Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

KAUST Repository

Belkhatir, Zehor

2015-11-05

This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

Testing for one Generalized Linear Single Order Parameter

DEFF Research Database (Denmark)

Ellegaard, Niels Langager; Christensen, Tage Emil; Dyre, Jeppe

We examine a linear single order parameter model for thermoviscoelastic relaxation in viscous liquids, allowing for a distribution of relaxation times. In this model the relaxation of volume and entalpy is completely described by the relaxation of one internal order parameter. In contrast to prior...... work the order parameter may be chosen to have a non-exponential relaxation. The model predictions contradict the general consensus of the properties of viscous liquids in two ways: (i) The model predicts that following a linear isobaric temperature step, the normalized volume and entalpy relaxation...... responses or extrapolate from measurements of a glassy state away from equilibrium. Starting from a master equation description of inherent dynamics, we calculate the complex thermodynamic response functions. We device a way of testing for the generalized single order parameter model by measuring 3 complex...

Linear Parameter Varying Versus Linear Time Invariant Reduced Order Controller Design of Turboprop Aircraft Dynamics

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Widowati

2012-07-01

Full Text Available The applicability of parameter varying reduced order controllers to aircraft model is proposed. The generalization of the balanced singular perturbation method of linear time invariant (LTI system is used to reduce the order of linear parameter varying (LPV system. Based on the reduced order model the low-order LPV controller is designed by using synthesis technique. The performance of the reduced order controller is examined by applying it to lateral-directional control of aircraft model having 20th order. Furthermore, the time responses of the closed loop system with reduced order LPV controllers and reduced order LTI controller is compared. From the simulation results, the 8th order LPV controller can maintain stability and to provide the same level of closed-loop systems performance as the full-order LPV controller. It is different with the reduced-order LTI controller that cannot maintain stability and performance for all allowable parameter trajectories.

A linear combination of modified Bessel functions

Science.gov (United States)

Shitzer, A.; Chato, J. C.

1971-01-01

A linear combination of modified Bessel functions is defined, discussed briefly, and tabulated. This combination was found to recur in the analysis of various heat transfer problems and in the analysis of the thermal behavior of living tissue when modeled by cylindrical shells.

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

Science.gov (United States)

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

Linear matrix differential equations of higher-order and applications

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Mustapha Rachidi

2008-07-01

Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

Science.gov (United States)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Effect of impedance and higher order chromaticity on the measurement of linear chromaticity

OpenAIRE

V. H. Ranjbar; C. Y. Tan

2011-01-01

The combined effect of impedance and higher order chromaticity can act on the beam in a nontrivial manner which can cause a tune shift which depends on the relative momenta with respect to the “on momentum” particle (Δp/p). Experimentally, this tune shift affects the measurement of the linear chromaticity which is traditionally measured with a change of Δp/p. The theory behind this effect will be derived in this paper. Computer simulations and experimental data from the Tevatron will be used ...

Linear combinations come alive in crossover designs.

Science.gov (United States)

Shuster, Jonathan J

2017-10-30

Before learning anything about statistical inference in beginning service courses in biostatistics, students learn how to calculate the mean and variance of linear combinations of random variables. Practical precalculus examples of the importance of these exercises can be helpful for instructors, the target audience of this paper. We shall present applications to the "1-sample" and "2-sample" methods for randomized short-term 2-treatment crossover studies, where patients experience both treatments in random order with a "washout" between the active treatment periods. First, we show that the 2-sample method is preferred as it eliminates "conditional bias" when sample sizes by order differ and produces a smaller variance. We also demonstrate that it is usually advisable to use the differences in posttests (ignoring baseline and post washout values) rather than the differences between the changes in treatment from the start of the period to the end of the period ("delta of delta"). Although the intent is not to provide a definitive discussion of crossover designs, we provide a section and references to excellent alternative methods, where instructors can provide motivation to students to explore the topic in greater detail in future readings or courses. Copyright © 2017 John Wiley & Sons, Ltd.

Improving biomedical information retrieval by linear combinations of different query expansion techniques.

Science.gov (United States)

Abdulla, Ahmed AbdoAziz Ahmed; Lin, Hongfei; Xu, Bo; Banbhrani, Santosh Kumar

2016-07-25

Biomedical literature retrieval is becoming increasingly complex, and there is a fundamental need for advanced information retrieval systems. Information Retrieval (IR) programs scour unstructured materials such as text documents in large reserves of data that are usually stored on computers. IR is related to the representation, storage, and organization of information items, as well as to access. In IR one of the main problems is to determine which documents are relevant and which are not to the user's needs. Under the current regime, users cannot precisely construct queries in an accurate way to retrieve particular pieces of data from large reserves of data. Basic information retrieval systems are producing low-quality search results. In our proposed system for this paper we present a new technique to refine Information Retrieval searches to better represent the user's information need in order to enhance the performance of information retrieval by using different query expansion techniques and apply a linear combinations between them, where the combinations was linearly between two expansion results at one time. Query expansions expand the search query, for example, by finding synonyms and reweighting original terms. They provide significantly more focused, particularized search results than do basic search queries. The retrieval performance is measured by some variants of MAP (Mean Average Precision) and according to our experimental results, the combination of best results of query expansion is enhanced the retrieved documents and outperforms our baseline by 21.06 %, even it outperforms a previous study by 7.12 %. We propose several query expansion techniques and their combinations (linearly) to make user queries more cognizable to search engines and to produce higher-quality search results.

Effect of impedance and higher order chromaticity on the measurement of linear chromaticity

Directory of Open Access Journals (Sweden)

V. H. Ranjbar

2011-08-01

Full Text Available The combined effect of impedance and higher order chromaticity can act on the beam in a nontrivial manner which can cause a tune shift which depends on the relative momenta with respect to the “on momentum” particle (Δp/p. Experimentally, this tune shift affects the measurement of the linear chromaticity which is traditionally measured with a change of Δp/p. The theory behind this effect will be derived in this paper. Computer simulations and experimental data from the Tevatron will be used to support the theory.

Convolution of second order linear recursive sequences II.

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Szakács Tamás

2017-12-01

Full Text Available We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]. In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

An Online Method for Interpolating Linear Parametric Reduced-Order Models

KAUST Repository

Amsallem, David; Farhat, Charbel

2011-01-01

A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.

Arrhythmia recognition and classification using combined linear and nonlinear features of ECG signals.

Science.gov (United States)

Elhaj, Fatin A; Salim, Naomie; Harris, Arief R; Swee, Tan Tian; Ahmed, Taqwa

2016-04-01

Arrhythmia is a cardiac condition caused by abnormal electrical activity of the heart, and an electrocardiogram (ECG) is the non-invasive method used to detect arrhythmias or heart abnormalities. Due to the presence of noise, the non-stationary nature of the ECG signal (i.e. the changing morphology of the ECG signal with respect to time) and the irregularity of the heartbeat, physicians face difficulties in the diagnosis of arrhythmias. The computer-aided analysis of ECG results assists physicians to detect cardiovascular diseases. The development of many existing arrhythmia systems has depended on the findings from linear experiments on ECG data which achieve high performance on noise-free data. However, nonlinear experiments characterize the ECG signal more effectively sense, extract hidden information in the ECG signal, and achieve good performance under noisy conditions. This paper investigates the representation ability of linear and nonlinear features and proposes a combination of such features in order to improve the classification of ECG data. In this study, five types of beat classes of arrhythmia as recommended by the Association for Advancement of Medical Instrumentation are analyzed: non-ectopic beats (N), supra-ventricular ectopic beats (S), ventricular ectopic beats (V), fusion beats (F) and unclassifiable and paced beats (U). The characterization ability of nonlinear features such as high order statistics and cumulants and nonlinear feature reduction methods such as independent component analysis are combined with linear features, namely, the principal component analysis of discrete wavelet transform coefficients. The features are tested for their ability to differentiate different classes of data using different classifiers, namely, the support vector machine and neural network methods with tenfold cross-validation. Our proposed method is able to classify the N, S, V, F and U arrhythmia classes with high accuracy (98.91%) using a combined support

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner

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Yubo Wang

2017-06-01

Full Text Available It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC. In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976 ratio and outperforms existing methods such as short-time Fourier transfrom (STFT, continuous Wavelet transform (CWT and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Time-Frequency Analysis of Non-Stationary Biological Signals with Sparse Linear Regression Based Fourier Linear Combiner.

Science.gov (United States)

Wang, Yubo; Veluvolu, Kalyana C

2017-06-14

It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.

Algebraic Properties of First Integrals for Scalar Linear Third-Order ODEs of Maximal Symmetry

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K. S. Mahomed

2013-01-01

Full Text Available By use of the Lie symmetry group methods we analyze the relationship between the first integrals of the simplest linear third-order ordinary differential equations (ODEs and their point symmetries. It is well known that there are three classes of linear third-order ODEs for maximal cases of point symmetries which are 4, 5, and 7. The simplest scalar linear third-order equation has seven-point symmetries. We obtain the classifying relation between the symmetry and the first integral for the simplest equation. It is shown that the maximal Lie algebra of a first integral for the simplest equation y′′′=0 is unique and four-dimensional. Moreover, we show that the Lie algebra of the simplest linear third-order equation is generated by the symmetries of the two basic integrals. We also obtain counting theorems of the symmetry properties of the first integrals for such linear third-order ODEs. Furthermore, we provide insights into the manner in which one can generate the full Lie algebra of higher-order ODEs of maximal symmetry from two of their basic integrals.

High-order quantum algorithm for solving linear differential equations

International Nuclear Information System (INIS)

Berry, Dominic W

2014-01-01

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms to general inhomogeneous sparse linear differential equations, which describe many classical physical systems. We examine the use of high-order methods (where the error over a time step is a high power of the size of the time step) to improve the efficiency. These provide scaling close to Δt 2 in the evolution time Δt. As with other algorithms of this type, the solution is encoded in amplitudes of the quantum state, and it is possible to extract global features of the solution. (paper)

High-Order Sparse Linear Predictors for Audio Processing

DEFF Research Database (Denmark)

Giacobello, Daniele; van Waterschoot, Toon; Christensen, Mads Græsbøll

2010-01-01

Linear prediction has generally failed to make a breakthrough in audio processing, as it has done in speech processing. This is mostly due to its poor modeling performance, since an audio signal is usually an ensemble of different sources. Nevertheless, linear prediction comes with a whole set...... of interesting features that make the idea of using it in audio processing not far fetched, e.g., the strong ability of modeling the spectral peaks that play a dominant role in perception. In this paper, we provide some preliminary conjectures and experiments on the use of high-order sparse linear predictors...... in audio processing. These predictors, successfully implemented in modeling the short-term and long-term redundancies present in speech signals, will be used to model tonal audio signals, both monophonic and polyphonic. We will show how the sparse predictors are able to model efficiently the different...

ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

Science.gov (United States)

Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

2018-04-01

In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

Science.gov (United States)

Shang, Shang; Bai, Jing; Song, Xiaolei; Wang, Hongkai; Lau, Jaclyn

2007-01-01

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

On a class of fourth order linear recurrence equations

Directory of Open Access Journals (Sweden)

Sui-Sun Cheng

1984-01-01

Full Text Available This paper is concerned with sequences that satisfy a class of fourth order linear recurrence equations. Basic properties of such sequences are derived. In addition, we discuss the oscillatory and nonoscillatory behavior of such sequences.

On oscillation of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, A.; Šremr, Jiří

2011-01-01

Roč. 54, - (2011), s. 69-81 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear second-order ordinary differential equation * Kamenev theorem * oscillation Subject RIV: BA - General Mathematics http://www.rmi.ge/jeomj/memoirs/vol54/abs54-4.htm

A combined QSAR and partial order ranking approach to risk assessment.

Science.gov (United States)

Carlsen, L

2006-04-01

QSAR generated data appear as an attractive alternative to experimental data as foreseen in the proposed new chemicals legislation REACH. A preliminary risk assessment for the aquatic environment can be based on few factors, i.e. the octanol-water partition coefficient (Kow), the vapour pressure (VP) and the potential biodegradability of the compound in combination with the predicted no-effect concentration (PNEC) and the actual tonnage in which the substance is produced. Application of partial order ranking, allowing simultaneous inclusion of several parameters leads to a mutual prioritisation of the investigated substances, the prioritisation possibly being further analysed through the concept of linear extensions and average ranks. The ranking uses endpoint values (log Kow and log VP) derived from strictly linear 'noise-deficient' QSAR models as input parameters. Biodegradation estimates were adopted from the BioWin module of the EPI Suite. The population growth impairment of Tetrahymena pyriformis was used as a surrogate for fish lethality.

Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries

Science.gov (United States)

Dorodnitsyn, Vladimir A.; Kozlov, Roman; Meleshko, Sergey V.; Winternitz, Pavel

2018-05-01

A recent article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs, which have infinite-dimensional Lie point symmetry groups due to the linear superposition principle. Their symmetry algebra always contains a two-dimensional subalgebra realized by linearly connected vector fields. We identify all classes of linear first-order DODSs that have additional symmetries, not due to linearity alone, and we present representatives of each class. These additional symmetries are then used to construct exact analytical particular solutions using symmetry reduction.

Growth of meromorphic solutions of higher-order linear differential equations

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Wenjuan Chen

2009-01-01

Full Text Available In this paper, we investigate the higher-order linear differential equations with meromorphic coefficients. We improve and extend a result of M.S. Liu and C.L. Yuan, by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen, and the extended Winman-Valiron theory which proved by J. Wang and H.X. Yi. In addition, we also consider the nonhomogeneous linear differential equations.

Linear reversible second-order cellular automata and their first-order matrix equivalents

International Nuclear Information System (INIS)

Macfarlane, A J

2004-01-01

Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, t=0, 1, 2, ..., from their simplest initial states and on the basis of updating rules in modulo 2 arithmetic, are presented. In these, shaded and unshaded squares denote cells whose cell variables are equal to one and zero respectively. This paper is devoted to finding general formulas for, and explicit numerical evaluations of, the weights N(t) of the states or configurations of RCA1-3, i.e. the total number of shaded cells in tth line of their displays. This is achieved by means of the replacement of RCA1-3 by the equivalent linear first-order matrix automata MCA1-3, for which the cell variables are 2x2 matrices, instead of just numbers (element of Z 2 ) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first 2 M times, M=0, 1, 2, ..

A unified approach to fixed-order controller design via linear matrix inequalities

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T. Iwasaki

1995-01-01

Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem,-stabilization as a robust stabilization problem, and robust L∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type BGC+(BGCT+Q<0 for the unknown matrix G. Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X∈1 and X−1∈2 where 1 and 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

Oscillation of solutions of some higher order linear differential equations

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Hong-Yan Xu

2009-11-01

Full Text Available In this paper, we deal with the order of growth and the hyper order of solutions of higher order linear differential equations $$f^{(k}+B_{k-1}f^{(k-1}+\\cdots+B_1f'+B_0f=F$$ where $B_j(z (j=0,1,\\ldots,k-1$ and $F$ are entire functions or polynomials. Some results are obtained which improve and extend previous results given by Z.-X. Chen, J. Wang, T.-B. Cao and C.-H. Li.

About a definition of metric over an abelian linearly ordered group

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Bice Cavallo

2012-06-01

Full Text Available A G-metric over an abelian linearly ordered group G = (G,⊙,≤ is a binary operation, d G , verifying suitable properties. We consider a particular G metric derived by the group operation ⊙ and the total weak order ≤, and show that it provides a base for the order topology associated to G.

A Design of Mechanical Frequency Converter Linear and Non-linear Spring Combination for Energy Harvesting

International Nuclear Information System (INIS)

Yamamoto, K; Fujita, T; Kanda, K; Maenaka, K; Badel, A; Formosa, F

2014-01-01

In this study, the improvement of energy harvesting from wideband vibration with random change by using a combination of linear and nonlinear spring system is investigated. The system consists of curved beam spring for non-linear buckling, which supports the linear mass-spring resonator. Applying shock acceleration generates a snap through action to the buckling spring. From the FEM analysis, we showed that the snap through acceleration from the buckling action has no relationship with the applied shock amplitude and duration. We use this uniform acceleration as an impulse shock source for the linear resonator. It is easy to obtain the maximum shock response from the uniform snap through acceleration by using a shock response spectrum (SRS) analysis method. At first we investigated the relationship between the snap-through behaviour and an initial curved deflection. Then a time response result for non-linear springs with snap through and minimum force that makes a buckling behaviour were obtained by FEM analysis. By obtaining the optimum SRS frequency for linear resonator, we decided its resonant frequency with the MATLAB simulator

On spectral properties of linear combinations of idempotents

Czech Academy of Sciences Publication Activity Database

Du, H.-K.; Deng, Ch-Y.; Mbekhta, M.; Müller, Vladimír

2007-01-01

Roč. 180, č. 3 (2007), s. 211-217 ISSN 0039-3223 R&D Projects: GA ČR(CZ) GA201/06/0128 Institutional research plan: CEZ:AV0Z10190503 Keywords : linear combinations of idempotents * closed range * complemented subspaces Subject RIV: BA - General Mathematics Impact factor: 0.568, year: 2007

A unified approach to fixed-order controller design via linear matrix inequalities

Directory of Open Access Journals (Sweden)

Iwasaki T.

1995-01-01

Full Text Available We consider the design of fixed-order (or low-order linear controllers which meet certain performance and/or robustness specifications. The following three problems are considered; covariance control as a nominal performance problem, 𝒬 -stabilization as a robust stabilization problem, and robust L ∞ control problem as a robust performance problem. All three control problems are converted to a single linear algebra problem of solving a linear matrix inequality (LMI of the type B G C + ( B G C T + Q < 0 for the unknown matrix G . Thus this paper addresses the fixed-order controller design problem in a unified way. Necessary and sufficient conditions for the existence of a fixed-order controller which satisfies the design specifications for each problem are derived, and an explicit controller formula is given. In any case, the resulting problem is shown to be a search for a (structured positive definite matrix X such that X ∈ 𝒞 1 and X − 1 ∈ 𝒞 2 where 𝒞 1 and 𝒞 2 are convex sets defined by LMIs. Computational aspects of the nonconvex LMI problem are discussed.

On nonnegative solutions of second order linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Lomtatidze, Alexander; Vodstrčil, Petr

2004-01-01

Roč. 32, č. 1 (2004), s. 59-88 ISSN 1512-0015 Institutional research plan: CEZ:AV0Z1019905 Keywords : second order linear functional differential equations * nonnegative solution * two-point boundary value problem Subject RIV: BA - General Mathematics

CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

International Nuclear Information System (INIS)

Roldan, Omar

2017-01-01

We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which can iteratively be used to obtain the lensing solution at the desired order.

CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

Energy Technology Data Exchange (ETDEWEB)

Roldan, Omar, E-mail: oaroldan@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, RJ (Brazil)

2017-08-01

We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which can iteratively be used to obtain the lensing solution at the desired order.

Projective Synchronization of N-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

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Baogui Xin

2012-01-01

Full Text Available Based on linear feedback control technique, a projective synchronization scheme of N-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

Accelerating transient simulation of linear reduced order models.

Energy Technology Data Exchange (ETDEWEB)

Thornquist, Heidi K.; Mei, Ting; Keiter, Eric Richard; Bond, Brad

2011-10-01

Model order reduction (MOR) techniques have been used to facilitate the analysis of dynamical systems for many years. Although existing model reduction techniques are capable of providing huge speedups in the frequency domain analysis (i.e. AC response) of linear systems, such speedups are often not obtained when performing transient analysis on the systems, particularly when coupled with other circuit components. Reduced system size, which is the ostensible goal of MOR methods, is often insufficient to improve transient simulation speed on realistic circuit problems. It can be shown that making the correct reduced order model (ROM) implementation choices is crucial to the practical application of MOR methods. In this report we investigate methods for accelerating the simulation of circuits containing ROM blocks using the circuit simulator Xyce.

Asymptotic integration of a linear fourth order differential equation of Poincaré type

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Anibal Coronel

2015-11-01

Full Text Available This article deals with the asymptotic behavior of nonoscillatory solutions of fourth order linear differential equation where the coefficients are perturbations of constants. We define a change of variable and deduce that the new variable satisfies a third order nonlinear differential equation. We assume three hypotheses. The first hypothesis is related to the constant coefficients and set up that the characteristic polynomial associated with the fourth order linear equation has simple and real roots. The other two hypotheses are related to the behavior of the perturbation functions and establish asymptotic integral smallness conditions of the perturbations. Under these general hypotheses, we obtain four main results. The first two results are related to the application of a fixed point argument to prove that the nonlinear third order equation has a unique solution. The next result concerns with the asymptotic behavior of the solutions of the nonlinear third order equation. The fourth main theorem is introduced to establish the existence of a fundamental system of solutions and to precise the formulas for the asymptotic behavior of the linear fourth order differential equation. In addition, we present an example to show that the results introduced in this paper can be applied in situations where the assumptions of some classical theorems are not satisfied.

Linear reversible second-order cellular automata and their first-order matrix equivalents

Science.gov (United States)

Macfarlane, A. J.

2004-11-01

Linear or one-dimensional reversible second-order cellular automata, exemplified by three cases named as RCA1-3, are introduced. Displays of their evolution in discrete time steps, &{\\in}Z_2;) as for RCA1-3. MCA1-3 are tractable because it has been possible to generalize to them the heavy duty methods already well-developed for ordinary first-order cellular automata like those of Wolfram's Rules 90 and 150. While the automata MCA1-3 are thought to be of genuine interest in their own right, with untapped further mathematical potential, their treatment has been applied here to expediting derivation of a large body of general and explicit results for N(t) for RCA1-3. Amongst explicit results obtained are formulas also for each of RCA1-3 for the total weight of the configurations of the first &2^M; times, M =0, 1, 2,\\ldots.

On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

International Nuclear Information System (INIS)

Man, Yiu-Kwong

2010-01-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided. (fast track communication)

A Solution to the Fundamental Linear Fractional Order Differential Equation

Science.gov (United States)

Hartley, Tom T.; Lorenzo, Carl F.

1998-01-01

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

Synthesis of models for order-sorted first-order theories using linear algebra and constraint solving

Directory of Open Access Journals (Sweden)

Salvador Lucas

2015-12-01

Full Text Available Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In this setting, Order-Sorted First-Order Logic provides a powerful framework to represent declarative programs. It also provides a target logic to obtain models for other logics via transformations. We investigate the automatic generation of numerical models for order-sorted first-order logics and its use in program analysis, in particular in termination analysis of declarative programs. We use convex domains to give domains to the different sorts of an order-sorted signature; we interpret the ranked symbols of sorted signatures by means of appropriately adapted convex matrix interpretations. Such numerical interpretations permit the use of existing algorithms and tools from linear algebra and arithmetic constraint solving to synthesize the models.

POSITIVE SOLUTIONS TO SEMI-LINEAR SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACE

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

In this paper,we study the existence of positive periodic solution to some second- order semi-linear differential equation in Banach space.By the fixed point index theory, we prove that the semi-linear differential equation has two positive periodic solutions.

Focal decompositions for linear differential equations of the second order

Directory of Open Access Journals (Sweden)

L. Birbrair

2003-01-01

two-points problems to itself such that the image of the focal decomposition associated to the first equation is a focal decomposition associated to the second one. In this paper, we present a complete classification for linear second-order equations with respect to this equivalence relation.

Computerized implementation of higher-order electron-correlation methods and their linear-scaling divide-and-conquer extensions.

Science.gov (United States)

Nakano, Masahiko; Yoshikawa, Takeshi; Hirata, So; Seino, Junji; Nakai, Hiromi

2017-11-05

We have implemented a linear-scaling divide-and-conquer (DC)-based higher-order coupled-cluster (CC) and Møller-Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC-based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2) TQ ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC-based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Event generation for next to leading order chargino production at the international linear collider

Energy Technology Data Exchange (ETDEWEB)

Robens, T.

2006-10-15

At the International Linear Collider (ILC), parameters of supersymmetry (SUSY) can be determined with an experimental accuracy matching the precision of next-to-leading order (NLO) and higher-order theoretical predictions. Therefore, these contributions need to be included in the analysis of the parameters. We present a Monte-Carlo event generator for simulating chargino pair production at the ILC at next-to-leading order in the electroweak couplings. We consider two approaches of including photon radiation. A strict fixed-order approach allows for comparison and consistency checks with published semianalytic results in the literature. A version with soft- and hard-collinear resummation of photon radiation, which combines photon resummation with the inclusion of the NLO matrix element for the production process, avoids negative event weights, so the program can simulate physical (unweighted) event samples. Photons are explicitly generated throughout the range where they can be experimentally resolved. In addition, it includes further higher-order corrections unaccounted for by the fixed-order method. Inspecting the dependence on the cutoffs separating the soft and collinear regions, we evaluate the systematic errors due to soft and collinear approximations for NLO and higher-order contributions. In the resummation approach, the residual uncertainty can be brought down to the per-mil level, coinciding with the expected statistical uncertainty at the ILC. We closely investigate the two-photon phase space for the resummation method. We present results for cross sections and event generation for both approaches. (orig.)

Non-linear second-order periodic systems with non-smooth potential

Indian Academy of Sciences (India)

In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on ...

Non-linear second-order periodic systems with non-smooth potential

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

Abstract. In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth ...

Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

OpenAIRE

Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

2017-01-01

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

The separation-combination method of linear structures in remote sensing image interpretation and its application

International Nuclear Information System (INIS)

Liu Linqin

1991-01-01

The separation-combination method a new kind of analysis method of linear structures in remote sensing image interpretation is introduced taking northwestern Fujian as the example, its practical application is examined. The practice shows that application results not only reflect intensities of linear structures in overall directions at different locations, but also contribute to the zonation of linear structures and display their space distribution laws. Based on analyses of linear structures, it can provide more information concerning remote sensing on studies of regional mineralization laws and the guide to ore-finding combining with mineralization

Factorization of a class of almost linear second-order differential equations

International Nuclear Information System (INIS)

Estevez, P G; Kuru, S; Negro, J; Nieto, L M

2007-01-01

A general type of almost linear second-order differential equations, which are directly related to several interesting physical problems, is characterized. The solutions of these equations are obtained using the factorization technique, and their non-autonomous invariants are also found by means of scale transformations

Some oscillation criteria for the second-order linear delay differential equation

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2011-01-01

Roč. 136, č. 2 (2011), s. 195-204 ISSN 0862-7959 Institutional research plan: CEZ:AV0Z10190503 Keywords : second-order linear differential equation with a delay * oscillatory solution Subject RIV: BA - General Mathematics http://www.dml.cz/handle/10338.dmlcz/141582

Utility of low-order linear nuclear-power-plant models in plant diagnostics and control

International Nuclear Information System (INIS)

Tylee, J.L.

1981-01-01

A low-order, linear model of a pressurized water reactor (PWR) plant is described and evaluated. The model consists of 23 linear, first-order difference equations and simulates all subsystems of both the primary and secondary sides of the plant. Comparisons between the calculated model response and available test data show the model to be an adequate representation of the actual plant dynamics. Suggested use for the model in an on-line digital plant diagnostics and control system are presented

Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

Science.gov (United States)

Merrikh-Bayat, Farshad

2011-04-01

One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

Tools to identify linear combination of prognostic factors which maximizes area under receiver operator curve.

Science.gov (United States)

Todor, Nicolae; Todor, Irina; Săplăcan, Gavril

2014-01-01

The linear combination of variables is an attractive method in many medical analyses targeting a score to classify patients. In the case of ROC curves the most popular problem is to identify the linear combination which maximizes area under curve (AUC). This problem is complete closed when normality assumptions are met. With no assumption of normality search algorithm are avoided because it is accepted that we have to evaluate AUC n(d) times where n is the number of distinct observation and d is the number of variables. For d = 2, using particularities of AUC formula, we described an algorithm which lowered the number of evaluations of AUC from n(2) to n(n-1) + 1. For d > 2 our proposed solution is an approximate method by considering equidistant points on the unit sphere in R(d) where we evaluate AUC. The algorithms were applied to data from our lab to predict response of treatment by a set of molecular markers in cervical cancers patients. In order to evaluate the strength of our algorithms a simulation was added. In the case of no normality presented algorithms are feasible. For many variables computation time could be increased but acceptable.

Myshkis type oscillation criteria for second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2015-01-01

Roč. 178, č. 1 (2015), s. 143-161 ISSN 0026-9255 Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillation criteria Subject RIV: BA - General Mathematics Impact factor: 0.664, year: 2015 http://link.springer.com/article/10.1007%2Fs00605-014-0719-y

Fast Algorithms for High-Order Sparse Linear Prediction with Applications to Speech Processing

DEFF Research Database (Denmark)

Jensen, Tobias Lindstrøm; Giacobello, Daniele; van Waterschoot, Toon

2016-01-01

In speech processing applications, imposing sparsity constraints on high-order linear prediction coefficients and prediction residuals has proven successful in overcoming some of the limitation of conventional linear predictive modeling. However, this modeling scheme, named sparse linear prediction...... problem with lower accuracy than in previous work. In the experimental analysis, we clearly show that a solution with lower accuracy can achieve approximately the same performance as a high accuracy solution both objectively, in terms of prediction gain, as well as with perceptual relevant measures, when...... evaluated in a speech reconstruction application....

Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

Directory of Open Access Journals (Sweden)

Hai Zhang

2014-01-01

Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

Fast solution of elliptic partial differential equations using linear combinations of plane waves.

Science.gov (United States)

Pérez-Jordá, José M

2016-02-01

Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

Undecidability of the Logic of Overlap Relation over Discrete Linear Orderings

DEFF Research Database (Denmark)

Bresolin, Davide; Della Monica, Dario; Goranko, Valentin

2010-01-01

. Still, decidability is the rule for the fragments of HS with only one modal operator, based on an Allen’s relation. In this paper, we show that the logic O of the Overlap relation, when interpreted over discrete linear orderings, is an exception. The proof is based on a reduction from the undecidable...

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

Energy Technology Data Exchange (ETDEWEB)

Shang, Yu; Yu, Guoqiang, E-mail: guoqiang.yu@uky.edu [Department of Biomedical Engineering, University of Kentucky, Lexington, Kentucky 40506 (United States)

2014-09-29

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

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

International Nuclear Information System (INIS)

Shang, Yu; Yu, Guoqiang

2014-01-01

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

Multi-criteria approach with linear combination technique and analytical hierarchy process in land evaluation studies

Directory of Open Access Journals (Sweden)

Orhan Dengiz

2018-01-01

Full Text Available Land evaluation analysis is a prerequisite to achieving optimum utilization of the available land resources. Lack of knowledge on best combination of factors that suit production of yields has contributed to the low production. The aim of this study was to determine the most suitable areas for agricultural uses. For that reasons, in order to determine land suitability classes of the study area, multi-criteria approach was used with linear combination technique and analytical hierarchy process by taking into consideration of some land and soil physico-chemical characteristic such as slope, texture, depth, derange, stoniness, erosion, pH, EC, CaCO3 and organic matter. These data and land mapping unites were taken from digital detailed soil map scaled as 1:5.000. In addition, in order to was produce land suitability map GIS was program used for the study area. This study was carried out at Mahmudiye, Karaamca, Yazılı, Çiçeközü, Orhaniye and Akbıyık villages in Yenişehir district of Bursa province. Total study area is 7059 ha. 6890 ha of total study area has been used as irrigated agriculture, dry farming agriculture, pasture while, 169 ha has been used for non-agricultural activities such as settlement, road water body etc. Average annual temperature and precipitation of the study area are 16.1oC and 1039.5 mm, respectively. Finally after determination of land suitability distribution classes for the study area, it was found that 15.0% of the study area has highly (S1 and moderately (S2 while, 85% of the study area has marginally suitable and unsuitable coded as S3 and N. It was also determined some relation as compared results of linear combination technique with other hierarchy approaches such as Land Use Capability Classification and Suitability Class for Agricultural Use methods.

First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

Directory of Open Access Journals (Sweden)

Heinz Toparkus

2014-04-01

Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001.xml?format=INT

On oscillations of solutions to second-order linear delay differential equations

Czech Academy of Sciences Publication Activity Database

Opluštil, Z.; Šremr, Jiří

2013-01-01

Roč. 20, č. 1 (2013), s. 65-94 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : linear second-order delay differential equation * oscillatory solution Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-1/gmj-2013-0001/gmj-2013-0001. xml ?format=INT

Classes and Theories of Trees Associated with a Class Of Linear Orders

DEFF Research Database (Denmark)

Goranko, Valentin; Kellerman, Ruaan

2011-01-01

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between...... these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general...... results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees....

String Chopping and Time-ordered Products of Linear String-localized Quantum Fields

Science.gov (United States)

Cardoso, Lucas T.; Mund, Jens; Várilly, Joseph C.

2018-03-01

For a renormalizability proof of perturbative models in the Epstein-Glaser scheme with string-localized quantum fields, one needs to know what freedom one has in the definition of time-ordered products of the interaction Lagrangian. This paper provides a first step in that direction. The basic issue is the presence of an open set of n-tuples of strings which cannot be chronologically ordered. We resolve it by showing that almost all such string configurations can be dissected into finitely many pieces which can indeed be chronologically ordered. This fixes the time-ordered products of linear field factors outside a nullset of string configurations. (The extension across the nullset, as well as the definition of time-ordered products of Wick monomials, will be discussed elsewhere).

A simple smoothness indicator for the WENO scheme with adaptive order

Science.gov (United States)

Huang, Cong; Chen, Li Li

2018-01-01

The fifth order WENO scheme with adaptive order is competent for solving hyperbolic conservation laws, its reconstruction is a convex combination of a fifth order linear reconstruction and three third order linear reconstructions. Note that, on uniform mesh, the computational cost of smoothness indicator for fifth order linear reconstruction is comparable with the sum of ones for three third order linear reconstructions, thus it is too heavy; on non-uniform mesh, the explicit form of smoothness indicator for fifth order linear reconstruction is difficult to be obtained, and its computational cost is much heavier than the one on uniform mesh. In order to overcome these problems, a simple smoothness indicator for fifth order linear reconstruction is proposed in this paper.

A puzzling combination: disorder X order

International Nuclear Information System (INIS)

Hasenfratz, P.

1979-01-01

There are several examples indicating that the operator combination 'disorder X order' creates anomalous spin and/or statistics. In 2 + 1 dimensions there is a similar anomaly related to the disorder operator carrying Z(N) topological charge believed to have an important role in quark confinement. The conventionally defined total angular momentum has an anomalous term 1/2 sigma 3 ((1/√3) lambda 8 ) and can take the values 1/2 (1/3) in the presence of 'disorder X order' in 2 + 1 dimensional SU(2) (SU(3)) gauge theories. It is argued that the existence of a stable soliton solution or the introduction of Higgs fields are not important for the anomaly. (Auth.)

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

Science.gov (United States)

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear

Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

KAUST Repository

Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

2017-01-01

This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating

Differential algebraic method for arbitrary order curvilinear-axis combined geometric-chromatic aberration analysis

International Nuclear Information System (INIS)

Cheng Min; Tang Tiantong; Lu Yilong; Yao Zhenhua

2003-01-01

The principle of differential algebra is applied to analyse and calculate arbitrary order curvilinear-axis combined geometric-chromatic aberrations of electron optical systems. Expressions of differential algebraic form of high order combined aberrations are obtained and arbitrary order combined aberrations can be calculated numerically. As an example, a typical wide electron beam focusing system with curved optical axes named magnetic immersion lens has been studied. All the second-order and third-order combined geometric-chromatic aberrations of the lens have been calculated, and the patterns of the corresponding geometric aberrations and combined aberrations have been given as well

Growth and Zeros of Meromorphic Solutions to Second-Order Linear Differential Equations

Directory of Open Access Journals (Sweden)

Maamar Andasmas

2016-04-01

Full Text Available The main purpose of this article is to investigate the growth of meromorphic solutions to homogeneous and non-homogeneous second order linear differential equations f00+Af0+Bf = F, where A(z, B (z and F (z are meromorphic functions with finite order having only finitely many poles. We show that, if there exist a positive constants σ > 0, α > 0 such that |A(z| ≥ eα|z|σ as |z| → +∞, z ∈ H, where dens{|z| : z ∈ H} > 0 and ρ = max{ρ(B, ρ(F} < σ, then every transcendental meromorphic solution f has an infinite order. Further, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros.

