Consistent Partial Least Squares Path Modeling via Regularization.
Jung, Sunho; Park, JaeHong
2018-01-01
Partial least squares (PLS) path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc), designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.
Consistent Partial Least Squares Path Modeling via Regularization
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Sunho Jung
2018-02-01
Full Text Available Partial least squares (PLS path modeling is a component-based structural equation modeling that has been adopted in social and psychological research due to its data-analytic capability and flexibility. A recent methodological advance is consistent PLS (PLSc, designed to produce consistent estimates of path coefficients in structural models involving common factors. In practice, however, PLSc may frequently encounter multicollinearity in part because it takes a strategy of estimating path coefficients based on consistent correlations among independent latent variables. PLSc has yet no remedy for this multicollinearity problem, which can cause loss of statistical power and accuracy in parameter estimation. Thus, a ridge type of regularization is incorporated into PLSc, creating a new technique called regularized PLSc. A comprehensive simulation study is conducted to evaluate the performance of regularized PLSc as compared to its non-regularized counterpart in terms of power and accuracy. The results show that our regularized PLSc is recommended for use when serious multicollinearity is present.
Nambudiripad, K B M
2014-01-01
After presenting the theory in engineers' language without the unfriendly abstraction of pure mathematics, several illustrative examples are discussed in great detail to see how the various functions of the Bessel family enter into the solution of technically important problems. Axisymmetric vibrations of a circular membrane, oscillations of a uniform chain, heat transfer in circular fins, buckling of columns of varying cross-section, vibrations of a circular plate and current density in a conductor of circular cross-section are considered. The problems are formulated purely from physical considerations (using, for example, Newton's law of motion, Fourier's law of heat conduction electromagnetic field equations, etc.) Infinite series expansions, recurrence relations, manipulation of expressions involving Bessel functions, orthogonality and expansion in Fourier-Bessel series are also covered in some detail. Some important topics such as asymptotic expansions, generating function and Sturm-Lioville theory are r...
Nugraha, A. T.; Agustinah, T.
2018-01-01
Quadcopter an unstable system, underactuated and nonlinear in quadcopter control research developments become an important focus of attention. In this study, following the path control method for position on the X and Y axis, used structure-Generator Tracker Command (CGT) is tested. Attitude control and position feedback quadcopter is compared using the optimal output. The addition of the H∞ performance optimal output feedback control is used to maintain the stability and robustness of quadcopter. Iterative numerical techniques Linear Matrix Inequality (LMI) is used to find the gain controller. The following path control problems is solved using the method of LQ regulators with output feedback. Simulations show that the control system can follow the paths that have been defined in the form of a reference signal square shape. The result of the simulation suggest that the method which used can bring the yaw angle at the expected value algorithm. Quadcopter can do automatically following path with cross track error mean X=0.5 m and Y=0.2 m.
Conformable Fractional Bessel Equation and Bessel Functions
Gökdoğan, Ahmet; Ünal, Emrah; Çelik, Ercan
2015-01-01
In this work, we study the fractional power series solutions around regular singular point x=0 of conformable fractional Bessel differential equation and fractional Bessel functions. Then, we compare fractional solutions with ordinary solutions. In addition, we present certain property of fractional Bessel functions.
Yuniarto, Budi; Kurniawan, Robert
2017-03-01
PLS Path Modeling (PLS-PM) is different from covariance based SEM, where PLS-PM use an approach based on variance or component, therefore, PLS-PM is also known as a component based SEM. Multiblock Partial Least Squares (MBPLS) is a method in PLS regression which can be used in PLS Path Modeling which known as Multiblock PLS Path Modeling (MBPLS-PM). This method uses an iterative procedure in its algorithm. This research aims to modify MBPLS-PM with Back Propagation Neural Network approach. The result is MBPLS-PM algorithm can be modified using the Back Propagation Neural Network approach to replace the iterative process in backward and forward step to get the matrix t and the matrix u in the algorithm. By modifying the MBPLS-PM algorithm using Back Propagation Neural Network approach, the model parameters obtained are relatively not significantly different compared to model parameters obtained by original MBPLS-PM algorithm.
Partial least squares path modeling basic concepts, methodological issues and applications
Noonan, Richard
2017-01-01
This edited book presents the recent developments in partial least squares-path modeling (PLS-PM) and provides a comprehensive overview of the current state of the most advanced research related to PLS-PM. The first section of this book emphasizes the basic concepts and extensions of the PLS-PM method. The second section discusses the methodological issues that are the focus of the recent development of the PLS-PM method. The third part discusses the real world application of the PLS-PM method in various disciplines. The contributions from expert authors in the field of PLS focus on topics such as the factor-based PLS-PM, the perfect match between a model and a mode, quantile composite-based path modeling (QC-PM), ordinal consistent partial least squares (OrdPLSc), non-symmetrical composite-based path modeling (NSCPM), modern view for mediation analysis in PLS-PM, a multi-method approach for identifying and treating unobserved heterogeneity, multigroup analysis (PLS-MGA), the assessment of the common method b...
Babusci, D.; Dattoli, G.; Germano, B.; Martinelli, M. R.; Ricci, P. E.
2011-01-01
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.
Return polynomials for non-intersecting paths above a surface on the directed square lattice
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Brak, R. [Deartment of Mathematics, University of Melbourne, Parkville, VIC (Australia)]. E-mail: r.brak@ms.unimelb.edu.au; Essam, J.W. [Department of Mathematics, Royal Holloway College, University of London, Egham, Surrey (United Kingdom)]. E-mail: j.essam@alpha1.rhul.ac.uk
2001-12-14
We enumerate sets of n non-intersecting, t-step paths on the directed square lattice which are excluded from the region below the surface y=0 to which they are initially attached. In particular we obtain a product formula for the number of star configurations in which the paths have arbitrary fixed endpoints. We also consider the 'return' polynomial, R-'{sup W}{sub t}(y;k)={sigma}{sub m{>=}}{sub 0}r-'{sup W}{sub t}(y;m)k{sup m} where r-'{sup W}{sub t}(y;m) is the number of n-path configurations of watermelon type having deviation {gamma} for which the path closest to the surface returns to the surface m times. The 'marked return' polynomial is defined by u-'{sup W}{sub t}(y;k{sub 1}){identical_to}R-'{sup W}{sub 1}(y;k{sub 1}+l)={sigma}{sub m{>=}}{sub 0}u-'{sup W}{sub t}(y;m)k{sub 1}{sup m} where u-'{sup W}{sub t}(y;m) is the number of marked configurations having at least m returns, just m of which are marked. Both r-'{sup W}{sub t}(y;m) and u-'{sup W}(y;m) are expressed in terms of the numbers of paths ignoring returns but introducing a suitably modified endpoint condition. This enables u-'{sup W}{sub t}(y;m) to be written in product form for arbitrary y, but for r-'{sup W}{sub t}(y;m) this can only be done in the case y=0. (author)
Unified Bessel, Modified Bessel, Spherical Bessel and Bessel-Clifford Functions
Yaşar, Banu Yılmaz; Özarslan, Mehmet Ali
2016-01-01
In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\\i}ymaz O. A certain generalized Pochhammer symbol and its applications to hypergeometric functions. Applied Mathematics and Computation, 2014, 226 : 484-491] is defined. Several potentially useful properties of the unified family such as generating function, integral representation, Laplace transform and Mellin tran...
Laser-driven acceleration with Bessel beam
International Nuclear Information System (INIS)
Imasaki, Kazuo; Li, Dazhi
2005-01-01
A new approach of laser-driven acceleration with Bessel beam is described. Bessel beam, in contrast to the Gaussian beam, shows diffraction-free'' characteristics in its propagation, which implies potential in laser-driven acceleration. But a normal laser, even if the Bessel beam, laser can not accelerate charged particle efficiently because the difference of velocity between the particle and photon makes cyclic acceleration and deceleration phase. We proposed a Bessel beam truncated by a set of annular slits those makes several special regions in its travelling path, where the laser field becomes very weak and the accelerated particles are possible to receive no deceleration as they undergo decelerating phase. Thus, multistage acceleration is realizable with high gradient. In a numerical computation, we have shown the potential of multistage acceleration based on a three-stage model. (author)
Spherical Bessel transform via exponential sum approximation of spherical Bessel function
Ikeno, Hidekazu
2018-02-01
A new algorithm for numerical evaluation of spherical Bessel transform is proposed in this paper. In this method, the spherical Bessel function is approximately represented as an exponential sum with complex parameters. This is obtained by expressing an integral representation of spherical Bessel function in complex plane, and discretizing contour integrals along steepest descent paths and a contour path parallel to real axis using numerical quadrature rule with the double-exponential transformation. The number of terms in the expression is reduced using the modified balanced truncation method. The residual part of integrand is also expanded by exponential functions using Prony-like method. The spherical Bessel transform can be evaluated analytically on arbitrary points in half-open interval.
On numerical Bessel transformation
International Nuclear Information System (INIS)
Sommer, B.; Zabolitzky, J.G.
1979-01-01
The authors present a computer program to calculate the three dimensional Fourier or Bessel transforms and definite integrals with Bessel functions. Numerical integration of systems containing Bessel functions occurs in many physical problems, e.g. electromagnetic form factor of nuclei, all transitions involving multipole expansions at high momenta. Filon's integration rule is extended to spherical Bessel functions. The numerical error is of the order of the Simpson error term of the function which has to be transformed. Thus one gets a stable integral even at large arguments of the transformed function. (Auth.)
Terahertz plasmonic Bessel beamformer
International Nuclear Information System (INIS)
Monnai, Yasuaki; Shinoda, Hiroyuki; Jahn, David; Koch, Martin; Withayachumnankul, Withawat
2015-01-01
We experimentally demonstrate terahertz Bessel beamforming based on the concept of plasmonics. The proposed planar structure is made of concentric metallic grooves with a subwavelength spacing that couple to a point source to create tightly confined surface waves or spoof surface plasmon polaritons. Concentric scatterers periodically incorporated at a wavelength scale allow for launching the surface waves into free space to define a Bessel beam. The Bessel beam defined at 0.29 THz has been characterized through terahertz time-domain spectroscopy. This approach is capable of generating Bessel beams with planar structures as opposed to bulky axicon lenses and can be readily integrated with solid-state terahertz sources
International Nuclear Information System (INIS)
Hirosato, S.; Yamazaki, K.; Tsuruta, T.; Haraguchi, Y.; Kosaka, M.; Gao, Y.; Muramatsu, K.; Kobayashi, K.
2011-01-01
We have developed an open-type magnetically shielded room composed of magnetic square cylinders that has been used for an actual MRI in a hospital. To improve shielding performance, we propose here a method to control the path of the magnetic flux in the wall composed of the magnetic square cylinders by changing the magnetic permeability in each direction of the square cylinders spatially. First, we discuss a method to control the magnetic permeability in each direction of the square cylinders independently by inserting slits without changing the outside dimensions of the square cylinders, by using 3-D magnetic field analysis. Then, the effectiveness of the design of controlling the flux pass was shown by magnetic field analysis and experiments. (author)
On the Laws of Total Local Times for -Paths and Bridges of Symmetric Lévy Processes
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Masafumi Hayashi
2013-01-01
Full Text Available The joint law of the total local times at two levels for -paths of symmetric Lévy processes is shown to admit an explicit representation in terms of the laws of the squared Bessel processes of dimensions two and zero. The law of the total local time at a single level for bridges is also discussed.
The use of partial least squares path modeling in international marketing
Henseler, Jörg; Ringle, Christian M.; Sinkovics, Rudolf R.
2009-01-01
In order to determine the status quo of PLS path modeling in international marketing research, we conducted an exhaustive literature review. An evaluation of double-blind reviewed journals through important academic publishing databases (e.g., ABI/Inform, Elsevier ScienceDirect, Emerald Insight,
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Avakian, Harut [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Gamberg, Leonard [Pennsylvania State Univ., University Park, PA (United States); Rossi, Patrizia [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Prokudin, Alexei [Pennsylvania State Univ., University Park, PA (United States)
2016-05-01
We review the concept of Bessel weighted asymmetries for semi-inclusive deep inelastic scattering and focus on the cross section in Fourier space, conjugate to the outgoing hadron’s transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy and hard scale Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.
Directory of Open Access Journals (Sweden)
Giuseppe Dattoli
1996-05-01
Full Text Available q analog of bessel functions, symmetric under the interchange of q and q^ −1 are introduced. The definition is based on the generating function realized as product of symmetric q-exponential functions with appropriate arguments. Symmetric q-Bessel function are shown to satisfy various identities as well as second-order q-differential equations, which in the limit q → 1 reproduce those obeyed by the usual cylindrical Bessel functions. A brief discussion on the possible algebraic setting for symmetric q-Bessel functions is also provided.
Acoustic manipulation: Bessel beams and active carriers
Rajabi, Majid; Mojahed, Alireza
2017-10-01
In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.
Laser-driven acceleration with Bessel and Gaussian beams
International Nuclear Information System (INIS)
Hafizi, B.; Esarey, E.; Sprangle, P.
1997-01-01
The possibility of enhancing the energy gain in laser-driven accelerators by using Bessel laser beams is examined. Scaling laws are derived for the propagation length, acceleration gradient, and energy gain in various accelerators for both Gaussian and Bessel beam drivers. For equal beam powers, the energy gain can be increased by a factor of N 1/2 by utilizing a Bessel beam with N lobes, provided that the acceleration gradient is linearly proportional to the laser field. This is the case in the inverse free electron laser and the inverse Cherenkov accelerators. If the acceleration gradient is proportional to the square of the laser field (e.g., the laser wakefield, plasma beat wave, and vacuum beat wave accelerators), the energy gain is comparable with either beam profile. copyright 1997 American Institute of Physics
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Yun-Xia Liu
Full Text Available Multidrug-resistant tuberculosis (MDR-TB resulting from various factors has raised serious public health concerns worldwide. Identifying the ecological risk factors associated with MDR-TB is critical to its prevention and control. This study aimed to explore the association between the development of MDR-TB and the risk factors at the group-level (ecological risk factors in China.Data on MDR-TB in 120 counties were obtained from the National Tuberculosis Information Management System, and data on risk-factor variables were extracted from the Health Statistical Yearbook, provincial databases, and the meteorological bureau of each province (municipality. Partial Least Square Path Modeling was used to detect the associations.The median proportion of MDR-TB in new TB cases was 3.96% (range, 0-39.39%. Six latent factors were extracted from the ecological risk factors, which explained 27.60% of the total variance overall in the prevalence of MDR-TB. Based on the results of PLS-PM, TB prevention, health resources, health services, TB treatment, TB detection, geography and climate factors were all associated with the risk of MDR-TB, but socioeconomic factors were not significant.The development of MDR-TB was influenced by TB prevention, health resources, health services, TB treatment, TB detection, geography and climate factors. Such information may help us to establish appropriate public health intervention strategies to prevent and control MDR-TB and yield benefits to the entire public health system in China.
Computation of hyperspherical Bessel functions
Tram, Thomas
2013-01-01
In this paper we present a fast and accurate numerical algorithm for the computation of hyperspherical Bessel functions of large order and real arguments. For the hyperspherical Bessel functions of closed type, no stable algorithm existed so far due to the lack of a backwards recurrence. We solved this problem by establishing a relation to Gegenbauer polynomials. All our algorithms are written in C and are publicly available at Github [https://github.com/lesgourg/class_public]. A Python wrapp...
Three-dimensional Bessel light bullets in self-focusing Kerr media
International Nuclear Information System (INIS)
Zhong Weiping; Belic, Milivoj; Huang Tingwen
2010-01-01
We study three-dimensional (3D) Bessel light-bullet solutions of the nonlinear Schroedinger equation with a photonic lattice potential in the form of squared Bessel functions in polar coordinates, both analytically and numerically. Analytical solutions are obtained by the Hartree approximation, and numerical simulations are performed, to compare with the analytical solutions and to confirm the stability of localized solutions. The 3D spatial wave packets are built by the products of hyperbolic secant and Bessel functions. These solitons appear in different forms, such as 3D vortex solitons and multipole solitons.
Fischer, Katharina E
2012-08-02
Decision-making in healthcare is complex. Research on coverage decision-making has focused on comparative studies for several countries, statistical analyses for single decision-makers, the decision outcome and appraisal criteria. Accounting for decision processes extends the complexity, as they are multidimensional and process elements need to be regarded as latent constructs (composites) that are not observed directly. The objective of this study was to present a practical application of partial least square path modelling (PLS-PM) to evaluate how it offers a method for empirical analysis of decision-making in healthcare. Empirical approaches that applied PLS-PM to decision-making in healthcare were identified through a systematic literature search. PLS-PM was used as an estimation technique for a structural equation model that specified hypotheses between the components of decision processes and the reasonableness of decision-making in terms of medical, economic and other ethical criteria. The model was estimated for a sample of 55 coverage decisions on the extension of newborn screening programmes in Europe. Results were evaluated by standard reliability and validity measures for PLS-PM. After modification by dropping two indicators that showed poor measures in the measurement models' quality assessment and were not meaningful for newborn screening, the structural equation model estimation produced plausible results. The presence of three influences was supported: the links between both stakeholder participation or transparency and the reasonableness of decision-making; and the effect of transparency on the degree of scientific rigour of assessment. Reliable and valid measurement models were obtained to describe the composites of 'transparency', 'participation', 'scientific rigour' and 'reasonableness'. The structural equation model was among the first applications of PLS-PM to coverage decision-making. It allowed testing of hypotheses in situations where there
Directory of Open Access Journals (Sweden)
Fischer Katharina E
2012-08-01
Full Text Available Abstract Background Decision-making in healthcare is complex. Research on coverage decision-making has focused on comparative studies for several countries, statistical analyses for single decision-makers, the decision outcome and appraisal criteria. Accounting for decision processes extends the complexity, as they are multidimensional and process elements need to be regarded as latent constructs (composites that are not observed directly. The objective of this study was to present a practical application of partial least square path modelling (PLS-PM to evaluate how it offers a method for empirical analysis of decision-making in healthcare. Methods Empirical approaches that applied PLS-PM to decision-making in healthcare were identified through a systematic literature search. PLS-PM was used as an estimation technique for a structural equation model that specified hypotheses between the components of decision processes and the reasonableness of decision-making in terms of medical, economic and other ethical criteria. The model was estimated for a sample of 55 coverage decisions on the extension of newborn screening programmes in Europe. Results were evaluated by standard reliability and validity measures for PLS-PM. Results After modification by dropping two indicators that showed poor measures in the measurement models’ quality assessment and were not meaningful for newborn screening, the structural equation model estimation produced plausible results. The presence of three influences was supported: the links between both stakeholder participation or transparency and the reasonableness of decision-making; and the effect of transparency on the degree of scientific rigour of assessment. Reliable and valid measurement models were obtained to describe the composites of ‘transparency’, ‘participation’, ‘scientific rigour’ and ‘reasonableness’. Conclusions The structural equation model was among the first applications of PLS-PM to
Extension of Oppenheim's Problem to Bessel Functions
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Zhu Ling
2007-01-01
Full Text Available Our aim is to extend some trigonometric inequalities to Bessel functions. Moreover, we deduce the hyperbolic analogue of these trigonometric inequalities, and we extend these inequalities to modified Bessel functions.
Nonparaxial Bessel and Bessel-Gauss pincers light-sheets
Mitri, F. G.
2017-01-01
Nonparaxial optical Bessel and Bessel-Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions
Qi, Zhi
2014-01-01
In this article we introduce a new category of special functions called fundamental Bessel functions arising from the Voronoi summation formula for $\\mathrm{GL}_n (\\mathbb{R})$. The fundamental Bessel functions of rank one and two are the oscillatory exponential functions $e^{\\pm i x}$ and the classical Bessel functions respectively. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel equations.
Bessel functions: parallel display and processing.
Lohmann, A W; Ojeda-Castañeda, J; Serrano-Heredia, A
1994-01-01
We present an optical setup that converts planar binary curves into two-dimensional amplitude distributions, which are proportional, along one axis, to the Bessel function of order n, whereas along the other axis the order n increases. This Bessel displayer can be used for parallel Bessel transformation of a signal. Experimental verifications are included.
Topological setting of Bessel functions
International Nuclear Information System (INIS)
Mekhfi, M.
1995-11-01
We start from the topology of the punctured plane encoded within its homotopy group which is isomorphic to the set of integers Z. We then realize group elements Π(n), n is an element of Z as differential operators on the space of analytic functions. Using plausible physical arguments we select a subset of functions which we identify with integer orders reduced Bessel functions. On the other hand we propose a unifying new formula of topological origin, generating real orders Bessel functions out of integers orders ones, the generator being an operator built entirely out of the Π s . We thus have shown that the topology (of the puntured plane) is underlying the inner structure of Bessel functions, in addition it unifies them independently of the orders being integers or reals. (author). 4 refs
Henseler, Jorg; Chin, Wynne W.
2010-01-01
In social and business sciences, the importance of the analysis of interaction effects between manifest as well as latent variables steadily increases. Researchers using partial least squares (PLS) to analyze interaction effects between latent variables need an overview of the available approaches as well as their suitability. This article…
Techniques to sort Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2013-09-01
Full Text Available -polar coordinate transformation, translating helically phased beams into a transverse phase gradient. By introducing two cylindrical lenses we can focus each of the azimuthal modes associated with each Bessel beam to a different lateral position in the Fourier...
Theory of generalized Bessel functions
International Nuclear Information System (INIS)
Dattoli, G.; Giannessi, L.; Mezi, L.; Torre, A.
1990-01-01
In this paper it is discussed the theory of generalized Bessel functions which are of noticeable importance in the analysis of scattering processes for which the dipole approximation cannot be used. These functions have been introduced in their standard form and their modified version. The relevant generating functions and Graf-type addition theorems have been stated. The usefulness of the results to construct a fast algorithm for their quantitative computation is also devised. It is commented on the possibility of getting two-index generalized Bessel functions in e.g. the study of sum rules of the type Σ n=-∞ ∞ t n J n 3 (x), where J n is the cylindrical Bessel function of the first kind. The usefulness of the results for problems of practical interest is finally commented on. It is shown that a modified Anger function can be advantageously introduced to get an almost straightforward computation of the Bernstein sum rule in the theory of ion waves
Bortolon, Catherine; Krikorian, Alicia; Carayol, Marion; Brouillet, Denis; Romieu, Gilles; Ninot, Gregory
2014-04-01
The aim of this study is to examine factors contributing to cancer-related fatigue (CRF) in breast cancer patients who have undergone surgery. Sixty women (mean age: 50.0) completed self-rated questionnaires assessing components of CRF, muscular and cognitive functions. Also, physiological and subjective data were gathered. Data were analyzed using partial least squares variance-based structural equation modeling in order to examine factors contributing to CRF after breast surgery. The tested model was robust in terms of its measurement quality (reliability and validity). According to the structural model results, emotional distress (β = 0.59; p accounting for 61% of the explained variance. Also, emotional distress (β = 0.41; p accounted for 41% of the explained variance. However, the relationship between low physical function and CRF was weak and nonsignificant (β = 0.01; p > 0.05). Emotional distress, altered vigilance capacity, and pain are associated with CRF in postsurgical breast cancer. In addition, emotional distress and pain are related to diminished physical function, which, in turn, has no significant impact on CRF. The current model should be examined in subsequent phases of the treatment (chemotherapy and/or radiotherapy) when side effects are more pronounced and may lead to increased intensity of CRF and low physical function. Copyright © 2013 John Wiley & Sons, Ltd.
General description of transverse mode Bessel beams and construction of basis Bessel fields
Wang, Jia Jie; Wriedt, Thomas; Lock, James A.; Jiao, Yong Chang
2017-07-01
Based on an analysis of polarized Bessel beams using the Hertz vector potentials and the angular spectrum representation (ASR), a general description of transverse mode Bessel beams is proposed. As opposed to the cases of linearly and circularly polarized Bessel beams, the magnetic and electric fields of a Bessel beam in a transverse mode are orthogonal to each other. Both sets of fields together form a complete set of basis Bessel fields, in terms of which an arbitrary Bessel beam can be regarded as a linear combination. The completeness of the basis Bessel fields is analyzed from the perspectives of waveguide theory and vector wave functions. Decompositions of linearly polarized, circularly polarized, and circularly symmetric n-order Bessel beams in terms of basis Bessel fields are given. The results presented in this paper provide a fresh perspective on the description of Bessel beams, which are useful in casting insights into the experimental generation of Bessel beams and the interpretation of light scattering-related problems in practice.
Poisson processes and a Bessel function integral
Steutel, F.W.
1985-01-01
The probability of winning a simple game of competing Poisson processes turns out to be equal to the well-known Bessel function integral J(x, y) (cf. Y. L. Luke, Integrals of Bessel Functions, McGraw-Hill, New York, 1962). Several properties of J, some of which seem to be new, follow quite easily
The Bessel polynomials and their differential operators
International Nuclear Information System (INIS)
Onyango Otieno, V.P.
1987-10-01
Differential operators associated with the ordinary and the generalized Bessel polynomials are defined. In each case the commutator bracket is constructed and shows that the differential operators associated with the Bessel polynomials and their generalized form are not commutative. Some applications of these operators to linear differential equations are also discussed. (author). 4 refs
Optical tractor Bessel polarized beams
Mitri, F. G.; Li, R. X.; Guo, L. X.; Ding, C. Y.
