victim’s ‘dying declaration’, inquest, registering of the ‘First Information Report’, collecting evidence, arrest and framing of the charges. PMID:26376482
Discrete Deterministic and Stochastic Petri Nets
NASA Technical Reports Server (NTRS)
Zijal, Robert; Ciardo, Gianfranco
1996-01-01
Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.
Discrete Inverse and State Estimation Problems
NASA Astrophysics Data System (ADS)
Wunsch, Carl
2006-06-01
The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra. Provides a comprehensive introduction to discrete methods of inference from incomplete information Based upon 25 years of practical experience using real data and models Develops sequential and whole-domain analysis methods from simple least-squares Contains many examples and problems, and web-based support through MIT opencourseware
An essay on discrete foundations for physics
Noyes, H.P.; McGoveran, D.O.
1988-07-01
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non-uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.
An essay on discrete foundations for physics
Noyes, H.P.; McGoveran, D.O.
1988-10-05
We base our theory of physics and cosmology on the five principles of finiteness, discreteness, finite computability, absolute non- uniqueness, and strict construction. Our modeling methodology starts from the current practice of physics, constructs a self-consistent representation based on the ordering operator calculus and provides rules of correspondence that allow us to test the theory by experiment. We use program universe to construct a growing collection of bit strings whose initial portions (labels) provide the quantum numbers that are conserved in the events defined by the construction. The labels are followed by content strings which are used to construct event-based finite and discrete coordinates. On general grounds such a theory has a limiting velocity, and positions and velocities do not commute. We therefore reconcile quantum mechanics with relativity at an appropriately fundamental stage in the construction. We show that events in different coordinate systems are connected by the appropriate finite and discrete version of the Lorentz transformation, that 3-momentum is conserved in events, and that this conservation law is the same as the requirement that different paths can ''interfere'' only when they differ by an integral number of deBroglie wavelengths. 38 refs., 12 figs., 3 tabs.
How to detect the integrability of discrete systems
NASA Astrophysics Data System (ADS)
Grammaticos, B.; Halburd, R. G.; Ramani, A.; Viallet, C.-M.
2009-10-01
Several integrability tests for discrete equations will be reviewed. All tests considered can be applied directly to a given discrete equation and do not rely on the a priori knowledge of the existence of related structures such as Lax pairs. Specifically, singularity confinement, algebraic entropy, Nevanlinna theory, Diophantine integrability and discrete systems over finite fields will be described.
5 CFR 7.1 - Discretion in filling vacancies.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Discretion in filling vacancies. 7.1 Section 7.1 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE RULES GENERAL PROVISIONS (RULE VII) § 7.1 Discretion in filling vacancies. In his discretion, an appointing officer may fill...
Breaking and Restoring of Diffeomorphism Symmetry in Discrete Gravity
Bahr, B.; Dittrich, B.
2009-12-15
We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so-called perfect actions, with exact symmetries and we will review first steps towards this end.
Light Adaptation of Discrete Waves in the Limulus Photoreceptor
Srebro, Richard; Behbehani, Mahmood
1972-01-01
Light adaptation affects discrete waves in two ways. It reduces their average size and decreases the probability that a photon incident at the cornea causes a discrete wave. There is no effect of light adaptation on the latency of discrete waves, or on their time-course. PMID:5042025
Fluctuations and discreteness in diffusion limited growth
NASA Astrophysics Data System (ADS)
Devita, Jason P.
This thesis explores the effects of fluctuations and discreteness on the growth of physical systems where diffusion plays an important role. It focuses on three related problems, all dependent on diffusion in a fundamental way, but each with its own unique challenges. With diffusion-limited aggregation (DLA), the relationship between noisy and noise-free Laplacian growth is probed by averaging the results of noisy growth. By doing so in a channel geometry, we are able to compare to known solutions of the noise-free problem. We see that while the two are comparable, there are discrepancies which are not well understood. In molecular beam epitaxy (MBE), we create efficient computational algorithms, by replacing random walkers (diffusing atoms) with approximately equivalent processes. In one case, the atoms are replaced by a continuum field. Solving for the dynamics of the field yields---in an average sense---the dynamics of the atoms. In the other case, the atoms are treated as individual random-walking particles, but the details of the dynamics are changed to an (approximately) equivalent set of dynamics. This approach involves allowing adatoms to take long hops. We see approximately an order of magnitude speed up for simulating island dynamics, mound growth, and Ostwald ripening. Some ideas from the study of MBE are carried over to the study of front propagation in reaction-diffusion systems. Many of the analytic results about front propagation are derived from continuum models. It is unclear, however, that these results accurately describe the properties of a discrete system. It is reasonable to think that discrete systems will converge to the continuum results when sufficiently many particles are included. However, computational evidence of this is difficult to obtain, since the interesting properties tend to depend on a power law of the logarithm of the number of particles. Thus, the number of particles included in simulations must be exceedingly large. By
Projected discrete ordinates methods for numerical transport problems
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra
NASA Astrophysics Data System (ADS)
Rezakhah, Saeid; Maleki, Yasaman
2016-07-01
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time processes. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also, a new method for estimation time dependent Hurst parameter of such processes is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S & P500 and Dow Jones indices for some special periods.
Synaptic plasticity with discrete state synapses
NASA Astrophysics Data System (ADS)
Abarbanel, Henry D. I.; Talathi, Sachin S.; Gibb, Leif; Rabinovich, M. I.
2005-09-01
Experimental observations on synaptic plasticity at individual glutamatergic synapses from the CA3 Shaffer collateral pathway onto CA1 pyramidal cells in the hippocampus suggest that the transitions in synaptic strength occur among discrete levels at individual synapses [C. C. H. Petersen , Proc. Natl. Acad. Sci. USA 85, 4732 (1998); O’Connor, Wittenberg, and Wang, D. H. O’Connor , Proc. Natl. Acad. Sci. USA (to be published); J. M. Montgomery and D. V. Madison, Trends Neurosci. 27, 744 (2004)]. This happens for both long term potentiation (LTP) and long term depression (LTD) induction protocols. O’Connor, Wittenberg, and Wang have argued that three states would account for their observations on individual synapses in the CA3-CA1 pathway. We develop a quantitative model of this three-state system with transitions among the states determined by a competition between kinases and phosphatases shown by D. H. O’Connor , to be determinant of LTP and LTD, respectively. Specific predictions for various plasticity protocols are given by coupling this description of discrete synaptic α -amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor ligand gated ion channel conductance changes to a model of postsynaptic membrane potential and associated intracellular calcium fluxes to yield the transition rates among the states. We then present various LTP and LTD induction protocols to the model system and report the resulting whole cell changes in AMPA conductance. We also examine the effect of our discrete state synaptic plasticity model on the synchronization of realistic oscillating neurons. We show that one-to-one synchronization is enhanced by the plasticity we discuss here and the presynaptic and postsynaptic oscillations are in phase. Synaptic strength saturates naturally in this model and does not require artificial upper or lower cutoffs, in contrast to earlier models of plasticity.
Efficient Associative Computation with Discrete Synapses.
Knoblauch, Andreas
2016-01-01
Neural associative networks are a promising computational paradigm for both modeling neural circuits of the brain and implementing associative memory and Hebbian cell assemblies in parallel VLSI or nanoscale hardware. Previous work has extensively investigated synaptic learning in linear models of the Hopfield type and simple nonlinear models of the Steinbuch/Willshaw type. Optimized Hopfield networks of size n can store a large number of about n(2)/k memories of size k (or associations between them) but require real-valued synapses, which are expensive to implement and can store at most C = 0.72 bits per synapse. Willshaw networks can store a much smaller number of about n(2)/k(2) memories but get along with much cheaper binary synapses. Here I present a learning model employing synapses with discrete synaptic weights. For optimal discretization parameters, this model can store, up to a factor ζ close to one, the same number of memories as for optimized Hopfield-type learning--for example, ζ = 0.64 for binary synapses, ζ = 0.88 for 2 bit (four-state) synapses, ζ = 0.96 for 3 bit (8-state) synapses, and ζ > 0.99 for 4 bit (16-state) synapses. The model also provides the theoretical framework to determine optimal discretization parameters for computer implementations or brainlike parallel hardware including structural plasticity. In particular, as recently shown for the Willshaw network, it is possible to store C(I) = 1 bit per computer bit and up to C(S) = log n bits per nonsilent synapse, whereas the absolute number of stored memories can be much larger than for the Willshaw model. PMID:26599711
Interventional tool tracking using discrete optimization.
Heibel, Hauke; Glocker, Ben; Groher, Martin; Pfister, Marcus; Navab, Nassir
2013-03-01
This work presents a novel scheme for tracking of motion and deformation of interventional tools such as guide-wires and catheters in fluoroscopic X-ray sequences. Being able to track and thus to estimate the correct positions of these tools is crucial in order to offer guidance enhancement during interventions. The task of estimating the apparent motion is particularly challenging due to the low signal-to-noise ratio (SNR) of fluoroscopic images and due to combined motion components originating from patient breathing and tool interactions performed by the physician. The presented approach is based on modeling interventional tools with B-splines whose optimal configuration of control points is determined through efficient discrete optimization. Each control point corresponds to a discrete random variable in a Markov random field (MRF) formulation where a set of labels represents the deformation space. In this context, the optimal curve corresponds to the maximum a posteriori (MAP) estimate of the MRF energy. The main motivation for employing a discrete approach is the possibility to incorporate a multi-directional search space which is robust to local minima. This is of particular interest for curve tracking under large deformation. This work analyzes feasibility of employing efficient first-order MRFs for tracking. In particular it shows how to achieve a good compromise between energy approximations and computational efficiency. Experimental results suggest to define both the external and internal energy in terms of pairwise potential functions. The method was successfully applied to the tracking of guide-wires in fluoroscopic X-ray sequences of several hundred frames which requires extremely robust techniques. Comparisons with state-of-the-art guide-wire tracking algorithms confirm the effectiveness of the proposed method. PMID:23232412
Efficient discretization in finite difference method
NASA Astrophysics Data System (ADS)
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
Discrete time modelization of human pilot behavior
NASA Technical Reports Server (NTRS)
Cavalli, D.; Soulatges, D.
1975-01-01
This modelization starts from the following hypotheses: pilot's behavior is a time discrete process, he can perform only one task at a time and his operating mode depends on the considered flight subphase. Pilot's behavior was observed using an electro oculometer and a simulator cockpit. A FORTRAN program has been elaborated using two strategies. The first one is a Markovian process in which the successive instrument readings are governed by a matrix of conditional probabilities. In the second one, strategy is an heuristic process and the concepts of mental load and performance are described. The results of the two aspects have been compared with simulation data.
Discrete analog computing with rotor-routers.
Propp, James
2010-09-01
Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed (information is spread throughout the system). It is also possible to efficiently check that a computation has been carried out correctly in less time than the computation itself required, provided one has a certificate that can itself be computed by the rotor-router network. Rotor-router networks can be viewed as both discrete analogs of continuous linear systems and deterministic analogs of stochastic processes. PMID:20887076
Construction of Discrete Time Shadow Price
Rogala, Tomasz Stettner, Lukasz
2015-12-15
In the paper expected utility from consumption over finite time horizon for discrete time markets with bid and ask prices and strictly concave utility function is considered. The notion of weak shadow price, i.e. an illiquid price, depending on the portfolio, under which the model without bid and ask price is equivalent to the model with bid and ask price is introduced. Existence and the form of weak shadow price is shown. Using weak shadow price usual (called in the paper strong) shadow price is then constructed.
Compartmentalization analysis using discrete fracture network models
La Pointe, P.R.; Eiben, T.; Dershowitz, W.; Wadleigh, E.
1997-08-01
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph the theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Discrete Space Theory of Radiative Transfer: Application
NASA Astrophysics Data System (ADS)
Rao, M. Srinivasa
2010-06-01
The method of obtaining the solution of radiative transfer equation using discrete space theory (DST) is described with (1) interaction principle for different geometries (2) star product (3) calculation of radiation field at internal points. Some of the important steps to obtain the solution of radiative transfer equation in spherical symmetry are also mentioned. Applications of DST are discussed with their results in two cases (a) study of reflection effect in close binary systems and (b) to compute KI 769.9 nm emission line profiles from N-type stars.
Discrete Space Theory of Radiative Transfer: Application
NASA Astrophysics Data System (ADS)
Rao, M. Srinivasa
The method of obtaining the solution of radiative transfer equation using discrete space theory (DST) is described with (1) interaction principle for different geometries (2) star product (3) calculation of radiation field at internal points. Some of the important steps to obtain the solution of radiative transfer equation in spherical symmetry are also mentioned. Applications of DST are discussed with their results in two cases (a) study of reflection effect in close binary systems and (b) to compute KI 769.9 nm emission line profiles from N-type stars.
Optical tomography with discretized path integral.
Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi
2015-07-01
We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well. PMID:26839903
Discrete Analysis of Clay Layer Tensile Strength
NASA Astrophysics Data System (ADS)
Lê, T. N. H.; Plé, O.; Villard, P.; Gotteland, P.; Gourc, J. P.
2009-06-01
The Discrete Element Method is used to investigate the tensile behaviour and cracks mechanisms of a clay material submitted to bending loading. It is the case of compacted clay liners in landfill cap cover application. Such as the soil tested in this study is plastic clay, the distinct elements model was calibrated with previous data results by taking into account cohesive properties. Various contact and cohesion laws are tested to show that the numerical model is able to reproduce the failure mechanism. Numerical results are extending to simulate a landfill cap cover.
Discrete computer analysis in petroleum geology
Zakharian, A.Z.
1995-08-01
Computer analysis must not be resembling on geologist`s work, having its own way because of uncertainty and shortness of geological information even on mature stage of exploration, when our original system of formal discrete computer analysis, realised on {open_quotes}FoxPro for Windows{close_quotes} with not substantial but probabilistic (without ever driving the usual maps) representation of geological situation was used for picking out the sets of best points for exploration drilling in south part of Dheprovsko-Donetzky oil-gas basin.
Compartmentalization analysis using discrete fracture network models
La Pointe, P.R.; Eiben, T.; Dershowitz, W.; Wadleigh, E.
1997-12-31
This paper illustrates how Discrete Fracture Network (DFN) technology can serve as a basis for the calculation of reservoir engineering parameters for the development of fractured reservoirs. It describes the development of quantitative techniques for defining the geometry and volume of structurally controlled compartments. These techniques are based on a combination of stochastic geometry, computational geometry, and graph theory. The parameters addressed are compartment size, matrix block size and tributary drainage volume. The concept of DFN models is explained and methodologies to compute these parameters are demonstrated.
Partitioning technique for discrete quantum systems
Jin, L.; Song, Z.
2011-06-15
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.
Coagulation and fragmentation with discrete mass loss
NASA Astrophysics Data System (ADS)
Blair, Pamela N.; Lamb, Wilson; Stewart, Iain W.
2007-05-01
A nonlinear integro-differential equation that models a coagulation and multiple fragmentation process in which discrete fragmentation mass loss can occur is examined using the theory of strongly continuous semigroups of operators. Under the assumptions that the coagulation kernel is bounded and the fragmentation rate function a satisfies a linear growth condition, global existence and uniqueness of solutions that lose mass in accordance with the model are established. In the case when no coagulation is present and the fragmentation process is governed by power-law kernels, an explicit formula is given for the substochastic semigroup associated with the resulting mass-loss fragmentation equation.
Discrete Wigner functions and quantum computational speedup
Galvao, Ernesto F.
2005-04-01
Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] have recently defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize the set C{sub d} of states having non-negative W simultaneously in all definitions of W in this class. For d{<=}5 I show C{sub d} is the convex hull of stabilizer states. This supports the conjecture that negativity of W is necessary for exponential speedup in pure-state quantum computation.
Discrete quantum spectrum of black holes
NASA Astrophysics Data System (ADS)
Lochan, Kinjalk; Chakraborty, Sumanta
2016-04-01
The quantum genesis of Hawking radiation is a long-standing puzzle in black hole physics. Semi-classically one can argue that the spectrum of radiation emitted by a black hole look very much sparse unlike what is expected from a thermal object. It was demonstrated through a simple quantum model that a quantum black hole will retain a discrete profile, at least in the weak energy regime. However, it was suggested that this discreteness might be an artifact of the simplicity of eigen-spectrum of the model considered. Different quantum theories can, in principle, give rise to different complicated spectra and make the radiation from black hole dense enough in transition lines, to make them look continuous in profile. We show that such a hope from a geometry-quantized black hole is not realized as long as large enough black holes are dubbed with a classical mass area relation in any gravity theory ranging from GR, Lanczos-Lovelock to f(R) gravity. We show that the smallest frequency of emission from black hole in any quantum description, is bounded from below, to be of the order of its inverse mass. That leaves the emission with only two possibilities. It can either be non-thermal, or it can be thermal only with the temperature being much larger than 1/M.
Analysis of discretization errors in LES
NASA Technical Reports Server (NTRS)
Ghosal, Sandip
1995-01-01
All numerical simulations of turbulence (DNS or LES) involve some discretization errors. The integrity of such simulations therefore depend on our ability to quantify and control such errors. In the classical literature on analysis of errors in partial differential equations, one typically studies simple linear equations (such as the wave equation or Laplace's equation). The qualitative insight gained from studying such simple situations is then used to design numerical methods for more complex problems such as the Navier-Stokes equations. Though such an approach may seem reasonable as a first approximation, it should be recognized that strongly nonlinear problems, such as turbulence, have a feature that is absent in linear problems. This feature is the simultaneous presence of a continuum of space and time scales. Thus, in an analysis of errors in the one dimensional wave equation, one may, without loss of generality, rescale the equations so that the dependent variable is always of order unity. This is not possible in the turbulence problem since the amplitudes of the Fourier modes of the velocity field have a continuous distribution. The objective of the present research is to provide some quantitative measures of numerical errors in such situations. Though the focus of this work is LES, the methods introduced here can be just as easily applied to DNS. Errors due to discretization of the time-variable are neglected for the purpose of this analysis.
A Discrete Model for Color Naming
NASA Astrophysics Data System (ADS)
Menegaz, G.; Le Troter, A.; Sequeira, J.; Boi, J. M.
2006-12-01
The ability to associate labels to colors is very natural for human beings. Though, this apparently simple task hides very complex and still unsolved problems, spreading over many different disciplines ranging from neurophysiology to psychology and imaging. In this paper, we propose a discrete model for computational color categorization and naming. Starting from the 424 color specimens of the OSA-UCS set, we propose a fuzzy partitioning of the color space. Each of the 11 basic color categories identified by Berlin and Kay is modeled as a fuzzy set whose membership function is implicitly defined by fitting the model to the results of an ad hoc psychophysical experiment (Experiment 1). Each OSA-UCS sample is represented by a feature vector whose components are the memberships to the different categories. The discrete model consists of a three-dimensional Delaunay triangulation of the CIELAB color space which associates each OSA-UCS sample to a vertex of a 3D tetrahedron. Linear interpolation is used to estimate the membership values of any other point in the color space. Model validation is performed both directly, through the comparison of the predicted membership values to the subjective counterparts, as evaluated via another psychophysical test (Experiment 2), and indirectly, through the investigation of its exploitability for image segmentation. The model has proved to be successful in both cases, providing an estimation of the membership values in good agreement with the subjective measures as well as a semantically meaningful color-based segmentation map.
Harmonic Pinnacles in the Discrete Gaussian Model
NASA Astrophysics Data System (ADS)
Lubetzky, Eyal; Martinelli, Fabio; Sly, Allan
2016-06-01
The 2 D Discrete Gaussian model gives each height function {η : Z^2to{Z}} a probability proportional to {exp(-β {H}(η))}, where {β} is the inverse-temperature and {{H}(η) = sum_{x˜ y}(η_x-η_y)^2} sums over nearest-neighbor bonds. We consider the model at large fixed {β}, where it is flat unlike its continuous analog (the Discrete Gaussian Free Field). We first establish that the maximum height in an {L× L} box with 0 boundary conditions concentrates on two integers M, M + 1 with {M˜ √{(1/2πβ)log Llog log L}}. The key is a large deviation estimate for the height at the origin in {{Z}2}, dominated by "harmonic pinnacles", integer approximations of a harmonic variational problem. Second, in this model conditioned on {η≥ 0} (a floor), the average height rises, and in fact the height of almost all sites concentrates on levels H, H + 1 where {H˜ M/√{2}}. This in particular pins down the asymptotics, and corrects the order, in results of Bricmont et al. (J. Stat. Phys. 42(5-6):743-798, 1986), where it was argued that the maximum and the height of the surface above a floor are both of order {√{log L}}. Finally, our methods extend to other classical surface models (e.g., restricted SOS), featuring connections to p-harmonic analysis and alternating sign matrices.
Discrete elements for 3D microfluidics
Bhargava, Krisna C.; Thompson, Bryant; Malmstadt, Noah
2014-01-01
Microfluidic systems are rapidly becoming commonplace tools for high-precision materials synthesis, biochemical sample preparation, and biophysical analysis. Typically, microfluidic systems are constructed in monolithic form by means of microfabrication and, increasingly, by additive techniques. These methods restrict the design and assembly of truly complex systems by placing unnecessary emphasis on complete functional integration of operational elements in a planar environment. Here, we present a solution based on discrete elements that liberates designers to build large-scale microfluidic systems in three dimensions that are modular, diverse, and predictable by simple network analysis techniques. We develop a sample library of standardized components and connectors manufactured using stereolithography. We predict and validate the flow characteristics of these individual components to design and construct a tunable concentration gradient generator with a scalable number of parallel outputs. We show that these systems are rapidly reconfigurable by constructing three variations of a device for generating monodisperse microdroplets in two distinct size regimes and in a high-throughput mode by simple replacement of emulsifier subcircuits. Finally, we demonstrate the capability for active process monitoring by constructing an optical sensing element for detecting water droplets in a fluorocarbon stream and quantifying their size and frequency. By moving away from large-scale integration toward standardized discrete elements, we demonstrate the potential to reduce the practice of designing and assembling complex 3D microfluidic circuits to a methodology comparable to that found in the electronics industry. PMID:25246553
Discrete dynamics and non-Markovianity
NASA Astrophysics Data System (ADS)
Luoma, Kimmo; Piilo, Jyrki
2016-06-01
We study discrete quantum dynamics where a single evolution step consists of unitary system transformation followed by decoherence via coupling to an environment. Often, non-Markovian memory effects are attributed to structured environments, whereas, here, we take a more general approach within a discrete setting. In addition of controlling the structure of the environment, we are interested in how local unitaries on the open system allow the appearance and control of memory effects. Our first simple qubit model where local unitary is followed by dephasing illustrates how memory effects arise, despite having no structure in the environment the system is coupled with. We, then, elaborate on this observation by constructing a model for an open quantum walk where the unitary coin and transfer operation is augmented with the dephasing of the coin. The results demonstrate tha,t in the limit of strong dephasing within each evolution step, the combined coin-position open system always displays memory effects, and their quantities are independent of the structure of the environment. Our construction makes possible an experimentally realizable open quantum walk with photons exhibiting non-Markovian features.
A Family of Discrete Magnetically Switchable Nanoballs
Duriska, Martin B.; Neville, Suzanne M.; Moubaraki, Boujemaa; Murray, Keith S.; Balde, Chérif; Létard, Jean-François; Kepert, Cameron J.; Batten, Stuart R.
2012-08-01
The thermal and light-induced magnetic properties of a family of discrete magnetically switchable 'nanoball' species (3 nm in diameter) is reported. The self-assembly of these materials is accomplished by the use of the metallo building block, [Cu([Tp{sup 4-py}])(NCCH{sub 3})] ([Tp{sup 4-py}]=tris-[3-(4{prime}-pyridyl)pyrazol-1-yl]hydroborate), combined with a [Fe(NCX){sub 2}] (X = S, Se and BH{sub 3}) species. We previously showed that the thiocyanate analogue (Fe(NCS)-nano) undergoes a thermal and light-induced spin crossover (SCO) - the largest such discrete SCO material reported. Now included in this family are the Se and BH{sub 3} analogues, Fe(NCSe)-nano and Fe(NCBH{sub 3})-nano, which show increased thermal transition temperatures (T{sub 1/2} = 124 K, 162 and 173 K). This variation in transition temperature over the series S < Se < BH{sub 3} results in diverse photomagnetic properties, such that the light-induced excited spin state trapping (LIESST) effect is exhibited to varying degrees and at different temperatures by the S, Se and BH{sub 3} analogues.
Discrete Bubble Modeling for Cavitation Bubbles
NASA Astrophysics Data System (ADS)
Choi, Jin-Keun; Chahine, Georges; Hsiao, Chao-Tsung
2007-03-01
Dynaflow, Inc. has conducted extensive studies on non-spherical bubble dynamics and interactions with solid and free boundaries, vortical flow structures, and other bubbles. From these studies, emerged a simplified Surface Averaged Pressure (SAP) spherical bubble dynamics model and a Lagrangian bubble tracking scheme. In this SAP scheme, the pressure and velocity of the surrounding flow field are averaged on the bubble surface, and then used for the bubble motion and volume dynamics calculations. This model is implemented using the Fluent User Defined Function (UDF) as Discrete Bubble Model (DBM). The Bubble dynamics portion can be solved using an incompressible liquid modified Rayleigh-Plesset equation or a compressible liquid modified Gilmore equation. The Discrete Bubble Model is a very suitable tool for the studies on cavitation inception of foils and turbo machinery, bubble nuclei effects, noise from the bubbles, and can be used in many practical problems in industrial and naval applications associated with flows in pipes, jets, pumps, propellers, ships, and the ocean. Applications to propeller cavitation, wake signatures of waterjet propelled ships, bubble-wake interactions, modeling of cavitating jets, and bubble entrainments around a ship will be presented.