Thin Cloud Detection Method by Linear Combination Model of Cloud Image

Science.gov (United States)

Liu, L.; Li, J.; Wang, Y.; Xiao, Y.; Zhang, W.; Zhang, S.

2018-04-01

The existing cloud detection methods in photogrammetry often extract the image features from remote sensing images directly, and then use them to classify images into cloud or other things. But when the cloud is thin and small, these methods will be inaccurate. In this paper, a linear combination model of cloud images is proposed, by using this model, the underlying surface information of remote sensing images can be removed. So the cloud detection result can become more accurate. Firstly, the automatic cloud detection program in this paper uses the linear combination model to split the cloud information and surface information in the transparent cloud images, then uses different image features to recognize the cloud parts. In consideration of the computational efficiency, AdaBoost Classifier was introduced to combine the different features to establish a cloud classifier. AdaBoost Classifier can select the most effective features from many normal features, so the calculation time is largely reduced. Finally, we selected a cloud detection method based on tree structure and a multiple feature detection method using SVM classifier to compare with the proposed method, the experimental data shows that the proposed cloud detection program in this paper has high accuracy and fast calculation speed.

On-chip power-combining techniques for watt-level linear power amplifiers in 0.18 μm CMOS

International Nuclear Information System (INIS)

Ren Zhixiong; Zhang Kefeng; Liu Lanqi; Li Cong; Chen Xiaofei; Liu Dongsheng; Liu Zhenglin; Zou Xuecheng

2015-01-01

Three linear CMOS power amplifiers (PAs) with high output power (more than watt-level output power) for high data-rate mobile applications are introduced. To realize watt-level output power, there are two 2.4 GHz PAs using an on-chip parallel combining transformer (PCT) and one 1.95 GHz PA using an on-chip series combining transformer (SCT) to combine output signals of multiple power stages. Furthermore, some linearization techniques including adaptive bias, diode linearizer, multi-gated transistors (MGTR) and the second harmonic control are applied in these PAs. Using the proposed power combiner, these three PAs are designed and fabricated in TSMC 0.18 μm RFCMOS process. According to the measurement results, the proposed two linear 2.4 GHz PAs achieve a gain of 33.2 dB and 34.3 dB, a maximum output power of 30.7 dBm and 29.4 dBm, with 29% and 31.3% of peak PAE, respectively. According to the simulation results, the presented linear 1.95 GHz PA achieves a gain of 37.5 dB, a maximum output power of 34.3 dBm with 36.3% of peak PAE. (paper)

Color ordering in QCD

OpenAIRE

Schuster, Theodor

2013-01-01

We derive color decompositions of arbitrary tree and one-loop QCD amplitudes into color ordered objects called primitive amplitudes. Furthermore, we derive general fermion flip and reversion identities spanning the null space among the primitive amplitudes and use them to prove that all color ordered tree amplitudes of massless QCD can be written as linear combinations of color ordered tree amplitudes of $\\mathcal{N}=4$ super Yang-Mills theory.

Bounded solutions of self-adjoint second order linear difference equations with periodic coeffients

Directory of Open Access Journals (Sweden)

Encinas A.M.

2018-02-01

Full Text Available In this work we obtain easy characterizations for the boundedness of the solutions of the discrete, self–adjoint, second order and linear unidimensional equations with periodic coefficients, including the analysis of the so-called discrete Mathieu equations as particular cases.

Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

KAUST Repository

Belkhatir, Zehor

2017-06-28

This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input’s amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zeros of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052. xml

Hyers-Ulam stability for second-order linear differential equations with boundary conditions

Directory of Open Access Journals (Sweden)

Pasc Gavruta

2011-06-01

Full Text Available We prove the Hyers-Ulam stability of linear differential equations of second-order with boundary conditions or with initial conditions. That is, if y is an approximate solution of the differential equation $y''+ eta (x y = 0$ with $y(a = y(b =0$, then there exists an exact solution of the differential equation, near y.

Remark on zeros of solutions of second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2016-01-01

Roč. 23, č. 4 (2016), s. 571-577 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : second-order linear equation * zero s of solutions * periodic boundary value problem Subject RIV: BA - General Mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2016.23.issue-4/gmj-2016-0052/gmj-2016-0052.xml

The assessment of changes in brain volume using combined linear measurements

International Nuclear Information System (INIS)

Gomori, J.M.; Steiner, I.; Melamed, E.; Cooper, G.

1984-01-01

All linear measurements employed for evaluation of brain atrophy, were performed on 148 computed tomograms of patients aged 28 to 84 without evidence of any nervous system disorder. These included size of lateral, third and fourth ventricles, width of the Sylvian and frontal interhemispheric fissures and cortical sulci and size of the pre-pontine cistern. Various parameters indicated decrease in brain mass with age. Since the atrophic process is a diffuse phenomenon, integration of several measurements evaluating separate brain regions was made. The bicaudate ratio and the Sylvian fissure ratio (representing both central and cortical atrophy) were combined arithmetically, resulting in a correlation of 0.6390 with age (p<0.0005). With a computed canonical correlation analysis: a formula was obtained which combined measurements of the lateral and third ventricles, the Sylvian fissure and the pre-pontine cistern. This formula yealded a correlation of 0.67795 (p<0.0005). These linear measurements will enable simple and reliable assessment of reduction in brain volume during the normal aging process and in disorders accompanied by brain atrophy. (orig.)

Maximum principles for boundary-degenerate second-order linear elliptic differential operators

OpenAIRE

Feehan, Paul M. N.

2012-01-01

We prove weak and strong maximum principles, including a Hopf lemma, for smooth subsolutions to equations defined by linear, second-order, partial differential operators whose principal symbols vanish along a portion of the domain boundary. The boundary regularity property of the smooth subsolutions along this boundary vanishing locus ensures that these maximum principles hold irrespective of the sign of the Fichera function. Boundary conditions need only be prescribed on the complement in th...

Internal crisis in a second-order non-linear non-autonomous electronic oscillator

International Nuclear Information System (INIS)

Stavrinides, S.G.; Deliolanis, N.C.; Miliou, A.N.; Laopoulos, Th.; Anagnostopoulos, A.N.

2008-01-01

The internal crisis of a second-order non-linear non-autonomous chaotic electronic circuit is studied. The phase portraits consist of two interacting sub-attractors, a chaotic and a periodic one. Maximal Lyapunov exponents were calculated, for both the periodic and the chaotic waveforms, in order to confirm their nature. Transitions between the chaotic and the periodic sub-attractors become more frequent by increasing the circuit driving frequency. The frequency distribution of the corresponding laminar lengths and their average values indicate that an internal crisis takes place in this circuit, manifested in the intermittent behaviour of the corresponding orbits

Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2007-01-01

In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...

Variations in the Solution of Linear First-Order Differential Equations. Classroom Notes

Science.gov (United States)

Seaman, Brian; Osler, Thomas J.

2004-01-01

A special project which can be given to students of ordinary differential equations is described in detail. Students create new differential equations by changing the dependent variable in the familiar linear first-order equation (dv/dx)+p(x)v=q(x) by means of a substitution v=f(y). The student then creates a table of the new equations and…

CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

OpenAIRE

Roldan, Omar

2017-01-01

We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instan...

Characterization of the order relation on the set of completely n-positive linear maps between C*-algebras

Directory of Open Access Journals (Sweden)

Maria Joita

2007-12-01

Full Text Available In this paper we characterize the order relation on the set of all nondegenerate completely n-positive linear maps between C*-algebras in terms of a self-dual Hilbert module induced by each completely n-positive linear map.

Fault tolerance in parity-state linear optical quantum computing

International Nuclear Information System (INIS)

Hayes, A. J. F.; Ralph, T. C.; Haselgrove, H. L.; Gilchrist, Alexei

2010-01-01

We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest level of code concatenation in order to efficiently correct errors arising from the inherent nondeterminism of two-qubit linear-optical gates. When combined with teleported error-correction (using either a Steane or Golay code) at higher levels of concatenation, the parity-state scheme is found to achieve a saving of approximately three orders of magnitude in resources when compared to the cluster state scheme, at a cost of a somewhat reduced noise threshold.

Contact symmetries of general linear second-order ordinary differential equations: letter to the editor

NARCIS (Netherlands)

Martini, Ruud; Kersten, P.H.M.

1983-01-01

Using 1-1 mappings, the complete symmetry groups of contact transformations of general linear second-order ordinary differential equations are determined from two independent solutions of those equations, and applied to the harmonic oscillator with and without damping.

On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2

Directory of Open Access Journals (Sweden)

Tian-Xiao He

2009-01-01

Full Text Available Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2. The applications of the method to the Fibonacci and Lucas numbers, Chebyshev polynomials, the generalized Gegenbauer-Humbert polynomials are also discussed. The derived idea provides a general method to construct identities of number or polynomial sequences defined by linear recurrence relations. The applications using the method to solve some algebraic and ordinary differential equations are presented.

Remark on periodic boundary-value problem for second-order linear ordinary differential equations

Czech Academy of Sciences Publication Activity Database

Dosoudilová, M.; Lomtatidze, Alexander

2018-01-01

Roč. 2018, č. 13 (2018), s. 1-7 ISSN 1072-6691 Institutional support: RVO:67985840 Keywords : second-order linear equation * periodic boundary value problem * unique solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.954, year: 2016 https://ejde.math.txstate.edu/Volumes/2018/13/abstr.html

Contactless and absolute linear displacement detection based upon 3D printed magnets combined with passive radio-frequency identification

Science.gov (United States)

Windl, Roman; Abert, Claas; Bruckner, Florian; Huber, Christian; Vogler, Christoph; Weitensfelder, Herbert; Suess, Dieter

2017-11-01

Within this work a passive and wireless magnetic sensor, to monitor linear displacements, is proposed. We exploit recent advances in 3D printing and fabricate a polymer bonded magnet with a spatially linear magnetic field component corresponding to the length of the magnet. Regulating the magnetic compound fraction during printing allows specific shaping of the magnetic field distribution. A giant magnetoresistance magnetic field sensor is combined with a radio-frequency identification tag in order to passively monitor the exerted magnetic field of the printed magnet. Due to the tailored magnetic field, a displacement of the magnet with respect to the sensor can be detected within the sub-mm regime. The sensor design provides good flexibility by controlling the 3D printing process according to application needs. Absolute displacement detection using low cost components and providing passive operation, long term stability, and longevity renders the proposed sensor system ideal for structural health monitoring applications.

Contactless and absolute linear displacement detection based upon 3D printed magnets combined with passive radio-frequency identification

Directory of Open Access Journals (Sweden)

Roman Windl

2017-11-01

Full Text Available Within this work a passive and wireless magnetic sensor, to monitor linear displacements, is proposed. We exploit recent advances in 3D printing and fabricate a polymer bonded magnet with a spatially linear magnetic field component corresponding to the length of the magnet. Regulating the magnetic compound fraction during printing allows specific shaping of the magnetic field distribution. A giant magnetoresistance magnetic field sensor is combined with a radio-frequency identification tag in order to passively monitor the exerted magnetic field of the printed magnet. Due to the tailored magnetic field, a displacement of the magnet with respect to the sensor can be detected within the sub-mm regime. The sensor design provides good flexibility by controlling the 3D printing process according to application needs. Absolute displacement detection using low cost components and providing passive operation, long term stability, and longevity renders the proposed sensor system ideal for structural health monitoring applications.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Science.gov (United States)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

Directory of Open Access Journals (Sweden)

Shahid Hasnain

2017-07-01

Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Solving the linearized forward-speed radiation problem using a high-order finite difference method on overlapping grids

DEFF Research Database (Denmark)

Amini Afshar, Mostafa; Bingham, Harry B.

2017-01-01

. Frequency-domain results are then obtained from a Fourier transform of the force and motion signals. In order to make a robust Fourier transform, and capture the response around the critical frequency, the tail of the force signal is asymptotically extrapolated assuming a linear decay rate. Fourth......The linearized potential flow approximation for the forward speed radiation problem is solved in the time domain using a high-order finite difference method. The finite-difference discretization is developed on overlapping, curvilinear body-fitted grids. To ensure numerical stability...

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

Science.gov (United States)

Melcher, Kevin J.

1997-01-01

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended

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

Science.gov (United States)

Shang, Yu; Yu, Guoqiang

2014-09-29

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

On the summability of divergent power series solutions for certain first-order linear PDEs

Directory of Open Access Journals (Sweden)

Masaki Hibino

2015-01-01

Full Text Available This article is concerned with the study of the Borel summability of divergent power series solutions for certain singular first-order linear partial differential equations of nilpotent type. Our main purpose is to obtain conditions which coefficients of equations should satisfy in order to ensure the Borel summability of divergent solutions. We will see that there is a close affinity between the Borel summability of divergent solutions and global analytic continuation properties for coefficients of equations.

Combining states without scale hierarchies with ordered parton showers

Energy Technology Data Exchange (ETDEWEB)

Fischer, Nadine [Monash University, School of Physics and Astronomy, Clayton, VIC (Australia); Prestel, Stefan [Fermi National Accelerator Laboratory, Batavia, IL (United States)

2017-09-15

We present a parameter-free scheme to combine fixed-order multi-jet results with parton-shower evolution. The scheme produces jet cross sections with leading-order accuracy in the complete phase space of multiple emissions, resumming large logarithms when appropriate, while not arbitrarily enforcing ordering on momentum configurations beyond the reach of the parton-shower evolution equation. This requires the development of a matrix-element correction scheme for complex phase-spaces including ordering conditions as well as a systematic scale-setting procedure for unordered phase-space points. The resulting algorithm does not require a merging-scale parameter. We implement the new method in the Vincia framework and compare to LHC data. (orig.)

Predictive inference for best linear combination of biomarkers subject to limits of detection.

Science.gov (United States)

Coolen-Maturi, Tahani

2017-08-15

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine, machine learning and credit scoring. The receiver operating characteristic (ROC) curve is a useful tool to assess the ability of a diagnostic test to discriminate between two classes or groups. In practice, multiple diagnostic tests or biomarkers are combined to improve diagnostic accuracy. Often, biomarker measurements are undetectable either below or above the so-called limits of detection (LoD). In this paper, nonparametric predictive inference (NPI) for best linear combination of two or more biomarkers subject to limits of detection is presented. NPI is a frequentist statistical method that is explicitly aimed at using few modelling assumptions, enabled through the use of lower and upper probabilities to quantify uncertainty. The NPI lower and upper bounds for the ROC curve subject to limits of detection are derived, where the objective function to maximize is the area under the ROC curve. In addition, the paper discusses the effect of restriction on the linear combination's coefficients on the analysis. Examples are provided to illustrate the proposed method. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria

Directory of Open Access Journals (Sweden)

Mervan Pašić

2016-10-01

Full Text Available We study non-monotone positive solutions of the second-order linear differential equations: $(p(tx'' + q(t x = e(t$, with positive $p(t$ and $q(t$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\\theta (t$ of the corresponding integrable linear equation: $(p(t\\theta''=e(t$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.

Importance of the alignment of polar π conjugated molecules inside carbon nanotubes in determining second-order non-linear optical properties.

Science.gov (United States)

Yumura, Takashi; Yamamoto, Wataru

2017-09-20

We employed density functional theory (DFT) calculations with dispersion corrections to investigate energetically preferred alignments of certain p,p'-dimethylaminonitrostilbene (DANS) molecules inside an armchair (m,m) carbon nanotube (n × DANS@(m,m)), where the number of inner molecules (n) is no greater than 3. Here, three types of alignments of DANS are considered: a linear alignment in a parallel fashion and stacking alignments in parallel and antiparallel fashions. According to DFT calculations, a threshold tube diameter for containing DANS molecules in linear or stacking alignments was found to be approximately 1.0 nm. Nanotubes with diameters smaller than 1.0 nm result in the selective formation of linearly aligned DANS molecules due to strong confinement effects within the nanotubes. By contrast, larger diameter nanotubes allow DANS molecules to align in a stacking and linear fashion. The type of alignment adopted by the DANS molecules inside a nanotube is responsible for their second-order non-linear optical properties represented by their static hyperpolarizability (β 0 values). In fact, we computed β 0 values of DANS assemblies taken from optimized n × DANS@(m,m) structures, and their values were compared with those of a single DANS molecule. DFT calculations showed that β 0 values of DANS molecules depend on their alignment, which decrease in the following order: linear alignment > parallel stacking alignment > antiparallel stacking alignment. In particular, a linear alignment has a β 0 value more significant than that of the same number of isolated molecules. Therefore, the linear alignment of DANS molecules, which is only allowed inside smaller diameter nanotubes, can strongly enhance their second-order non-linear optical properties. Since the nanotube confinement determines the alignment of DANS molecules, a restricted nanospace can be utilized to control their second-order non-linear optical properties. These DFT findings can assist in the

On one two-point BVP for the fourth order linear ordinary differential equation

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan; Manjikashvili, M.

2017-01-01

Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077. xml

On one two-point BVP for the fourth order linear ordinary differential equation

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan; Manjikashvili, M.

2017-01-01

Roč. 24, č. 2 (2017), s. 265-275 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : fourth order linear ordinary differential equations * two-point boundary value problems Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2016-0077/gmj-2016-0077.xml

Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces

Directory of Open Access Journals (Sweden)

Yongjin Li

2013-08-01

Full Text Available We prove the Hyers-Ulam stability of linear second-order differential equations in complex Banach spaces. That is, if y is an approximate solution of the differential equation $y''+ alpha y'(t +eta y = 0$ or $y''+ alpha y'(t +eta y = f(t$, then there exists an exact solution of the differential equation near to y.

Weak linear degeneracy and lifespan of classical solutions for first order quasilinear hyperbolic systems

International Nuclear Information System (INIS)

Li Tatsien

1994-01-01

By means of the concept of the weak linear degeneracy, one gets the global existence and the sharp estimate of the lifespan of C 1 solutions to the Cauchy problem for general first order quasilinear hyperbolic systems with small initial data with compact support. (author). 23 refs, 1 fig

Inducing elliptically polarized high-order harmonics from aligned molecules with linearly polarized femtosecond pulses

DEFF Research Database (Denmark)

Etches, Adam; Madsen, Christian Bruun; Madsen, Lars Bojer

2010-01-01

A recent paper reported elliptically polarized high-order harmonics from aligned N2 using a linearly polarized driving field [X. Zhou et al., Phys. Rev. Lett. 102, 073902 (2009)]. This observation cannot be explained in the standard treatment of the Lewenstein model and has been ascribed to many...

Solution of second order linear fuzzy difference equation by Lagrange's multiplier method

Directory of Open Access Journals (Sweden)

Sankar Prasad Mondal

2016-06-01

Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.

Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions.

Science.gov (United States)

Ziener, Christian H; Kurz, Felix T; Buschle, Lukas R; Kampf, Thomas

2015-01-01

The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros [Formula: see text] and [Formula: see text] are considered in the complex plane for real as well as complex values of the index [Formula: see text] and approximations for the exceptional zero [Formula: see text] are obtained. A numerical scheme based on the discretization of the two-dimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.

A New Approach with Combined Stereotactic Trans-multiarc Beams for Radiosurgery Based on the Linear Accelerator : Photon Knife

International Nuclear Information System (INIS)

Choi, Tae Jin; Kim, Jin Hee; Kim, Ok Bae

1996-01-01

Purpose : To get an acute steepness of dose gradients at outside the target volume in intracranial lesion and a less limitation of beam selection avoiding the high dose at normal brain tissue, this Photon Knife Radiosurgery System was developed in order to provide the three-dimensional dose distribution through the reconstruction of CT scan and the combined stereotactic tranmultiarc beam mode based on linear accelerator photon beam. Methods and Materials : This stereotactic radiosurgery, Photon Knife based on linear accelerator photon beam was provided the non-coplanar multiarc and trans-multiarc irradiations. The stereotactic trans-multiarc beam mode can be obtained from the patient position in decubitus. This study has provided the 3-dimensional isodose curve and anatomical structures with the surface rendering technique. Results : In this study, it shows that the dose distributions of stereotactic beam mode are significantly depended on the selected couch and gantry angle in same collimator size. Practical dose distribution of combined stereotactic trans-multiarc beam has shown a more small rim thickness than that of the non-coplanar multiarc beam mode in axial, sagittal and coronal plane in our study. 3-Dimensional dose line displayed with surface rendering of irregular target shape is helpful to determine the target dose and to predict the prognosis in follow-up radiosurgery. Conclusion : 3-Dimensional dose line displayed with surface rendering of irregular target shape is essential in stereotactic radiosurgery. This combined stereotactic trans-multiarc beam has shown a less limitation of the selection couch and gantry beam angles for the target surrounding critical organs. It has shown that the dose distribution of combined trans-multiarc beam greatly depended on the couch and gantry angles. In our experiments. the absorbed dose has been decreased to 27 % /mm in maximum at the interval of 50% to 80% of isodose line

Stochastic Parameter Estimation of Non-Linear Systems Using Only Higher Order Spectra of the Measured Response

Science.gov (United States)

Vasta, M.; Roberts, J. B.

1998-06-01

Methods for using fourth order spectral quantities to estimate the unknown parameters in non-linear, randomly excited dynamic systems are developed. Attention is focused on the case where only the response is measurable and the excitation is unmeasurable and known only in terms of a stochastic process model. The approach is illustrated through application to a non-linear oscillator with both non-linear damping and stiffness and with excitation modelled as a stationary Gaussian white noise process. The methods have applications in studies of the response of structures to random environmental loads, such as wind and ocean wave forces.

Controllable excitation of higher-order rogue waves in nonautonomous systems with both varying linear and harmonic external potentials

Science.gov (United States)

Jia, Heping; Yang, Rongcao; Tian, Jinping; Zhang, Wenmei

2018-05-01

The nonautonomous nonlinear Schrödinger (NLS) equation with both varying linear and harmonic external potentials is investigated and the semirational rogue wave (RW) solution is presented by similarity transformation. Based on the solution, the interactions between Peregrine soliton and breathers, and the controllability of the semirational RWs in periodic distribution and exponential decreasing nonautonomous systems with both linear and harmonic potentials are studied. It is found that the harmonic potential only influences the constraint condition of the semirational solution, the linear potential is related to the trajectory of the semirational RWs, while dispersion and nonlinearity determine the excitation position of the higher-order RWs. The higher-order RWs can be partly, completely and biperiodically excited in periodic distribution system and the diverse excited patterns can be generated for different parameter relations in exponential decreasing system. The results reveal that the excitation of the higher-order RWs can be controlled in the nonautonomous system by choosing dispersion, nonlinearity and external potentials.

A novel algebraic procedure for solving non-linear evolution equations of higher order

International Nuclear Information System (INIS)

Huber, Alfred

2007-01-01

We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients.

Science.gov (United States)

Boyko, Vyacheslav M; Popovych, Roman O; Shapoval, Nataliya M

2013-01-01

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.

OSCILLATION OF A SECOND-ORDER HALF-LINEAR NEUTRAL DAMPED DIFFERENTIAL EQUATION WITH TIME-DELAY

Institute of Scientific and Technical Information of China (English)

无

2012-01-01

In this paper,the oscillation for a class of second-order half-linear neutral damped differential equation with time-delay is studied.By means of Yang-inequality,the generalized Riccati transformation and a certain function,some new sufficient conditions for the oscillation are given for all solutions to the equation.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

Science.gov (United States)

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

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

Science.gov (United States)

Shang, Yu; Li, Ting; Chen, Lei; Lin, Yu; Toborek, Michal; Yu, Guoqiang

2014-05-01

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

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

Science.gov (United States)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Passive impedance-based second-order sliding mode control for non-linear teleoperators

Directory of Open Access Journals (Sweden)

Luis G García-Valdovinos

2017-02-01

Full Text Available Bilateral teleoperation systems have attracted significant attention in the last decade mainly because of technological advancements in both the communication channel and computers performance. In addition, non-linear multi-degree-of-freedom bilateral teleoperators along with state observers have become an open research area. In this article, a model-free exact differentiator is used to estimate the full state along with a chattering-free second-order sliding mode controller to guarantee a robust impedance tracking under both constant and an unknown time delay of non-linear multi-degree-of-freedom robots. The robustness of the proposed controller is improved by introducing a change of coordinates in terms of a new nominal reference similar to that used in adaptive control theory. Experimental results that validate the predicted behaviour are presented and discussed using a Phantom Premium 1.0 as the master robot and a Catalyst-5 virtual model as the slave robot. The dynamics of the Catalyst-5 system is solved online.

Simultaneous and Sequential MS/MS Scan Combinations and Permutations in a Linear Quadrupole Ion Trap.

Science.gov (United States)

Snyder, Dalton T; Szalwinski, Lucas J; Cooks, R Graham

2017-10-17

Methods of performing precursor ion scans as well as neutral loss scans in a single linear quadrupole ion trap have recently been described. In this paper we report methodology for performing permutations of MS/MS scan modes, that is, ordered combinations of precursor, product, and neutral loss scans following a single ion injection event. Only particular permutations are allowed; the sequences demonstrated here are (1) multiple precursor ion scans, (2) precursor ion scans followed by a single neutral loss scan, (3) precursor ion scans followed by product ion scans, and (4) segmented neutral loss scans. (5) The common product ion scan can be performed earlier in these sequences, under certain conditions. Simultaneous scans can also be performed. These include multiple precursor ion scans, precursor ion scans with an accompanying neutral loss scan, and multiple neutral loss scans. We argue that the new capability to perform complex simultaneous and sequential MS n operations on single ion populations represents a significant step in increasing the selectivity of mass spectrometry.

Calculating Higher-Order Moments of Phylogenetic Stochastic Mapping Summaries in Linear Time

Science.gov (United States)

Dhar, Amrit

2017-01-01

Abstract Stochastic mapping is a simulation-based method for probabilistically mapping substitution histories onto phylogenies according to continuous-time Markov models of evolution. This technique can be used to infer properties of the evolutionary process on the phylogeny and, unlike parsimony-based mapping, conditions on the observed data to randomly draw substitution mappings that do not necessarily require the minimum number of events on a tree. Most stochastic mapping applications simulate substitution mappings only to estimate the mean and/or variance of two commonly used mapping summaries: the number of particular types of substitutions (labeled substitution counts) and the time spent in a particular group of states (labeled dwelling times) on the tree. Fast, simulation-free algorithms for calculating the mean of stochastic mapping summaries exist. Importantly, these algorithms scale linearly in the number of tips/leaves of the phylogenetic tree. However, to our knowledge, no such algorithm exists for calculating higher-order moments of stochastic mapping summaries. We present one such simulation-free dynamic programming algorithm that calculates prior and posterior mapping variances and scales linearly in the number of phylogeny tips. Our procedure suggests a general framework that can be used to efficiently compute higher-order moments of stochastic mapping summaries without simulations. We demonstrate the usefulness of our algorithm by extending previously developed statistical tests for rate variation across sites and for detecting evolutionarily conserved regions in genomic sequences. PMID:28177780

High order Fuchsian equations for the square lattice Ising model: χ-tilde(5)

International Nuclear Information System (INIS)

Bostan, A; Boukraa, S; Guttmann, A J; Jensen, I; Hassani, S; Zenine, N; Maillard, J-M

2009-01-01

We consider the Fuchsian linear differential equation obtained (modulo a prime) for χ-tilde (5) , the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the corresponding linear differential operator from calculations using just a single prime. A particular linear combination of χ-tilde (1) and χ-tilde (3) can be removed from χ-tilde (5) and the resulting series is annihilated by a high order globally nilpotent linear ODE. The corresponding (minimal order) linear differential operator, of order 29, splits into factors of small orders. A fifth-order linear differential operator occurs as the left-most factor of the 'depleted' differential operator and it is shown to be equivalent to the symmetric fourth power of L E , the linear differential operator corresponding to the elliptic integral E. This result generalizes what we have found for the lower order terms χ-tilde (3) and χ-tilde (4) . We conjecture that a linear differential operator equivalent to a symmetric (n - 1) th power of L E occurs as a left-most factor in the minimal order linear differential operators for all χ-tilde (n) 's

An arbitrary-order staggered time integrator for the linear acoustic wave equation

Science.gov (United States)

Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

2018-02-01

We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

KAUST Repository

Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

KAUST Repository

Liu, Da-Yan

2015-04-30

This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

Combining Step Gradients and Linear Gradients in Density.

Science.gov (United States)

Kumar, Ashok A; Walz, Jenna A; Gonidec, Mathieu; Mace, Charles R; Whitesides, George M

2015-06-16

Combining aqueous multiphase systems (AMPS) and magnetic levitation (MagLev) provides a method to produce hybrid gradients in apparent density. AMPS—solutions of different polymers, salts, or surfactants that spontaneously separate into immiscible but predominantly aqueous phases—offer thermodynamically stable steps in density that can be tuned by the concentration of solutes. MagLev—the levitation of diamagnetic objects in a paramagnetic fluid within a magnetic field gradient—can be arranged to provide a near-linear gradient in effective density where the height of a levitating object above the surface of the magnet corresponds to its density; the strength of the gradient in effective density can be tuned by the choice of paramagnetic salt and its concentrations and by the strength and gradient in the magnetic field. Including paramagnetic salts (e.g., MnSO4 or MnCl2) in AMPS, and placing them in a magnetic field gradient, enables their use as media for MagLev. The potential to create large steps in density with AMPS allows separations of objects across a range of densities. The gradients produced by MagLev provide resolution over a continuous range of densities. By combining these approaches, mixtures of objects with large differences in density can be separated and analyzed simultaneously. Using MagLev to add an effective gradient in density also enables tuning the range of densities captured at an interface of an AMPS by simply changing the position of the container in the magnetic field. Further, by creating AMPS in which phases have different concentrations of paramagnetic ions, the phases can provide different resolutions in density. These results suggest that combining steps in density with gradients in density can enable new classes of separations based on density.

Cosmological perturbations beyond linear order

CERN Multimedia

CERN. Geneva

2013-01-01

Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.

From sequences to polynomials and back, via operator orderings

Energy Technology Data Exchange (ETDEWEB)

Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118 (United States); De Angelis, Valerio, E-mail: vdeangel@xula.edu [Department of Mathematics, Xavier University of Louisiana, New Orleans, Louisiana 70125 (United States); Vignat, Christophe, E-mail: vignat@tulane.edu [Department of Mathematics, Tulane University, New Orleans, Louisiana 70118, USA and L.S.S. Supelec, Universite d' Orsay (France)

2013-12-15

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

Energy Technology Data Exchange (ETDEWEB)

Cobb, J.W.

1995-02-01

There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

Distributed CMOS Bidirectional Amplifiers Broadbanding and Linearization Techniques

CERN Document Server

El-Khatib, Ziad; Mahmoud, Samy A

2012-01-01

This book describes methods to design distributed amplifiers useful for performing circuit functions such as duplexing, paraphrase amplification, phase shifting power splitting and power combiner applications.  A CMOS bidirectional distributed amplifier is presented that combines for the first time device-level with circuit-level linearization, suppressing the third-order intermodulation distortion. It is implemented in 0.13μm RF CMOS technology for use in highly linear, low-cost UWB Radio-over-Fiber communication systems. Describes CMOS distributed amplifiers for optoelectronic applications such as Radio-over-Fiber systems, base station transceivers and picocells; Presents most recent techniques for linearization of CMOS distributed amplifiers; Includes coverage of CMOS I-V transconductors, as well as CMOS on-chip inductor integration and modeling; Includes circuit applications for UWB Radio-over-Fiber networks.

Evaluation of film dosemeters by linear programming

International Nuclear Information System (INIS)

Kragh, P.; Nitschke, J.

1992-01-01

An evaluation method for multi-component dosemeters is described which uses linear programming in order to decrease the dependence on energy and direction. The results of this method are more accurate than those obtained with the evaluation methods so far applied in film dosimetry. In addition, systematic errors can be given when evaluating individual measurements. Combined linear programming, as a special case of the presented method, is described taking a film dosemeter of particular type as an example. (orig.) [de

Numerical analysis of non-linear vibrations of a fractionally damped cylindrical shell under the conditions of combinational internal resonance

Directory of Open Access Journals (Sweden)

Rossikhin Yury A.

2018-01-01

Full Text Available Non-linear damped vibrations of a cylindrical shell embedded into a fractional derivative medium are investigated for the case of the combinational internal resonance, resulting in modal interaction, using two different numerical methods with further comparison of the results obtained. The damping properties of the surrounding medium are described by the fractional derivative Kelvin-Voigt model utilizing the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential equations of the second order are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitude-and-phase modulations for the case of the combinational internal resonance. A good agreement in results is declared.

Third-Order Elliptic Lowpass Filter for Multi-Standard Baseband Chain Using Highly Linear Digitally Programmable OTA

Science.gov (United States)

Elamien, Mohamed B.; Mahmoud, Soliman A.

2018-03-01

In this paper, a third-order elliptic lowpass filter is designed using highly linear digital programmable balanced OTA. The filter exhibits a cutoff frequency tuning range from 2.2 MHz to 7.1 MHz, thus, it covers W-CDMA, UMTS, and DVB-H standards. The programmability concept in the filter is achieved by using digitally programmable operational transconductors amplifier (DPOTA). The DPOTA employs three linearization techniques which are the source degeneration, double differential pair and the adaptive biasing. Two current division networks (CDNs) are used to control the value of the transconductance. For the DPOTA, the third-order harmonic distortion (HD3) remains below -65 dB up to 0.4 V differential input voltage at 1.2 V supply voltage. The DPOTA and the filter are designed and simulated in 90 nm CMOS technology with LTspice simulator.

A method for fitting regression splines with varying polynomial order in the linear mixed model.

Science.gov (United States)

Edwards, Lloyd J; Stewart, Paul W; MacDougall, James E; Helms, Ronald W

2006-02-15

The linear mixed model has become a widely used tool for longitudinal analysis of continuous variables. The use of regression splines in these models offers the analyst additional flexibility in the formulation of descriptive analyses, exploratory analyses and hypothesis-driven confirmatory analyses. We propose a method for fitting piecewise polynomial regression splines with varying polynomial order in the fixed effects and/or random effects of the linear mixed model. The polynomial segments are explicitly constrained by side conditions for continuity and some smoothness at the points where they join. By using a reparameterization of this explicitly constrained linear mixed model, an implicitly constrained linear mixed model is constructed that simplifies implementation of fixed-knot regression splines. The proposed approach is relatively simple, handles splines in one variable or multiple variables, and can be easily programmed using existing commercial software such as SAS or S-plus. The method is illustrated using two examples: an analysis of longitudinal viral load data from a study of subjects with acute HIV-1 infection and an analysis of 24-hour ambulatory blood pressure profiles.

The fourth-order non-linear sigma models and asymptotic freedom in four dimensions

International Nuclear Information System (INIS)

Buchbinder, I.L.; Ketov, S.V.

1991-01-01

Starting with the most general Lagrangian of the fourth-order non-linear sigma model in four space-time dimensions, we calculate the one-loop, on-shell ultra-violet-divergent part of the effective action. The formalism is based on the background field method and the generalised Schwinger-De Witt technique. The multiplicatively renormalisable case is investigated in some detail. The renormalisation group equations are obtained, and the conditions for a realisation of asymptotic freedom are considered. (orig.)