2017-01-01
Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications.
Two-photon polymerization of cylinder microstructures by femtosecond Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Yang, Liang [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026 (China); Laser Zentrum Hannover e.V., 30419 Hannover (Germany); El-Tamer, Ayman; Hinze, Ulf; Chichkov, Boris N [Laser Zentrum Hannover e.V., 30419 Hannover (Germany); Li, Jiawen, E-mail: jwl@ustc.edu.cn; Hu, Yanlei; Huang, Wenhao; Chu, Jiaru [Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, Hefei 230026 (China)
2014-07-28
In this work, we present an approach to modulate femtosecond laser beams into Bessel beams with a spatial light modulator (SLM) for two-photon polymerization applications. Bessel beams with different parameters are generated and annular optical fields are produced at the focal plane of the objective. Uniform cylinder microstructures are fabricated by a single illumination during a few seconds without stage translation. By modulating the holograms encoded on the SLM, the diameters of the fabricated annular structures can be flexibly controlled in a wide range with no need of changing the optical elements and realignment of the optical path.
Optical tractor Bessel polarized beams
International Nuclear Information System (INIS)
Mitri, F.G.; Li, R.X.; Guo, L.X.; Ding, C.Y.
2017-01-01
Axial and transverse radiation force cross-sections of optical tractor Bessel polarized beams are theoretically investigated for a dielectric sphere with particular emphasis on the beam topological charge (or order), half-cone angle and polarization. The angular spectrum decomposition method (ASDM) is used to derive the non-paraxial electromagnetic (EM) field components of the Bessel beams. The multipole expansion method using vector spherical harmonics is utilized and appropriate beam-shape coefficients are derived in order to compute the radiation force cross-sections. The analysis has no limitation to a particular range of frequencies such that the Rayleigh, Mie or geometrical optics regimes can all be considered effectively using the present rigorous formalism. The focus of this investigation is to identify some of the tractor beam conditions so as to achieve retrograde motion of a dielectric sphere located arbitrarily in space. Numerical computations for the axial and transverse radiation force cross-sections are presented for linear, right-circular, radial, azimuthal and mixed polarizations of the individual plane waves forming the Bessel beams of zeroth- and first-order (with positive or negative helicity), respectively. As the sphere shifts off the beam's axis, the axial pulling (tractor) force is weakened. Moreover, the transverse radiation force cross-section field changes with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on the choice of ka and the half-cone angle α_0. These results are particularly important in the development of emergent technologies for the photophoretic assembly of optically-engineered (meta)materials with designed properties using optical tractor (vortex) beams, particle manipulation, levitation and positioning, and other applications. - Highlights: • Optical tractor Bessel polarized beams are
Harmonic Analysis Associated with the Generalized q-Bessel Operator
Directory of Open Access Journals (Sweden)
Ahmed Abouelaz
2016-01-01
Full Text Available In this article, we give a new harmonic analysis associated with the generalized q-Bessel operator. We introduce the generalized $q$-Bessel transform, the generalized q-Bessel translation and the generalized $q$-Bessel convolution product.
Materials processing with superposed Bessel beams
Yu, Xiaoming; Trallero-Herrero, Carlos A.; Lei, Shuting
2016-01-01
We report experimental results of femtosecond laser processing on the surface of glass and metal thin film using superposed Bessel beams. These beams are generated by a combination of a spatial light modulator (SLM) and an axicon with >50% efficiency, and they possess the long depth-of-focus (propagation-invariant) property as found in ordinary Bessel beams. Through micromachining experiments using femtosecond laser pulses, we show that multiple craters can be fabricated on glass with single-shot exposure, and the 1+(1) superposed beam can reduce collateral damage caused by the rings in zero-order Bessel beams in the scribing of metal thin film.
Computer program for Bessel and Hankel functions
Kreider, Kevin L.; Saule, Arthur V.; Rice, Edward J.; Clark, Bruce J.
1991-01-01
A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.
Inequalities for the Modified k-Bessel Function
Directory of Open Access Journals (Sweden)
Saiful Rahman Mondal
2017-07-01
Full Text Available The article considers the generalized k-Bessel functions and represents it as Wright functions. Then we study the monotonicity properties of the ratio of two different orders k- Bessel functions, and the ratio of the k-Bessel and the k-Bessel functions. The log-convexity with respect to the order of the k-Bessel also given. An investigation regarding the monotonicity of the ratio of the k-Bessel and k-confluent hypergeometric functions are discussed.
Bessel-like beams modulated by arbitrary radial functions
Herman; Wiggins
2000-06-01
An approximate method for determining the radial and axial intensity of a Bessel-like beam is presented for the general case in which a radial Bessel distribution of any order is modulated by an arbitrary function. For Bessel-Gauss, generalized Bessel-Gauss, and Bessel-super-Gauss beams, this simple approximation yields results that are very close to the exact values, while they are exact for Bessel beams. A practical beam that can be generated with a combination of simple lenses is also analyzed and illustrated.
Bessel functions for root systems via the trigonometric setting
DEFF Research Database (Denmark)
Ørsted, Bent; Said, S.B.
2005-01-01
In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases.......In this paper, we study generalized Bessel functions related to root systems and give explicit formulas in several cases....
Materials processing with superposed Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Yu, Xiaoming [Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506 (United States); Trallero-Herrero, Carlos A. [J. R. Macdonald Laboratory, Department of Physics, Kansas State University, Manhattan, KS 66506 (United States); Lei, Shuting, E-mail: lei@ksu.edu [Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506 (United States)
2016-01-01
Graphical abstract: - Highlights: • Superpositions of Bessel beams can be generated with >50% efficiency using an SLM and an axicon. • These beams have orders-of-magnitude increase in depth-of-focus compared to Gaussian beams. • Multiple craters can be fabricated on glass with single-shot exposure. • The 1+(−1) superposition can reduce collateral damage caused by the rings in the zero-order Bessel beams. - Abstract: We report experimental results of femtosecond laser processing on the surface of glass and metal thin film using superposed Bessel beams. These beams are generated by a combination of a spatial light modulator (SLM) and an axicon with >50% efficiency, and they possess the long depth-of-focus (propagation-invariant) property as found in ordinary Bessel beams. Through micromachining experiments using femtosecond laser pulses, we show that multiple craters can be fabricated on glass with single-shot exposure, and the 1+(−1) superposed beam can reduce collateral damage caused by the rings in zero-order Bessel beams in the scribing of metal thin film.
Generation of Nondiffracting Electron Bessel Beams
Directory of Open Access Journals (Sweden)
Vincenzo Grillo
2014-01-01
Full Text Available Almost 30 years ago, Durnin discovered that an optical beam with a transverse intensity profile in the form of a Bessel function of the first order is immune to the effects of diffraction. Unlike most laser beams, which spread upon propagation, the transverse distribution of these Bessel beams remains constant. Electrons also obey a wave equation (the Schrödinger equation, and therefore Bessel beams also exist for electron waves. We generate an electron Bessel beam by diffracting electrons from a nanoscale phase hologram. The hologram imposes a conical phase structure on the electron wave-packet spectrum, thus transforming it into a conical superposition of infinite plane waves, that is, a Bessel beam. We verify experimentally that these beams can propagate for 0.6 m without measurable spreading and can also reconstruct their intensity distributions after being partially obstructed by an obstacle. Finally, we show by numerical calculations that the performance of an electron microscope can be increased dramatically through use of these beams.
Generating bessel functions in mie scattering calculations using continued fractions.
Lentz, W J
1976-03-01
A new method of generating the Bessel functions and ratios of Bessel functions necessary for Mie calculations is presented. Accuracy is improved while eliminating the need for extended precision word lengths or large storage capability. The algorithm uses a new technique of evaluating continued fractions that starts at the beginning rather than the tail and has a built-in error check. The continued fraction representations for both spherical Bessel functions and ratios of Bessel functions of consecutive order are presented.
A Determinant Expression for the Generalized Bessel Polynomials
Directory of Open Access Journals (Sweden)
Sheng-liang Yang
2013-01-01
Full Text Available Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.
Microwave bessel beams generation using guided modes
Salem, Mohamed; Kamel, Aladin Hassan; Niver, Edip
2011-01-01
A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.
Generalized Bessel functions in tunnelling ionization
International Nuclear Information System (INIS)
Reiss, H R; Krainov, V P
2003-01-01
We develop two new approximations for the generalized Bessel function that frequently arises in the analytical treatment of strong-field processes, especially in non-perturbative multiphoton ionization theories. Both these new forms are applicable to the tunnelling environment in atomic ionization, and are analytically much simpler than the currently used low-frequency asymptotic approximation for the generalized Bessel function. The second of the new forms is an approximation to the first, and it is the second new form that exhibits the well-known tunnelling exponential
Microwave bessel beams generation using guided modes
Salem, Mohamed
2011-06-01
A novel method is devised for Bessel beams generation in the microwave regime. The beam is decomposed in terms of a number of guided transverse electric modes of a metallic waveguide. Modal expansion coefficients are computed from the modal power orthogonality relation. Excitation is achieved by means of a number of inserted coaxial loop antennas, whose currents are calculated from the excitation coefficients of the guided modes. The efficiency of the method is evaluated and its feasibility is discussed. Obtained results can be utilized to practically realize microwave Bessel beam launchers. © 2006 IEEE.
Kou, Na; Yu, Shixing; Li, Long
2017-01-01
A high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz. The APMS transmitarray is composed of four-layer conformal square-loop (FCSL) surfaces with both amplitude and phase modulation. The APMS can transform a quasi-spherical wave emitted from the feeding source into a pseudo non-diffractive high-order Bessel vortex beam with OAM. The APMS for a second-order Bessel beam carrying OAM in the n = 2 mode is designed, fabricated, and measured. Full-wave simulation and measurement results confirm that Bessel vortex beams with OAM can be effectively generated using the proposed APMS transmitarray.
Controlled acceleration of superimposed Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2013-06-01
Full Text Available spatial light modulator (SLM) to create superimposed, non-canonical, higher-order Bessel beams and a CCD camera to investigate the propagation of the resulting field. It is already known that the intensity profile of the resulting field experiences...
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the
A linear combination of modified Bessel functions
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.
Monotonicity and bounds on Bessel functions
Directory of Open Access Journals (Sweden)
Larry Landau
2000-07-01
Full Text Available survey my recent results on monotonicity with respect to order of general Bessel functions, which follow from a new identity and lead to best possible uniform bounds. Application may be made to the "spreading of the wave packet" for a free quantum particle on a lattice and to estimates for perturbative expansions.
Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid
Mitri, F. G.
2015-12-01
Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ = π / 2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz') waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ = 0) and backward (θ = π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.
Open-path Fourier transform infrared (OP/FTIR) spectrometry was used to measure the concentrations of ammonia, methane, and other atmospheric gases at an integrated swine production facility. The concentration-pathlength products of the target gases at this site often exceeded th...
BESSEL FILTER AND CHAOS: THREE-IN-ONE ACTION
DEFF Research Database (Denmark)
Tamaševicius, Arunas; Mykolaitis, Gytis; Bumeliene, Skaidra
2006-01-01
Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented.......Low-pass active Bessel filters are proposed to be used in a chaotic oscillator. The Bessel unit plays the role of three-in-one: the delay line, the amplifier, and the filter. Results of Spice simulations and hardware experiments are presented....
Generating and measuring non-diffracting vector Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2014-03-01
Full Text Available We demonstrate how to create non-diffracting vector Bessel beams by implementing a spatial light modulator (SLM) to generate scalar Bessel beams which are then converted into vector fields by the use of an azimuthally-varying birefringent plate...
Higher-order chaotic oscillator using active bessel filter
DEFF Research Database (Denmark)
Lindberg, Erik; Mykolaitis, Gytis; Bumelien, Skaidra
2010-01-01
A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending...
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
Directory of Open Access Journals (Sweden)
Soon-Mo Jung
2011-01-01
Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.
Azimuthally matched interactions and azimuthal correlation of Bessel light beams
International Nuclear Information System (INIS)
Khilo, N A
2000-01-01
A theoretical investigation is reported of the regime of azimuthally matched interactions in the process of conversion of the frequency of Bessel light beams. It is shown that this nonlinear interaction regime is accompanied by the establishment of correlations of the mutual azimuthal orientations of plane-wave components of Bessel beams and by an increase in the overlap integral. (nonlinear optical phenomena)
Optical trapping with Bessel beams generated from semiconductor lasers
International Nuclear Information System (INIS)
Sokolovskii, G S; Dudelev, V V; Losev, S N; Soboleva, K K; Deryagin, A G; Kuchinskii, V I; Sibbett, W; Rafailov, E U
2014-01-01
In this paper, we study generation of Bessel beams from semiconductor lasers with high beam propagation parameter M 2 and their utilization for optical trapping and manipulation of microscopic particles including living cells. The demonstrated optical tweezing with diodegenerated Bessel beams paves the way to replace their vibronic-generated counterparts for a range of applications towards novel lab-on-a-chip configurations
Higher-order harmonics of limited diffraction Bessel beams
Ding; Lu
2000-03-01
We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.
Zernike vs. Bessel circular functions in visual optics.
Trevino, Juan P; Gómez-Correa, Jesus E; Iskander, D Robert; Chávez-Cerda, Sabino
2013-07-01
We propose the Bessel Circular Functions as alternatives of the Zernike Circle Polynomials to represent relevant circular ophthalmic surfaces. We assess the fitting capabilities of the orthogonal Bessel Circular Functions by comparing them to Zernike Circle Polynomials for approximating a variety of computationally generated surfaces which can represent ophthalmic surfaces. The Bessel Circular Functions showed better modelling capabilities for surfaces with abrupt variations such as the anterior eye surface at the limbus region, and influence functions. From our studies we find that the Bessel Circular Functions can be more suitable for studying particular features of post surgical corneal surfaces. We show that given their boundary conditions and free oscillating properties, the Bessel Circular Functions are an alternative for representing specific wavefronts and can be better than the Zernike Circle Polynomials for some important cases of corneal surfaces, influence functions and the complete anterior corneal surface. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.
Theory of generalized Bessel functions: Pt. 2
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.; Chiccoli, C.
1991-01-01
In this paper the systematic study of the generalized Bessel functions (GBF), recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate, is continuated. The relations among different GBF are analysed and their importance for the solution of differential finite-difference equation of the Raman-Nath type is discussed. Numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF are presented
Efficient sorting of Bessel beams [Conference paper
CSIR Research Space (South Africa)
Mhlanga, T
2013-02-01
Full Text Available measured in entanglement and shown an increased spiral bandwidth17. Exploiting these properties of Bessel beams will make them very useful in the field of long-range, broad bandwidth communication systems. However, in order for these fields to be a... success in the area of optical communication, efficient techniques for extracting the information they carry (i.e. their azimuthal mode indices) need to exist. The ‘fork’ diffraction grating can be used to couple light of a particular OAM state into a...
Bessel light sheet structured illumination microscopy
Noshirvani Allahabadi, Golchehr
Biomedical study researchers using animals to model disease and treatment need fast, deep, noninvasive, and inexpensive multi-channel imaging methods. Traditional fluorescence microscopy meets those criteria to an extent. Specifically, two-photon and confocal microscopy, the two most commonly used methods, are limited in penetration depth, cost, resolution, and field of view. In addition, two-photon microscopy has limited ability in multi-channel imaging. Light sheet microscopy, a fast developing 3D fluorescence imaging method, offers attractive advantages over traditional two-photon and confocal microscopy. Light sheet microscopy is much more applicable for in vivo 3D time-lapsed imaging, owing to its selective illumination of tissue layer, superior speed, low light exposure, high penetration depth, and low levels of photobleaching. However, standard light sheet microscopy using Gaussian beam excitation has two main disadvantages: 1) the field of view (FOV) of light sheet microscopy is limited by the depth of focus of the Gaussian beam. 2) Light-sheet images can be degraded by scattering, which limits the penetration of the excitation beam and blurs emission images in deep tissue layers. While two-sided sheet illumination, which doubles the field of view by illuminating the sample from opposite sides, offers a potential solution, the technique adds complexity and cost to the imaging system. We investigate a new technique to address these limitations: Bessel light sheet microscopy in combination with incoherent nonlinear Structured Illumination Microscopy (SIM). Results demonstrate that, at visible wavelengths, Bessel excitation penetrates up to 250 microns deep in the scattering media with single-side illumination. Bessel light sheet microscope achieves confocal level resolution at a lateral resolution of 0.3 micron and an axial resolution of 1 micron. Incoherent nonlinear SIM further reduces the diffused background in Bessel light sheet images, resulting in
International Nuclear Information System (INIS)
Gouesbet, Gérard
2016-01-01
Localized approximation procedures are efficient ways to evaluate beam shape coefficients of a laser beam. They are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Relying on the concept of N-beams, it is demonstrated that care must be taken when constructing a localized approximation for a Bessel beam, namely a localized Bessel beam is satisfactorily close enough to the intended beam only when the axicon angle is small enough. - Highlights: • Localized approximation has been used to evaluate BSCs of Bessel beams. • N-beam procedure fails to provide a localized approximation for Bessel beams. • Localized approximation should be used only for small axicon angles.
A theorem regarding roots of the zero-order Bessel function of the first kind
Lin, X.-A.; Agrawal, O. P.
1993-01-01
This paper investigates a problem on the steady-state, conduction-convection heat transfer process in cylindrical porous heat exchangers. The governing partial differential equations for the system are obtained using the energy conservation law. Solution of these equations and the concept of enthalpy lead to a new approach to prove a theorem that the sum of inverse squares of all the positive roots of the zero order Bessel function of the first kind equals to one-forth. As a corollary, it is shown that the sum of one over pth power (p greater than or equal to 2) of the roots converges to some constant.
Spin polarisation with electron Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Schattschneider, P., E-mail: schattschneider@ifp.tuwien.ac.at [Institut für Festkörperphysik, Technische Universität Wien, A-1040 Wien (Austria); USTEM, Technische Universität Wien, A-1040 Wien (Austria); Grillo, V. [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco delle Scienze 37a, I-43100 Parma (Italy); Aubry, D. [Centrale Supelec, MSSMast CNRS 8579, F-92295 Châtenay-Malabry (France)
2017-05-15
The theoretical possibility to use an electron microscope as a spin polarizer is studied. It turns out that a Bessel beam passing a standard magnetic objective lens is intrinsically spin polarized when post-selected on-axis. In the limit of infinitely small detectors, the spin polarisation tends to 100 %. Increasing the detector size, the polarisation decreases rapidly, dropping below 10{sup −4} for standard settings of medium voltage microscopes. For extremely low voltages, the Figure of Merit increases by two orders of magnitude, approaching that of existing Mott detectors. Our findings may lead to new desings of spin filters, an attractive option in view of its inherent combination with the electron microscope, especially at low voltage. - Highlights: • TEM round magnetic lenses can act as spin polarizers when a Bessel beam is sent through. • This is found on theoretical grounds and demonstrated numerically for a few cases. • The effect is small, but can reach a Figure of Merit similar to existing Mott detectors. • This opens the possibility to construct nanometer-sized spin filters or detectors.
Bessel beam CARS of axially structured samples
Heuke, Sandro; Zheng, Juanjuan; Akimov, Denis; Heintzmann, Rainer; Schmitt, Michael; Popp, Jürgen
2015-06-01
We report about a Bessel beam CARS approach for axial profiling of multi-layer structures. This study presents an experimental implementation for the generation of CARS by Bessel beam excitation using only passive optical elements. Furthermore, an analytical expression is provided describing the generated anti-Stokes field by a homogeneous sample. Based on the concept of coherent transfer functions, the underling resolving power of axially structured geometries is investigated. It is found that through the non-linearity of the CARS process in combination with the folded illumination geometry continuous phase-matching is achieved starting from homogeneous samples up to spatial sample frequencies at twice of the pumping electric field wave. The experimental and analytical findings are modeled by the implementation of the Debye Integral and scalar Green function approach. Finally, the goal of reconstructing an axially layered sample is demonstrated on the basis of the numerically simulated modulus and phase of the anti-Stokes far-field radiation pattern.
Spatial-temporal dynamics of broadband terahertz Bessel beam propagation
International Nuclear Information System (INIS)
Semenova, V A; Kulya, M S; Bespalov, V G
2016-01-01
The unique properties of narrowband and broadband terahertz Bessel beams have led to a number of their applications in different fields, for example, for the depth of focusing and resolution enhancement in terahertz imaging. However, broadband terahertz Bessel beams can probably be also used for the diffraction minimization in the short-range broadband terahertz communications. For this purpose, the study of spatial-temporal dynamics of the broadband terahertz Bessel beams is needed. Here we present a simulation-based study of the propagating in non-dispersive medium broadband Bessel beams generated by a conical axicon lens. The algorithm based on scalar diffraction theory was used to obtain the spatial amplitude and phase distributions of the Bessel beam in the frequency range from 0.1 to 3 THz at the distances 10-200 mm from the axicon. Bessel beam field is studied for the different spectral components of the initial pulse. The simulation results show that for the given parameters of the axicon lens one can obtain the Gauss-Bessel beam generation in the spectral range from 0.1 to 3 THz. The length of non-diffraction propagation for a different spectral components was measured, and it was shown that for all spectral components of the initial pulse this length is about 130 mm. (paper)
Behavior of obliquely incident vector Bessel beams at planar interfaces
Salem, Mohamed
2013-01-01
We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster\\'s angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.
Behavior of obliquely incident vector Bessel beams at planar interfaces
Salem, Mohamed; Bagci, Hakan
2013-01-01
We investigate the behavior of full-vector electromagnetic Bessel beams obliquely incident at an interface between two electrically different media. We employ a Fourier transform domain representation of Bessel beams to determine their behavior upon reflection and transmission. This transform, which is geometric in nature, consists of elliptical support curves with complex weighting associated with them. The behavior of the scattered field at an interface is highly complex, owing to its full-vector nature; nevertheless, this behavior has a straightforward representation in the transform domain geometry. The analysis shows that the reflected field forms a different vector Bessel beam, but in general, the transmitted field cannot be represented as a Bessel beam. Nevertheless, using this approach, we demonstrate a method to propagate a Bessel beam in the refractive medium by launching a non- Bessel beam at the interface. Several interesting phenomena related to the behavior of Bessel beams are illustrated, such as polarized reflection at Brewster's angle incidence, and the Goos-Hänchen and Imbert-Federov shifts in the case of total reflection. © 2013 Optical Society of America.
Bessel collocation approach for approximate solutions of Hantavirus infection model
Directory of Open Access Journals (Sweden)
Suayip Yuzbasi
2017-11-01
Full Text Available In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.
Second-harmonic generation of practical Bessel beams
Huang, Jin H.; Ding, Desheng; Hsu, Yin-Sung
2009-11-01
A fast Gaussian expansion approach is used to investigate fundamental and second-harmonic generation in practical Bessel beams of finite aperture. The analysis is based on the integral solutions of the KZK equation under the quasilinear approximation. The influence of the medium's attenuation on the beam profile is considered. Analysis results show that the absorption parameter has a significant effect on the far-field beam profile of the second harmonic. Under certain circumstances, the second harmonic of a practical Bessel beam still has the main properties of an ideal Bessel beam of infinite aperture when it propagates within its depth of field.
Higher-order harmonics of general limited diffraction Bessel beams
International Nuclear Information System (INIS)
Ding De-Sheng; Huang Jin-Huang
2016-01-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m -th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. (special topic)
Higher-order harmonics of general limited diffraction Bessel beams
Ding, De-Sheng; Huang, Jin-Huang
2016-12-01
In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th-order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example. Project supported by the National Natural Science Foundation of China (Grant Nos. 11074038 and 11374051).
Generating superpositions of higher order bessel beams [Conference paper
CSIR Research Space (South Africa)
Vasilyeu, R
2009-10-01
Full Text Available An experimental setup to generate a superposition of higher-order Bessel beams by means of a spatial light modulator and ring aperture is presented. The experimentally produced fields are in good agreement with those calculated theoretically....
A simple derivation of new sum rules of Bessel functions
International Nuclear Information System (INIS)
Ciocci, F.; Dattoli, G.; Dipace, A.
1985-01-01
In this note it is exploited a recently suggested technique to get simple expressions for a class of sum rules of Bessel functions appearing in plasma physics; their relevance to the numerical evaluation of the Turkin function is also discussed
Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering
International Nuclear Information System (INIS)
Boer, D.; Gamberg, L.; Musch, B.U.; Prokudin, A.
2011-01-01
The concept of weighted asymmetries is revisited for semi-inclusive deep inelastic scattering. We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.
Talbot self-imaging phenomenon under Bessel beam illumination
Chakraborty, Rijuparna; Chowdhury, Subhajit Dutta; Chakraborty, Ajoy Kumar
2018-06-01
In this paper, we report the results of our theoretical studies on the phenomenon of self-imaging of periodic object under the illumination of zero-order Bessel beam. Our theoretical analysis indicates that the self-images are visible only after the walk-off distance of the Bessel beam used. It is also observed that the self-images bend around the optical axis of the setup. Besides, the present study justifies the importance of the conditions stipulated by Montgomery.