Pattern Formation in Spatially Discrete Systems
NASA Astrophysics Data System (ADS)
Méndez, Vicenç; Fedotov, Sergei; Horsthemke, Werner
The preceding chapters have dealt with the spatiotemporal behavior of spatially continuous systems. We now turn our attention to the dynamical behavior and stability properties of spatially discrete systems. A wide variety of phenomena in chemistry, biology, physics, and other fields involve the coupling between nonlinear, discrete units. Examples include arrays of Josephson junctions, chains of coupled diode resonators, coupled chemical or biochemical reactors, myelinated nerve fibers, neuronal networks, and patchy ecosystems. Such networks of coupled nonlinear units often combine dynamical and structural complexity [422]. Cells in living tissues, for example, are arranged in a variety of geometries. One-dimensional rings of cells were already considered by Turing [440]. Other types of lattices, such as open-ended linear arrays, tubes, rectangular and hexagonal arrays, and irregular arrangements in two or three dimensions are also found, see for example [5]. Cells interact with adjacent cells in various distinct ways. For example, signaling between cells may occur via diffusion through gap junctions [352, 230] or by membrane-bound proteins, juxtacrine signaling [339, 340, 471].
Time Discretization Approach to Dynamic Localization Conditions
NASA Astrophysics Data System (ADS)
Papp, E.
An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is written down. For this purpose the method of characteristics such as applied by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)] has been modified by using a different integration variable. Handling this wavefunction one is faced with the selection of admissible time values. This results in a conditionally exactly solvable problem, now by accounting specifically for the implementation of a time discretization working in conjunction with a related dynamic localization condition. In addition, one resorts to the strong field limit, which amounts to replace, to leading order, the large order zeros of the Bessel function J0(z), used before in connection with the cosinusoidal modulation, by integral multiples of π. Here z stands for the ratio between the field amplitude and the frequency. The modulation function of the electric field vanishes on the nodal points of the time grid, which stands for an effective field-free behavior. This opens the way to propose quickly tractable dynamic localization conditions for arbitrary periodic modulations. We have also found that the present time discretization approach produces the minimization of the mean square displacement characterizing the usual exact wavefunction. Other realizations and comparisons have also been presented.
Discrete distributed strain sensing of intelligent structures
NASA Technical Reports Server (NTRS)
Anderson, Mark S.; Crawley, Edward F.
1992-01-01
Techniques are developed for the design of discrete highly distributed sensor systems for use in intelligent structures. First the functional requirements for such a system are presented. Discrete spatially averaging strain sensors are then identified as satisfying the functional requirements. A variety of spatial weightings for spatially averaging sensors are examined, and their wave number characteristics are determined. Preferable spatial weightings are identified. Several numerical integration rules used to integrate such sensors in order to determine the global deflection of the structure are discussed. A numerical simulation is conducted using point and rectangular sensors mounted on a cantilevered beam under static loading. Gage factor and sensor position uncertainties are incorporated to assess the absolute error and standard deviation of the error in the estimated tip displacement found by numerically integrating the sensor outputs. An experiment is carried out using a statically loaded cantilevered beam with five point sensors. It is found that in most cases the actual experimental error is within one standard deviation of the absolute error as found in the numerical simulation.
Compressor Stability Enhancement Using Discrete Tip Injection
NASA Technical Reports Server (NTRS)
Suder, Kenneth L.; Hathaway, Michael D.; Thorp, Scott A.; Strazisar, Anthony J.; Bright, Michelle B.
2001-01-01
Mass injection upstream of the tip of a high-speed axial compressor rotor is a stability enhancement approach known to be effective in suppressing small in tip-critical rotors. This process is examined in a transonic axial compressor rotor through experiments and time-averaged Navier-Stokes CFD simulations. Measurements and simulations for discrete injection are presented for a range of injection rates and distributions of injectors around the annulus. The simulations indicate that tip injection increases stability by unloading the rotor tip and that increasing injection velocity improves the effectiveness of tip injection. For the tested rotor, experimental results demonstrate that at 70 percent speed the stalling flow coefficient can be reduced by 30 percent using an injected mass- flow equivalent to 1 percent of the annulus flow. At design speed, the stalling flow coefficient was reduced by 6 percent using an injected mass-fiow equivalent to 2 percent of the annulus flow. The experiments show that stability enhancement is related to the mass-averaged axial velocity at the tip. For a given injected mass-flow, the mass-averaged axial velocity at the tip is increased by injecting flow over discrete portions of the circumference as opposed to full-annular injection. The implications of these results on the design of recirculating casing treatments and other methods to enhance stability will be discussed.
DelGrande, J. Mark; Mathews, Kirk A.
2001-09-15
Conventional discrete ordinates transport calculations often produce negative fluxes due to unphysical negative scattering cross sections and/or as artifacts of spatial differencing schemes such as diamond difference. Inherently nonnegative spatial methods, such as the nonlinear, exponential characteristic spatial quadrature, eliminate negative fluxes while providing excellent accuracy, presuming the group-to-group, ordinate-to-ordinate cross sections are all nonnegative. A hybrid approach is introduced in which the flow from spatial cell to spatial cell uses discrete ordinates spatial quadratures, while anisotropic scattering of flux from one energy-angle bin (energy group and discrete element of solid angle) to another such bin is modeled using a Monte Carlo simulation to evaluate the bin-to-bin cross sections. The directional elements tile the sphere of directions; the ordinates for the spatial quadrature are at the centroids of the elements. The method is developed and contrasted with previous schemes for positive cross sections. An algorithm for evaluating the Monte Carlo (MC)-discrete elements (MC-DE) cross sections is described, and some test cases are presented. Transport calculations using MC-DE cross sections are compared with calculations using conventional cross sections and with MCNP calculations. In this testing, the new method is about as accurate as the conventional approach, and often is more accurate. The exponential characteristic spatial quadrature, using the MC-DE cross sections, is shown to provide useful results where linear characteristic and spherical harmonics provide negative scalar fluxes in every cell in a region.
A discretization of Boltzmann's collision operator with provable convergence
NASA Astrophysics Data System (ADS)
Brechtken, Stefan
2014-12-01
The discretization of the right-hand side of the Boltzmann equation (aka the collision operator) on uniform grids generally suffers from some well known problems prohibiting the construction of deterministic high order discretizations which exactly sustain the basic properties of the collision operator. These problems mainly relate to problems arising from the discretization of spheres on uniform grids and the necessity that the discretization must possess some symmetry properties in order to provide the discrete versions of properties stemming from the continuous collision operator (number of collision invariants, avoidance of artificial collision invariants, type of equilibrium solutions, H-Theorem). We present a scheme to construct discretizations in 2 dimensions with arbitrarily high convergence orders on uniform grids, which are comparable to the approach by Rogier and Schneider [1] and the subsequent works by Michel and Schneider as well as Panferov and Heintz [2, 3] who used Farey sequences for the discretization. Moreover we take a closer look at this discretization in the framework of discrete velocity models to present results governing the correct collision invariants, lack of artificial collision invariants, the H-Theorem and the correct equilibrium solutions. Furthermore we classify lattice group models (LGpM) in the context of DVMs to transfer the high convergence order of these discretizations into the context of LGpMs and finally we take a short look at the numerical complexity.
NASA Astrophysics Data System (ADS)
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2016-05-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of
Beta oscillations define discrete perceptual cycles in the somatosensory domain.
Baumgarten, Thomas J; Schnitzler, Alfons; Lange, Joachim
2015-09-29
Whether seeing a movie, listening to a song, or feeling a breeze on the skin, we coherently experience these stimuli as continuous, seamless percepts. However, there are rare perceptual phenomena that argue against continuous perception but, instead, suggest discrete processing of sensory input. Empirical evidence supporting such a discrete mechanism, however, remains scarce and comes entirely from the visual domain. Here, we demonstrate compelling evidence for discrete perceptual sampling in the somatosensory domain. Using magnetoencephalography (MEG) and a tactile temporal discrimination task in humans, we find that oscillatory alpha- and low beta-band (8-20 Hz) cycles in primary somatosensory cortex represent neurophysiological correlates of discrete perceptual cycles. Our results agree with several theoretical concepts of discrete perceptual sampling and empirical evidence of perceptual cycles in the visual domain. Critically, these results show that discrete perceptual cycles are not domain-specific, and thus restricted to the visual domain, but extend to the somatosensory domain. PMID:26324922
Beta oscillations define discrete perceptual cycles in the somatosensory domain
Baumgarten, Thomas J.; Schnitzler, Alfons; Lange, Joachim
2015-01-01
Whether seeing a movie, listening to a song, or feeling a breeze on the skin, we coherently experience these stimuli as continuous, seamless percepts. However, there are rare perceptual phenomena that argue against continuous perception but, instead, suggest discrete processing of sensory input. Empirical evidence supporting such a discrete mechanism, however, remains scarce and comes entirely from the visual domain. Here, we demonstrate compelling evidence for discrete perceptual sampling in the somatosensory domain. Using magnetoencephalography (MEG) and a tactile temporal discrimination task in humans, we find that oscillatory alpha- and low beta-band (8–20 Hz) cycles in primary somatosensory cortex represent neurophysiological correlates of discrete perceptual cycles. Our results agree with several theoretical concepts of discrete perceptual sampling and empirical evidence of perceptual cycles in the visual domain. Critically, these results show that discrete perceptual cycles are not domain-specific, and thus restricted to the visual domain, but extend to the somatosensory domain. PMID:26324922
FPGA Implementation of Highly Modular Fast Universal Discrete Transforms
NASA Astrophysics Data System (ADS)
Potipantong, Panan; Sirisuk, Phaophak; Oraintara, Soontorn; Worapishet, Apisak
This paper presents an FPGA implementation of highly modular universal discrete transforms. The implementation relies upon the unified discrete Fourier Hartley transform (UDFHT), based on which essential sinusoidal transforms including discrete Fourier transform (DFT), discrete Hartley transform (DHT), discrete cosine transform (DCT) and discrete sine transform (DST) can be realized. It employs a reconfigurable, scalable and modular architecture that consists of a memory-based FFT processor equipped with pre- and post-processing units. Besides, a pipelining technique is exploited to seamlessly harmonize the operation between each sub-module. Experimental results based on Xilinx Virtex-II Pro are given to examine the performance of the proposed UDFHT implementation. Two practical applications are also shown to demonstrate the flexibility and modularity of the proposed work.
Discrete events and solar wind energization
NASA Technical Reports Server (NTRS)
Yang, W.-H.; Schunk, R. W.
1989-01-01
Based on a multiple-magnetic-reconnection picture, an estimation of the energy flux suggests that small-scale EUV exploding events may contribute a significant amount of energy (of order of 100,000 erg/sq cm sec) to solar atmospheric heating and solar-wind acceleration. Most of the dissipated magnetic energy is converted into thermal energy and plasma turbulence. On a related aspect, a numerical study based on the nonlinear one-fluid hydrodynamic equations shows a self-smoothing effect, whereby a multistream structure of the solar wind formed near the sun can be gradually smoothed during its propagation through interplanetary space. This calculation gives support for the possible contribution of discrete energetic events to high-speed solar wind streams.
Exact evolution of discrete relativistic cosmological models
Clifton, Timothy; Tavakol, Reza; Gregoris, Daniele; Rosquist, Kjell E-mail: danielegregoris@libero.it E-mail: r.tavakol@qmul.ac.uk
2013-11-01
We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions.
Cosmology of biased discrete symmetry breaking
NASA Technical Reports Server (NTRS)
Gelmini, Graciela B.; Gleiser, Marcelo; Kolb, Edward W.
1988-01-01
The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.
Discrete energy transport in collagen molecules
NASA Astrophysics Data System (ADS)
Alain, Mvogo; Germain, H. Ben-Bolie; Timoléon, C. Kofané
2014-09-01
The modulational instability in the three coupled α-polypeptide chains of a collagen molecule is investigated. Choosing symmetric and asymmetric solutions, and applying the so-called rotating-wave approximation, we describe the dynamics of the system by the discrete nonlinear Schrödinger (DNLS) equation. The linear stability analysis of the continuous wave solution is performed. The numerical simulations show the generation of trains of solitonic structures in the lattice with increasing amplitude as time progresses. The effect of damping and noise forces of the physiological temperature (T = 300 K) introduces an erratic behavior to the formed patterns, reinforcing the idea that the energy used in metabolic processes is confined to specific regions for efficiency.
Entanglement Swapping between Discrete and Continuous Variables
NASA Astrophysics Data System (ADS)
Takeda, Shuntaro; Fuwa, Maria; van Loock, Peter; Furusawa, Akira
2015-03-01
We experimentally realize "hybrid" entanglement swapping between discrete-variable (DV) and continuous-variable (CV) optical systems. DV two-mode entanglement as obtainable from a single photon split at a beam splitter is robustly transferred by means of efficient CV entanglement and operations, using sources of squeezed light and homodyne detections. The DV entanglement after the swapping is verified without postselection by the logarithmic negativity of up to 0.28 ±0.01 . Furthermore, our analysis shows that the optimally transferred state can be postselected into a highly entangled state that violates a Clauser-Horne-Shimony-Holt inequality by more than 4 standard deviations, and thus it may serve as a resource for quantum teleportation and quantum cryptography.
Automatic Mesh Coarsening for Discrete Ordinates Codes
Turner, Scott A.
1999-03-11
This paper describes the use of a ''mesh potential'' function for automatic coarsening of meshes in discrete ordinates neutral particle transport codes. For many transport calculations, a user may find it helpful to have the code determine a ''good'' neutronics mesh. The complexity of a problem involving millions of mesh cells, dozens of materials, and many energy groups makes it difficult to determine an adequate level of mesh refinement with a minimum number of cells. A method has been implemented in PARTISN (Parallel Time-dependent SN) to calculate a ''mesh potential'' in each original cell of a problem, and use this information to determine the maximum coarseness allowed in the mesh while maintaining accuracy in the solution. Results are presented for a simple x-y-z fuel/control/reflector problem.
Energy-pointwise discrete ordinates transport methods
Williams, M.L.; Asgari, M.; Tashakorri, R.
1997-06-01
A very brief description is given of a one-dimensional code, CENTRM, which computes a detailed, space-dependent flux spectrum in a pointwise-energy representation within the resolved resonance range. The code will become a component in the SCALE system to improve computation of self-shielded cross sections, thereby enhancing the accuracy of codes such as KENO. CENTRM uses discrete-ordinates transport theory with an arbitrary angular quadrature order and a Legendre expansion of scattering anisotropy for moderator materials and heavy nuclides. The CENTRM program provides capability to deterministically compute full energy range, space-dependent angular flux spectra, rigorously accounting for resonance fine-structure and scattering anisotropy effects.
Stochastic discrete model of karstic networks
NASA Astrophysics Data System (ADS)
Jaquet, O.; Siegel, P.; Klubertanz, G.; Benabderrhamane, H.
Karst aquifers are characterised by an extreme spatial heterogeneity that strongly influences their hydraulic behaviour and the transport of pollutants. These aquifers are particularly vulnerable to contamination because of their highly permeable networks of conduits. A stochastic model is proposed for the simulation of the geometry of karstic networks at a regional scale. The model integrates the relevant physical processes governing the formation of karstic networks. The discrete simulation of karstic networks is performed with a modified lattice-gas cellular automaton for a representative description of the karstic aquifer geometry. Consequently, more reliable modelling results can be obtained for the management and the protection of karst aquifers. The stochastic model was applied jointly with groundwater modelling techniques to a regional karst aquifer in France for the purpose of resolving surface pollution issues.
Isomer ratio calculations using modeled discrete levels
Gardner, M.A.; Gardner, D.G.; Hoff, R.W.
1984-10-16
Isomer ratio calculations were made for the reactions: /sup 175/Lu(n,..gamma..)/sup 176m,g/Lu, /sup 175/Lu(n,2n)/sup 174m,g/Lu, /sup 237/Np(n,2n)/sup 236m,g/Np, /sup 241/Am(n,..gamma..)/sup 242m,g/Am, and /sup 243/Am(n,..gamma..)/sup 244m,g/Am using modeled level structures in the deformed, odd-odd product nuclei. The hundreds of discrete levels and their gamma-ray branching ratios provided by the modeling are necessary to achieve agreement with experiment. Many rotational bands must be included in order to obtain a sufficiently representative selection of K quantum numbers. The levels of each band must be extended to appropriately high values of angular momentum.
Joint regression analysis for discrete longitudinal data.
Madsen, L; Fang, Y
2011-09-01
We introduce an approximation to the Gaussian copula likelihood of Song, Li, and Yuan (2009, Biometrics 65, 60-68) used to estimate regression parameters from correlated discrete or mixed bivariate or trivariate outcomes. Our approximation allows estimation of parameters from response vectors of length much larger than three, and is asymptotically equivalent to the Gaussian copula likelihood. We estimate regression parameters from the toenail infection data of De Backer et al. (1996, British Journal of Dermatology 134, 16-17), which consist of binary response vectors of length seven or less from 294 subjects. Although maximizing the Gaussian copula likelihood yields estimators that are asymptotically more efficient than generalized estimating equation (GEE) estimators, our simulation study illustrates that for finite samples, GEE estimators can actually be as much as 20% more efficient. PMID:21039391
Covalent Polymers Containing Discrete Heterocyclic Anion Receptors
Rambo, Brett M.; Silver, Eric S.; Bielawski, Christopher W.; Sessler, Jonathan L.
2010-01-01
This chapter covers recent advances in the development of polymeric materials containing discrete heterocyclic anion receptors, and focuses on advances in anion binding and chemosensor chemistry. The development of polymers specific for anionic species is a relatively new and flourishing area of materials chemistry. The incorporation of heterocyclic receptors capable of complexing anions through non-covalent interactions (e.g., hydrogen bonding and electrostatic interactions) provides a route to not only sensitive but also selective polymer materials. Furthermore, these systems have been utilized in the development of polymers capable of extracting anionic species from aqueous environments. These latter materials may lead to advances in water purification and treatment of diseases resulting from surplus ions. PMID:20871791
Discrete Fourier transforms of nonuniformly spaced data
NASA Technical Reports Server (NTRS)
Swan, P. R.
1982-01-01
Time series or spatial series of measurements taken with nonuniform spacings have failed to yield fully to analysis using the Discrete Fourier Transform (DFT). This is due to the fact that the formal DFT is the convolution of the transform of the signal with the transform of the nonuniform spacings. Two original methods are presented for deconvolving such transforms for signals containing significant noise. The first method solves a set of linear equations relating the observed data to values defined at uniform grid points, and then obtains the desired transform as the DFT of the uniform interpolates. The second method solves a set of linear equations relating the real and imaginary components of the formal DFT directly to those of the desired transform. The results of numerical experiments with noisy data are presented in order to demonstrate the capabilities and limitations of the methods.
Texture classification using discrete Tchebichef moments.
Marcos, J Víctor; Cristóbal, Gabriel
2013-08-01
In this paper, a method to characterize texture images based on discrete Tchebichef moments is presented. A global signature vector is derived from the moment matrix by taking into account both the magnitudes of the moments and their order. The performance of our method in several texture classification problems was compared with that achieved through other standard approaches. These include Haralick's gray-level co-occurrence matrices, Gabor filters, and local binary patterns. An extensive texture classification study was carried out by selecting images with different contents from the Brodatz, Outex, and VisTex databases. The results show that the proposed method is able to capture the essential information about texture, showing comparable or even higher performance than conventional procedures. Thus, it can be considered as an effective and competitive technique for texture characterization. PMID:24323217
Entanglement swapping between discrete and continuous variables.
Takeda, Shuntaro; Fuwa, Maria; van Loock, Peter; Furusawa, Akira
2015-03-13
We experimentally realize "hybrid" entanglement swapping between discrete-variable (DV) and continuous-variable (CV) optical systems. DV two-mode entanglement as obtainable from a single photon split at a beam splitter is robustly transferred by means of efficient CV entanglement and operations, using sources of squeezed light and homodyne detections. The DV entanglement after the swapping is verified without postselection by the logarithmic negativity of up to 0.28±0.01. Furthermore, our analysis shows that the optimally transferred state can be postselected into a highly entangled state that violates a Clauser-Horne-Shimony-Holt inequality by more than 4 standard deviations, and thus it may serve as a resource for quantum teleportation and quantum cryptography. PMID:25815914
Discrete impulses in ephaptically coupled nerve fibers.
Maïna, I; Tabi, C B; Ekobena Fouda, H P; Mohamadou, A; Kofané, T C
2015-04-01
We exclusively analyze the condition for modulated waves to emerge in two ephaptically coupled nerve fibers. Through the multiple scale expansion, it is shown that a set of coupled cable-like Hodgkin-Huxley equations can be reduced to a single differential-difference nonlinear equation. The standard approach of linear stability analysis of a plane wave is used to predict regions of parameters where nonlinear structures can be observed. Instability features are shown to be importantly controlled not only by the ephaptic coupling parameter, but also by the discreteness parameter. Numerical simulations, to verify our analytical predictions, are performed, and we explore the longtime dynamics of slightly perturbed plane waves in the coupled nerve fibers. On initially exciting only one fiber, quasi-perfect interneuronal communication is discussed along with the possibility of recruiting damaged or non-myelinated nerve fibers, by myelinated ones, into conduction. PMID:25933666
Algorithms for error localization of discrete data
Liepins, G.E.
1984-07-01
A self-contained derivation and evaluation of the three principal algorithms for error localization of discrete data are provided: (1) generation of a sufficient set of edits by single-sweep with fathoming (suggested by the original work by Fellegi and Holt), and (2) sequential row generation (developed by Garfinkel), and (3) modifications of the Chernikova algorithm (suggested by work of Rubin and Sande). The first two approaches can be characterized as Boolean-based, whereas the last is a nonpivoting extremal ray search. The background to the Boolean approaches to data editing is provided, as are Burger's results on extremal rays, Chernikova's original algorithm, and Rubin's modifications. For selected results, new elementary proofs are given in the appendix. For the Chernikova algorithm, novel use is made of the problem structure of localization to minimize the undesirable tendency to generate excessively large matrices.
Semigroups And Computer Algebra In Discrete Structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2010-10-01
Some concepts in semigroup theory are interpreted in discrete structures such as finite lattices, binary relations, and finite semilattices. An algebraic approach to the pseudoinverse generalization problem in Boolean vector spaces is used. By analogy with the linear spaces in the linear algebra semilattice homomorphisms, isomorphisms, projections on Boolean vector spaces are defined and some properties of them are investigated in detail. Maps, corresponding to them in the linear algebra, are connected with matrices and their pseudouinverse. Important properties of these maps, which are essential for solving linear systems, remain the same in the Boolean vector spaces. Stochastic experiments using the maps defined and computer algebra methods have been made for solving linear equations Ax = b. The Hamming distance between b and the projection p(b) = Ax of b is equal or close to the least possible one, if the system has no solutions.
Holography and Mottness: A Discrete Marriage
NASA Astrophysics Data System (ADS)
Phillips, Philip
2012-02-01
Gauge-gravity duality has allowed us to solve the physics of certain strongly coupled quantum mechanical systems using gravity. I will show how a space-time consisting of a charged black hole and a bulk Pauli coupling corresponds to a boundary theory with a dynamically generated gap (with no obvious symmetry breaking) and a massive rearrangement of the spectral weight as in classic Mott systems such as VO2. In this holographic set-up, the gap opens only when discrete scale invariance is present. This raises the possibility that the elusive symmetry that might be broken in Mott insulators, in general, might pertain to scale invariance. The relevance of this claim to recent theories of Mott systems that possess massless charged bosons is explored.
Quadratic relations in continuous and discrete Painlevé equations
NASA Astrophysics Data System (ADS)
Ramani, A.; Grammaticos, B.; Tamizhmani, T.
2000-04-01
The quadratic relations between the solutions of a Painlevé equation and that of a different one, or the same one with a different set of parameters, are investigated in the continuous and discrete cases. We show that the quadratic relations existing for the continuous PII , PIII , PV and PVI have analogues as well as consequences in the discrete case. Moreover, the discrete Painlevé equations have quadratic relations of their own without any reference to the continuous case.
Identification of parameters of discrete-continuous models
Cekus, Dawid Warys, Pawel
2015-03-10
In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.
Global stability for a class of discrete SIR epidemic models.