Combined First and Second Order Total Variation Inpainting using Split Bregman

KAUST Repository

Papafitsoros, Konstantinos

2013-07-12

In this article we discuss the implementation of the combined first and second order total variation inpainting that was introduced by Papafitsoros and Schdönlieb. We describe the algorithm we use (split Bregman) in detail, and we give some examples that indicate the difference between pure first and pure second order total variation inpainting.

Combined First and Second Order Total Variation Inpainting using Split Bregman

KAUST Repository

Papafitsoros, Konstantinos; Schoenlieb, Carola Bibiane; Sengul, Bati

2013-01-01

In this article we discuss the implementation of the combined first and second order total variation inpainting that was introduced by Papafitsoros and Schdönlieb. We describe the algorithm we use (split Bregman) in detail, and we give some examples that indicate the difference between pure first and pure second order total variation inpainting.

Linear viscoelastic characterization from filament stretching rheometry

DEFF Research Database (Denmark)

Wingstrand, Sara Lindeblad; Alvarez, Nicolas J.; Hassager, Ole

to measure both linear and nonlinear dynamics on a single apparatus. With a software modification to the FSR motor control, we show that linear viscoelasticity can be measured via small amplitude squeeze flow (SASF). Squeeze flow is a combination of both shear and extensional flow applied by axially......Traditionally, linear viscoelasticity is measured using small amplitude oscillatory shear flow. Due to experimental difficulties, shear flows are predominately confined to the linear and mildly nonlinear regime. On the other hand, extensional flows have proven more practical in measuring...... viscoelasticity well into the nonlinear regime. Therefore at present, complete rheological characterization of a material requires two apparatuses: a shear and an extensional rheometer. This work is focused on developing a linear viscoelastic protocol for the filament stretching rheometer (FSR) in order...

Multi-linear sparse reconstruction for SAR imaging based on higher-order SVD

Science.gov (United States)

Gao, Yu-Fei; Gui, Guan; Cong, Xun-Chao; Yang, Yue; Zou, Yan-Bin; Wan, Qun

2017-12-01

This paper focuses on the spotlight synthetic aperture radar (SAR) imaging for point scattering targets based on tensor modeling. In a real-world scenario, scatterers usually distribute in the block sparse pattern. Such a distribution feature has been scarcely utilized by the previous studies of SAR imaging. Our work takes advantage of this structure property of the target scene, constructing a multi-linear sparse reconstruction algorithm for SAR imaging. The multi-linear block sparsity is introduced into higher-order singular value decomposition (SVD) with a dictionary constructing procedure by this research. The simulation experiments for ideal point targets show the robustness of the proposed algorithm to the noise and sidelobe disturbance which always influence the imaging quality of the conventional methods. The computational resources requirement is further investigated in this paper. As a consequence of the algorithm complexity analysis, the present method possesses the superiority on resource consumption compared with the classic matching pursuit method. The imaging implementations for practical measured data also demonstrate the effectiveness of the algorithm developed in this paper.

Adaptive rival penalized competitive learning and combined linear predictor model for financial forecast and investment.

Science.gov (United States)

Cheung, Y M; Leung, W M; Xu, L

1997-01-01

We propose a prediction model called Rival Penalized Competitive Learning (RPCL) and Combined Linear Predictor method (CLP), which involves a set of local linear predictors such that a prediction is made by the combination of some activated predictors through a gating network (Xu et al., 1994). Furthermore, we present its improved variant named Adaptive RPCL-CLP that includes an adaptive learning mechanism as well as a data pre-and-post processing scheme. We compare them with some existing models by demonstrating their performance on two real-world financial time series--a China stock price and an exchange-rate series of US Dollar (USD) versus Deutschmark (DEM). Experiments have shown that Adaptive RPCL-CLP not only outperforms the other approaches with the smallest prediction error and training costs, but also brings in considerable high profits in the trading simulation of foreign exchange market.

Finiteness of Ricci flat supersymmetric non-linear sigma-models

International Nuclear Information System (INIS)

Alvarez-Gaume, L.; Ginsparg, P.

1985-01-01

Combining the constraints of Kaehler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear sigma-models with target space an arbitrary riemannian manifold M. We show that the constraint of N=2 supersymmetry requires that all counterterms to the metric beyond one-loop order are cohomologically trivial. It follows that such supersymmetric non-linear sigma-models defined on locally symmetric spaces are super-renormalizable and that N=4 models are on-shell ultraviolet finite to all orders of perturbation theory. (orig.)

Zeroth-order design report for the next linear collider. Volume 1

Energy Technology Data Exchange (ETDEWEB)

Raubenheimer, T.O. [ed.

1996-05-01

This Zeroth Order Design Report (ZDR) for the Next Linear Collider (NLC) has been completed as a feasibility study for a TeV-scale linear collider that incorporates a room-temperature accelerator powered by rf microwaves at 11.424 GHz--similar to that presently used in the SLC, but at four times the rf frequency. The purpose of this study is to examine the complete systems of such a collider, to understand how the parts fit together, and to make certain that every required piece has been included. The design presented here is not fully engineered in any sense, but to be assured that the NLC can be built, attention has been given to a number of critical components and issues that present special challenges. More engineering and development of a number of mechanical and electrical systems remain to be done, but the conclusion of this study is that indeed the NLC is technically feasible and can be expected to reach the performance levels required to perform research at the TeV energy scale. Volume one covers the following: the introduction; electron source; positron source; NLC damping rings; bunch compressors and prelinac; low-frequency linacs and compressors; main linacs; design and dynamics; and RF systems for main linacs.

Zeroth-order design report for the next linear collider. Volume 1

International Nuclear Information System (INIS)

Raubenheimer, T.O.

1996-05-01

This Zeroth Order Design Report (ZDR) for the Next Linear Collider (NLC) has been completed as a feasibility study for a TeV-scale linear collider that incorporates a room-temperature accelerator powered by rf microwaves at 11.424 GHz--similar to that presently used in the SLC, but at four times the rf frequency. The purpose of this study is to examine the complete systems of such a collider, to understand how the parts fit together, and to make certain that every required piece has been included. The design presented here is not fully engineered in any sense, but to be assured that the NLC can be built, attention has been given to a number of critical components and issues that present special challenges. More engineering and development of a number of mechanical and electrical systems remain to be done, but the conclusion of this study is that indeed the NLC is technically feasible and can be expected to reach the performance levels required to perform research at the TeV energy scale. Volume one covers the following: the introduction; electron source; positron source; NLC damping rings; bunch compressors and prelinac; low-frequency linacs and compressors; main linacs; design and dynamics; and RF systems for main linacs

Feasibility of combining linear theory and impact theory methods for the analysis and design of high speed configurations

Science.gov (United States)

Brooke, D.; Vondrasek, D. V.

1978-01-01

The aerodynamic influence coefficients calculated using an existing linear theory program were used to modify the pressures calculated using impact theory. Application of the combined approach to several wing-alone configurations shows that the combined approach gives improved predictions of the local pressure and loadings over either linear theory alone or impact theory alone. The approach not only removes most of the short-comings of the individual methods, as applied in the Mach 4 to 8 range, but also provides the basis for an inverse design procedure applicable to high speed configurations.

Robust Management of Combined Heat and Power Systems via Linear Decision Rules

DEFF Research Database (Denmark)

Zugno, Marco; Morales González, Juan Miguel; Madsen, Henrik

2014-01-01

The heat and power outputs of Combined Heat and Power (CHP) units are jointly constrained. Hence, the optimal management of systems including CHP units is a multicommodity optimization problem. Problems of this type are stochastic, owing to the uncertainty inherent both in the demand for heat and...... linear decision rules to guarantee both tractability and a correct representation of the dynamic aspects of the problem. Numerical results from an illustrative example confirm the value of the proposed approach....

Testing the dual-route model of perceived gaze direction: Linear combination of eye and head cues.

Science.gov (United States)

Otsuka, Yumiko; Mareschal, Isabelle; Clifford, Colin W G

2016-06-01

We have recently proposed a dual-route model of the effect of head orientation on perceived gaze direction (Otsuka, Mareschal, Calder, & Clifford, 2014; Otsuka, Mareschal, & Clifford, 2015), which computes perceived gaze direction as a linear combination of eye orientation and head orientation. By parametrically manipulating eye orientation and head orientation, we tested the adequacy of a linear model to account for the effect of horizontal head orientation on perceived direction of gaze. Here, participants adjusted an on-screen pointer toward the perceived gaze direction in two image conditions: Normal condition and Wollaston condition. Images in the Normal condition included a change in the visible part of the eye along with the change in head orientation, while images in the Wollaston condition were manipulated to have identical eye regions across head orientations. Multiple regression analysis with explanatory variables of eye orientation and head orientation revealed that linear models account for most of the variance both in the Normal condition and in the Wollaston condition. Further, we found no evidence that the model with a nonlinear term explains significantly more variance. Thus, the current study supports the dual-route model that computes the perceived gaze direction as a linear combination of eye orientation and head orientation.

Dynamics of High-Order Spin-Orbit Couplings about Linear Momenta in Compact Binary Systems*

International Nuclear Information System (INIS)

Huang Li; Wu Xin; Huang Guo-Qing; Mei Li-Jie

2017-01-01

This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta. When this Hamiltonian form is transformed to a Lagrangian form, besides the terms corresponding to the same order terms in the Hamiltonian, several additional terms, third post-Newtonian (3PN), 4PN, 5PN, 6PN and 7PN order spin-spin coupling terms, yield in the Lagrangian. That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations. The full Lagrangian without the spin-spin couplings truncated is integrable and regular. Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped. These results are also supported numerically. (paper)

Linear magnetic spring and spring/motor combination

Science.gov (United States)

Patt, Paul J. (Inventor); Stolfi, Fred R. (Inventor)

1991-01-01

A magnetic spring, or a spring and motor combination, providing a linear spring force characteristic in each direction from a neutral position, in which the spring action may occur for any desired coordinate of a typical orthogonal coordinate system. A set of magnets are disposed, preferably symmetrically about a coordinate axis, poled orthogonally to the desired force direction. A second set of magnets, respectively poled opposite the first set, are arranged on the sprung article. The magnets of one of the sets are spaced a greater distance apart than those of the other, such that an end magnet from each set forms a pair having preferably planar faces parallel to the direction of spring force, the faces being offset so that in a neutral position the outer edge of the closer spaced magnet set is aligned with the inner edge of the greater spaced magnet set. For use as a motor, a coil can be arranged with conductors orthogonal to both the magnet pole directions and the direction of desired spring force, located across from the magnets of one set and fixed with respect to the magnets of the other set. In a cylindrical coordinate system having axial spring force, the magnets are radially poled and motor coils are concentric with the cylinder axis.

Syntheses, structures and third-order non-linear optical properties of homometal clusters containing molybdenum

International Nuclear Information System (INIS)

Li Yong; Lu Jing; Cui Xiaobing; Xu Jiqing; Li Kechang; Sun Huaying; Li Guanghua; Pan Lingyun; Yang Qingxin

2005-01-01

Both the homometal cluster [P(ph 4 )] 2 [Mo 2 O 2 (μ-S) 2 (S 2 ) 2 ] (1) and [Mo 2 O 2 (μ-S) 2 (Et 2 dtc) 2 ] (2) (Et 2 dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145x10 -30 esu for (1) and 5.428x10 -30 esu for (2)

A speed estimation unit for induction motors based on adaptive linear combiner

International Nuclear Information System (INIS)

Marei, Mostafa I.; Shaaban, Mostafa F.; El-Sattar, Ahmed A.

2009-01-01

This paper presents a new induction motor speed estimation technique, which can estimate the rotor resistance as well, from the measured voltage and current signals. Moreover, the paper utilizes a novel adaptive linear combiner (ADALINE) structure for speed and rotor resistance estimations. This structure can deal with the multi-output systems and it is called MO-ADALINE. The model of the induction motor is arranged in a linear form, in the stationary reference frame, to cope with the proposed speed estimator. There are many advantages of the proposed unit such as wide speed range capability, immunity against harmonics of measured waveforms, and precise estimation of the speed and the rotor resistance at different dynamic changes. Different types of induction motor drive systems are used to evaluate the dynamic performance and to examine the accuracy of the proposed unit for speed and rotor resistance estimation.

A Combined First and Second Order Variational Approach for Image Reconstruction

KAUST Repository

Papafitsoros, K.

2013-05-10

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler\\'s elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images-a known disadvantage of the ROF model-while being simple and efficiently numerically solvable. ©Springer Science+Business Media New York 2013.

A Reduced-Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography

Science.gov (United States)

Zha, Yuanyuan; Yeh, Tian-Chyi J.; Illman, Walter A.; Zeng, Wenzhi; Zhang, Yonggen; Sun, Fangqiang; Shi, Liangsheng

2018-03-01

Hydraulic tomography (HT) is a recently developed technology for characterizing high-resolution, site-specific heterogeneity using hydraulic data (nd) from a series of cross-hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large-scale 3-D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced-Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen-Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross-covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3-D transient HT analysis of data from a highly heterogeneous field site.

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

A unified framework for testing in the linear regression model under unknown order of fractional integration

DEFF Research Database (Denmark)

Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp

We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...

A non-linear reduced order methodology applicable to boiling water reactor stability analysis

International Nuclear Information System (INIS)

Prill, Dennis Paul

2013-01-01

Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character

Non linear dynamics of memristor based 3rd order oscillatory system

KAUST Repository

Talukdar, Abdul Hafiz Ibne

2012-07-23

In this paper, we report for the first time the nonlinear dynamics of three memristor based phase shift oscillators, and consider them as a plausible solution for the realization of parametric oscillation as an autonomous linear time variant system. Sustained oscillation is reported through oscillating resistance while time dependent poles are present. The memristor based phase shift oscillator is explored further by varying the parameters so as to present the resistance of the memristor as a time varying parameter, thus potentially eliminating the need of external periodic forces in order for it to oscillate. Multi memristors, used simultaneously with similar and different parameters, are investigated in this paper. Mathematical formulas for analyzing such oscillators are verified with simulation results and are found to be in good agreement. © 2011 Elsevier Ltd. All rights reserved.

Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

DEFF Research Database (Denmark)

Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

2004-01-01

of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....

Study on Fuzzy Adaptive Fractional Order PIλDμ Control for Maglev Guiding System

Science.gov (United States)

Hu, Qing; Hu, Yuwei

The mathematical model of the linear elevator maglev guiding system is analyzed in this paper. For the linear elevator needs strong stability and robustness to run, the integer order PID was expanded to the fractional order, in order to improve the steady state precision, rapidity and robustness of the system, enhance the accuracy of the parameter in fractional order PIλDμ controller, the fuzzy control is combined with the fractional order PIλDμ control, using the fuzzy logic achieves the parameters online adjustment. The simulations reveal that the system has faster response speed, higher tracking precision, and has stronger robustness to the disturbance.

Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term

Directory of Open Access Journals (Sweden)

Qiong Liu

2012-01-01

Full Text Available We study the following fourth-order elliptic equations: Δ2+Δ=(,,∈Ω,=Δ=0,∈Ω, where Ω⊂ℝ is a bounded domain with smooth boundary Ω and (, is asymptotically linear with respect to at infinity. Using an equivalent version of Cerami's condition and the symmetric mountain pass lemma, we obtain the existence of multiple solutions for the equations.

High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium

Science.gov (United States)

Barnett, Alex H.; Nelson, Bradley J.; Mahoney, J. Matthew

2015-09-01

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve, the square of the wavenumber (refractive index) varies linearly in one coordinate, i.e. (Δ + E +x2) u (x1 ,x2) = 0 where E is a constant; this models quantum particles of fixed energy in a uniform gravitational field, and has broader applications to stratified media in acoustics, optics and seismology. We evaluate the fundamental solution efficiently with exponential accuracy via numerical saddle-point integration, using the truncated trapezoid rule with typically 102 nodes, with an effort that is independent of the frequency parameter E. By combining with a high-order Nyström quadrature, we are able to solve the scattering from obstacles 50 wavelengths across to 11 digits of accuracy in under a minute on a desktop or laptop.

Zeroth-order design report for the next linear collider. Volume 2

International Nuclear Information System (INIS)

Raubenheimer, T.O.

1996-05-01

This Zeroth-Order Design Report (ZDR) for the Next Linear Collider (NLC) has been completed as a feasibility study for a TeV-scale linear collider that incorporates a room-temperature accelerator powered by rf microwaves at 11.424 GHz--similar to that presently used in the SLC, but at four times the rf frequency. The purpose of this study is to examine the complete systems of such a collider, to understand how the parts fit together, and to make certain that every required piece has been included. The ''design'' presented here is not fully engineered in any sense, but to be assured that the NLC can be built, attention has been given to a number of critical components and issues that present special challenges. More engineering and development of a number of mechanical and electrical systems remain to be done, but the conclusion of this study is that indeed the NLC is technically feasible and can be expected to reach the performance levels required to perform research at the TeV energy scale. Volume II covers the following: collimation systems; IP switch and big bend; final focus; the interaction region; multiple bunch issues; control systems; instrumentation; machine protection systems; NLC reliability considerations; NLC conventional facilities. Also included are four appendices on the following topics: An RF power source upgrade to the NLC; a second interaction region for gamma-gamma, gamma-electron; ground motion: theory and measurement; and beam-based feedback: theory and implementation

Zeroth-order design report for the next linear collider. Volume 2

Energy Technology Data Exchange (ETDEWEB)

Raubenheimer, T.O. [ed.

1996-05-01

This Zeroth-Order Design Report (ZDR) for the Next Linear Collider (NLC) has been completed as a feasibility study for a TeV-scale linear collider that incorporates a room-temperature accelerator powered by rf microwaves at 11.424 GHz--similar to that presently used in the SLC, but at four times the rf frequency. The purpose of this study is to examine the complete systems of such a collider, to understand how the parts fit together, and to make certain that every required piece has been included. The ``design`` presented here is not fully engineered in any sense, but to be assured that the NLC can be built, attention has been given to a number of critical components and issues that present special challenges. More engineering and development of a number of mechanical and electrical systems remain to be done, but the conclusion of this study is that indeed the NLC is technically feasible and can be expected to reach the performance levels required to perform research at the TeV energy scale. Volume II covers the following: collimation systems; IP switch and big bend; final focus; the interaction region; multiple bunch issues; control systems; instrumentation; machine protection systems; NLC reliability considerations; NLC conventional facilities. Also included are four appendices on the following topics: An RF power source upgrade to the NLC; a second interaction region for gamma-gamma, gamma-electron; ground motion: theory and measurement; and beam-based feedback: theory and implementation.

Path integral solution of linear second order partial differential equations I: the general construction

International Nuclear Information System (INIS)

LaChapelle, J.

2004-01-01

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

General solutions of second-order linear difference equations of Euler type

Directory of Open Access Journals (Sweden)

Akane Hongyo

2017-01-01

Full Text Available The purpose of this paper is to give general solutions of linear difference equations which are related to the Euler-Cauchy differential equation \\(y^{\\prime\\prime}+(\\lambda/t^2y=0\\ or more general linear differential equations. We also show that the asymptotic behavior of solutions of the linear difference equations are similar to solutions of the linear differential equations.

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Linear perturbation of spherically symmetric flows: a first-order upwind scheme for the gas dynamics equations in Lagrangian coordinates

International Nuclear Information System (INIS)

Clarisse, J.M.

2007-01-01

A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)

The linear programming bound for binary linear codes

NARCIS (Netherlands)

Brouwer, A.E.

1993-01-01

Combining Delsarte's (1973) linear programming bound with the information that certain weights cannot occur, new upper bounds for dmin (n,k), the maximum possible minimum distance of a binary linear code with given word length n and dimension k, are derived.

Quantum tests for the linearity and permutation invariance of Boolean functions

Energy Technology Data Exchange (ETDEWEB)

Hillery, Mark [Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10021 (United States); Andersson, Erika [SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)

2011-12-15

The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is {epsilon}-far from having that property. The performance of the algorithm is judged by how many calls need to be made to the black box in order to determine, with high probability, which of the two alternatives is the case. Here we present two quantum algorithms, the first to determine whether the function is linear and the second to determine whether it is symmetric (invariant under permutations of the arguments). Both require order {epsilon}{sup -2/3} calls to the oracle, which is better than known classical algorithms. In addition, in the case of linearity testing, if the function is linear, the quantum algorithm identifies which linear function it is. The linearity test combines the Bernstein-Vazirani algorithm and amplitude amplification, while the test to determine whether a function is symmetric uses projective measurements and amplitude amplification.

Effects of combined linear and nonlinear periodic training on physical fitness and competition times in finswimmers.

Science.gov (United States)

Yu, Kyung-Hun; Suk, Min-Hwa; Kang, Shin-Woo; Shin, Yun-A

2014-10-01

The purpose of this study was to investigate the effect of combined linear and nonlinear periodic training on physical fitness and competition times in finswimmers. The linear resistance training model (6 days/week) and nonlinear underwater training (4 days/week) were applied to 12 finswimmers (age, 16.08± 1.44 yr; career, 3.78± 1.90 yr) for 12 weeks. Body composition measures included weight, body mass index (BMI), percent fat, and fat-free mass. Physical fitness measures included trunk flexion forward, trunk extension backward, sargent jump, 1-repetition-maximum (1 RM) squat, 1 RM dead lift, knee extension, knee flexion, trunk extension, trunk flexion, and competition times. Body composition and physical fitness were improved after the 12-week periodic training program. Weight, BMI, and percent fat were significantly decreased, and trunk flexion forward, trunk extension backward, sargent jump, 1 RM squat, 1 RM dead lift, and knee extension (right) were significantly increased. The 50- and 100-m times significantly decreased in all 12 athletes. After 12 weeks of training, all finswimmers who participated in this study improved their times in a public competition. These data indicate that combined linear and nonlinear periodic training enhanced the physical fitness and competition times in finswimmers.

New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems

Directory of Open Access Journals (Sweden)

Heonjong Yoo

2017-01-01

Full Text Available The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III–(V, they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.

INTELLIGENT FRACTIONAL ORDER ITERATIVE LEARNING CONTROL USING FEEDBACK LINEARIZATION FOR A SINGLE-LINK ROBOT

Directory of Open Access Journals (Sweden)

Iman Ghasemi

2017-05-01

Full Text Available In this paper, iterative learning control (ILC is combined with an optimal fractional order derivative (BBO-Da-type ILC and optimal fractional and proportional-derivative (BBO-PDa-type ILC. In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where  to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both  and  learning law i.e. proportional , derivative  and  are optimized using Biogeography-Based optimization algorithm (BBO. Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC

High Order A-stable Continuous General Linear Methods for Solution of Systems of Initial Value Problems in ODEs

Directory of Open Access Journals (Sweden)

Dauda GuliburYAKUBU

2012-12-01

Full Text Available Accurate solutions to initial value systems of ordinary differential equations may be approximated efficiently by Runge-Kutta methods or linear multistep methods. Each of these has limitations of one sort or another. In this paper we consider, as a middle ground, the derivation of continuous general linear methods for solution of stiff systems of initial value problems in ordinary differential equations. These methods are designed to combine the advantages of both Runge-Kutta and linear multistep methods. Particularly, methods possessing the property of A-stability are identified as promising methods within this large class of general linear methods. We show that the continuous general linear methods are self-starting and have more ability to solve the stiff systems of ordinary differential equations, than the discrete ones. The initial value systems of ordinary differential equations are solved, for instance, without looking for any other method to start the integration process. This desirable feature of the proposed approach leads to obtaining very high accuracy of the solution of the given problem. Illustrative examples are given to demonstrate the novelty and reliability of the methods.

Non-linear operation of nanomechnical systems combining photothermal excitation and magneto-motive detection

International Nuclear Information System (INIS)

Koenig, Daniel R; Metzger, Constanze; Camerer, Stephan; Kotthaus, Joerg P

2006-01-01

We present a non-linear operation of a nanomechanical beam resonator by photothermal excitation at 4 K. The resonators dimensions are 10 μm in length, 200 nm in width, and 200 nm in height. The actuation mechanism is based on a pulsed diode laser focused onto the centre of the beam resonator. Thermally induced stress caused by the different thermal expansion coefficients of the bi-layer system periodically deflects the resonator. Magnetomotively detected amplitudes up to 150 nm are reached at the fundamental resonance mode at a frequency of 8.9 MHz. Furthermore, the third eigenmode of the resonator at a frequency 36 MHz is also excited. We conclude that the photothermal excitation at 4 K should be applicable up to the GHz regime, the operation in the non-linear regime can be used for performance enhancement of nanomechanical systems, and the combination of photothermal excitation and magneto-motive detection avoids undesired cross talk

Fatigue damage estimation in non-linear systems using a combination of Monte Carlo simulation and the First Order Reliability Method

DEFF Research Database (Denmark)

Jensen, Jørgen Juncher

2015-01-01

For non-linear systems the estimation of fatigue damage under stochastic loadings can be rather time-consuming. Usually Monte Carlo simulation (MCS) is applied, but the coefficient-of-variation (COV) can be large if only a small set of simulations can be done due to otherwise excessive CPU time...

Higher order correlations in computed particle distributions

International Nuclear Information System (INIS)

Hanerfeld, H.; Herrmannsfeldt, W.; Miller, R.H.

1989-03-01

The rms emittances calculated for beam distributions using computer simulations are frequently dominated by higher order aberrations. Thus there are substantial open areas in the phase space plots. It has long been observed that the rms emittance is not an invariant to beam manipulations. The usual emittance calculation removes the correlation between transverse displacement and transverse momentum. In this paper, we explore the possibility of defining higher order correlations that can be removed from the distribution to result in a lower limit to the realizable emittance. The intent is that by inserting the correct combinations of linear lenses at the proper position, the beam may recombine in a way that cancels the effects of some higher order forces. An example might be the non-linear transverse space charge forces which cause a beam to spread. If the beam is then refocused so that the same non-linear forces reverse the inward velocities, the resulting phase space distribution may reasonably approximate the original distribution. The approach to finding the location and strength of the proper lens to optimize the transported beam is based on work by Bruce Carlsten of Los Alamos National Laboratory. 11 refs., 4 figs

Integral linear momentum balance in combining flows for calculating the pressure drop coefficients

International Nuclear Information System (INIS)

Bollmann, A.

1983-01-01

Equations for calculating the loss coefficient in combining flows in tee functions are obtained by an integral linear momentum balance. It is a practice, when solving this type of problem, to neglect the pressure difference in the upstream location as well as the wall-fluid interaction in the lateral branch of the junction. In this work it is demonstrated the influence of the above parameters on the loss coefficient based on experimental values and by apropriate algebraic manipulation of the loss coefficient values published by previous investigators. (Author) [pt

Non-linear electrodynamics in Kaluza-Klein theory

International Nuclear Information System (INIS)

Kerner, R.

1987-01-01

The most general variational principle based on the invariants of the Riemann tensor and leading to the second order differential equations should contain, in dimensions higher than four, the invariants of the Gauss-Bonnet type. In five dimensions the lagrangian should be a linear combination of the scalar curvature and the second-order invariant. The equations of the electromagnetic field are derived in the absence of scalar and gravitational fields of the Kaluza-Klein model. They yield the unique extension of Maxwell's system in the Kaluza-Klein theory. Some properties of eventual solutions are discussed [fr

Boosted regression trees, multivariate adaptive regression splines and their two-step combinations with multiple linear regression or partial least squares to predict blood-brain barrier passage: a case study.

Science.gov (United States)

Deconinck, E; Zhang, M H; Petitet, F; Dubus, E; Ijjaali, I; Coomans, D; Vander Heyden, Y

2008-02-18

The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.

High-order sliding mode observer for fractional commensurate linear systems with unknown input

KAUST Repository

Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

2017-01-01

In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.

High-order sliding mode observer for fractional commensurate linear systems with unknown input

KAUST Repository

Belkhatir, Zehor

2017-05-20

In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.

Recursive Algorithm For Linear Regression

Science.gov (United States)

Varanasi, S. V.

1988-01-01

Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.

Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

Science.gov (United States)

Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

2017-04-01

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

Study on Differential Algebraic Method of Aberrations up to Arbitrary Order for Combined Electromagnetic Focusing Systems

Institute of Scientific and Technical Information of China (English)

CHENG Min; TANG Tiantong; YAO Zhenhua; ZHU Jingping

2001-01-01

Differential algebraic method is apowerful technique in computer numerical analysisbased on nonstandard analysis and formal series the-ory. It can compute arbitrary high order derivativeswith excellent accuracy. The principle of differentialalgebraic method is applied to calculate high orderaberrations of combined electromagnetic focusing sys-tems. As an example, third-order geometric aberra-tion coefficients of an actual combined electromagneticfocusing system were calculated. The arbitrary highorder aberrations are conveniently calculated by dif-ferential algebraic method and the fifth-order aberra-tion diagrams are given.

Linearly and circularly polarized laser photoinduced molecular order in azo dye doped polymer films

Directory of Open Access Journals (Sweden)

Saad Bendaoud

2017-01-01

Full Text Available Photo-induced behavior of Azo Disperse one (AZD1 doped Poly(Methyl MethAcrylate (PMMA using both linear and circular polarized light is studied. The anisotropy is not erased by the circular polarization light. The circular polarization light combined with relatively long lifetime of the cis state in azo dye doped polymers activate all transverse directions of the angular hole burning through the spot in the film inducing anisotropy. Under circular polarized light, there is no orientation perpendicularly to the helex described by the rotating electric field vector, trans molecules reorients in the propagation direction of the pump beam. The polarization state of the probe beam after propagation through the pumped spot depends strongly on the angle of incidence of both pump and probe beams on the input face. In the case where circular polarized pump and probe beams are under the same angle of incidence, the probe beam “sees” anisotropic film as if it is isotropic. Results of this work shows the possibility to reorient azobenzene-type molecules in two orthogonal directions using alternately linearly and circularly polarized beams.

Approximate Forward Difference Equations for the Lower Order Non-Stationary Statistics of Geometrically Non-Linear Systems subject to Random Excitation

DEFF Research Database (Denmark)

Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.

Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....

Linear stability analysis of flow instabilities with a nodalized reduced order model in heated channel

International Nuclear Information System (INIS)

Paul, Subhanker; Singh, Suneet

2015-01-01

The prime objective of the presented work is to develop a Nodalized Reduced Order Model (NROM) to carry linear stability analysis of flow instabilities in a two-phase flow system. The model is developed by dividing the single phase and two-phase region of a uniformly heated channel into N number of nodes followed by time dependent spatial linear approximations for single phase enthalpy and two-phase quality between the consecutive nodes. Moving boundary scheme has been adopted in the model, where all the node boundaries vary with time due to the variation of boiling boundary inside the heated channel. Using a state space approach, the instability thresholds are delineated by stability maps plotted in parameter planes of phase change number (N pch ) and subcooling number (N sub ). The prime feature of the present model is that, though the model equations are simpler due to presence of linear-linear approximations for single phase enthalpy and two-phase quality, yet the results are in good agreement with the existing models (Karve [33]; Dokhane [34]) where the model equations run for several pages and experimental data (Solberg [41]). Unlike the existing ROMs, different two-phase friction factor multiplier correlations have been incorporated in the model. The applicability of various two-phase friction factor multipliers and their effects on stability behaviour have been depicted by carrying a comparative study. It is also observed that the Friedel model for friction factor calculations produces the most accurate results with respect to the available experimental data. (authors)

A Framework for Mathematical Thinking: The Case of Linear Algebra

Science.gov (United States)

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

Non-Linear Metamodeling Extensions to the Robust Parameter Design of Computer Simulations

Science.gov (United States)

2016-09-15

The combined-array RSM approach has been applied to a piston simulation [11] and an economic order quantity inventory model [12, 13]. A textbook ...are limited when applied to simulations. In the former case, the mean and variance models can be inadequate due to a high level of non-linearity...highly non-linear nature of typical simulations. In the multi-response RPD problem, the objective is to find the optimal control parameter levels

Linear-chain model to explain density of states and Tsub(c) changes with atomic ordering

International Nuclear Information System (INIS)

Junod, A.

1978-01-01

The effect of long-range atomic order on the electronic density of states has been recalculated for the A15-type structure within the linear-chain model. It is found that a defect concentration c reduces the density of states at the Fermi level by a factor (1 + c/c 0 )(c/c 0 ) -3 [ln(1 + c/c 0 )] 3 . This result is in qualitative agreement with experimental data on the specific heat, magnetic susceptibility and superconducting transition temperature of V 3 Au. (author)

Special set linear algebra and special set fuzzy linear algebra

OpenAIRE

Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.

2009-01-01

The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...

Finite-dimensional linear algebra

CERN Document Server

Gockenbach, Mark S

2010-01-01

Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq

Hybrid approximations via second order combined dynamic derivatives on time scales

Directory of Open Access Journals (Sweden)

Qin Sheng

2007-09-01

Full Text Available This article focuses on the approximation of conventional second order derivative via the combined (diamond-$\\alpha$ dynamic derivative on time scales with necessary smoothness conditions embedded. We will show the constraints under which the second order dynamic derivative provides a consistent approximation to the conventional second derivative; the cases where the dynamic derivative approximates the derivative only via a proper modification of the existing formula; and the situations in which the dynamic derivative can never approximate consistently even with the help of available structure correction methods. Constructive error analysis will be given via asymptotic expansions for practical hybrid modeling and computational applications.

Construction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets with an application to decision making

Czech Academy of Sciences Publication Activity Database

De Miguel, L.; Bustince, H.; Fernandez, J.; Indurain, E.; Kolesárová, A.; Mesiar, Radko

2016-01-01

Roč. 27, č. 1 (2016), s. 189-197 ISSN 1566-2535 Institutional support: RVO:67985556 Keywords : Mulit-expert decision making * Interval-valued Atanassov intuitionistic fuzzy set * Interval linear order Subject RIV: BA - General Mathematics Impact factor: 5.667, year: 2016 http://library.utia.cas.cz/separaty/2016/E/mesiar-0462471.pdf

Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA

Energy Technology Data Exchange (ETDEWEB)

Alioli, Simone; Bauer, Christian W.; Berggren, Calvin; Vermilion, Christopher K.; Walsh, Jonathan R.; Zuberi, Saba [California Univ., Berkeley, CA (United States). Ernest Orlando Lawrence Berkeley National Laboratory; Hornig, Andrew [Washington Univ., Seattle, WA (United States). Dept. of Physics; Tackmann, Frank J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie

2012-11-15

We extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in {alpha}{sub s} at both small and large jet resolutions, which has not been achieved so far. This requires the combination of the higher-order resummation of large Sudakov logarithms at small values of the jet resolution variable with the full next-to-leading order (NLO) matrix-element corrections at large values. As a by-product, this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. In this paper, we focus on the general construction of our method and discuss its application to e{sup +}e{sup -} and pp collisions. We present first results of the implementation in the GENEVA Monte Carlo framework. We employ N-jettiness as the jet resolution variable, combining its next-to-next-to-leading logarithmic resummation with fully exclusive NLO matrix elements, and PYTHIA 8 as the backend for further parton showering and hadronization. For hadronic collisions, we take Drell-Yan production as an example to apply our construction. For e{sup +}e{sup -} {yields} jets, taking {alpha}{sub s}(m{sub Z}) = 0.1135 from fits to LEP thrust data, together with the PYTHIA 8 hadronization model, we obtain good agreement with LEP data for a variety of 2-jet observables.

Linear feedback control, adaptive feedback control and their combination for chaos (lag) synchronization of LC chaotic systems

International Nuclear Information System (INIS)

Yan Zhenya; Yu Pei

2007-01-01

In this paper, we study chaos (lag) synchronization of a new LC chaotic system, which can exhibit not only a two-scroll attractor but also two double-scroll attractors for different parameter values, via three types of state feedback controls: (i) linear feedback control; (ii) adaptive feedback control; and (iii) a combination of linear feedback and adaptive feedback controls. As a consequence, ten families of new feedback control laws are designed to obtain global chaos lag synchronization for τ < 0 and global chaos synchronization for τ = 0 of the LC system. Numerical simulations are used to illustrate these theoretical results. Each family of these obtained feedback control laws, including two linear (adaptive) functions or one linear function and one adaptive function, is added to two equations of the LC system. This is simpler than the known synchronization controllers, which apply controllers to all equations of the LC system. Moreover, based on the obtained results of the LC system, we also derive the control laws for chaos (lag) synchronization of another new type of chaotic system

Combined slope ratio analysis and linear-subtraction: An extension of the Pearce ratio method

Science.gov (United States)

De Waal, Sybrand A.