Fourier expansions and multivariable Bessel functions concerning radiation programmes
International Nuclear Information System (INIS)
Dattoli, G.; Richetta, M.; Torre, A.; Chiccoli, C.; Lorenzutta, S.; Maino, G.
1996-01-01
The link between generalized Bessel functions and other special functions is investigated using the Fourier series and the generalized Jacobi-Anger expansion. A new class of multivariable Hermite polynomials is then introduced and their relevance to physical problems discussed. As an example of the power of the method, applied to radiation physics, we analyse the role played by multi-variable Bessel functions in the description of radiation emitted by a charge constrained to a nonlinear oscillation. (author)
Generation and application of bessel beams in electron microscopy
Energy Technology Data Exchange (ETDEWEB)
Grillo, Vincenzo, E-mail: vincenzo.grillo@cnr.it [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); CNR-IMEM, Parco Area delle Scienze 37/A, I-43124 Parma (Italy); Harris, Jérémie [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada); Gazzadi, Gian Carlo [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Balboni, Roberto [CNR-IMM Bologna, Via P. Gobetti 101, 40129 Bologna (Italy); Mafakheri, Erfan [Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Dennis, Mark R. [H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL (United Kingdom); Frabboni, Stefano [CNR-Istituto Nanoscienze, Centro S3, Via G Campi 213/a, I-41125 Modena (Italy); Dipartimento di Fisica Informatica e Matematica, Università di Modena e Reggio Emilia, via G Campi 213/a, I-41125 Modena (Italy); Boyd, Robert W.; Karimi, Ebrahim [Department of Physics, University of Ottawa, 25 Templeton St., Ottawa, Ontario, Canada K1N 6N5 (Canada)
2016-07-15
We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process. - Highlights: • Bessel beams with different convergence, topological charge, visible fringes are demonstrated. • The relation between the Fresnel hologram and the probe shape is explained by detailed calculations and experiments. • Among the holograms here presented the highest relative efficiency is 37%, the best result ever reached for blazed holograms.
Vectorial diffraction properties of THz vortex Bessel beams.
Wu, Zhen; Wang, Xinke; Sun, Wenfeng; Feng, Shengfei; Han, Peng; Ye, Jiasheng; Yu, Yue; Zhang, Yan
2018-01-22
A vortex Bessel beam combines the merits of an optical vortex and a Bessel beam, including a spiral wave front and a non-diffractive feature, which has immense application potentials in optical trapping, optical fabrication, optical communications, and so on. Here, linearly and circularly polarized vortex Bessel beams in the terahertz (THz) frequency range are generated by utilizing a THz quarter wave plate, a spiral phase plate, and Teflon axicons with different opening angles. Taking advantage of a THz focal-plane imaging system, vectorial diffraction properties of the THz vortex Bessel beams are comprehensively characterized and discussed, including the transverse (Ex, Ey) and longitudinal (Ez) polarization components. The experimental phenomena are accurately simulated by adopting the vectorial Rayleigh diffraction integral. By varying the opening angle of the axicon, the characteristic parameters of these THz vortex Bessel beams are exhibited and compared, including the light spot size, the diffraction-free range, and the phase evolution process. This work provides the precise experimental and theoretical bases for the comprehension and application of a THz vortex Bessel beam.
Generation and application of Bessel beam in alignment works
International Nuclear Information System (INIS)
Gale, D. M.
2009-01-01
The divergence of a Gaussian laser beam is a limiting factor for optical alignment tasks at large distances. Bessel beams have almost zero divergence but are still not widely used. We discuss the construction of an alignment telescope based on Bessel beam generation using a commercial laser diode module. The Bessel beam is generated with conical or plano-convex lenses, and projected using a commercial CCD camera lens to extend the useful range of the beam. Our Bessel beams have diameters of between 0.5 - 1mm over beam lengths of 15m, representing a six-fold improvement compared to Gaussian beams, while the transverse beam structure (Bessel pattern) provides an excellent alignment aid for use with beam target. Another advantage of Bessel beams is their self-regeneration property, which allows the use of multiple beam targets with minimum beam degradation. We are using our crosshair targets with crosshair targets to align optical components in a large astronomical telescope, and can achieve precisions of tens of microns over distances of 20m using purely visual methods. (Author)
Generation and application of bessel beams in electron microscopy
International Nuclear Information System (INIS)
Grillo, Vincenzo; Harris, Jérémie; Gazzadi, Gian Carlo; Balboni, Roberto; Mafakheri, Erfan; Dennis, Mark R.; Frabboni, Stefano; Boyd, Robert W.; Karimi, Ebrahim
2016-01-01
We report a systematic treatment of the holographic generation of electron Bessel beams, with a view to applications in electron microscopy. We describe in detail the theory underlying hologram patterning, as well as the actual electron-optical configuration used experimentally. We show that by optimizing our nanofabrication recipe, electron Bessel beams can be generated with relative efficiencies reaching 37±3%. We also demonstrate by tuning various hologram parameters that electron Bessel beams can be produced with many visible rings, making them ideal for interferometric applications, or in more highly localized forms with fewer rings, more suitable for imaging. We describe the settings required to tune beam localization in this way, and explore beam and hologram configurations that allow the convergences and topological charges of electron Bessel beams to be controlled. We also characterize the phase structure of the Bessel beams generated with our technique, using a simulation procedure that accounts for imperfections in the hologram manufacturing process. - Highlights: • Bessel beams with different convergence, topological charge, visible fringes are demonstrated. • The relation between the Fresnel hologram and the probe shape is explained by detailed calculations and experiments. • Among the holograms here presented the highest relative efficiency is 37%, the best result ever reached for blazed holograms.
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
DEFF Research Database (Denmark)
Forchhammer, Søren; Kim, Chul E
1988-01-01
Digital squares are defined and their geometric properties characterized. A linear time algorithm is presented that considers a convex digital region and determines whether or not it is a digital square. The algorithm also determines the range of the values of the parameter set of its preimages....... The analysis involves transforming the boundary of a digital region into parameter space of slope and y-intercept...
International Nuclear Information System (INIS)
Doha, E H; Ahmed, H M
2004-01-01
A formula expressing explicitly the derivatives of Bessel polynomials of any degree and for any order in terms of the Bessel polynomials themselves is proved. Another explicit formula, which expresses the Bessel expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of its original Bessel coefficients, is also given. A formula for the Bessel coefficients of the moments of one single Bessel polynomial of certain degree is proved. A formula for the Bessel coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its Bessel coefficients is also obtained. Application of these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations in the expansion coefficients of the solution, is explained. An algebraic symbolic approach (using Mathematica) in order to build and solve recursively for the connection coefficients between Bessel-Bessel polynomials is described. An explicit formula for these coefficients between Jacobi and Bessel polynomials is given, of which the ultraspherical polynomial and its consequences are important special cases. Two analytical formulae for the connection coefficients between Laguerre-Bessel and Hermite-Bessel are also developed
Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam
International Nuclear Information System (INIS)
Mitri, F.G.
2016-01-01
An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas. - Highlights: • Optical nondiffracting nonparaxial fractional Bessel vortex beam is considered. • Negative spin torque on an absorptive dielectric Rayleigh sphere is predicted numerically. • Negative spin torque occurs as the sphere departs from the center of the beam.
CSIR Research Space (South Africa)
Belyi, VN
2011-05-01
Full Text Available The authors investigate the generation and transformation of Bessel beams through linear and nonlinear optical crystals. They outline the generation of high-order vortices due to propagation of Bessel beams along the optical axis of uniaxial...
Filtered Bessel functions in computerized tomography
International Nuclear Information System (INIS)
Rathore, R.K.S.; Munshi, P.; Bhatia, V.K.; Pandimani, S.
1988-01-01
Computer Aided Tomography (CAT) is widely used in the medical imaging area for the detection of cancerous tissues. It has also proved to be a good technique for measuring point-density (void-fraction) in two-phase flow systems. The present day CAT-scanners employ alogorithms which are essentially a discrete implementation of the Radon Inversion Formulae. These methods of reconstructing density distributions are fast and easy to implement. The present work is an attempt to simplify (and consequently to speed-up) the existing algorithms for the cases of radially symmetric density distribution. The method uses Radon Inversion Formulae and involves Bessels's Function of Fourier frequency. The algorithm was tested on some known distributions and the reconstruction is excellent. Data for bubbly-flow was also processed to obtain a point density distribution. The range of investigation was 0.6 ≤ ≤ 0.9 g/cm 3 , where ' ' denotes average cross-sectional value. The values of CT > are within ±0.03 g/cm 3 of the true values , for the data sets considered. The results are comparable with another simple method involving radial polynominals. It is observed that the simplified Radon Inversion Formulae for the radially symmetric case gives good results and can be implemented with ease. (orig.)
Indian Academy of Sciences (India)
Admin
2012-09-07
Sep 7, 2012 ... must first talk of permutations and Latin squares. A permutation of a finite set of objects is a linear arrange- ment of ... with a special element 1 ... Of course, this has .... tion method to disprove Euler's conjecture for infinitely.
Scattering of linearly polarized Bessel beams by dielectric spheres
Shoorian, Hamed
2017-09-01
The scattering of a Linearly Polarized Bessel Beam (LPBB) by an isotropic and homogenous dielectric sphere is investigated. Using analytical relation between the cylindrical and the spherical vector wave functions, all the closed- form analytical expressions, in terms of spherical wave-functions expansions, are derived for the scattered field. It is shown that in the case of conical angle of incident Bessel beam is equal to zero, the Linearly Polarized Bessel Beam becomes a plane wave and its scattering coefficients become the same as the expansion coefficients of plane wave in Mie theory. The transverse Cartesian and spherical components of the electric field, scattered by a sphere are shown in the z-plane for different cases, moreover the intensity of the incident Bessel beam and the effects of its conical angle on the scattered field and the field inside the sphere are investigated. To quantitatively study the scattering phenomenon and the variations of the fields inside and outside of the sphere, the scattering and absorption efficiencies are obtained for the scattering of the linearly-polarized Bessel beam, and are compared with those of the plane wave scattering.
International Nuclear Information System (INIS)
Fan Hongyi; Wang Yong
2006-01-01
With the help of Bose operator identities and entangled state representation and based on our previous work [Phys. Lett. A 325 (2004) 188] we derive some new generalized Bessel equations which also have Bessel function as their solution. It means that for these intricate higher-order differential equations, we can get Bessel function solutions without using the expatiatory power-series expansion method.
Lyon, Betty Clayton
1990-01-01
One method of making magic squares using a prolongated square is illustrated. Discussed are third-order magic squares, fractional magic squares, fifth-order magic squares, decimal magic squares, and even magic squares. (CW)
DEFF Research Database (Denmark)
Rose, Jeremy; Sæbø, Øystein
2005-01-01
On-line political communities, such as the Norwegian site Demokratitorget (Democracy Square), are often designed according to a set of un-reflected assumptions about the political interests of their potential members. In political science, democracy is not taken as given in this way, but can...... be represented by different models which characterize different relationships between politicians and the citizens they represent. This paper uses quantitative and qualitative content analysis to analyze the communication mediated by the Democracy Square discussion forum in the first ten months of its life......-Republican model. In the qualitative analysis the discourse is analysed as repeating genres – patterns in the communication form which also reflect the conflict of interest between citizens and politicians. Though the analysis gives insight into the nature of the discourse the site supports, little is known about...
Bessel functions in mass action modeling of memories and remembrances
Energy Technology Data Exchange (ETDEWEB)
Freeman, Walter J. [Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720-3206 (United States); Capolupo, Antonio [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy); Kozma, Robert [Department of Mathematics, Memphis University, Memphis, TN 38152 (United States); Olivares del Campo, Andrés [The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BZ (United Kingdom); Vitiello, Giuseppe, E-mail: vitiello@sa.infn.it [Dipartimento di Fisica, E.R. Caianiello Universitá di Salerno, and INFN Gruppo collegato di Salerno, Fisciano 84084 (Italy)
2015-10-02
Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory. - Highlights: • We consider data from observations of impulse responses of cortex to electric shocks. • These data are fitted by Bessel functions which may be represented by couples of damped/amplified oscillators. • We study the data by using couples of damped/amplified oscillators. • We discuss lifetime and other properties of the considered brain processes.
Series of Bessel and Kummer-type functions
Baricz, Arpad; Pogány, Tibor K
2017-01-01
This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.
1972-01-01
With the existing Systems for using the accelerated protons, it is possible to supply only one slow ejected beam (feeding the East Hall) and, at the same time, to have only a small percentage of the beam on an internal target (feeding the South Hall). The arrangement will be replaced by a new System called SQUARE (Semi- QUAdrupole Resonant Extraction) which will give greater flexibility in supplying the three areas.
Bessel beam fluorescence lifetime tomography of live embryos (Conference Presentation)
Xu, Dongli; Peng, Leilei
2016-03-01
Optical tomography allows isotropic 3D imaging of embryos. Scanning-laser optical tomography (SLOT) has superior light collecting efficiency than wide-field optical tomography, making it ideal for fluorescence imaging of live embryos. We previously reported an imaging system that combines SLOT with a novel Fourier-multiplexed fluorescence lifetime imaging (FmFLIM) technique named FmFLIM-SLOT. FmFLIM-SLOT performs multiplexed FLIM-FRET readout of multiple FRET sensors in live embryos. Here we report a recent effort on improving the spatial resolution of the FmFLIM-SLOT system in order to image complex biochemical processes in live embryos at the cellular level. Optical tomography has to compromise between resolution and the depth of view. In SLOT, the commonly-used focused Gaussian beam diverges quickly from the focal plane, making it impossible to achieve high resolution imaging in a large volume specimen. We thus introduce Bessel beam laser-scanning tomography, which illuminates the sample with a spatial-light-modulator-generated Bessel beam that has an extended focal depth. The Bessel beam is scanned across the whole specimen. Fluorescence projection images are acquired at equal angular intervals as the sample rotates. Reconstruction artifacts due to annular-rings of the Bessel beam are removed by a modified 3D filtered back projection algorithm. Furthermore, in combination of Fourier-multiplexing fluorescence lifetime imaging (FmFLIM) method, the Bessel FmFLIM-SLOT system is capable of perform 3D lifetime imaging of live embryos at cellular resolution. The system is applied to in-vivo imaging of transgenic Zebrafish embryos. Results prove that Bessel FmFLIM-SLOT is a promising imaging method in development biology research.
Elliptic integral evaluations of Bessel moments
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Glasser, M.L.
2008-01-06
We record what is known about the closed forms for variousBessel function moments arising in quantum field theory, condensed mattertheory and other parts of mathematical physics. More generally, wedevelop formulae for integrals of products of six or fewer Besselfunctions. In consequence, we are able to discover and prove closed formsfor c(n,k) := Int_0 inf tk K_0 n(t) dt, with integers n = 1, 2, 3, 4 andk greater than or equal to 0, obtaining new results for the even momentsc3,2k and c4,2k . We also derive new closed forms for the odd momentss(n,2k+1) := Int_0 inf t(2k+1) I_0(t) K_0n(t) dt,with n = 3, 4 and fort(n,2k+1) := Int_0 inf t(2k+1) I_02(t) K_0(n-2) dt, with n = 5, relatingthe latter to Green functions on hexagonal, diamond and cubic lattices.We conjecture the values of s(5,2k+1), make substantial progress on theevaluation of c(5,2k+1), s(6,2k+1) and t(6,2k+1) and report more limitedprogress regarding c(5,2k), c(6,2k+1) and c(6,2k). In the process, weobtain 8 conjectural evaluations, each of which has been checked to 1200decimal places. One of these lies deep in 4-dimensional quantum fieldtheory and two are probably provable by delicate combinatorics. Thereremains a hard core of five conjectures whose proofs would be mostinstructive, to mathematicians and physicists alike.
Practical realization of a microwave Bessel beam launcher
Manzhura, Oksana
2011-08-01
An experimental setup is realized to practically generate Bessel beams in the microwave regime. The setup, which consists of a series of circular loop antennas inserted coaxially inside a circular metallic waveguide, excites the waveguide\\'s transverse-electric modes such that their superposition forms a Bessel beam at the open-end of the waveguide. The excitation currents are calculated from the needed excitation coefficients of each guided mode, which, in turn, are calculated from the modal decomposition of the beam. The efficiency of the setup is evaluated and the obtained experimental results are compared to the theoretical estimates. © 2011 IEEE.
THz computed tomography system with zero-order Bessel beam
Niu, Liting; Wu, Qiao; Wang, Kejia; Liu, Jinsong; Yang, Zhengang
2018-01-01
Terahertz (THz) waves can penetrate many optically opaque dielectric materials such as plastics, ceramics and colorants. It is effective to reveal the internal structures of these materials. We have built a THz Computed Tomography (CT) system with 0.3 THz zero-order Bessel beam to improve the depth of focus of this imaging system for the non-diffraction property of Bessel beam. The THz CT system has been used to detect a paper cup with a metal rod inside. Finally, the acquired projection data have been processed by the filtered back-projection algorithm and the reconstructed image of the sample has been obtained.
Wave-optics description of self-healing mechanism in Bessel beams.
Aiello, Andrea; Agarwal, Girish S
2014-12-15
Bessel beams' great importance in optics lies in that these propagate without spreading and can reconstruct themselves behind an obstruction placed across their path. However, a rigorous wave-optics explanation of the latter property is missing. In this work, we study the reconstruction mechanism by means of a wave-optics description. We obtain expressions for the minimum distance beyond the obstruction at which the beam reconstructs itself, which are in close agreement with the traditional one determined from geometrical optics. Our results show that the physics underlying the self-healing mechanism can be entirely explained in terms of the propagation of plane waves with radial wave vectors lying on a ring.
Scattering of a high-order Bessel beam by a spheroidal particle
Han, Lu
2018-05-01
Within the framework of generalized Lorenz-Mie theory (GLMT), scattering from a homogeneous spheroidal particle illuminated by a high-order Bessel beam is formulated analytically. The high-order Bessel beam is expanded in terms of spheroidal vector wave functions, where the spheroidal beam shape coefficients (BSCs) are computed conveniently using an intrinsic method. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident Bessel beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by nonspherical particles and particle manipulation applications using Bessel beams.
Modified Bessel P-integrals and P-derivatives and their properties
International Nuclear Information System (INIS)
Volosivets, S S
2014-01-01
We study the modified Bessel P-integral, whose properties are similar to those of the Bessel potential, and the modified Bessel P-derivative. These operators are inverse to each other. We prove analogues of the embedding theorems of Hardy, Littlewood, Stein, Zygmund and Lizorkin concerning the images of L p (R) under the action of Bessel potentials. We give applications of the Bessel integral and derivative to the integrability of the P-adic Fourier transform and to approximation theory (an embedding theorem of Ul'yanov type)
FUNPACK-2, Subroutine Library, Bessel Function, Elliptical Integrals, Min-max Approximation
International Nuclear Information System (INIS)
Cody, W.J.; Garbow, Burton S.
1975-01-01
1 - Description of problem or function: FUNPACK is a collection of FORTRAN subroutines to evaluate certain special functions. The individual subroutines are (Identification/Description): NATSI0 F2I0 Bessel function I 0 ; NATSI1 F2I1 Bessel function I 1 ; NATSJ0 F2J0 Bessel function J 0 ; NATSJ1 F2J1 Bessel function J 1 ; NATSK0 F2K0 Bessel function K 0 ; NATSK1 F2K1 Bessel function K 1 ; NATSBESY F2BY Bessel function Y ν ; DAW F1DW Dawson's integral; DELIPK F1EK Complete elliptic integral of the first kind; DELIPE F1EE Complete elliptic integral of the second kind; DEI F1EI Exponential integrals; NATSPSI F2PS Psi (logarithmic derivative of gamma function); MONERR F1MO Error monitoring package . 2 - Method of solution: FUNPACK uses evaluation of min-max approximations
Quasi-fractional approximation to the Bessel functions
International Nuclear Information System (INIS)
Guerrero, P.M.L.
1989-01-01
In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4
On functions defined by sums of products of Bessel functions
International Nuclear Information System (INIS)
Martin, P A
2008-01-01
Various functions, defined as infinite series of products of Bessel functions of the first kind, are studied. Integral representations are obtained, and then used to deduce asymptotic approximations. Although several methods have been investigated (including power series expansions and integral transforms), methods based on Fourier series emerge as the most useful
Superiority of Bessel function over Zernicke polynomial as base ...
Indian Academy of Sciences (India)
Abstract. Here we describe the superiority of Bessel function as base function for radial expan- sion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev's model for ...
Further properties of the zeros of Bessel functions
Directory of Open Access Journals (Sweden)
Carla Giordano
1987-11-01
Full Text Available New monotonicity and convexity properties for the zeros cνk (k=1,2,... of the Bessel functions are proved. New inequalities for cνk are also given. These inequalities are useful for small values of ν.
On a family of Bessel type functions: Estimations, series, overconvergence
Paneva-Konovska, Jordanka
2017-12-01
A family of the Bessel-Maitland functions are considered in this paper and some useful estimations are obtained for them. Series defined by means of these functions are considered and their behaviour on the boundaries of the convergence domains is discussed. Using the obtained estimations, necessary and sufficient conditions for the series overconvergence, as well as Hadamard type theorem are proposed.
On the product and ratio of Bessel random variables
Directory of Open Access Journals (Sweden)
Saralees Nadarajah
2005-01-01
Full Text Available The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.
Generating superpositions of higher–order Bessel beams [Journal article
CSIR Research Space (South Africa)
Vasilyeu, R
2009-12-01
Full Text Available The authors report the first experimental generation of the superposition of higher-order Bessel beams, by means of a spatial light modulator (SLM) and a ring slit aperture. They present illuminating a ring slit aperture with light which has...
Two-photon optics of Bessel-Gaussian modes
CSIR Research Space (South Africa)
McLaren, M
2013-09-01
Full Text Available In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum...
Resonant Self-Trapping and Absorption of Intense Bessel Beams
International Nuclear Information System (INIS)
Fan, J.; Parra, E.; Milchberg, H. M.
2000-01-01
We report the observation of resonant self-trapping and enhanced laser-plasma heating resulting from propagation of high intensity Bessel beams in neutral gas. The enhancement in absorption and plasma heating is directly correlated to the spatial trapping of laser radiation. (c) 2000 The American Physical Society
Special features of local spatial spectrum of Bessel light beams
CSIR Research Space (South Africa)
Belyi, VN
2011-11-01
Full Text Available In this paper the authors consider the angular spectrum of an apertured Bessel beam when the aperture is circular and shifted laterally with respect to the optical axis. Since the perturbation of the resulting angular spectrum is due to a spatially...
Effective and efficient method of calculating Bessel beam fields
CSIR Research Space (South Africa)
Litvin, IA
2005-01-01
Full Text Available Bessel beams have gathered much interest of late due to their properties of near diffraction free propagation and self reconstruction after obstacles. Such laser beams have already found applications in fields such as optical tweezers and as pump...
Asymmetric skew Bessel processes and their applications to finance
Decamps, M.; Goovaerts, M.J.; Schoutens, W.
2006-01-01
In this paper, we extend the Harrison and Shepp's construction of the skew Brownian motion (1981) and we obtain a diffusion similar to the two-dimensional Bessel process with speed and scale densities discontinuous at one point. Natural generalizations to multi-dimensional and fractional order
Heat kernel analysis for Bessel operators on symmetric cones
DEFF Research Database (Denmark)
Möllers, Jan
2014-01-01
. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space...
Comparison of square law, linear and bessel detectors for CA and OS CFAR algorithms
CSIR Research Space (South Africa)
Melebari, A
2015-10-01
Full Text Available . These detectors have difference detection performances and computational costs. In this paper, the detection performances of these three detectors are investigated for CA-CFAR and Order Statistic CFAR (OS-CFAR) algorithms using simulated and measured data of semi...
Mean intensity of the fundamental Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In the given article mean intensity of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is studied. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian beam of optical radiation. Distributions of mean intensity of a fundamental Bessel- Gaussian beam optical beam in longitudinal and transverse to a direction of propagation of optical radiation are investigated in detail. Influence of atmospheric turbulence on change of radius of the central part of a Bessel optical beam is estimated. Values of parameters at which it is possible to generate in turbulent atmosphere a nondiffracting pseudo-Bessel optical beam by means of a fundamental Bessel-Gaussian optical beam are established.
VizieR Online Data Catalog: Bessel (1825) calculation for geodesic measurements (Karney+, 2010)
Karney, C. F. F.; Deakin, R. E.
2010-06-01
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. Included here are the tables that accompanied Bessel's paper (with corrections). The tables were crafted by Bessel to be minimize the labor of hand calculations. To this end, he adjusted the intervals in the tables, the number of terms included in the series, and the number of significant digits given so that the final results are accurate to about 8 places. For that reason, the most useful form of the tables is as the PDF file which provides the tables in a layout close to the original. Also provided is the LaTeX source file for the PDF file. Finally, the data has been put into a format so that it can be read easily by computer programs. All the logarithms are in base 10 (common logarithms). The characteristic and the mantissa should be read separately (indicated as x.c and x.m in the file description). Thus the first entry in the table, -4.4, should be parsed as "-4" (the characteristic) and ".4" (the mantissa); the anti-log for this entry is 10(-4+0.4)=2.5e-4. The "Delta" columns give the first difference of the preceding column, i.e., the difference of the preceding column in the next row and the preceding column in the current row. In the printed tables these are expressed as "units in the last place" and the differences are of the rounded representations in the preceding columns (to minimize interpolation errors). In table1.dat these are given scaled to a match the format used for the preceding column, as indicated by the units given for these columns. The unit log(") (in the description within square brackets [arcsec]) means the logarithm of a quantity expressed in arcseconds. (3 data files).