Enatsu, Yoichi; Nakata, Yukihiko; Muroya, Yoshiaki
2010-04-01
In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method. Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are harmless for the global stability of the endemic equilibrium of the model. PMID:20462293
Anomaly Detection for Discrete Sequences: A Survey
Chandola, Varun; Banerjee, Arindam; Kumar, Vipin
2012-01-01
This survey attempts to provide a comprehensive and structured overview of the existing research for the problem of detecting anomalies in discrete/symbolic sequences. The objective is to provide a global understanding of the sequence anomaly detection problem and how existing techniques relate to each other. The key contribution of this survey is the classification of the existing research into three distinct categories, based on the problem formulation that they are trying to solve. These problem formulations are: 1) identifying anomalous sequences with respect to a database of normal sequences; 2) identifying an anomalous subsequence within a long sequence; and 3) identifying a pattern in a sequence whose frequency of occurrence is anomalous. We show how each of these problem formulations is characteristically distinct from each other and discuss their relevance in various application domains. We review techniques from many disparate and disconnected application domains that address each of these formulations. Within each problem formulation, we group techniques into categories based on the nature of the underlying algorithm. For each category, we provide a basic anomaly detection technique, and show how the existing techniques are variants of the basic technique. This approach shows how different techniques within a category are related or different from each other. Our categorization reveals new variants and combinations that have not been investigated before for anomaly detection. We also provide a discussion of relative strengths and weaknesses of different techniques. We show how techniques developed for one problem formulation can be adapted to solve a different formulation, thereby providing several novel adaptations to solve the different problem formulations. We also highlight the applicability of the techniques that handle discrete sequences to other related areas such as online anomaly detection and time series anomaly detection.
What is integrability of discrete variational systems?
Boll, Raphael; Petrera, Matteo; Suris, Yuri B.
2014-01-01
We propose a notion of a pluri-Lagrangian problem, which should be understood as an analogue of multi-dimensional consistency for variational systems. This is a development along the line of research of discrete integrable Lagrangian systems initiated in 2009 by Lobb and Nijhoff, however, having its more remote roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics and their quasiclassical limit, as well as in the theory of variational symmetries going back to Noether. A d-dimensional pluri-Lagrangian problem can be described as follows: given a d-form on an m-dimensional space (called multi-time, m>d), whose coefficients depend on a sought-after function x of m independent variables (called field), find those fields x which deliver critical points to the action functionals for any d-dimensional manifold Σ in the multi-time. We derive the main building blocks of the multi-time Euler–Lagrange equations for a discrete pluri-Lagrangian problem with d=2, the so-called corner equations, and discuss the notion of consistency of the system of corner equations. We analyse the system of corner equations for a special class of three-point two-forms, corresponding to integrable quad-equations of the ABS list. This allows us to close a conceptual gap of the work by Lobb and Nijhoff by showing that the corresponding two-forms are closed not only on solutions of (non-variational) quad-equations, but also on general solutions of the corresponding corner equations. We also find an example of a pluri-Lagrangian system not coming from a multi-dimensionally consistent system of quad-equations. PMID:24511254
Correlations and discreteness in nonlinear QCD evolution
Armesto, N.; Milhano, J.
2006-06-01
We consider modifications of the standard nonlinear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities y=({alpha}{sub s}N{sub c}/{pi})Y<10. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cutoff evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cutoff. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients.
Distributed discrete event simulation. Final report
De Vries, R.C.
1988-02-01
The presentation given here is restricted to discrete event simulation. The complexity of and time required for many present and potential discrete simulations exceeds the reasonable capacity of most present serial computers. The desire, then, is to implement the simulations on a parallel machine. However, certain problems arise in an effort to program the simulation on a parallel machine. In one category of methods deadlock care arise and some method is required to either detect deadlock and recover from it or to avoid deadlock through information passing. In the second category of methods, potentially incorrect simulations are allowed to proceed. If the situation is later determined to be incorrect, recovery from the error must be initiated. In either case, computation and information passing are required which would not be required in a serial implementation. The net effect is that the parallel simulation may not be much better than a serial simulation. In an effort to determine alternate approaches, important papers in the area were reviewed. As a part of that review process, each of the papers was summarized. The summary of each paper is presented in this report in the hopes that those doing future work in the area will be able to gain insight that might not otherwise be available, and to aid in deciding which papers would be most beneficial to pursue in more detail. The papers are broken down into categories and then by author. Conclusions reached after examining the papers and other material, such as direct talks with an author, are presented in the last section. Also presented there are some ideas that surfaced late in the research effort. These promise to be of some benefit in limiting information which must be passed between processes and in better understanding the structure of a distributed simulation. Pursuit of these ideas seems appropriate.
Discrete integrable systems generated by Hermite-Padé approximants
NASA Astrophysics Data System (ADS)
Aptekarev, Alexander I.; Derevyagin, Maxim; Van Assche, Walter
2016-05-01
We consider Hermite-Padé approximants in the framework of discrete integrable systems defined on the lattice {{{Z}}2} . We show that the concept of multiple orthogonality is intimately related to the Lax representations for the entries of the nearest neighbor recurrence relations and it thus gives rise to a discrete integrable system. We show that the converse statement is also true. More precisely, given the discrete integrable system in question there exists a perfect system of two functions, i.e. a system for which the entire table of Hermite-Padé approximants exists. In addition, we give a few algorithms to find solutions of the discrete system.
Energetically stable discretizations for charge transport and electrokinetic models
NASA Astrophysics Data System (ADS)
Metti, Maximilian S.; Xu, Jinchao; Liu, Chun
2016-02-01
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to particle density functions, and a discrete energy estimate is established that takes the same form as the energy law for the continuous PNP system. This energy estimate is extended to finite element solutions to an electrokinetic model, which couples the PNP system with the incompressible Navier-Stokes equations. Numerical experiments are conducted to validate convergence of the computed solution and verify the discrete energy estimate.
Mimetic discretization of two-dimensional magnetic diffusion equations
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Reynolds, James; Nelson, Eric
2013-08-01
In case of non-constant resistivity, cylindrical coordinates, and highly distorted polygonal meshes, a consistent discretization of the magnetic diffusion equations requires new discretization tools based on a discrete vector and tensor calculus. We developed a new discretization method using the mimetic finite difference framework. It is second-order accurate on arbitrary polygonal meshes and a consistent calculation of the Joule heating is intrinsic within it. The second-order convergence rates in L2 and L1 norms were verified with numerical experiments.
Universal quantum computation using the discrete-time quantum walk
Lovett, Neil B.; Cooper, Sally; Everitt, Matthew; Trevers, Matthew; Kendon, Viv
2010-04-15
A proof that continuous-time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by A. M. Childs [Phys. Rev. Lett. 102, 180501 (2009)]. We present a version based instead on the discrete-time quantum walk. We show that the discrete-time quantum walk is able to implement the same universal gate set and thus both discrete and continuous-time quantum walks are computational primitives. Additionally, we give a set of components on which the discrete-time quantum walk provides perfect state transfer.
A priori discretization quality metrics for distributed hydrologic modeling applications
NASA Astrophysics Data System (ADS)
Liu, Hongli; Tolson, Bryan; Craig, James; Shafii, Mahyar; Basu, Nandita
2016-04-01
In distributed hydrologic modelling, a watershed is treated as a set of small homogeneous units that address the spatial heterogeneity of the watershed being simulated. The ability of models to reproduce observed spatial patterns firstly depends on the spatial discretization, which is the process of defining homogeneous units in the form of grid cells, subwatersheds, or hydrologic response units etc. It is common for hydrologic modelling studies to simply adopt a nominal or default discretization strategy without formally assessing alternative discretization levels. This approach lacks formal justifications and is thus problematic. More formalized discretization strategies are either a priori or a posteriori with respect to building and running a hydrologic simulation model. A posteriori approaches tend to be ad-hoc and compare model calibration and/or validation performance under various watershed discretizations. The construction and calibration of multiple versions of a distributed model can become a seriously limiting computational burden. Current a priori approaches are more formalized and compare overall heterogeneity statistics of dominant variables between candidate discretization schemes and input data or reference zones. While a priori approaches are efficient and do not require running a hydrologic model, they do not fully investigate the internal spatial pattern changes of variables of interest. Furthermore, the existing a priori approaches focus on landscape and soil data and do not assess impacts of discretization on stream channel definition even though its significance has been noted by numerous studies. The primary goals of this study are to (1) introduce new a priori discretization quality metrics considering the spatial pattern changes of model input data; (2) introduce a two-step discretization decision-making approach to compress extreme errors and meet user-specified discretization expectations through non-uniform discretization threshold
Discrete Element Modelling of Floating Debris
NASA Astrophysics Data System (ADS)
Mahaffey, Samantha; Liang, Qiuhua; Parkin, Geoff; Large, Andy; Rouainia, Mohamed
2016-04-01
Flash flooding is characterised by high velocity flows which impact vulnerable catchments with little warning time and as such, result in complex flow dynamics which are difficult to replicate through modelling. The impacts of flash flooding can be made yet more severe by the transport of both natural and anthropogenic debris, ranging from tree trunks to vehicles, wheelie bins and even storage containers, the effects of which have been clearly evident during recent UK flooding. This cargo of debris can have wide reaching effects and result in actual flood impacts which diverge from those predicted. A build-up of debris may lead to partial channel blockage and potential flow rerouting through urban centres. Build-up at bridges and river structures also leads to increased hydraulic loading which may result in damage and possible structural failure. Predicting the impacts of debris transport; however, is difficult as conventional hydrodynamic modelling schemes do not intrinsically include floating debris within their calculations. Subsequently a new tool has been developed using an emerging approach, which incorporates debris transport through the coupling of two existing modelling techniques. A 1D hydrodynamic modelling scheme has here been coupled with a 2D discrete element scheme to form a new modelling tool which predicts the motion and flow-interaction of floating debris. Hydraulic forces arising from flow around the object are applied to instigate its motion. Likewise, an equivalent opposing force is applied to fluid cells, enabling backwater effects to be simulated. Shock capturing capabilities make the tool applicable to predicting the complex flow dynamics associated with flash flooding. The modelling scheme has been applied to experimental case studies where cylindrical wooden dowels are transported by a dam-break wave. These case studies enable validation of the tool's shock capturing capabilities and the coupling technique applied between the two numerical
Dynamics of discrete screw dislocations on glide directions
NASA Astrophysics Data System (ADS)
Alicandro, R.; De Luca, L.; Garroni, A.; Ponsiglione, M.
2016-07-01
We consider a simple discrete model for screw dislocations in crystals. Using a variational discrete scheme we study the motion of a configuration of dislocations toward low energy configurations. We deduce an effective fully overdamped dynamics that follows the maximal dissipation criterion introduced in Cermelli and Gurtin (1999) and predicts motion along the glide directions of the crystal.
Geometric interpretations of the Discrete Fourier Transform (DFT)
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1984-01-01
One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.
On the discrete reconciliation of relativity and quantum mechanics
Noyes, H.P.
1987-03-01
A way is sketched to replace physics based on arbitrary units of mass, length, and time by counting in terms of these quantized values and to replace continuum mathematical physics by computer science. The consequences of such a discrete physics are summarized. These are obtained by postulating finiteness, discreteness, finite computability, absolute non-uniqueness, and additivity. (LEW)
49 CFR 216.27 - Reservation of authority and discretion.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Reservation of authority and discretion. 216.27 Section 216.27 Transportation Other Regulations Relating to Transportation (Continued) FEDERAL RAILROAD..., LOCOMOTIVE AND EQUIPMENT Emergency Order-Track § 216.27 Reservation of authority and discretion. The FRA...
Transfer of dipolar gas through the discrete localized mode.
Bai, Xiao-Dong; Zhang, Ai-Xia; Xue, Ju-Kui
2013-12-01
By considering the discrete nonlinear Schrödinger model with dipole-dipole interactions for dipolar condensate, the existence, the types, the stability, and the dynamics of the localized modes in a nonlinear lattice are discussed. It is found that the contact interaction and the dipole-dipole interactions play important roles in determining the existence, the type, and the stability of the localized modes. Because of the coupled effects of the contact interaction and the dipole-dipole interactions, rich localized modes and their stability nature can exist: when the contact interaction is larger and the dipole-dipole interactions is smaller, a discrete bright breather occurs. In this case, while the on-site interaction can stabilize the discrete breather, the dipole-dipole interactions will destabilize the discrete breather; when both the contact interaction and the dipole-dipole interactions are larger, a discrete kink appears. In this case, both the on-site interaction and the dipole-dipole interactions can stabilize the discrete kink, but the discrete kink is more unstable than the ordinary discrete breather. The predicted results provide a deep insight into the dynamics of blocking, filtering, and transfer of the norm in nonlinear lattices for dipolar condensates. PMID:24483540
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
5 CFR 7.1 - Discretion in filling vacancies.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 5 Administrative Personnel 1 2014-01-01 2014-01-01 false Discretion in filling vacancies. 7.1 Section 7.1 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE RULES GENERAL PROVISIONS... Regulations. He shall exercise his discretion in all personnel actions solely on the basis of merit...
Teach Children with Autism with the Discrete-Trial Approach.
ERIC Educational Resources Information Center
Din, Feng S.; McLaughlin, Donna
This paper discusses the outcomes of a study that investigated whether applying the discrete-trial approach is effective in teaching children with autism to learn functional and pre-academic skills. Participants were four young children with autism (ages 3-4) attending a preschool special education program of an urban public school. Discrete-trial…
Transequatorial propagation through equatorial plasma bubbles - Discrete events
NASA Astrophysics Data System (ADS)
Heron, M. L.
1980-08-01
The discrete nature of VHF transequatorial propagation path openings is pointed out. These events are shown to be consistent with the concept of guided propagation inside equatorial plasma bubbles. The important prediction of this work is that observations on discrete transequatorial VHF links may be used to track the production and development of equatorial plasma bubbles.
Coxeter's frieze patterns and discretization of the Virasoro orbit
NASA Astrophysics Data System (ADS)
Ovsienko, Valentin; Tabachnikov, Serge
2015-01-01
We show that the space of classical Coxeter's frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of Kirillov's symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.
Non-Lipschitz Dynamics Approach to Discrete Event Systems
NASA Technical Reports Server (NTRS)
Zak, M.; Meyers, R.
1995-01-01
This paper presents and discusses a mathematical formalism for simulation of discrete event dynamics (DED) - a special type of 'man- made' system designed to aid specific areas of information processing. A main objective is to demonstrate that the mathematical formalism for DED can be based upon the terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.
Two-dimensional discrete Ginzburg-Landau solitons
Efremidis, Nikolaos K.; Christodoulides, Demetrios N.; Hizanidis, Kyriakos
2007-10-15
We study the two-dimensional discrete Ginzburg-Landau equation. In the linear limit, the dispersion and gain curves as well as the diffraction pattern are determined analytically. In the nonlinear case, families of two-dimensional discrete solitons are found numerically as well as approximately in the high-confinement limit. The instability dynamics are analyzed by direct simulations.
Wheat mill stream properties for discrete element method modeling
Technology Transfer Automated Retrieval System (TEKTRAN)
A discrete phase approach based on individual wheat kernel characteristics is needed to overcome the limitations of previous statistical models and accurately predict the milling behavior of wheat. As a first step to develop a discrete element method (DEM) model for the wheat milling process, this s...
Laurent phenomenon algebras and the discrete BKP equation
NASA Astrophysics Data System (ADS)
Okubo, Naoto
2016-09-01
We construct the Laurent phenomenon algebras the cluster variables of which satisfy the discrete BKP equation, the discrete Sawada–Kotera equation and other difference equations obtained by its reduction. These Laurent phenomenon algebras are constructed from seeds with a generalization of mutation-period property. We show that a reduction of a seed corresponds to a reduction of a difference equation.
How Bob Barker Would (Probably) Teach Discrete Mathematics
ERIC Educational Resources Information Center
Urness, Timothy
2010-01-01
This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…
Discretion in Student Discipline: Insight into Elementary Principals' Decision Making
ERIC Educational Resources Information Center
Findlay, Nora M.
2015-01-01
Little research exists that examines the exercise of discretion by principals in their disciplinary decision making. This study sought to understand the application of values by principals as they engage in student disciplinary decision making within legally fixed parameters of their administrative discretion. This qualitative methodology used…
31 CFR 101.8 - Discretion of the Secretary.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 31 Money and Finance: Treasury 1 2014-07-01 2014-07-01 false Discretion of the Secretary. 101.8 Section 101.8 Money and Finance: Treasury Regulations Relating to Money and Finance MONETARY OFFICES, DEPARTMENT OF THE TREASURY MITIGATION OF FORFEITURE OF COUNTERFEIT GOLD COINS § 101.8 Discretion of...
31 CFR 101.8 - Discretion of the Secretary.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 31 Money and Finance: Treasury 1 2013-07-01 2013-07-01 false Discretion of the Secretary. 101.8 Section 101.8 Money and Finance: Treasury Regulations Relating to Money and Finance MONETARY OFFICES, DEPARTMENT OF THE TREASURY MITIGATION OF FORFEITURE OF COUNTERFEIT GOLD COINS § 101.8 Discretion of...
Discrete Latent Markov Models for Normally Distributed Response Data
ERIC Educational Resources Information Center
Schmittmann, Verena D.; Dolan, Conor V.; van der Maas, Han L. J.; Neale, Michael C.
2005-01-01
Van de Pol and Langeheine (1990) presented a general framework for Markov modeling of repeatedly measured discrete data. We discuss analogical single indicator models for normally distributed responses. In contrast to discrete models, which have been studied extensively, analogical continuous response models have hardly been considered. These…
Discretizing singular point sources in hyperbolic wave propagation problems
NASA Astrophysics Data System (ADS)
Petersson, N. Anders; O'Reilly, Ossian; Sjögreen, Björn; Bydlon, Samuel
2016-09-01
We develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as the number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.
A Two-Timescale Discretization Scheme for Collocation
NASA Technical Reports Server (NTRS)
Desai, Prasun; Conway, Bruce A.
2004-01-01
The development of a two-timescale discretization scheme for collocation is presented. This scheme allows a larger discretization to be utilized for smoothly varying state variables and a second finer discretization to be utilized for state variables having higher frequency dynamics. As such. the discretization scheme can be tailored to the dynamics of the particular state variables. In so doing. the size of the overall Nonlinear Programming (NLP) problem can be reduced significantly. Two two-timescale discretization architecture schemes are described. Comparison of results between the two-timescale method and conventional collocation show very good agreement. Differences of less than 0.5 percent are observed. Consequently. a significant reduction (by two-thirds) in the number of NLP parameters and iterations required for convergence can be achieved without sacrificing solution accuracy.
Setting up virgin stress conditions in discrete element models
Rojek, J.; Karlis, G.F.; Malinowski, L.J.; Beer, G.
2013-01-01
In the present work, a methodology for setting up virgin stress conditions in discrete element models is proposed. The developed algorithm is applicable to discrete or coupled discrete/continuum modeling of underground excavation employing the discrete element method (DEM). Since the DEM works with contact forces rather than stresses there is a need for the conversion of pre-excavation stresses to contact forces for the DEM model. Different possibilities of setting up virgin stress conditions in the DEM model are reviewed and critically assessed. Finally, a new method to obtain a discrete element model with contact forces equivalent to given macroscopic virgin stresses is proposed. The test examples presented show that good results may be obtained regardless of the shape of the DEM domain. PMID:27087731
Structure of an energetic narrow discrete arc
NASA Technical Reports Server (NTRS)
Mcfadden, J. P.; Carlson, C. W.; Boehm, M. H.
1990-01-01
Particle distributions, waves, dc electric fields, and magnetic fields were measured by two sounding rockets at altitudes of 950 and 430 km through an energetic (greater than 5 keV) narrow (about 10 km) stable discrete arc. Although the payloads' magnetic footprints were separated by only 50 km, differences in the arc's structure were observed including the spatial width, peak energy, and characteristic spectra. The energetic electron precipitation included both slowly varying isotropic fluxes that formed an inverted-V energy-time signature and rapidly varying field-aligned fluxes at or below the isotropic spectral peak. The isotropic precipitation had a flux discontinuity inside the arc indicating the arc was present on a boundary between two different magnetospheric plasmas. Dispersive and nondispersive bursts of field-aligned electrons were measured throughout the arc, appearing over broad energy ranges or as monoenergetic beams. Dispersive bursts gave variable source distances less than 8000 km. Plateauing of some of the most intense bursts suggests that waves stabilized these electrons. During the lower altitude arc crossing, the field-aligned component formed a separate inverted-V energy-time signature whose peak energy was half the isotropic peak energy.
Dynamics of a discrete auroral arc
NASA Technical Reports Server (NTRS)
Bruening, K.; Goertz, C. K.
1986-01-01
Porcupine Flight 4 data were used to determine the field-aligned currents associated with a southward moving discrete auroral arc in the postmidnight sector. Three different methods were used for determining the field-aligned current which should give identical results if the arcs are quasi-stationary and no parallel electric field exists between the payload and the dynamo region of the ionosphere. As long as the rocket is above the arc, the three methods agree. The integral of precipitating electron flux, the local magnetic field perturbations, and the divergence of the horizontal Pedersen current all indicate an upward current of 5 + or - 3 microamperes/sq m. Immediately north of the arc a strong downward current of about 10-20 microamperes/sq m is detected. The magnitude, however, is not well known because the rocket's velocity relative to the arc cannot be clearly established. Further north of the southward moving arc, the two methods that can be applied (magnetic field perturbations and divergence of the horizontal Pedersen current) yield contradictory results not only about the magnitude of the current but also about the direction of the current. It is suggested that this discrepancy is due to time-dependent electric field.
Discrete interferometer with individual trapped atoms
NASA Astrophysics Data System (ADS)
Steffen, Andreas; Alberti, Andrea; Alt, Wolfgang; Belmechri, Noomen; Hild, Sebastian; Karski, Michal; Widera, Artur; Meschede, Dieter; Quantum Technology Team
2011-05-01
Coherent control and delocalization of individual atoms is a pivotal challenge in quantum technologies. As a new step on this road, we present an individual atom interferometer that is capable of splitting a trapped Cs atom by up to 10 μm , allowing us to measure potential gradients on the microscale. The atom is confined in a 1D optical lattice, which is capable of performing discrete state-dependent shifts to split the atom by the desired number of sites. We establish a high degree of control, as the initial atom position, vibrational state and spin state can all be prepared with above 95% fidelity. To unravel decoherence effects and phase influences, we have explored several basic interferometer geometries, among other things demonstrating a positional spin echo to cancel background effects. As a test case, an inertial force has been applied and successfully measured using the atomic phase. This will offer us a new tool to investigate the interaction between two atoms in a controlled model system.
Dynamics of a discrete auroral arc
NASA Astrophysics Data System (ADS)
Bruening, K.; Goertz, C. K.
1986-06-01
Porcupine Flight 4 data were used to determine the field-aligned currents associated with a southward moving discrete auroral arc in the postmidnight sector. Three different methods were used for determining the field-aligned current which should give identical results if the arcs are quasi-stationary and no parallel electric field exists between the payload and the dynamo region of the ionosphere. As long as the rocket is above the arc, the three methods agree. The integral of precipitating electron flux, the local magnetic field perturbations, and the divergence of the horizontal Pedersen current all indicate an upward current of 5 + or - 3 microamperes/sq m. Immediately north of the arc a strong downward current of about 10-20 microamperes/sq m is detected. The magnitude, however, is not well known because the rocket's velocity relative to the arc cannot be clearly established. Further north of the southward moving arc, the two methods that can be applied (magnetic field perturbations and divergence of the horizontal Pedersen current) yield contradictory results not only about the magnitude of the current but also about the direction of the current. It is suggested that this discrepancy is due to time-dependent electric field.
Simulating Electrophoresis with Discrete Charge and Drag
NASA Astrophysics Data System (ADS)
Mowitz, Aaron J.; Witten, Thomas A.
A charged asymmetric rigid cluster of colloidal particles in saline solution can respond in exotic ways to an electric field: it may spin or move transversely. These distinctive motions arise from the drag force of the neutralizing countercharge surrounding the cluster. Because of this drag, calculating the motion of arbitrary asymmetric objects with nonuniform charge is impractical by conventional methods. Here we present a new method of simulating electrophoresis, in which we replace the continuous object and the surrounding countercharge with discrete point-draggers, called Stokeslets. The balance of forces imposes a linear, self-consistent relation among the drag and Coulomb forces on the Stokeslets, which allows us to easily determine the object's motion via matrix inversion. By explicitly enforcing charge+countercharge neutrality, the simulation recovers the distinctive features of electrophoretic motion to few-percent accuracy using as few as 1000 Stokeslets. In particular, for uniformly charged objects, we observe the characteristic Smoluchowski independence of mobility on object size and shape. We then discuss electrophoretic motion of asymmetric objects, where our simulation method is particularly advantageous. This work is supported by a Grant from the US-Israel Binational Science Foundation.
Discrete breathers in alpha-uranium
NASA Astrophysics Data System (ADS)
Murzaev, Ramil T.; Babicheva, Rita I.; Zhou, Kun; Korznikova, Elena A.; Fomin, Sergey Yu.; Dubinko, Vladimir I.; Dmitriev, Sergey V.