1996-07-01

A new technique, called combined slope ratio analysis, has been developed by extending the Pearce element ratio or conserved-denominator method (Pearce, 1968) to its logical conclusions. If two stoichiometric substances are mixed and certain chemical components are uniquely contained in either one of the two mixing substances, then by treating these unique components as conserved, the composition of the substance not containing the relevant component can be accurately calculated within the limits allowed by analytical and geological error. The calculated composition can then be subjected to rigorous statistical testing using the linear-subtraction method recently advanced by Woronow (1994). Application of combined slope ratio analysis to the rocks of the Uwekahuna Laccolith, Hawaii, USA, and the lavas of the 1959-summit eruption of Kilauea Volcano, Hawaii, USA, yields results that are consistent with field observations.

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

International Nuclear Information System (INIS)

Greenough, J.A.; Rider, W.J.

2004-01-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the 'peak' shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are

A quantitative comparison of numerical methods for the compressible Euler equations: fifth-order WENO and piecewise-linear Godunov

Science.gov (United States)

Greenough, J. A.; Rider, W. J.

2004-05-01

A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube problem, (3) the "peak" shock tube problem, (4) a version of the Shu and Osher shock entropy wave interaction and (5) the Woodward and Colella interacting shock wave problem. For each problem and method, run times, density error norms and convergence rates are reported for each method as produced from a common code test-bed. The linear problem exhibits the advertised convergence rate for both methods as well as the expected large disparity in overall error levels; WENO5 has the smaller errors and an enormous advantage in overall efficiency (in accuracy per unit CPU time). For the nonlinear problems with discontinuities, however, we generally see both first-order self-convergence of error as compared to an exact solution, or when an analytic solution is not available, a converged solution generated on an extremely fine grid. The overall comparison of error levels shows some variation from problem to problem. For Sod's shock tube, PLMDE has nearly half the error, while on the peak problem the errors are nearly the same. For the interacting blast wave problem the two methods again produce a similar level of error with a slight edge for the PLMDE. On the other hand, for the Shu-Osher problem, the errors are similar on the coarser grids, but favors WENO by a factor of nearly 1.5 on the finer grids used. In all cases holding mesh resolution constant though, PLMDE is less costly in terms of CPU time by approximately a factor of 6. If the CPU cost is taken as fixed, that is run times are

Maxima and Minima in Fuzzified Linear Orderings

Czech Academy of Sciences Publication Activity Database

Běhounek, Libor

2016-01-01

Roč. 289, 15 April (2016), s. 82-93 ISSN 0165-0114 R&D Projects: GA ČR GPP103/10/P234; GA MŠk ED1.1.00/02.0070 Grant - others:GA MŠk(CZ) EE2.3.30.0010 Institutional support: RVO:67985807 Keywords : fuzzy relations * similarity relations * fuzzy orderings * higher-order fuzzy logic Subject RIV: BA - General Mathematics Impact factor: 2.718, year: 2016

Model-independent separation of poorly resolved hypperfine split spectra by a linear combination method

International Nuclear Information System (INIS)

Nagy, D.L.; Dengler, J.; Ritter, G.

1988-01-01

A model-independent evaluation of the components of poorly resolved Moessbauer spectra based on a linear combination method is possible if there is a parameter as a function of which the shape of the individual components do not but their intensities do change and the dependence of the intensities on this parameter is known. The efficiency of the method is demonstrated on the example of low temperature magnetically split spectra of the high-T c superconductor YBa 2 (Cu 0.9 Fe 0 .1 ) 3 O 7-y . (author)

High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices

Science.gov (United States)

Dunham, Benjamin Z.

This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions--most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series--without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed "stencils," each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the "forward mode" is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N--i.e., O(1)--the N x N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive--e.g., a N x N x N rank-three tensor can be found in O(N2). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of

Multineuron spike train analysis with R-convolution linear combination kernel.

Science.gov (United States)

Tezuka, Taro

2018-06-01

A spike train kernel provides an effective way of decoding information represented by a spike train. Some spike train kernels have been extended to multineuron spike trains, which are simultaneously recorded spike trains obtained from multiple neurons. However, most of these multineuron extensions were carried out in a kernel-specific manner. In this paper, a general framework is proposed for extending any single-neuron spike train kernel to multineuron spike trains, based on the R-convolution kernel. Special subclasses of the proposed R-convolution linear combination kernel are explored. These subclasses have a smaller number of parameters and make optimization tractable when the size of data is limited. The proposed kernel was evaluated using Gaussian process regression for multineuron spike trains recorded from an animal brain. It was compared with the sum kernel and the population Spikernel, which are existing ways of decoding multineuron spike trains using kernels. The results showed that the proposed approach performs better than these kernels and also other commonly used neural decoding methods. Copyright © 2018 Elsevier Ltd. All rights reserved.

Linearity enigmas in ecology

Energy Technology Data Exchange (ETDEWEB)

Patten, B.C.

1983-04-01

Two issues concerning linearity or nonlinearity of natural systems are considered. Each is related to one of the two alternative defining properties of linear systems, superposition and decomposition. Superposition exists when a linear combination of inputs to a system results in the same linear combination of outputs that individually correspond to the original inputs. To demonstrate this property it is necessary that all initial states and inputs of the system which impinge on the output in question be included in the linear combination manipulation. As this is difficult or impossible to do with real systems of any complexity, nature appears nonlinear even though it may be linear. A linear system that displays nonlinear behavior for this reason is termed pseudononlinear. The decomposition property exists when the dynamic response of a system can be partitioned into an input-free portion due to state plus a state-free portion due to input. This is a characteristic of all linear systems, but not of nonlinear systems. Without the decomposition property, it is not possible to distinguish which portions of a system's behavior are due to innate characteristics (self) vs. outside conditions (environment), which is an important class of questions in biology and ecology. Some philosophical aspects of these findings are then considered. It is suggested that those ecologists who hold to the view that organisms and their environments are separate entities are in effect embracing a linear view of nature, even though their belief systems and mathematical models tend to be nonlinear. On the other hand, those who consider that organism-environment complex forms a single inseparable unit are implictly involved in non-linear thought, which may be in conflict with the linear modes and models that some of them use. The need to rectify these ambivalences on the part of both groups is indicated.

Chaos as an intermittently forced linear system.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2015-01-01

the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems......SUMMARY Many dynamical systems are modeled as vector second-order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between....... The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyright © 2014 John Wiley & Sons, Ltd....

A computational methodology for a micro launcher engine test bench using a combined linear static and dynamic in frequency response analysis

Directory of Open Access Journals (Sweden)

Ion DIMA

2017-03-01

Full Text Available This article aims to provide a quick methodology to determine the critical values of the forces, displacements and stress function of frequency, under a combined linear static (101 Solution - Linear Static and dynamic load in frequency response (108 Solution - Frequency Response, Direct Method, applied to a micro launcher engine test bench, using NASTRAN 400 Solution - Implicit Nonlinear. NASTRAN/PATRAN software is used. Practically in PATRAN the preprocessor has to define a linear or nonlinear static load at step 1 and a dynamic in frequency response load (time dependent at step 2. In Analyze the following options are chosen: for Solution Type Implicit Nonlinear Solution (SOL 400 is selected, for Subcases Static Load and Transient Dynamic is chosen and for Subcase Select the two cases static and dynamic will be selected. NASTRAN solver will overlap results from static analysis with the dynamic analysis. The running time will be reduced three times if using Krylov solver. NASTRAN SYSTEM (387 = -1 instruction is used in order to activate Krylov option. Also, in Analysis the OP2 Output Format shall be selected, meaning that in bdf NASTRAN input file the PARAM POST 1 instruction shall be written. The structural damping can be defined in two different ways: either at the material card or using the PARAM, G, 0.05 instruction (in this example a damping coefficient by 5% was used. The SDAMPING instruction in pair with TABDMP1 work only for dynamic in frequency response, modal method, or in direct method with viscoelastic material, not for dynamic in frequency response, direct method (DFREQ, with linear elastic material. The Direct method – DFREQ used in this example is more accurate. A set in translation of boundary conditions was used and defined at the base of the test bench.

Physical origin of third order non-linear optical response of porphyrin nanorods

International Nuclear Information System (INIS)

Mongwaketsi, N.; Khamlich, S.; Pranaitis, M.; Sahraoui, B.; Khammar, F.; Garab, G.; Sparrow, R.; Maaza, M.

2012-01-01

The non-linear optical properties of porphyrin nanorods were studied using Z-scan, Second and Third harmonic generation techniques. We investigated in details the heteroaggregate behaviour formation of [H 4 TPPS 4 ] 2- and [SnTPyP] 2+ mixture by means of the UV-VIS spectroscopy and aggregates structure and morphology by transmission electron microscopy. The porphyrin nanorods under investigation were synthesized by self assembly and molecular recognition method. They have been optimized in view of future application in the construction of the light harvesting system. The focus of this study was geared towards understanding the influence of the type of solvent used on these porphyrins nanorods using spectroscopic and microscopic techniques. Highlights: ► We synthesized porphyrin nanorods by self assembly and molecular recognition method. ► TEM images confirmed solid cylindrical shapes. ► UV-VIS spectroscopy showed the decrease in the absorbance peaks of the precursors. ► The enhanced third-order nonlinearities were observed.

Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng

2004-01-01

Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair

On the asymptotic expansions of solutions of an nth order linear differential equation with power coefficients

International Nuclear Information System (INIS)

Paris, R.B.; Wood, A.D.

1984-11-01

The asymptotic expansions of solutions of a class of linear ordinary differential equations of arbitrary order n, containing a factor zsup(m) multiplying the lower order derivatives, are investigated for large values of z in the complex plane. Four classes of solutions are considered which exhibit the following behaviour as /z/ → infinity in certain sectors: (i) solutions whose behaviour is either exponentially large or algebraic (involving p ( < n) algebraic expansions), (ii) solutions which are exponentially small (iii) solutions with a single algebraic expansion and (iv) solutions which are even and odd functions of z whenever n+m is even. The asymptotic expansions of these solutions in a full neigbourhood of the point at infinity are obtained by means of the theory of the solutions in the case m=O developed in a previous paper

Linearly constrained minimax optimization

DEFF Research Database (Denmark)

Madsen, Kaj; Schjær-Jacobsen, Hans

1978-01-01

We present an algorithm for nonlinear minimax optimization subject to linear equality and inequality constraints which requires first order partial derivatives. The algorithm is based on successive linear approximations to the functions defining the problem. The resulting linear subproblems...

Oscillatory solutions of the Cauchy problem for linear differential equations

Directory of Open Access Journals (Sweden)

Gro Hovhannisyan

2015-06-01

Full Text Available We consider the Cauchy problem for second and third order linear differential equations with constant complex coefficients. We describe necessary and sufficient conditions on the data for the existence of oscillatory solutions. It is known that in the case of real coefficients the oscillatory behavior of solutions does not depend on initial values, but we show that this is no longer true in the complex case: hence in practice it is possible to control oscillatory behavior by varying the initial conditions. Our Proofs are based on asymptotic analysis of the zeros of solutions, represented as linear combinations of exponential functions.

An Improved Isotropic Periodic Sum Method That Uses Linear Combinations of Basis Potentials

KAUST Repository

Takahashi, Kazuaki Z.; Narumi, Tetsu; Suh, Donguk; Yasuoka, Kenji

2012-01-01

Isotropic periodic sum (IPS) is a technique that calculates long-range interactions differently than conventional lattice sum methods. The difference between IPS and lattice sum methods lies in the shape and distribution of remote images for long-range interaction calculations. The images used in lattice sum calculations are identical to those generated from periodic boundary conditions and are discretely positioned at lattice points in space. The images for IPS calculations are "imaginary", which means they do not explicitly exist in a simulation system and are distributed isotropically and periodically around each particle. Two different versions of the original IPS method exist. The IPSn method is applied to calculations for point charges, whereas the IPSp method calculates polar molecules. However, both IPSn and IPSp have their advantages and disadvantages in simulating bulk water or water-vapor interfacial systems. In bulk water systems, the cutoff radius effect of IPSn strongly affects the configuration, whereas IPSp does not provide adequate estimations of water-vapor interfacial systems unless very long cutoff radii are used. To extend the applicability of the IPS technique, an improved IPS method, which has better accuracy in both homogeneous and heterogeneous systems has been developed and named the linear-combination-based isotropic periodic sum (LIPS) method. This improved IPS method uses linear combinations of basis potentials. We performed molecular dynamics (MD) simulations of bulk water and water-vapor interfacial systems to evaluate the accuracy of the LIPS method. For bulk water systems, the LIPS method has better accuracy than IPSn in estimating thermodynamic and configurational properties without the countercharge assumption, which is used for IPSp. For water-vapor interfacial systems, LIPS has better accuracy than IPSp and properly estimates thermodynamic and configurational properties. In conclusion, the LIPS method can successfully estimate

An Improved Isotropic Periodic Sum Method That Uses Linear Combinations of Basis Potentials

KAUST Repository

Takahashi, Kazuaki Z.

2012-11-13

Isotropic periodic sum (IPS) is a technique that calculates long-range interactions differently than conventional lattice sum methods. The difference between IPS and lattice sum methods lies in the shape and distribution of remote images for long-range interaction calculations. The images used in lattice sum calculations are identical to those generated from periodic boundary conditions and are discretely positioned at lattice points in space. The images for IPS calculations are "imaginary", which means they do not explicitly exist in a simulation system and are distributed isotropically and periodically around each particle. Two different versions of the original IPS method exist. The IPSn method is applied to calculations for point charges, whereas the IPSp method calculates polar molecules. However, both IPSn and IPSp have their advantages and disadvantages in simulating bulk water or water-vapor interfacial systems. In bulk water systems, the cutoff radius effect of IPSn strongly affects the configuration, whereas IPSp does not provide adequate estimations of water-vapor interfacial systems unless very long cutoff radii are used. To extend the applicability of the IPS technique, an improved IPS method, which has better accuracy in both homogeneous and heterogeneous systems has been developed and named the linear-combination-based isotropic periodic sum (LIPS) method. This improved IPS method uses linear combinations of basis potentials. We performed molecular dynamics (MD) simulations of bulk water and water-vapor interfacial systems to evaluate the accuracy of the LIPS method. For bulk water systems, the LIPS method has better accuracy than IPSn in estimating thermodynamic and configurational properties without the countercharge assumption, which is used for IPSp. For water-vapor interfacial systems, LIPS has better accuracy than IPSp and properly estimates thermodynamic and configurational properties. In conclusion, the LIPS method can successfully estimate

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

Science.gov (United States)

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

Analysis of the 'dilemma effect' in fifth-order deflection aberration

International Nuclear Information System (INIS)

Zhang Xiaobing; Yin Hanchun; Lei Wei; Xue Kunxing; Tong Linsu

1999-01-01

In this paper, the coma of the fifth-order aberration at a large deflection angle has been analyzed by using multipole field theory. The dilemma effect exists in the comas of fifth-order aberration. The dilemma effect, whose value D r is constant and independent of the 10-pole field, is the linear combination of coma aberrations. The coma of the fifth-order aberration is corrected by adjusting the 10-pole field distribution when D r is zero or small. The factors that influence the dilemma effect have been calculated and analyzed

1/N-expansion of the non-linear σ-model: The first three orders

International Nuclear Information System (INIS)

Flyvbjerg, H.; Varsted, S.

1990-01-01

The two-point function of the O(N)-symmetric non-linear σ-model is expanded in 1/N, keeping terms of three leading orders. The mass gap and the magnetic susceptibility are obtained from the two-point function. They are evaluated on square lattices for N=3 and N=4. The systematic errors of the 1/N-series truncated after the first, second, or third term are found by using recent high precision Monte Carlo results as bench marks. For all three truncations, we find systematic errors which are smaller than the expected magnitude of neglected terms, both for the mass gap and for the susceptibility. This result is uniform in the inverse coupling β, and valid for N as small as 3. We conclude that the 1/N-series approach the exact results as rapidly as one could ever hope for. (orig.)

Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

Science.gov (United States)

Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

2010-05-01

The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low

Nonoscillation criteria for half-linear second order difference equations

Czech Academy of Sciences Publication Activity Database

Došlý, Ondřej; Řehák, Pavel

2001-01-01

Roč. 42, - (2001), s. 453-464 ISSN 0898-1221 R&D Projects: GA ČR GA201/98/0677; GA ČR GA201/99/0295 Keywords : half-linear difference equation%nonoscillation criteria%variational principle Subject RIV: BA - General Mathematics Impact factor: 0.383, year: 2001

Multidisciplinary Inverse Reliability Analysis Based on Collaborative Optimization with Combination of Linear Approximations

Directory of Open Access Journals (Sweden)

Xin-Jia Meng

2015-01-01

Full Text Available Multidisciplinary reliability is an important part of the reliability-based multidisciplinary design optimization (RBMDO. However, it usually has a considerable amount of calculation. The purpose of this paper is to improve the computational efficiency of multidisciplinary inverse reliability analysis. A multidisciplinary inverse reliability analysis method based on collaborative optimization with combination of linear approximations (CLA-CO is proposed in this paper. In the proposed method, the multidisciplinary reliability assessment problem is first transformed into a problem of most probable failure point (MPP search of inverse reliability, and then the process of searching for MPP of multidisciplinary inverse reliability is performed based on the framework of CLA-CO. This method improves the MPP searching process through two elements. One is treating the discipline analyses as the equality constraints in the subsystem optimization, and the other is using linear approximations corresponding to subsystem responses as the replacement of the consistency equality constraint in system optimization. With these two elements, the proposed method realizes the parallel analysis of each discipline, and it also has a higher computational efficiency. Additionally, there are no difficulties in applying the proposed method to problems with nonnormal distribution variables. One mathematical test problem and an electronic packaging problem are used to demonstrate the effectiveness of the proposed method.

Eigenstates of complex linear combinations of J1, J2, J3 for any representation of SU(2)

International Nuclear Information System (INIS)

Bacry, H.; Technion-Israel Inst. of Tech., Haifa. Dept. of Physics)

1977-05-01

The states which minimalize the uncertainty relation ΔJ 1 ΔJ 2 >=1/2/ 3 >/ are eigenstates of complex linear combinations of J 1 and J 2 . This kind of states is shown to have a very simple geometrical interpretation in the constellation formalism. A detailed description is given in the present pap

Combining large number of weak biomarkers based on AUC.

Science.gov (United States)

Yan, Li; Tian, Lili; Liu, Song

2015-12-20

Combining multiple biomarkers to improve diagnosis and/or prognosis accuracy is a common practice in clinical medicine. Both parametric and non-parametric methods have been developed for finding the optimal linear combination of biomarkers to maximize the area under the receiver operating characteristic curve (AUC), primarily focusing on the setting with a small number of well-defined biomarkers. This problem becomes more challenging when the number of observations is not order of magnitude greater than the number of variables, especially when the involved biomarkers are relatively weak. Such settings are not uncommon in certain applied fields. The first aim of this paper is to empirically evaluate the performance of existing linear combination methods under such settings. The second aim is to propose a new combination method, namely, the pairwise approach, to maximize AUC. Our simulation studies demonstrated that the performance of several existing methods can become unsatisfactory as the number of markers becomes large, while the newly proposed pairwise method performs reasonably well. Furthermore, we apply all the combination methods to real datasets used for the development and validation of MammaPrint. The implication of our study for the design of optimal linear combination methods is discussed. Copyright © 2015 John Wiley & Sons, Ltd.

A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories

Directory of Open Access Journals (Sweden)

V. V. Zozulya

2013-01-01

Full Text Available A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

Multiple linear combination (MLC) regression tests for common variants adapted to linkage disequilibrium structure.

Science.gov (United States)

Yoo, Yun Joo; Sun, Lei; Poirier, Julia G; Paterson, Andrew D; Bull, Shelley B

2017-02-01

By jointly analyzing multiple variants within a gene, instead of one at a time, gene-based multiple regression can improve power, robustness, and interpretation in genetic association analysis. We investigate multiple linear combination (MLC) test statistics for analysis of common variants under realistic trait models with linkage disequilibrium (LD) based on HapMap Asian haplotypes. MLC is a directional test that exploits LD structure in a gene to construct clusters of closely correlated variants recoded such that the majority of pairwise correlations are positive. It combines variant effects within the same cluster linearly, and aggregates cluster-specific effects in a quadratic sum of squares and cross-products, producing a test statistic with reduced degrees of freedom (df) equal to the number of clusters. By simulation studies of 1000 genes from across the genome, we demonstrate that MLC is a well-powered and robust choice among existing methods across a broad range of gene structures. Compared to minimum P-value, variance-component, and principal-component methods, the mean power of MLC is never much lower than that of other methods, and can be higher, particularly with multiple causal variants. Moreover, the variation in gene-specific MLC test size and power across 1000 genes is less than that of other methods, suggesting it is a complementary approach for discovery in genome-wide analysis. The cluster construction of the MLC test statistics helps reveal within-gene LD structure, allowing interpretation of clustered variants as haplotypic effects, while multiple regression helps to distinguish direct and indirect associations. © 2016 The Authors Genetic Epidemiology Published by Wiley Periodicals, Inc.

Linear and quasi-linear equations of parabolic type

CERN Document Server

Ladyženskaja, O A; Ural′ceva, N N; Uralceva, N N

1968-01-01

Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

Singularity-free static centrally symmetric solutions of some fourth order gravitational field equations

International Nuclear Information System (INIS)

Fiedler, B.; Schimming, R.

1983-01-01

The fourth order field equations proposed by TREDER with a linear combination of BACH's tensor and EINSTEIN's tensor on the left-hand side admit static centrally symmetric solutions which are analytical and non-flat in some neighborhood of the centre of symmetry. (author)

On the classical theory of ordinary linear differential equations of the second order and the Schroedinger equation for power law potentials

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1983-01-01

The power law potentials in the Schroedinger equation solved recently are shown to come from the classical treatment of the singularities of a linear, second order differential equation. This allows to enlarge the class of solvable power law potentials. (Author) [pt

Single image super-resolution using locally adaptive multiple linear regression.

Science.gov (United States)

Yu, Soohwan; Kang, Wonseok; Ko, Seungyong; Paik, Joonki

2015-12-01

This paper presents a regularized superresolution (SR) reconstruction method using locally adaptive multiple linear regression to overcome the limitation of spatial resolution of digital images. In order to make the SR problem better-posed, the proposed method incorporates the locally adaptive multiple linear regression into the regularization process as a local prior. The local regularization prior assumes that the target high-resolution (HR) pixel is generated by a linear combination of similar pixels in differently scaled patches and optimum weight parameters. In addition, we adapt a modified version of the nonlocal means filter as a smoothness prior to utilize the patch redundancy. Experimental results show that the proposed algorithm better restores HR images than existing state-of-the-art methods in the sense of the most objective measures in the literature.

A high-order finite-difference linear seakeeping solver tool for calculation of added resistance in waves

DEFF Research Database (Denmark)

Amini Afshar, Mostafa; Bingham, Harry B.; Read, Robert

During recent years a computational strategy has been developed at the Technical University of Denmark for numerical simulation of water wave problems based on the high-order nite-dierence method, [2],[4]. These methods exhibit a linear scaling of the computational eort as the number of grid points...... increases. This understanding is being applied to develop a tool for predicting the added resistance (drift force) of ships in ocean waves. We expect that the optimal scaling properties of this solver will allow us to make a convincing demonstration of convergence of the added resistance calculations based...... on both near-eld and far-eld methods. The solver has been written inside a C++ library known as Overture [3], which can be used to solve partial dierential equations on overlapping grids based on the high-order nite-dierence method. The resulting code is able to solve, in the time domain, the linearised...

Modeling of non-linear CHP efficiency curves in distributed energy systems

DEFF Research Database (Denmark)

Milan, Christian; Stadler, Michael; Cardoso, Gonçalo

2015-01-01

Distributed energy resources gain an increased importance in commercial and industrial building design. Combined heat and power (CHP) units are considered as one of the key technologies for cost and emission reduction in buildings. In order to make optimal decisions on investment and operation...... for these technologies, detailed system models are needed. These models are often formulated as linear programming problems to keep computational costs and complexity in a reasonable range. However, CHP systems involve variations of the efficiency for large nameplate capacity ranges and in case of part load operation......, which can be even of non-linear nature. Since considering these characteristics would turn the models into non-linear problems, in most cases only constant efficiencies are assumed. This paper proposes possible solutions to address this issue. For a mixed integer linear programming problem two...

A second-order virtual node algorithm for nearly incompressible linear elasticity in irregular domains

Science.gov (United States)

Zhu, Yongning; Wang, Yuting; Hellrung, Jeffrey; Cantarero, Alejandro; Sifakis, Eftychios; Teran, Joseph M.

2012-08-01

We present a cut cell method in R2 for enforcing Dirichlet and Neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains. Virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy. We use a mixed formulation utilizing a MAC-type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers. These discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells. Numerical experiments suggest second order accuracy in L∞. We target high-resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution.

Partially ordered sets in complex networks

International Nuclear Information System (INIS)

Xuan Qi; Du Fang; Wu Tiejun

2010-01-01

In this paper, a partial-order relation is defined among vertices of a network to describe which vertex is more important than another on its contribution to the connectivity of the network. A maximum linearly ordered subset of vertices is defined as a chain and the chains sharing the same end-vertex are grouped as a family. Through combining the same vertices appearing in different chains, a directed chain graph is obtained. Based on these definitions, a series of new network measurements, such as chain length distribution, family diversity distribution, as well as the centrality of families, are proposed. By studying the partially ordered sets in three kinds of real-world networks, many interesting results are revealed. For instance, the similar approximately power-law chain length distribution may be attributed to a chain-based positive feedback mechanism, i.e. new vertices prefer to participate in longer chains, which can be inferred by combining the notable preferential attachment rule with a well-ordered recommendation manner. Moreover, the relatively large average incoming degree of the chain graphs may indicate an efficient substitution mechanism in these networks. Most of the partially ordered set-based properties cannot be explained by the current well-known scale-free network models; therefore, we are required to propose more appropriate network models in the future.

Linearization Technologies for Broadband Radio-Over-Fiber Transmission Systems

Directory of Open Access Journals (Sweden)

Xiupu Zhang

2014-11-01

Full Text Available Linearization technologies that can be used for linearizing RoF transmission are reviewed. Three main linearization methods, i.e. electrical analog linearization, optical linearization, and electrical digital linearization are presented and compared. Analog linearization can be achieved using analog predistortion circuits, and can be used for suppression of odd order nonlinear distortion components, such as third and fifth order. Optical linearization includes mixed-polarization, dual-wavelength, optical channelization and the others, implemented in optical domain, to suppress both even and odd order nonlinear distortion components, such as second and third order. Digital predistortion has been a widely used linearization method for RF power amplifiers. However, digital linearization that requires analog to digital converter is severely limited to hundreds of MHz bandwidth. Instead, analog and optical linearization provide broadband linearization with up to tens of GHz. Therefore, for broadband radio over fiber transmission that can be used for future broadband cloud radio access networks, analog and optical linearization are more appropriate than digital linearization. Generally speaking, both analog and optical linearization are able to improve spur-free dynamic range greater than 10 dB over tens of GHz. In order for current digital linearization to be used for broadband radio over fiber transmission, the reduced linearization complexity and increased linearization bandwidth are required. Moreover, some digital linearization methods in which the complexity can be reduced, such as Hammerstein type, may be more promising and require further investigation.

Adaptive Linear and Normalized Combination of Radial Basis Function Networks for Function Approximation and Regression

Directory of Open Access Journals (Sweden)

Yunfeng Wu

2014-01-01

Full Text Available This paper presents a novel adaptive linear and normalized combination (ALNC method that can be used to combine the component radial basis function networks (RBFNs to implement better function approximation and regression tasks. The optimization of the fusion weights is obtained by solving a constrained quadratic programming problem. According to the instantaneous errors generated by the component RBFNs, the ALNC is able to perform the selective ensemble of multiple leaners by adaptively adjusting the fusion weights from one instance to another. The results of the experiments on eight synthetic function approximation and six benchmark regression data sets show that the ALNC method can effectively help the ensemble system achieve a higher accuracy (measured in terms of mean-squared error and the better fidelity (characterized by normalized correlation coefficient of approximation, in relation to the popular simple average, weighted average, and the Bagging methods.

EXPALS, Least Square Fit of Linear Combination of Exponential Decay Function

International Nuclear Information System (INIS)

Douglas Gardner, C.

1980-01-01

1 - Description of problem or function: This program fits by least squares a function which is a linear combination of real exponential decay functions. The function is y(k) = summation over j of a(j) * exp(-lambda(j) * k). Values of the independent variable (k) and the dependent variable y(k) are specified as input data. Weights may be specified as input information or set by the program (w(k) = 1/y(k)). 2 - Method of solution: The Prony-Householder iteration method is used. For unequally-spaced data, a number of interpolation options are provided. This revision includes an option to call a differential correction subroutine REFINE to improve the approximation to unequally-spaced data when equal-interval interpolation is faulty. If convergence is achieved, the probable errors in the computed parameters are calculated also. 3 - Restrictions on the complexity of the problem: Generally, it is desirable to have at least 10n observations where n equals the number of terms and to input k+n significant figures if k significant figures are expected

Fractional order differentiation by integration: An application to fractional linear systems

KAUST Repository

Liu, Dayan

2013-02-04

In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

Linear pulse amplifier

International Nuclear Information System (INIS)

Tjutju, R.L.

1977-01-01

Pulse amplifier is standard significant part of spectrometer. Apart from other type of amplification, it's a combination of amplification and pulse shaping. Because of its special purpose the device should fulfill the following : High resolution is desired to gain a high yield comparable to its actual state of condition. High signal to noise is desired to nhν resolution. High linearity to facilitate calibration. A good overload recovery, in order to the device will capable of analizing a low energy radiation which appear joinly on the high energy fields. Other expections of the device are its economical and practical use its extentive application. For that reason it's built on a standard NIM principle. Taking also into account the above mentioned considerations. High quality component parts are used throughout, while its availability in the domestic market is secured. (author)

Symmetries of the Space of Linear Symplectic Connections

Science.gov (United States)

Fox, Daniel J. F.

2017-01-01

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical points of a functional constructed from it interpolate between the equations for preferred symplectic connections and the equations for critical symplectic connections. The commutative algebra of formal sums of symmetric tensors on a symplectic manifold carries a pair of compatible Poisson structures, one induced from the canonical Poisson bracket on the space of functions on the cotangent bundle polynomial in the fibers, and the other induced from the algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of the cotangent bundle. These structures are shown to be compatible, and the required Lie algebras are constructed as central extensions of their! linear combinations restricted to formal sums of symmetric tensors whose first order term is a multiple of the differential of its zeroth order term.

Test accelerator for linear collider

International Nuclear Information System (INIS)

Takeda, S.; Akai, K.; Akemoto, M.; Araki, S.; Hayano, H.; Hugo, T.; Ishihara, N.; Kawamoto, T.; Kimura, Y.; Kobayashi, H.; Kubo, T.; Kurokawa, S.; Matsumoto, H.; Mizuno, H.; Odagiri, J.; Otake, Y.; Sakai, H.; Shidara, T.; Shintake, T.; Suetake, M.; Takashima, T.; Takata, K.; Takeuchi, Y.; Urakawa, J.; Yamamoto, N.; Yokoya, K.; Yoshida, M.; Yoshioka, M.; Yamaoka, Y.

1989-01-01

KEK has proposed to build Test Accelerator Facility (TAF) capable of producing a 2.5 GeV electron beam for the purpose of stimulating R ampersand D for linear collider in TeV region. The TAF consists of a 1.5 GeV S-band linear accelerator, 1.5 GeV damping ring and 1.0 GeV X-band linear accelerator. The TAF project will be carried forward in three phases. Through Phase-I and Phase-II, the S-band and X-band linacs will be constructed, and in Phase-III, the damping ring will be completed. The construction of TAF Phase-I has started, and the 0.2 GeV S-band injector linac has been almost completed. The Phase-I linac is composed of a 240 keV electron gun, subharmonic bunchers, prebunchers and traveling buncher followed by high-gradient accelerating structures. The SLAC 5045 klystrons are driven at 450 kV in order to obtain the rf-power of 100 MW in a 1 μs pulse duration. The rf-power from a pair of klystrons are combined into an accelerating structure. The accelerating gradient up to 100 MeV/m will be obtained in a 0.6 m long structure. 5 refs., 3 figs., 2 tabs

Isotropic-resolution linear-array-based photoacoustic computed tomography through inverse Radon transform

Science.gov (United States)

Li, Guo; Xia, Jun; Li, Lei; Wang, Lidai; Wang, Lihong V.

2015-03-01

Linear transducer arrays are readily available for ultrasonic detection in photoacoustic computed tomography. They offer low cost, hand-held convenience, and conventional ultrasonic imaging. However, the elevational resolution of linear transducer arrays, which is usually determined by the weak focus of the cylindrical acoustic lens, is about one order of magnitude worse than the in-plane axial and lateral spatial resolutions. Therefore, conventional linear scanning along the elevational direction cannot provide high-quality three-dimensional photoacoustic images due to the anisotropic spatial resolutions. Here we propose an innovative method to achieve isotropic resolutions for three-dimensional photoacoustic images through combined linear and rotational scanning. In each scan step, we first elevationally scan the linear transducer array, and then rotate the linear transducer array along its center in small steps, and scan again until 180 degrees have been covered. To reconstruct isotropic three-dimensional images from the multiple-directional scanning dataset, we use the standard inverse Radon transform originating from X-ray CT. We acquired a three-dimensional microsphere phantom image through the inverse Radon transform method and compared it with a single-elevational-scan three-dimensional image. The comparison shows that our method improves the elevational resolution by up to one order of magnitude, approaching the in-plane lateral-direction resolution. In vivo rat images were also acquired.

Full-order Luenberger observer based on fuzzy-logic control for sensorless field-oriented control of a single-sided linear induction motor.

Science.gov (United States)

Holakooie, Mohammad Hosein; Ojaghi, Mansour; Taheri, Asghar

2016-01-01

This paper investigates sensorless indirect field oriented control (IFOC) of SLIM with full-order Luenberger observer. The dynamic equations of SLIM are first elaborated to draw full-order Luenberger observer with some simplifying assumption. The observer gain matrix is derived from conventional procedure so that observer poles are proportional to SLIM poles to ensure the stability of system for wide range of linear speed. The operation of observer is significantly impressed by adaptive scheme. A fuzzy logic control (FLC) is proposed as adaptive scheme to estimate linear speed using speed tuning signal. The parameters of FLC are tuned using an off-line method through chaotic optimization algorithm (COA). The performance of the proposed observer is verified by both numerical simulation and real-time hardware-in-the-loop (HIL) implementation. Moreover, a detailed comparative study among proposed and other speed observers is obtained under different operation conditions. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

A wild model of linear arithmetic and discretely ordered modules

Czech Academy of Sciences Publication Activity Database

Glivický, Petr; Pudlák, Pavel

2017-01-01

Roč. 63, č. 6 (2017), s. 501-508 ISSN 0942-5616 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : linear arithmetics Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.250, year: 2016

Fault tolerant linear actuator

Science.gov (United States)

Tesar, Delbert

2004-09-14

In varying embodiments, the fault tolerant linear actuator of the present invention is a new and improved linear actuator with fault tolerance and positional control that may incorporate velocity summing, force summing, or a combination of the two. In one embodiment, the invention offers a velocity summing arrangement with a differential gear between two prime movers driving a cage, which then drives a linear spindle screw transmission. Other embodiments feature two prime movers driving separate linear spindle screw transmissions, one internal and one external, in a totally concentric and compact integrated module.