Further 'comment on 'Generalized Bessel functions in tunnelling ionization''
International Nuclear Information System (INIS)
Reiss, H R; Krainov, V P
2005-01-01
J Bauer, in commenting on our tunnelling approximation for the generalized Bessel function, points out that when the approximation is applied to strong-field ionization, it is suitable only for the lowest-energy part of an ionization spectrum. We do not disagree. We point out several things: the results of Bauer are to be expected; linear polarization results are dominated by the lowest part of the multiphoton spectrum; and we do not recommend practical use of this tunnelling approximation, since the asymptotic approximation is so much better. We show comparisons of momentum distributions calculated with the tunnelling approximation and those with the complete strong-field approximation, which show in more detail than spectrum comparisons that the tunnelling approximation to the generalized Bessel function is applicable only to the low-momentum part of the distribution, and neglects altogether the high-momentum portion. (reply)
Polarization properties of linearly polarized parabolic scaling Bessel beams
Energy Technology Data Exchange (ETDEWEB)
Guo, Mengwen; Zhao, Daomu, E-mail: zhaodaomu@yahoo.com
2016-10-07
The intensity profiles for the dominant polarization, cross polarization, and longitudinal components of modified parabolic scaling Bessel beams with linear polarization are investigated theoretically. The transverse intensity distributions of the three electric components are intimately connected to the topological charge. In particular, the intensity patterns of the cross polarization and longitudinal components near the apodization plane reflect the sign of the topological charge. - Highlights: • We investigated the polarization properties of modified parabolic scaling Bessel beams with linear polarization. • We studied the evolution of transverse intensity profiles for the three components of these beams. • The intensity patterns of the cross polarization and longitudinal components can reflect the sign of the topological charge.
Optimized Kaiser-Bessel Window Functions for Computed Tomography.
Nilchian, Masih; Ward, John Paul; Vonesch, Cedric; Unser, Michael
2015-11-01
Kaiser-Bessel window functions are frequently used to discretize tomographic problems because they have two desirable properties: 1) their short support leads to a low computational cost and 2) their rotational symmetry makes their imaging transform independent of the direction. In this paper, we aim at optimizing the parameters of these basis functions. We present a formalism based on the theory of approximation and point out the importance of the partition-of-unity condition. While we prove that, for compact-support functions, this condition is incompatible with isotropy, we show that minimizing the deviation from the partition of unity condition is highly beneficial. The numerical results confirm that the proposed tuning of the Kaiser-Bessel window functions yields the best performance.
Particle confinement by a radially polarized laser Bessel beam
Laredo, Gilad; Kimura, Wayne D.; Schächter, Levi
2017-03-01
The stable trajectory of a charged particle in an external guiding field is an essential condition for its acceleration or for forcing it to generate radiation. Examples of possible guiding devices include a solenoidal magnetic field or permanent periodic magnet in klystrons, a wiggler in free-electron lasers, the lattice of any accelerator, and finally the crystal lattice for the case of channeling radiation. We demonstrate that the trajectory of a point-charge in a radially polarized laser Bessel beam may be stable similarly to the case of a positron that bounces back and forth in the potential well generated by two adjacent atomic planes. While in the case of channeling radiation, the transverse motion is controlled by a harmonic oscillator equation, for a Bessel beam the transverse motion is controlled by the Mathieu equation. Some characteristics of the motion are presented.
The Generation Mechanism of Airy—Bessel Wave Packets in Free Space
International Nuclear Information System (INIS)
Ren Zhi-Jun; Ying Chao-Fu; Fan Chang-Jiang; Wu Qiong
2012-01-01
Localized optical Airy—Bessel configuration wave packets were first generated on the basis of a grating-telescope combination [Nat. Photon. 4(2010) 103]. By studying the spatially induced group velocity dispersion effect of ultrashort pulsed Bessel beams during propagation, we find the universal physical foundation of generating Airy—Bessel wave packets (ABWs) in free space. The research results are expected to open up more common channels for generating stable linear localized ABWs
Mark Setterfield
2015-01-01
Path dependency is defined, and three different specific concepts of path dependency – cumulative causation, lock in, and hysteresis – are analyzed. The relationships between path dependency and equilibrium, and path dependency and fundamental uncertainty are also discussed. Finally, a typology of dynamical systems is developed to clarify these relationships.
Compact and continuous embeddings of logarithmic Bessel potential spaces
Czech Academy of Sciences Publication Activity Database
Edmunds, D. E.; Gurka, P.; Opic, Bohumír
2005-01-01
Roč. 168, č. 3 (2005), s. 229-250 ISSN 0039-3223 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bessel potential spaces * spaces of Hölder-continuous functions * Lorentz-Zygmund spaces Subject RIV: BA - General Mathematics Impact factor: 0.538, year: 2005
Stability of cylindrical plasma in the Bessel function model
International Nuclear Information System (INIS)
Yamagishi, T.; Gimblett, C.G.
1988-01-01
The stability of free boundary ideal and tearing modes in a cylindrical plasma is studied by examining the discontinuity (Δ') of the helical flux function given by the force free Bessel function model at the singular surface. The m = O and m = 1 free boundary tearing modes become strongly unstable when the singular surface is just inside the plasma boundary for a wide range of longitudinal wave numbers. (author)
Extensions of Bessel sequences to dual pairs of frames
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2013-01-01
Tight frames in Hilbert spaces have been studied intensively for the past years. In this paper we demonstrate that it often is an advantage to use pairs of dual frames rather than tight frames. We show that in any separable Hilbert space, any pairs of Bessel sequences can be extended to a pair of...... be extended to a pair of dual frames. © 2012 Elsevier Inc. All rights reserved....
Square well approximation to the optical potential
International Nuclear Information System (INIS)
Jain, A.K.; Gupta, M.C.; Marwadi, P.R.
1976-01-01
Approximations for obtaining T-matrix elements for a sum of several potentials in terms of T-matrices for individual potentials are studied. Based on model calculations for S-wave for a sum of two separable non-local potentials of Yukawa type form factors and a sum of two delta function potentials, it is shown that the T-matrix for a sum of several potentials can be approximated satisfactorily over all the energy regions by the sum of T-matrices for individual potentials. Based on this, an approximate method for finding T-matrix for any local potential by approximating it by a sum of suitable number of square wells is presented. This provides an interesting way to calculate the T-matrix for any arbitary potential in terms of Bessel functions to a good degree of accuracy. The method is applied to the Saxon-Wood potentials and good agreement with exact results is found. (author)
Multipole expansion of acoustical Bessel beams with arbitrary order and location.
Gong, Zhixiong; Marston, Philip L; Li, Wei; Chai, Yingbin
2017-06-01
An exact solution of expansion coefficients for a T-matrix method interacting with acoustic scattering of arbitrary order Bessel beams from an obstacle of arbitrary location is derived analytically. Because of the failure of the addition theorem for spherical harmonics for expansion coefficients of helicoidal Bessel beams, an addition theorem for cylindrical Bessel functions is introduced. Meanwhile, an analytical expression for the integral of products including Bessel and associated Legendre functions is applied to eliminate the integration over the polar angle. Note that this multipole expansion may also benefit other scattering methods and expansions of incident waves, for instance, partial-wave series solutions.
The Bessel functions J0 and J1 of complex argument
International Nuclear Information System (INIS)
Ardill, R.W.B.; Moriarty, K.J.M.
1977-01-01
The Bessel function appears in a wide range of physical applications. The package Bessel contains complex function routines to calculate J 0 (z) and J 1 (z) for complex z. Bessel functions of higher order n 0 (z) and J 1 (z) for all values of mod(z) up to machine overflow. For mod(z) 10, the results diverge quite rapidly from their actual values. The accuracy for mod(z)<=10 is sufficient for most physical applications, and the polynomial approximations provide a quicker calculation of Bessel functions than the use of the ascending series formula used previously, particularly for values of mod(z) near 10. (Auth.)
Higher-order Bessel like beams with z-dependent cone angles
CSIR Research Space (South Africa)
Ismail, Y
2010-08-01
Full Text Available .64.81.22. Terms of Use: http://spiedl.org/terms Fig.5: Optical design to generate z-dependent Bessel-like beams 4. CONSIDERING A MATHEMATICAL APPROACH TO EXPLAINING Z-DEPENDENT BLB?S The stationary phase method is implemented in order to confirm... on higher-order z-dependent BLB?s [6]. 5. EXPERIMENTALLY GENERATED Z-DEPENDENT BESSEL-LIKE BEAMS From the above in can be deduced that these beams are Bessel-like hence they are so named z-dependent Bessel-like beams. These beams are produced however...
Self-healing of Bessel-like beams with longitudinally dependent cone angles
International Nuclear Information System (INIS)
Litvin, I; Burger, L; Forbes, A
2015-01-01
Bessel beams have been extensively studied, but to date have been created over a finite region inside the laboratory. Recently Bessel-like beams with longitudinally dependent cone angles have been introduced allowing for a potentially infinite quasi non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed in the field, with the distance increasing as the Bessel-like beam propagates farther. We outline the theoretical concept for this self-healing and confirm it experimentally. (paper)
Nonparaxial Bessel and Bessel–Gauss pincers light-sheets
Energy Technology Data Exchange (ETDEWEB)
Mitri, F.G., E-mail: F.G.Mitri@ieee.org
2017-01-23
Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
Optical breakdown of helium in Bessel laser radiation beams
International Nuclear Information System (INIS)
Andreev, N E; Pleshanov, I V; Margolin, L Ya; Pyatnitskii, Lev N
1998-01-01
Numerical simulation is used to investigate the dynamics of formation of a helium plasma in Bessel beams, shaped by an axicon and a phase converter from a laser radiation pulse with Gaussian temporal and radial intensity profiles. The beam intensities at the breakdown threshold are determined as a function of the pulse duration for various radial field distributions in a beam characterised by Bessel functions of order m (m = 0 - 5). It is shown that in the investigated range of parameters the threshold intensity is independent of m. The temporal and spatial evolution of the resultant plasma, and the dependence of the plasma characteristics on the pulse parameters are considered. Conditions are found for the formation of tubular plasma channels in beams of orders m≥1. The adopted model of the optical breakdown of helium is shown to be satisfactory because of a good agreement between the results of calculations of the moment of breakdown in a zeroth-order Bessel beam and experimental results. (interaction of laser radiation with matter. laser plasma)
Nonparaxial Bessel and Bessel–Gauss pincers light-sheets
International Nuclear Information System (INIS)
Mitri, F.G.
2017-01-01
Highlights: • Bessel and Bessel–Gauss autofocusing light sheets (i.e. beams in 2D) are developed. • The light-sheets are synthesized based on the angular spectrum decomposition method. • Computations of the scattering, radiation force and torque benefit from the solutions. - Abstract: Nonparaxial optical Bessel and Bessel–Gauss pincers optical-sheets are introduced based upon the angular spectrum decomposition in plane waves. The angular spectrum function and the beam-shape coefficients are expressed by means of improper integrals computed numerically. The radiated component of the electric field is also evaluated, displaying unique features of the nonparaxial Bessel pincers light-sheets. This new type of auto-focusing light-sheets finds potential applications in the development of novel methods in optical light-sheet tweezers for particle manipulation in opto-fluidics, particle sizing and imaging. Numerical predictions for the scattering, radiation force and torque, and particle dynamics also benefit from the developed beam solution.
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.I.
1980-01-01
A Hilbert space of paths, the elements of which are determined by trigonometric series, was proposed and used recently by Truman. This space is shown to consist precisely of all absolutely continuous paths ending in the origin with square-integrable derivatives
Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam
Mitri, F. G.
2016-10-01
An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas.
Mitri, F G
2017-02-01
The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto
K-Bessel functions associated to a 3-rank Jordan algebra
Directory of Open Access Journals (Sweden)
Hacen Dib
2005-01-01
Full Text Available Using the Bessel-Muirhead system, we can express the K-Bessel function defined on a Jordan algebra as a linear combination of the J-solutions. We determine explicitly the coefficients when the rank of this Jordan algebra is three after a reduction to the rank two. The main tools are some algebraic identities developed for this occasion.
Bessel equation as an operator identity's matrix element in quantum mechanics
International Nuclear Information System (INIS)
Fan Hongyi; Li Chao
2004-01-01
We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented
The Bessel-Struve intertwining operator on ℂ and mean-periodic functions
Directory of Open Access Journals (Sweden)
A. Gasmi
2004-01-01
Full Text Available We give a description of all transmutation operators from the Bessel-Struve operator to the second-derivative operator. Next we define and characterize the mean-periodic functions on the space ℋ of entire functions and we characterize the continuous linear mappings from ℋ into itself which commute with Bessel-Struve operator.
Kerimov, M. K.
2018-01-01
This paper is the fourth in a series of survey articles concerning zeros of Bessel functions and methods for their computation. Various inequalities, estimates, expansions, etc. for positive zeros are analyzed, and some results are described in detail with proofs.
On the validity of localized approximation for an on-axis zeroth-order Bessel beam
International Nuclear Information System (INIS)
Gouesbet, Gérard; Lock, J.A.; Ambrosio, L.A.; Wang, J.J.
2017-01-01
Localized approximation procedures are efficient ways to evaluate beam shape coefficients of laser beams, and are particularly useful when other methods are ineffective or inefficient. Several papers in the literature have reported the use of such procedures to evaluate the beam shape coefficients of Bessel beams. Examining the specific case of an on-axis zeroth-order Bessel beam, we demonstrate that localized approximation procedures are valid only for small axicon angles. - Highlights: • The localized approximation has been widely used to evaluate the Beam Shape Coefficients (BSCs) of Bessel beams. • The validity of this approximation is examined in the case of an on-axis zeroth-order Bessel beam. • It is demonstrated, in this specific example, that the localized approximation is efficient only for small enough axicon angles. • It is easily argued that this result must remain true for any kind of Bessel beams.
International Nuclear Information System (INIS)
He, Xi; Wu, Fengtie; Chen, Ziyang; Pu, Jixiong; Chavez-Cerda, Sabino
2016-01-01
The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams. (paper)
Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In this paper the theoretical research of coherent properties of the vortex Bessel-Gaussian optical beams propagating in turbulent atmosphere are developed. The approach to the analysis of this problem is based on the analytical solution of the equation for the transverse second-order mutual coherence function of a field of optical radiation. The behavior of integral scale of coherence degree of vortex Bessel-Gaussian optical beams depending on parameters of an optical beam and characteristics of turbulent atmosphere is particularly considered. It is shown that the integral scale of coherence degree of a vortex Bessel-Gaussian optical beam essentially depends on value of a topological charge of a vortex optical beam. With increase in a topological charge of a vortex Bessel-Gaussian optical beam the value of integral scale of coherence degree of a vortex Bessel-Gaussian optical beam are decreased.
Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere
Lukin, Igor P.
2017-11-01
In this article the coherence of a fundamental Bessel-Gaussian optical beam in turbulent atmosphere is analyzed. The problem analysis is based on the solution of the equation for the transverse second-order mutual coherence function of a fundamental Bessel-Gaussian optical beam of optical radiation. The behavior of a coherence degree of a fundamental Bessel-Gaussian optical beam depending on parameters of an optical beam and characteristics of turbulent atmosphere is examined. It was revealed that at low levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam has the characteristic oscillating appearance. At high levels of fluctuations in turbulent atmosphere the coherence degree of a fundamental Bessel-Gaussian optical beam is described by an one-scale decreasing curve which in process of increase of level of fluctuations on a line of formation of a laser beam becomes closer to the same characteristic of a spherical optical wave.
Low-frequency acousto-optic backscattering of Bessel light beams
Khilo, Nikolai A.; Belyi, Vladimir N.; Khilo, Petr A.; Kazak, Nikolai S.
2018-05-01
The use of Bessel light beams, as well as Bessel acoustic beams, substantially enhances the capabilities of acousto-optic methods for control of optical field. We present a theoretical study of the process of optical Bessel beams conversion by means of backward acousto-optic scattering on a Bessel acoustic field in a transversely isotropic crystal. It is shown that, with an appropriate choice of Bessel beams parameters, the backscattering in visible spectral range can be realized at relatively low acoustic frequencies less than one gigahertz. Under conditions of phase matching and transverse spatial synchronism, the efficiency of backscattering is sufficiently high, which is interesting, for example, for construction of acousto-optic spectral analyzers.
Optical force exerted on a Rayleigh particle by a vector arbitrary-order Bessel beam
International Nuclear Information System (INIS)
Yang, Ruiping; Li, Renxian
2016-01-01
An analytical description of optical force on a Rayleigh particle by a vector Bessel beam is investigated. Linearly, radially, azimuthally, and circularly polarized Bessel beams are considered. The radial, azimuthal, and axial forces by a vector Bessel beam are numerically simulated. The effect of polarization, order of beams, and half-cone angle to the optical force are mainly discussed. For Bessel beams of larger half-cone angle, the non-paraxiality of beams plays an important role in optical forces. Numerical calculations show that optical forces, especially azimuthal forces, are very sensitive to the polarization of beams. - Highlights: • Optical force exerted on a Rayleigh particle by a vector Bessel beam is analytically derived. • Radial, azimuthal, and axial forces are numerically analyzed. • The effect of polarization, order of beam, and non-paraxiality is analyzed.
Directory of Open Access Journals (Sweden)
Ruben Alejandro Cerutti
2010-02-01
Full Text Available En este trabajo se obtiene la inversión de un operador del tipo convolución usando técnicas de integrales hipersingulares. El operador de Bessel-Riesz de una función ϕ perteneciente a S , el espacio de funciones de prueba de Schwartz, es definido por la convolución con las funciones generalizadas (fórmula expresables en términos de la función de Bessel de primera especie (formula es también una combinación lineal infinita del núcleo ultrahiperbólico de Riesz de diferentes ordenes. Este hecho nos permite invertir los potenciales de Bessel-Riesz de un modo análogo a lo αhecho en el caso de los potenciales ultrahiperbólicos de Bessel (cf. [01] y los potenciales causales de Riesz (cf. [2].In this paper the inversion of a convolution type operator is obtained by using hypersingular integral technics. The Bessel-Riesz operator of a function ϕ belonging to S , the space of test functions of Schwartz, is definied by the convolution with the generalized functions (formula expressible in terms of the Bessel function of first kind (formula . γ is also an infinite linear combination of the ultrahyperbolic Riesz kernel of differents orders. This fact allows us to invert the Bessel-Riesz potential in an analogue manner of the ultrahyperbolic Bessel potentials (cf. [01] and causal Riesz potentials (cf. [2].
Computation of bessel functions in light scattering studies.
Ross, W D
1972-09-01
Computations of light scattering require finding Bessel functions of a series of orders. These are found most easily by recurrence, but excessive rounding errors may accumulate. Satisfactory procedures for cylinder and sphere functions are described. If argument z is real, find Y(n)(z) by recurrence to high orders. From two high orders of Y(n)(z) estimate J(n)(z). Use backward recurrence to maximum J(n)(z). Correct by forward recurrence to maximum. If z is complex, estimate high orders of J(n)(z) without Y(n)(z) and use backward recurrence.
An optical tweezer in asymmetrical vortex Bessel-Gaussian beams
Energy Technology Data Exchange (ETDEWEB)
Kotlyar, V. V.; Kovalev, A. A., E-mail: alexeysmr@mail.ru; Porfirev, A. P. [Image Processing Systems Institute, 151 Molodogvardeiskaya St., 443001 Samara (Russian Federation); Department of Technical cybernetics, Samara State Aerospace University, Samara 443086 (Russian Federation)
2016-07-14
We study an optical micromanipulation that comprises trapping, rotating, and transporting 5-μm polystyrene microbeads in asymmetric Bessel-Gaussian (BG) laser beams. The beams that carry orbital angular momentum are generated by means of a liquid crystal microdisplay and focused by a microobjective with a numerical aperture of NA = 0.85. We experimentally show that given a constant topological charge, the rate of microparticle motion increases near linearly with increasing asymmetry of the BG beam. Asymmetric BG beams can be used instead of conventional Gaussian beam for trapping and transferring live cells without thermal damage.
Investigation of local spatial spectra of Bessel light beams
CSIR Research Space (South Africa)
Belyi, VN
2009-08-01
Full Text Available plane of lens and illuminated by plane wave. The superposition of plane waves in such scheme is proposed to be generated by point sources distributed within the circular diaphragm. In a case when diaphragm is placed outside of lens focus [2], Bessel... beam can be described as an image in lens of spherical waves superposition formed by some effective circular source in object plane of lens. In the scheme of BLB obtaining based on axicons, the appearance of superposition of plane waves can be studied...
1975-06-01
Traditionally, synchronization of concurrent processes is coded in line by operations on semaphores or similar objects. Path expressions move the...discussion about a variety of synchronization primitives . An analysis of their relative power is found in [3]. Path expressions do not introduce yet...another synchronization primitive . A path expression relates to such primitives as a for- or while-statement of an ALGOL-like language relates to a JUMP
Ultrafast Bessel beams: advanced tools for laser materials processing
Stoian, Razvan; Bhuyan, Manoj K.; Zhang, Guodong; Cheng, Guanghua; Meyer, Remy; Courvoisier, Francois
2018-05-01
Ultrafast Bessel beams demonstrate a significant capacity of structuring transparent materials with a high degree of accuracy and exceptional aspect ratio. The ability to localize energy on the nanometer scale (bypassing the 100-nm milestone) makes them ideal tools for advanced laser nanoscale processing on surfaces and in the bulk. This allows to generate and combine micron and nano-sized features into hybrid structures that show novel functionalities. Their high aspect ratio and the accurate location can equally drive an efficient material modification and processing strategy on large dimensions. We review, here, the main concepts of generating and using Bessel non-diffractive beams and their remarkable features, discuss general characteristics of their interaction with matter in ablation and material modification regimes, and advocate their use for obtaining hybrid micro and nanoscale structures in two and three dimensions (2D and 3D) performing complex functions. High-throughput applications are indicated. The example list ranges from surface nanostructuring and laser cutting to ultrafast laser welding and the fabrication of 3D photonic systems embedded in the volume.
Engineering the on-axis intensity of Bessel beam by a feedback tuning loop
Li, Runze; Yu, Xianghua; Yang, Yanlong; Peng, Tong; Yao, Baoli; Zhang, Chunmin; Ye, Tong
2018-02-01
The Bessel beam belongs to a typical class of non-diffractive optical fields that are characterized by their invariant focal profiles along the propagation direction. However, ideal Bessel beams only rigorously exist in theory; Bessel beams generated in the lab are quasi-Bessel beams with finite focal extensions and varying intensity profiles along the propagation axis. The ability to engineer the on-axis intensity profile to the desired shape is essential for many applications. Here we demonstrate an iterative optimization-based approach to engineering the on-axis intensity of Bessel beams. The genetic algorithm is used to demonstrate this approach. Starting with a traditional axicon phase mask, in the design process, the computed on-axis beam profile is fed into a feedback tuning loop of an iterative optimization process, which searches for an optimal radial phase distribution that can generate a generalized Bessel beam with the desired onaxis intensity profile. The experimental implementation involves a fine-tuning process that adjusts the originally targeted profile so that the optimization process can optimize the phase mask to yield an improved on-axis profile. Our proposed method has been demonstrated in engineering several zeroth-order Bessel beams with customized on-axis profiles. High accuracy and high energy throughput merit its use in many applications.
International Nuclear Information System (INIS)
Li Shun; Zhang Sijiong
2014-01-01
A numerical model is presented to simulate the influence function of deformable mirror actuators. The numerical model is formed by Bessel Fourier orthogonal functions, which are constituted of Bessel orthogonal functions and a Fourier basis. A detailed comparison is presented between the new Bessel Fourier model, the Zernike model, the Gaussian influence function and the modified Gaussian influence function. Numerical experiments indicate that the new numerical model is easy to use and more accurate compared with other numerical models. The new numerical model can be used for describing deformable mirror performances and numerical simulations of adaptive optics systems. (research papers)
Comment on 'Analytical results for a Bessel function times Legendre polynomials class integrals'
International Nuclear Information System (INIS)
Cregg, P J; Svedlindh, P
2007-01-01
A result is obtained, stemming from Gegenbauer, where the products of certain Bessel functions and exponentials are expressed in terms of an infinite series of spherical Bessel functions and products of associated Legendre functions. Closed form solutions for integrals involving Bessel functions times associated Legendre functions times exponentials, recently elucidated by Neves et al (J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from the orthogonality properties of the associated Legendre functions. This result offers greater flexibility in the treatment of classical Heisenberg chains and may do so in other problems such as occur in electromagnetic diffraction theory. (comment)
Bessel-function analysis of the optimized star coupler for uniform power splitting.