2016-07-01
Uranium is an important radioactive material used in the field of nuclear energy and it is interesting from the scientific point of view because it possesses unique structure and properties. There exist several experimental reports on anomalies of physical properties of uranium that have not been yet explained. Manley et al. [Phys. Rev. Lett. 96, 125501 (2006); Phys. Rev. B 77, 214305 (2008)] speculate that the excitation of discrete breathers (DBs) could be the reason for anisotropy of thermal expansion and for the deviation of heat capacity from the theoretical prediction in the high temperature range. In the present work, with the use of molecular dynamics, the existence of DBs in α-uranium is demonstrated and their properties are studied. It is found that DB frequency lies above the phonon band and increases with DB amplitude. DB is localized on half a dozen of atoms belonging to a straight atomic chain. DB in uranium, unlike DBs in fcc, bcc and hcp metals, is almost immobile. Thus, the DB reported in this study cannot contribute to thermal conductivity and the search for other types of DBs in α-uranium should be continued. Our results demonstrate that even metals with low-symmetry crystal lattices such as the orthorhombic lattice of α-uranium can support DBs.
Information storage capacity of discrete spin systems
Yoshida, Beni
2013-11-15
Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations. -- Highlights: •We propose a spin model with fractal ground states and study its coding properties. •We show that the model asymptotically saturates a theoretical limit on information storage capacity. •We discuss its relations to various theoretical physics problems.
Discrete element modeling of subglacial sediment deformation
NASA Astrophysics Data System (ADS)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.; Tulaczyk, Slawek; Larsen, Nicolaj K.; Tylmann, Karol
2013-12-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis of the material dynamics and the shear zone development during progressive shear strain. The geometry of the heterogeneous stress network is visible in the form of force-carrying grain bridges and adjacent, volumetrically dominant, inactive zones. We demonstrate how the shear zone thickness and dilation depend on the level of normal (overburden) stress, and we show how high normal stress can mobilize material to great depths. The particle rotational axes tend to align with progressive shear strain, with rotations both along and reverse to the shear direction. The results from successive laboratory ring-shear experiments on simple granular materials are compared to results from similar numerical experiments. The simulated DEM material and all tested laboratory materials deform by an elastoplastic rheology under the applied effective normal stress. These results demonstrate that the DEM is a viable alternative to continuum models for small-scale analysis of sediment deformation. It can be used to simulate the macromechanical behavior of simple granular sediments, and it provides an opportunity to study how microstructures in subglacial sediments are formed during progressive shear strain.
Variance Reduction for a Discrete Velocity Gas
NASA Astrophysics Data System (ADS)
Morris, A. B.; Varghese, P. L.; Goldstein, D. B.
2011-05-01
We extend a variance reduction technique developed by Baker and Hadjiconstantinou [1] to a discrete velocity gas. In our previous work, the collision integral was evaluated by importance sampling of collision partners [2]. Significant computational effort may be wasted by evaluating the collision integral in regions where the flow is in equilibrium. In the current approach, substantial computational savings are obtained by only solving for the deviations from equilibrium. In the near continuum regime, the deviations from equilibrium are small and low noise evaluation of the collision integral can be achieved with very coarse statistical sampling. Spatially homogenous relaxation of the Bobylev-Krook-Wu distribution [3,4], was used as a test case to verify that the method predicts the correct evolution of a highly non-equilibrium distribution to equilibrium. When variance reduction is not used, the noise causes the entropy to undershoot, but the method with variance reduction matches the analytic curve for the same number of collisions. We then extend the work to travelling shock waves and compare the accuracy and computational savings of the variance reduction method to DSMC over Mach numbers ranging from 1.2 to 10.
Discrete Element Modeling for Mobility and Excavation
NASA Astrophysics Data System (ADS)
Knuth, M. A.; Hopkins, M. A.
2011-12-01
The planning and completion of mobility and excavation efforts on the moon requires a thorough understanding of the planetary regolith. In this work, a discrete element method (DEM) model is created to replicate those activities in the laboratory and for planning mission activities in the future. The crux of this work is developing a particle bed that best replicates the regolith tool/wheel interaction seen in the laboratory. To do this, a DEM geotechnical triaxial strength cell was created allowing for comparison of laboratory JSC-1a triaxial tests to DEM simulated soils. This model relies on a triangular lattice membrane covered triaxial cell for determining the macroscopic properties of the modeled granular material as well as a fast and efficient contact detection algorithm for a variety of grain shapes. Multiple grain shapes with increasing complexity (ellipsoid, poly-ellipsoid and polyhedra) have been developed and tested. This comparison gives us a basis to begin scaling DEM grain size and shape to practical values for mobility and excavation modeling. Next steps include development of a DEM scoop for percussive excavation testing as well as continued analysis of rover wheel interactions using a wide assortment of grain shape and size distributions.
Dimensional flow in discrete quantum geometries
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes
2015-04-01
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension d at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number 0 <α
HODIF:High-Order Discretizations, Interpolations and
Kennedy, Christopher A.; Carpenter, Mark H.; Ray, Jaideen
2006-06-20
This software, a library, contains FORTRAN77 subroutines to calculate first and second derivatives up to 8th order, interpolations (1D and 2D) up to 10th order and filters up to 14th order. Only even orders are addressed and finite-difference stencils are implemented on a vertex-centered mesh. The primary aim of this library is to be used in block-structured adaptive mesh simulations where high order is desired. The interpolants in this library are essentially designed to do prolongations and restrictions between levels of rfinement - however, they assume that the refinement ratio is 2. The filters are provided to remove high wavenumber content from solutions in case Runge phenomenon occurs - a common occurrence in case of marginal resolution of the solution. Details of the derivation and use are to be found in "Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations and filters", by J. Ray, C.A. Kennedy, S. Lefantzi and H.N. Najm, Sandia Technical Report, SAND2005-7981. The software comes with a User's Guide and examples how to use it.
HODIF:High-Order Discretizations, Interpolations and
Energy Science and Technology Software Center (ESTSC)
2006-06-20
This software, a library, contains FORTRAN77 subroutines to calculate first and second derivatives up to 8th order, interpolations (1D and 2D) up to 10th order and filters up to 14th order. Only even orders are addressed and finite-difference stencils are implemented on a vertex-centered mesh. The primary aim of this library is to be used in block-structured adaptive mesh simulations where high order is desired. The interpolants in this library are essentially designed to domore » prolongations and restrictions between levels of rfinement - however, they assume that the refinement ratio is 2. The filters are provided to remove high wavenumber content from solutions in case Runge phenomenon occurs - a common occurrence in case of marginal resolution of the solution. Details of the derivation and use are to be found in "Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations and filters", by J. Ray, C.A. Kennedy, S. Lefantzi and H.N. Najm, Sandia Technical Report, SAND2005-7981. The software comes with a User's Guide and examples how to use it.« less
Discrete range clustering using Monte Carlo methods
NASA Technical Reports Server (NTRS)
Chatterji, G. B.; Sridhar, B.
1993-01-01
For automatic obstacle avoidance guidance during rotorcraft low altitude flight, a reliable model of the nearby environment is needed. Such a model may be constructed by applying surface fitting techniques to the dense range map obtained by active sensing using radars. However, for covertness, passive sensing techniques using electro-optic sensors are desirable. As opposed to the dense range map obtained via active sensing, passive sensing algorithms produce reliable range at sparse locations, and therefore, surface fitting techniques to fill the gaps in the range measurement are not directly applicable. Both for automatic guidance and as a display for aiding the pilot, these discrete ranges need to be grouped into sets which correspond to objects in the nearby environment. The focus of this paper is on using Monte Carlo methods for clustering range points into meaningful groups. One of the aims of the paper is to explore whether simulated annealing methods offer significant advantage over the basic Monte Carlo method for this class of problems. We compare three different approaches and present application results of these algorithms to a laboratory image sequence and a helicopter flight sequence.
Discrete Signal Processing on Graphs: Sampling Theory
NASA Astrophysics Data System (ADS)
Chen, Siheng; Varma, Rohan; Sandryhaila, Aliaksei; Kovacevic, Jelena
2015-12-01
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited under the graph Fourier transform. The sampled signal coefficients form a new graph signal, whose corresponding graph structure preserves the first-order difference of the original graph signal. For general graphs, an optimal sampling operator based on experimentally designed sampling is proposed to guarantee perfect recovery and robustness to noise; for graphs whose graph Fourier transforms are frames with maximal robustness to erasures as well as for Erd\\H{o}s-R\\'enyi graphs, random sampling leads to perfect recovery with high probability. We further establish the connection to the sampling theory of finite discrete-time signal processing and previous work on signal recovery on graphs. To handle full-band graph signals, we propose a graph filter bank based on sampling theory on graphs. Finally, we apply the proposed sampling theory to semi-supervised classification on online blogs and digit images, where we achieve similar or better performance with fewer labeled samples compared to previous work.
Monarch butterfly spatially discrete advection model.
Yakubu, Abdul-Aziz; Sáenz, Roberto; Stein, Julie; Jones, Laura E
2004-08-01
We study the population cycles of the Monarch butterfly using one of the simplest systems incorporating both migration and local dynamics. The annual migration of the Monarch involves four generations. Members of Generations 1-3 (occasionally 4) migrate from the over-wintering site in Central Mexico to breeding grounds that extend as far north as the Northern United States and Southern Canada. A portion of the Generation 3 and all members of the Generation 4 butterflies begin their return to the over-wintering grounds in August through October where they enter reproductive diapause for several months. We developed a simple discrete-time island chain model in which different fecundity functions are used to model the reproductive strategies of each generation. The fecundity functions are selected from broad classes of functions that capture the effects of either contest or scramble intraspecific competition in the Monarch population. The objectives of our research are multiple and include the study of the generationally dependent intraspecific competition and its effect on the pool size of migrants as well as the persistence of the overall butterfly populations. The stage structure used in modeling the Monarch butterfly dynamics and their generationally dependent reproductive strategies naturally support fluctuating patterns and multiple attractors. The implications of these fluctuations and attractors on the long-term survival of the Monarch butterfly population are explored. PMID:15234616
Discrete analysis of stochastic NMR.II
NASA Astrophysics Data System (ADS)
Wong, S. T. S.; Rods, M. S.; Newmark, R. D.; Budinger, T. F.
Stochastic NMR is an efficient technique for high-field in vivo imaging and spectroscopic studies where the peak RF power required may be prohibitively high for conventional pulsed NMR techniques. A stochastic NMR experiment excites the spin system with a sequence of RF pulses where the flip angles or the phases of the pulses are samples of a discrete stochastic process. In a previous paper the stochastic experiment was analyzed and analytic expressions for the input-output cross-correlations, average signal power, and signal spectral density were obtained for a general stochastic RF excitation. In this paper specific cases of excitation with random phase, fixed flip angle, and excitation with two random components in quadrature are analyzed. The input-output cross-correlation for these two types of excitations is shown to be Lorentzian. Line broadening is the only spectral distortion as the RF excitation power is increased. The systematic noise power is inversely proportional to the number of data points N used in the spectral reconstruction. The use of a complete maximum length sequence (MLS) may improve the signal-to-systematic-noise ratio by 20 dB relative to random binary excitation, but peculiar features in the higher-order autocorrelations of MLS cause noise-like distortion in the reconstructed spectra when the excitation power is high. The amount of noise-like distortion depends on the choice of the MLS generator.
Tejero, E. M.; Gatling, G.
2009-03-15
A method for approximating arbitrary axial magnetic field profiles for a given solenoidal electromagnet coil array is described. The method casts the individual contributions from each coil as a truncated orthonormal basis for the space within the array. This truncated basis allows for the linear decomposition of an arbitrary profile function, which returns the appropriate currents for each coil to best reproduce the desired profile. We present the mathematical details of the method along with a detailed example of its use. The results from the method are used in a simulation and compared with magnetic field measuremen0008.
Discrete Pathophysiology is Uncommon in Patients with Nonspecific Arm Pain
Kortlever, Joost T.P.; Janssen, Stein J.; Molleman, Jeroen; Hageman, Michiel G.J.S.; Ring, David
2016-01-01
Background: Nonspecific symptoms are common in all areas of medicine. Patients and caregivers can be frustrated when an illness cannot be reduced to a discrete pathophysiological process that corresponds with the symptoms. We therefore asked the following questions: 1) Which demographic factors and psychological comorbidities are associated with change from an initial diagnosis of nonspecific arm pain to eventual identification of discrete pathophysiology that corresponds with symptoms? 2) What is the percentage of patients eventually diagnosed with discrete pathophysiology, what are those pathologies, and do they account for the symptoms? Methods: We evaluated 634 patients with an isolated diagnosis of nonspecific upper extremity pain to see if discrete pathophysiology was diagnosed on subsequent visits to the same hand surgeon, a different hand surgeon, or any physician within our health system for the same pain. Results: There were too few patients with discrete pathophysiology at follow-up to address the primary study question. Definite discrete pathophysiology that corresponded with the symptoms was identified in subsequent evaluations by the index surgeon in one patient (0.16% of all patients) and cured with surgery (nodular fasciitis). Subsequent doctors identified possible discrete pathophysiology in one patient and speculative pathophysiology in four patients and the index surgeon identified possible discrete pathophysiology in four patients, but the five discrete diagnoses accounted for only a fraction of the symptoms. Conclusion: Nonspecific diagnoses are not harmful. Prospective randomized research is merited to determine if nonspecific, descriptive diagnoses are better for patients than specific diagnoses that imply pathophysiology in the absence of discrete verifiable pathophysiology. PMID:27517064
Discrete Wavelength-Locked External Cavity Laser
NASA Technical Reports Server (NTRS)
Pilgrim, Jeffrey S.; Silver, Joel A.
2004-01-01
A prototype improved external cavity laser (ECL) was demonstrated in the second phase of a continuing effort to develop wavelength-agile lasers for fiber-optic communications and trace-gas-sensing applications. This laser is designed to offer next-generation performance for incorporation into fiber-optic networks. By eliminating several optical components and simplifying others used in prior designs, the design of this laser reduces costs, making lasers of this type very competitive in a price-sensitive market. Diode lasers have become enabling devices for fiber optic networks because of their cost, compactness, and spectral properties. ECLs built around diode laser gain elements further enhance capabilities by virtue of their excellent spectral properties with significantly increased (relative to prior lasers) wavelength tuning ranges. It is essential to exploit the increased spectral coverage of ECLs while simultaneously insuring that they operate only at precisely defined communication channels (wavelengths). Heretofore, this requirement has typically been satisfied through incorporation of add-in optical components that lock the ECL output wavelengths to these specific channels. Such add-in components contribute substantially to the costs of ECL lasers to be used as sources for optical communication networks. Furthermore, the optical alignment of these components, needed to attain the required wavelength precision, is a non-trivial task and can contribute substantially to production costs. The design of the present improved ECL differs significantly from the designs of prior ECLs. The present design relies on inherent features of components already included within an ECL, with slight modifications so that these components perform their normal functions while simultaneously effecting locking to the required discrete wavelengths. Hence, add-in optical components and the associated cost of alignment can be eliminated. The figure shows the locking feedback signal
A discrete perspective on nonlinear dimension reduction
NASA Astrophysics Data System (ADS)
Bogner, Christina; Trancón y Widemann, Baltasar; Lange, Holger
2013-04-01
Environmental data sets are often large and high-dimensional and thus difficult to visualize and analyze. In hydrology, for example, we often deal with time series from long-term physical and chemical monitoring of stream water, groundwater or soils. These data can be seen as a multivariate characteristic of chemico-physical properties of water or soil and are used to infer processes in ecosystems. Despite their high dimensionality, ecological data are often assumed to have a simple underlying intrinsic structure. It means that despite their high-dimensional nature they can be summarized in less dimensions without a serious loss of information. Therefore, dimensionality reduction techniques are often the first step to data analysis. They are used to visualize data as well as to uncover the intrinsic (low-dimensional) structure. As an example application, we use high-dimensional hydrochemical data at the headwater catchment level (ion concentrations from first-order streams). We investigate the Isometric Feature Mapping (Isomap), a popular method for non-linear dimension reduction. Here, the topology of the data set is approximated by constructing a local neighbourhood graph. However, the assumption of smoothness underlying this approximation is difficult to justify for many environmental data sets, and issues of measurement errors and sampling gaps render Isomap analyses questionable. Thus, we extend our methodology by an analogous, but more robust, discrete (non-smooth) transformation leading to a set of binary data. For the latter, a plethora of data-mining techniques, in particular unsupervised and semi-supervised machine learning algorithms, exists. These can be employed to automate or support classification and feature detection tasks, taking the non-linear structure of available data into account. First results of this newly developed analysis method will be presented.
Discrete Element Modeling of Triboelectrically Charged Particles
NASA Technical Reports Server (NTRS)
Hogue, Michael D.; Calle, Carlos I.; Weitzman, Peter S.; Curry, David R.
2008-01-01
Tribocharging of particles is common in many processes including fine powder handling and mixing, printer toner transport and dust extraction. In a lunar environment with its high vacuum and lack of water, electrostatic forces are an important factor to consider when designing and operating equipment. Dust mitigation and management is critical to safe and predictable performance of people and equipment. The extreme nature of lunar conditions makes it difficult and costly to carry out experiments on earth which are necessary to better understand how particles gather and transfer charge between each other and with equipment surfaces. DEM (Discrete Element Modeling) provides an excellent virtual laboratory for studying tribocharging of particles as well as for design of devices for dust mitigation and for other purposes related to handling and processing of lunar regolith. Theoretical and experimental work has been performed pursuant to incorporating screened Coulombic electrostatic forces into EDEM, a commercial DEM software package. The DEM software is used to model the trajectories of large numbers of particles for industrial particulate handling and processing applications and can be coupled with other solvers and numerical models to calculate particle interaction with surrounding media and force fields. While simple Coulombic force between two particles is well understood, its operation in an ensemble of particles is more complex. When the tribocharging of particles and surfaces due to frictional contact is also considered, it is necessary to consider longer range of interaction of particles in response to electrostatic charging. The standard DEM algorithm accounts for particle mechanical properties and inertia as a function of particle shape and mass. If fluid drag is neglected, then particle dynamics are governed by contact between particles, between particles and equipment surfaces and gravity forces. Consideration of particle charge and any tribocharging and
LAN attack detection using Discrete Event Systems.
Hubballi, Neminath; Biswas, Santosh; Roopa, S; Ratti, Ritesh; Nandi, Sukumar
2011-01-01
Address Resolution Protocol (ARP) is used for determining the link layer or Medium Access Control (MAC) address of a network host, given its Internet Layer (IP) or Network Layer address. ARP is a stateless protocol and any IP-MAC pairing sent by a host is accepted without verification. This weakness in the ARP may be exploited by malicious hosts in a Local Area Network (LAN) by spoofing IP-MAC pairs. Several schemes have been proposed in the literature to circumvent these attacks; however, these techniques either make IP-MAC pairing static, modify the existing ARP, patch operating systems of all the hosts etc. In this paper we propose a Discrete Event System (DES) approach for Intrusion Detection System (IDS) for LAN specific attacks which do not require any extra constraint like static IP-MAC, changing the ARP etc. A DES model is built for the LAN under both a normal and compromised (i.e., spoofed request/response) situation based on the sequences of ARP related packets. Sequences of ARP events in normal and spoofed scenarios are similar thereby rendering the same DES models for both the cases. To create different ARP events under normal and spoofed conditions the proposed technique uses active ARP probing. However, this probing adds extra ARP traffic in the LAN. Following that a DES detector is built to determine from observed ARP related events, whether the LAN is operating under a normal or compromised situation. The scheme also minimizes extra ARP traffic by probing the source IP-MAC pair of only those ARP packets which are yet to be determined as genuine/spoofed by the detector. Also, spoofed IP-MAC pairs determined by the detector are stored in tables to detect other LAN attacks triggered by spoofing namely, man-in-the-middle (MiTM), denial of service etc. The scheme is successfully validated in a test bed. PMID:20804980
Discrete element modelling of subglacial sediment deformation
NASA Astrophysics Data System (ADS)
Christensen, A. D.; Egholm, D. L.; Piotrowski, J. A.; Tulaczyk, S.
2012-04-01
Soft, deformable sediments are often present under glaciers. Subglacial sediments deform under the differential load of the ice, and this causes the overlying glacier to accelerate its motion. Understanding the rheology of subglacial sediment is therefore important for models of glacial dynamics. Previous studies of the mechanical behaviour of subglacial sediments have primarily relied on analytical considerations and laboratory shearing experiments. As a novel approach, the Discrete Element Method (DEM) is used to explore the highly nonlinear dynamics of a granular bed that is exposed to stress conditions comparable to subglacial environments. The numerical approach allows close monitoring of the mechanical and rheological behaviour under a range of conditions. Of special interest is bed shear strength, strain distribution and -localization, mode of deformation, and role of effective normal pressure during shearing. As a calibration benchmark, results from laboratory ring-shear experiments on granular material are compared to similar numerical experiments. The continuously recorded stress dynamics in the laboratory shear experiments are compared to DEM experiments, and the micro-mechanical parameters in the contact model of the DEM code are calibrated to match the macroscopic Mohr-Coulomb failure criteria parameters, constrained from successive laboratory shear tests under a range of normal pressures. The data-parallel nature of the basic DEM formulation makes the problem ideal for utilizing the high arithmetic potential of modern general-purpose GPUs. Using the Nvidia Cuda C toolkit, the algorithm is formulated for spherical particles in three dimensions with a soft-body contact model. Scene rendering is performed using a custom Cuda ray-tracing algorithm. Efforts on optimization of the particle algorithm are discussed, and future plans of expansion are presented.
High-temperature discrete dislocation plasticity
NASA Astrophysics Data System (ADS)
Keralavarma, S. M.; Benzerga, A. A.
2015-09-01
A framework for solving problems of dislocation-mediated plasticity coupled with point-defect diffusion is presented. The dislocations are modeled as line singularities embedded in a linear elastic medium while the point defects are represented by a concentration field as in continuum diffusion theory. Plastic flow arises due to the collective motion of a large number of dislocations. Both conservative (glide) and nonconservative (diffusion-mediated climb) motions are accounted for. Time scale separation is contingent upon the existence of quasi-equilibrium dislocation configurations. A variational principle is used to derive the coupled governing equations for point-defect diffusion and dislocation climb. Superposition is used to obtain the mechanical fields in terms of the infinite-medium discrete dislocation fields and an image field that enforces the boundary conditions while the point-defect concentration is obtained by solving the stress-dependent diffusion equations on the same finite-element grid. Core-level boundary conditions for the concentration field are avoided by invoking an approximate, yet robust kinetic law. Aspects of the formulation are general but its implementation in a simple plane strain model enables the modeling of high-temperature phenomena such as creep, recovery and relaxation in crystalline materials. With emphasis laid on lattice vacancies, the creep response of planar single crystals in simple tension emerges as a natural outcome in the simulations. A large number of boundary-value problem solutions are obtained which depict transitions from diffusional to power-law creep, in keeping with long-standing phenomenological theories of creep. In addition, some unique experimental aspects of creep in small scale specimens are also reproduced in the simulations.
Fast and Accurate Learning When Making Discrete Numerical Estimates.
Sanborn, Adam N; Beierholm, Ulrik R
2016-04-01
Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates. PMID:27070155
Fast and Accurate Learning When Making Discrete Numerical Estimates
Sanborn, Adam N.; Beierholm, Ulrik R.
2016-01-01
Many everyday estimation tasks have an inherently discrete nature, whether the task is counting objects (e.g., a number of paint buckets) or estimating discretized continuous variables (e.g., the number of paint buckets needed to paint a room). While Bayesian inference is often used for modeling estimates made along continuous scales, discrete numerical estimates have not received as much attention, despite their common everyday occurrence. Using two tasks, a numerosity task and an area estimation task, we invoke Bayesian decision theory to characterize how people learn discrete numerical distributions and make numerical estimates. Across three experiments with novel stimulus distributions we found that participants fell between two common decision functions for converting their uncertain representation into a response: drawing a sample from their posterior distribution and taking the maximum of their posterior distribution. While this was consistent with the decision function found in previous work using continuous estimation tasks, surprisingly the prior distributions learned by participants in our experiments were much more adaptive: When making continuous estimates, participants have required thousands of trials to learn bimodal priors, but in our tasks participants learned discrete bimodal and even discrete quadrimodal priors within a few hundred trials. This makes discrete numerical estimation tasks good testbeds for investigating how people learn and make estimates. PMID:27070155
Discrete elements method of neutral particle transport. Doctoral thesis
Mathews, K.A.
1983-10-01
A new 'discrete elements' (LN) transport method is derived and compared to the discrete ordinates SN method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, LN is more consistently convergent toward a Monte Carlo benchmark solution than SN, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the LN method. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The zeroth and first angular moments of the directional flux, over each element, are estimated by numerical quadrature and yield a flux-weighted average streaming direction for the element. (Data for this estimation are fluxes in fixed directions calculated as in SN.)
A Discrete Lagrangian Algorithm for Optimal Routing Problems
Kosmas, O. T.; Vlachos, D. S.; Simos, T. E.
2008-11-06
The ideas of discrete Lagrangian methods for conservative systems are exploited for the construction of algorithms applicable in optimal ship routing problems. The algorithm presented here is based on the discretisation of Hamilton's principle of stationary action Lagrangian and specifically on the direct discretization of the Lagrange-Hamilton principle for a conservative system. Since, in contrast to the differential equations, the discrete Euler-Lagrange equations serve as constrains for the optimization of a given cost functional, in the present work we utilize this feature in order to minimize the cost function for optimal ship routing.