Passive longitudinal phase space linearizer

Directory of Open Access Journals (Sweden)

P. Craievich

2010-03-01

Full Text Available We report on the possibility to passively linearize the bunch compression process in electron linacs for the next generation x-ray free electron lasers. This can be done by using the monopole wakefields in a dielectric-lined waveguide. The optimum longitudinal voltage loss over the length of the bunch is calculated in order to compensate both the second-order rf time curvature and the second-order momentum compaction terms. Thus, the longitudinal phase space after the compression process is linearized up to a fourth-order term introduced by the convolution between the bunch and the monopole wake function.

Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

International Nuclear Information System (INIS)

Ducru, Pablo; Josey, Colin; Dibert, Karia; Sobes, Vladimir; Forget, Benoit; Smith, Kord

2017-01-01

This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T_j). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T_0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T_j). The choice of the L_2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T_j) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T_m_i_n,T_m_a_x]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope "2"3"8U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of "2"3"8U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.

Nonlinear aeroacoustic characterization of Helmholtz resonators with a local-linear neuro-fuzzy network model

Science.gov (United States)

Förner, K.; Polifke, W.

2017-10-01

The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.

A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

Directory of Open Access Journals (Sweden)

Carlos Aguilar-Ibanez

2016-01-01

Full Text Available This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction.

Linear fixed-field multipass arcs for recirculating linear accelerators

Directory of Open Access Journals (Sweden)

V. S. Morozov

2012-06-01

Full Text Available Recirculating linear accelerators (RLA’s provide a compact and efficient way of accelerating particle beams to medium and high energies by reusing the same linac for multiple passes. In the conventional scheme, after each pass, the different energy beams coming out of the linac are separated and directed into appropriate arcs for recirculation, with each pass requiring a separate fixed-energy arc. In this paper we present a concept of an RLA return arc based on linear combined-function magnets, in which two and potentially more consecutive passes with very different energies are transported through the same string of magnets. By adjusting the dipole and quadrupole components of the constituting linear combined-function magnets, the arc is designed to be achromatic and to have zero initial and final reference orbit offsets for all transported beam energies. We demonstrate the concept by developing a design for a droplet-shaped return arc for a dogbone RLA capable of transporting two beam passes with momenta different by a factor of 2. We present the results of tracking simulations of the two passes and lay out the path to end-to-end design and simulation of a complete dogbone RLA.

Theoretical analysis of balanced truncation for linear switched systems

DEFF Research Database (Denmark)

Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef

2012-01-01

In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians and their singu......In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians...... for showing this independence is realization theory of linear switched systems. [1] H. R. Shaker and R. Wisniewski, "Generalized gramian framework for model/controller order reduction of switched systems", International Journal of Systems Science, Vol. 42, Issue 8, 2011, 1277-1291. [2] H. R. Shaker and R....... Wisniewski, "Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians", Journal of Control Science and Engineering, 2009....

First-order system least squares for the pure traction problem in planar linear elasticity

Energy Technology Data Exchange (ETDEWEB)

Cai, Z.; Manteuffel, T.; McCormick, S.; Parter, S.

1996-12-31

This talk will develop two first-order system least squares (FOSLS) approaches for the solution of the pure traction problem in planar linear elasticity. Both are two-stage algorithms that first solve for the gradients of displacement, then for the displacement itself. One approach, which uses L{sup 2} norms to define the FOSLS functional, is shown under certain H{sup 2} regularity assumptions to admit optimal H{sup 1}-like performance for standard finite element discretization and standard multigrid solution methods that is uniform in the Poisson ratio for all variables. The second approach, which is based on H{sup -1} norms, is shown under general assumptions to admit optimal uniform performance for displacement flux in an L{sup 2} norm and for displacement in an H{sup 1} norm. These methods do not degrade as other methods generally do when the material properties approach the incompressible limit.

First order linear ordinary differential equations in associative algebras

Directory of Open Access Journals (Sweden)

Gordon Erlebacher

2004-01-01

Full Text Available In this paper, we study the linear differential equation $$ frac{dx}{dt}=sum_{i=1}^n a_i(t x b_i(t + f(t $$ in an associative but non-commutative algebra $mathcal{A}$, where the $b_i(t$ form a set of commuting $mathcal{A}$-valued functions expressed in a time-independent spectral basis consisting of mutually annihilating idempotents and nilpotents. Explicit new closed solutions are derived, and examples are presented to illustrate the theory.

Pseudo Boolean Programming for Partially Ordered Genomes

Science.gov (United States)

Angibaud, Sébastien; Fertin, Guillaume; Thévenin, Annelyse; Vialette, Stéphane

Comparing genomes of different species is a crucial problem in comparative genomics. Different measures have been proposed to compare two genomes: number of common intervals, number of adjacencies, number of reversals, etc. These measures are classically used between two totally ordered genomes. However, genetic mapping techniques often give rise to different maps with some unordered genes. Starting from a partial order between genes of a genome, one method to find a total order consists in optimizing a given measure between a linear extension of this partial order and a given total order of a close and well-known genome. However, for most common measures, the problem turns out to be NP-hard. In this paper, we propose a (0,1)-linear programming approach to compute a linear extension of one genome that maximizes the number of common intervals (resp. the number of adjacencies) between this linear extension and a given total order. Next, we propose an algorithm to find linear extensions of two partial orders that maximize the number of adjacencies.

The AOLI Non-Linear Curvature Wavefront Sensor: High sensitivity reconstruction for low-order AO

Science.gov (United States)

Crass, Jonathan; King, David; Mackay, Craig

2013-12-01

Many adaptive optics (AO) systems in use today require bright reference objects to determine the effects of atmospheric distortions on incoming wavefronts. This requirement is because Shack Hartmann wavefront sensors (SHWFS) distribute incoming light from reference objects into a large number of sub-apertures. Bright natural reference objects occur infrequently across the sky leading to the use of laser guide stars which add complexity to wavefront measurement systems. The non-linear curvature wavefront sensor as described by Guyon et al. has been shown to offer a significant increase in sensitivity when compared to a SHWFS. This facilitates much greater sky coverage using natural guide stars alone. This paper describes the current status of the non-linear curvature wavefront sensor being developed as part of an adaptive optics system for the Adaptive Optics Lucky Imager (AOLI) project. The sensor comprises two photon-counting EMCCD detectors from E2V Technologies, recording intensity at four near-pupil planes. These images are used with a reconstruction algorithm to determine the phase correction to be applied by an ALPAO 241-element deformable mirror. The overall system is intended to provide low-order correction for a Lucky Imaging based multi CCD imaging camera. We present the current optical design of the instrument including methods to minimise inherent optical effects, principally chromaticity. Wavefront reconstruction methods are discussed and strategies for their optimisation to run at the required real-time speeds are introduced. Finally, we discuss laboratory work with a demonstrator setup of the system.

A linear combination of pharmacophore hypotheses as a new tool in search of new active compounds--an application for 5-HT1A receptor ligands.

Directory of Open Access Journals (Sweden)

Dawid Warszycki

Full Text Available This study explores a new approach to pharmacophore screening involving the use of an optimized linear combination of models instead of a single hypothesis. The implementation and evaluation of the developed methodology are performed for a complete known chemical space of 5-HT1AR ligands (3616 active compounds with K i < 100 nM acquired from the ChEMBL database. Clusters generated from three different methods were the basis for the individual pharmacophore hypotheses, which were assembled into optimal combinations to maximize the different coefficients, namely, MCC, accuracy and recall, to measure the screening performance. Various factors that influence filtering efficiency, including clustering methods, the composition of test sets (random, the most diverse and cluster population-dependent and hit mode (the compound must fit at least one or two models from a final combination were investigated. This method outmatched both single hypothesis and random linear combination approaches.

Polarization and ellipticity of high-order harmonics from aligned molecules generated by linearly polarized intense laser pulses

International Nuclear Information System (INIS)

Le, Anh-Thu; Lin, C. D.; Lucchese, R. R.

2010-01-01

We present theoretical calculations for polarization and ellipticity of high-order harmonics from aligned N 2 , CO 2 , and O 2 molecules generated by linearly polarized lasers. Within the rescattering model, the two polarization amplitudes of the harmonics are determined by the photo-recombination amplitudes for photons emitted with polarization parallel or perpendicular to the direction of the same returning electron wave packet. Our results show clear species-dependent polarization states, in excellent agreement with experiments. We further note that the measured polarization ellipse of the harmonic furnishes the needed parameters for a 'complete' experiment in molecules.

Improving predictions for collider observables by consistently combining fixed order calculations with resummed results in perturbation theory

International Nuclear Information System (INIS)

Schoenherr, Marek

2011-01-01

With the constantly increasing precision of experimental data acquired at the current collider experiments Tevatron and LHC the theoretical uncertainty on the prediction of multiparticle final states has to decrease accordingly in order to have meaningful tests of the underlying theories such as the Standard Model. A pure leading order calculation, defined in the perturbative expansion of said theory in the interaction constant, represents the classical limit to such a quantum field theory and was already found to be insufficient at past collider experiments, e.g. LEP or HERA. Such a leading order calculation can be systematically improved in various limits. If the typical scales of a process are large and the respective coupling constants are small, the inclusion of fixed-order higher-order corrections then yields quickly converging predictions with much reduced uncertainties. In certain regions of the phase space, still well within the perturbative regime of the underlying theory, a clear hierarchy of the inherent scales, however, leads to large logarithms occurring at every order in perturbation theory. In many cases these logarithms are universal and can be resummed to all orders leading to precise predictions in these limits. Multiparticle final states now exhibit both small and large scales, necessitating a description using both resummed and fixed-order results. This thesis presents the consistent combination of two such resummation schemes with fixed-order results. The main objective therefor is to identify and properly treat terms that are present in both formulations in a process and observable independent manner. In the first part the resummation scheme introduced by Yennie, Frautschi and Suura (YFS), resumming large logarithms associated with the emission of soft photons in massive QED, is combined with fixed-order next-to-leading matrix elements. The implementation of a universal algorithm is detailed and results are studied for various precision

Non-Commutative Orders. A Preliminary Study

International Nuclear Information System (INIS)

Brzezinski, T.

2011-01-01

The first steps towards linearization of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that makes the linearization (almost) automatic. The linearization is then achieved by replacing sets by coalgebras and the Cartesian product by the tensor product of vector spaces. As a result, definitions of orders and equivalence relations on coalgebras are proposed. These are illustrated by explicit examples that include relations on coalgebras spanned by grouplike elements (or linearized sets), the diagonal relation, and an order on a three-dimensional non-cocommutative coalgebra. Although relations on coalgebras are defined for vector spaces, all the definitions are formulated in a way that is immediately applicable to other braided monoidal categories. (author)

A reduced-order vortex model of three-dimensional unsteady non-linear aerodynamics

Science.gov (United States)

Eldredge, Jeff D.

2014-11-01

Rapid, large-amplitude maneuvers of low aspect ratio wings are inherent to biologically-inspired flight. These give rise to unsteady phenomena associated with the interactions among the coherent structures shed from wing edges. The objective of this work is to distill these phenomena into a low-order physics-based dynamical model. The model is based on interconnected vortex loops, composed of linear segments between a small number of vertices. Thus, the dynamics of the fluid are reduced to tracking the evolution of the vertices, whose motions are determined from the velocity field induced by the loops and wing motion. The feature that distinguishes this method from previous treatments is that the vortex loops, analogous to point vortices in our two-dimensional model, have time-varying strength. That is, the flux of vorticity from the wing is concentrated in the constituent segments. Chains of interconnected loops can be shed from any edge of the wing. The evolution equation for the loop vertices is based on the impulse matching principle developed in previous work. We demonstrate the model in various maneuvers, including impulse starts of low aspect ratio wings, oscillatory pitching, etc., and compare with experimental results and high-fidelity simulations where applicable. This work was supported by AFOSR under Award FA9550-11-1-0098.

Expanded porphyrins as third order non-linear optical materials ...

Indian Academy of Sciences (India)

WINTEC

function correlations ... An understanding of the structure–function corre- lations of these expanded porphyrins is an important first step for ... where χ (2) and χ (3) are the quadratic χ (2) (first- order) and χ (3) cubic (second-order) susceptibilities.

Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ Model under Restricted Space: A Non-Linear Programming Approach

Directory of Open Access Journals (Sweden)

M. Pattnaik

2013-08-01

Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.

Polarized Uniform Linear Array System: Beam Radiation Pattern, Beamforming Diversity Order, and Channel Capacity

Directory of Open Access Journals (Sweden)

Xin Su

2015-01-01

Full Text Available There have been many studies regarding antenna polarization; however, there have been few publications on the analysis of the channel capacity for polarized antenna systems using the beamforming technique. According to Chung et al., the channel capacity is determined by the density of scatterers and the transmission power, which is obtained based on the assumption that scatterers are uniformly distributed on a 3D spherical scattering model. However, it contradicts the practical scenario, where scatterers may not be uniformly distributed under outdoor environment, and lacks the consideration of fading channel gain. In this study, we derive the channel capacity of polarized uniform linear array (PULA systems using the beamforming technique in a practical scattering environment. The results show that, for PULA systems, the channel capacity, which is boosted by beamforming diversity, can be determined using the channel gain, beam radiation pattern, and beamforming diversity order (BDO, where the BDO is dependent on the antenna characteristics and array configurations.

Genome-scale regression analysis reveals a linear relationship for promoters and enhancers after combinatorial drug treatment

KAUST Repository

Rapakoulia, Trisevgeni

2017-08-09

Motivation: Drug combination therapy for treatment of cancers and other multifactorial diseases has the potential of increasing the therapeutic effect, while reducing the likelihood of drug resistance. In order to reduce time and cost spent in comprehensive screens, methods are needed which can model additive effects of possible drug combinations. Results: We here show that the transcriptional response to combinatorial drug treatment at promoters, as measured by single molecule CAGE technology, is accurately described by a linear combination of the responses of the individual drugs at a genome wide scale. We also find that the same linear relationship holds for transcription at enhancer elements. We conclude that the described approach is promising for eliciting the transcriptional response to multidrug treatment at promoters and enhancers in an unbiased genome wide way, which may minimize the need for exhaustive combinatorial screens.

On the motion of non-linear oscillators with a fractional-order restoring force and time variable parameters

International Nuclear Information System (INIS)

Kovacic, Ivana

2009-01-01

An analytical approach to determine the approximate solution for the periodic motion of non-conservative oscillators with a fractional-order restoring force and slowly varying parameters is presented. The solution has the form of the first-order differential equation for the amplitude and phase of motion. The method used is based on the combination of the Krylov-Bogoliubov method with Hamilton's variational principle with the uncommutative rule for the variation of velocity. The conservative systems with slowly varying parameters are also considered. The corresponding adiabatic invariant is obtained. Two examples are given to illustrate derived theoretical results.

Study of the linear and non-linear coupling of the LH wave to the tokamak plasmas

International Nuclear Information System (INIS)

Preynas, M.

2012-10-01

In order to achieve long pulse operation with a tokamak, additional heating and current drive systems are necessary. High frequency antennas, which deliver several megawatts of power to the plasma, are currently used in several tokamaks. Moreover, a good control of the coupling of the wave launched by the antenna to the edge plasma is required to optimize the efficiency of heating and current drive LH systems. However, non-linear effects which depend on the level of injected power in the plasma strongly damage the coupling of the LH wave at particular edge parameters (density and temperature profiles). Results presented in the manuscript deal with the study of the linear and non-linear coupling of the LH wave to the plasma. In the framework of the commissioning of the Passive Active Multijunction antenna in 2009 on the Tore Supra tokamak aiming at validating the LH system suggested for ITER, the characterisation of its coupling properties was realized from low power experiments. The experimental results, which are compared with the linear coupling code ALOHA, have validated the theoretical predictions of good coupling at edge plasma density around the cut-off density. Besides, the ponderomotive effect is clearly identified as responsible for the deterioration in the coupling of the wave, which is measured under particular edge plasma conditions. A theoretical model combining the coupling of the LH wave with the ponderomotive force is suggested to explain the experimental observations. Thus, a new full wave code (named PICCOLO-2D) was developed and results from simulations validate the working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling on Tore Supra. (author)

Vascular stents: Coupling full 3-D with reduced-order structural models

International Nuclear Information System (INIS)

Avdeev, I; Shams, M

2010-01-01

Self-expanding nitinol stents are used to treat peripheral arterial disease. The peripheral arteries are subjected to a combination of mechanical forces such as compression, torsion, bending, and contraction. Most commercially available peripheral self-expanding stents are composed of a series of sub-millimeter V-shaped struts, which are laser-cut from a nitinol tube and surface-treated for better fatigue performance. The numerical stent models must accurately predict location and distribution of local stresses and strains caused by large arterial deformations. Full 3-D finite element non-linear analysis of an entire stent is computationally expensive to the point of being prohibitive, especially for longer stents. Reduced-order models based on beam or shell elements are fairly accurate in capturing global deformations, but are not very helpful in predicting stent failure. We propose a mixed approach that combines the full 3-D model and reduced-order models. Several global-local, full 3-D/reduced-order finite element models of a peripheral self-expanding stent were validated and compared with experimental data. The kinematic constraint method used to couple various elements together was found to be very efficient and easily applicable to commercial FEA codes. The proposed mixed models can be used to accurately predict stent failure based on realistic (patient-specific), non-linear kinematic behavior of peripheral arteries.

MODY - calculation of ordered structures by symmetry-adapted functions

Science.gov (United States)

Białas, Franciszek; Pytlik, Lucjan; Sikora, Wiesława

2016-01-01

In this paper we focus on the new version of computer program MODY for calculations of symmetryadapted functions based on the theory of groups and representations. The choice of such a functional frame of coordinates for description of ordered structures leads to a minimal number of parameters which must be used for presentation of such structures and investigations of their properties. The aim of this work is to find those parameters, which are coefficients of a linear combination of calculated functions, leading to construction of different types of structure ordering with a given symmetry. A spreadsheet script for simplification of this work has been created and attached to the program.

Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

International Nuclear Information System (INIS)

Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

1983-01-01

In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

ECG artifact cancellation in surface EMG signals by fractional order calculus application.

Science.gov (United States)

Miljković, Nadica; Popović, Nenad; Djordjević, Olivera; Konstantinović, Ljubica; Šekara, Tomislav B

2017-03-01

New aspects for automatic electrocardiography artifact removal from surface electromyography signals by application of fractional order calculus in combination with linear and nonlinear moving window filters are explored. Surface electromyography recordings of skeletal trunk muscles are commonly contaminated with spike shaped artifacts. This artifact originates from electrical heart activity, recorded by electrocardiography, commonly present in the surface electromyography signals recorded in heart proximity. For appropriate assessment of neuromuscular changes by means of surface electromyography, application of a proper filtering technique of electrocardiography artifact is crucial. A novel method for automatic artifact cancellation in surface electromyography signals by applying fractional order calculus and nonlinear median filter is introduced. The proposed method is compared with the linear moving average filter, with and without prior application of fractional order calculus. 3D graphs for assessment of window lengths of the filters, crest factors, root mean square differences, and fractional calculus orders (called WFC and WRC graphs) have been introduced. For an appropriate quantitative filtering evaluation, the synthetic electrocardiography signal and analogous semi-synthetic dataset have been generated. The examples of noise removal in 10 able-bodied subjects and in one patient with muscle dystrophy are presented for qualitative analysis. The crest factors, correlation coefficients, and root mean square differences of the recorded and semi-synthetic electromyography datasets showed that the most successful method was the median filter in combination with fractional order calculus of the order 0.9. Statistically more significant (p ECG peak reduction was obtained by the median filter application compared to the moving average filter in the cases of low level amplitude of muscle contraction compared to ECG spikes. The presented results suggest that the

Linear Fixed-Field Multi-Pass Arcs for Recirculating Linear Accelerators

International Nuclear Information System (INIS)

Morozov, V.S.; Bogacz, S.A.; Roblin, Y.R.; Beard, K.B.

2012-01-01

Recirculating Linear Accelerators (RLA's) provide a compact and efficient way of accelerating particle beams to medium and high energies by reusing the same linac for multiple passes. In the conventional scheme, after each pass, the different energy beams coming out of the linac are separated and directed into appropriate arcs for recirculation, with each pass requiring a separate fixed-energy arc. In this paper we present a concept of an RLA return arc based on linear combined-function magnets, in which two and potentially more consecutive passes with very different energies are transported through the same string of magnets. By adjusting the dipole and quadrupole components of the constituting linear combined-function magnets, the arc is designed to be achromatic and to have zero initial and final reference orbit offsets for all transported beam energies. We demonstrate the concept by developing a design for a droplet-shaped return arc for a dog-bone RLA capable of transporting two beam passes with momenta different by a factor of two. We present the results of tracking simulations of the two passes and lay out the path to end-to-end design and simulation of a complete dog-bone RLA.

Semidefinite linear complementarity problems

International Nuclear Information System (INIS)

Eckhardt, U.

1978-04-01

Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.) [de

Linear methods in band theory

DEFF Research Database (Denmark)

Andersen, O. Krogh

1975-01-01

of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...

Competitive inhibition can linearize dose-response and generate a linear rectifier.

Science.gov (United States)

Savir, Yonatan; Tu, Benjamin P; Springer, Michael

2015-09-23

Many biological responses require a dynamic range that is larger than standard bi-molecular interactions allow, yet the also ability to remain off at low input. Here we mathematically show that an enzyme reaction system involving a combination of competitive inhibition, conservation of the total level of substrate and inhibitor, and positive feedback can behave like a linear rectifier-that is, a network motif with an input-output relationship that is linearly sensitive to substrate above a threshold but unresponsive below the threshold. We propose that the evolutionarily conserved yeast SAGA histone acetylation complex may possess the proper physiological response characteristics and molecular interactions needed to perform as a linear rectifier, and we suggest potential experiments to test this hypothesis. One implication of this work is that linear responses and linear rectifiers might be easier to evolve or synthetically construct than is currently appreciated.

The impact of the transient uptake flux on bioaccumulation : Linear adsorption and first-order internalisation coupled with spherical semi-infinite mass transport

NARCIS (Netherlands)

Galceran, J.; Monné, J.; Puy, J.; Leeuwen, van H.P.

2004-01-01

The uptake of a chemical species (such as an organic molecule or a toxic metal ion) by an organism is modelled considering linear pre-adsorption followed by a first-order internalisation. The active biosurface is supposed to be spherical or semi-spherical and the mass transport in the medium is

Numerical linear algebra theory and applications

CERN Document Server

Beilina, Larisa; Karchevskii, Mikhail

2017-01-01

This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

Reduced order surrogate modelling (ROSM) of high dimensional deterministic simulations

Science.gov (United States)

Mitry, Mina

Often, computationally expensive engineering simulations can prohibit the engineering design process. As a result, designers may turn to a less computationally demanding approximate, or surrogate, model to facilitate their design process. However, owing to the the curse of dimensionality, classical surrogate models become too computationally expensive for high dimensional data. To address this limitation of classical methods, we develop linear and non-linear Reduced Order Surrogate Modelling (ROSM) techniques. Two algorithms are presented, which are based on a combination of linear/kernel principal component analysis and radial basis functions. These algorithms are applied to subsonic and transonic aerodynamic data, as well as a model for a chemical spill in a channel. The results of this thesis show that ROSM can provide a significant computational benefit over classical surrogate modelling, sometimes at the expense of a minor loss in accuracy.

Generation of intense high-order vortex harmonics.

Science.gov (United States)

Zhang, Xiaomei; Shen, Baifei; Shi, Yin; Wang, Xiaofeng; Zhang, Lingang; Wang, Wenpeng; Xu, Jiancai; Yi, Longqiong; Xu, Zhizhan

2015-05-01

This Letter presents for the first time a scheme to generate intense high-order optical vortices that carry orbital angular momentum in the extreme ultraviolet region based on relativistic harmonics from the surface of a solid target. In the three-dimensional particle-in-cell simulation, the high-order harmonics of the high-order vortex mode is generated in both reflected and transmitted light beams when a linearly polarized Laguerre-Gaussian laser pulse impinges on a solid foil. The azimuthal mode of the harmonics scales with its order. The intensity of the high-order vortex harmonics is close to the relativistic region, with the pulse duration down to attosecond scale. The obtained intense vortex beam possesses the combined properties of fine transversal structure due to the high-order mode and the fine longitudinal structure due to the short wavelength of the high-order harmonics. In addition to the application in high-resolution detection in both spatial and temporal scales, it also presents new opportunities in the intense vortex required fields, such as the inner shell ionization process and high energy twisted photons generation by Thomson scattering of such an intense vortex beam off relativistic electrons.

Linear mixed-effects models to describe individual tree crown width for China-fir in Fujian Province, southeast China.

Science.gov (United States)

Hao, Xu; Yujun, Sun; Xinjie, Wang; Jin, Wang; Yao, Fu

2015-01-01

A multiple linear model was developed for individual tree crown width of Cunninghamia lanceolata (Lamb.) Hook in Fujian province, southeast China. Data were obtained from 55 sample plots of pure China-fir plantation stands. An Ordinary Linear Least Squares (OLS) regression was used to establish the crown width model. To adjust for correlations between observations from the same sample plots, we developed one level linear mixed-effects (LME) models based on the multiple linear model, which take into account the random effects of plots. The best random effects combinations for the LME models were determined by the Akaike's information criterion, the Bayesian information criterion and the -2logarithm likelihood. Heteroscedasticity was reduced by three residual variance functions: the power function, the exponential function and the constant plus power function. The spatial correlation was modeled by three correlation structures: the first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)], and the compound symmetry structure (CS). Then, the LME model was compared to the multiple linear model using the absolute mean residual (AMR), the root mean square error (RMSE), and the adjusted coefficient of determination (adj-R2). For individual tree crown width models, the one level LME model showed the best performance. An independent dataset was used to test the performance of the models and to demonstrate the advantage of calibrating LME models.

The linear-non-linear frontier for the Goldstone Higgs

International Nuclear Information System (INIS)

Gavela, M.B.; Saa, S.; Kanshin, K.; Machado, P.A.N.

2016-01-01

The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)

The linear-non-linear frontier for the Goldstone Higgs

Energy Technology Data Exchange (ETDEWEB)

Gavela, M.B.; Saa, S. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Kanshin, K. [Universita di Padova, Dipartimento di Fisica e Astronomia ' G. Galilei' , Padua (Italy); INFN, Padova (Italy); Machado, P.A.N. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Fermi National Accelerator Laboratory, Theoretical Physics Department, Batavia, IL (United States)

2016-12-15

The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)

Optically stimulated luminescence from quartz measured using the linear modulation technique

International Nuclear Information System (INIS)

Bulur, E.; Boetter-Jensen, L.; Murray, A.S.

2000-01-01

The optically stimulated luminescence (OSL) from heated natural quartz has been investigated using the linear modulation technique (LMT), in which the excitation light intensity is increased linearly during stimulation. In contrast to conventional stimulation, which usually produces a monotonically decreasing signal, linearly increasing the stimulation power gives peaks in the signal as a function of time. In cases where the OSL signal contains more than one component, the linear increase in power of the stimulation light may result in a curve containing overlapping peaks, where the most easily stimulated component occurs at a shorter time. This allows the separation of the overlapping OSL components, which are assumed to originate from different traps. The LM-OSL curve from quartz shows an initial peak followed by a broad one. Deconvolution using curve fitting has shown that the composite OSL curve from quartz can be approximated well by using a linear combination of first-order peaks. In addition to the three known components, i.e. fast, medium and slow components from continuous-wave-OSL studies, an additional slow component is also identified for the first time. The dose responses and thermal stabilities of the various components are also studied

Ranking Forestry Investments With Parametric Linear Programming

Science.gov (United States)

Paul A. Murphy

1976-01-01

Parametric linear programming is introduced as a technique for ranking forestry investments under multiple constraints; it combines the advantages of simple tanking and linear programming as capital budgeting tools.

The Effect of Creative Tasks on Electrocardiogram: Using Linear and Nonlinear Features in Combination with Classification Approaches

Directory of Open Access Journals (Sweden)

Sahar Zakeri

2017-02-01

Full Text Available Objective: Interest in the subject of creativity and its impacts on human life is growing extensively. However, only a few surveys pay attention to the relation between creativity and physiological changes. This paper presents a novel approach to distinguish between creativity states from electrocardiogram signals. Nineteen linear and nonlinear features of the cardiac signal were extracted to detect creativity states. Method: ECG signals of 52 participants were recorded while doing three tasks of Torrance Tests of Creative Thinking (TTCT/ figural B. To remove artifacts, notch filter 50 Hz and Chebyshev II were applied. According to TTCT scores, participants were categorized into the high and low creativity groups: Participants with scores higher than 70 were assigned into the high creativity group and those with scores less than 30 were considered as low creativity group. Some linear and nonlinear features were extracted from the ECGs. Then, Support Vector Machine (SVM and Adaptive Neuro-Fuzzy Inference System (ANFIS were used to classify the groups.Results: Applying the Wilcoxon test, significant differences were observed between rest and each three tasks of creativity. However, better discrimination was performed between rest and the first task. In addition, there were no statistical differences between the second and third task of the test. The results indicated that the SVM effectively detects all the three tasks from the rest, particularly the task 1 and reached the maximum accuracy of 99.63% in the linear analysis. In addition, the high creative group was separated from the low creative group with the accuracy of 98.41%.Conclusion: the combination of SVM classifier with linear features can be useful to show the relation between creativity and physiological changes.

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schoedinger equation admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The admissible potentials come into families evolved from equations having a fixed number of elementary singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

Primordial black holes in linear and non-linear regimes

Energy Technology Data Exchange (ETDEWEB)

Allahyari, Alireza; Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

2017-06-01

We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.

An A Posteriori Error Analysis of Mixed Finite Element Galerkin Approximations to Second Order Linear Parabolic Problems

KAUST Repository

Memon, Sajid; Nataraj, Neela; Pani, Amiya Kumar

2012-01-01

In this article, a posteriori error estimates are derived for mixed finite element Galerkin approximations to second order linear parabolic initial and boundary value problems. Using mixed elliptic reconstructions, a posteriori error estimates in L∞(L2)- and L2(L2)-norms for the solution as well as its flux are proved for the semidiscrete scheme. Finally, based on a backward Euler method, a completely discrete scheme is analyzed and a posteriori error bounds are derived, which improves upon earlier results on a posteriori estimates of mixed finite element approximations to parabolic problems. Results of numerical experiments verifying the efficiency of the estimators have also been provided. © 2012 Society for Industrial and Applied Mathematics.

The non-linear ion trap. Part 5. Nature of non-linear resonances and resonant ion ejection

Science.gov (United States)

Franzen, J.

1994-01-01

The superposition of higher order multipole fields on the basic quadrupole field in ion traps generates a non-harmonic oscillator system for the ions. Fourier analyses of simulated secular oscillations in non-linear ion traps, therefore, not only reveal the sideband frequencies, well-known from the Mathieu theory, but additionally a commonwealth of multipole-specific overtones (or higher harmonics), and corresponding sidebands of overtones. Non-linear resonances occur when the overtone frequencies match sideband frequencies. It can be shown that in each of the resonance conditions, not just one overtone matches one sideband, instead, groups of overtones match groups of sidebands. The generation of overtones is studied by Fourier analysis of computed ion oscillations in the direction of thez axis. Even multipoles (octopole, dodecapole, etc.) generate only odd orders of higher harmonics (3, 5, etc.) of the secular frequency, explainable by the symmetry with regard to the planez = 0. In contrast, odd multipoles (hexapole, decapole, etc.) generate all orders of higher harmonics. For all multipoles, the lowest higher harmonics are found to be strongest. With multipoles of higher orders, the strength of the overtones decreases weaker with the order of the harmonics. Forz direction resonances in stationary trapping fields, the function governing the amplitude growth is investigated by computer simulations. The ejection in thez direction, as a function of timet, follows, at least in good approximation, the equation wheren is the order of multipole, andC is a constant. This equation is strictly valid for the electrically applied dipole field (n = 1), matching the secular frequency or one of its sidebands, resulting in a linear increase of the amplitude. It is valid also for the basic quadrupole field (n = 2) outside the stability area, giving an exponential increase. It is at least approximately valid for the non-linear resonances by weak superpositions of all higher odd

Linearly Refined Session Types

Directory of Open Access Journals (Sweden)

Pedro Baltazar

2012-11-01

Full Text Available Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation, combining types with logical formulae that may refer to program values and can constrain types using arbitrary predicates. We present a pi calculus with assume and assert operations, typed using a session discipline that incorporates refinement formulae written in a fragment of Multiplicative Linear Logic. Our original combination of session and refinement types, together with the well established benefits of linearity, allows very fine-grained specifications of communication protocols in which refinement formulae are treated as logical resources rather than persistent truths.

The Schroedinger equation for central power law potentials and the classical theory of ordinary linear differential equations of the second order

International Nuclear Information System (INIS)

Lima, M.L.; Mignaco, J.A.

1985-01-01

It is shown that the rational power law potentials in the two-body radial Schrodinger equations admit a systematic treatment available from the classical theory of ordinary linear differential equations of the second order. The resulting potentials come into families evolved from equations having a fixed number of elementary regular singularities. As a consequence, relations are found and discussed among the several potentials in a family. (Author) [pt

CSSI-PRO: a method for secondary structure type editing, assignment and estimation in proteins using linear combination of backbone chemical shifts

International Nuclear Information System (INIS)

Swain, Monalisa; Atreya, Hanudatta S.

2009-01-01

Estimation of secondary structure in polypeptides is important for studying their structure, folding and dynamics. In NMR spectroscopy, such information is generally obtained after sequence specific resonance assignments are completed. We present here a new methodology for assignment of secondary structure type to spin systems in proteins directly from NMR spectra, without prior knowledge of resonance assignments. The methodology, named Combination of Shifts for Secondary Structure Identification in Proteins (CSSI-PRO), involves detection of specific linear combination of backbone 1 H α and 13 C' chemical shifts in a two-dimensional (2D) NMR experiment based on G-matrix Fourier transform (GFT) NMR spectroscopy. Such linear combinations of shifts facilitate editing of residues belonging to α-helical/β-strand regions into distinct spectral regions nearly independent of the amino acid type, thereby allowing the estimation of overall secondary structure content of the protein. Comparison of the predicted secondary structure content with those estimated based on their respective 3D structures and/or the method of Chemical Shift Index for 237 proteins gives a correlation of more than 90% and an overall rmsd of 7.0%, which is comparable to other biophysical techniques used for structural characterization of proteins. Taken together, this methodology has a wide range of applications in NMR spectroscopy such as rapid protein structure determination, monitoring conformational changes in protein-folding/ligand-binding studies and automated resonance assignment

Order-disorder-reorder process in thermally treated dolomite samples: a combined powder and single-crystal X-ray diffraction study

Science.gov (United States)

Zucchini, A.; Comodi, P.; Katerinopoulou, A.; Balic-Zunic, T.; McCammon, C.; Frondini, F.

2012-04-01

A combined powder and single-crystal X-ray diffraction analysis of dolomite [CaMg(CO3)2] heated to 1,200°C at 3 GPa was made to study the order-disorder-reorder process. The order/disorder transition is inferred to start below 1,100°C, and complete disorder is attained at approximately 1,200°C. Twinned crystals characterized by high internal order were found in samples annealed over 1,100°C, and their fraction was found to increase with temperature. Evidences of twinning domains combined with probable remaining disordered portions of the structure imply that reordering processes occur during the quench. Twin domains are hereby proposed as a witness to thermally induced intra-layer-type cation disordering.