Song, G Hugh; Park, Mahn Yong
2004-08-01
An optimized N x N planar optic star coupler that utilizes directional coupling of arrayed waveguides for uniform power splitting is analyzed on the basis of special properties of the involved Bessel-function series. The analysis has provided a remarkably simple, novel basic design formula for such a device with much needed physical insights into the unique diffraction properties. For the analysis of diffraction from the end of directionally coupled arrayed waveguides, many useful formulas around the Bessel functions, such as the addition theorem and the Kepler-Bessel series, have been given in new forms.
A Limit Relation for Dunkl-Bessel Functions of Type A and B
Directory of Open Access Journals (Sweden)
Margit Rösler
2008-12-01
Full Text Available We prove a limit relation for the Dunkl-Bessel function of type BN with multiplicity parameters k_1 on the roots ±ei and k_2 on ±e_i±e_j where k_1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkl-type Bessel function of type A_{N−1} with multiplicity k_2. For certain values of k_2 an improved estimate is obtained from a corresponding limit relation for Bessel functions on matrix cones.
CSIR Research Space (South Africa)
Milione, G
2015-02-01
Full Text Available be simply understood via geometric optics [3]. When a portion of a Bessel beam is obstructed in one plane, the unobstructed conical rays interfere in its shadow region in another plane, as shown in Fig. 1(e). Due to this property, Bessel beams have been... extensively studied and have been used for a number of applications; for comprehensive reviews see [4–7]. For example, when using a Bessel beam for optical trapping, it is possible to simultaneously trap multiple particles in well separated planes [8...
Photoacoustic transformation of Bessel light beams in magnetoactive superlattices
Energy Technology Data Exchange (ETDEWEB)
Mityurich, G. S., E-mail: George-mityurich@mail.ru [Belarusian Trade and Economics University of Consumer Cooperatives (Belarus); Chernenok, E. V.; Sviridova, V. V.; Serdyukov, A. N. [Gomel State University (Belarus)
2015-03-15
Photoacoustic transformation of the TE mode of a Bessel light beam (BLB) has been studied for piezoelectric detection in short-period superlattices formed by magnetoactive crystals of bismuth germanate (Bi{sub 12}GeO{sub 20}) and bismuth silicate (Bi{sub 12}SiO{sub 20}) types. It is shown that the resulting signal amplitude can be controlled using optical schemes of BLB formation with a tunable cone angle. A resonant increase in the signal amplitude has been found in the megahertz range of modulation frequencies and its dependences on the BLB modulation frequency, geometric sizes of the two-layer structure and piezoelectric transducer, radial coordinate of the polarization BLB mode, and dissipative superlattice parameters are analyzed.
Amos-type bounds for modified Bessel function ratios☆
Hornik, Kurt; Grün, Bettina
2013-01-01
We systematically investigate lower and upper bounds for the modified Bessel function ratio Rν=Iν+1/Iν by functions of the form Gα,β(t)=t/(α+t2+β2) in case Rν is positive for all t>0, or equivalently, where ν≥−1 or ν is a negative integer. For ν≥−1, we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If ν≥−1/2, the minimal elements are tangent to Rν in exactly one point 0≤t≤∞, and have Rν as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if ν is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively. PMID:24926105
Roots of two transcendental equations involving spherical bessel functions
International Nuclear Information System (INIS)
Pexton, R.L.; Steiger, A.D.
1977-01-01
Roots of the transcendental equations j/sub l/(αlambda) y/sub l/(lambda) =j/sub l/(lambda) y/sub l/(αlambda) and [xj/sub l/(x)]'/sub x alphaeta yl-italic/(x)]'/sub x eta/=xj/sub l/(x)]'/sub x eta yl-italic/(x)]'/sub x alphaeta/for the spherical Bessel functions of the first and second kind, j/sub l/(z) and y/sub l/(z), have been computed. The ranges for the parameter α, the order l and the root index n are: α=0.1(0.1)0.7,l=1(1)15,n=1(1)30
Amos-type bounds for modified Bessel function ratios.
Hornik, Kurt; Grün, Bettina
2013-12-01
We systematically investigate lower and upper bounds for the modified Bessel function ratio [Formula: see text] by functions of the form [Formula: see text] in case [Formula: see text] is positive for all [Formula: see text], or equivalently, where [Formula: see text] or [Formula: see text] is a negative integer. For [Formula: see text], we give an explicit description of the set of lower bounds and show that it has a greatest element. We also characterize the set of upper bounds and its minimal elements. If [Formula: see text], the minimal elements are tangent to [Formula: see text] in exactly one point [Formula: see text], and have [Formula: see text] as their lower envelope. We also provide a new family of explicitly computable upper bounds. Finally, if [Formula: see text] is a negative integer, we explicitly describe the sets of lower and upper bounds, and give their greatest and least elements, respectively.
Precise analytic approximations for the Bessel function J1 (x)
Maass, Fernando; Martin, Pablo
2018-03-01
Precise and straightforward analytic approximations for the Bessel function J1 (x) have been found. Power series and asymptotic expansions have been used to determine the parameters of the approximation, which is as a bridge between both expansions, and it is a combination of rational and trigonometric functions multiplied with fractional powers of x. Here, several improvements with respect to the so called Multipoint Quasirational Approximation technique have been performed. Two procedures have been used to determine the parameters of the approximations. The maximum absolute errors are in both cases smaller than 0.01. The zeros of the approximation are also very precise with less than 0.04 per cent for the first one. A second approximation has been also determined using two more parameters, and in this way the accuracy has been increased to less than 0.001.
Bessel smoothing filter for spectral-element mesh
Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.
2017-06-01
Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the
Elliptic integral evaluations of Bessel moments and applications
International Nuclear Information System (INIS)
Bailey, David H; Borwein, Jonathan M; Broadhurst, David; Glasser, M L
2008-01-01
We record and substantially extend what is known about the closed forms for various Bessel function moments arising in quantum field theory, condensed matter theory and other parts of mathematical physics. In particular, we develop formulae for integrals of products of six or fewer Bessel functions. In consequence, we are able to discover and prove closed forms for c n,k := ∫ ∞ 0 t k K n 0 (t) dt with integers n 1, 2, 3, 4 and k ≥ 0, obtaining new results for the even moments c 3,2k and c 4,2k . We also derive new closed forms for the odd moments s n,2k+1 := ∫ ∞ 0 t 2k+1 I 0 (t)K n-1 0 (t) dt with n = 3, 4 and for t n,2k+1 :∫ ∞ 0 t 2k+1 I 2 0 (t)K n-2 0 (t) dt with n = 5, relating the latter to Green functions on hexagonal, diamond and cubic lattices. We conjecture the values of s 5,2k+1 , make substantial progress on the evaluation of c 5,2k+1 , s 6,2k+1 and t 6,2k+1 and report more limited progress regarding c 5,2k , c 6,2k+1 and c 6,2k . In the process, we obtain eight conjectural evaluations, each of which has been checked to 1200 decimal places. One of these lies deep in four-dimensional quantum field theory and two are probably provable by delicate combinatorics. There remains a hard core of five conjectures whose proofs would be most instructive, to mathematicians and physicists alike
Theory of third-harmonic generation using Bessel beams, and self-phase-matching
International Nuclear Information System (INIS)
Tewari, S.P.; Huang, H.; Boyd, R.W.
1996-01-01
Taking Bessel beams (J 0 beam) as a representation of a conical beam, and a slowly varying envelope approximation (SVEA) we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phase-matching integral of the theory. A method to calculate the transverse-phase-matching integral containing four Bessel functions is described which avoids the computer calculations of the Bessel functions. In order to consolidate the SVEA result an alternate method is used to obtain the exact result for the third-harmonic generation. The conditions are identified in which the exact result goes over to the result of the SVEA. The theory for multiple Bessel beams is also discussed which has been shown to be the source of the wide width of the efficiency curve of the third-harmonic generation observed in experiments. copyright 1996 The American Physical Society
Application of a non-integer Bessel uniform approximation to inelastic molecular collisions
International Nuclear Information System (INIS)
Connor, J.N.L.; Mayne, H.R.
1979-01-01
A non-integer Bessel uniform approximation has been used to calculate transition probabilities for collinear atom-oscillator collisions. The collision systems used are a harmonic oscillator interacting via a Lennard-Jones potential and a Morse oscillator interacting via an exponential potential. Both classically allowed and classically forbidden transitions have been treated. The order of the Bessel function is chosen by a physical argument that makes use of information contained in the final-action initial-angle plot. Limitations of this procedure are discussed. It is shown that the non-integer Bessel approximation is accurate for elastic 0 → 0 collisions at high collision energies, where the integer Bessel approximation is inaccurate or inapplicable. (author)
Generation of the second harmonics of Bessel light beams in a KTP crystal
International Nuclear Information System (INIS)
Belyi, V N; Kazak, N S; Kondratyuk, N V; Khilo, N A; Shagov, A A
1998-01-01
Theoretical and experimental investigations were made of the characteristic features of doubling the frequency of Bessel light beams by the oe - e interaction in a KTP crystal. All possible and scalar interactions of plane-wave components of Bessel beams were observed experimentally. The spatial structure of the second harmonic in the far zone consisted of a central spot and a concentric ring. The diffraction divergence of the central beam was weak ( ∼ 1.7 mrad). The energy conversion efficiency was ∼ 21% for a Bessel beam, which was three times higher than the efficiency of conversion of the initial laser beam. A theoretical model was based on representation of the field of the second harmonic as a superposition of Bessel beams, which provided a correct description of the observed spatial and energy characteristics of the second harmonic. (nonlinear optical phenomena and devices)
Semi-Inclusive Deep Inelastic Scattering and Bessel-Weighted Asymmetries
International Nuclear Information System (INIS)
Gamberg, Leonard; Boer, Daniel; Musch, Bernhard; Prokudin, Alexei
2012-01-01
We consider the cross section in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.
Orthogonality, Lommel integrals and cross product zeros of linear combinations of Bessel functions.
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.
Bessel harmonic analysis and approximation of functions on the half-line
International Nuclear Information System (INIS)
Platonov, Sergei S
2007-01-01
We study problems of approximation of functions on [0,+∞) in the metric of L p with power weight using generalized Bessel shifts. We prove analogues of direct Jackson theorems for the modulus of smoothness of arbitrary order defined in terms of generalized Bessel shifts. We establish the equivalence of the modulus of smoothness and the K-functional. We define function spaces of Nikol'skii-Besov type and describe them in terms of best approximations. As a tool for approximation, we use a certain class of entire functions of exponential type. In this class, we prove analogues of Bernstein's inequality and others for the Bessel differential operator and its fractional powers. The main tool we use to solve these problems is Bessel harmonic analysis
On a new class of integrals involving Bessel functions of the first kind
Directory of Open Access Journals (Sweden)
P. Agarwal
2014-06-01
Full Text Available In recent years, several integral formulas involving a variety of special functions have been developed by many authors. Also many integral formulas containing the Bessel function $J_\
On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind
Directory of Open Access Journals (Sweden)
Dinesh Kumar
2015-01-01
Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.
q-Sumudu transforms of q-analogues of Bessel functions.
Uçar, Faruk
2014-01-01
The main purpose of this paper is to evaluate q-Sumudu transforms of a product of q-Bessel functions. Interesting special cases of theorems are also discussed. Further, the results proved in this paper may find certain applications of q-Sumudu transforms to the solutions of the q-integrodifferential equations involving q-Bessel functions. The results may help to extend the q-theory of orthogonal functions.
Symbolic methods for the evaluation of sum rules of Bessel functions
International Nuclear Information System (INIS)
Babusci, D.; Dattoli, G.; Górska, K.; Penson, K. A.
2013-01-01
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics
On sharp estimates of the convergence of double Fourier-Bessel series
Abilov, V. A.; Abilova, F. V.; Kerimov, M. K.
2017-11-01
The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier-Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.
Expansion of infinite series containing modified Bessel functions of the second kind
International Nuclear Information System (INIS)
Fucci, Guglielmo; Kirsten, Klaus
2015-01-01
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the parameters in the argument of the modified Bessel function of the second kind is small compared to the others. We apply the results obtained for the asymptotic expansion to specific problems that arise in the ambit of quantum field theory. (paper)
On the Computation and Applications of Bessel Functions with Pure Imaginary Indices
Matyshev, A. A.; Fohtung, E.
2009-01-01
Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Recently they were found to be of great importance in semiconductor material characterization as they are manifested in the strain state of crystalline material. A new algorithm which can be used for the computation of the normal and modifed Bessel functions with pure imaginary index is proposed. The developed algorit...
Wang, Zhi-Bin; Zhang, Rui; Wang, Yao-Li; Huang, Yan-Fei; Chen, You-Hua; Wang, Li-Fu; Yang, Qiang
2014-02-01
As the existing photoelastic-modulator(PEM) modulating frequency in the tens of kHz to hundreds of kHz between, leading to frequency of modulated interference signal is higher, so ordinary array detector cannot effectively caprure interference signal..A new beat frequency modulation method based on dual-photoelastic-modulator (Dual-PEM) and Fourier-Bessel transform is proposed as an key component of dual-photoelastic-modulator-based imaging spectrometer (Dual-PEM-IS) combined with charge coupled device (CCD). The dual-PEM are operated as an electro-optic circular retardance modulator, Operating the PEMs at slightly different resonant frequencies w1 and w2 respectively, generates a differential signal at a much lower heterodyne frequency that modulates the incident light. This method not only retains the advantages of the existing PEM, but also the frequency of modulated photocurrent decreased by 2-3 orders of magnitude (10-500 Hz) and can be detected by common array detector, and the incident light spectra can be obtained by Fourier-Bessel transform of low frequency component in the modulated signal. The method makes the PEM has the dual capability of imaging and spectral measurement. The basic principle is introduced, the basic equations is derived, and the feasibility is verified through the corresponding numerical simulation and experiment. This method has' potential applications in imaging spectrometer technology, and analysis of the effect of deviation of the optical path difference. This work provides the necessary theoretical basis for remote sensing of new Dual-PEM-IS and for engineering implementation of spectra inversion.
Arbitrary scattering of an acoustical Bessel beam by a rigid spheroid with large aspect-ratio
Gong, Zhixiong; Li, Wei; Mitri, Farid G.; Chai, Yingbin; Zhao, Yao
2016-11-01
In this paper, the T-matrix (null-field) method is applied to investigate the acoustic scattering by a large-aspect-ratio rigid spheroid immersed in a non-viscous fluid under the illumination of an unbounded zeroth-order Bessel beam with arbitrary orientation. Based on the proposed method, a MATLAB software package is constructed accordingly, and then verified and validated to compute the acoustic scattering by a rigid oblate or prolate spheroid in the Bessel beam. Several numerical examples are carried out to investigate the novel phenomenon of acoustic scattering by spheroids in Bessel beams with arbitrary incidence, with particular emphasis on the aspect ratio (i.e. the ratio of the polar radius over the equatorial radius of the spheroid), the half-cone angle of Bessel beam, the dimensionless frequency, as well as the angle of incidence. The quasi-periodic oscillations are observed in the plots of the far-field backscattering form function modulus versus the dimensionless frequency, owing to the interference between the specular reflection and the Franz wave circumnavigating the spheroid in the surrounding fluid. Furthermore, the 3D far-field scattering directivity patterns at end-on incidence and 2D polar plots at arbitrary angles of incidence are exhibited, which could provide new insights into the physical mechanisms of Bessel beam scattering by flat or elongated spheroid. This research work may provide an impetus for the application of acoustic Bessel beam in engineering practices.
Luo, Zhi; Yin, Kai; Dong, Xinran; Duan, Ji’an
2018-05-01
A numerical algorithm, modelling the transformation from a Gaussian beam to a Bessel beam, is presented for the purpose to study the optimal condition for employing an axicon-generated Bessel beam to fabricate cylindrical microlens arrays (CMLAs). By applying the numerical algorithm to simulate the spatial intensity distribution behind the axicon under different defects of a rotund-apex and different diameter ratios of an incident beam to the axicon, we find that the diffraction effects formed by the axicon edge can be almost eliminated when the diameter ratio is less than 1:2, but the spatial intensity distribution is disturbed dramatically even a few tens of microns deviation of the apex, especially for the front part of the axicon-generated Bessel beam. Fortunately, the lateral intensity profile in the rear part still maintains a desirable Bessel curve. Therefore, the rear part of the Bessel area and the less than 1:2 diameter ratio are the optimal choice for employing an axicon-generated Bessel beam to implement surface microstructures fabrication. Furthermore, by applying the optimal conditions to direct writing microstructures on fused silica with a femtosecond (fs) laser, a large area close-packed CMLA is fabricated. The CMLA presents high quality and uniformity and its optical performance is also demonstrated.
Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.
Lukin, Igor P
2016-04-20
The orbital angular momentum of vortex Bessel-Gaussian beams propagating in turbulent atmosphere is studied theoretically. The field of an optical beam is determined through the solution of the paraxial wave equation for a randomly inhomogeneous medium with fluctuations of the refraction index of the turbulent atmosphere. Peculiarities in the behavior of the total power of the vortex Bessel-Gaussian beam at the receiver (or transmitter) are examined. The dependence of the total power of the vortex Bessel-Gaussian beam on optical beam parameters, namely, the transverse wave number of optical radiation, amplitude factor radius, and, especially, topological charge of the optical beam, is analyzed in detail. It turns out that the mean value of the orbital angular momentum of the vortex Bessel-Gaussian beam remains constant during propagation in the turbulent atmosphere. It is shown that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam propagating in turbulent atmosphere calculated with the "mean-intensity" approximation is equal to zero identically. Thus, it is possible to declare confidently that the variance of fluctuations of the orbital angular momentum of the vortex Bessel-Gaussian beam in turbulent atmosphere is not very large.
Watson, Gale A.
2003-01-01
Demonstrates the transformations that are possible to construct a variety of magic squares, including modifications to challenge students from elementary grades through algebra. Presents an example of using magic squares with students who have special needs. (YDS)
DEFF Research Database (Denmark)
Madsen, Mogens Ove
Begrebet Path Dependence blev oprindelig udviklet inden for New Institutionel Economics af bl.a. David, Arthur og North. Begrebet har spredt sig vidt i samfundsvidenskaberne og undergået en udvikling. Dette paper propagerer for at der er sket så en så omfattende udvikling af begrebet, at man nu kan...... tale om 1. og 2. generation af Path Dependence begrebet. Den nyeste udvikling af begrebet har relevans for metodologi-diskusionerne i relation til Keynes...
The generalized Abel-Plana formula with applications to Bessel functions and casimir effect
International Nuclear Information System (INIS)
Saharian, Aram A.
2007-08-01
One of the most efficient methods for the evaluation of the vacuum expectation values for physical observables in the Casimir effect is based on using the Abel-Plana summation formula. This enables to derive the renormalized quantities in a manifestly cutoff independent way and to present them in the form of strongly convergent integrals. However, applications of the Abel- Plana formula, in its usual form, are restricted by simple geometries when the eigenmodes have a simple dependence on quantum numbers. The author generalized the Abel-Plana formula which essentially enlarges its application range. Based on this generalization, formulae have been obtained for various types of series over the zeros of combinations of Bessel functions and for integrals involving these functions. It has been shown that these results generalize the special cases existing in literature. Further, the derived summation formulae have been used to summarize series arising in the direct mode summation approach to the Casimir effect for spherically and cylindrically symmetric boundaries, for boundaries moving with uniform proper acceleration, and in various braneworld scenarios. This allows to extract from the vacuum expectation values of local physical observables the parts corresponding to the geometry without boundaries and to present the boundary-induced parts in terms of integrals strongly convergent for the points away from the boundaries. As a result, the renormalization procedure for these observables is reduced to the corresponding procedure for bulks without boundaries. The present paper reviews these results. We also aim to collect the results on vacuum expectation values for local physical observables such as the field square and the energy-momentum tensor in manifolds with boundaries for various bulk and boundary geometries. (author)
Higher order Riesz transforms associated with Bessel operators
Betancor, Jorge J.; Fariña, Juan C.; Martinez, Teresa; Rodríguez-Mesa, Lourdes
2008-10-01
In this paper we investigate Riesz transforms R μ ( k) of order k≥1 related to the Bessel operator Δμ f( x)=- f”( x)-((2μ+1)/ x) f’( x) and extend the results of Muckenhoupt and Stein for the conjugate Hankel transform (a Riesz transform of order one). We obtain that for every k≥1, R μ ( k) is a principal value operator of strong type ( p, p), p∈(1,∞), and weak type (1,1) with respect to the measure dλ( x)= x 2μ+1 dx in (0,∞). We also characterize the class of weights ω on (0,∞) for which R μ ( k) maps L p (ω) into itself and L 1(ω) into L 1,∞(ω) boundedly. This class of weights is wider than the Muckenhoupt class mathcal{A}p^μ of weights for the doubling measure dλ. These weighted results extend the ones obtained by Andersen and Kerman.
Anisotropic resonator analysis using the Fourier-Bessel mode solver
Gauthier, Robert C.
2018-03-01
A numerical mode solver for optical structures that conform to cylindrical symmetry using Faraday's and Ampere's laws as starting expressions is developed when electric or magnetic anisotropy is present. The technique builds on the existing Fourier-Bessel mode solver which allows resonator states to be computed exploiting the symmetry properties of the resonator and states to reduce the matrix system. The introduction of anisotropy into the theoretical frame work facilitates the inclusion of PML borders permitting the computation of open ended structures and a better estimation of the resonator state quality factor. Matrix populating expressions are provided that can accommodate any material anisotropy with arbitrary orientation in the computation domain. Several example of electrical anisotropic computations are provided for rationally symmetric structures such as standard optical fibers, axial Bragg-ring fibers and bottle resonators. The anisotropy present in the materials introduces off diagonal matrix elements in the permittivity tensor when expressed in cylindrical coordinates. The effects of the anisotropy of computed states are presented and discussed.
DEFF Research Database (Denmark)
Karnøe, Peter; Garud, Raghu
2012-01-01
This paper employs path creation as a lens to follow the emergence of the Danish wind turbine cluster. Supplier competencies, regulations, user preferences and a market for wind power did not pre-exist; all had to emerge in a tranformative manner involving multiple actors and artefacts. Competenc......This paper employs path creation as a lens to follow the emergence of the Danish wind turbine cluster. Supplier competencies, regulations, user preferences and a market for wind power did not pre-exist; all had to emerge in a tranformative manner involving multiple actors and artefacts....... Competencies emerged through processes and mechanisms such as co-creation that implicated multiple learning processes. The process was not an orderly linear one as emergent contingencies influenced the learning processes. An implication is that public policy to catalyse clusters cannot be based...
Electromagnetic scattering by a uniaxial anisotropic sphere located in an off-axis Bessel beam.
Qu, Tan; Wu, Zhen-Sen; Shang, Qing-Chao; Li, Zheng-Jun; Bai, Lu
2013-08-01
Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.
Misiurewicz, Michal
2013-01-01
If students are presented the standard proof of irrationality of [square root]2, can they generalize it to a proof of the irrationality of "[square root]p", "p" a prime if, instead of considering divisibility by "p", they cling to the notions of even and odd used in the standard proof?
Least Square NUFFT Methods Applied to 2D and 3D Radially Encoded MR Image Reconstruction
Song, Jiayu; Liu, Qing H.; Gewalt, Sally L.; Cofer, Gary; Johnson, G. Allan
2009-01-01
Radially encoded MR imaging (MRI) has gained increasing attention in applications such as hyperpolarized gas imaging, contrast-enhanced MR angiography, and dynamic imaging, due to its motion insensitivity and improved artifact properties. However, since the technique collects k-space samples nonuniformly, multidimensional (especially 3D) radially sampled MRI image reconstruction is challenging. The balance between reconstruction accuracy and speed becomes critical when a large data set is processed. Kaiser-Bessel gridding reconstruction has been widely used for non-Cartesian reconstruction. The objective of this work is to provide an alternative reconstruction option in high dimensions with on-the-fly kernels calculation. The work develops general multi-dimensional least square nonuniform fast Fourier transform (LS-NUFFT) algorithms and incorporates them into a k-space simulation and image reconstruction framework. The method is then applied to reconstruct the radially encoded k-space, although the method addresses general nonuniformity and is applicable to any non-Cartesian patterns. Performance assessments are made by comparing the LS-NUFFT based method with the conventional Kaiser-Bessel gridding method for 2D and 3D radially encoded computer simulated phantoms and physically scanned phantoms. The results show that the LS-NUFFT reconstruction method has better accuracy-speed efficiency than the Kaiser-Bessel gridding method when the kernel weights are calculated on the fly. The accuracy of the LS-NUFFT method depends on the choice of scaling factor, and it is found that for a particular conventional kernel function, using its corresponding deapodization function as scaling factor and utilizing it into the LS-NUFFT framework has the potential to improve accuracy. When a cosine scaling factor is used, in particular, the LS-NUFFT method is faster than Kaiser-Bessel gridding method because of a quasi closed-form solution. The method is successfully applied to 2D and
F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements
Karney, C. F. F.; Deakin, R. E.