Discretized Weyl-orbit functions: modified multiplication and Galois symmetry
NASA Astrophysics Data System (ADS)
Hrivnák, J.; Walton, M. A.
2015-05-01
We note a remarkable similarity between the discretized Weyl-orbit functions and affine modular data associated with Wess-Zumino-Novikov-Witten (WZNW) conformal field theories. Known properties of the modular data are exploited here to uncover analogous results for the discretized orbit functions. We show that the product of orbit functions is modified in analogy with the truncation of tensor products known as affine fusion, governing the interactions in WZNW models. A Galois symmetry, like that of affine modular data, is also described for the discretized orbit functions.
A Stochastic Model for Discrete Waves in the Limulus Photoreceptor
Srebro, Richard; Behbehani, Mahmood
1971-01-01
A stochastic model that links the absorption of a photon to the production of a discrete wave in the photoreceptor of the lateral eye of Limulus is proposed. By separating a discrete wave into an initial component due directly to the absorption of a photon, and a second quasi all-or-nothing component, a mathematical description of the latencies of discrete waves is deduced and some important features of their time courses are suggested. The predictions of the model are compared to observations from 60 different ommatidia. PMID:5095679
Multidimensional electron-photon transport with standard discrete ordinates codes
Drumm, C.R.
1995-12-31
A method is described for generating electron cross sections that are compatible with standard discrete ordinates codes without modification. There are many advantages of using an established discrete ordinates solver, e.g. immediately available adjoint capability. Coupled electron-photon transport capability is needed for many applications, including the modeling of the response of electronics components to space and man-made radiation environments. The cross sections have been successfully used in the DORT, TWODANT and TORT discrete ordinates codes. The cross sections are shown to provide accurate and efficient solutions to certain multidimensional electronphoton transport problems.
Global convergence analysis of a discrete time nonnegative ICA algorithm.
Ye, Mao
2006-01-01
When the independent sources are known to be nonnegative and well-grounded, which means that they have a nonzero pdf in the region of zero, Oja and Plumbley have proposed a "Nonnegative principal component analysis (PCA)" algorithm to separate these positive sources. Generally, it is very difficult to prove the convergence of a discrete-time independent component analysis (ICA) learning algorithm. However, by using the skew-symmetry property of this discrete-time "Nonnegative PCA" algorithm, if the learning rate satisfies suitable condition, the global convergence of this discrete-time algorithm can be proven. Simulation results are employed to further illustrate the advantages of this theory. PMID:16526495
Unitary discrete linear canonical transform: analysis and application.
Zhao, Liang; Healy, John J; Sheridan, John T
2013-03-01
The numerical approximation of the linear canonical transforms (LCTs) is important in modeling coherent wave field propagation through first-order optical systems and in many digital signal processing applications. The continuous LCTs are unitary, but discretization can destroy this property. We present a sufficient condition on the sampling rates chosen in the discretization to ensure unitarity. We discuss the various subsets of the unitary matrices examined in this paper that have been proposed elsewhere. We offer a proof of the existence of all of the unitary matrices we discuss. We examine the consequences of these results, particularly in relation to the use of discrete transforms in iterative phase retrieval applications. PMID:23458814
Anomalous Discrete Symmetries in Three Dimensions and Group Cohomology
NASA Astrophysics Data System (ADS)
Kapustin, Anton; Thorngren, Ryan
2014-06-01
We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a nonvanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G1×G2 such that gauging G1 necessarily breaks G2 and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.
Anomalous discrete symmetries in three dimensions and group cohomology.
Kapustin, Anton; Thorngren, Ryan
2014-06-13
We study 't Hooft anomalies for a global discrete internal symmetry G. We construct examples of bosonic field theories in three dimensions with a nonvanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G(1) × G(2) such that gauging G(1) necessarily breaks G(2) and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions. PMID:24972194
Discrete Quantum Gravity in the Regge Calculus Formalism
Khatsymovsky, V.M.
2005-09-01
We discuss an approach to the discrete quantum gravity in the Regge calculus formalism that was developed in a number of our papers. The Regge calculus is general relativity for a subclass of general Riemannian manifolds called piecewise flat manifolds. The Regge calculus deals with a discrete set of variables, triangulation lengths, and contains continuous general relativity as a special limiting case where the lengths tend to zero. In our approach, the quantum length expectations are nonzero and of the order of the Plank scale, 10{sup -33} cm, implying a discrete spacetime structure on these scales.
Discretization chaos - Feedback control and transition to chaos
NASA Technical Reports Server (NTRS)
Grantham, Walter J.; Athalye, Amit M.
1990-01-01
Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.
Multiplexing of discrete chaotic signals in presence of noise
NASA Astrophysics Data System (ADS)
Nagaraj, Nithin; Vaidya, Prabhakar G.
2009-09-01
Multiplexing of discrete chaotic signals in presence of noise is investigated. The existing methods are based on chaotic synchronization, which is susceptible to noise, precision limitations, and requires more iterates. Furthermore, most of these methods fail for multiplexing more than two discrete chaotic signals. We propose novel methods to multiplex multiple discrete chaotic signals based on the principle of symbolic sequence invariance in presence of noise and finite precision implementation of finding the initial condition of an arbitrarily long symbolic sequence of a chaotic map. Our methods work for single precision and as less as 35 iterates. For two signals, our method is robust up to 50% noise level.
Energy Criterion for the Spectral Stability of Discrete Breathers.
Kevrekidis, Panayotis G; Cuevas-Maraver, Jesús; Pelinovsky, Dmitry E
2016-08-26
Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the emergence of instabilities of discrete breathers analogous to the well-established Vakhitov-Kolokolov criterion for solitary waves. The criterion involves the change of monotonicity of the discrete breather's energy as a function of the breather frequency. Our analysis suggests and numerical results corroborate that breathers with increasing (decreasing) energy-frequency dependence are generically unstable in soft (hard) nonlinear potentials. PMID:27610856
Tomographically complete sets of orthonormal bases in finite systems
NASA Astrophysics Data System (ADS)
Shalaby, M.; Vourdas, A.
2011-08-01
Quantum systems where the position and momentum are in the ring { Z}_d (d is an odd integer) are considered. A tomographically complete set of bases, i.e. a set of bases such that probabilities from tomography experiments corresponding to these bases, can be used for the calculation of an arbitrary density matrix, is considered. Such a set of bases is constructed by considering a factorization of a system with dimension d = p1p2 (where p1, p2 are prime numbers) in terms of two subsystems with dimensions p1 and p2. Appropriate combination of the mutually unbiased bases in the subsystems, leads to a tomographically complete set of bases in the full system. This set leads to probabilities along all the lines through the origin (0, 0) in the { Z}_d\\times { Z}_d phase space, with exactly d points. It is shown that the number of these lines is ψ(d) (the Dedekind function). The general theory is exemplified with examples.
Joint probability distributions for projection probabilities of random orthonormal states
NASA Astrophysics Data System (ADS)
Alonso, L.; Gorin, T.
2016-04-01
The quantum chaos conjecture applied to a finite dimensional quantum system implies that such a system has eigenstates that show similar statistical properties as the column vectors of random orthogonal or unitary matrices. Here, we consider the different probabilities for obtaining a specific outcome in a projective measurement, provided the system is in one of its eigenstates. We then give analytic expressions for the joint probability density for these probabilities, with respect to the ensemble of random matrices. In the case of the unitary group, our results can be applied, also, to the phenomenon of universal conductance fluctuations, where the same mathematical quantities describe partial conductances in a two-terminal mesoscopic scattering problem with a finite number of modes in each terminal.
PREFACE: DISCRETE 2012 - Third Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Branco, G. C.; Emmanuel-Costa, D.; González Felipe, R.; Joaquim, F. R.; Lavoura, L.; Palomares-Ruiz, S.; Rebelo, M. N.; Romão, J. C.; Silva, J. P.
2013-07-01
The Third Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2012) was held at Instituto Superior Técnico, Portugal, from 3-7 December 2012 and was organised by Centro de Física Teórica de Partículas (CFTP) of Instituto Superior Técnico, Universidade Técnica de Lisboa. This is the sequel to the Symposia that was successfully organised in Valéncia in 2008 and in Rome in 2010. The topics covered included: T, C, P, CP symmetries CPT symmetry, decoherence, Lorentz symmetry breaking Discrete symmetries and models of flavour mixing Baryogenesis, leptogenesis Neutrino physics Electroweak symmetry breaking and physics beyond the Standard Model Accidental symmetries (B, L conservation) Experimental prospects at LHC Dark matter searches Super flavour factories, and other new experimental facilities The Symposium was organised in plenary sessions with a total of 24 invited talks, and parallel sessions with a total of 70 talks, including both invited and selected contributions from the submitted abstracts. The speakers of the plenary sessions were: Ignatios Antoniadis, Abdelhak Djouadi, Rabindra Mohapatra, André Rubbia, Alexei Yu Smirnov, José Bernabéu, Marco Cirelli, Apostolos Pilaftsis, Antonio Di Domenico, Robertus Potting, João Varela, Frank Rathmann, Michele Gallinaro, Dumitru Ghilencea, Neville Harnew, John Walsh, Patrícia Conde Muíño, Juan Aguilar-Saavedra, Nick Mavromatos, Ulrich Nierste, Ferruccio Feruglio, Vasiliki Mitsou, Masanori Yamauchi, and Marcello Giorgi. The Symposium was attended by about 140 participants. Among the social events, there was a social dinner in the historical Associação Comercial de Lisboa, which included a musical performance of 'Fado', the traditional music from Lisbon. The next symposium of the series will be organised by King's College, London University, UK, from 1-5 December 2014. Guest Editors G C Branco, D Emmanuel-Costa, R González Felipe, F R Joaquim, L Lavoura, S Palomares-Ruiz, M N Rebelo, J C
Implementing the Standards. Teaching Discrete Mathematics in Grades 7-12.
ERIC Educational Resources Information Center
Hart, Eric W.; And Others
1990-01-01
Discrete mathematics are defined briefly. A course in discrete mathematics for high school students and teaching discrete mathematics in grades 7 and 8 including finite differences, recursion, and graph theory are discussed. (CW)
Discrete Element Modeling of Complex Granular Flows
NASA Astrophysics Data System (ADS)
Movshovitz, N.; Asphaug, E. I.
2010-12-01
Granular materials occur almost everywhere in nature, and are actively studied in many fields of research, from food industry to planetary science. One approach to the study of granular media, the continuum approach, attempts to find a constitutive law that determines the material's flow, or strain, under applied stress. The main difficulty with this approach is that granular systems exhibit different behavior under different conditions, behaving at times as an elastic solid (e.g. pile of sand), at times as a viscous fluid (e.g. when poured), or even as a gas (e.g. when shaken). Even if all these physics are accounted for, numerical implementation is made difficult by the wide and often discontinuous ranges in continuum density and sound speed. A different approach is Discrete Element Modeling (DEM). Here the goal is to directly model every grain in the system as a rigid body subject to various body and surface forces. The advantage of this method is that it treats all of the above regimes in the same way, and can easily deal with a system moving back and forth between regimes. But as a granular system typically contains a multitude of individual grains, the direct integration of the system can be very computationally expensive. For this reason most DEM codes are limited to spherical grains of uniform size. However, spherical grains often cannot replicate the behavior of real world granular systems. A simple pile of spherical grains, for example, relies on static friction alone to keep its shape, while in reality a pile of irregular grains can maintain a much steeper angle by interlocking force chains. In the present study we employ a commercial DEM, nVidia's PhysX Engine, originally designed for the game and animation industry, to simulate complex granular flows with irregular, non-spherical grains. This engine runs as a multi threaded process and can be GPU accelerated. We demonstrate the code's ability to physically model granular materials in the three regimes
Discrete element modelling of bedload transport
NASA Astrophysics Data System (ADS)
Loyer, A.; Frey, P.
2011-12-01
Discrete element modelling (DEM) has been widely used in solid mechanics and in granular physics. In this type of modelling, each individual particle is taken into account and intergranular interactions are modelled with simple laws (e.g. Coulomb friction). Gravity and contact forces permit to solve the dynamical behaviour of the system. DEM is interesting to model configurations and access to parameters not directly available in laboratory experimentation, hence the term "numerical experimentations" sometimes used to describe DEM. DEM was used to model bedload transport experiments performed at the particle scale with spherical glass beads in a steep and narrow flume. Bedload is the larger material that is transported on the bed on stream channels. It has a great geomorphic impact. Physical processes ruling bedload transport and more generally coarse-particle/fluid systems are poorly known, arguably because granular interactions have been somewhat neglected. An existing DEM code (PFC3D) already computing granular interactions was used. We implemented basic hydrodynamic forces to model the fluid interactions (buoyancy, drag, lift). The idea was to use the minimum number of ingredients to match the experimental results. Experiments were performed with one-size and two-size mixtures of coarse spherical glass beads entrained by a shallow turbulent and supercritical water flow down a steep channel with a mobile bed. The particle diameters were 4 and 6mm, the channel width 6.5mm (about the same width as the coarser particles) and the channel inclination was typically 10%. The water flow rate and the particle rate were kept constant at the upstream entrance and adjusted to obtain bedload transport equilibrium. Flows were filmed from the side by a high-speed camera. Using image processing algorithms made it possible to determine the position, velocity and trajectory of both smaller and coarser particles. Modelled and experimental particle velocity and concentration depth
Discrete element modelling of bed load transport
NASA Astrophysics Data System (ADS)
Maurin, Raphael; Chareyre, Bruno; Chauchat, Julien; Frey, Philippe
2013-04-01
Discrete element method (DEM) is a numerical method to simulate an assembly of particles, which has been widely used in mechanics (soil, rock) and granular physics. DEM consists in considering undeformable particles and modelling the intergranular interactions with simple laws (e.g. linear elastic and Coulomb friction law). The expression of the equation of motion on each particle considering the nearest neighbor interactions allows then to solve the dynamical behavior of the system explicitely. Since its introduction more than thirty years ago, this type of model has proven its ability to well describe the behavior of granular media in several different situations, from quasi-static system to flow of granular media. Bedload transport in streams is characterized by particle transport restricted to the interface between fluid flow and immerged granular media, where particles are rolling, sliding or in saltation over the bed. This situation corresponds to the larger particles transported on the bed in stream channels and has a great influence on geomorphology. Physical mechanisms and processes ruling bedload transport and more generally coarse-particle/fluid systems are poorly known. This is partly due to the small attention given to the role of granular interactions. Starting from these considerations, we used DEM to reproduce experiments carried out with spherical glass beads in an experimental steep and narrow flume. This was done in order to focus on granular interactions and to have access to parameters not available in the experiment. DEM open-source code Yade was coupled with a simplified fluid model, taking into account the different hydrodynamical interactions (buoyancy, drag, lift...) experienced by the particles. Numerical results obtained from the simulation are compared with an experimental data set established previously at the laboratory. It consists in monodisperse and bidisperse mixtures of coarse spherical glass beads entrained by a shallow
Discrete element modeling of subglacial sediment deformation
NASA Astrophysics Data System (ADS)
Damsgaard, A.; Egholm, D. L.; Piotrowski, J. A.; Tulaczyk, S. M.; Larsen, N. K.
2013-12-01
The Discrete Element Method (DEM) is used to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. In the DEM, the material is simulated on a grain-by-grain basis, and defining the micromechanical properties of the inter-particle contacts parameterizes the model. For validating the numerical approach, the macromechanical behavior of the numerical material is compared to the results from successive laboratory ring-shear experiments. Overall, there is a good agreement between the geotechnical behavior of the real granular materials and the numerical results. The materials deform by an elasto-plastic rheology under the applied effective normal stress and horizontal shearing. The peak and ultimate shear strengths depend linearly on the magnitude of the normal stress by the Mohr-Coulomb constitutive relationship. The numerical approach allows for a detailed analysis of the material dynamics and shear zone development during progressive shear strain. We demonstrate how the shear zone thickness and dilation increase with the magnitude of the normal stress. The stresses are distributed heterogeneously through the granular material along stress-carrying force chains. Between the force chains are the volumetrically dominant inactive zones. Overall, the force chain orientation is parallel to the maximum compressive stress. The data-parallel nature of the basic DEM formulation makes the problem ideal for utilizing the high arithmetic potential of modern general-purpose GPUs. Using the Nvidia CUDA C toolkit, the algorithm is formulated for spherical particles in three dimensions with a linear-elastic soft-body contact model. We have coupled the DEM model to a model for porewater flow, and we present early results of particle-porewater interactions. The two-way mechanical coupling is used to investigate pore-pressure feedbacks, which may be very important for the dynamics of soft
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin Sargsyan, Khachik Debusschere, Bert Najm, Habib N.
2015-01-15
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker–Planck equation. The Fokker–Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Implementation of quantum and classical discrete fractional Fourier transforms
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-01-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089
31 CFR 101.8 - Discretion of the Secretary.
Code of Federal Regulations, 2010 CFR
2010-07-01
... FORFEITURE OF COUNTERFEIT GOLD COINS § 101.8 Discretion of the Secretary. The Secretary of the Treasury... not convinced that the petitoner was an innocent purchaser or holder without knowledge that the...
46 CFR 296.23 - Discretion within priority.
Code of Federal Regulations, 2010 CFR
2010-10-01
... within a priority— (1) In accordance with operational requirements specified by the SecDef; (2) In the...; and (3) Subject to the approval of the SecDef. (c) The Secretary does not have discretion to...
Hybrid discrete/continuum algorithms for stochastic reaction networks
NASA Astrophysics Data System (ADS)
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2015-01-01
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. The performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2014-10-22
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.
Implementation of quantum and classical discrete fractional Fourier transforms
NASA Astrophysics Data System (ADS)
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-03-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Applying Multivariate Discrete Distributions to Genetically Informative Count Data.
Kirkpatrick, Robert M; Neale, Michael C
2016-03-01
We present a novel method of conducting biometric analysis of twin data when the phenotypes are integer-valued counts, which often show an L-shaped distribution. Monte Carlo simulation is used to compare five likelihood-based approaches to modeling: our multivariate discrete method, when its distributional assumptions are correct, when they are incorrect, and three other methods in common use. With data simulated from a skewed discrete distribution, recovery of twin correlations and proportions of additive genetic and common environment variance was generally poor for the Normal, Lognormal and Ordinal models, but good for the two discrete models. Sex-separate applications to substance-use data from twins in the Minnesota Twin Family Study showed superior performance of two discrete models. The new methods are implemented using R and OpenMx and are freely available. PMID:26497008
Distinguishing between discreteness effects in stochastic reaction processes.
Haruna, Taichi
2015-05-01
The effect of discreteness on stochastic dynamics of chemically reacting systems is studied analytically. We apply the scheme bridging the chemical master equation and the chemical Fokker-Planck equation by a parameter representing the degree of discreteness previously proposed by the author for two concrete systems. One is an autocatalytic reaction system, and the other is a branching-annihilation reaction system. It is revealed that the change in characteristic time scales when discreteness is decreased is yielded between the two systems for different reasons. In the former system, it originates from the boundaries where one of the chemical species is zero, whereas in the latter system, it is due to modification of the most probable extinction path caused by discreteness loss. PMID:26066219
Discrete Feature Approach for Heterogeneous Reservoir Production Enhancement
Dershowitz, William S.; Curran, Brendan; Einstein, Herbert; LaPointe, Paul; Shuttle, Dawn; Klise, Kate
2002-07-26
The report presents summaries of technology development for discrete feature modeling in support of the improved oil recovery (IOR) for heterogeneous reservoirs. In addition, the report describes the demonstration of these technologies at project study sites.
Discrete-time quantum walk approach to state transfer
Kurzynski, Pawel; Wojcik, Antoni
2011-06-15
We show that a quantum-state transfer, previously studied as a continuous-time process in networks of interacting spins, can be achieved within the model of discrete-time quantum walks with a position-dependent coin. We argue that, due to additional degrees of freedom, discrete-time quantum walks allow one to observe effects which cannot be observed in the corresponding continuous-time case. First, we study a discrete-time version of the engineered coupling protocol due to Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)] and then we discuss the general idea of conversion between continuous-time quantum walks and discrete-time quantum walks.
Energy Exchange Between the Discrete Breathers in Graphane
NASA Astrophysics Data System (ADS)
Baimova, J. A.; Dmitriev, S. V.
2015-10-01
Discrete breathers in graphane (fully hydrogenated graphene) are studied by the molecular dynamics method. It has previously been demonstrated that in graphane, there are discrete breathers in the form of single hydrogen atoms oscillating with the big amplitude in the direction perpendicular to the graphane plane with a frequency lying in the bandgap of the phonon spectrum. In this work, the possibility of the existence of longlived clusters of discrete breathers of different configurations is shown, their properties are studied, and the possibility of energy exchange between the discrete breathers in the cluster is demonstrated. These results are important for the discussion of physical processes occurring during dehydrogenation of graphane at high temperatures, which, in turn, is of great importance for the development of the hydrogen storage and transport devices based on sp2-carbon materials.
Singularity confinement for matrix discrete Painlevé equations
NASA Astrophysics Data System (ADS)
Cassatella-Contra, Giovanni A.; Mañas, Manuel; Tempesta, Piergiulio
2014-09-01
We study the analytic properties of a matrix discrete system introduced by Cassatella and Mañas (2012 Stud. Appl. Math. 128 252-74). The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This paves the way to a generalization of Painlevé analysis to discrete matrix models.
A separable two-dimensional discrete Hartley transform
NASA Technical Reports Server (NTRS)
Watson, A. B.; Poirson, A.
1985-01-01
Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.
Non-autonomous discrete Boussinesq equation: Solutions and consistency
NASA Astrophysics Data System (ADS)
Nong, Li-Juan; Zhang, Da-Juan
2014-07-01
A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter δ. Tree-dimendional consistency and Lax pair of the obtained equation are discussed.
Strongly asymmetric discrete Painlevé equations: The additive case
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
2014-05-15
We examine a class of discrete Painlevé equations which present a strong asymmetry. These equations can be written as a system of two equations, the right-hand-sides of which do not have the same functional form. We limit here our investigation to two canonical families of the Quispel-Roberts-Thompson (QRT) classification both of which lead to difference equations. Several new integrable discrete systems are identified.
Efficient entanglement criteria for discrete, continuous, and hybrid variables
NASA Astrophysics Data System (ADS)
Gessner, Manuel; Pezzè, Luca; Smerzi, Augusto
2016-08-01
We develop a method to construct entanglement criteria for arbitrary multipartite systems of discrete or continuous variables and hybrid combinations of both. While any set of local operators generates a sufficient condition for entanglement of arbitrary quantum states, a suitable set leads to a necessary and sufficient criterion for pure states. The criteria are readily implementable with existing technology and reveal entanglement that remains undetected by the respective state-of-the-art methods for discrete and continuous variables.
Riesz Riemann-Liouville difference on discrete domains.
Wu, Guo-Cheng; Baleanu, Dumitru; Xie, He-Ping
2016-08-01
A Riesz difference is defined by the use of the Riemann-Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically. PMID:27586625
Averaging analysis for discrete time and sampled data adaptive systems
NASA Technical Reports Server (NTRS)
Fu, Li-Chen; Bai, Er-Wei; Sastry, Shankar S.
1986-01-01
Earlier continuous time averaging theorems are extended to the nonlinear discrete time case. Theorems for the study of the convergence analysis of discrete time adaptive identification and control systems are used. Instability theorems are also derived and used for the study of robust stability and instability of adaptive control schemes applied to sampled data systems. As a by product, the effects of sampling on unmodeled dynamics in continuous time systems are also studied.
Riesz Riemann-Liouville difference on discrete domains
NASA Astrophysics Data System (ADS)
Wu, Guo-Cheng; Baleanu, Dumitru; Xie, He-Ping
2016-08-01
A Riesz difference is defined by the use of the Riemann-Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically.
Discrete Feature Approach for Heterogeneous Reservoir Production Enhancement
Dershowitz, William S.; Cladouhos, Trenton
2001-09-06
This progress report describes activities during the period January 1, 1999 to June 30, 1999. Work was carried out on 21 tasks. The major activity during the reporting period was the development and preliminary application of discrete fracture network (DFN) models for Stoney Point, South Oregon Basin, and North Oregon Basins project study sites. In addition, research was carried out on analysis algorithms for discrete future orientation.
Construction of Superconvergent Discretizations with Differential-Difference Invariants
R.A. Axford
2005-08-12
To incorporate symmetry properties of second-order differential equations into finite difference equations, the concept of differential-difference invariants is introduced. This concept is applied to discretizing homogeneous eigenvalue problems and inhomogeneous two-point boundary value problems with various combinations of Dirichlet, Neumann, and Robin boundary conditions. It is demonstrated that discretizations constructed with differential-difference invariants yield exact results for eigenvalue spectra and superconvergent results for numerical solutions of differential equations.
Isolation of Discrete Nanoparticle-DNA Conjugates for Plasmonic Applications
Alivisatos, Paul; Claridge, Shelley A.; Liang, Huiyang W.; Basu, Sourav Roger; Frechet, Jean M.J.; Alivisatos, A. Paul
2008-04-11
Discrete DNA-gold nanoparticle conjugates with DNA lengths as short as 15 bases for both 5 nm and 20 nm gold particles have been purified by anion-exchange HPLC. Conjugates comprising short DNA (<40 bases) and large gold particles (>_ 20 nm) are difficult to purify by other means, and are potential substrates for plasmon coupling experiments. Conjugate purity is demonstrated by hybridizing complementary conjugates to form discrete structures, which are visualized by TEM.