Power and Sample Size Calculations for Testing Linear Combinations of Group Means under Variance Heterogeneity with Applications to Meta and Moderation Analyses

Science.gov (United States)

Shieh, Gwowen; Jan, Show-Li

2015-01-01

The general formulation of a linear combination of population means permits a wide range of research questions to be tested within the context of ANOVA. However, it has been stressed in many research areas that the homogeneous variances assumption is frequently violated. To accommodate the heterogeneity of variance structure, the…

Experimental verification of a self-consistent theory of the first-, second-, and third-order (non)linear optical response

International Nuclear Information System (INIS)

Perez-Moreno, Javier; Hung, Sheng-Ting; Kuzyk, Mark G.; Zhou, Juefei; Ramini, Shiva K.; Clays, Koen

2011-01-01

We show that a combination of linear absorption spectroscopy, hyper-Rayleigh scattering, and a theoretical analysis using sum rules to reduce the size of the parameter space leads to a prediction of the imaginary part of the second hyperpolarizability of the dye AF-455 that agrees with the experimental data gathered through two-photon absorption spectroscopy. Our procedure, which demands self-consistency between several measurement techniques and does not use adjustable parameters, provides a means for determining transition moments between the dominant excited states based strictly on experimental characterization. This is made possible by our new approach that uses sum rules and molecular symmetry to rigorously reduce the number of required physical quantities.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

Science.gov (United States)

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

General solution of the Bagley-Torvik equation with fractional-order derivative

Science.gov (United States)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Runge-Kutta Methods for Linear Ordinary Differential Equations

Science.gov (United States)

Zingg, David W.; Chisholm, Todd T.

1997-01-01

Three new Runge-Kutta methods are presented for numerical integration of systems of linear inhomogeneous ordinary differential equations (ODES) with constant coefficients. Such ODEs arise in the numerical solution of the partial differential equations governing linear wave phenomena. The restriction to linear ODEs with constant coefficients reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. This freedom is used to develop methods which are more efficient than conventional Runge-Kutta methods. A fourth-order method is presented which uses only two memory locations per dependent variable, while the classical fourth-order Runge-Kutta method uses three. This method is an excellent choice for simulations of linear wave phenomena if memory is a primary concern. In addition, fifth- and sixth-order methods are presented which require five and six stages, respectively, one fewer than their conventional counterparts, and are therefore more efficient. These methods are an excellent option for use with high-order spatial discretizations.

Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

KAUST Repository

Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel

2015-01-01

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search

On the Linear Stability of the Fifth-Order WENO Discretization

KAUST Repository

Motamed, Mohammad; Macdonald, Colin B.; Ruuth, Steven J.

2010-01-01

, the fifth-order extrapolated BDF scheme gave superior results in practice to high-order Runge-Kutta methods whose stability domain includes the imaginary axis. Numerical tests are presented which confirm the analysis. © Springer Science+Business Media, LLC

Combining higher-order resummation with multiple NLO calculations and parton showers in the Geneva Monte Carlo framework

International Nuclear Information System (INIS)

Alioli, Simone; Bauer, Christian W.; Berggren, Calvin; Vermilion, Christopher K.; Walsh, Jonathan R.; Zuberi, Saba; Hornig, Andrew; Tackmann, Frank J.

2013-05-01

We discuss the GENEVA Monte Carlo framework, which combines higher-order resummation (NNLL) of large Sudakov logarithms with multiple next-to-leading-order (NLO) matrix-element corrections and parton showering (using PYTHIA 8) to give a complete description at the next higher perturbative accuracy in α s at both small and large jet resolution scales. Results for e + e - →jets compared to LEP data and pp→(Z/γ * →l + l - )+jets are presented.

Linear collider: a preview

Energy Technology Data Exchange (ETDEWEB)

Wiedemann, H.

1981-11-01

Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center.

Linear collider: a preview

International Nuclear Information System (INIS)

Wiedemann, H.

1981-11-01

Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center

Enhancement of loss detection capability using a combination of the Kalman Filter/Linear Smoother and controllable unit accounting approach

International Nuclear Information System (INIS)

Pike, D.H.; Morrison, G.W.

1979-01-01

An approach to loss detection is presented which combines the optimal loss detection capability of state estimation techniques with a controllable unit accounting approach. The state estimation theory makes use of a linear system model which is capable of modeling the interaction of various controllable unit areas within a given facility. An example is presented which illustrates the increase in loss detection probability which is realizable with state estimation techniques. Comparisons are made with a Shewhart Control Chart and the CUSUM statistic

Non-linear perturbations of a spherically collapsing star

International Nuclear Information System (INIS)

Brizuela, David

2009-01-01

Linear perturbation theory has been a successful tool in General Relativity, and can be considered as complementary to full nonlinear simulations. Going to second and higher perturbative orders improves the approximation and offers a controlled way to analyze the nonlinearities of the theory, though the problem becomes much harder computationally. We present a systematic approach to the treatment of high order metric perturbations, focusing on the scenario of nonspherical perturbations of a dynamical spherical background. It is based on the combination of adapted geometrical variables and the use of efficient computer algebra techniques. After dealing with a number of theoretical issues, like the construction of gauge invariants, we apply the formalism to the particular case of a perfect fluid star surrounded by a vacuum exterior. We describe the regularization of the divergences of the perturbations at null infinity and the matching conditions through the surface of the star.

Further linear algebra

CERN Document Server

Blyth, T S

2002-01-01

Most of the introductory courses on linear algebra develop the basic theory of finite­ dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num­ ber of illustrative and worked examples, as well as many exercises that are strategi­ cally placed throughout the text. Solutions to the ex...

Combining support vector machines with linear quadratic regulator adaptation for the online design of an automotive active suspension system

International Nuclear Information System (INIS)

Chiou, J-S; Liu, M-T

2008-01-01

As a powerful machine-learning approach to pattern recognition problems, the support vector machine (SVM) is known to easily allow generalization. More importantly, it works very well in a high-dimensional feature space. This paper presents a nonlinear active suspension controller which achieves a high level performance by compensating for actuator dynamics. We use a linear quadratic regulator (LQR) to ensure optimal control of nonlinear systems. An LQR is used to solve the problem of state feedback and an SVM is used to address the question of the estimation and examination of the state. These two are then combined and designed in a way that outputs feedback control. The real-time simulation demonstrates that an active suspension using the combined SVM-LQR controller provides passengers with a much more comfortable ride and better road handling

Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials

Directory of Open Access Journals (Sweden)

Wu Guo-Cheng

2017-01-01

Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.

Progress in linear optics, non-linear optics and surface alignment of liquid crystals

Science.gov (United States)

Ong, H. L.; Meyer, R. B.; Hurd, A. J.; Karn, A. J.; Arakelian, S. M.; Shen, Y. R.; Sanda, P. N.; Dove, D. B.; Jansen, S. A.; Hoffmann, R.

We first discuss the progress in linear optics, in particular, the formulation and application of geometrical-optics approximation and its generalization. We then discuss the progress in non-linear optics, in particular, the enhancement of a first-order Freedericksz transition and intrinsic optical bistability in homeotropic and parallel oriented nematic liquid crystal cells. Finally, we discuss the liquid crystal alignment and surface effects on field-induced Freedericksz transition.

Regularized iterative integration combined with non-linear diffusion filtering for phase-contrast x-ray computed tomography.

Science.gov (United States)

Burger, Karin; Koehler, Thomas; Chabior, Michael; Allner, Sebastian; Marschner, Mathias; Fehringer, Andreas; Willner, Marian; Pfeiffer, Franz; Noël, Peter

2014-12-29

Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.

Revival structures of linear molecules in a field-free alignment condition as probed by high-order harmonic generation

International Nuclear Information System (INIS)

Lee, G. H.; Kim, H. T.; Park, J. Y.; Nam, C. H.; Kim, T. K.; Lee, J. H.; Ihee, H.

2006-01-01

Revival structures (rotational coherence) of three linear molecules (N 2 , O 2 , and CO 2 ) in a field free alignment condition have been investigated using high-order harmonic generation. The harmonic yields of these molecules were measured in a pump-probe manner by using a weak femtosecond (fs) laser pulse for field-free alignment of molecules and another intense fs laser pulse for harmonic generation. The harmonic intensities from 23rd to 29th order with respect to the time delay between the pump and the probe pulses showed revival structures in the condition of a field-free alignment of molecules. While the revival structure of a N 2 molecule had one-fourth the period of the full revival time and different degrees of modulation among different fractional revival times, the revival structures of O 2 and CO 2 molecules showed one-eighth the periods of the full revival time and similar degrees of modulation among all fractional revival times. The revival structures could be interpreted in terms of the nature of the highest occupied molecular orbital and the total nuclear spin.

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

Directory of Open Access Journals (Sweden)

Sifeu Takougang Kingni

2017-01-01

Full Text Available A linear resistive-capacitive-inductance shunted junction (LRCLSJ model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system.

Schwarzian conditions for linear differential operators with selected differential Galois groups

International Nuclear Information System (INIS)

Abdelaziz, Y; Maillard, J-M

2017-01-01

We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions can be generalized to arbitrary order linear differential operators with polynomial coefficients having selected differential Galois groups. For order three and order four linear differential operators we show that this pullback invariance up to conjugation eventually reduces to symmetric powers of an underlying order-two operator. We give, precisely, the conditions to have modular correspondences solutions for such Schwarzian differential equations, which was an open question in a previous paper. We analyze in detail a pullbacked hypergeometric example generalizing modular forms, that ushers a pullback invariance up to operator homomorphisms. We finally consider the more general problem of the equivalence of two different order-four linear differential Calabi–Yau operators up to pullbacks and conjugation, and clarify the cases where they have the same Yukawa couplings. (paper)

Schwarzian conditions for linear differential operators with selected differential Galois groups

Science.gov (United States)

Abdelaziz, Y.; Maillard, J.-M.

2017-11-01

We show that non-linear Schwarzian differential equations emerging from covariance symmetry conditions imposed on linear differential operators with hypergeometric function solutions can be generalized to arbitrary order linear differential operators with polynomial coefficients having selected differential Galois groups. For order three and order four linear differential operators we show that this pullback invariance up to conjugation eventually reduces to symmetric powers of an underlying order-two operator. We give, precisely, the conditions to have modular correspondences solutions for such Schwarzian differential equations, which was an open question in a previous paper. We analyze in detail a pullbacked hypergeometric example generalizing modular forms, that ushers a pullback invariance up to operator homomorphisms. We finally consider the more general problem of the equivalence of two different order-four linear differential Calabi-Yau operators up to pullbacks and conjugation, and clarify the cases where they have the same Yukawa couplings.

Non linear self consistency of microtearing modes

International Nuclear Information System (INIS)

Garbet, X.; Mourgues, F.; Samain, A.

1987-01-01

The self consistency of a microtearing turbulence is studied in non linear regimes where the ergodicity of the flux lines determines the electron response. The current which sustains the magnetic perturbation via the Ampere law results from the combines action of the radial electric field in the frame where the island chains are static and of the thermal electron diamagnetism. Numerical calculations show that at usual values of β pol in Tokamaks the turbulence can create a diffusion coefficient of order ν th p 2 i where p i is the ion larmor radius and ν th the electron ion collision frequency. On the other hand, collisionless regimes involving special profiles of each mode near the resonant surface seem possible

Modeling Pan Evaporation for Kuwait by Multiple Linear Regression

Science.gov (United States)

Almedeij, Jaber

2012-01-01

Evaporation is an important parameter for many projects related to hydrology and water resources systems. This paper constitutes the first study conducted in Kuwait to obtain empirical relations for the estimation of daily and monthly pan evaporation as functions of available meteorological data of temperature, relative humidity, and wind speed. The data used here for the modeling are daily measurements of substantial continuity coverage, within a period of 17 years between January 1993 and December 2009, which can be considered representative of the desert climate of the urban zone of the country. Multiple linear regression technique is used with a procedure of variable selection for fitting the best model forms. The correlations of evaporation with temperature and relative humidity are also transformed in order to linearize the existing curvilinear patterns of the data by using power and exponential functions, respectively. The evaporation models suggested with the best variable combinations were shown to produce results that are in a reasonable agreement with observation values. PMID:23226984

Linear and Nonlinear Rheology Combined with Dielectric Spectroscopy of Hybrid Polymer Nanocomposites for Semiconductive Applications

Science.gov (United States)

Kádár, Roland; Abbasi, Mahdi; Figuli, Roxana; Rigdahl, Mikael; Wilhelm, Manfred

2017-01-01

The linear and nonlinear oscillatory shear, extensional and combined rheology-dielectric spectroscopy of hybrid polymer nanocomposites for semiconductive applications were investigated in this study. The main focus was the influence of processing conditions on percolated poly(ethylene-butyl acrylate) (EBA) nanocomposite hybrids containing graphite nanoplatelets (GnP) and carbon black (CB). The rheological response of the samples was interpreted in terms of dispersion properties, filler distortion from processing, filler percolation, as well as the filler orientation and distribution dynamics inside the matrix. Evidence of the influence of dispersion properties was found in linear viscoelastic dynamic frequency sweeps, while the percolation of the nanocomposites was detected in nonlinearities developed in dynamic strain sweeps. Using extensional rheology, hybrid samples with better dispersion properties lead to a more pronounced strain hardening behavior, while samples with a higher volume percentage of fillers caused a drastic reduction in strain hardening. The rheo-dielectric time-dependent response showed that in the case of nanocomposites containing only GnP, the orientation dynamics leads to non-conductive samples. However, in the case of hybrids, the orientation of the GnP could be offset by the dispersing of the CB to bridge the nanoplatelets. The results were interpreted in the framework of a dual PE-BA model, where the fillers would be concentrated mainly in the BA regions. Furthermore, better dispersed hybrids obtained using mixing screws at the expense of filler distortion via extrusion processing history were emphasized through the rheo-dielectric tests. PMID:28336857

Linear and Nonlinear Rheology Combined with Dielectric Spectroscopy of Hybrid Polymer Nanocomposites for Semiconductive Applications

Directory of Open Access Journals (Sweden)

Roland Kádár

2017-01-01

Full Text Available The linear and nonlinear oscillatory shear, extensional and combined rheology-dielectric spectroscopy of hybrid polymer nanocomposites for semiconductive applications were investigated in this study. The main focus was the influence of processing conditions on percolated poly(ethylene-butyl acrylate (EBA nanocomposite hybrids containing graphite nanoplatelets (GnP and carbon black (CB. The rheological response of the samples was interpreted in terms of dispersion properties, filler distortion from processing, filler percolation, as well as the filler orientation and distribution dynamics inside the matrix. Evidence of the influence of dispersion properties was found in linear viscoelastic dynamic frequency sweeps, while the percolation of the nanocomposites was detected in nonlinearities developed in dynamic strain sweeps. Using extensional rheology, hybrid samples with better dispersion properties lead to a more pronounced strain hardening behavior, while samples with a higher volume percentage of fillers caused a drastic reduction in strain hardening. The rheo-dielectric time-dependent response showed that in the case of nanocomposites containing only GnP, the orientation dynamics leads to non-conductive samples. However, in the case of hybrids, the orientation of the GnP could be offset by the dispersing of the CB to bridge the nanoplatelets. The results were interpreted in the framework of a dual PE-BA model, where the fillers would be concentrated mainly in the BA regions. Furthermore, better dispersed hybrids obtained using mixing screws at the expense of filler distortion via extrusion processing history were emphasized through the rheo-dielectric tests.

A study of operating parameters on the linear spark ignition engine

International Nuclear Information System (INIS)

Lim, Ocktaeck; Hung, Nguyen Ba; Oh, Seokyoung; Kim, Gangchul; Song, Hanho; Iida, Norimasa

2015-01-01

Highlights: • An experimental and simulation study of a linear engine is conducted. • The effects of operating parameters on the generating power are investigated. • The air gap length has a significant influence on the generating power. • The generating power of the linear engine is optimized with the value of 111.3 W. • There are no problems for the linear engine after 100 h of durable test. - Abstract: In this paper, we present our experiment and simulation study of a free piston linear engine based on operating conditions and structure of the linear engine for generating electric power. The free piston linear engine includes a two-stroke free piston engine, linear generators, and compressors. In the experimental study, the effects of key parameters such as input caloric value, equivalence ratio, spark timing delay, electrical resistance, and air gap length on the piston dynamics and electric power output are investigated. Propane is used as a fuel in the free piston linear engine, and it is premixed with the air to make a homogeneous charge before go into the cylinder. The air and fuel mass flow rate are varied by a mass flow controller. The experimental results show that the maximum generating power is found with the value of 111 W at the input caloric value of 5.88 kJ/s, spark timing delay of 1.5 ms, equivalence ratio of 1.0, electric resistance of 30 Ω, and air gap length of 1.0 mm. In order to check the durability of the linear engine, a durable test is conducted during 100 h. The experimental results show that there are no problems for the linear engine after about one hundred hours of the durable test. Beside experimental study, a simulation study is conducted to predict operating behavior of the linear engine. In the simulation study, the two-stroke free piston linear engine is modeled and simulated through a combination of three mathematical models including a dynamic model, a linear alternator model and a thermodynamic model. These

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

Science.gov (United States)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

An evaluation of the performance of an integrated solar combined cycle plant provided with air-linear parabolic collectors

International Nuclear Information System (INIS)

Amelio, Mario; Ferraro, Vittorio; Marinelli, Valerio; Summaria, Antonio

2014-01-01

An evaluation of the performance of an innovative solar system integrated in a combined cycle plant is presented, in which the heat transfer fluid flowing in linear parabolic collectors is the same oxidant air that is introduced into the combustion chamber of the plant. This peculiarity allows a great simplification of the plant. There is a 22% saving of fossil fuel results in design conditions and 15.5% on an annual basis, when the plant works at nominal volumetric flow rate in the daily hours. The net average year efficiency is 60.9% against the value of 51.4% of a reference combined cycle plant without solar integration. Moreover, an economic evaluation of the plant is carried out, which shows that the extra-cost of the solar part is recovered in about 5 years. - Highlights: • A model to calculate an innovative ISCCS (Integrated solar Combined Cycle Systems) solar plant is presented. • The plant uses air as heat transfer fluid as well as oxidant in the combustor. • The plant presents a very high thermodynamic efficiency. • The plant is very simple in comparison with existing ISCCS

Equivalence Checking of Combinational Circuits using Boolean Expression Diagrams

DEFF Research Database (Denmark)

Hulgaard, Henrik; Williams, Poul Frederick; Andersen, Henrik Reif

1999-01-01

The combinational logic-level equivalence problem is to determine whether two given combinational circuits implement the same Boolean function. This problem arises in a number of CAD applications, for example when checking the correctness of incremental design changes (performed either manually...... or by a design automation tool).This paper introduces a data structure called Boolean Expression Diagrams (BEDs) and two algorithms for transforming a BED into a Reduced Ordered Binary Decision Diagram (OBDD). BEDs are capable of representing any Boolean circuit in linear space and can exploit structural...... similarities between the two circuits that are compared. These properties make BEDs suitable for verifying the equivalence of combinational circuits. BEDs can be seen as an intermediate representation between circuits (which are compact) and OBDDs (which are canonical).Based on a large number of combinational...

Non-linear multivariate and multiscale monitoring and signal denoising strategy using Kernel Principal Component Analysis combined with Ensemble Empirical Mode Decomposition method

Science.gov (United States)

Žvokelj, Matej; Zupan, Samo; Prebil, Ivan

2011-10-01

The article presents a novel non-linear multivariate and multiscale statistical process monitoring and signal denoising method which combines the strengths of the Kernel Principal Component Analysis (KPCA) non-linear multivariate monitoring approach with the benefits of Ensemble Empirical Mode Decomposition (EEMD) to handle multiscale system dynamics. The proposed method which enables us to cope with complex even severe non-linear systems with a wide dynamic range was named the EEMD-based multiscale KPCA (EEMD-MSKPCA). The method is quite general in nature and could be used in different areas for various tasks even without any really deep understanding of the nature of the system under consideration. Its efficiency was first demonstrated by an illustrative example, after which the applicability for the task of bearing fault detection, diagnosis and signal denosing was tested on simulated as well as actual vibration and acoustic emission (AE) signals measured on purpose-built large-size low-speed bearing test stand. The positive results obtained indicate that the proposed EEMD-MSKPCA method provides a promising tool for tackling non-linear multiscale data which present a convolved picture of many events occupying different regions in the time-frequency plane.

Bunch monitor for an S-band electron linear accelerator

International Nuclear Information System (INIS)

Otake, Yuji; Nakahara, Kazuo

1991-01-01

The measurement of bunch characteristics in an S-band electron linear accelerator is required in order to evaluate the quality of accelerated electron beams. A new-type bunch monitor has been developed which combines micro-stripline technology with an air insulator and wall-current monitoring technology. The obtained time resolution of the monitor was more than 150 ps. This result shows that the monitor can handle the bunch number of an S-band linac. The structure of the monitor is suitable for being installed in the vacuum area, since it is constructed of only metal and ceramic parts. It can therefore easily be employed in an actual machine

The AOLI low-order non-linear curvature wavefront sensor: laboratory and on-sky results

Science.gov (United States)

Crass, Jonathan; King, David; MacKay, Craig

2014-08-01

Many adaptive optics (AO) systems in use today require the use of bright reference objects to determine the effects of atmospheric distortions. Typically these systems use Shack-Hartmann Wavefront sensors (SHWFS) to distribute incoming light from a reference object between a large number of sub-apertures. Guyon et al. evaluated the sensitivity of several different wavefront sensing techniques and proposed the non-linear Curvature Wavefront Sensor (nlCWFS) offering improved sensitivity across a range of orders of distortion. On large ground-based telescopes this can provide nearly 100% sky coverage using natural guide stars. We present work being undertaken on the nlCWFS development for the Adaptive Optics Lucky Imager (AOLI) project. The wavefront sensor is being developed as part of a low-order adaptive optics system for use in a dedicated instrument providing an AO corrected beam to a Lucky Imaging based science detector. The nlCWFS provides a total of four reference images on two photon-counting EMCCDs for use in the wavefront reconstruction process. We present results from both laboratory work using a calibration system and the first on-sky data obtained with the nlCWFS at the 4.2 metre William Herschel Telescope, La Palma. In addition, we describe the updated optical design of the wavefront sensor, strategies for minimising intrinsic effects and methods to maximise sensitivity using photon-counting detectors. We discuss on-going work to develop the high speed reconstruction algorithm required for the nlCWFS technique. This includes strategies to implement the technique on graphics processing units (GPUs) and to minimise computing overheads to obtain a prior for a rapid convergence of the wavefront reconstruction. Finally we evaluate the sensitivity of the wavefront sensor based upon both data and low-photon count strategies.

The reliability of linear position transducer, force plate and combined measurement of explosive power-time variables during a loaded jump squat in elite athletes.

Science.gov (United States)

Hansen, Keir T; Cronin, John B; Newton, Michael J

2011-03-01

The purpose of this study was to determine the between day reliability of power-time measures calculated with data collected using the linear position transducer or the force plate independently, or a combination of the two technologies. Twenty-five male rugby union players performed three jump squats on two occasions one week apart. Ground reaction forces were measured via a force plate and position data were collected using a linear position transducer. From these data, a number of power-time variables were calculated for each method. The force plate, linear position transducer and a combined method were all found to be a reliable means of measuring peak power (ICC = 0.87-0.95, CV = 3.4%-8.0%). The absolute consistency of power-time measures varied between methods (CV = 8.0%-53.4%). Relative consistency of power-time measures was generally comparable between methods and measures, and for many variables was at an acceptable level (ICC = 0.77-0.94). Although a number of time-dependent power variables can be reliably calculated from data acquired from the three methods investigated, the reliability of a number of these measures is below that which is acceptable for use in research and for practical applications.

Accommodation of practical constraints by a linear programming jet select. [for Space Shuttle

Science.gov (United States)

Bergmann, E.; Weiler, P.

1983-01-01

An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

Linear Motor Motion Control Experiment System Design Based on LabVIEW

Directory of Open Access Journals (Sweden)

Cuixian He

2018-01-01

Full Text Available In order to meet the needs of experimental training of electrical information industry, a linear motor motion experiment system based on LabVIEW was developed. This system is based on the STM32F103ZET6 system processor controller, a state signal when the motor moves through the grating encoder feedback controller to form a closed loop, through the RS232 serial port communication with the host computer, the host computer is designed in the LabVIEW interactive environment monitoring software. Combined with the modular design concept proposed overall program, given the detailed hardware circuit, targeted for the software function design, to achieve man-machine interface. The system control of high accuracy, good stability, meet the training requirements for laboratory equipment, but also as a reference embodiment of the linear motor monitoring system.

Oscillation of two-dimensional linear second-order differential systems

International Nuclear Information System (INIS)

Kwong, M.K.; Kaper, H.G.

1985-01-01

This article is concerned with the oscillatory behavior at infinity of the solution y: [a, ∞) → R 2 of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon[a, ∞); Q is a continuous matrix-valued function on [a, ∞) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t → ∞. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references

Quasi-linear score for capturing heterogeneous structure in biomarkers.

Science.gov (United States)

Omae, Katsuhiro; Komori, Osamu; Eguchi, Shinto

2017-06-19

Linear scores are widely used to predict dichotomous outcomes in biomedical studies because of their learnability and understandability. Such approaches, however, cannot be used to elucidate biodiversity when there is heterogeneous structure in target population. Our study was focused on describing intrinsic heterogeneity in predictions. Because heterogeneity can be captured by a clustering method, integrating different information from different clusters should yield better predictions. Accordingly, we developed a quasi-linear score, which effectively combines the linear scores of clustered markers. We extended the linear score to the quasi-linear score by a generalized average form, the Kolmogorov-Nagumo average. We observed that two shrinkage methods worked well: ridge shrinkage for estimating the quasi-linear score, and lasso shrinkage for selecting markers within each cluster. Simulation studies and applications to real data show that the proposed method has good predictive performance compared with existing methods. Heterogeneous structure is captured by a clustering method. Quasi-linear scores combine such heterogeneity and have a better predictive ability compared with linear scores.

LINEAR MODEL FOR NON ISOSCELES ABSORBERS.

Energy Technology Data Exchange (ETDEWEB)

BERG,J.S.

2003-05-12

Previous analyses have assumed that wedge absorbers are triangularly shaped with equal angles for the two faces. In this case, to linear order, the energy loss depends only on the position in the direction of the face tilt, and is independent of the incoming angle. One can instead construct an absorber with entrance and exit faces facing rather general directions. In this case, the energy loss can depend on both the position and the angle of the particle in question. This paper demonstrates that and computes the effect to linear order.

Acoustic emission linear pulse holography

Science.gov (United States)

Collins, H.D.; Busse, L.J.; Lemon, D.K.

1983-10-25

This device relates to the concept of and means for performing Acoustic Emission Linear Pulse Holography, which combines the advantages of linear holographic imaging and Acoustic Emission into a single non-destructive inspection system. This unique system produces a chronological, linear holographic image of a flaw by utilizing the acoustic energy emitted during crack growth. The innovation is the concept of utilizing the crack-generated acoustic emission energy to generate a chronological series of images of a growing crack by applying linear, pulse holographic processing to the acoustic emission data. The process is implemented by placing on a structure an array of piezoelectric sensors (typically 16 or 32 of them) near the defect location. A reference sensor is placed between the defect and the array.

UQlust: combining profile hashing with linear-time ranking for efficient clustering and analysis of big macromolecular data.

Science.gov (United States)

Adamczak, Rafal; Meller, Jarek

2016-12-28

Advances in computing have enabled current protein and RNA structure prediction and molecular simulation methods to dramatically increase their sampling of conformational spaces. The quickly growing number of experimentally resolved structures, and databases such as the Protein Data Bank, also implies large scale structural similarity analyses to retrieve and classify macromolecular data. Consequently, the computational cost of structure comparison and clustering for large sets of macromolecular structures has become a bottleneck that necessitates further algorithmic improvements and development of efficient software solutions. uQlust is a versatile and easy-to-use tool for ultrafast ranking and clustering of macromolecular structures. uQlust makes use of structural profiles of proteins and nucleic acids, while combining a linear-time algorithm for implicit comparison of all pairs of models with profile hashing to enable efficient clustering of large data sets with a low memory footprint. In addition to ranking and clustering of large sets of models of the same protein or RNA molecule, uQlust can also be used in conjunction with fragment-based profiles in order to cluster structures of arbitrary length. For example, hierarchical clustering of the entire PDB using profile hashing can be performed on a typical laptop, thus opening an avenue for structural explorations previously limited to dedicated resources. The uQlust package is freely available under the GNU General Public License at https://github.com/uQlust . uQlust represents a drastic reduction in the computational complexity and memory requirements with respect to existing clustering and model quality assessment methods for macromolecular structure analysis, while yielding results on par with traditional approaches for both proteins and RNAs.

Biology-Inspired Robust Dive Plane Control of Non-Linear AUV Using Pectoral-Like Fins

Directory of Open Access Journals (Sweden)

Subramanian Ramasamy

2010-01-01

Full Text Available The development of a control system for the dive plane control of non-linear biorobotic autonomous underwater vehicles, equipped with pectoral-like fins, is the subject of this paper. Marine animals use pectoral fins for swimming smoothly. The fins are assumed to be oscillating with a combined pitch and heave motion and therefore produce unsteady control forces. The objective is to control the depth of the vehicle. The mean angle of pitch motion of the fin is used as a control variable. A computational-fluid-dynamics-based parameterisation of the fin forces is used for control system design. A robust servo regulator for the control of the depth of the vehicle, based on the non-linear internal model principle, is derived. For the control law derivation, an exosystem of third order is introduced, and the non-linear time-varying biorobotic autonomous underwater vehicle model, including the fin forces, is represented as a non-linear autonomous system in an extended state space. The control system includes the internal model of a k-fold exosystem, where k is a positive integer chosen by the designer. It is shown that in the closed-loop system, all the harmonic components of order up to k of the tracking error are suppressed. Simulation results are presented which show that the servo regulator accomplishes accurate depth control despite uncertainties in the model parameters.

Critical Combinations of Higher-Order Terms in Einstein-Maxwell Theory and Compactification

Directory of Open Access Journals (Sweden)

Nahomi Kan

2015-01-01

Full Text Available We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, particularly in the background of spontaneous compactification. Two classes of theories are proposed in this paper. The first model as a generalization of the critical gravity with the Maxwell field could have a de Sitter solution. We consider the Lanczos-Lovelock term and Horndeski term as well as the higher-order Maxwell term for the second model, which contains a possible longer expansion time for the inflationary phase. It is interesting that both models can be regarded as the generalization of the Randjbar-Daemi, Salam and Strathdee (RSS model and give the well behavior for inflation stage under the specific assumptions.

Multivariate covariance generalized linear models

DEFF Research Database (Denmark)

Bonat, W. H.; Jørgensen, Bent

2016-01-01

are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions......We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...

DESIGN NOTE: From nanometre to millimetre: a feasibility study of the combination of scanning probe microscopy and combined optical and x-ray interferometry

Science.gov (United States)

Yacoot, Andrew; Koenders, Ludger

2003-09-01

This feasibility study investigates the potential combination of an x-ray interferometer and optical interferometer as a one-dimensional long range high resolution scanning stage for an atomic force microscope (AFM) in order to overcome the problems of non-linearity associated with conventional AFMs and interferometers. Preliminary results of measurements of the uniformity of the period of a grating used as a transfer standards show variations in period at the nanometre level.

Resent advance in electron linear accelerators

International Nuclear Information System (INIS)

Takeda, Seishi; Tsumori, Kunihiko; Takamuku, Setsuo; Okada, Toichi; Hayashi, Koichiro; Kawanishi, Masaharu

1986-01-01

In recently constructed electron linear accelerators, there has been remarkable advance both in acceleration of a high-current single bunch electron beam for radiation research and in generation of high accelerating gradient for high energy accelerators. The ISIR single bunch electron linear accelerator has been modified an injector to increase a high-current single bunch charge up to 67 nC, which is ten times greater than the single bunch charge expected in early stage of construction. The linear collider projects require a high accelerating gradient of the order of 100 MeV/m in the linear accelerators. High-current and high-gradient linear accelerators make it possible to obtain high-energy electron beam with small-scale linear accelerators. The advance in linear accelerators stimulates the applications of linear accelerators not only to fundamental research of science but also to industrial uses. (author)

Conservative fourth-order time integration of non-linear dynamic systems

DEFF Research Database (Denmark)

Krenk, Steen

2015-01-01

An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...

Higher-order (non-)modularity

DEFF Research Database (Denmark)

Appel, Claus; van Oostrom, Vincent; Simonsen, Jakob Grue

2010-01-01

We show that, contrary to the situation in first-order term rewriting, almost none of the usual properties of rewriting are modular for higher-order rewriting, irrespective of the higher-order rewriting format. We show that for the particular format of simply typed applicative term rewriting...... systems modularity of confluence, normalization, and termination can be recovered by imposing suitable linearity constraints....

Second order sliding mode control for a quadrotor UAV.

Science.gov (United States)

Zheng, En-Hui; Xiong, Jing-Jing; Luo, Ji-Liang

2014-07-01

A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Performance of an Axisymmetric Rocket Based Combined Cycle Engine During Rocket Only Operation Using Linear Regression Analysis

Science.gov (United States)

Smith, Timothy D.; Steffen, Christopher J., Jr.; Yungster, Shaye; Keller, Dennis J.

1998-01-01

The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.

An interconnecting bus power optimization method combining interconnect wire spacing with wire ordering

International Nuclear Information System (INIS)

Zhu Zhang-Ming; Hao Bao-Tian; En Yun-Fei; Yang Yin-Tang; Li Yue-Jin

2011-01-01

On-chip interconnect buses consume tens of percents of dynamic power in a nanometer scale integrated circuit and they will consume more power with the rapid scaling down of technology size and continuously rising clock frequency, therefore it is meaningful to lower the interconnecting bus power in design. In this paper, a simple yet accurate interconnect parasitic capacitance model is presented first and then, based on this model, a novel interconnecting bus optimization method is proposed. Wire spacing is a process for spacing wires for minimum dynamic power, while wire ordering is a process that searches for wire orders that maximally enhance it. The method, i.e., combining wire spacing with wire ordering, focuses on bus dynamic power optimization with a consideration of bus performance requirements. The optimization method is verified based on various nanometer technology parameters, showing that with 50% slack of routing space, 25.71% and 32.65% of power can be saved on average by the proposed optimization method for a global bus and an intermediate bus, respectively, under a 65-nm technology node, compared with 21.78% and 27.68% of power saved on average by uniform spacing technology. The proposed method is especially suitable for computer-aided design of nanometer scale on-chip buses. (interdisciplinary physics and related areas of science and technology)

Optimization of a constrained linear monochromator design for neutral atom beams.

Science.gov (United States)

Kaltenbacher, Thomas

2016-04-01

A focused ground state, neutral atom beam, exploiting its de Broglie wavelength by means of atom optics, is used for neutral atom microscopy imaging. Employing Fresnel zone plates as a lens for these beams is a well established microscopy technique. To date, even for favorable beam source conditions a minimal focus spot size of slightly below 1μm was reached. This limitation is essentially given by the intrinsic spectral purity of the beam in combination with the chromatic aberration of the diffraction based zone plate. Therefore, it is important to enhance the monochromaticity of the beam, enabling a higher spatial resolution, preferably below 100nm. We propose to increase the monochromaticity of a neutral atom beam by means of a so-called linear monochromator set-up - a Fresnel zone plate in combination with a pinhole aperture - in order to gain more than one order of magnitude in spatial resolution. This configuration is known in X-ray microscopy and has proven to be useful, but has not been applied to neutral atom beams. The main result of this work is optimal design parameters based on models for this linear monochromator set-up followed by a second zone plate for focusing. The optimization was performed for minimizing the focal spot size and maximizing the centre line intensity at the detector position for an atom beam simultaneously. The results presented in this work are for, but not limited to, a neutral helium atom beam. Copyright © 2016 Elsevier B.V. All rights reserved.