2010-08-01
Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3
Light scattering of a Bessel beam by a nucleated biological cell: An eccentric sphere model
Wang, Jia Jie; Han, Yi Ping; Chang, Jiao Yong; Chen, Zhu Yang
2018-02-01
Within the framework of generalized Lorenz-Mie theory (GLMT), an eccentrically stratified dielectric sphere model illuminated by an arbitrarily incident Bessel beam is applied to investigate the scattering characteristics of a single nucleated biological cell. The Bessel beam propagating in an arbitrary direction is expanded in terms of vector spherical wave functions (VSWFs), where the beam shape coefficients (BSCs) are calculated rigorously in a closed analytical form. The effects of the half-cone angle of Bessel beam, the location of the particle in the beam, the size ratio of nucleus to cell, and the location of the nucleus inside the cell on the scattering properties of a nucleated cell are analyzed. The results provide useful references for optical diagnostic and imaging of particle having nucleated structure.
Lötstedt, Erik; Jentschura, Ulrich D
2009-02-01
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schrödinger-Volkov and Dirac-Volkov solution is expanded into plane waves. For the evaluation of cross sections of quantum electrodynamic processes in a linearly polarized laser field, it is often necessary to evaluate large arrays of generalized Bessel functions, of arbitrary index but with fixed arguments. We show that the generalized Bessel function can be evaluated, in a numerically stable way, by utilizing a recurrence relation and a normalization condition only, without having to compute any initial value. We demonstrate the utility of the method by illustrating the quantum-classical correspondence of the Dirac-Volkov solutions via numerical calculations.
Limitations to laser machining of silicon using femtosecond micro-Bessel beams in the infrared
International Nuclear Information System (INIS)
Grojo, David; Mouskeftaras, Alexandros; Delaporte, Philippe; Lei, Shuting
2015-01-01
We produce and characterize high-angle femtosecond Bessel beams at 1300-nm wavelength leading to nonlinearly ionized plasma micro-channels in both glass and silicon. With microjoule pulse energy, we demonstrate controlled through-modifications in 150-μm glass substrates. In silicon, strong two-photon absorption leads to larger damages at the front surface but also a clamping of the intensity inside the bulk at a level of ≈4 × 10 11 W cm −2 which is below the threshold for volume and rear surface modification. We show that the intensity clamping is associated with a strong degradation of the Bessel-like profile. The observations highlight that the inherent limitation to ultrafast energy deposition inside semiconductors with Gaussian focusing [Mouskeftaras et al., Appl. Phys. Lett. 105, 191103 (2014)] applies also for high-angle Bessel beams
Approximate solutions of the hyperchaotic Rössler system by using the Bessel collocation scheme
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Şuayip Yüzbaşı
2015-02-01
Full Text Available The purpose of this study is to give a Bessel polynomial approximation for the solutions of the hyperchaotic Rössler system. For this purpose, the Bessel collocation method applied to different problems is developed for the mentioned system. This method is based on taking the truncated Bessel expansions of the functions in the hyperchaotic Rössler systems. The suggested secheme converts the problem into a system of nonlinear algebraic equations by means of the matrix operations and collocation points, The accuracy and efficiency of the proposed approach are demonstrated by numerical applications and performed with the help of a computer code written in Maple. Also, comparison between our method and the differential transformation method is made with the accuracy of solutions.
Photorefractive Axicon: Study of Light-induced Effect by Bessel Beam in Photorefractive Crystal
International Nuclear Information System (INIS)
Vieira, T A; Gesualdi, M R R; Zamboni-Rached, M; Muramatsu, M
2011-01-01
In this work, we present the theoretical and computational study of the original analysis of the light-induced effects by Bessel beams in photorefractive crystals. Modern applications of these beams as: metrological, alignment of optical systems, optical tweezers, non linear optics, optical communication, and others, becoming a very interesting substitute for a Gaussian beam when this is subject to diffraction and dispersion effects to large distance propagation. On the other hand, the photorefractive crystals are very important materials for applications in non-linear optics, holographic storage, interferometry and optical information processing. We perform an analysis of the index refraction modulation generated by Bessel beam in photorefractive medium discussing the possibility this optical material to control and generation of Bessel beam properties.
Spatial characterization of Bessel-like beams for strong-field physics.
Summers, Adam M; Yu, Xiaoming; Wang, Xinya; Raoul, Maxime; Nelson, Josh; Todd, Daniel; Zigo, Stefan; Lei, Shuting; Trallero-Herrero, Carlos A
2017-02-06
We present a compact, simple design for the generation and tuning of both the spot size and effective focal length of Bessel-like beams. In particular, this setup provides an important tool for the use of Bessel-like beams with high-power, femtosecond laser systems. Using a shallow angle axicon in conjunction with a spherical lens, we show that it is possible to focus Bessel-like modes to comparable focal spot sizes to sharp axicons while maintaining a long effective focal length. The resulting focal profiles are characterized in detail using an accurate high dynamic range imaging technique. Quantitatively, we introduce a metric (R0.8) which defines the spot-size containing 80% of the total energy. Our setup overcomes the typical compromise between long working distances and small spot sizes. This is particularly relevant for strong-field physics where most experiments must operate in vacuum.
Gaussian vs. Bessel light-sheets: performance analysis in live large sample imaging
Reidt, Sascha L.; Correia, Ricardo B. C.; Donnachie, Mark; Weijer, Cornelis J.; MacDonald, Michael P.
2017-08-01
Lightsheet fluorescence microscopy (LSFM) has rapidly progressed in the past decade from an emerging technology into an established methodology. This progress has largely been driven by its suitability to developmental biology, where it is able to give excellent spatial-temporal resolution over relatively large fields of view with good contrast and low phototoxicity. In many respects it is superseding confocal microscopy. However, it is no magic bullet and still struggles to image deeply in more highly scattering samples. Many solutions to this challenge have been presented, including, Airy and Bessel illumination, 2-photon operation and deconvolution techniques. In this work, we show a comparison between a simple but effective Gaussian beam illumination and Bessel illumination for imaging in chicken embryos. Whilst Bessel illumination is shown to be of benefit when a greater depth of field is required, it is not possible to see any benefits for imaging into the highly scattering tissue of the chick embryo.
Analytical study on the self-healing property of Bessel beam
Chu, X.
2012-10-01
With the help of Babinet principle, an analytical expression for the self-healing of Bessel beam is derived by using the Gaussian absorption function to describe the obstacle. Based on the analytical expression, the self-healing properties of Bessel beam are studied. It shows that Bessel beam has the ability to reconstruct its beam shape disturbed by an obstacle. However, during the self-healing process, not only the intensity of the beam behind the obstacle but also the other part will be affected by the obstruction. Meanwhile, the highlight spot, which intensity is larger than that without the obstacle will appear, and the size and strength of the highlight spot is determined by the size of the obstacle. From the change of Poynting vector and Babinet principle, the physical interpretations for the self-healing ability, the effects of the obstruction on the other part and the appearance of highlight spot are given.
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.; Mancho, A.M.
2000-01-01
The theory of generalized Bessel functions has found significant applications in the analysis of radiation phenomena, associated with charges moving in magnetic devices. In this paper we exploit the monomiality principle to discuss the theory of two-variable Laguerre polynomials and introduce the associated Laguerre-Bessel functions. We study their properties (addition and multiplication theorems, generating function, recurrence relations and so on) and discuss the link with the ordinary case. The usefulness of the obtained results to treat problems relevant to the paraxial propagation of electromagnetic waves is also discussed.
Generalized coherent states related to the associated Bessel functions and Morse potential
International Nuclear Information System (INIS)
Mojaveri, B; Amiri Faseghandis, S
2014-01-01
Using the associated Bessel functions, a shape-invariant Lie algebra spanned by ladder operators plus the identity operator, is realized. The Hilbert space of the associated Bessel functions, representing the Lie algebra, are established and two kinds of generalized coherent states as an appropriate superposition of these functions are constructed. By implying appropriate similarity transformation on the constructed coherent states, the generalized coherent states for the Morse potential are obtained. By considering some statistical characteristics, it is revealed that the constructed coherent states indeed possess nonclassical features, such as squeezing and sub-Poissonian statistics. (paper)
Study of graphitic microstructure formation in diamond bulk by pulsed Bessel beam laser writing
Kumar, S.; Sotillo, B.; Chiappini, A.; Ramponi, R.; Di Trapani, P.; Eaton, S. M.; Jedrkiewicz, O.
2017-11-01
The advantages of using Bessel beams for the generation of graphitic structures in diamond bulk are presented. We show that by irradiating the sample with a pulsed Bessel beam whose non-diffracting zone is of the same order of the sample thickness, it is possible to produce without any sample translation straight graphitic through-microstructures, whose size depends on the input pulse energy. The microstructure growth is investigated as a function of the number of irradiating pulses, and the femtosecond and picosecond regimes are contrasted.
Studies on the zeros of Bessel functions and methods for their computation
Kerimov, M. K.
2014-09-01
The zeros of Bessel functions play an important role in computational mathematics, mathematical physics, and other areas of natural sciences. Studies addressing these zeros (their properties, computational methods) can be found in various sources. This paper offers a detailed overview of the results concerning the real zeros of the Bessel functions of the first and second kinds and general cylinder functions. The author intends to publish several overviews on this subject. In this first publication, works dealing with real zeros are analyzed. Primary emphasis is placed on classical results, which are still important. Some of the most recent publications are also discussed.
Extension of filament propagation in water with Bessel-Gaussian beams
Energy Technology Data Exchange (ETDEWEB)
Kaya, G.; Sayrac, M.; Boran, Y.; Kolomenskii, A. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Kaya, N.; Schuessler, H. A. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar); Strohaber, J. [Department of Physics, Texas A& M University, College Station, Texas 77843 (United States); Department of Physics, Florida A& M University, Tallahassee, Florida 32307 (United States); Amani, M. [Science and Petroleum, Texas A& M University at Qatar, Doha 23874 (Qatar)
2016-03-15
We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.
Experimental generation and application of the superposition of higher-order Bessel beams
CSIR Research Space (South Africa)
Dudley, Angela L
2009-07-01
Full Text Available Academy of Sciences of Belarus 4 School of Physics, University of Stellenbosch Presented at the 2009 South African Institute of Physics Annual Conference University of KwaZulu-Natal Durban, South Africa 6-10 July 2009 Page 2 © CSIR 2008... www.csir.co.za Generation of Bessel Fields: • METHOD 1: Ring Slit Aperture • METHOD 2: Axicon Adaptation of method 1 to produce superpositions of higher-order Bessel beams: J. Durnin, J.J. Miceli and J.H. Eberly, Phys. Rev. Lett. 58 1499...
Orbital angular momentum of a high-order Bessel light beam
International Nuclear Information System (INIS)
Volke-Sepulveda, K; Garces-Chavez, V; Chavez-Cerda, S; Arlt, J; Dholakia, K
2002-01-01
The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page
Extension of filament propagation in water with Bessel-Gaussian beams
Directory of Open Access Journals (Sweden)
G. Kaya
2016-03-01
Full Text Available We experimentally studied intense femtosecond pulse filamentation and propagation in water for Bessel-Gaussian beams with different numbers of radial modal lobes. The transverse modes of the incident Bessel-Gaussian beam were created from a Gaussian beam of a Ti:sapphire laser system by using computer generated hologram techniques. We found that filament propagation length increased with increasing number of lobes under the conditions of the same peak intensity, pulse duration, and the size of the central peak of the incident beam, suggesting that the radial modal lobes may serve as an energy reservoir for the filaments formed by the central intensity peak.
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-08-01
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
Path integration in conical space
International Nuclear Information System (INIS)
Inomata, Akira; Junker, Georg
2012-01-01
Quantum mechanics in conical space is studied by the path integral method. It is shown that the curvature effect gives rise to an effective potential in the radial path integral. It is further shown that the radial path integral in conical space can be reduced to a form identical with that in flat space when the discrete angular momentum of each partial wave is replaced by a specific non-integral angular momentum. The effective potential is found proportional to the squared mean curvature of the conical surface embedded in Euclidean space. The path integral calculation is compatible with the Schrödinger equation modified with the Gaussian and the mean curvature. -- Highlights: ► We study quantum mechanics on a cone by the path integral approach. ► The path integral depends only on the metric and the curvature effect is built in. ► The approach is consistent with the Schrödinger equation modified by an effective potential. ► The effective potential is found to be of the “Jensen–Koppe” and “da Costa” type.
Algorithm 831: modified Bessel functions of imaginary order and positive argument
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2004-01-01
textabstract77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions Kia (x), Lia (x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation x2w'' + xw' + (a2
Evaluating the Financial Flows of Bessel Processes by Using Spectral Analysis
Directory of Open Access Journals (Sweden)
Burtnyak Ivan V.
2017-07-01
Full Text Available The article solves the two-parameter task of evaluating the intensity of diffuse Bessel processes by the methods of spectral theory. In particular, barriers for cost of options, where the derivative of financial flows turns into zero, have been considered, and a task for the two-barrier option has been solved, which corresponds to Bessel process. A Green’s function has been built for the diffusion Bessel process of the two-barrier option, decomposed according to the first-type system of Bessel functions. The barriers are taken in such a way that the derivative of financial flow in terms of price is turned to zero, i.e. there are the points where flow can acquire extreme values. On the basis of Green’s function, the value of securities has been calculated. It is handier to use similar barriers when monitoring a stock market. The Green’s function for this task, which represents the probability of spreading the option price, is represented through the Fourier series. This provides an opportunity to evaluate the intensity of financial flows in stock markets.
Directory of Open Access Journals (Sweden)
Burtnyak Ivan V.
2017-06-01
Full Text Available In the paper we apply the spectral theory to find the price for derivatives of financial assets assuming that the processes described are Markov processes and such that can be considered in the Hilbert space L^2 using the Sturm-Liouville theory. Bessel diffusion processes are used in studying Asian options. We consider the financial flows generated by the Bessel diffusions by expressing them in terms of the system of Bessel functions of the first kind, provided that they take into account the linear combination of the flow and its spatial derivative. Such expression enables calculating the size of the market portfolio and provides a measure of the amount of internal volatility in the market at any given moment, allows investigating the dynamics of the equity market. The expansion of the Green function in terms of the system of Bessel functions is expressed by an analytic formula that is convenient in calculating the volume of financial flows. All assumptions are natural, result in analytic formulas that are consistent with the empirical data and, when applied in practice, adequately reflect the processes in equity markets.
Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone
Salem, Mohamed; Bagci, Hakan
2013-01-01
The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms
Improved fixation quality provided by a Bessel beacon in an adaptive optics system.
Lambert, Andrew J; Daly, Elizabeth M; Dainty, Christopher J
2013-07-01
We investigate whether a structured probe beam that creates the beacon for use in a retinal imaging adaptive optics system can provide useful side effects. In particular we investigate whether a Bessel beam that is seen by the subject as a set of concentric rings has a dampening effect on fixation variations of the subject under observation. This calming effect would allow longer periods of observation, particularly for patients with abnormal fixation. An experimental adaptive optics system developed for retinal imaging is used to monitor the fluctuations in aberrations for artificial and human subjects. The probe beam is alternated between a traditional beacon and one provided by a Bessel beam created by SLM. Time-frequency analysis is used to indicate the differences in power and time variation during fixation depending on whether the Bessel beam or the traditional beacon is employed. Comparison is made with the response for an artificial eye to discount systemic variations. Significant evidence is accrued to indicate the reduced fluctuations in fixation when the Bessel beam is employed to create the beacon. © 2013 The Authors Ophthalmic & Physiological Optics © 2013 The College of Optometrists.
An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions
Dodonov, V. V.; Klimov, A. B.
1993-01-01
We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.
Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function
International Nuclear Information System (INIS)
Sato, Masumi
1985-01-01
Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)
Physical Applications of a Simple Approximation of Bessel Functions of Integer Order
Barsan, V.; Cojocaru, S.
2007-01-01
Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…
Optimality of embeddings of Bessel-potential-type spaces into Lorentz-Karamata spaces
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Opic, Bohumír; Neves, J. S.
2004-01-01
Roč. 134, č. 6 (2004), s. 1127-1147 ISSN 0308-2105 R&D Projects: GA ČR GA201/01/0333 Institutional research plan: CEZ:AV0Z1019905 Keywords : slowly varying functions * Lorentz-Karamata spaces * Bessel potentials Subject RIV: BA - General Mathematics Impact factor: 0.487, year: 2004
Spherical Bessel functions jsub(n) and ysub(n) of integer order and real argument
International Nuclear Information System (INIS)
Ardill, R.W.B.; Moriarty, K.J.M.
1978-01-01
The spherical Bessel function appears in a variety of physical applications, and especially in phase shift analysis. The package SPHBES contains a subroutine to calculate jsub(n)(x) and ysub(n)(x) for any integer order n and real argument x. The functions jsub(n)(x) and ysub(n)(x) are produced simultaneously and efficiently. (Auth.)
Superpositions of higher-order bessel beams and nondiffracting speckle fields
CSIR Research Space (South Africa)
Dudley, Angela L
2009-08-01
Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...
Self-healing of Bessel-like beams with longitudinally dependent cone angles
CSIR Research Space (South Africa)
Litvin, I
2015-09-01
Full Text Available non-diffracting propagation region. Here we show that such beams can self-heal. Moreover, in contrast to Bessel beams where the self-healing distance is constant, here the self-healing distance is dependent on where the obstruction is placed...
Shape invariant higher-order Bessel-like beams carrying orbital angular momentum
CSIR Research Space (South Africa)
Ismail, Y
2012-09-01
Full Text Available -1 Journal of Optics September 2012/ Vol. 14 Shape invariant higher-order Bessel-like beams carrying orbital angular momentum Y Ismail1,2, N Khilo3, V Belyi3 and A Forbes1,2 1 School of Physics, University of KwaZulu-Natal, Private Bag X54001...
Superpositions of higher-order bessel beams and nondiffracting speckle fields - (SAIP 2009)
CSIR Research Space (South Africa)
Dudley, Angela L
2009-07-01
Full Text Available speckle fields. The paper reports on illuminating a ring slit aperture with light which has an azimuthal phase dependence, such that the field produced is a superposition of two higher-order Bessel beams. In the case that the phase dependence of the light...
Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams
International Nuclear Information System (INIS)
Mitri, F.G.; Li, R.X.; Yang, R.P.; Guo, L.X.; Ding, C.Y.
2016-01-01
The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam′s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on
International Nuclear Information System (INIS)
Akita, Junji; Honma, Toei.
1975-01-01
Object: To provide a square through tube involving thermal movement in pipelines such as water supply pump driving turbine exhaust pipe (square-shaped), which is wide in freedom with respect to shape and dimension thereof for efficient installation at site. Structure: In a through tube to be airtightly retained for purpose of decontamination in an atomic power plant, comprising a seal rubber plate, a band and a bolt and a nut for securing said plate, the seal rubber plate being worked into the desired shape so that it may be placed in intimate contact with the concrete floor surface by utilization of elasticity of rubber, thereby providing airtightness at a corner portion of the square tube. (Kamimura, M.)
International Nuclear Information System (INIS)
Ryu, C; Henderson, K C; Boshier, M G
2014-01-01
Bessel beams are plane waves with amplitude profiles described by Bessel functions. They are important because they propagate ‘diffraction-free’ and because they can carry orbital angular momentum. Here we report the creation of a Bessel beam of de Broglie matter waves. The Bessel beam is produced by the free evolution of a thin toroidal atomic Bose–Einstein condensate (BEC) which has been set into rotational motion. By attempting to stir it at different rotation rates, we show that the toroidal BEC can only be made to rotate at discrete, equally spaced frequencies, demonstrating that circulation is quantized in atomic BECs. The method used here can be viewed as a form of wavefunction engineering which might be developed to implement cold atom matter wave holography. (paper)
Turquet, Léo; Kakko, Joona-Pekko; Karvonen, Lasse; Jiang, Hua; Kauppinen, Esko; Lipsanen, Harri; Kauranen, Martti; Bautista, Godofredo
2017-08-01
Non-diffractive Bessel beams are receiving significant interest in optical microscopy due to their remarkably large depth of field. For example, studies have shown the superiority of Bessel beams over Gaussian beams for volumetric imaging of three-dimensionally thick or extended samples. However, the vectorial aspects of the focal fields of Bessel beams are generally obscured when traditional methods are used to characterize their three-dimensional point-spread function in space, which contains contributions from all optical field components. Here, we show experimentally the three-dimensional spatial distribution and enhanced depth of field of the longitudinal electric field components of a focused linearly-polarized Bessel beam. This is done through second-harmonic generation from well-defined vertically-aligned gallium-arsenide nanowires, whose second-order response is primarily driven by the longitudinal fields at the beam focus.
Occupation times and exact asymptotics of small deviations of Bessel processes for Lp-norms with p>0
International Nuclear Information System (INIS)
Fatalov, V R
2007-01-01
We prove theorems on exact asymptotics of the distributions of integral functionals of the occupation time of Bessel processes. Using these results, we obtain exact asymptotics of small deviations for Bessel processes in the L p -norm. We use Laplace's method for the occupation times of Markov processes with continuous time. Computations are carried out for p=2 and p=1. We also solve extremal problems for the action functional
Kerimov, M. K.
2016-07-01
This work continues the study of real zeros of first- and second-kind Bessel functions and Bessel general functions with real variables and orders begun in the first part of this paper (see M.K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014)). Some new results concerning such zeros are described and analyzed. Special attention is given to the monotonicity, convexity, and concavity of zeros with respect to their ranks and other parameters.
High-power Bessel beams with orbital angular momentum in the terahertz range
Choporova, Yu. Yu.; Knyazev, B. A.; Kulipanov, G. N.; Pavelyev, V. S.; Scheglov, M. A.; Vinokurov, N. A.; Volodkin, B. O.; Zhabin, V. N.
2017-08-01
In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of ±1 and ±2 formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at f =5.6 MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about L /r ≈190 and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, "diffraction-free" propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by π , the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 μ m in our case
International Nuclear Information System (INIS)
Li, Renxian; Ren, Kuan Fang; Han, Xiang'e; Wu, Zhensen; Guo, Lixin; Gong, Shuxi
2013-01-01
Debye series expansion (DSE) is employed to the analysis of radiation pressure force (RPF) exerted on biological cells induced by high-order Bessel beams (BB). The beam shape coefficients (BSCs) for high-order Bessel beams are calculated using analytical expressions obtained by the integral localized approximation (ILA). Different types of cells, including a real Chinese Hamster Ovary (CHO) cell and a lymphocyte which are respectively modeled by a coated and five-layered sphere, are considered. The RPF induced by high-order Bessel beams is compared with that by Gaussian beams and zeroth-order Bessel beams, and the effect of different scattering processes on RPF is studied. Numerical calculations show that high-order Bessel beams with zero central intensity can also transversely trap particle in the beam center, and some scattering processes can provide longitudinal pulling force. -- Highlights: ► BSCs for high-order Bessel beam (HOBB) is derived using ILA. ► DSE is employed to study the RPF induced by HOBB exerted on multilayered cells. ► RPF is decided by radius relative to the interval of peaks in intensity profile. ► HOBB can also transversely trap high-index particle in the vicinity of beam axis. ► RPF for some scattering processes can longitudinally pull particles back
Expansion of a zero-order Bessel beam in spheroidal coordinates by generalized Lorenz–Mie theory
International Nuclear Information System (INIS)
Han, L.; Han, Y.P.; Cui, Z.W.; Wang, J.J.
2014-01-01
An analytic solution to the scattering of the zero-order Bessel beam by a spheroidal particle is constructed on the basis of the generalized Lorenz–Mie theory (GLMT). The spheroidal beam shape coefficients (BSCs) of the zero-order Bessel beam are directly expressed in spheroidal coordinates and computed conveniently using an intrinsic method. Utilizing the tangential continuity of the electromagnetic fields, the expression coefficients of scattered and internal fields are determined. Numerical results concerning scattered field in the far zone are displayed for various parameters of the incident electromagnetic beam and of the scatter. These results are expected to provide useful insights into the scattering of a Bessel beam by spheroidal particles and particle manipulation applications using Bessel beams. - Highlights: • The scattering of zero-order Bessel beam by dielectric spheroid is investigated. • The analytic solution is constructed within the framework of the GLMT. • The spheroidal beam shape coefficients of the zero-order Bessel beam are computed by use an intrinsic method. • Numerical results concerning scattered field are displayed for various parameters
Path Creation, Path Dependence and Breaking Away from the Path
Wang, Jens; Hedman, Jonas; Tuunainen, Virpi Kristiina
2016-01-01
The explanation of how and why firms succeed or fail is a recurrent research challenge. This is particularly important in the context of technological innovations. We focus on the role of historical events and decisions in explaining such success and failure. Using a case study of Nokia, we develop and extend a multi-layer path dependence framework. We identify four layers of path dependence: technical, strategic and leadership, organizational, and external collaboration. We show how path dep...
Bessel beam transformation in c-cuts of uniaxial crystals by varying the source wavelength
Energy Technology Data Exchange (ETDEWEB)
Paranin, V. D. [Samara State Aerospace University, 34, Moskovskoe shosse, Samara, 443086 (Russian Federation)
2016-04-13
Transformation of Bessel beam of a zero order to Bessel beam of the second order in c-cut of CaCO{sub 3} crystal is experimentally investigated. Possibility of output beam control at changing of wavelength and using of a diffraction axicon is shown. Full transformation of beams at changing of wavelength Δλ=1.5 nanometers is received at initial wavelength λ=637.5 nanometers for a crystal of CaCO{sub 3} with 15 mm long and a diffraction axicon with period of 2 microns. The theoretical value of necessary wavelength changing is Δλ=1.7 nanometers that is according with experimental results.