The ergodic decomposition of stationary discrete random processes
NASA Technical Reports Server (NTRS)
Gray, R. M.; Davisson, L. D.
1974-01-01
The ergodic decomposition is discussed, and a version focusing on the structure of individual sample functions of stationary processes is proved for the special case of discrete-time random processes with discrete alphabets. The result is stronger in this case than the usual theorem, and the proof is both intuitive and simple. Estimation-theoretic and information-theoretic interpretations are developed and applied to prove existence theorems for universal source codes, both noiseless and with a fidelity criterion.
Discrete spectral incoherent solitons in nonlinear media with noninstantaneous response
Michel, Claire; Kibler, Bertrand; Picozzi, Antonio
2011-02-15
We show theoretically that nonlinear optical media characterized by a finite response time may support the existence of discrete spectral incoherent solitons. The structure of the soliton consists of three incoherent spectral bands that propagate in frequency space toward the low-frequency components in a discrete fashion and with a constant velocity. Discrete spectral incoherent solitons do not exhibit a confinement in the space-time domain, but exclusively in the frequency domain. The kinetic theory describes in detail all the essential properties of discrete spectral incoherent solitons: A quantitative agreement has been obtained between simulations of the kinetic equation and the nonlinear Schroedinger equation. Discrete spectral incoherent solitons may be supported in both the normal dispersion regime or the anomalous dispersion regime. These incoherent structures find their origin in the causality condition inherent to the nonlinear response function of the material. Considering the concrete example of the Raman effect, we show that discrete incoherent solitons may be spontaneously generated through the process of supercontinuum generation in photonic crystal fibers.
On discrete control of nonlinear systems with applications to robotics
NASA Technical Reports Server (NTRS)
Eslami, Mansour
1989-01-01
Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.
Discrete Randomness in Discrete Time Quantum Walk: Study Via Stochastic Averaging
NASA Astrophysics Data System (ADS)
Ellinas, D.; Bracken, A. J.; Smyrnakis, I.
2012-10-01
The role of classical noise in quantum walks (QW) on integers is investigated in the form of discrete dichotomic random variable affecting its reshuffling matrix parametrized as a SU2)/U (1) coset element. Analysis in terms of quantum statistical moments and generating functions, derived by the completely positive trace preserving (CPTP) map governing evolution, reveals a pronounced eventual transition in walk's diffusion mode, from a quantum ballistic regime with rate O(t) to a classical diffusive regime with rate O(√{t}), when condition (strength of noise parameter)2 × (number of steps) = 1, is satisfied. The role of classical randomness is studied showing that the randomized QW, when treated on the stochastic average level by means of an appropriate CPTP averaging map, turns out to be equivalent to a novel quantized classical walk without randomness. This result emphasizes the dual role of quantization/randomization in the context of classical random walk.
Chakrabarti, C. . Dept. of Electrical Engineering); Ja Ja, J. . Dept. of Electrical Engineering)
1990-11-01
This paper proposes two-dimensional systolic array implementations for computing the discrete Hartley (DHT) and the discrete cosine transforms (DCT) when the transform size N is decomposable into mutually prime factors. The existing two-dimensional formulations for DHT and DCT are modified and the corresponding algorithms are mapped into two-dimensional systolic arrays. The resulting architecture is fully pipelined with no control units. The hardware design is based on bit serial left to right MSB to LSB binary arithmetic.
Discrete choice experiments of pharmacy services: a systematic review.
Vass, Caroline; Gray, Ewan; Payne, Katherine
2016-06-01
Background Two previous systematic reviews have summarised the application of discrete choice experiments to value preferences for pharmacy services. These reviews identified a total of twelve studies and described how discrete choice experiments have been used to value pharmacy services but did not describe or discuss the application of methods used in the design or analysis. Aims (1) To update the most recent systematic review and critically appraise current discrete choice experiments of pharmacy services in line with published reporting criteria and; (2) To provide an overview of key methodological developments in the design and analysis of discrete choice experiments. Methods The review used a comprehensive strategy to identify eligible studies (published between 1990 and 2015) by searching electronic databases for key terms related to discrete choice and best-worst scaling (BWS) experiments. All healthcare choice experiments were then hand-searched for key terms relating to pharmacy. Data were extracted using a published checklist. Results A total of 17 discrete choice experiments eliciting preferences for pharmacy services were identified for inclusion in the review. No BWS studies were identified. The studies elicited preferences from a variety of populations (pharmacists, patients, students) for a range of pharmacy services. Most studies were from a United Kingdom setting, although examples from Europe, Australia and North America were also identified. Discrete choice experiments for pharmacy services tended to include more attributes than non-pharmacy choice experiments. Few studies reported the use of qualitative research methods in the design and interpretation of the experiments (n = 9) or use of new methods of analysis to identify and quantify preference and scale heterogeneity (n = 4). No studies reported the use of Bayesian methods in their experimental design. Conclusion Incorporating more sophisticated methods in the design of pharmacy
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
NASA Astrophysics Data System (ADS)
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Estimation of discretization errors in contact pressure measurements.
Fregly, Benjamin J; Sawyer, W Gregory
2003-04-01
Contact pressure measurements in total knee replacements are often made using a discrete sensor such as the Tekscan K-Scan sensor. However, no method currently exists for predicting the magnitude of sensor discretization errors in contact force, peak pressure, average pressure, and contact area, making it difficult to evaluate the accuracy of such measurements. This study identifies a non-dimensional area variable, defined as the ratio of the number of perimeter elements to the total number of elements with pressure, which can be used to predict these errors. The variable was evaluated by simulating discrete pressure sensors subjected to Hertzian and uniform pressure distributions with two different calibration procedures. The simulations systematically varied the size of the sensor elements, the contact ellipse aspect ratio, and the ellipse's location on the sensor grid. In addition, contact pressure measurements made with a K-Scan sensor on four different total knee designs were used to evaluate the magnitude of discretization errors under practical conditions. The simulations predicted a strong power law relationship (r(2)>0.89) between worst-case discretization errors and the proposed non-dimensional area variable. In the total knee experiments, predicted discretization errors were on the order of 1-4% for contact force and peak pressure and 3-9% for average pressure and contact area. These errors are comparable to those arising from inserting a sensor into the joint space or truncating pressures with pressure sensitive film. The reported power law regression coefficients provide a simple way to estimate the accuracy of experimental measurements made with discrete pressure sensors when the contact patch is approximately elliptical. PMID:12600352
A discrete dislocation transformation model for austenitic single crystals
NASA Astrophysics Data System (ADS)
Shi, J.; Turteltaub, S.; Van der Giessen, E.; Remmers, J. J. C.
2008-07-01
A discrete model for analyzing the interaction between plastic flow and martensitic phase transformations is developed. The model is intended for simulating the microstructure evolution in a single crystal of austenite that transforms non-homogeneously into martensite. The plastic flow in the untransformed austenite is simulated using a plane-strain discrete dislocation model. The phase transformation is modeled via the nucleation and growth of discrete martensitic regions embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plasto-transformation problem is solved using the superposition of analytical solutions for the discrete dislocations and discrete transformation regions embedded in an infinite homogeneous medium and the numerical solution of a complementary problem used to enforce the actual boundary conditions and the heterogeneities in the medium. In order to describe the nucleation and growth of martensitic regions, a nucleation criterion and a kinetic law suitable for discrete regions are specified. The constitutive rules used in discrete dislocation simulations are supplemented with additional evolution rules to account for the phase transformation. To illustrate the basic features of the model, simulations of specimens under plane-strain uniaxial extension and contraction are analyzed. The simulations indicate that plastic flow reduces the average stress at which transformation begins, but it also reduces the transformation rate when compared with benchmark simulations without plasticity. Furthermore, due to local stress fluctuations caused by dislocations, martensitic systems can be activated even though transformation would not appear to be favorable based on the average stress. Conversely, the simulations indicate that the plastic hardening behavior is influenced by the reduction in the effective austenitic grain size due to the evolution of transformation. During cyclic simulations, the coupled plasticity
Compensatory neurofuzzy model for discrete data classification in biomedical
NASA Astrophysics Data System (ADS)
Ceylan, Rahime
2015-03-01
Biomedical data is separated to two main sections: signals and discrete data. So, studies in this area are about biomedical signal classification or biomedical discrete data classification. There are artificial intelligence models which are relevant to classification of ECG, EMG or EEG signals. In same way, in literature, many models exist for classification of discrete data taken as value of samples which can be results of blood analysis or biopsy in medical process. Each algorithm could not achieve high accuracy rate on classification of signal and discrete data. In this study, compensatory neurofuzzy network model is presented for classification of discrete data in biomedical pattern recognition area. The compensatory neurofuzzy network has a hybrid and binary classifier. In this system, the parameters of fuzzy systems are updated by backpropagation algorithm. The realized classifier model is conducted to two benchmark datasets (Wisconsin Breast Cancer dataset and Pima Indian Diabetes dataset). Experimental studies show that compensatory neurofuzzy network model achieved 96.11% accuracy rate in classification of breast cancer dataset and 69.08% accuracy rate was obtained in experiments made on diabetes dataset with only 10 iterations.
Modeling rammed earth wall using discrete element method
NASA Astrophysics Data System (ADS)
Bui, T.-T.; Bui, Q.-B.; Limam, A.; Morel, J.-C.
2016-03-01
Rammed earth is attracting renewed interest throughout the world thanks to its "green" characteristics in the context of sustainable development. Several research studies have thus recently been carried out to investigate this material. Some of them attempted to simulate the rammed earth's mechanical behavior by using analytical or numerical models. Most of these studies assumed that there was a perfect cohesion at the interface between earthen layers. This hypothesis proved to be acceptable for the case of vertical loading, but it could be questionable for horizontal loading. To address this problem, discrete element modeling seems to be relevant to simulate a rammed earth wall. To our knowledge, no research has been conducted thus far using discrete element modeling to study a rammed earth wall. This paper presents an assessment of the discrete element modeling's robustness for rammed earth walls. Firstly, a brief description of the discrete element modeling is presented. Then the parameters necessary for discrete element modeling of the material law of the earthen layers and their interfaces law following the Mohr-Coulomb model with a tension cut-off and post-peak softening were given. The relevance of the model and the material parameters were assessed by comparing them with experimental results from the literature. The results showed that, in the case of vertical loading, interfaces did not have an important effect. In the case of diagonal loading, model with interfaces produced better results. Interface characteristics can vary from 85 to 100% of the corresponding earthen layer's characteristics.
An innovative lossless compression method for discrete-color images.
Alzahir, Saif; Borici, Arber
2015-01-01
In this paper, we present an innovative method for lossless compression of discrete-color images, such as map images, graphics, GIS, as well as binary images. This method comprises two main components. The first is a fixed-size codebook encompassing 8×8 bit blocks of two-tone data along with their corresponding Huffman codes and their relative probabilities of occurrence. The probabilities were obtained from a very large set of discrete color images which are also used for arithmetic coding. The second component is the row-column reduction coding, which will encode those blocks that are not in the codebook. The proposed method has been successfully applied on two major image categories: 1) images with a predetermined number of discrete colors, such as digital maps, graphs, and GIS images and 2) binary images. The results show that our method compresses images from both categories (discrete color and binary images) with 90% in most case and higher than the JBIG-2 by 5%-20% for binary images, and by 2%-6.3% for discrete color images on average. PMID:25330487
Discrete-time minimal control synthesis adaptive algorithm
NASA Astrophysics Data System (ADS)
di Bernardo, M.; di Gennaro, F.; Olm, J. M.; Santini, S.
2010-12-01
This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.
Discrete Variational Approach for Modeling Laser-Plasma Interactions
NASA Astrophysics Data System (ADS)
Reyes, J. Paxon; Shadwick, B. A.
2014-10-01
The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.
Peculiar symmetry structure of some known discrete nonautonomous equations
NASA Astrophysics Data System (ADS)
Garifullin, R. N.; Habibullin, I. T.; Yamilov, R. I.
2015-06-01
We study the generalized symmetry structure of three known discrete nonautonomous equations. One of them is the semidiscrete dressing chain of Shabat. Two others are completely discrete equations defined on the square lattice. The first one is a discrete analogue of the dressing chain introduced by Levi and Yamilov. The second one is a nonautonomous generalization of the potential discrete KdV equation or, in other words, the H1 equation of the well-known Adler-Bobenko-Suris list. We demonstrate that these equations have generalized symmetries in both directions if and only if their coefficients, depending on the discrete variables, are periodic. The order of the simplest generalized symmetry in at least one direction depends on the period and may be arbitrarily high. We substantiate this picture by some theorems in the case of small periods. In case of an arbitrarily large period, we show that it is possible to construct two hierarchies of generalized symmetries and conservation laws. The same picture should take place in case of any nonautonomous equation of the Adler-Bobenko-Suris list.
On the Importance of the Dynamics of Discretizations
NASA Technical Reports Server (NTRS)
Sweby, Peter K.; Yee, H. C.; Rai, ManMohan (Technical Monitor)
1995-01-01
It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.
Discrete-continuous variable structural synthesis using dual methods
NASA Technical Reports Server (NTRS)
Schmit, L. A.; Fleury, C.
1980-01-01
Approximation concepts and dual methods are extended to solve structural synthesis problems involving a mix of discrete and continuous sizing type of design variables. Pure discrete and pure continuous variable problems can be handled as special cases. The basic mathematical programming statement of the structural synthesis problem is converted into a sequence of explicit approximate primal problems of separable form. These problems are solved by constructing continuous explicit dual functions, which are maximized subject to simple nonnegativity constraints on the dual variables. A newly devised gradient projection type of algorithm called DUAL 1, which includes special features for handling dual function gradient discontinuities that arise from the discrete primal variables, is used to find the solution of each dual problem. Computational implementation is accomplished by incorporating the DUAL 1 algorithm into the ACCESS 3 program as a new optimizer option. The power of the method set forth is demonstrated by presenting numerical results for several example problems, including a pure discrete variable treatment of a metallic swept wing and a mixed discrete-continuous variable solution for a thin delta wing with fiber composite skins.
PREFACE: DISCRETE 2010: Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Bini, Cesare; Bloise, Caterina; Bossi, Fabio; Faccini, Riccardo; Gauzzi, Paolo; Isidori, Gino; Lipari, Paolo; Ludovici, Lucio; Silvestrini, Luca
2011-12-01
The Symposium DISCRETE2010 on Prospects in the Physics of Discrete Symmetries was held at the Sapienza Universitàa di Roma, Italy from 6-11 December 2010. This second edition, after the successful one in Valencia in 2008, covered all theoretical and experimental progress in the field, and aimed at a thorough discussion on the latest developments. The topics covered included: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence, Lorentz symmetry breaking; neutrino mass and mixing; cosmology and astroparticles, dark matter searches; experimental prospects at LHC, Super flavor factories, and new facilities. The Symposium was organized in plenary sessions with a total of 23 invited talks, and parallel sessions with a total of 80 talks including both invited and selected contributions from the submitted abstracts. The speakers of the plenary sessions were: Achille Stocchi, Andreas Weiler, Kevin Pitts, Tim Gershon, Marco Sozzi, Neal Weiner, Vasiliki Mitsou, Bernard Sadoulet, Gianfranco Bertone, J. Eric Grove, Mauro Mezzetto, Alexei Yu Smirnov, Oliviero Cremonesi, Antonio Riotto, Reno Mandolesi, Brett Altschul, Jose Bernabeu, Lawrence Hall, Marco Grassi, Yannis K. Semertzidis, Riccardo Barbieri, Gigi Rolandi, Luciano Maiani. The Symposium venue was the CNR (Consiglio Nazionale delle Ricerche) headquarter building, close to the Sapienza University. At the end of the Symposium a special open session, devoted to a wider audience, was held at the Pontifical University of the Holy Cross, in the historical center of Rome. The symposium was attended by about 140 participants, about half coming from Italy, and the rest mainly from other European countries and United States. Among the social events was a concert at the Aula Magna of the Sapienza University, and a social dinner in the historical Palazzo Pallavicini-Rospigliosi on the Quirinale Hill. The next symposium of the series will be organised by IST, Universidade Tàecnica de Lisboa
NASA Technical Reports Server (NTRS)
Kantor, A. V.; Timonin, V. G.; Azarova, Y. S.
1974-01-01
The method of adaptive discretization is the most promising for elimination of redundancy from telemetry messages characterized by signal shape. Adaptive discretization with associative sorting was considered as a way to avoid the shortcomings of adaptive discretization with buffer smoothing and adaptive discretization with logical switching in on-board information compression devices (OICD) in spacecraft. Mathematical investigations of OICD are presented.
Bell-Curve Genetic Algorithm for Mixed Continuous and Discrete Optimization Problems
NASA Technical Reports Server (NTRS)
Kincaid, Rex K.; Griffith, Michelle; Sykes, Ruth; Sobieszczanski-Sobieski, Jaroslaw
2002-01-01
In this manuscript we have examined an extension of BCB that encompasses a mix of continuous and quasi-discrete, as well as truly-discrete applications. FVe began by testing two refinements to the discrete version of BCB. The testing of midpoint versus fitness (Tables 1 and 2) proved inconclusive. The testing of discrete normal tails versus standard mutation showed was conclusive and demonstrated that the discrete normal tails are better. Next, we implemented these refinements in a combined continuous and discrete BCB and compared the performance of two discrete distance on the hub problem. Here we found when "order does matter" it pays to take it into account.
PREFACE: DISCRETE '08: Symposium on Prospects in the Physics of Discrete Symmetries
NASA Astrophysics Data System (ADS)
Bernabéu, José; Botella, Francisco J.; Mavromatos, Nick E.; Mitsou, Vasiliki A.
2009-07-01
The Symposium DISCRETE'08 on Prospects in the Physics of Discrete Symmetries was held at the Instituto de Física Corpuscular (IFIC) in Valencia, Spain from 11 to 16 December 2008. IFIC is a joint centre of the Consejo Superior de Investigaciones Científicas (CSIC) and the Universitat de València (UVEG). The aim of the Symposium was to bring together experts on the field of Discrete Symmetries in order to discuss its prospects on the eve of the LHC era. The general state of the art for CP, T and CPT symmetries was reviewed and their interplay with Baryogenesis, Early Cosmology, Quantum Gravity, String Theory and the Dark Sector of the Universe was emphasised. Connections with physics beyond the Standard Model, in particular Supersymmetry, were investigated. Experimental implications in current and proposed facilities received particular attention. The scientific programme consisted of 24 invited Plenary Talks and 93 contributions selected among the submitted papers. Young researchers, in particular, were encouraged to submit an abstract. The Special Lecture on ''CERN and the Future of Particle Physics'', given by the CERN Director General Rolf-Dieter Heuer to close the Symposium, was of particular relevance. On the last day of the Symposium, an open meeting took place between Professor Heuer and the Spanish community of particle physics. The Symposium covered recent developments on the subject of Discrete Symmetries in the following topics: Quantum Vacuum Entanglement, Symmetrisation Principle CPT in Quantum Gravity and String Theory, Decoherence, Lorentz Violation Ultra-high-energy Messengers Time Reversal CP violation in the SM and beyond Neutrino Mass, Mixing and CP Baryogenesis, Leptogenesis Family Symmetries Supersymmetry and other searches Experimental Prospects: LHC, Super-B Factories, DAΦNE-2, Neutrino Beams The excellence of most of the presentations during the Symposium was pointed out by many participants. The broad spectrum of topics under the
Optimization of Operations Resources via Discrete Event Simulation Modeling
NASA Technical Reports Server (NTRS)
Joshi, B.; Morris, D.; White, N.; Unal, R.
1996-01-01
The resource levels required for operation and support of reusable launch vehicles are typically defined through discrete event simulation modeling. Minimizing these resources constitutes an optimization problem involving discrete variables and simulation. Conventional approaches to solve such optimization problems involving integer valued decision variables are the pattern search and statistical methods. However, in a simulation environment that is characterized by search spaces of unknown topology and stochastic measures, these optimization approaches often prove inadequate. In this paper, we have explored the applicability of genetic algorithms to the simulation domain. Genetic algorithms provide a robust search strategy that does not require continuity and differentiability of the problem domain. The genetic algorithm successfully minimized the operation and support activities for a space vehicle, through a discrete event simulation model. The practical issues associated with simulation optimization, such as stochastic variables and constraints, were also taken into consideration.
A three-level BDDC algorithm for Mortar discretizations
Kim, H.; Tu, X.
2007-12-09
In this paper, a three-level BDDC algorithm is developed for the solutions of large sparse algebraic linear systems arising from the mortar discretization of elliptic boundary value problems. The mortar discretization is considered on geometrically non-conforming subdomain partitions. In two-level BDDC algorithms, the coarse problem needs to be solved exactly. However, its size will increase with the increase of the number of the subdomains. To overcome this limitation, the three-level algorithm solves the coarse problem inexactly while a good rate of convergence is maintained. This is an extension of previous work, the three-level BDDC algorithms for standard finite element discretization. Estimates of the condition numbers are provided for the three-level BDDC method and numerical experiments are also discussed.
Dissipative discrete breathers: periodic, quasiperiodic, chaotic, and mobile.
Martínez, P J; Meister, M; Floría, L M; Falo, F
2003-06-01
The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations. PMID:12777126
Discreteness-induced transitions in multibody reaction systems.
Saito, Yohei; Sughiyama, Yuki; Kaneko, Kunihiko; Kobayashi, Tetsuya J
2016-08-01
A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be attributed to either a relative increase in the noise intensity or to the discreteness of the state space due to the small system size. The former mechanism has been intensively investigated using several toy and realistic models. However, the latter has rarely been analyzed and is sometimes confused with the former, because a toy model that extracts the essence of the discreteness-induced transition mechanism is lacking. In this work, we propose a one- and three-body reaction system as a minimal model of the discreteness-induced transition and derive the conditions under which this transition occurs in more complex systems. This work enriches our understanding of the influence of small system size on system behavior. PMID:27627279
Stability analysis of the Euler discretization for SIR epidemic model
Suryanto, Agus
2014-06-19
In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaos phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.
Emotion word recognition: discrete information effects first, continuous later?
Briesemeister, Benny B; Kuchinke, Lars; Jacobs, Arthur M
2014-05-20
Manipulations of either discrete emotions (e.g. happiness) or affective dimensions (e.g. positivity) have a long tradition in emotion research, but interactive effects have never been studied, based on the assumption that the two underlying theories are incompatible. Recent theorizing suggests, however, that the human brain relies on two affective processing systems, one working on the basis of discrete emotion categories, and the other working along affective dimensions. Presenting participants with an orthogonal manipulation of happiness and positivity in a lexical decision task, the present study meant to test the appropriateness of this assumption in emotion word recognition. Behavioral and electroencephalographic data revealed independent effects for both variables, with happiness affecting the early visual N1 component, while positivity affected an N400-like component and the late positive complex. These results are interpreted as evidence for a sequential processing of affective information, with discrete emotions being the basis for later dimensional appraisal processes. PMID:24713350
Supervised and unsupervised discretization methods for evolutionary algorithms
Cantu-Paz, E
2001-01-24
This paper introduces simple model-building evolutionary algorithms (EAs) that operate on continuous domains. The algorithms are based on supervised and unsupervised discretization methods that have been used as preprocessing steps in machine learning. The basic idea is to discretize the continuous variables and use the discretization as a simple model of the solutions under consideration. The model is then used to generate new solutions directly, instead of using the usual operators based on sexual recombination and mutation. The algorithms presented here have fewer parameters than traditional and other model-building EAs. They expect that the proposed algorithms that use multivariate models scale up better to the dimensionality of the problem than existing EAs.
Hybrid discrete/continuum algorithms for stochastic reaction networks
Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.
2014-10-22
Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discretemore » and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.« less
Correction of Discretization Errors Simulated at Supply Wells.
MacMillan, Gordon J; Schumacher, Jens
2015-01-01
Many hydrogeology problems require predictions of hydraulic heads in a supply well. In most cases, the regional hydraulic response to groundwater withdrawal is best approximated using a numerical model; however, simulated hydraulic heads at supply wells are subject to errors associated with model discretization and well loss. An approach for correcting the simulated head at a pumping node is described here. The approach corrects for errors associated with model discretization and can incorporate the user's knowledge of well loss. The approach is model independent, can be applied to finite difference or finite element models, and allows the numerical model to remain somewhat coarsely discretized and therefore numerically efficient. Because the correction is implemented external to the numerical model, one important benefit of this approach is that a response matrix, reduced model approach can be supported even when nonlinear well loss is considered. PMID:25142180
A space-time discretization procedure for wave propagation problems
NASA Technical Reports Server (NTRS)
Davis, Sanford
1989-01-01
Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.
Are nonlinear discrete cellular automata compatible with quantum mechanics?
NASA Astrophysics Data System (ADS)
Elze, Hans-Thomas
2015-07-01
We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises “Hamiltonian CA” with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The dynamics is linear, quite similar to unitary evolution described by the Schrödinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon's sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.