Ordered mesoporous polyaniline film as a new matrix for enzyme immobilization and biosensor construction

International Nuclear Information System (INIS)

Xu Qin; Zhu Junjie; Hu Xiaoya

2007-01-01

Ordered mesoporous polyaniline film has been fabricated by electrodepositing from the hexagonal lyotropic liquid crystalline (LCC). Horseradish peroxidase (HRP), as a symbol biomolecule, was successfully immobilized on the film to construct a new kind of hydrogen peroxide biosensor. The biosensor combined the advantages of the good conductivity of polyaniline and the higher surface area of the ordered mesoporous film. Polyaniline could be served as a wire to relay electron between HRP and the electrode. The high surface area of the film supplied more sites for HRP immobilization, therefore increased the catalytic activity of the biosensor. The ordered mesoporous character of the film increased the rate of mass transport, which resulted in the improvement of sensor response and linearity. The biosensor displayed excellent electrocatalytic response to the detection of H 2 O 2 in a concentration range from 1.0 μM to 2.0 mM with a detection limit of 0.63 μM. Good reproducibility, stability, high precision, wide linearity and low detection limit were assessed for the biosensor

Observation of the state of the nuclear reactor core by means of non-linear observation algorithms

International Nuclear Information System (INIS)

Maciel Palacio, F.E.; Espana, M.D.

1990-01-01

A combined, variable-adaptive structure, non-linear observer was designed in order to observe the state of the nuclear reactor core, based on the Absolute Stability Theory. The observer was proved under noise and modelling error conditions. Successful results were obtained in the observation of the states in both cases, showing clear improvement in the observation due to the application of adaptive and variable structure ideas. (Author) [es

Linear superposition solutions to nonlinear wave equations

International Nuclear Information System (INIS)

Liu Yu

2012-01-01

The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

Solid phase microextraction of diclofenac using molecularly imprinted polymer sorbent in hollow fiber combined with fiber optic-linear array spectrophotometry

Science.gov (United States)

Pebdani, Arezou Amiri; Shabani, Ali Mohammad Haji; Dadfarnia, Shayessteh; Khodadoust, Saeid

2015-08-01

A simple solid phase microextraction method based on molecularly imprinted polymer sorbent in the hollow fiber (MIP-HF-SPME) combined with fiber optic-linear array spectrophotometer has been applied for the extraction and determination of diclofenac in environmental and biological samples. The effects of different parameters such as pH, times of extraction, type and volume of the organic solvent, stirring rate and donor phase volume on the extraction efficiency of the diclofenac were investigated and optimized. Under the optimal conditions, the calibration graph was linear (r2 = 0.998) in the range of 3.0-85.0 μg L-1 with a detection limit of 0.7 μg L-1 for preconcentration of 25.0 mL of the sample and the relative standard deviation (n = 6) less than 5%. This method was applied successfully for the extraction and determination of diclofenac in different matrices (water, urine and plasma) and accuracy was examined through the recovery experiments.

Simulation of nonlinear benchmarks and sheet metal forming processes using linear and quadratic solid–shell elements combined with advanced anisotropic behavior models

Directory of Open Access Journals (Sweden)

Wang Peng

2016-01-01

Full Text Available A family of prismatic and hexahedral solid‒shell (SHB elements with their linear and quadratic versions is presented in this paper to model thin 3D structures. Based on reduced integration and special treatments to eliminate locking effects and to control spurious zero-energy modes, the SHB solid‒shell elements are capable of modeling most thin 3D structural problems with only a single element layer, while describing accurately the various through-thickness phenomena. In this paper, the SHB elements are combined with fully 3D behavior models, including orthotropic elastic behavior for composite materials and anisotropic plastic behavior for metallic materials, which allows describing the strain/stress state in the thickness direction, in contrast to traditional shell elements. All SHB elements are implemented into ABAQUS using both standard/quasi-static and explicit/dynamic solvers. Several benchmark tests have been conducted, in order to first assess the performance of the SHB elements in quasi-static and dynamic analyses. Then, deep drawing of a hemispherical cup is performed to demonstrate the capabilities of the SHB elements in handling various types of nonlinearities (large displacements and rotations, anisotropic plasticity, and contact. Compared to classical ABAQUS solid and shell elements, the results given by the SHB elements show good agreement with the reference solutions.

Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

KAUST Repository

N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

KAUST Repository

N'Doye, Ibrahima

2015-07-01

This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

Group quantization on configuration space: Gauge symmetries and linear fields

International Nuclear Information System (INIS)

Navarro, M.; Aldaya, V.; Calixto, M.

1997-01-01

A new, configuration-space picture of a formalism of group quantization, the GAQ formalism, is presented in the context of a previous algebraic generalization. This presentation serves to make a comprehensive discussion in which other extensions of the formalism, principally to incorporate gauge symmetries, are developed as well. Both images are combined in order to analyze, in a systematic manner and with complete generality, the case of linear fields (Abelian current groups). To illustrate these developments we particularize them for several fields and, in particular, we carry out the quantization of the Abelian Chern endash Simons models over an arbitrary closed surface in detail. copyright 1997 American Institute of Physics

Distributed fault-tolerant time-varying formation control for high-order linear multi-agent systems with actuator failures.

Science.gov (United States)

Hua, Yongzhao; Dong, Xiwang; Li, Qingdong; Ren, Zhang

2017-11-01

This paper investigates the fault-tolerant time-varying formation control problems for high-order linear multi-agent systems in the presence of actuator failures. Firstly, a fully distributed formation control protocol is presented to compensate for the influences of both bias fault and loss of effectiveness fault. Using the adaptive online updating strategies, no global knowledge about the communication topology is required and the bounds of actuator failures can be unknown. Then an algorithm is proposed to determine the control parameters of the fault-tolerant formation protocol, where the time-varying formation feasible conditions and an approach to expand the feasible formation set are given. Furthermore, the stability of the proposed algorithm is proven based on the Lyapunov-like theory. Finally, two simulation examples are given to demonstrate the effectiveness of the theoretical results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

Science.gov (United States)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

Linear combination of auditory steady-state responses evoked by co-modulated tones

DEFF Research Database (Denmark)

Guérit, François; Marozeau, Jeremy; Epp, Bastian

2017-01-01

Up to medium intensities and in the 80–100-Hz region, the auditory steady-state response (ASSR) to a multi-tone carrier is commonly considered to be a linear sum of the dipoles from each tone specific ASSR generator. Here, this hypothesis was investigated when a unique modulation frequency is used...... for all carrier components. Listeners were presented with a co-modulated dual-frequency carrier (1 and 4 kHz), from which the modulator starting phase Ui of the 1-kHz component was systematically varied. The results support the hypothesis of a linear superposition of the dipoles originating from different...

Explicit fourth-order stiffness representation in non-linear dynamics

DEFF Research Database (Denmark)

Krenk, Steen

2013-01-01

global form of the effective internal force is presented, in which it is represented by its algebraic mean value plus a higher order term in the form of the product of the increment of the tangent stiffness matrix at the interval end-points and the corresponding displacement increment. This explicit...

High linearity 5.2-GHz power amplifier MMIC using CPW structure technology with a linearizer circuit

International Nuclear Information System (INIS)

Wu Chiasong; Lin Tah-Yeong; Wu Hsien-Ming

2010-01-01

A built-in linearizer was applied to improve the linearity in a 5.2-GHz power amplifier microwave monolithic integrated circuit (MMIC), which was undertaken with 0.15-μm AlGaAs/InGaAs D-mode PHEMT technology. The power amplifier (PA) was studied taking into account the linearizer circuit and the coplanar waveguide (CPW) structures. Based on these technologies, the power amplifier, which has a chip size of 1.44 x 1.10 mm 2 , obtained an output power of 13.3 dBm and a power gain of 14 dB in the saturation region. An input third-order intercept point (HP 3 ) of -3 dBm, an output third-order intercept point (OIP 3 ) of 21.1 dBm and a power added efficiency (PAE) of 22% were attained, respectively. Finally, the overall power characterization exhibited high gain and high linearity, which illustrates that the power amplifier has a compact circuit size and exhibits favorable RF characteristics. This power circuit demonstrated high RF characterization and could be used for microwave power circuit applications at 5.2 GHz. (semiconductor integrated circuits)

On combining principal components with Fisher's linear discriminants for supervised learning

NARCIS (Netherlands)

Pechenizkiy, M.; Tsymbal, A.; Puuronen, S.

2006-01-01

"The curse of dimensionality" is pertinent to many learning algorithms, and it denotes the drastic increase of computational complexity and classification error in high dimensions. In this paper, principal component analysis (PCA), parametric feature extraction (FE) based on Fisher’s linear

Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel

Energy Technology Data Exchange (ETDEWEB)

Rebolini, Elisa, E-mail: elisa.rebolini@kjemi.uio.no; Toulouse, Julien, E-mail: julien.toulouse@upmc.fr [Laboratoire de Chimie Théorique, Sorbonne Universités, UPMC Univ Paris 06, CNRS, 4 place Jussieu, F-75005 Paris (France)

2016-03-07

We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT and aims at improving the accuracy of calculations of electronic excitation energies of molecular systems. A detailed derivation of the frequency-dependent second-order Bethe-Salpeter correlation kernel is given using many-body Green-function theory. Preliminary tests of this range-separated TDDFT method are presented for the calculation of excitation energies of the He and Be atoms and small molecules (H{sub 2}, N{sub 2}, CO{sub 2}, H{sub 2}CO, and C{sub 2}H{sub 4}). The results suggest that the addition of the long-range second-order Bethe-Salpeter correlation kernel overall slightly improves the excitation energies.

Development of a high-order finite volume method with multiblock partition techniques

Directory of Open Access Journals (Sweden)

E. M. Lemos

2012-03-01

Full Text Available This work deals with a new numerical methodology to solve the Navier-Stokes equations based on a finite volume method applied to structured meshes with co-located grids. High-order schemes used to approximate advective, diffusive and non-linear terms, connected with multiblock partition techniques, are the main contributions of this paper. Combination of these two techniques resulted in a computer code that involves high accuracy due the high-order schemes and great flexibility to generate locally refined meshes based on the multiblock approach. This computer code has been able to obtain results with higher or equal accuracy in comparison with results obtained using classical procedures, with considerably less computational effort.

Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay

Directory of Open Access Journals (Sweden)

M. Mallika Arjunan

2014-01-01

Full Text Available In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii's fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.

Development of a sub-nanometer positioning device: combining a new linear motor with linear motion ball guide ways

International Nuclear Information System (INIS)

Otsuka, J; Tanaka, T; Masuda, I

2010-01-01

A new type of linear motor described in this note has some advantages compared with conventional motors. The attractive magnetic force between the stator (permanent magnets) and mover (armature) is diminished almost to zero. The efficiency is better because the magnetic flux leakage is very small, the size of motor is smaller and detent (force ripple) is smaller than for conventional motors. Therefore, we think that this motor is greatly suitable for ultra-precision positioning as an actuator. An ultra-precision positioning device using this motor and linear motion ball guide ways is newly developed by making the device very rigid and using a suitable control method. Moreover, the positioning performance is evaluated by a positioning resolution, and deviation and dispersion errors. As a result of repeated step response tests, the positioning resolution is 0.3 nm, with the deviation error and dispersion error (3σ) being sub-nanometer. Consequently, the positioning device achieves sub-nanometer positioning. (technical design note)

First and second order operator splitting methods for the phase field crystal equation

International Nuclear Information System (INIS)

Lee, Hyun Geun; Shin, Jaemin; Lee, June-Yub

2015-01-01

In this paper, we present operator splitting methods for solving the phase field crystal equation which is a model for the microstructural evolution of two-phase systems on atomic length and diffusive time scales. A core idea of the methods is to decompose the original equation into linear and nonlinear subequations, in which the linear subequation has a closed-form solution in the Fourier space. We apply a nonlinear Newton-type iterative method to solve the nonlinear subequation at the implicit time level and thus a considerably large time step can be used. By combining these subequations, we achieve the first- and second-order accuracy in time. We present numerical experiments to show the accuracy and efficiency of the proposed methods

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization

Science.gov (United States)

Li, Zukui; Ding, Ran; Floudas, Christodoulos A.

2011-01-01

Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. PMID:21935263

Single-order-parameter description of glass-forming liquids

DEFF Research Database (Denmark)

Ellegaard, Niels Langager; Christensen, Tage Emil; Christiansen, Peder Voetmann

2007-01-01

Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear...... dynamic Prigogine-Defay ratio" with the property that if this ratio is unity at one frequency, then it is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter which may be nonexponential...

Direction of Effects in Multiple Linear Regression Models.

Science.gov (United States)

Wiedermann, Wolfgang; von Eye, Alexander

2015-01-01

Previous studies analyzed asymmetric properties of the Pearson correlation coefficient using higher than second order moments. These asymmetric properties can be used to determine the direction of dependence in a linear regression setting (i.e., establish which of two variables is more likely to be on the outcome side) within the framework of cross-sectional observational data. Extant approaches are restricted to the bivariate regression case. The present contribution extends the direction of dependence methodology to a multiple linear regression setting by analyzing distributional properties of residuals of competing multiple regression models. It is shown that, under certain conditions, the third central moments of estimated regression residuals can be used to decide upon direction of effects. In addition, three different approaches for statistical inference are discussed: a combined D'Agostino normality test, a skewness difference test, and a bootstrap difference test. Type I error and power of the procedures are assessed using Monte Carlo simulations, and an empirical example is provided for illustrative purposes. In the discussion, issues concerning the quality of psychological data, possible extensions of the proposed methods to the fourth central moment of regression residuals, and potential applications are addressed.

Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.

Science.gov (United States)

Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad

2016-02-01

In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.

Combining linear polarization spectroscopy and the Representative Layer Theory to measure the Beer-Lambert law absorbance of highly scattering materials.

Science.gov (United States)

Gobrecht, Alexia; Bendoula, Ryad; Roger, Jean-Michel; Bellon-Maurel, Véronique

2015-01-01

Visible and Near Infrared (Vis-NIR) Spectroscopy is a powerful non destructive analytical method used to analyze major compounds in bulk materials and products and requiring no sample preparation. It is widely used in routine analysis and also in-line in industries, in-vivo with biomedical applications or in-field for agricultural and environmental applications. However, highly scattering samples subvert Beer-Lambert law's linear relationship between spectral absorbance and the concentrations. Instead of spectral pre-processing, which is commonly used by Vis-NIR spectroscopists to mitigate the scattering effect, we put forward an optical method, based on Polarized Light Spectroscopy to improve the absorbance signal measurement on highly scattering samples. This method selects part of the signal which is less impacted by scattering. The resulted signal is combined in the Absorption/Remission function defined in Dahm's Representative Layer Theory to compute an absorbance signal fulfilling Beer-Lambert's law, i.e. being linearly related to concentration of the chemicals composing the sample. The underpinning theories have been experimentally evaluated on scattering samples in liquid form and in powdered form. The method produced more accurate spectra and the Pearson's coefficient assessing the linearity between the absorbance spectra and the concentration of the added dye improved from 0.94 to 0.99 for liquid samples and 0.84-0.97 for powdered samples. Copyright © 2014 Elsevier B.V. All rights reserved.

Fitting and forecasting coupled dark energy in the non-linear regime

Energy Technology Data Exchange (ETDEWEB)

Casas, Santiago; Amendola, Luca; Pettorino, Valeria; Vollmer, Adrian [Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, Heidelberg, 69120 Germany (Germany); Baldi, Marco, E-mail: casas@thphys.uni-heidelberg.de, E-mail: l.amendola@thphys.uni-heidelberg.de, E-mail: mail@marcobaldi.it, E-mail: v.pettorino@thphys.uni-heidelberg.de, E-mail: vollmer@thphys.uni-heidelberg.de [Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Università di Bologna, viale Berti Pichat, 6/2, Bologna, I-40127 Italy (Italy)

2016-01-01

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β{sup 2}, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.

Fitting and forecasting coupled dark energy in the non-linear regime

International Nuclear Information System (INIS)

Casas, Santiago; Amendola, Luca; Pettorino, Valeria; Vollmer, Adrian; Baldi, Marco

2016-01-01

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used to test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β 2 , with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications

Structured Control of Affine Linear Parameter Varying Systems

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2011-01-01

This paper presents a new procedure to design structured controllers for discrete-time affine linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, fixed order output feedback, simultaneous plant-control design, among others. A parametervarying...... non-convex condition for an upper bound on the induced L2-norm performance is solved by an iterative linear matrix inequalities (LMI) optimization algorithm. Numerical examples demostrate the effectiveness of the proposed approach....

Age related neuromuscular changes in sEMG of m. Tibialis Anterior using higher order statistics (Gaussianity & linearity test).

Science.gov (United States)

Siddiqi, Ariba; Arjunan, Sridhar P; Kumar, Dinesh K

2016-08-01

Age-associated changes in the surface electromyogram (sEMG) of Tibialis Anterior (TA) muscle can be attributable to neuromuscular alterations that precede strength loss. We have used our sEMG model of the Tibialis Anterior to interpret the age-related changes and compared with the experimental sEMG. Eighteen young (20-30 years) and 18 older (60-85 years) performed isometric dorsiflexion at 6 different percentage levels of maximum voluntary contractions (MVC), and their sEMG from the TA muscle was recorded. Six different age-related changes in the neuromuscular system were simulated using the sEMG model at the same MVCs as the experiment. The maximal power of the spectrum, Gaussianity and Linearity Test Statistics were computed from the simulated and experimental sEMG. A correlation analysis at α=0.05 was performed between the simulated and experimental age-related change in the sEMG features. The results show the loss in motor units was distinguished by the Gaussianity and Linearity test statistics; while the maximal power of the PSD distinguished between the muscular factors. The simulated condition of 40% loss of motor units with halved the number of fast fibers best correlated with the age-related change observed in the experimental sEMG higher order statistical features. The simulated aging condition found by this study corresponds with the moderate motor unit remodelling and negligible strength loss reported in literature for the cohorts aged 60-70 years.

RANSAC approach for automated registration of terrestrial laser scans using linear features

Directory of Open Access Journals (Sweden)

K. Al-Durgham

2013-10-01

Full Text Available The registration process of terrestrial laser scans (TLS targets the problem of how to combine several laser scans in order to attain better information about features than what could be obtained through single scan. The main goal of the registration process is to estimate the parameters which determine geometrical variation between the origins of datasets collected from different locations. Scale, shifts, and rotation parameters are usually used to describe such variation. This paper presents a framework for the registration of overlapping terrestrial laser scans by establishing an automatic matching strategy that uses 3D linear features. More specifically, invariant separation characteristics between 3D linear features extracted from laser scans will be used to establish hypothesized conjugate linear features between the laser scans. These candidate matches are then used to geo-reference scans relative to a common reference frame. The registration workflow simulates the well-known RANndom Sample Consensus method (RANSAC for determining the registration parameters, whereas the iterative closest projected point (ICPP is utilized to determine the most probable solution of the transformation parameters from several solutions. The experimental results prove that the proposed methodology can be used for the automatic registration of terrestrial laser scans using linear features.

Nonautonomous linear system of the terrestrial carbon cycle

Science.gov (United States)

Luo, Y.

2012-12-01

Carbon cycle has been studied by uses of observation through various networks, field and laboratory experiments, and simulation models. Much less has been done on theoretical thinking and analysis to understand fundament properties of carbon cycle and then guide observatory, experimental, and modeling research. This presentation is to explore what would be the theoretical properties of terrestrial carbon cycle and how those properties can be used to make observatory, experimental, and modeling research more effective. Thousands of published data sets from litter decomposition and soil incubation studies almost all indicate that decay processes of litter and soil organic carbon can be well described by first order differential equations with one or more pools. Carbon pool dynamics in plants and soil after disturbances (e.g., wildfire, clear-cut of forests, and plows of soil for cropping) and during natural recovery or ecosystem restoration also exhibit characteristics of first-order linear systems. Thus, numerous lines of empirical evidence indicate that the terrestrial carbon cycle can be adequately described as a nonautonomous linear system. The linearity reflects the nature of the carbon cycle that carbon, once fixed by photosynthesis, is linearly transferred among pools within an ecosystem. The linear carbon transfer, however, is modified by nonlinear functions of external forcing variables. In addition, photosynthetic carbon influx is also nonlinearly influenced by external variables. This nonautonomous linear system can be mathematically expressed by a first-order linear ordinary matrix equation. We have recently used this theoretical property of terrestrial carbon cycle to develop a semi-analytic solution of spinup. The new methods have been applied to five global land models, including NCAR's CLM and CABLE models and can computationally accelerate spinup by two orders of magnitude. We also use this theoretical property to develop an analytic framework to

Forecast combinations

OpenAIRE

Aiolfi, Marco; Capistrán, Carlos; Timmermann, Allan

2010-01-01

We consider combinations of subjective survey forecasts and model-based forecasts from linear and non-linear univariate specifications as well as multivariate factor-augmented models. Empirical results suggest that a simple equal-weighted average of survey forecasts outperform the best model-based forecasts for a majority of macroeconomic variables and forecast horizons. Additional improvements can in some cases be gained by using a simple equal-weighted average of survey and model-based fore...

On Solving Linear Recurrences

Science.gov (United States)

Dobbs, David E.

2013-01-01

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

Estimation of ibuprofen and famotidine in tablets by second order derivative spectrophotometery method

Directory of Open Access Journals (Sweden)

Dimal A. Shah

2017-02-01

Full Text Available A simple and accurate method for the analysis of ibuprofen (IBU and famotidine (FAM in their combined dosage form was developed using second order derivative spectrophotometery. IBU and FAM were quantified using second derivative responses at 272.8 nm and 290 nm in the spectra of their solutions in methanol. The calibration curves were linear in the concentration range of 100–600 μg/mL for IBU and 5–25 μg/mL for FAM. The method was validated and found to be accurate and precise. Developed method was successfully applied for the estimation of IBU and FAM in their combined dosage form.

Displacement measurement system for linear array detector

International Nuclear Information System (INIS)

Zhang Pengchong; Chen Ziyu; Shen Ji

2011-01-01

It presents a set of linear displacement measurement system based on encoder. The system includes displacement encoders, optical lens and read out circuit. Displacement read out unit includes linear CCD and its drive circuit, two amplifier circuits, second order Butterworth low-pass filter and the binarization circuit. The coding way is introduced, and various parts of the experimental signal waveforms are given, and finally a linear experimental test results are given. The experimental results are satisfactory. (authors)

Simulation of a medical linear accelerator for teaching purposes.

Science.gov (United States)

Anderson, Rhys; Lamey, Michael; MacPherson, Miller; Carlone, Marco

2015-05-08

Simulation software for medical linear accelerators that can be used in a teaching environment was developed. The components of linear accelerators were modeled to first order accuracy using analytical expressions taken from the literature. The expressions used constants that were empirically set such that realistic response could be expected. These expressions were programmed in a MATLAB environment with a graphical user interface in order to produce an environment similar to that of linear accelerator service mode. The program was evaluated in a systematic fashion, where parameters affecting the clinical properties of medical linear accelerator beams were adjusted independently, and the effects on beam energy and dose rate recorded. These results confirmed that beam tuning adjustments could be simulated in a simple environment. Further, adjustment of service parameters over a large range was possible, and this allows the demonstration of linear accelerator physics in an environment accessible to both medical physicists and linear accelerator service engineers. In conclusion, a software tool, named SIMAC, was developed to improve the teaching of linear accelerator physics in a simulated environment. SIMAC performed in a similar manner to medical linear accelerators. The authors hope that this tool will be valuable as a teaching tool for medical physicists and linear accelerator service engineers.

Hamiltonian structure of linearly extended Virasoro algebra

International Nuclear Information System (INIS)

Arakelyan, T.A.; Savvidi, G.K.

1991-01-01

The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order

Classical higher-order processes

DEFF Research Database (Denmark)

Montesi, Fabrizio

2017-01-01

Classical Processes (CP) is a calculus where the proof theory of classical linear logic types processes à la Π-calculus, building on a Curry-Howard correspondence between session types and linear propositions. We contribute to this research line by extending CP with process mobility, inspired...... by the Higher-Order Π-calculus. The key to our calculus is that sequents are asymmetric: one side types sessions as in CP and the other types process variables, which can be instantiated with process values. The controlled interaction between the two sides ensures that process variables can be used at will......, but always respecting the linear usage of sessions expected by the environment....

Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

International Nuclear Information System (INIS)

Hwang, Jai-chan; Noh, Hyerim

2005-01-01

We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon

Analysis of blood pressure signal in patients with different ventricular ejection fraction using linear and non-linear methods.

Science.gov (United States)

Arcentales, Andres; Rivera, Patricio; Caminal, Pere; Voss, Andreas; Bayes-Genis, Antonio; Giraldo, Beatriz F

2016-08-01

Changes in the left ventricle function produce alternans in the hemodynamic and electric behavior of the cardiovascular system. A total of 49 cardiomyopathy patients have been studied based on the blood pressure signal (BP), and were classified according to the left ventricular ejection fraction (LVEF) in low risk (LR: LVEF>35%, 17 patients) and high risk (HR: LVEF≤35, 32 patients) groups. We propose to characterize these patients using a linear and a nonlinear methods, based on the spectral estimation and the recurrence plot, respectively. From BP signal, we extracted each systolic time interval (STI), upward systolic slope (BPsl), and the difference between systolic and diastolic BP, defined as pulse pressure (PP). After, the best subset of parameters were obtained through the sequential feature selection (SFS) method. According to the results, the best classification was obtained using a combination of linear and nonlinear features from STI and PP parameters. For STI, the best combination was obtained considering the frequency peak and the diagonal structures of RP, with an area under the curve (AUC) of 79%. The same results were obtained when comparing PP values. Consequently, the use of combined linear and nonlinear parameters could improve the risk stratification of cardiomyopathy patients.

Warehouse order-picking process. Order-picker routing problem

Directory of Open Access Journals (Sweden)

E. V. Korobkov

2015-01-01

Full Text Available This article continues “Warehouse order-picking process” cycle and describes order-picker routing sub-problem of a warehouse order-picking process. It draws analogies between the orderpickers’ routing problem and traveling salesman’s problem, shows differences between the standard problem statement of a traveling salesman and routing problem of warehouse orderpickers, and gives the particular Steiner’s problem statement of a traveling salesman.Warehouse layout with a typical order is represented by a graph, with some its vertices corresponding to mandatory order-picker’s visits and some other ones being noncompulsory. The paper describes an optimal Ratliff-Rosenthal algorithm to solve order-picker’s routing problem for the single-block warehouses, i.e. warehouses with only two crossing aisles, defines seven equivalent classes of partial routing sub-graphs and five transitions used to have an optimal routing sub-graph of a order-picker. An extension of optimal Ratliff-Rosenthal order-picker routing algorithm for multi-block warehouses is presented and also reasons for using the routing heuristics instead of exact optimal algorithms are given. The paper offers algorithmic description of the following seven routing heuristics: S-shaped, return, midpoint, largest gap, aisle-by-aisle, composite, and combined as well as modification of combined heuristics. The comparison of orderpicker routing heuristics for one- and two-block warehouses is to be described in the next article of the “Warehouse order-picking process” cycle.

Solid phase microextraction of diclofenac using molecularly imprinted polymer sorbent in hollow fiber combined with fiber optic-linear array spectrophotometry.

Science.gov (United States)

Pebdani, Arezou Amiri; Shabani, Ali Mohammad Haji; Dadfarnia, Shayessteh; Khodadoust, Saeid

2015-08-05

A simple solid phase microextraction method based on molecularly imprinted polymer sorbent in the hollow fiber (MIP-HF-SPME) combined with fiber optic-linear array spectrophotometer has been applied for the extraction and determination of diclofenac in environmental and biological samples. The effects of different parameters such as pH, times of extraction, type and volume of the organic solvent, stirring rate and donor phase volume on the extraction efficiency of the diclofenac were investigated and optimized. Under the optimal conditions, the calibration graph was linear (r(2)=0.998) in the range of 3.0-85.0 μg L(-1) with a detection limit of 0.7 μg L(-1) for preconcentration of 25.0 mL of the sample and the relative standard deviation (n=6) less than 5%. This method was applied successfully for the extraction and determination of diclofenac in different matrices (water, urine and plasma) and accuracy was examined through the recovery experiments. Copyright © 2015 Elsevier B.V. All rights reserved.

Linear Synchronous Motor Repeatability Tests

International Nuclear Information System (INIS)

Ward, C.R.

2002-01-01

A cart system using linear synchronous motors was being considered for the Plutonium Immobilization Plant (PIP). One of the applications in the PIP was the movement of a stack of furnace trays, filled with the waste form (pucks) from a stacking/unstacking station to several bottom loaded furnaces. A system was ordered to perform this function in the PIP Ceramic Prototype Test Facility (CPTF). This system was installed and started up in SRTC prior to being installed in the CPTF. The PIP was suspended and then canceled after the linear synchronous motor system was started up. This system was used to determine repeatability of a linear synchronous motor cart system for the Modern Pit Facility

Linear devices in combined high-level radiation environments

International Nuclear Information System (INIS)

van Vonno, N.W.

1987-01-01

The design of precision analog integrated circuits for use in combined high-level radiation environments has traditionally been on a full-custom basis. The use of semicustom design methods has become prevalent in digital devices, with standard cell libraries and gate arrays readily available from multiple vendors. This paper addresses the application of semicustom design techniques to analog parts. In all cases the emphasis is on bipolar technology, since this provides an optimal combination of precision and radiation hardness. A mixed mode analog/digital (A/D) cell family for implementing semicustom designs is described, together with the fabrication process used. Specific processing and design methods are used to provide circuit hardness against neutron, total gamma dose, and transient gamma environments. Semicustom mixed analog/digital design is seen as an appropriate methodology for implementation of medium-performance mixed mode functions for radiation-hardened applications. This leads to trade-offs in process complexity and performance. Full custom design remains necessary for demanding applications such as high-speed A/D conversion and associated sample/hold functions. An A/D cell family optimized for hardness is described, together with the bipolar process used to implement it

Linear and Non-Linear Response of Liquid and Solid Particles to Energetic Radiation

Science.gov (United States)

1991-03-11

but with the beam left within and upon the surface of a spherical particle illuminat - circularly polarized. (The fifth-order corrected, linearly po...specific situation. Figure 1 shows a schematic of the imaging system under consideration. The incident illuminat - ing radiation is generated from a pulsed

Phase and fringe order determination in wavelength scanning interferometry.

Science.gov (United States)

Moschetti, Giuseppe; Forbes, Alistair; Leach, Richard K; Jiang, Xiang; O'Connor, Daniel

2016-04-18

A method to obtain unambiguous surface height measurements using wavelength scanning interferometry with an improved repeatability, comparable to that obtainable using phase shifting interferometry, is reported. Rather than determining the conventional fringe frequency-derived z height directly, the method uses the frequency to resolve the fringe order ambiguity, and combine this information with the more accurate and repeatable fringe phase derived z height. A theoretical model to evaluate the method's performance in the presence of additive noise is derived and shown to be in good agreement with experiments. The measurement repeatability is improved by a factor of ten over that achieved when using frequency information alone, reaching the sub-nanometre range. Moreover, the z-axis non-linearity (bleed-through or ripple error) is reduced by a factor of ten. These order of magnitude improvements in measurement performance are demonstrated through a number of practical measurement examples.

Non-Linear Dynamics of Saturn's Rings

Science.gov (United States)

Esposito, L. W.

2016-12-01

Non-linear processes can explain why Saturn's rings are so active and dynamic. Ring systems differ from simple linear systems in two significant ways: 1. They are systems of granular material: where particle-to-particle collisions dominate; thus a kinetic, not a fluid description needed. Stresses are strikingly inhomogeneous and fluctuations are large compared to equilibrium. 2. They are strongly forced by resonances: which drive a non-linear response, that push the system across thresholds that lead to persistent states. Some of this non-linearity is captured in a simple Predator-Prey Model: Periodic forcing from the moon causes streamline crowding; This damps the relative velocity. About a quarter phase later, the aggregates stir the system to higher relative velocity and the limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average. Summary of Halo Results: A predator-prey model for ring dynamics produces transient structures like `straw' that can explain the halo morphology and spectroscopy: Cyclic velocity changes cause perturbed regions to reach higher collision speeds at some orbital phases, which preferentially removes small regolith particles; surrounding particles diffuse back too slowly to erase the effect: this gives the halo morphology; this requires energetic collisions (v ≈ 10m/sec, with throw distances about 200km, implying objects of scale R ≈ 20km).Transform to Duffing Eqn : With the coordinate transformation, z = M2/3, the Predator-Prey equations can be combined to form a single second-order differential equation with harmonic resonance forcing.Ring dynamics and history implications: Moon-triggered clumping explains both small and large particles at resonances. We calculate the stationary size distribution using a cell-to-cell mapping procedure that converts the phase-plane trajectories to a Markov chain. Approximating it as an asymmetric random walk with reflecting boundaries

Application of Mass Lumped Higher Order Finite Elements

International Nuclear Information System (INIS)

J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau

2005-01-01

There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied

A combined linear optimisation methodology for water resources allocation in Alfeios River Basin (Greece) under uncertain and vague system conditions

Science.gov (United States)

Bekri, Eleni; Yannopoulos, Panayotis; Disse, Markus

2013-04-01

In the present study, a combined linear programming methodology, based on Li et al. (2010) and Bekri et al. (2012), is employed for optimizing water allocation under uncertain system conditions in the Alfeios River Basin, in Greece. The Alfeios River is a water resources system of great natural, ecological, social and economic importance for Western Greece, since it has the longest and highest flow rate watercourse in the Peloponnisos region. Moreover, the river basin was exposed in the last decades to a plethora of environmental stresses (e.g. hydrogeological alterations, intensively irrigated agriculture, surface and groundwater overexploitation and infrastructure developments), resulting in the degradation of its quantitative and qualitative characteristics. As in most Mediterranean countries, water resource management in Alfeios River Basin has been focused up to now on an essentially supply-driven approach. It is still characterized by a lack of effective operational strategies. Authority responsibility relationships are fragmented, and law enforcement and policy implementation are weak. The present regulated water allocation puzzle entails a mixture of hydropower generation, irrigation, drinking water supply and recreational activities. Under these conditions its water resources management is characterised by high uncertainty and by vague and imprecise data. The considered methodology has been developed in order to deal with uncertainties expressed as either probability distributions, or/and fuzzy boundary intervals, derived by associated α-cut levels. In this framework a set of deterministic submodels is studied through linear programming. The ad hoc water resources management and alternative management patterns in an Alfeios subbasin are analyzed and evaluated under various scenarios, using the above mentioned methodology, aiming to promote a sustainable and equitable water management. Li, Y.P., Huang, G.H. and S.L., Nie, (2010), Planning water resources

A Type System for the Vectorial Aspect of the Linear-Algebraic Lambda-Calculus

Directory of Open Access Journals (Sweden)

Pablo Arrighi

2012-07-01

Full Text Available We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms resulting from the reduction of programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We show that the resulting typed lambda-calculus is strongly normalizing and features a weak subject-reduction.

Higher-order techniques for some problems of nonlinear control

Directory of Open Access Journals (Sweden)

Sarychev Andrey V.

2002-01-01

Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.