Yao, Hainan; Wang, Fei; Cai, Yangjian
2018-01-01
Two-index Bessel beams (TIBBs) was introduced by Ornigotti and Aiello (2014) theoretically. In this paper, we propose a simple experimental scheme for generation of two-index Bessel-Gauss beams (TIBGBs), as an extension of the TIBBs. The scheme is based on manipulating the amplitude and phase in the Fourier plane with the use of a spatial light modulator and a spiral phase plate. Furthermore, we experimentally report the generation of the several examples of the TIBGBs based on the proposed optical system. The focusing properties of the TIBGB with indices p = 1 and l = 2 passing through a single lens are investigated both theoretically and experimentally. The experimental results agree well with theoretical predictions.
A symmetric integral identity for Bessel functions with applications to integral geometry
Salman, Yehonatan
2017-12-01
In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.
Construction of normal-regular decisions of Bessel typed special system
Tasmambetov, Zhaksylyk N.; Talipova, Meiramgul Zh.
2017-09-01
Studying a special system of differential equations in the separate production of the second order is solved by the degenerate hypergeometric function reducing to the Bessel functions of two variables. To construct a solution of this system near regular and irregular singularities, we use the method of Frobenius-Latysheva applying the concepts of rank and antirank. There is proved the basic theorem that establishes the existence of four linearly independent solutions of studying system type of Bessel. To prove the existence of normal-regular solutions we establish necessary conditions for the existence of such solutions. The existence and convergence of a normally regular solution are shown using the notion of rank and antirank.
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid
Mitri, F. G.
2015-01-01
Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (\\theta = \\pi) in the near-field an...
CMB in a box: Causal structure and the Fourier-Bessel expansion
International Nuclear Information System (INIS)
Abramo, L. Raul; Reimberg, Paulo H.; Xavier, Henrique S.
2010-01-01
This paper makes two points. First, we show that the line-of-sight solution to cosmic microwave anisotropies in Fourier space, even though formally defined for arbitrarily large wavelengths, leads to position-space solutions which only depend on the sources of anisotropies inside the past light cone of the observer. This foretold manifestation of causality in position (real) space happens order by order in a series expansion in powers of the visibility γ=e -μ , where μ is the optical depth to Thomson scattering. We show that the contributions of order γ N to the cosmic microwave background (CMB) anisotropies are regulated by spacetime window functions which have support only inside the past light cone of the point of observation. Second, we show that the Fourier-Bessel expansion of the physical fields (including the temperature and polarization momenta) is an alternative to the usual Fourier basis as a framework to compute the anisotropies. The viability of the Fourier-Bessel series for treating the CMB is a consequence of the fact that the visibility function becomes exponentially small at redshifts z>>10 3 , effectively cutting off the past light cone and introducing a finite radius inside which initial conditions can affect physical observables measured at our position x-vector=0 and time t 0 . Hence, for each multipole l there is a discrete tower of momenta k il (not a continuum) which can affect physical observables, with the smallest momenta being k 1l ∼l. The Fourier-Bessel modes take into account precisely the information from the sources of anisotropies that propagates from the initial value surface to the point of observation - no more, no less. We also show that the physical observables (the temperature and polarization maps), and hence the angular power spectra, are unaffected by that choice of basis. This implies that the Fourier-Bessel expansion is the optimal scheme with which one can compute CMB anisotropies.
Asymptotic formulae for the Lommel and Bessel functions and their derivatives.
Aleksandrova, N I
2014-10-01
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.
Chen, J; Yuan, X-C; Zhao, X; Fang, Z L; Zhu, S W
2009-11-01
We propose a generalized approach to producing optical vortices with suppressed sidelobes using a variable Bessel-like function added to the conventional spiral phase plate. Experimental verifications are implemented by a phase-only spatial light modulator. It is demonstrated that the method is valid for optical vortex beams with arbitrary topological charges and without changing the primary ring size as a unique property among the existing techniques.
Factorization of products of discontinuous functions applied to Fourier-Bessel basis.
Popov, Evgeny; Nevière, Michel; Bonod, Nicolas
2004-01-01
The factorization rules of Li [J. Opt. Soc. Am. A 13, 1870 (1996)] are generalized to a cylindrical geometry requiring the use of a Bessel function basis. A theoretical study confirms the validity of the Laurent rule when a product of two continuous functions or of one continuous and one discontinuous function is factorized. The necessity of applying the so-called inverse rule in factorizing a continuous product of two discontinuous functions in a truncated basis is demonstrated theoretically and numerically.
Analytic approximation for the modified Bessel function I -2/3(x)
Martin, Pablo; Olivares, Jorge; Maass, Fernando
2017-12-01
In the present work an analytic approximation to modified Bessel function of negative fractional order I -2/3(x) is presented. The validity of the approximation is for every positive value of the independent variable. The accuracy is high in spite of the small number (4) of parameters used. The approximation is a combination of elementary functions with rational ones. Power series and assymptotic expansions are simultaneously used to obtain the approximation.
Certain new unified integrals associated with the product of generalized Bessel functions
Directory of Open Access Journals (Sweden)
Praveen Agarwal
2016-02-01
Full Text Available Our focus to presenting two very general integral formulas whose integrands are the integrand given in the Oberhettinger's integral formula and a finite product of the generalized Bessel function of the first kind, which are expressed in terms of the generalized Lauricella functions. Among a large number of interesting and potentially useful special cases of our main results, some integral formulas involving such elementary functions are also considered.
The application of a Bessel transform to the determination of stellar rotational velocities
International Nuclear Information System (INIS)
Deeming, T.J.
1977-01-01
A method for analysing line profiles by means of a transform using Bessel functions is described. This yields the stellar rotational velocity γ sin i, to an accuracy of about +-1 km s -1 for rotational velocities greater than about 5 km s -1 , provided that rotation is the major source of line broadening. The theory of the method is a special case of a general theory of linear transforms in data analysis, which is outlined in an appendix. (Auth.)
Fourier Bessel transform method for efficiently calculating the magnetic field of solenoids
International Nuclear Information System (INIS)
Nachamkin, J.; Maggiore, C.J.
1980-01-01
A numerical procedure for calculating the magnetic field of a selenoid is derived. Based on the properties of Bessel functions, the procedure is shown to be convergent everywhere, including within the windings of the solenoid. The most critical part of the procedure is detailed in the main text. A simple method is used to ensure numerical significance while allowing economical computational times. In the appendix the procedure is generalized to universal convergence by appropriate partitioning of the solenoid windings
A note on a hyper-cubic Mahler measure and associated Bessel integral
International Nuclear Information System (INIS)
Glasser, M L
2012-01-01
The Mahler measure for the n-variable polynomial k + ∑(x j + 1/x j ) is reduced to a single integral of the n-th power of the modified Bessel function I 0 . Several special cases are examined in detail. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday. (paper)
A generalization for the infinite integral over three spherical Bessel functions
International Nuclear Information System (INIS)
Mehrem, R; Hohenegger, A
2010-01-01
A new formula is derived that generalizes an earlier result for the infinite integral over three spherical Bessel functions. The analytical result involves a finite sum over associated Legendre functions, P m l (x) of degree l and order m. The sum allows for the values of |m| that are greater than l. A generalization for the associated Legendre functions to allow for any rational m for a specific l is also shown.
Enhancement of photorefractive two wave mixing gain with a Bessel pump beam
International Nuclear Information System (INIS)
Biswas, Dhruba J.; Padma Nilaya, J.; Danailov, Miltcho, B.
2001-07-01
The performance of a photo-refractive amplifier has been shown to greatly improve when a diffraction free beam is employed as the pump source. It has been established experimentally that this behaviour owes primarily to the ability of this beam to propagate in the photo-refractive crystal will less fanning. A qualitative explanation for the reduction of fanning with Bessel beam is offered. (author)
Radiophotoluminescence of alkali-halide crystals stimulated by Bessel laser beam
Lyakh, V V; Kochubey, D I; Gyunsburg, K E; Zvezdova, N P; Kochubey, D I; Sedova, Y G; Koronkevich, V P; Poleschuk, A G; Sedukhin, A G
2000-01-01
A new approach to realization of optimal high-resolution reading of deep X-ray images in X-ray-sensitive materials on the base of alkali-halide crystals modified with admixtures has been suggested and investigated experimentally. A possibility to use diffraction axicons with ring aperture for forming micron bright light beams (spatially truncated Bessel beams) which can efficiently de-excite radiophotoluminescence centers lying at large depth in crystals is also presented.
International Nuclear Information System (INIS)
Dory, R.A.; Uckan, N.A.; Ard, W.B.
1986-10-01
The ELMO Bumpy Square (EBS) concept consists of four straight magnetic mirror arrays linked by four high-field corner coils. Extensive calculations show that this configuration offers major improvements over the ELMO Bumpy Torus (EBT) in particle confinement, heating, transport, ring production, and stability. The components of the EBT device at Oak Ridge National Laboratory can be reconfigured into a square arrangement having straight sides composed of EBT coils, with new microwave cavities and high-field corners designed and built for this application. The elimination of neoclassical convection, identified as the dominant mechanism for the limited confinement in EBT, will give the EBS device substantially improved confinement and the flexibility to explore the concepts that produce this improvement. The primary goals of the EBS program are twofold: first, to improve the physics of confinement in toroidal systems by developing the concepts of plasma stabilization using the effects of energetic electrons and confinement optimization using magnetic field shaping and electrostatic potential control to limit particle drift, and second, to develop bumpy toroid devices as attractive candidates for fusion reactors. This report presents a brief review of the physics analyses that support the EBS concept, discussions of the design and expected performance of the EBS device, a description of the EBS experimental program, and a review of the reactor potential of bumpy toroid configurations. Detailed information is presented in the appendices
Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.
Mitri, Farid G
2015-10-01
Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.
Efficient second-harmonic imaging of collagen in histological slides using Bessel beam excitation
Vuillemin, Nelly; Mahou, Pierre; Débarre, Delphine; Gacoin, Thierry; Tharaux, Pierre-Louis; Schanne-Klein, Marie-Claire; Supatto, Willy; Beaurepaire, Emmanuel
2016-07-01
Second-harmonic generation (SHG) is the most specific label-free indicator of collagen accumulation in widespread pathologies such as fibrosis, and SHG-based measurements hold important potential for biomedical analyses. However, efficient collagen SHG scoring in histological slides is hampered by the limited depth-of-field of usual nonlinear microscopes relying on focused Gaussian beam excitation. In this work we analyze theoretically and experimentally the use of Bessel beam excitation to address this issue. Focused Bessel beams can provide an axially extended excitation volume for nonlinear microscopy while preserving lateral resolution. We show that shaping the focal volume has consequences on signal level and scattering directionality in the case of coherent signals (such as SHG) which significantly differ from the case of incoherent signals (two-photon excited fluorescence, 2PEF). We demonstrate extended-depth SHG-2PEF imaging of fibrotic mouse kidney histological slides. Finally, we show that Bessel beam excitation combined with spatial filtering of the harmonic light in wave vector space can be used to probe collagen accumulation more efficiently than the usual Gaussian excitation scheme. These results open the way to SHG-based histological diagnoses.
Multidimensional digital image representations using generalized Kaiser-Bessel window functions.
Lewitt, R M
1990-10-01
Inverse problems that require the solution of integral equations are inherent in a number of indirect imaging applications, such as computerized tomography. Numerical solutions based on discretization of the mathematical model of the imaging process, or on discretization of analytic formulas for iterative inversion of the integral equations, require a discrete representation of an underlying continuous image. This paper describes discrete image representations, in n-dimensional space, that are constructed by the superposition of shifted copies of a rotationally symmetric basis function. The basis function is constructed using a generalization of the Kaiser-Bessel window function of digital signal processing. The generalization of the window function involves going from one dimension to a rotationally symmetric function in n dimensions and going from the zero-order modified Bessel function of the standard window to a function involving the modified Bessel function of order m. Three methods are given for the construction, in n-dimensional space, of basis functions having a specified (finite) number of continuous derivatives, and formulas are derived for the Fourier transform, the x-ray transform, the gradient, and the Laplacian of these basis functions. Properties of the new image representations using these basis functions are discussed, primarily in the context of two-dimensional and three-dimensional image reconstruction from line-integral data by iterative inversion of the x-ray transform. Potential applications to three-dimensional image display are also mentioned.
The nonlocal problem for a hyperbolic equation with Bessel operator in a rectangular domain
Directory of Open Access Journals (Sweden)
Natalya V. Zaitseva
2016-12-01
Full Text Available We consider a boundary value problem for a hyperbolic equation with Bessel differential operator in a rectangular domain with integral nonlocal boundary value condition of the first kind. The equivalence between boundary value problem with integral nonlocal condition of the first kind and a local boundary value problem with mixed boundary conditions of the first and third kinds is proved. The existence and uniqueness of solution of the equivalent problem are established by means of the spectral method. At the uniqueness proof the completeness of the eigenfunction system of the spectral problem is used . At the existence proof the assessment of coefficients of series, the asymptotic formula for Bessel function of the first kind and asymptotic formula for eigenvalues are used. Sufficient conditions on the functions defining initial data of the problem are received. The solution of the problem is obtained in explicit form. The solution is obtained in the form of the Fourier–Bessel series. Its convergence is proved in the class of regular solutions.
Rapid volumetric imaging with Bessel-Beam three-photon microscopy
Chen, Bingying; Huang, Xiaoshuai; Gou, Dongzhou; Zeng, Jianzhi; Chen, Guoqing; Pang, Meijun; Hu, Yanhui; Zhao, Zhe; Zhang, Yunfeng; Zhou, Zhuan; Wu, Haitao; Cheng, Heping; Zhang, Zhigang; Xu, Chris; Li, Yulong; Chen, Liangyi; Wang, Aimin
2018-01-01
Owing to its tissue-penetration ability, multi-photon fluorescence microscopy allows for the high-resolution, non-invasive imaging of deep tissue in vivo; the recently developed three-photon microscopy (3PM) has extended the depth of high-resolution, non-invasive functional imaging of mouse brains to beyond 1.0 mm. However, the low repetition rate of femtosecond lasers that are normally used in 3PM limits the temporal resolution of point-scanning three-photon microscopy. To increase the volumetric imaging speed of 3PM, we propose a combination of an axially elongated needle-like Bessel-beam with three-photon excitation (3PE) to image biological samples with an extended depth of focus. We demonstrate the higher signal-to-background ratio (SBR) of the Bessel-beam 3PM compared to the two-photon version both theoretically and experimentally. Finally, we perform simultaneous calcium imaging of brain regions at different axial locations in live fruit flies and rapid volumetric imaging of neuronal structures in live mouse brains. These results highlight the unique advantage of conducting rapid volumetric imaging with a high SBR in the deep brain in vivo using scanning Bessel-3PM.
Feynman's path integrals and Bohm's particle paths
International Nuclear Information System (INIS)
Tumulka, Roderich
2005-01-01
Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schroedinger's equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation. (letters and comments)
Path coupling and aggregate path coupling
Kovchegov, Yevgeniy
2018-01-01
This book describes and characterizes an extension to the classical path coupling method applied to statistical mechanical models, referred to as aggregate path coupling. In conjunction with large deviations estimates, the aggregate path coupling method is used to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. The book shows how the parameter regions for rapid mixing for several classes of statistical mechanical models are derived using the aggregate path coupling method.
Williams, Horace E.
1974-01-01
A method for generating 3x3 magic squares is developed. A series of questions relating to these magic squares is posed. An invesitgation using matrix methods is suggested with some questions for consideration. (LS)
International Nuclear Information System (INIS)
Mitri, F.G.
2014-01-01
The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves
Energy Technology Data Exchange (ETDEWEB)
Mitri, F.G., E-mail: mitri@chevron.com
2014-03-15
The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves.
Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers
International Nuclear Information System (INIS)
Mitri, F.G.
2008-01-01
Starting from the exact acoustic scattering from a sphere immersed in an ideal fluid and centered along the propagation axis of a standing or quasi-standing zero-order Bessel beam, explicit partial-wave representations for the radiation force are derived. A standing or a quasi-standing acoustic field is the result of propagating two equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis but in opposite sense. The Bessel beam is characterized by the half-cone angle β of its plane wave components, such that β = 0 represents a plane wave. It is assumed here that the half-cone angle β for each of the counter-propagating acoustic Bessel beams is equal. Fluid, elastic and viscoelastic spheres immersed in water are treated as examples. Results indicate the capability of manipulating spherical targets based on their mechanical and acoustical properties. This condition provides an impetus for further designing acoustic tweezers operating with standing or quasi-standing Bessel acoustic waves. Potential applications include particle manipulation in micro-fluidic lab-on-chips as well as in reduced gravity environments
Kerimov, M. K.
2016-12-01
This paper continues the study of real zeros of Bessel functions begun in the previous parts of this work (see M. K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337-1388 (2014); 56 (7), 1175-1208 (2016)). Some new results regarding the monotonicity, convexity, concavity, and other properties of zeros are described. Additionally, the zeros of q-Bessel functions are investigated.
Sherstyukov, V. B.; Sumin, E. V.
2017-12-01
Modified Bessel functions of the first kind Iv (z) (Infeld functions) where v > -1 are considered. Due to the constraint on the parameter v, all zeros of the function Iv (z) except z = 0 are simple, located on the imaginary axis by symmetric pairs and form an infinite countable set. On the basis on previous research of the authors dealing with general Bessel functions of the first kind Jv (z), a question about reciprocal expansion 1/Iv (z) in series of simple fractions of a certain structure (Krein’s series) is studied. The general formulas to calculate of special infinite sums containing degrees of Infeld function zeros are an important consequence of obtained expansion in simple fractions of the value 1/Iv (z) with any v > -1. The possibility of concrete definition of established summation relationships at different values of parameters and their connection with analogous relationships for the Bessel functions of the first kind Jv (z) is discussed.
Shen, Yizhu; Yang, Jiawei; Meng, Hongfu; Dou, Wenbin; Hu, Sanming
2018-04-01
Metasurfaces, orbital angular momenta (OAM), and non-diffractive Bessel beams have been attracting worldwide research. Combining the benefits of these three promising techniques, this paper proposes a metasurface-based reflective-type approach to generate a first-order Bessel beam carrying OAM. To validate this approach, a millimeter-wave metasurface is analyzed, designed, fabricated, and measured. Experimental results agree well with simulation. Moreover, this reflective-type metasurface, generating a Bessel beam with OAM, is inherently integrated with a planar feeding source in the same single-layer printed circuit board. Therefore, the proposed design features low profile, low cost, easy integration with front-end active circuits, and no alignment error between the feeding source and the metasurface.
Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation
International Nuclear Information System (INIS)
Raptis, A.D.; Cash, J.R.
1987-01-01
A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)
Directory of Open Access Journals (Sweden)
Fatima G. Khushtova
2016-03-01
Full Text Available In this paper Cauchy problem for a parabolic equation with Bessel operator and with Riemann–Liouville partial derivative is considered. The representation of the solution is obtained in terms of integral transform with Wright function in the kernel. It is shown that when this equation becomes the fractional diffusion equation, obtained solution becomes the solution of Cauchy problem for the corresponding equation. The uniqueness of the solution in the class of functions that satisfy the analogue of Tikhonov condition is proved.
International Nuclear Information System (INIS)
Poquerusse, A.; Alexiou, S.
1999-01-01
In this work we review the status of the standard line broadening theory for plasmas and fill in the existing gap, i.e., the partially overlapping case for ions lines, by deriving expressions as well as fast and accurate numerical approximations for the relevant functions, namely the modified Bessel function of imaginary order and its derivative with respect to argument. These functions also arise in the context of the theory of Coulomb excitation. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Solved problems in analysis as applied to gamma, beta, Legendre and Bessel functions
Farrell, Orin J
2013-01-01
Nearly 200 problems, each with a detailed, worked-out solution, deal with the properties and applications of the gamma and beta functions, Legendre polynomials, and Bessel functions. The first two chapters examine gamma and beta functions, including applications to certain geometrical and physical problems such as heat-flow in a straight wire. The following two chapters treat Legendre polynomials, addressing applications to specific series expansions, steady-state heat-flow temperature distribution, gravitational potential of a circular lamina, and application of Gauss's mechanical quadrature
On the propagation of transient waves in a viscoelastic Bessel medium
Colombaro, Ivano; Giusti, Andrea; Mainardi, Francesco
2017-06-01
In this paper, we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave front. To do so, we take profit of a revisited version of the so called Buchen-Mainardi algorithm. Secondly, we provide an analytic expression for the long-time behavior of the response function of the material. This result is obtained by means of the Tauberian theorems for the Laplace transform. Finally, we relate the obtained results to a peculiar model for fluid-filled elastic tubes.
Certain fractional integral formulas involving the product of generalized Bessel functions.
Baleanu, D; Agarwal, P; Purohit, S D
2013-01-01
We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
Baleanu, D.; Agarwal, P.; Purohit, S. D.
2013-01-01
We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions. PMID:24379745
Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.
Porras, Miguel A; Ramos, Francisco
2017-09-01
The applications of vortex solitons are severely limited by the diffraction and self-defocusing spreading of the background beam where they are nested. Nonlinear Bessel beams in self-defocusing media are nondiffracting, flattop beams where the nested vortex solitons can survive for propagation distances that are one order of magnitude larger than in the Gaussian or super-Gaussian beams. The dynamics of the vortex solitons is studied numerically and found to approach that in the ideal, uniform background, preventing vortex spiraling and decay, which eases vortex steering for applications.
Bessel Plasmon-Polaritons at the Boundaries of Metamaterials with Near-Zero Dielectric Constants
Kurilkina, S. N.; Belyi, V. N.; Kazak, N. S.; Binhussain, M. A.
2015-07-01
The conditions for and features of the excitation of Bessel plasmon-polaritons (BPP) are examined at the boundary of a hyperbolic metamaterial with a near-zero dielectric constant made of a dielectric matrix with metal nanorods embedded in it normal to its surface. This material is compared with BPP that have traditional surface plasmons. The effect of the absorption of the metamaterial on the excitation of BPP is studied. The possibility of changes in the direction of the radial energy fl ows in BPP excited at the surface of an isotropic medium, a hyperbolic metamaterial, is demonstrated and the conditions for these changes are determined.
All-optical 3D atomic loops generated with Bessel light fields
International Nuclear Information System (INIS)
Volke-Sepulveda, Karen; Jauregui, RocIo
2009-01-01
The propagation invariance of Bessel beams as well as their transversal structure is used to perform a comparative analysis of their effect on cold atoms for four different configurations and combinations thereof. We show that, even at temperatures for which the classical description of the atom's centre-of-mass motion is valid, the interchange of momentum, energy and orbital angular momentum between light and atoms yields efficient tools for all-optical trapping, transporting and, in general, manipulating the state of motion of cold atoms.
Transmission of a Bessel beam through a circular aperture in an impedance screen
International Nuclear Information System (INIS)
Umul, Yusuf Ziya
2014-01-01
The scattering effect of a circular aperture, located in an impedance plane, on a Bessel beam is investigated by decomposing the scattered wave into two subcomponents, namely the geometrical optics and diffracted fields. The diffracted waves are investigated with the aid of the geometrical theory of diffraction. The detour parameter is evaluated and the existence zones of the geometrical optics fields are determined. The various aspects of the reflected and transmitted scattered waves, including the self healing of the beam, are studied numerically. (letter)
Measuring a narrow Bessel beam spot by scanning a charge-coupled device (CCD) pixel
International Nuclear Information System (INIS)
Tiwari, S K; Ram, S P; Jayabalan, J; Mishra, S R
2010-01-01
By scanning a charge-coupled device (CCD) camera transverse to the beam axis and observing the variation in counts on a marked pixel, we demonstrate that we can measure a laser beam spot size smaller than the size of the CCD-pixel. We find this method particularly attractive for measuring the size of central spot of a Bessel beam, for which the established scanning knife-edge method does not work appropriately because of the large contribution of the rings surrounding the central spot to the signal
International Nuclear Information System (INIS)
Paranin, V D; Karpeev, S V; Khonina, S N; Tukmakov, K N
2016-01-01
Transformation of zero-order Bessel beams into a second-order vortex beam in the process of propagation in a c-cut of lithium niobate LiNbO 3 crystal has been investigated experimentally. The possibility of controlling beam transformation by means of changing the curve radius of the illuminating beam is shown. The possibility of Bessel beam transforming by compact devices on the basis of thin c-cuts of uniaxial crystals with a diffraction mask formed on their surface is proved. (paper)
Fractional path planning and path tracking
International Nuclear Information System (INIS)
Melchior, P.; Jallouli-Khlif, R.; Metoui, B.