Li, Zhelong; Zhang, Dongxiao; Li, Xiqing
2010-02-15
Advances in pore structure characterization and lattice-Boltzmann (LB) simulations of flow fields in pore spaces are making mechanistic simulations of colloid transport in real porous media a realistic goal. The primary challenge to reach this goal may be the computational demand of LB flow simulations in discretized porous medium domains at an assemblage scale. In this work, flow fields in simple cubic and dense packing systems were simulated at different discretization resolutions using the LB method. The simulated flow fields were incorporated into to a three-dimensional particle tracking model to simulate colloid transport in the two systems. The simulated colloid deposition tended to become asymptotic at a critical discretization resolution (voxel-grain size ratio = 0.01) at groundwater flow regimes for colloids down to submicrometer level under favorable conditions and down to around 1 microm under unfavorable conditions. The average simulated fluid velocities near grain surfaces were extracted to explain the sensitivities of simulated depositions to space discretization under both conditions. At the critical discretization resolution, current computation capacity would allow flow simulations and particle tracking in assemblage porous medium domains. In addition, particle tracking simulations revealed that colloids may be retained in flow vortices under conditions both favorable and unfavorable for deposition. Colloid retention in flow vortices has been proposed only very recently. Here we provide a mechanistic confirmation to this novel retention process. PMID:20088544
Threshold signature scheme based on factoring and discrete logarithms
NASA Astrophysics Data System (ADS)
Mohamad, S. A.; Ismail, E. S.
2012-09-01
Recently, many documents or messages from an organization need to be signed by more than one person. For that reason, many threshold signatures based on various problems in number theory have been developed. In this paper, a threshold signature scheme based on two most popular number theory problems, namely factoring and discrete logarithms, was proposed. The advantage of this new scheme is based on the fact that it is very hard to solve both factoring and discrete logarithms problems simultaneously. This scheme is also shown secure against several attacks and requires a reasonable time complexity in both signing and verifying phase.
Discrete Lange-Newell criterion for dissipative systems.
Ndzana, Fabien I I; Mohamadou, Alidou; Kofané, Timoleon Crépin
2009-05-01
We report on the derivation of the discrete complex Ginzburg-Landau equation with first- and second-neighbor couplings using a nonlinear electrical network. Furthermore, we discuss theoretically and numerically modulational instability of plane carrier waves launched through the line. It is pointed out that the underlying analysis not only spells out the discrete Lange-Newell criterion by the means of the linear stability analysis at which the modulational instability occurs for the generation of a train of ultrashort pulses, but also characterizes the long-time dynamical behavior of the system when the instability grows. PMID:19518586
Strongly asymmetric discrete Painlevé equations: The multiplicative case
NASA Astrophysics Data System (ADS)
Grammaticos, B.; Ramani, A.; Tamizhmani, K. M.; Tamizhmani, T.; Satsuma, J.
2016-04-01
We examine a class of multiplicative discrete Painlevé equations which may possess a strongly asymmetric form. When the latter occurs, the equation is written as a system of two equations the right hand sides of which have different functional forms. The present investigation focuses upon two canonical families of the Quispel-Roberts-Thompson classification which contain equations associated with the affine Weyl groups D5 ( 1 ) and E6 ( 1 ) (or groups appearing lower in the degeneration cascade of these two). Many new discrete Painlevé equations with strongly asymmetric forms are obtained.
A Versatile and Scalable Strategy to Discrete Oligomers.
Lawrence, Jimmy; Lee, Sang-Ho; Abdilla, Allison; Nothling, Mitchell D; Ren, Jing M; Knight, Abigail S; Fleischmann, Carolin; Li, Youli; Abrams, Austin S; Schmidt, Bernhard V K J; Hawker, Michael C; Connal, Luke A; McGrath, Alaina J; Clark, Paul G; Gutekunst, Will R; Hawker, Craig J
2016-05-18
A versatile strategy is reported for the multigram synthesis of discrete oligomers from commercially available monomer families, e.g., acrylates, styrenics, and siloxanes. Central to this strategy is the identification of reproducible procedures for the separation of oligomer mixtures using automated flash chromatography systems with the effectiveness of this approach demonstrated through the multigram preparation of discrete oligomer libraries (Đ = 1.0). Synthetic availability, coupled with accurate structural control, allows these functional building blocks to be harnessed for both fundamental studies as well as targeted technological applications. PMID:27152711
Casting metal nanowires within discrete self-assembled peptide nanotubes.
Reches, Meital; Gazit, Ehud
2003-04-25
Tubular nanostructures are suggested to have a wide range of applications in nanotechnology. We report our observation of the self-assembly of a very short peptide, the Alzheimer's beta-amyloid diphenylalanine structural motif, into discrete and stiff nanotubes. Reduction of ionic silver within the nanotubes, followed by enzymatic degradation of the peptide backbone, resulted in the production of discrete nanowires with a long persistence length. The same dipeptide building block, made of D-phenylalanine, resulted in the production of enzymatically stable nanotubes. PMID:12714741
Casting Metal Nanowires Within Discrete Self-Assembled Peptide Nanotubes
NASA Astrophysics Data System (ADS)
Reches, Meital; Gazit, Ehud
2003-04-01
Tubular nanostructures are suggested to have a wide range of applications in nanotechnology. We report our observation of the self-assembly of a very short peptide, the Alzheimer's β-amyloid diphenylalanine structural motif, into discrete and stiff nanotubes. Reduction of ionic silver within the nanotubes, followed by enzymatic degradation of the peptide backbone, resulted in the production of discrete nanowires with a long persistence length. The same dipeptide building block, made of D-phenylalanine, resulted in the production of enzymatically stable nanotubes.
Systolic array for fast computation of discrete cosine transform
NASA Astrophysics Data System (ADS)
Liu, Jianguo; Li, H. F.; Chan, Francis H. Y.; Lam, F. K.
1998-09-01
Discrete cosine transform (DCT) is widely used in signal processing. This paper presents a novel approach to perform DCT. DCT is expressed in terms of discrete moments and a systolic array for computing DCT with only a few multiplications and without any cosine evaluations has been proposed. The execution time of the systolic array is only O(Nlog2N/log2log2N) in computing 1D DCT. The approach is also applicable to multiple dimensional DCT and DCT inverses.
Hierarchical Discrete Event Supervisory Control of Aircraft Propulsion Systems
NASA Technical Reports Server (NTRS)
Yasar, Murat; Tolani, Devendra; Ray, Asok; Shah, Neerav; Litt, Jonathan S.
2004-01-01
This paper presents a hierarchical application of Discrete Event Supervisory (DES) control theory for intelligent decision and control of a twin-engine aircraft propulsion system. A dual layer hierarchical DES controller is designed to supervise and coordinate the operation of two engines of the propulsion system. The two engines are individually controlled to achieve enhanced performance and reliability, necessary for fulfilling the mission objectives. Each engine is operated under a continuously varying control system that maintains the specified performance and a local discrete-event supervisor for condition monitoring and life extending control. A global upper level DES controller is designed for load balancing and overall health management of the propulsion system.
Long-lived discrete breathers in free-standing graphene
NASA Astrophysics Data System (ADS)
Fraile, Alberto; Koukaras, Emmanuel N.; Papagelis, Konstantinos; Lazarides, Nikos; Tsironis, G. P.
2016-06-01
Intrinsic localized modes or discrete breathers are investigated by molecular dynamics simulations in free-standing graphene. Discrete breathers are generated either through thermal quenching of the graphene lattice or by proper initialization, with frequencies and lifetimes sensitively depending on the interatomic potential describing the carbon-carbon interaction. In the most realistic scenario, for which temperature-dependent molecular dynamics simulations in three dimension using a graphene-specific interatomic potential are performed, the breather lifetimes increase to hundreds of picoseconds even at relatively high temperatures. These lifetimes are much higher than those anticipated from earlier calculations, and may enable direct breather observation in Raman spectroscopy experiments.
Asymptotic analysis of spatial discretizations in implicit Monte Carlo
Densmore, Jeffery D
2008-01-01
We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large, We demonstrate the validity of our analysis with a set of numerical examples.
Asymptotic analysis of spatial discretizations in implicit Monte Carlo
Densmore, Jeffery D
2009-01-01
We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.
Testing discrete symmetries at a super τ -charm factory
NASA Astrophysics Data System (ADS)
Bevan, Adrian John
2016-02-01
Tests of discrete symmetry violation have played an important role in understanding the structure of weak interactions in the Standard Model of particle physics. Historically, these measurements have been extensively performed in experiments with large samples of K and B mesons. A high luminosity τ-charm facility presents physicists with the opportunity to comprehensively explore discrete symmetry violation and test the Standard Model using τ leptons, charm mesons, and charmed baryons. This paper discusses several possible measurements for a future τ-charm factory.
Microfabricated, flowthrough porous apparatus for discrete detection of binding reactions
Beattie, Kenneth L.
1998-01-01
An improved microfabricated apparatus for conducting a multiplicity of individual and simultaneous binding reactions is described. The apparatus comprises a substrate on which are located discrete and isolated sites for binding reactions. The apparatus is characterized by discrete and isolated regions that extend through said substrate and terminate on a second surface thereof such that when a test sample is allowed to the substrate, it is capable of penetrating through each such region during the course of said binding reaction. The apparatus is especially useful for sequencing by hybridization of DNA molecules.
A note on a Discrete Boltzmann Equation with multiple collisions
NASA Astrophysics Data System (ADS)
Oliveira, Filipe; Soares, Ana Jacinta
2008-05-01
We compute a non-trivial explicit solution for the one-dimensional plane 6-velocity discrete Boltzmann model with multiple collisions introduced in [E. Longo, R. Monaco, On the discrete kinetic theory with multiple collisions: Plane six-velocity and unsteady Couette flow, in: Muntz, et al. (Eds.), The Proceedings of Rarefied Gas Dynamics, in: AIAA Publ., vol. 118, 1989, pp. 118-130] which asymptotically connects two particular equilibrium states. We prove that such a solution exists provided that a suitable condition on the differential elastic cross sections holds.
Reality Property of Discrete Wronski Map with Imaginary Step
NASA Astrophysics Data System (ADS)
Mukhin, Evgeny; Tarasov, Vitaly; Varchenko, Alexander
2012-05-01
For a set of quasi-exponentials with real exponents, we consider the discrete Wronskian (also known as Casorati determinant) with pure imaginary step 2 h. We prove that if the coefficients of the discrete Wronskian are real and the imaginary parts of its roots are bounded by | h|, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This result is a generalization of the statement of the B. and M. Shapiro conjecture on spaces of polynomials. The proof is based on the Bethe ansatz for the XXX model.
Binary classification of real sequences by discrete-time systems
NASA Technical Reports Server (NTRS)
Kaliski, M. E.; Johnson, T. L.
1979-01-01
This paper considers a novel approach to coding or classifying sequences of real numbers through the use of (generally nonlinear) finite-dimensional discrete-time systems. This approach involves a finite-dimensional discrete-time system (which we call a real acceptor) in cascade with a threshold type device (which we call a discriminator). The proposed classification scheme and the exact nature of the classification problem are described, along with two examples illustrating its applicability. Suggested approaches for further research are given.
A virial expansion for discrete charges buried in a membrane.
Tsien, R Y
1978-01-01
Recent experiments (1,2) have shown that hydrophobic ions adsorbed to lipid membranes repel each other significantly at densities as low as one charge every few tens of square nanometers. This paper shows how to calculate the mutual repulsion of a population of such ions, assumed to be discrete but free to diffuse laterally in the plane of the membrane. The results fall between those for uniformly smeared charges (the "three-capacitor" model) and those for discrete charges immobilized on a periodic lattice. PMID:728530
Methodology for characterizing modeling and discretization uncertainties in computational simulation
ALVIN,KENNETH F.; OBERKAMPF,WILLIAM L.; RUTHERFORD,BRIAN M.; DIEGERT,KATHLEEN V.
2000-03-01
This research effort focuses on methodology for quantifying the effects of model uncertainty and discretization error on computational modeling and simulation. The work is directed towards developing methodologies which treat model form assumptions within an overall framework for uncertainty quantification, for the purpose of developing estimates of total prediction uncertainty. The present effort consists of work in three areas: framework development for sources of uncertainty and error in the modeling and simulation process which impact model structure; model uncertainty assessment and propagation through Bayesian inference methods; and discretization error estimation within the context of non-deterministic analysis.
Discrete Random Media Techniques for Microwave Modeling of Vegetated Terrain
NASA Technical Reports Server (NTRS)
Lang, R. H.
1984-01-01
Microwave remote sensing of agricultural crops and forested regions is studied. Long term goals of the research involve modeling vegetation so that radar signatures can be used to infer the parameters which characterize the vegetation and underlying ground. Vegetation is modeled by discrete scatterers viz, leaves, stems, branches and trunks. These are replaced by glossy dielectric discs and cylinders. Rough surfaces are represented by their mean and spectral characteristics. Average scattered power is then calculated by employing discrete random media methodology such as the distorted Born approximation or transport theory. Both coherent and incoherent multiple scattering techniques are explored. Once direct methods are developed, inversion techniques can be investigated.
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Moulton, J.D.; Ascher, U.M.; Morel, J.E.
1996-12-31
Particular classes of nodal methods and mixed hybrid finite element methods lead to equivalent, robust and accurate discretizations of 2nd order elliptic PDEs. However, widespread popularity of these discretizations has been hindered by the awkward linear systems which result. The present work exploits this awkwardness, which provides a natural partitioning of the linear system, by defining two optimal preconditioners based on approximate Schur complements. Central to the optimal performance of these preconditioners is their sparsity structure which is compatible with Dendy`s black box multigrid code.
Discrete-time adaptive control of robot manipulators
NASA Technical Reports Server (NTRS)
Tarokh, M.
1989-01-01
A discrete-time model reference adaptive control scheme is developed for trajectory tracking of robot manipulators. Hyperstability theory is utilized to derive the adaptation laws for the controller gain matrices. It is shown that asymptotic trajectory tracking is achieved despite gross robot parameter variation and uncertainties. The method offers considerable design flexibility and enables the designer to improve the performance of the control system by adjusting free design parameters. The discrete-time adaptation algorithm is extremely simple and is therefore suitable for real-time implementation.
New discretization and solution techniques for incompressible viscous flow problems
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.; Nicolaides, R. A.; Liu, C. H.
1983-01-01
Several topics arising in the finite element solution of the incompressible Navier-Stokes equations are considered. Specifically, the question of choosing finite element velocity/pressure spaces is addressed, particularly from the viewpoint of achieving stable discretizations leading to convergent pressure approximations. The role of artificial viscosity in viscous flow calculations is studied, emphasizing work by several researchers for the anisotropic case. The last section treats the problem of solving the nonlinear systems of equations which arise from the discretization. Time marching methods and classical iterative techniques, as well as some modifications are mentioned.
Slow convergence to effective medium in finite discrete metamaterials
NASA Astrophysics Data System (ADS)
Lapine, M.; McPhedran, R. C.; Poulton, C. G.
2016-06-01
It is known that metamaterial properties may differ significantly from the predictions of effective-medium theory. In many cases this is due to the finite size and discrete structure, which cannot be neglected in practical samples with a relatively small amount of elements. We analyze the response of finite discrete metamaterial objects of a spherical shape and demonstrate the role of boundary effects in these structures, pointing out an interplay between the size of the structure and the dissipation. We conclude that the discrepancy between the actual resonance frequency of a sphere and the effective-medium prediction is inversely proportional to the size of the sphere.
Spatial and temporal conjugacy of meso-scale discrete aurora
NASA Astrophysics Data System (ADS)
Sato, Natsuo; Kadokura, Akira
2009-06-01
We report on spatial and temporal conjugacy of meso-scale (˜10-200 km) discrete aurora using highly similar auroras that were simultaneously acquired with all-sky TV cameras situated at two geomagnetically conjugate points, at Tjornes in Iceland and at Syowa Station in Antarctica. During this event, discrete auroras, including both east-west and north-south directed auroral forms, showed excellent similarity in terms of shapes, movements and luminosity variations at both observatories. Similar and dissimilar auroras appeared simultaneously in adjoining areas of the sky in both hemispheres.
Gravity cutoff in theories with large discrete symmetries.
Dvali, Gia; Redi, Michele; Sibiryakov, Sergey; Vainshtein, Arkady
2008-10-10
We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z(N) discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with N particle species, though a priori, a large discrete symmetry does not imply a large number of species. Thus, there emerges a potentially wide class of new theories that address the hierarchy problem by lowering the gravitational cutoff due to the existence of large Z(10(32))-type symmetries. PMID:18999587
A survey of algebraic actions of the discrete Heisenberg group
NASA Astrophysics Data System (ADS)
Lind, D.; Schmidt, K.
2015-08-01
The study of actions of countable groups by automorphisms of compact Abelian groups has recently undergone intensive development, revealing deep connections with operator algebras and other areas. The discrete Heisenberg group is the simplest non-commutative example, where dynamical phenomena related to its non-commutativity already illustrate many of these connections. The explicit structure of this group means that these phenomena have concrete descriptions, which are not only instances of the general theory but are also testing grounds for further work. This paper surveys what is known about such actions of the discrete Heisenberg group, providing numerous examples and emphasizing many of the open problems that remain. Bibliography: 71 titles.
An averaging analysis of discrete-time indirect adaptive control
NASA Technical Reports Server (NTRS)
Phillips, Stephen M.; Kosut, Robert L.; Franklin, Gene F.
1988-01-01
An averaging analysis of indirect, discrete-time, adaptive control systems is presented. The analysis results in a signal-dependent stability condition and accounts for unmodeled plant dynamics as well as exogenous disturbances. This analysis is applied to two discrete-time adaptive algorithms: an unnormalized gradient algorithm and a recursive least-squares (RLS) algorithm with resetting. Since linearization and averaging are used for the gradient analysis, a local stability result valid for small adaptation gains is found. For RLS with resetting, the assumption is that there is a long time between resets. The results for the two algorithms are virtually identical, emphasizing their similarities in adaptive control.
On classification of discrete, scalar-valued Poisson brackets
NASA Astrophysics Data System (ADS)
Parodi, E.
2012-10-01
We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on a target space of dimension 1. We prove that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be reduced to a cubic PB of the standard Volterra lattice by discrete Miura-type transformations. Finally, by improving a lattice consolidation procedure, we obtain new families of non-degenerate, vector-valued and first-order dDGPBs that can be considered in the framework of admissible Lie-Poisson group theory.
Single-tone parameter estimation from discrete-time observations
NASA Technical Reports Server (NTRS)
Rife, D. C.; Boorstyn, R. R.
1974-01-01
Estimation of the parameters of a single-frequency complex tone from a finite number of noisy discrete-time observations is discussed. The appropriate Cramer-Rao bounds and maximum-likelihood (ML) estimation algorithms are derived. Some properties of the ML estimators are proved. The relationship of ML estimation to the discrete Fourier transform is exploited to obtain practial algorithms. The threshold effect of one algorithm is analyzed and compared to simulation results. Other simulation results verify other aspects of the analysis.
Bai, Xiao-Dong; Xue, Ju-Kui
2012-12-01
By considering a general discrete nonlinear Schrödinger model with arbitrary values of nonlinearity power and disorder, the existence and stability of a discrete breather (DB) in a general nonlinear lattice are discussed. It is found that nonlinearity and disorder play important roles in determining the existence and stability of the DB. Nonlinearity (expressed by the interparticle interaction) and disorder can enhance the stability of the DB. Remarkably, we find that the DB is most stable when the nonlinearity power is equal to a critical value. The effects of nonlinearity, nonlinearity power, and disorder on the stability of the DB are strongly coupled. PMID:23368070
A COMPARISON OF INTERCELL METRICS ON DISCRETE GLOBAL GRID SYSTEMS
A discrete global grid system (DGGS) is a spatial data model that aids in global research by serving as a framework for environmental modeling, monitoring and sampling across the earth at multiple spatial scales. Topological and geometric criteria have been proposed to evaluate a...
Feedback-bounded stabilisation of certain discrete Volterra systems
NASA Astrophysics Data System (ADS)
Kotsios, Stelios
2016-06-01
Throughout this paper, we present a method for designing feedback-laws which stabilise nonlinear discrete Volterra systems. Our method is based on a factorisation algorithm which decomposes the original system as a composition of a δ-polynomial and a linear series.
Encapsulated ionic liquids (ENILs): from continuous to discrete liquid phase.
Palomar, Jose; Lemus, Jesus; Alonso-Morales, Noelia; Bedia, Jorge; Gilarranz, Miguel A; Rodriguez, Juan J
2012-10-14
Encapsulated ionic liquid (ENIL) material was developed, consisting of ionic liquid (IL) introduced into carbon submicrocapsules. ENILs contain >85% w/w of IL but discretized in submicroscopic encapsulated drops, drastically increasing the surface contact area with respect to the neat fluid. ENIL materials were here tested for gas separation processes, obtaining a drastic increase in mass transfer rate. PMID:22935733
3D imaging of nanomaterials by discrete tomography.
Batenburg, K J; Bals, S; Sijbers, J; Kübel, C; Midgley, P A; Hernandez, J C; Kaiser, U; Encina, E R; Coronado, E A; Van Tendeloo, G
2009-05-01
The field of discrete tomography focuses on the reconstruction of samples that consist of only a few different materials. Ideally, a three-dimensional (3D) reconstruction of such a sample should contain only one grey level for each of the compositions in the sample. By exploiting this property in the reconstruction algorithm, either the quality of the reconstruction can be improved significantly, or the number of required projection images can be reduced. The discrete reconstruction typically contains fewer artifacts and does not have to be segmented, as it already contains one grey level for each composition. Recently, a new algorithm, called discrete algebraic reconstruction technique (DART), has been proposed that can be used effectively on experimental electron tomography datasets. In this paper, we propose discrete tomography as a general reconstruction method for electron tomography in materials science. We describe the basic principles of DART and show that it can be applied successfully to three different types of samples, consisting of embedded ErSi(2) nanocrystals, a carbon nanotube grown from a catalyst particle and a single gold nanoparticle, respectively. PMID:19269094
Solitons in the discrete nonpolynomial Schrödinger equation
NASA Astrophysics Data System (ADS)
Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.; Salasnich, Luca
2008-07-01
We introduce a species of the discrete nonlinear Schrödinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrödinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile.
The Processing of Emotional Expressions as Discrete and Global Categories.
ERIC Educational Resources Information Center
Kestenbaum, Roberta
This study explored the use of analytic and holistic modes of processing in the recognition of emotional expressions as discrete and global categories. Five- and seven-year-olds and adults were presented with a series of slides that showed different parts of faces depicting either happiness, surprise, fear, or anger. Slides ranged from single…
Analyzing neuronal networks using discrete-time dynamics
NASA Astrophysics Data System (ADS)
Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David
2010-05-01
We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.
Continuous and discrete describing function analysis of the LST system
NASA Technical Reports Server (NTRS)
Kuo, B. C.; Singh, G.; Yackel, R. A.
1973-01-01
A describing function of the control moment gyros (CMG) frictional nonlinearity is derived using the analytic torque equation. Computer simulation of the simplified Large Space Telescope (LST) system with the analytic torque expression is discussed along with the transfer functions of the sampled-data LST system, and the discrete describing function of the GMC frictionality.
Exploring Discretization Error in Simulation-Based Aerodynamic Databases
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J.; Nemec, Marian
2010-01-01
This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.
Discrete representation of perceptual structure underlying consonant confusions.
Soli, S D; Arabie, P; Carroll, J D
1986-03-01
The perceptual representation of speech is generally assumed to be discrete rather than continuous, pointing to the need for general discrete analytic models to represent observed perceptual similarities among speech sounds. The INDCLUS (INdividual Differences CLUStering) model and algorithm [J.D. Carroll and P. Arabie, Psychometrika 48, 157-169 (1983)] can provide this generality, representing symmetric three-way similarity data (stimuli X stimuli X conditions) as an additive combination of overlapping, and generally not hierarchial, clusters whose weights (which are numerical values gauging the importance of the clusters) vary both as a function of the cluster and condition being considered. INDCLUS was used to obtain a discrete representation of underlying perceptual structure in the Miller and Nicely consonant confusion data [G.A. Miller and P.E. Nicely, J. Acoust. Soc. Am. 27, 338-352 (1955)]. A 14-cluster solution accounted for 82.9% of total variance across the 17 listening conditions. The cluster composition and the variations in cluster weights as a function of stimulus degradation were interpreted in terms of the common and unique perceptual attributes of the consonants within each cluster. Low-pass filtering and noise masking selectively degraded unique attributes, especially the cues for place of articulation, while high-pass filtering degraded both unique and common attributes. The clustering results revealed that perceptual similarities among consonants are accurately modeled by additive combinations of their specific and discrete acoustic attributes whose weights are determined by the nature of the stimulus degradation. PMID:3958325
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-04-15
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
Controlling the path of discretized light in waveguide lattices
Longhi, Stefano
2011-01-15
A general method for flexible control of the path of discretized light beams in homogeneous waveguide lattices, based on longitudinal modulation of the coupling constant, is theoretically proposed. As compared to beam steering and refraction achievable in graded-index waveguide arrays, the proposed approach enables the synthesis of rather arbitrary target paths.