A High-Order, Linear Time-Invariant Model for Application to Higher Harmonic Control and Flight Control System Interaction

Science.gov (United States)

Cheng, Rendy P.; Tischler, Mark B.; Celi, Roberto

2006-01-01

This research describes a new methodology for the extraction of a high-order, linear time invariant model, which allows the periodicity of the helicopter response to be accurately captured. This model provides the needed level of dynamic fidelity to permit an analysis and optimization of the AFCS and HHC algorithms. The key results of this study indicate that the closed-loop HHC system has little influence on the AFCS or on the vehicle handling qualities, which indicates that the AFCS does not need modification to work with the HHC system. However, the results show that the vibration response to maneuvers must be considered during the HHC design process, and this leads to much higher required HHC loop crossover frequencies. This research also demonstrates that the transient vibration responses during maneuvers can be reduced by optimizing the closed-loop higher harmonic control algorithm using conventional control system analyses.

Robust Adaptive Stabilization of Linear Time-Invariant Dynamic Systems by Using Fractional-Order Holds and Multirate Sampling Controls

Directory of Open Access Journals (Sweden)

S. Alonso-Quesada

2010-01-01

Full Text Available This paper presents a strategy for designing a robust discrete-time adaptive controller for stabilizing linear time-invariant (LTI continuous-time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced-order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast-sampled control signal. A suitable on-line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy.

Miniature linear cooler development

International Nuclear Information System (INIS)

Pruitt, G.R.

1993-01-01

An overview is presented of the status of a family of miniature linear coolers currently under development by Hughes Aircraft Co. for use in hand held, volume limited or power limited infrared applications. These coolers, representing the latest additions to the Hughes family of TOP trademark [twin-opposed piston] linear coolers, have been fabricated and tested in three different configurations. Each configuration is designed to utilize a common compressor assembly resulting in reduced manufacturing costs. The baseline compressor has been integrated with two different expander configurations and has been operated with two different levels of input power. These various configuration combinations offer a wide range of performance and interface characteristics which may be tailored to applications requiring limited power and size without significantly compromising cooler capacity or cooldown characteristics. Key cooler characteristics and test data are summarized for three combinations of cooler configurations which are representative of the versatility of this linear cooler design. Configurations reviewed include the shortened coldfinger [1.50 to 1.75 inches long], limited input power [less than 17 Watts] for low power availability applications; the shortened coldfinger with higher input power for lightweight, higher performance applications; and coldfingers compatible with DoD 0.4 Watt Common Module coolers for wider range retrofit capability. Typical weight of these miniature linear coolers is less than 500 grams for the compressor, expander and interconnecting transfer line. Cooling capacity at 80K at room ambient conditions ranges from 400 mW to greater than 550 mW. Steady state power requirements for maintaining a heat load of 150 mW at 80K has been shown to be less than 8 Watts. Ongoing reliability growth testing is summarized including a review of the latest test article results

Progress on $e^{+}e^{-}$ linear colliders

CERN Multimedia

CERN. Geneva. Audiovisual Unit; Siemann, Peter

2002-01-01

Physics issues. The physics program will be reviewed for e+e- linear colliders in the TeV energy range. At these prospective facilities central issues of particle physics can be addressed, the problem of mass, unification and structure of space-time. In this context the two lectures will focus on analyses of the Higgs mechanism, supersymmetry and extra space dimensions. Moreover, high-precision studies of the top-quark and the gauge boson sector will be discussed. Combined with LHC results, a comprehensive picture can be developed of physics at the electroweak scale and beyond. Designs and technologies (R. Siemann - 29, 30, 31 May) The physics and technologies of high energy linear colliders will be reviewed. Fundamental concepts of linear colliders will be introduced. They will be discussed in: the context of the Stanford Linear Collider where many ideas changed and new ones were developed in response to operational experience. the requirements for future linear colliders. The different approaches for reac...

Linear relations between leaf mass per area (LMA) and seasonal climate discovered through Linear Manifold Clustering (LMC)

Science.gov (United States)

Kiang, N. Y.; Haralick, R. M.; Diky, A.; Kattge, J.; Su, X.

2016-12-01

Leaf mass per area (LMA) is a critical variable in plant carbon allocation, correlates with leaf activity traits (photosynthetic activity, respiration), and is a controller of litterfall mass and hence carbon substrate for soil biogeochemistry. Recent advances in understanding the leaf economics spectrum (LES) show that LMA has a strong correlation with leaf life span, a trait that reflects ecological strategy, whereas physiological traits that control leaf activity scale with each other when mass-normalized (Osnas et al., 2013). These functional relations help reduce the number of independent variables in quantifying leaf traits. However, LMA is an independent variable that remains a challenge to specify in dynamic global vegetation models (DGVMs), when vegetation types are classified into a limited number of plant functional types (PFTs) without clear mechanistic drivers for LMA. LMA can range orders of magnitude across plant species, as well as vary within a single plant, both vertically and seasonally. As climate relations in combination with alternative ecological strategies have yet to be well identified for LMA, we have assembled 22,000 records of LMA spanning 0.004 - 33 mg/m2 from the numerous contributors to the TRY database (Kattge et al., 2011), with observations distributed over several climate zones and plant functional categories (growth form, leaf type, phenology). We present linear relations between LMA and climate variables, including seasonal temperature, precipitation, and radiation, as derived through Linear Manifold Clustering (LMC). LMC is a stochastic search technique for identifying linear dependencies between variables in high dimensional space. We identify a set of parsimonious classes of LMA-climate groups based on a metric of minimum description to identify structure in the data set, akin to data compression. The relations in each group are compared to Köppen-Geiger climate classes, with some groups revealing continuous linear relations

Linear morphoea follows Blaschko's lines.

Science.gov (United States)

Weibel, L; Harper, J I

2008-07-01

The aetiology of morphoea (or localized scleroderma) remains unknown. It has previously been suggested that lesions of linear morphoea may follow Blaschko's lines and thus reflect an embryological development. However, the distribution of linear morphoea has never been accurately evaluated. We aimed to identify common patterns of clinical presentation in children with linear morphoea and to establish whether linear morphoea follows the lines of Blaschko. A retrospective chart review of 65 children with linear morphoea was performed. According to clinical photographs the skin lesions of these patients were plotted on to standardized head and body charts. With the aid of Adobe Illustrator a final figure was produced including an overlay of all individual lesions which was used for comparison with the published lines of Blaschko. Thirty-four (53%) patients had the en coup de sabre subtype, 27 (41%) presented with linear morphoea on the trunk and/or limbs and four (6%) children had a combination of the two. In 55 (85%) children the skin lesions were confined to one side of the body, showing no preference for either left or right side. On comparing the overlays of all body and head lesions with the original lines of Blaschko there was an excellent correlation. Our data indicate that linear morphoea follows the lines of Blaschko. We hypothesize that in patients with linear morphoea susceptible cells are present in a mosaic state and that exposure to some trigger factor may result in the development of this condition.

Linear zonal atmospheric prediction for adaptive optics

Science.gov (United States)

McGuire, Patrick C.; Rhoadarmer, Troy A.; Coy, Hanna A.; Angel, J. Roger P.; Lloyd-Hart, Michael

2000-07-01

We compare linear zonal predictors of atmospheric turbulence for adaptive optics. Zonal prediction has the possible advantage of being able to interpret and utilize wind-velocity information from the wavefront sensor better than modal prediction. For simulated open-loop atmospheric data for a 2- meter 16-subaperture AO telescope with 5 millisecond prediction and a lookback of 4 slope-vectors, we find that Widrow-Hoff Delta-Rule training of linear nets and Back- Propagation training of non-linear multilayer neural networks is quite slow, getting stuck on plateaus or in local minima. Recursive Least Squares training of linear predictors is two orders of magnitude faster and it also converges to the solution with global minimum error. We have successfully implemented Amari's Adaptive Natural Gradient Learning (ANGL) technique for a linear zonal predictor, which premultiplies the Delta-Rule gradients with a matrix that orthogonalizes the parameter space and speeds up the training by two orders of magnitude, like the Recursive Least Squares predictor. This shows that the simple Widrow-Hoff Delta-Rule's slow convergence is not a fluke. In the case of bright guidestars, the ANGL, RLS, and standard matrix-inversion least-squares (MILS) algorithms all converge to the same global minimum linear total phase error (approximately 0.18 rad2), which is only approximately 5% higher than the spatial phase error (approximately 0.17 rad2), and is approximately 33% lower than the total 'naive' phase error without prediction (approximately 0.27 rad2). ANGL can, in principle, also be extended to make non-linear neural network training feasible for these large networks, with the potential to lower the predictor error below the linear predictor error. We will soon scale our linear work to the approximately 108-subaperture MMT AO system, both with simulations and real wavefront sensor data from prime focus.

Linear and nonlinear auditory response properties of interneurons in a high-order avian vocal motor nucleus during wakefulness.

Science.gov (United States)

Raksin, Jonathan N; Glaze, Christopher M; Smith, Sarah; Schmidt, Marc F

2012-04-01

Motor-related forebrain areas in higher vertebrates also show responses to passively presented sensory stimuli. However, sensory tuning properties in these areas, especially during wakefulness, and their relation to perception, are poorly understood. In the avian song system, HVC (proper name) is a vocal-motor structure with auditory responses well defined under anesthesia but poorly characterized during wakefulness. We used a large set of stimuli including the bird's own song (BOS) and many conspecific songs (CON) to characterize auditory tuning properties in putative interneurons (HVC(IN)) during wakefulness. Our findings suggest that HVC contains a diversity of responses that vary in overall excitability to auditory stimuli, as well as bias in spike rate increases to BOS over CON. We used statistical tests to classify cells in order to further probe auditory responses, yielding one-third of neurons that were either unresponsive or suppressed and two-thirds with excitatory responses to one or more stimuli. A subset of excitatory neurons were tuned exclusively to BOS and showed very low linearity as measured by spectrotemporal receptive field analysis (STRF). The remaining excitatory neurons responded well to CON stimuli, although many cells still expressed a bias toward BOS. These findings suggest the concurrent presence of a nonlinear and a linear component to responses in HVC, even within the same neuron. These characteristics are consistent with perceptual deficits in distinguishing BOS from CON stimuli following lesions of HVC and other song nuclei and suggest mirror neuronlike qualities in which "self" (here BOS) is used as a referent to judge "other" (here CON).

H∞ /H2 model reduction through dilated linear matrix inequalities

DEFF Research Database (Denmark)

Adegas, Fabiano Daher; Stoustrup, Jakob

2012-01-01

This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field{N}$. Arb......This paper presents sufficient dilated linear matrix inequalities (LMI) conditions to the $H_{infty}$ and $H_{2}$ model reduction problem. A special structure of the auxiliary (slack) variables allows the original model of order $n$ to be reduced to an order $r=n/s$ where $n,r,s in field...

Design of Linear-Quadratic-Regulator for a CSTR process

Science.gov (United States)

Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.

2017-11-01

This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.

Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms

Science.gov (United States)

Healy, John J.

2018-01-01

The linear canonical transforms (LCTs) are a parameterised group of linear integral transforms. The LCTs encompass a number of well-known transformations as special cases, including the Fourier transform, fractional Fourier transform, and the Fresnel integral. They relate the scalar wave fields at the input and output of systems composed of thin lenses and free space, along with other quadratic phase systems. In this paper, we perform a systematic search of all algorithms based on up to five stages of magnification, chirp multiplication and Fourier transforms. Based on that search, we propose a novel algorithm, for which we present numerical results. We compare the sampling requirements of three algorithms. Finally, we discuss some issues surrounding the composition of discrete LCTs.

LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections

International Nuclear Information System (INIS)

2007-01-01

1 - Description of program or function: LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form. Codes used subsequently need thus to consider only linear-linear data. IAEA1311/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: - Linear VERS. 2007-1 (JAN. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 600,000 points 2 - Method of solution: Each section of data is considered separately. Each section of File 3, 23, and 27 data consists of a table of cross section versus energy with any of five interpolation laws. LINEAR will replace each section with a new table of energy versus cross section data in which the interpolation law is always linear in energy and cross section. The histogram (constant cross section between two energies) interpolation law is converted to linear-linear by substituting two points for each initial point. The linear-linear is not altered. For the log-linear, linear-log and log- log laws, the cross section data are converted to linear by an interval halving algorithm. Each interval is divided in half until the value at the middle of the interval can be approximated by linear-linear interpolation to within a given accuracy. The LINEAR program uses a multipoint fractional error thinning algorithm to minimize the size of each cross section table

Materials analysis using x-ray linear attenuation coefficient measurements at four photon energies

International Nuclear Information System (INIS)

Midgley, S M

2005-01-01

The analytical properties of an accurate parameterization scheme for the x-ray linear attenuation coefficient are examined. The parameterization utilizes an additive combination of N compositional- and energy-dependent coefficients. The former were derived from a parameterization of elemental cross-sections using a polynomial in atomic number. The compositional-dependent coefficients are referred to as the mixture parameters, representing the electron density and higher order statistical moments describing elemental distribution. Additivity is an important property of the parameterization, allowing measured x-ray linear attenuation coefficients to be written as linear simultaneous equations, and then solved for the unknown coefficients. The energy-dependent coefficients can be determined by calibration from measurements with materials of known composition. The inverse problem may be utilized for materials analysis, whereby the simultaneous equations represent multi-energy linear attenuation coefficient measurements, and are solved for the mixture parameters. For in vivo studies, the choice of measurement energies is restricted to the diagnostic region (approximately 20 keV to 150 keV), where the parameterization requires N ≥ 4 energies. We identify a mathematical pathology that must be overcome in order to solve the inverse problem in this energy regime. An iterative inversion strategy is presented for materials analysis using four or more measurements, and then tested against real data obtained at energies 32 keV to 66 keV. The results demonstrate that it is possible to recover the electron density to within ±4% and fourth mixture parameter. It is also a key finding that the second and third mixture parameters cannot be recovered, as they are of minor importance in the parameterization at diagnostic x-ray energies

Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

KAUST Repository

N U+02BC Doye, Ibrahima

2018-02-13

In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

KAUST Repository

N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

2018-01-01

In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

Characterization of Symmetry Properties of First Integrals for Submaximal Linearizable Third-Order ODEs

Directory of Open Access Journals (Sweden)

K. S. Mahomed

2013-01-01

Full Text Available The relationship between first integrals of submaximal linearizable third-order ordinary differential equations (ODEs and their symmetries is investigated. We obtain the classifying relations between the symmetries and the first integral for submaximal cases of linear third-order ODEs. It is known that the maximum Lie algebra of the first integral is achieved for the simplest equation and is four-dimensional. We show that for the other two classes they are not unique. We also obtain counting theorems of the symmetry properties of the first integrals for these classes of linear third-order ODEs. For the 5 symmetry class of linear third-order ODEs, the first integrals can have 0, 1, 2, and 3 symmetries, and for the 4 symmetry class of linear third-order ODEs, they are 0, 1, and 2 symmetries, respectively. In the case of submaximal linear higher-order ODEs, we show that their full Lie algebras can be generated by the subalgebras of certain basic integrals.

Linearization: Geometric, Complex, and Conditional

Directory of Open Access Journals (Sweden)

Asghar Qadir

2012-01-01

Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.

Linear versus non-linear structural information limit in high-resolution transmission electron microscopy

International Nuclear Information System (INIS)

Van Aert, S.; Chen, J.H.; Van Dyck, D.

2010-01-01

A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has

Neutrino masses and their ordering: global data, priors and models

Science.gov (United States)

Gariazzo, S.; Archidiacono, M.; de Salas, P. F.; Mena, O.; Ternes, C. A.; Tórtola, M.

2018-03-01

We present a full Bayesian analysis of the combination of current neutrino oscillation, neutrinoless double beta decay and Cosmic Microwave Background observations. Our major goal is to carefully investigate the possibility to single out one neutrino mass ordering, namely Normal Ordering or Inverted Ordering, with current data. Two possible parametrizations (three neutrino masses versus the lightest neutrino mass plus the two oscillation mass splittings) and priors (linear versus logarithmic) are exhaustively examined. We find that the preference for NO is only driven by neutrino oscillation data. Moreover, the values of the Bayes factor indicate that the evidence for NO is strong only when the scan is performed over the three neutrino masses with logarithmic priors; for every other combination of parameterization and prior, the preference for NO is only weak. As a by-product of our Bayesian analyses, we are able to (a) compare the Bayesian bounds on the neutrino mixing parameters to those obtained by means of frequentist approaches, finding a very good agreement; (b) determine that the lightest neutrino mass plus the two mass splittings parametrization, motivated by the physical observables, is strongly preferred over the three neutrino mass eigenstates scan and (c) find that logarithmic priors guarantee a weakly-to-moderately more efficient sampling of the parameter space. These results establish the optimal strategy to successfully explore the neutrino parameter space, based on the use of the oscillation mass splittings and a logarithmic prior on the lightest neutrino mass, when combining neutrino oscillation data with cosmology and neutrinoless double beta decay. We also show that the limits on the total neutrino mass ∑ mν can change dramatically when moving from one prior to the other. These results have profound implications for future studies on the neutrino mass ordering, as they crucially state the need for self-consistent analyses which explore the

Ultrasonic Linear Motor with Two Independent Vibrations

Science.gov (United States)

Muneishi, Takeshi; Tomikawa, Yoshiro

2004-09-01

We propose a new structure of an ultrasonic linear motor in order to solve the problems of high-power ultrasonic linear motors that drive the XY-stage for electron beam equipment and to expand the application fields of the motor. We pay special attention to the following three points: (1) the vibration in two directions of the ultrasonic linear motor should not influence mutually each other, (2) the vibration in two directions should be divided into the stage traveling direction and the pressing direction of the ultrasonic linear motor, and (3) the rigidity of the stage traveling direction of the ultrasonic linear motor should be increased. As a result, the supporting method of ultrasonic linear motors is simplified. The efficiency of the motor is improved and temperature rise is reduced. The stage position drift is also improved.

Analysis of second order harmonic distortion due to transmitter non-linearity and chromatic and modal dispersion of optical OFDM SSB modulated signals in SMF-MMF fiber links

Science.gov (United States)

Patel, Dhananjay; Singh, Vinay Kumar; Dalal, U. D.

2017-01-01

Single mode fibers (SMF) are typically used in Wide Area Networks (WAN), Metropolitan Area Networks (MAN) and also find applications in Radio over Fiber (RoF) architectures supporting data transmission in Fiber to the Home (FTTH), Remote Antenna Units (RAUs), in-building networks etc. Multi-mode fibers (MMFs) with low cost, ease of installation and low maintenance are predominantly (85-90%) deployed in-building networks providing data access in local area networks (LANs). The transmission of millimeter wave signals through the SMF in WAN and MAN, along with the reuse of MMF in-building networks will not levy fiber reinstallation cost. The transmission of the millimeter waves experiences signal impairments due to the transmitter non-linearity and modal dispersion of the MMF. The MMF exhibiting large modal dispersion limits the bandwidth-length product of the fiber. The second and higher-order harmonics present in the optical signal fall within the system bandwidth. This causes degradation in the received signal and an unwanted radiation of power at the RAU. The power of these harmonics is proportional to the non-linearity of the transmitter and the modal dispersion of the MMF and should be maintained below the standard values as per the international norms. In this paper, a mathematical model is developed for Second-order Harmonic Distortion (HD2) generated due to non-linearity of the transmitter and chromatic-modal dispersion of the SMF-MMF optic link. This is also verified using a software simulation. The model consists of a Mach Zehnder Modulator (MZM) that generates two m-QAM OFDM Single Sideband (SSB) signals based on phase shift of the hybrid coupler (90° and 120°). Our results show that the SSB signal with 120° hybrid coupler has suppresses the higher-order harmonics and makes the system more robust against the HD2 in the SMF-MMF optic link.

Robust design in generelaised linear models for improving the quality of polyurethane soles

Directory of Open Access Journals (Sweden)

Castro, Armando Mares

2015-11-01

Full Text Available In a process that manufactures polyurethane soles by casting, a number of problems lead to different types of defects on the sole, causing significant economic losses for the company. In order to improve the product quality and decrease the number of defects, this study conducts an experimental design in the context of robust design. Since the response variable is binary, the statistical analysis was performed using generalised linear models. The operational methodology reduced the percentage of defects, while combining the experimental technique and control systems to achieve superior quality and a consequent reduction in costs.

Application of higher order spectral features and support vector machines for bearing faults classification.

Science.gov (United States)

Saidi, Lotfi; Ben Ali, Jaouher; Fnaiech, Farhat

2015-01-01

Condition monitoring and fault diagnosis of rolling element bearings timely and accurately are very important to ensure the reliability of rotating machinery. This paper presents a novel pattern classification approach for bearings diagnostics, which combines the higher order spectra analysis features and support vector machine classifier. The use of non-linear features motivated by the higher order spectra has been reported to be a promising approach to analyze the non-linear and non-Gaussian characteristics of the mechanical vibration signals. The vibration bi-spectrum (third order spectrum) patterns are extracted as the feature vectors presenting different bearing faults. The extracted bi-spectrum features are subjected to principal component analysis for dimensionality reduction. These principal components were fed to support vector machine to distinguish four kinds of bearing faults covering different levels of severity for each fault type, which were measured in the experimental test bench running under different working conditions. In order to find the optimal parameters for the multi-class support vector machine model, a grid-search method in combination with 10-fold cross-validation has been used. Based on the correct classification of bearing patterns in the test set, in each fold the performance measures are computed. The average of these performance measures is computed to report the overall performance of the support vector machine classifier. In addition, in fault detection problems, the performance of a detection algorithm usually depends on the trade-off between robustness and sensitivity. The sensitivity and robustness of the proposed method are explored by running a series of experiments. A receiver operating characteristic (ROC) curve made the results more convincing. The results indicated that the proposed method can reliably identify different fault patterns of rolling element bearings based on vibration signals. Copyright © 2014 ISA

Active disturbance rejection based trajectory linearization control for hypersonic reentry vehicle with bounded uncertainties.

Science.gov (United States)

Shao, Xingling; Wang, Honglun

2015-01-01

This paper investigates a novel compound control scheme combined with the advantages of trajectory linearization control (TLC) and alternative active disturbance rejection control (ADRC) for hypersonic reentry vehicle (HRV) attitude tracking system with bounded uncertainties. Firstly, in order to overcome actuator saturation problem, nonlinear tracking differentiator (TD) is applied in the attitude loop to achieve fewer control consumption. Then, linear extended state observers (LESO) are constructed to estimate the uncertainties acting on the LTV system in the attitude and angular rate loop. In addition, feedback linearization (FL) based controllers are designed using estimates of uncertainties generated by LESO in each loop, which enable the tracking error for closed-loop system in the presence of large uncertainties to converge to the residual set of the origin asymptotically. Finally, the compound controllers are derived by integrating with the nominal controller for open-loop nonlinear system and FL based controller. Also, comparisons and simulation results are presented to illustrate the effectiveness of the control strategy. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Graph-based linear scaling electronic structure theory

Energy Technology Data Exchange (ETDEWEB)

Niklasson, Anders M. N., E-mail: amn@lanl.gov; Negre, Christian F. A.; Cawkwell, Marc J.; Swart, Pieter J.; Germann, Timothy C.; Bock, Nicolas [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mniszewski, Susan M.; Mohd-Yusof, Jamal; Wall, Michael E.; Djidjev, Hristo [Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Rubensson, Emanuel H. [Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala (Sweden)

2016-06-21

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

Quasi-linear evolution of tearing modes

International Nuclear Information System (INIS)

Pellat, R.; Frey, M.; Tagger, M.

1983-07-01

The growth of a Tearing instability in Rutherford's nonlinear regime is investigated. Using a singular perturbation technique, lowest order Rutherford's result is recovered. To the following order it is shown that the mode generates a quasi-linear deformation of the equilibrium flux profile, whose resistive diffusion slows down the growth and shows the possibility of a saturation of the instability

Fractional approximations for linear first order differential equation with polynomial coefficients-application to E1(x) and Z(s)

International Nuclear Information System (INIS)

Martin, P.; Zamudio-Cristi, J.

1982-01-01

A method is described to obtain fractional approximations for linear first order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the highest and lowest power of the variable after the sustitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Pade method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which give three exact digits for most of the real values of the variable. Approximations of higher accuracy and of the same degree than other authors are also obtained. (Author) [pt

Acute hormonal and force responses to combined strength and endurance loadings in men and women: the "order effect".

Directory of Open Access Journals (Sweden)

Ritva S Taipale

Full Text Available PURPOSE: To examine acute responses and recovery of serum hormones and muscle force following combined strength (S and endurance (E loading sessions in which the order of exercises is reversed (ES vs. SE. METHODS: This cross-over study design included recreationally endurance trained men and women (age 21-45 years, n = 12 men n = 10 women who performed both loadings. Maximal bilateral isometric strength (MVC, isometric rate of force development (RFD and serum concentrations of testosterone (T, cortisol (C, growth hormone (GH, insulin-like growth factor 1 (IGF-1, binding protein 3 (IGFBP3 and sex hormone binding globulin (SHBG were measured during and after both loadings. RESULTS: Both of the present combined (ES and SE loadings led to a greater acute decrease in MVC in men than in women, while RFD was slightly affected only in men. Recovery of MVC and RFD to baseline was complete at 24 h regardless of the order of exercises. In men, neuromuscular fatigue was accompanied by increased C concentrations observed post SE. This was followed by decreased concentrations of T at 24 h and 48 h that were significantly lower than those observed following ES. GH response in men also differed significantly post loadings. In women, only a significant difference in T between ES and SE loadings was observed at post. CONCLUSION: These observed differences in hormonal responses despite similarities in neuromuscular fatigue in men indicate the presence of an order effect as the body was not fully recovered at 48 h following SE. These findings may be applicable in training prescription in order to optimize specific training adaptations.

Light propagation in linear optical media

CERN Document Server

Gillen, Glen D; Guha, Shekhar

2013-01-01

Light Propagation in Linear Optical Media describes light propagation in linear media by expanding on diffraction theories beyond what is available in classic optics books. In one volume, this book combines the treatment of light propagation through various media, interfaces, and apertures using scalar and vector diffraction theories. After covering the fundamentals of light and physical optics, the authors discuss light traveling within an anisotropic crystal and present mathematical models for light propagation across planar boundaries between different media. They describe the propagation o

Linear Power-Flow Models in Multiphase Distribution Networks: Preprint

Energy Technology Data Exchange (ETDEWEB)

Bernstein, Andrey; Dall' Anese, Emiliano

2017-05-26

This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- from advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.

Bayes linear statistics, theory & methods

CERN Document Server

Goldstein, Michael

2007-01-01

Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...

Accuracy of 1H magnetic resonance spectroscopy for quantification of 2-hydroxyglutarate using linear combination and J-difference editing at 9.4T.

Science.gov (United States)

Neuberger, Ulf; Kickingereder, Philipp; Helluy, Xavier; Fischer, Manuel; Bendszus, Martin; Heiland, Sabine

2017-12-01

Non-invasive detection of 2-hydroxyglutarate (2HG) by magnetic resonance spectroscopy is attractive since it is related to tumor metabolism. Here, we compare the detection accuracy of 2HG in a controlled phantom setting via widely used localized spectroscopy sequences quantified by linear combination of metabolite signals vs. a more complex approach applying a J-difference editing technique at 9.4T. Different phantoms, comprised out of a concentration series of 2HG and overlapping brain metabolites, were measured with an optimized point-resolved-spectroscopy sequence (PRESS) and an in-house developed J-difference editing sequence. The acquired spectra were post-processed with LCModel and a simulated metabolite set (PRESS) or with a quantification formula for J-difference editing. Linear regression analysis demonstrated a high correlation of real 2HG values with those measured with the PRESS method (adjusted R-squared: 0.700, pJ-difference editing method (adjusted R-squared: 0.908, pJ-difference editing method however had a significantly higher explanatory value over the regression model with the PRESS method (pJ-difference editing 2HG was discernible down to 1mM, whereas with the PRESS method 2HG values were not discernable below 2mM and with higher systematic errors, particularly in phantoms with high concentrations of N-acetyl-asparate (NAA) and glutamate (Glu). In summary, quantification of 2HG with linear combination of metabolite signals shows high systematic errors particularly at low 2HG concentration and high concentration of confounding metabolites such as NAA and Glu. In contrast, J-difference editing offers a more accurate quantification even at low 2HG concentrations, which outweighs the downsides of longer measurement time and more complex postprocessing. Copyright © 2017. Published by Elsevier GmbH.

Accuracy of 1H magnetic resonance spectroscopy for quantification of 2-hydroxyglutarate using linear combination and J-difference editing at 9.4 T

Energy Technology Data Exchange (ETDEWEB)

Neuberger, Ulf; Fischer, Manuel; Heiland, Sabine [Univ. of Heidelberg Medical Center, Heidelberg (Germany). Dept. of Neuroradiology; Univ. of Heidelberg Medical Center, Heidelberg (Germany). Div. of Experimental Radiology; Kickingereder, Philipp; Bendszus, Martin [Univ. of Heidelberg Medical Center, Heidelberg (Germany). Dept. of Neuroradiology; Helluy, Xavier [Bochum Univ. (Germany). Dept. of Biopsychology

2017-07-01

Non-invasive detection of 2-hydroxyglutarate (2HG) by magnetic resonance spectroscopy is attractive since it is related to tumor metabolism. Here, we compare the detection accuracy of 2HG in a controlled phantom setting via widely used localized spectroscopy sequences quantified by linear combination of metabolite signals vs. a more complex approach applying a J-difference editing technique at 9.4 T. Different phantoms, comprised out of a concentration series of 2HG and overlapping brain metabolites, were measured with an optimized point-resolved-spectroscopy sequence (PRESS) and an in-house developed J-difference editing sequence. The acquired spectra were post-processed with LCModel and a simulated metabolite set (PRESS) or with a quantification formula for J-difference editing. Linear regression analysis demonstrated a high correlation of real 2HG values with those measured with the PRESS method (adjusted R-squared: 0.700, p < 0.001) as well as with those measured with the J-difference editing method (adjusted R-squared: 0.908, p < 0.001). The regression model with the J-difference editing method however had a significantly higher explanatory value over the regression model with the PRESS method (p < 0.0001). Moreover, with J-difference editing 2HG was discernible down to 1 mM, whereas with the PRESS method 2HG values were not discernable below 2 mM and with higher systematic errors, particularly in phantoms with high concentrations of N-acetyl-asparate (NAA) and glutamate (Glu). In summary, quantification of 2HG with linear combination of metabolite signals shows high systematic errors particularly at low 2HG concentration and high concentration of confounding metabolites such as NAA and Glu. In contrast, J-difference editing offers a more accurate quantification even at low 2HG concentrations, which outweighs the downsides of longer measurement time and more complex postprocessing.

Efficient decomposition and linearization methods for the stochastic transportation problem

International Nuclear Information System (INIS)

Holmberg, K.

1993-01-01

The stochastic transportation problem can be formulated as a convex transportation problem with nonlinear objective function and linear constraints. We compare several different methods based on decomposition techniques and linearization techniques for this problem, trying to find the most efficient method or combination of methods. We discuss and test a separable programming approach, the Frank-Wolfe method with and without modifications, the new technique of mean value cross decomposition and the more well known Lagrangian relaxation with subgradient optimization, as well as combinations of these approaches. Computational tests are presented, indicating that some new combination methods are quite efficient for large scale problems. (authors) (27 refs.)

Linearization Method and Linear Complexity

Science.gov (United States)

Tanaka, Hidema

We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

Physics possibilities at a linear collider

Indian Academy of Sciences (India)

Up to now the standard model (SM) has passed all accelerator-based experimental tests. .... Higgs sector and of the MSSM as well as for testing grand unification. ..... SPS1a scenario [33] for a coherent combination of LHC and linear collider.

Protein domain organisation: adding order.

Science.gov (United States)

Kummerfeld, Sarah K; Teichmann, Sarah A

2009-01-29

Domains are the building blocks of proteins. During evolution, they have been duplicated, fused and recombined, to produce proteins with novel structures and functions. Structural and genome-scale studies have shown that pairs or groups of domains observed together in a protein are almost always found in only one N to C terminal order and are the result of a single recombination event that has been propagated by duplication of the multi-domain unit. Previous studies of domain organisation have used graph theory to represent the co-occurrence of domains within proteins. We build on this approach by adding directionality to the graphs and connecting nodes based on their relative order in the protein. Most of the time, the linear order of domains is conserved. However, using the directed graph representation we have identified non-linear features of domain organization that are over-represented in genomes. Recognising these patterns and unravelling how they have arisen may allow us to understand the functional relationships between domains and understand how the protein repertoire has evolved. We identify groups of domains that are not linearly conserved, but instead have been shuffled during evolution so that they occur in multiple different orders. We consider 192 genomes across all three kingdoms of life and use domain and protein annotation to understand their functional significance. To identify these features and assess their statistical significance, we represent the linear order of domains in proteins as a directed graph and apply graph theoretical methods. We describe two higher-order patterns of domain organisation: clusters and bi-directionally associated domain pairs and explore their functional importance and phylogenetic conservation. Taking into account the order of domains, we have derived a novel picture of global protein organization. We found that all genomes have a higher than expected degree of clustering and more domain pairs in forward and

Protein domain organisation: adding order

Directory of Open Access Journals (Sweden)

Kummerfeld Sarah K

2009-01-01

Full Text Available Abstract Background Domains are the building blocks of proteins. During evolution, they have been duplicated, fused and recombined, to produce proteins with novel structures and functions. Structural and genome-scale studies have shown that pairs or groups of domains observed together in a protein are almost always found in only one N to C terminal order and are the result of a single recombination event that has been propagated by duplication of the multi-domain unit. Previous studies of domain organisation have used graph theory to represent the co-occurrence of domains within proteins. We build on this approach by adding directionality to the graphs and connecting nodes based on their relative order in the protein. Most of the time, the linear order of domains is conserved. However, using the directed graph representation we have identified non-linear features of domain organization that are over-represented in genomes. Recognising these patterns and unravelling how they have arisen may allow us to understand the functional relationships between domains and understand how the protein repertoire has evolved. Results We identify groups of domains that are not linearly conserved, but instead have been shuffled during evolution so that they occur in multiple different orders. We consider 192 genomes across all three kingdoms of life and use domain and protein annotation to understand their functional significance. To identify these features and assess their statistical significance, we represent the linear order of domains in proteins as a directed graph and apply graph theoretical methods. We describe two higher-order patterns of domain organisation: clusters and bi-directionally associated domain pairs and explore their functional importance and phylogenetic conservation. Conclusion Taking into account the order of domains, we have derived a novel picture of global protein organization. We found that all genomes have a higher than expected

Linear complexity for multidimensional arrays - a numerical invariant

DEFF Research Database (Denmark)

Gomez-Perez, Domingo; Høholdt, Tom; Moreno, Oscar

2015-01-01

Linear complexity is a measure of how complex a one dimensional sequence can be. In this paper we extend the concept of linear complexity to multiple dimensions and present a definition that is invariant under well-orderings of the arrays. As a result we find that our new definition for the proce...

Combined Prediction Model of Death Toll for Road Traffic Accidents Based on Independent and Dependent Variables

Directory of Open Access Journals (Sweden)

Feng Zhong-xiang

2014-01-01

Full Text Available In order to build a combined model which can meet the variation rule of death toll data for road traffic accidents and can reflect the influence of multiple factors on traffic accidents and improve prediction accuracy for accidents, the Verhulst model was built based on the number of death tolls for road traffic accidents in China from 2002 to 2011; and car ownership, population, GDP, highway freight volume, highway passenger transportation volume, and highway mileage were chosen as the factors to build the death toll multivariate linear regression model. Then the two models were combined to be a combined prediction model which has weight coefficient. Shapley value method was applied to calculate the weight coefficient by assessing contributions. Finally, the combined model was used to recalculate the number of death tolls from 2002 to 2011, and the combined model was compared with the Verhulst and multivariate linear regression models. The results showed that the new model could not only characterize the death toll data characteristics but also quantify the degree of influence to the death toll by each influencing factor and had high accuracy as well as strong practicability.