29 CFR 541.202 - Discretion and independent judgment.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 29 Labor 3 2011-07-01 2011-07-01 false Discretion and independent judgment. 541.202 Section 541.202 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR REGULATIONS DEFINING AND DELIMITING THE EXEMPTIONS FOR EXECUTIVE, ADMINISTRATIVE, PROFESSIONAL, COMPUTER AND OUTSIDE SALES EMPLOYEES...
29 CFR 541.202 - Discretion and independent judgment.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 29 Labor 3 2013-07-01 2013-07-01 false Discretion and independent judgment. 541.202 Section 541.202 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR REGULATIONS DEFINING AND DELIMITING THE EXEMPTIONS FOR EXECUTIVE, ADMINISTRATIVE, PROFESSIONAL, COMPUTER AND OUTSIDE SALES EMPLOYEES...
Teaching Discrete Mathematics Entirely from Primary Historical Sources
ERIC Educational Resources Information Center
Barnett, Janet Heine; Bezhanishvili, Guram; Lodder, Jerry; Pengelley, David
2016-01-01
We describe teaching an introductory discrete mathematics course entirely from student projects based on primary historical sources. We present case studies of four projects that cover the content of a one-semester course, and mention various other courses that we have taught with primary source projects.
Hybrid discrete- and continuous-variable quantum information
NASA Astrophysics Data System (ADS)
Andersen, Ulrik L.; Neergaard-Nielsen, Jonas S.; van Loock, Peter; Furusawa, Akira
2015-09-01
Research in quantum information processing has followed two different directions: the use of discrete variables (qubits) and that of high-dimensional, continuous-variable Gaussian states (coherent and squeezed states). Recently, these two approaches have been converging in potentially more powerful hybrid protocols.
Discrete Waves and Phototransduction in Voltage-damped Ventral Photoreceptors
Behbehani, Michael; Srebro, Richard
1974-01-01
Discrete waves in the voltage-clamped photoreceptor of Limulus are remarkably similar in all essential properties to those found in an unclamped cell. The latency distribution of discrete waves is not affected by considerable changes in the holding potential in a voltage-clamped cell. Both large and small waves occur in voltage-clamped and unclamped cells and in approximately the same proportion. Large and small waves also share the same latency distributions and spectral sensitivity. We suggest that small waves may result from the activation of damaged membrane areas. Large waves have an average amplitude of approximately 5 nA in voltage-clamped photoreceptors. It probably requires several square microns of cell membrane to support this much photo-current. Thus the amplification inherent in the discrete wave process may involve spatial spread of activation from unimolecular dimensions to several square microns of cell membrane surface. Neither local current flow, nor pre-packaging of any transmitter substance appears to be involved in the amplification process. The possible mechanisms of the amplification are evaluated with relationship to the properties of discrete waves. PMID:4846766
An adaptive mesh refinement algorithm for the discrete ordinates method
Jessee, J.P.; Fiveland, W.A.; Howell, L.H.; Colella, P.; Pember, R.B.
1996-03-01
The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits the local grid refinement to minimize spatial discretization error of the RTE. An error estimator is applied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then solved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The following aspects of the algorithm are discussed: error estimation, grid generation, communication between refined levels, and solution sequencing. This initial formulation employs the step scheme, and is valid for absorbing and isotopically scattering media in two-dimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single-grid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard single-grid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until three-dimensional geometries are considered.
Fabrication and optical enhancing properties of discrete supercrystals.
Tebbe, Moritz; Lentz, Sarah; Guerrini, Luca; Fery, Andreas; Alvarez-Puebla, Ramon A; Pazos-Perez, Nicolas
2016-07-01
Discrete gold nanoparticle crystals with tunable size and morphology are fabricated via a fast and inexpensive template-assisted method. The highly precise hierarchical organization of the plasmonic building blocks yields superstructures with outstanding behaviour for surface-enhanced Raman scattering analysis. PMID:26898333
On Projecting Discretized Electromagnetic Fields with Unstructured Grids
Lee, Lie-Quan; Candel, Arno; Kabel, Andrea; Li, Zenghai; /SLAC
2008-08-13
A new method for projecting discretized electromagnetic fields on one unstructured grid to another grid is presented in this paper. Two examples are used for studying the errors of different projection methods. The analysis shows that the new method is very effective on balancing both the error of the electric field and that of the magnetic field (or curl of the electric field).
Constructing Contracts: Making Discrete Mathematics Relevant to Beginning Programmers
ERIC Educational Resources Information Center
Gegg-Harrison, Timothy S.
2005-01-01
Although computer scientists understand the importance of discrete mathematics to the foundations of their field, computer science (CS) students do not always see the relevance. Thus, it is important to find a way to show students its relevance. The concept of program correctness is generally taught as an activity independent of the programming…
29 CFR 541.202 - Discretion and independent judgment.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 29 Labor 3 2010-07-01 2010-07-01 false Discretion and independent judgment. 541.202 Section 541.202 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR REGULATIONS DEFINING AND DELIMITING THE EXEMPTIONS FOR EXECUTIVE, ADMINISTRATIVE, PROFESSIONAL, COMPUTER AND OUTSIDE SALES EMPLOYEES...
Nonlinear stability of discrete shocks for systems of conservation laws
NASA Astrophysics Data System (ADS)
Liu, Jian-Guo; Xin, Zhouping
1993-09-01
In this paper we study the asymptotic nonlinear stability of discrete shocks for the Lax-Friedrichs scheme for approximating general m×m systems of nonlinear hyperbolic conservation laws. It is shown that weak single discrete shocks for such a scheme are nonlinearly stable in the L p-norm for all p ≧ 1, provided that the sums of the initial perturbations equal zero. These results should shed light on the convergence of the numerical solution constructed by the Lax-Friedrichs scheme for the single-shock solution of system of hyperbolic conservation laws. If the Riemann solution corresponding to the given far-field states is a superposition of m single shocks from each characteristic family, we show that the corresponding multiple discrete shocks are nonlinearly stable in L p (P ≧ 2). These results are proved by using both a weighted estimate and a characteristic energy method based on the internal structures of the discrete shocks and the essential monotonicity of the Lax-Friedrichs scheme.
Conformal variations and quantum fluctuations in discrete gravity
NASA Astrophysics Data System (ADS)
Marzuoli, Annalisa; Merzi, Dario
2016-05-01
After an overview of variational principles for discrete gravity, and on the basis of the approach to conformal transformations in a simplicial PL setting proposed by Luo and Glickenstein, we present at a heuristic level an improved scheme for addressing the gravitational (Euclidean) path integral and geometrodynamics.
On discrete symmetries and torsion homology in F-theory
NASA Astrophysics Data System (ADS)
Mayrhofer, Christoph; Palti, Eran; Till, Oskar; Weigand, Timo
2015-06-01
We study the relation between discrete gauge symmetries in F-theory compactifications and torsion homology on the associated Calabi-Yau manifold. Focusing on the simplest example of a symmetry, we show that there are two physically distinct ways that such a discrete gauge symmetry can arise. First, compactifications of M-Theory on Calabi-Yau threefolds which support a genus-one fibration with a bi-section are known to be dual to six-dimensional F-theory vacua with a gauge symmetry. We show that the resulting five-dimensional theories do not have a symmetry but that the latter emerges only in the F-theory decompactification limit. Accordingly the genus-one fibred Calabi-Yau manifolds do not exhibit torsion in homology. Associated to the bi-section fibration is a Jacobian fibration which does support a section. Compactifying on these related but distinct varieties does lead to a symmetry in five dimensions and, accordingly, we find explicitly an associated torsion cycle. We identify the expected particle and membrane system of the discrete symmetry in terms of wrapped M2 and M5 branes and present a field-theory description of the physics for both cases in terms of circle reductions of six-dimensional theories. Our results and methods generalise straightforwardly to larger discrete symmetries and to four-dimensional compactifications.
Neutrino transitional magnetic moment and non-Abelian discrete symmetry
Chang, D. Fermi National Laboratory, P.O. Box 500, Batavia, IL ); Keung, W. Fermi National Laboratory, P.O. Box 500, Batavia, IL ); Senjanovic, G. Bartol Research Institute, University of Delaware, Newark, DE )
1990-09-01
We propose a mechanism which naturally will give rise to a small mass but a large transitional magnetic moment for the neutrino such that the solar-neutrino deficit problem can be explained. The idea is a discrete version of Voloshin's SU(2) mechanism. An example of such a mechanism using the quaternion group is illustrated.
Thermal modelling using discrete vasculature for thermal therapy: a review
Kok, H.P.; Gellermann, J.; van den Berg, C.A.T.; Stauffer, P.R.; Hand, J.W.; Crezee, J.
2013-01-01
Reliable temperature information during clinical hyperthermia and thermal ablation is essential for adequate treatment control, but conventional temperature measurements do not provide 3D temperature information. Treatment planning is a very useful tool to improve treatment quality and substantial progress has been made over the last decade. Thermal modelling is a very important and challenging aspect of hyperthermia treatment planning. Various thermal models have been developed for this purpose, with varying complexity. Since blood perfusion is such an important factor in thermal redistribution of energy in in vivo tissue, thermal simulations are most accurately performed by modelling discrete vasculature. This review describes the progress in thermal modelling with discrete vasculature for the purpose of hyperthermia treatment planning and thermal ablation. There has been significant progress in thermal modelling with discrete vasculature. Recent developments have made real-time simulations possible, which can provide feedback during treatment for improved therapy. Future clinical application of thermal modelling with discrete vasculature in hyperthermia treatment planning is expected to further improve treatment quality. PMID:23738700
Free vibration of hexagonal panels supported at discrete points
NASA Technical Reports Server (NTRS)
Wu, K. Chauncey
1991-01-01
An analytical study to determine the structural dynamic behavior of a hexagonal panel with discrete simple supports is presented. These panels are representative of the facets of a precision reflector surface. The effects of both support point location and panel curvature on the lowest natural frequency of the panel are quantified and discussed.
Algebraic K-theory of discrete subgroups of Lie groups.
Farrell, F T; Jones, L E
1987-05-01
Let G be a Lie group (with finitely many connected components) and Gamma be a discrete, cocompact, torsion-free subgroup of G. We rationally calculate the algebraic K-theory of the integral group ring ZGamma in terms of the homology of Gamma with trivial rational coefficients. PMID:16593834
Algebraic K-theory of discrete subgroups of Lie groups
Farrell, F. T.; Jones, L. E.
1987-01-01
Let G be a Lie group (with finitely many connected components) and Γ be a discrete, cocompact, torsion-free subgroup of G. We rationally calculate the algebraic K-theory of the integral group ring ZΓ in terms of the homology of Γ with trivial rational coefficients. PMID:16593834
Judgments of Discrete and Continuous Quantity: An Illusory Stroop Effect
ERIC Educational Resources Information Center
Barth, Hilary C.
2008-01-01
Evidence from human cognitive neuroscience, animal neurophysiology, and behavioral research demonstrates that human adults, infants, and children share a common nonverbal quantity processing system with nonhuman animals. This system appears to represent both discrete and continuous quantity, but the proper characterization of the relationship…
On Scaling Modes and Balancing Stochastic, Discretization, and Modeling Error
NASA Astrophysics Data System (ADS)
Brown, J.
2015-12-01
We consider accuracy-cost tradeoffs and the problem of finding Pareto optimal configurations for stochastic forward and inverse problems. As the target accuracy is changed, we should use different physical models, stochastic models, discretizations, and solution algorithms. In this spectrum, we see different scientifically-relevant scaling modes, thus different opportunities and limitations on parallel computers and emerging architectures.
Physical Education & Outdoor Education: Complementary but Discrete Disciplines
ERIC Educational Resources Information Center
Martin, Peter; McCullagh, John
2011-01-01
The Australian Council for Health, Physical Education and Recreation (ACHPER) includes Outdoor Education (OE) as a component of Physical Education (PE). Yet Outdoor Education is clearly thought of by many as a discrete discipline separate from Physical Education. Outdoor Education has a body of knowledge that differs from that of Physical…
Using Discrete Trial Instruction to Teach Children with Angelman Syndrome
ERIC Educational Resources Information Center
Summers, Jane; Szatmari, Peter
2009-01-01
Discrete trial instruction (DTI) was used to teach functional skills to three children with Angelman syndrome, a neurogenetic disorder that overlaps with autism and is associated with severe cognitive, speech, and motor impairments. Children received individual DTI teaching sessions 2 to 3 times per week over a 12-month period and displayed…
Analyzing Neuronal Networks Using Discrete-Time Dynamics
Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David
2010-01-01
We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect's Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network. PMID:20454529
Time to the Doctorate: Multilevel Discrete-Time Hazard Analysis
ERIC Educational Resources Information Center
Wao, Hesborn O.
2010-01-01
Secondary data on 1,028 graduate students nested within 24 programs and admitted into either a Ph. D. or Ed. D. program between 1990 and 2006 at an American public university were used to illustrate the benefits of employing multilevel discrete-time hazard analysis in understanding the timing of doctorate completion in Education and the factors…
Perfect decoupling of linear systems with discrete parameter uncertainties
NASA Technical Reports Server (NTRS)
Dorato, P.; Wang, S.-H.; Asher, R.
1977-01-01
A design procedure based on Gilbert's decoupling parameters for determining a fixed state feedback control law which decouples a linear system with discrete parameter uncertainties is described. Perfect decoupling conditions are established which involve a test for the existence of a solution to a system of linear equations. An actual solution of the linear equations yields the decoupling control law.
Power Analysis for Trials with Discrete-Time Survival Endpoints
ERIC Educational Resources Information Center
Jozwiak, Katarzyna; Moerbeek, Mirjam
2012-01-01
Studies on event occurrence aim to investigate if and when subjects experience a particular event. The timing of events may be measured continuously using thin precise units or discretely using time periods. The latter metric of time is often used in social science research and the generalized linear model (GLM) is an appropriate model for data…
Using a Card Trick to Teach Discrete Mathematics
ERIC Educational Resources Information Center
Simonson, Shai; Holm, Tara S.
2003-01-01
We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…
Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions.
ERIC Educational Resources Information Center
Holland, Paul W.; Thayer, Dorothy T.
2000-01-01
Applied the theory of exponential families of distributions to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. Considers efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and computationally efficient…
Finite strain discrete dislocation plasticity in a total Lagrangian setting
NASA Astrophysics Data System (ADS)
Irani, N.; Remmers, J. J. C.; Deshpande, V. S.
2015-10-01
We present two total Lagrangian formulations for finite strain discrete dislocation plasticity wherein the discrete dislocations are presumed to be adequately represented by singular linear elastic fields thereby extending the superposition method of Van der Giessen and Needleman (1995) to finite strains. The finite deformation effects accounted for are (i) finite lattice rotations and (ii) shape changes due to slip. The two formulations presented differ in the fact that in the "smeared-slip" formulation the discontinuous displacement field is smeared using finite element shape functions while in the "discrete-slip" formulation the weak form of the equilibrium statement is written to account for the slip displacement discontinuity. Both these total Lagrangian formulations use a hyper-elastic constitutive model for lattice elasticity. This overcomes the issues of using singular dislocation fields in a hypo-elastic constitutive relation as encountered in the updated Lagrangian formulation of Deshpande et al. (2003). Predictions of these formulations are presented for the relatively simple problems of tension and compression of single crystals oriented for single slip. These results show that unlike in small-strain discrete dislocation plasticity, finite strain effects result in a size dependent tension/compression asymmetry. Moreover, both formulations give nearly identical predictions and thus we expect that the "smeared-slip" formulation is likely to be preferred due to its relative computational efficiency and simplicity.
Limitations of Discrete Stereology: Steps Toward a More Functional Approach
NASA Astrophysics Data System (ADS)
Proussevitch, A. A.; Sahagian, D. L.; Jutzeler, M.
2012-12-01
Stereology is a statistical and mathematical means to obtain 3D information (such as size, shape, and spatial orientation statistical distributions) from observed 2D cross-section cuts through a volume containing many embedded objects. Examples are SEM imagery of voids in a volcanic rock or tephra, objects in an X-ray tomographic slice, a thin section, a polished section of granite, a planar outcrop of welded volcanic pyroclasts, or sizing of igneous, sedimentary and metamorphic formations from maps. There are three possible approaches to addressing the stereology formulation: 1. Rough approximation using binned data conversion, i.e. discrete stereology. (BAD) 2. Semi-functional data deconvolution, i.e. hybrid of discrete and functional stereology. (BETTER) 3. Solution with 2D-3D functional transformation, i.e. functional stereology (the next step) (BEST). Discrete Stereology: Historically, stereology has been limited to observations of object sizes grouped into discrete bins, or what we now call "discrete" stereology. This approach suffers from severe limitations when applied to natural materials. The most serious of which are exponential error propagation and bias introduced by small numbers of objects in the extremities of the size distribution, and compounded non-spherical shapes and preferred spatial orientations. These limitations do not allow for accurate size distributions of pyroclastic materials, vesicles, and crystals, except for impractically large sample populations. Semi-Functional Stereology: In order to improve the method, a simple first step already taken is "semi-functional" stereology. It combines both discrete object sizing and pre-defined functions of 2D and 3D distributions. Discrete binned observational data is represented by a histogram from which a best fit function for 2D distribution is assigned. This function is then discretized and a 3D distribution is derived from that as in discrete stereology. This approach eliminates some problems
Discrete Mechanics and Optimal Control for Space Trajectory Design
NASA Astrophysics Data System (ADS)
Moore, Ashley
Space trajectory design is often achieved through a combination of dynamical systems theory and optimal control. The union of trajectory design techniques utilizing invariant manifolds of the planar circular restricted three-body problem and the optimal control scheme Discrete Mechanics and Optimal Control (DMOC) facilitates the design of low-energy trajectories in the N-body problem. In particular, DMOC is used to optimize a trajectory from the Earth to the Moon in the 4-body problem, removing the mid-course change in velocity, Delta V, usually necessary for such a trajectory while still exploiting the structure from the invariant manifolds. This thesis also focuses on how to adapt DMOC, a method devised with a constant step size, for the highly nonlinear dynamics involved in trajectory design. Mesh refinement techniques that aim to reduce discretization errors in the solution and energy evolution and their effect on DMOC optimization are explored and compared with trajectories created using time adaptive variational integrators. Furthermore, a time adaptive form of DMOC is developed that allows for a variable step size that is updated throughout the optimization process. Time adapted DMOC is based on a discretization of Hamilton's principle applied to the time adapted Lagrangian of the optimal control problem. Variations of the discrete action of the optimal control Lagrangian lead to discrete Euler-Lagrange equations that can be enforced as constraints for a boundary value problem. This new form of DMOC leads to the accurate and efficient solution of optimal control problems with highly nonlinear dynamics. Time adapted DMOC is tested on several space trajectory problems including the elliptical orbit transfer in the 2-body problem and the reconfiguration of a cubesat.
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
ERIC Educational Resources Information Center
Falkenstine, Karen Jones; Collins, Belva C.; Schuster, John W.; Kleinert, Harold
2009-01-01
Special education teachers often search for effective strategies to teach a variety of skills to students with moderate to severe disabilities through small group instruction. The investigators examined the acquisition of academic skills as well as chained and discrete tasks presented as nontargeted information by a small group of students with…
Applications of Discrete Molecular Dynamics in biology and medicine.
Proctor, Elizabeth A; Dokholyan, Nikolay V
2016-04-01
Discrete Molecular Dynamics (DMD) is a physics-based simulation method using discrete energetic potentials rather than traditional continuous potentials, allowing microsecond time scale simulations of biomolecular systems to be performed on personal computers rather than supercomputers or specialized hardware. With the ongoing explosion in processing power even in personal computers, applications of DMD have similarly multiplied. In the past two years, researchers have used DMD to model structures of disease-implicated protein folding intermediates, study assembly of protein complexes, predict protein-protein binding conformations, engineer rescue mutations in disease-causative protein mutants, design a protein conformational switch to control cell signaling, and describe the behavior of polymeric dispersants for environmental cleanup of oil spills, among other innovative applications. PMID:26638022
Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices
NASA Astrophysics Data System (ADS)
Hoq, Q. E.; Kevrekidis, P. G.; Bishop, A. R.
2016-02-01
In the present work, we consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. We quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation of these instabilities to be the spontaneous rearrangement of the solution, for larger values of the coupling, into localized waveforms typically centered over fewer sites than the original unstable structure. For weak coupling, the instability appears to result in a robust breathing of the relevant waveforms.
Cometary activity, discrete outgassing areas, and dust-jet formation
NASA Technical Reports Server (NTRS)
Sekanina, Z.
1991-01-01
Conceptual models for various types of features observed in cometary comae (jets, spirals, halos, fans, etc.), their computer simulation, and the hydrodynamic models for jet formation are critically reviewed, and evidence for anisotropic, strongly collimated flows of ejecta emanating from discrete active regions (vents) on the rotating cometary nuclei is presented. Techniques employed to generate synthetic comet images that simulate the features observed are described, and their relevance to the primary objects of coma-morphology studies is discussed. Modeling of temporal variations in the water emission from discrete active regions suggests that production curves asymmetric with respect to perihelion should be commonplace. Critical comparisons with the activity profiles of Enke's comet and with light curves of disappearing comets and comets that undergo outbursts are presented. Recent developments in the understanding of the processes that cause the nongravitational perturbations of cometary motions are reviewed, and the observed discontinuities are identified with the birth of new sources and/or deactivation of old vents.
On the spectral and conservation properties of nonlinear discretization operators
NASA Astrophysics Data System (ADS)
Fauconnier, D.; Dick, E.
2011-06-01
Following the study of Pirozzoli [1], the objective of the present work is to provide a detailed theoretical analysis of the spectral properties and the conservation properties of nonlinear finite difference discretizations. First, a Nonlinear Spectral Analysis (NSA) is proposed in order to study the statistical behavior of the modified wavenumber of a nonlinear finite difference operator, for a large set of synthetic scalar fields with prescribed energy spectrum and random phase. Second, the necessary conditions for local and global conservation of momentum and kinetic energy are derived and verified for nonlinear discretizations. Because the nonlinear mechanisms result in a violation of the energy conservation conditions, the NSA is used to quantify the energy imbalance. Third, the effect of aliasing errors due to the nonlinearity is analyzed. Finally, the theoretical observations are verified for two simple, thought relevant, numerical simulations.
Discrete neural dynamic programming in wheeled mobile robot control
NASA Astrophysics Data System (ADS)
Hendzel, Zenon; Szuster, Marcin
2011-05-01
In this paper we propose a discrete algorithm for a tracking control of a two-wheeled mobile robot (WMR), using an advanced Adaptive Critic Design (ACD). We used Dual-Heuristic Programming (DHP) algorithm, that consists of two parametric structures implemented as Neural Networks (NNs): an actor and a critic, both realized in a form of Random Vector Functional Link (RVFL) NNs. In the proposed algorithm the control system consists of the DHP adaptive critic, a PD controller and a supervisory term, derived from the Lyapunov stability theorem. The supervisory term guaranties a stable realization of a tracking movement in a learning phase of the adaptive critic structure and robustness in face of disturbances. The discrete tracking control algorithm works online, uses the WMR model for a state prediction and does not require a preliminary learning. Verification has been conducted to illustrate the performance of the proposed control algorithm, by a series of experiments on the WMR Pioneer 2-DX.
Inference in infinite-dimensional inverse problems - Discretization and duality
NASA Technical Reports Server (NTRS)
Stark, Philip B.
1992-01-01
Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.
Discrete solitons and vortices in anisotropic hexagonal and honeycomb lattices
Hoq, Q. E.; Kevrekidis, P. G.; Bishop, A. R.
2016-01-14
We consider the self-focusing discrete nonlinear Schrödinger equation on hexagonal and honeycomb lattice geometries. Our emphasis is on the study of the effects of anisotropy, motivated by the tunability afforded in recent optical and atomic physics experiments. We find that multi-soliton and discrete vortex states undergo destabilizing bifurcations as the relevant anisotropy control parameter is varied. Furthermore, we quantify these bifurcations by means of explicit analytical calculations of the solutions, as well as of their spectral linearization eigenvalues. Finally, we corroborate the relevant stability picture through direct numerical computations. In the latter, we observe the prototypical manifestation of these instabilitiesmore » to be the spontaneous rearrangement of the solution, for larger values of the coupling, into localized waveforms typically centered over fewer sites than the original unstable structure. In weak coupling, the instability appears to result in a robust breathing of the relevant waveforms.« less
Discrete coherent and squeezed states of many-qudit systems
Klimov, Andrei B.; Munoz, Carlos; Sanchez-Soto, Luis L.
2009-10-15
We consider the phase space for n identical qudits (each one of dimension d, with d a primer number) as a grid of d{sup n}xd{sup n} points and use the finite Galois field GF(d{sup n}) to label the corresponding axes. The associated displacement operators permit to define s-parametrized quasidistributions on this grid, with properties analogous to their continuous counterparts. These displacements allow also for the construction of finite coherent states, once a fiducial state is fixed. We take this reference as one eigenstate of the discrete Fourier transform and study the factorization properties of the resulting coherent states. We extend these ideas to include discrete squeezed states, and show their intriguing relation with entangled states of different qudits.