2011-01-01
This paper presents the main results of the application of fractional approach in path planning and path tracking. A new robust path planning design for mobile robot was studied in dynamic environment. The normalized attractive force applied to the robot is based on a fictitious fractional attractive potential. This method allows to obtain robust path planning despite robot mass variation. The danger level of each obstacles is characterized by the fractional order of the repulsive potential of the obstacles. Under these conditions, the robot dynamic behavior was studied by analyzing its X - Y path planning with dynamic target or dynamic obstacles. The case of simultaneously mobile obstacles and target is also considered. The influence of the robot mass variation is studied and the robustness analysis of the obtained path shows the robustness improvement due to the non integer order properties. Pre shaping approach is used to reduce system vibration in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual vibration. This technique, developed by N.C. Singer and W.P.Seering, is used for flexible structure control, particularly in the aerospace field. In a previous work, this method was extended for explicit fractional derivative systems and applied to second generation CRONE control, the robustness was also studied. CRONE (the French acronym of C ommande Robuste d'Ordre Non Entier ) control system design is a frequency-domain based methodology using complex fractional integration.
Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces
International Nuclear Information System (INIS)
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth
2015-01-01
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape
Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces
Energy Technology Data Exchange (ETDEWEB)
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth, E-mail: rsignorell@ethz.ch [Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland)
2015-04-21
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth
2015-04-21
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.
Stability of aerosol droplets in Bessel beam optical traps under constant and pulsed external forces
David, Grégory; Esat, Kıvanç; Hartweg, Sebastian; Cremer, Johannes; Chasovskikh, Egor; Signorell, Ruth
2015-04-01
We report on the dynamics of aerosol droplets in optical traps under the influence of additional constant and pulsed external forces. Experimental results are compared with simulations of the three-dimensional droplet dynamics for two types of optical traps, the counter-propagating Bessel beam (CPBB) trap and the quadruple Bessel beam (QBB) trap. Under the influence of a constant gas flow (constant external force), the QBB trap is found to be more stable compared with the CPBB trap. By contrast, under pulsed laser excitation with laser pulse durations of nanoseconds (pulsed external force), the type of trap is of minor importance for the droplet stability. It typically needs pulsed laser forces that are several orders of magnitude higher than the optical forces to induce escape of the droplet from the trap. If the droplet strongly absorbs the pulsed laser light, these escape forces can be strongly reduced. The lower stability of absorbing droplets is a result of secondary thermal processes that cause droplet escape.
Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map
San Roman Alerigi, Damian; Alsunaidi, Mohammad; Ben Slimane, Ahmed; Ng, Tien Khee; Ooi, Boon S.; Zhang, Yaping
2012-01-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.
Walk-off reduction, using an external optical plate and Bessel-Gaussian interaction
Masoume, Mansouri; Mohsen, Askarbioki; Saeed Ghavami, Sabouri; Alireza, Khorsandi
2015-02-01
To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type II KTiOPO4 and type I β-BaB2O4 optical crystals, and the Gaussian output beam of a Q-switched Nd:YAG laser, a simple theoretical model was developed based on a rotatable BK7 plate of variable thickness. By rotating the plate up to 35° along the beam direction, we reduced the walk-off angle up to ˜ 13%. The same phenomenon is predicted by the model, confirming the performance of the model. It is found that, due to the walk-off effect, the intensity profile of the third-harmonic generation beam is slightly degraded. To compensate for the observed phenomena and further reduce the walk-off, we used a combination of a convex lens and an axicon to transform the beam profile of the interacting fundamental and second-harmonic generation waves to the zero-order Bessel-Gaussian form. As a result, the walk-off is decreased to ˜48.81 mrad, providing ˜30% relative reduction. By using the same BK7 plate rotated up to 35° along the third-harmonic beam direction, the walk-off angle is further reduced to 38.9 mrad. Moreover, it is observed that the beam profile of the emerged Bessel-Gaussian third-harmonic generation beam remains unchanged with no degradation.
Generation of J_0-Bessel-Gauss beam by a heterogeneous refractive index map
San Roman Alerigi, Damian
2012-07-01
In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J0-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si1-yOy/Si1-x-yGexCy platform or by photo-refractive media. The proposed device is 200 ?m in length and 25 ?m in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J0-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers. © 2012 Optical Society of America.
Directory of Open Access Journals (Sweden)
Zoran Gojković
2017-01-01
Full Text Available The physical surface of the earth has irregular shape which is not mathematically defined, therefore the shape of the Earth is approximated with mathematically defined surfaces such as ellipsoid and sphere. The developing of a global positioning systems, thus and modern navigation systems, as effect produce large amounts of data which contain the problem of homogeneity. This problem could be exceed if all the data are store in the same coordinate system. Hence the need for data transformation from local coordinate systems to the global coordinate systems. Global level implies WGS84 ellipsoid and UTM projection while national coordinate system of Republic Serbia is Gauss-Kruger with Bessel ellipsoid. This coordinate system of Republic Serbia on a global level has a local character. Applying appropriate mathematical models and functions it is possible to transform coordinates from one system to another and vice versa. The paper describes coordinate transformations from Gauss-Kruger coordinate system ellipsoid Bessel to UTM projection WGS84 ellipsoid and vice versa, and also an application which provides transformation of its kind that is made using open source environment. Name of the application is TRANS7_GK_UTM_GK and it can be found and used on the web page of the faculty for Mining and Geology under the link http://gk2utm.rgf.bg.ac.rs with a user guide.
On the Operator ⨁Bk Related to Bessel Heat Equation
Directory of Open Access Journals (Sweden)
Wanchak Satsanit
2010-01-01
Full Text Available We study the equation (∂/∂tu(x,t=c2⊕Bku(x,t with the initial condition u(x,0=f(x for x∈Rn+. The operator ⊕Bk is the operator iterated k-times and is defined by ⊕Bk=((∑i=1pBxi4-(∑j=p+1p+qBxi4k, where p+q=n is the dimension of the Rn+, Bxi=∂2/∂xi2+(2vi/xi(∂/∂xi, 2vi=2αi+1, αi>-1/2, i=1,2,3,…,n, and k is a nonnegative integer, u(x,t is an unknown function for (x,t=(x1,x2,…,xn,t∈Rn+×(0,∞, f(x is a given generalized function, and c is a positive constant. We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.
Numerical evaluation of integrals containing a spherical Bessel function by product integration
International Nuclear Information System (INIS)
Lehman, D.R.; Parke, W.C.; Maximon, L.C.
1981-01-01
A method is developed for numerical evaluation of integrals with k-integration range from 0 to infinity that contain a spherical Bessel function j/sub l/(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid: only a relatively small number of quadrature points is needed: for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw--Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented
From Square Dance to Mathematics
Bremer, Zoe
2010-01-01
In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…
Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Alexander, Andrew L.
2012-01-01
The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA). PMID:22963853
Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array
DEFF Research Database (Denmark)
Fox, Paul D.; Jiqi, Cheng; Jian-yu, Lu
2003-01-01
A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling and t...
A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Nash, Patrick L.
2008-01-01
Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium
Guo, Jian; Wei, Zhongchao; Liu, Yuebo; Huang, Aili
2015-02-01
Two amplitude modulation methods, including modified Bessel-like function modulation structure and trapezoid annulus structure, for suppressing sidelobes of optical vortices are studied. In the former approach, we propose that the order of the Bessel-like function can be an additional parameter to modulate diffraction patterns of optical vortices motivated by the idea of conventional annulus structures. Furthermore, new Bessel-like modulation functions are introduced to solve the problem of low diffraction efficiency of the original one. Trapezoid annulus structure is proposed as a compromise structure between the modified Bessel-like modulation structure and the conventional annulus one, and has advantages of both. It is demonstrated that these two approaches can achieve high-quality optical vortices with suppressed sidelobes effectively, and the relative structures behave as more flexible and applicable structures for producing optical vortices with large coverage of topological charges, which suggests great potential in simplifying the structure designing procedure. These reliable and generalized structures for generating high-quality optical vortices will help to promote the development of future optical communication and optical manipulation significantly.
A. Gil (Amparo); J. Segura (Javier); N.M. Temme (Nico)
2002-01-01
textabstractThe use of a uniform Airy-type asymptotic expansion for the computation of the modified Bessel functions of the third kind of imaginary orders ($K_{ia}(x)$) near the transition point $x=a$, is discussed. In [2], an algorithm for the evaluation of $K_{ia}(x)$ was presented, which made use
Two-color above-threshold ionization of atoms and ions in XUV Bessel beams and intense laser light
Seipt, D.; Müller, R. A.; Surzhykov, A.; Fritzsche, S.
2016-11-01
The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultraviolet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target atoms with regard to the beam axis. In addition, analog to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the standard circular dichroism, similar as for Bessel beams with a small opening angle. Detailed computations of the dichroism are performed and discussed for the 4 s valence-shell photoionization of Ca+ ions.
CSIR Research Space (South Africa)
Schulze, C
2014-09-01
Full Text Available We present the measurement of the orbital angular momentum (OAM) density of Bessel beams and superpositions thereof by projection into a Laguerre–Gaussian basis. This projection is performed by an all-optical inner product measurement performed...
International Nuclear Information System (INIS)
Khrapko, R.I.
1985-01-01
A uniform description of various path-dependent functions is presented with the help of expansion of the type of the Taylor series. So called ''path-integrals'' and ''path-tensor'' are introduced which are systems of many-component quantities whose values are defined for arbitrary paths in coordinated region of space in such a way that they contain a complete information on the path. These constructions are considered as elementary path-dependent functions and are used instead of power monomials in the usual Taylor series. Coefficients of such an expansion are interpreted as partial derivatives dependent on the order of the differentiations or else as nonstandard cavariant derivatives called two-point derivatives. Some examples of pathdependent functions are presented.Space curvature tensor is considered whose geometrica properties are determined by the (non-transitive) translator of parallel transport of a general type. Covariant operation leading to the ''extension'' of tensor fiels is pointed out
Iterated Leavitt Path Algebras
International Nuclear Information System (INIS)
Hazrat, R.
2009-11-01
Leavitt path algebras associate to directed graphs a Z-graded algebra and in their simplest form recover the Leavitt algebras L(1,k). In this note, we introduce iterated Leavitt path algebras associated to directed weighted graphs which have natural ± Z grading and in their simplest form recover the Leavitt algebras L(n,k). We also characterize Leavitt path algebras which are strongly graded. (author)
Energy Technology Data Exchange (ETDEWEB)
Janse van Rensburg, E J, E-mail: rensburg@yorku.c [Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3 (Canada)
2010-08-20
In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) {yields} f as f {yields} {infinity}, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) {yields} 2f as f {yields} {infinity}, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.
Janse van Rensburg, E. J.
2010-08-01
In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) → f as f → ∞, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) → 2f as f → ∞, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.
International Nuclear Information System (INIS)
Janse van Rensburg, E J
2010-01-01
In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) → f as f → ∞, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) → 2f as f → ∞, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.
International Nuclear Information System (INIS)
Li, Z.J.; Wu, Z.S.; Qu, T.; Shang, Q.C.; Bai, L.
2016-01-01
Based on the generalized multiparticle Mie theory, multiple scattering of an aggregate of uniaxial anisotropic spheres illuminated by a zero-order Bessel beam (ZOBB) with arbitrary propagation direction is investigated. The particle size and configuration are arbitrary. The arbitrary incident Bessel beam is expanded in terms of spherical vector wave functions (SVWFs). Utilizing the vector addition theorem of SVWFs, interactive and total scattering coefficients are derived through the continuous boundary conditions on which the interaction of the particles is considered. The accuracy of the theory and codes are verified by comparing results with those obtained for arbitrary plane wave incidence by CST simulation, and for ZOBB incidence by a numerical method. The effects of angle of incidence, pseudo-polarization angle, half-conical angle, beam center position, and permittivity tensor elements on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres, such as a linear chain, a 4×4×4 cube-shaped array, and other periodical structures consisting of massive spheres, are numerically analyzed. Selected results on the properties of typical particles such as TiO 2 , SiO 2 , or other particle lattices are calculated. This investigation could provide an effective test for further research on the scattering characteristics of an aggregate of anisotropic spheres by a high-order Bessel vortex beam. The results have important application in optical tweezers and particle manipulation. - Highlights: • Scattering of Bessel beam by an aggregate of uniaxial anisotropic spheres is studied. • The zero-order Bessel beam propagates and polarizes along arbitrary direction. • The accuracy of expansion coefficients, the scattering theory and codes is verified. • Effects of various parameters on scattering properties are numerically discussed. • Scattering properties of several type of periodical array are numerically analyzed.
Counting Triangles to Sum Squares
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
Multi-Dimensional Path Queries
DEFF Research Database (Denmark)
Bækgaard, Lars
1998-01-01
to create nested path structures. We present an SQL-like query language that is based on path expressions and we show how to use it to express multi-dimensional path queries that are suited for advanced data analysis in decision support environments like data warehousing environments......We present the path-relationship model that supports multi-dimensional data modeling and querying. A path-relationship database is composed of sets of paths and sets of relationships. A path is a sequence of related elements (atoms, paths, and sets of paths). A relationship is a binary path...
DEFF Research Database (Denmark)
Bessenrodt, Christine; Olsson, Jørn Børling; Sellers, James A.
2013-01-01
We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions.......We give a complete classification of the unique path partitions and study congruence properties of the function which enumerates such partitions....
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
The properties of path integrals associated with the allowance for nonstandard terms reflecting the operator nature of the canonical variables are considered. Rules for treating such terms (''equivalence rules'') are formulated. Problems with a boundary, the behavior of path integrals under canonical transformations, and the problem of quantization of dynamical systems with constraints are considered in the framework of the method
Generation and propagation of high-order Bessel vortices in linear and non-linear crystals
CSIR Research Space (South Africa)
Belyi, VN
2009-08-01
Full Text Available E⊥ of the electric field for these beams are given by the following expressions: ( ))2exp()()( )( )exp( 20 1 10 ϕρρ iqJqJ qw zikA i zoo −+⊥ += eeE , (1) с Uniaxial crystal θs Bs2ω(ρ) Bsω(ρ) Figure 1: Geometry of SHG when wave vectors cone of Bessel... beam at fundamental )(ρωBs and second harmonic frequencies )(2 ρωBs coincides with phase-matching cone of uniaxial crystal. Proc. of SPIE Vol. 7430 74300F-2 ( ))2exp()()()cos( )( )exp( 20 1 1 ϕρργ iqJqJ qw zikA i e zee e −+⊥ −= ee...
Tang, Bin; Jiang, Chun; Zhu, Haibin
2012-08-01
Based on the scalar diffraction theory and the fact that a hard-edged aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical solution for Bessel-Gaussian (BG) beams propagating through a double-apertured fractional Fourier transform (FrFT) system is derived in the cylindrical coordinate. By using the approximate analytical formulas, the propagation properties of BG beams passing through a double-apertured FrFT optical system have been studied in detail by some typical numerical examples. The results indicate that the double-apertured FrFT optical system provides a convenient way for controlling the properties of the BG beams by properly choosing the optical parameters.
Laser-plasma interactions with a Fourier-Bessel particle-in-cell method
Energy Technology Data Exchange (ETDEWEB)
Andriyash, Igor A., E-mail: igor.andriyash@gmail.com [Synchrotron SOLEIL, L' Orme des Merisiers, Saint Aubin, 91192 Gif-sur-Yvette (France); LOA, ENSTA ParisTech, CNRS, Ecole polytechnique, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex (France); Lehe, Remi [Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States); Lifschitz, Agustin [LOA, ENSTA ParisTech, CNRS, Ecole polytechnique, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex (France)
2016-03-15
A new spectral particle-in-cell (PIC) method for plasma modeling is presented and discussed. In the proposed scheme, the Fourier-Bessel transform is used to translate the Maxwell equations to the quasi-cylindrical spectral domain. In this domain, the equations are solved analytically in time, and the spatial derivatives are approximated with high accuracy. In contrast to the finite-difference time domain (FDTD) methods, that are used commonly in PIC, the developed method does not produce numerical dispersion and does not involve grid staggering for the electric and magnetic fields. These features are especially valuable in modeling the wakefield acceleration of particles in plasmas. The proposed algorithm is implemented in the code PLARES-PIC, and the test simulations of laser plasma interactions are compared to the ones done with the quasi-cylindrical FDTD PIC code CALDER-CIRC.
On the evaluation of the integral over the product of two spherical Bessel functions
International Nuclear Information System (INIS)
Maximon, L.C.
1991-01-01
The integral I l,l' (k,k')=∫ ∞ 0 j l (kr)j l' (k'r)r 2 dr, in which the spherical Bessel functions j l (kr) are the radial eigenfunctions of the three-dimensional wave equation in spherical coordinates, is evaluated in terms of distributions, in particular, step functions and delta functions. It will be shown that the behavior of I l,l' is very different in the cases l-l' even (0, ±2, ±4, ...) and l-l' odd (±1, ±3, ...). For l-l' even it is expressed in terms of the delta function, step functions, and Legendre polynomials. For l-l' odd it is expressed in terms of Legendre functions of the second kind and step functions; no delta functions appear
Pupil filter design by using a Bessel functions basis at the image plane.
Canales, Vidal F; Cagigal, Manuel P
2006-10-30
Many applications can benefit from the use of pupil filters for controlling the light intensity distribution near the focus of an optical system. Most of the design methods for such filters are based on a second-order expansion of the Point Spread Function (PSF). Here, we present a new procedure for designing radially-symmetric pupil filters. It is more precise than previous procedures as it considers the exact expression of the PSF, expanded as a function of first-order Bessel functions. Furthermore, this new method presents other advantages: the height of the side lobes can be easily controlled, it allows the design of amplitude-only, phase-only or hybrid filters, and the coefficients of the PSF expansion can be directly related to filter parameters. Finally, our procedure allows the design of filters with very different behaviours and optimal performance.
Monotonicity of the ratio of modified Bessel functions of the first kind with applications.
Yang, Zhen-Hang; Zheng, Shen-Zhou
2018-01-01
Let [Formula: see text] with [Formula: see text] be the modified Bessel functions of the first kind of order v . In this paper, we prove the monotonicity of the function [Formula: see text] on [Formula: see text] for different values of parameter p with [Formula: see text]. As applications, we deduce some new Simpson-Spector-type inequalities for [Formula: see text] and derive a new type of bounds [Formula: see text] ([Formula: see text]) for [Formula: see text]. In particular, we show that the upper bound [Formula: see text] for [Formula: see text] is the minimum over all upper bounds [Formula: see text], where [Formula: see text] and is not comparable with other sharpest upper bounds. We also find such type of upper bounds for [Formula: see text] with [Formula: see text] and for [Formula: see text] with [Formula: see text].
Generation of an elliptic hollow beam using Mathieu and Bessel functions.
Chakraborty, Rijuparna; Ghosh, Ajay
2006-09-01
A new (to our knowledge) technique for the generation of a propagation-invariant elliptic hollow beam is reported. It avoids the use of the radial Mathieu function and hence is mathematically simpler. Bessel functions with their arguments having elliptic locus are used to generate the mask, which is then recorded using holographic technique. To generate such an elliptic beam, both the angular Mathieu function, i.e., elliptic vortex term, and the expression for the circular vortex are used separately. The resultant mask is illuminated with a plane beam, and the proper filtering of its Fourier transform generates the expected elliptic beam. Results with both vortex terms are satisfactory. It has been observed that even for higher ellipticity the vortices do not separate.
Spherical space Bessel-Legendre-Fourier mode solver for Maxwell's wave equations
Alzahrani, Mohammed A.; Gauthier, Robert C.
2015-02-01
For spherically symmetric dielectric structures, a basis set composed of Bessel, Legendre and Fourier functions, BLF, are used to cast Maxwell's wave equations into an eigenvalue problem from which the localized modes can be determined. The steps leading to the eigenmatrix are reviewed and techniques used to reduce the order of matrix and tune the computations for particular mode types are detailed. The BLF basis functions are used to expand the electric and magnetic fields as well as the inverse relative dielectric profile. Similar to the common plane wave expansion technique, the BLF matrix returns the eigen-frequencies and eigenvectors, but in BLF only steady states, non-propagated, are obtained. The technique is first applied to a air filled spherical structure with perfectly conducting outer surface and then to a spherical microsphere located in air. Results are compared published values were possible.
Stored polarized beams: MILES, LIMES, SMILE, sine-Bessels and SODOM2 too
International Nuclear Information System (INIS)
Mane, S.R.
2008-01-01
The fundamental theory underlying several computational algorithms for the spin dynamics of stored polarized beams is analyzed. Particular attention is paid to the consequences of the use of finite-dimensional matrices and/or Fourier series. The single resonance model with a pair of diametrically opposed nonorthogonal pointlike Siberian Snakes is analyzed in detail to clarify several points pertaining to the above algorithms, and more generally to the spin dynamics of stored polarized beams in rings with Snakes. New analytical results are also presented, e.g. for the spin tune shift in the nonorthogonal Snakes model, and the sine-Bessel functions for the orthogonal Snakes model. Many results are derived using multiple algorithms, which serves as a check on their mutual consistency
Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.
Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino
2003-11-01
A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.
Electromagnetic scattering of a vector Bessel beam in the presence of an impedance cone
Salem, Mohamed
2013-07-01
The electromagnetic field scattering of a vector Bessel beam in the presence of an infinite circular cone with an impedance boundary on its surface is considered. The impinging field is normal to the tip of the cone and is expanded in terms of vector spherical wave functions; a Kontorovich-Lebedev (KL) transform is employed to expand the scattered fields. The problem is reduced to a singular integral equation with a variable coefficient of the non-convolution type. The singularities of the spectral function are deduced and representations for the field at the tip of the cone as well as other regions are given together with the conditions of validity of these representations. © 2013 IEEE.
Fahrbach, Florian O; Rohrbach, Alexander
2012-01-17
Laser beams that can self-reconstruct their initial beam profile even in the presence of massive phase perturbations are able to propagate deeper into inhomogeneous media. This ability has crucial advantages for light sheet-based microscopy in thick media, such as cell clusters, embryos, skin or brain tissue or plants, as well as scattering synthetic materials. A ring system around the central intensity maximum of a Bessel beam enables its self-reconstruction, but at the same time illuminates out-of-focus regions and deteriorates image contrast. Here we present a detection method that minimizes the negative effect of the ring system. The beam's propagation stability along one straight line enables the use of a confocal line principle, resulting in a significant increase in image contrast. The axial resolution could be improved by nearly 100% relative to the standard light-sheet techniques using scanned Gaussian beams, while demonstrating self-reconstruction also for high propagation depths.
Acoustical radiation torque and force for spheres and Bessel beam extinction efficiency
Marston, Philip L.; Zhang, Likun
2014-11-01
The scattering of optical and acoustical beams is relevant to the levitation and manipulation of drops. Here we examine theoretical developments in the acoustical case. We previously showed how the optical theorem for extinction can be extended to invariant beams. The example of a sphere in a Bessel beam facilitates the direct comparison with a circular disc computed using Babinet's principle and the Kirchhoff approximation. In related work, by considering traveling or standing wave first-order vortex beams we previously showed that the radiation torque is the ratio of the absorbed power and the radian acoustic frequency. By modifying the scattering to account for the viscosity of the surrounding fluid in the analysis of the absorbed power, approximations for radiation torque and force are obtained at long wavelengths in special cases and these can be compared with results published elsewhere.
Forces in Motzkin paths in a wedge
International Nuclear Information System (INIS)
Janse van Rensburg, E J
2006-01-01
Entropic forces in models of Motzkin paths in a wedge geometry are considered as models of forces in polymers in confined geometries. A Motzkin path in the square lattice is a path from the origin to a point in the line Y = X while it never visits sites below this line, and it is constrained to give unit length steps only in the north and east directions and steps of length √2 in the north-east direction. Motzkin path models may be generalized to ensembles of NE-oriented paths above the line Y = rX, where r > 0 is an irrational number. These are paths giving east, north and north-east steps from the origin in the square lattice, and confined to the r-wedge formed by the Y-axis and the line Y = rX. The generating function g r of these paths is not known, but if r > 1, then I determine its radius of convergence to be t r = min (r-1)/r≤y≤r/(r+1) [y y (1-r(1-y)) 1-r(1-y) (r(1-y)-y) r(1-y)-y ] and if r is an element of (0, 1), then t r = 1/3. The entropic force the path exerts on the line Y rX may be computed from this. An asymptotic expression for the force for large values of r is given by F(r) = log(2r)/r 2 - (1+2log(2r))/2r 3 + O (log(2r)/r 4 ). In terms of the vertex angle α of the r-wedge, the moment of the force about the origin has leading terms F(α) log(2/α) - (α/2)(1+2log(2/α)) + O(α 2 log(2/α)) as α → 0 + and F(α) = 0 if α is element of [π/4, π/2]. Moreover, numerical integration of the force shows that the total work done by closing the wedge is 1.085 07... lattice units. An alternative ensemble of NE-oriented paths may be defined by slightly changing the generating function g r . In this model, it is possible to determine closed-form expressions for the limiting free energy and the force. The leading term in an asymptotic expansions for this force agrees with the leading term in the asymptotic expansion of the above model, and the subleading term only differs by a factor of 2
Some results on square-free colorings of graphs
DEFF Research Database (Denmark)
Barat, Janos
2004-01-01
on the vertices or edges of a path. Conversely one can form sequences from a vertex or edge coloring of a graph in different ways. Thus there are several possibilities to generalize the square-free concept to graphs. Following Alon, Grytczuk, Haluszczak, Riordan and Bresar, Klavzar we study several so called...... square-free graph parameters, and answer some questions they posed. The main result is that the class of k-trees has bounded square-free vertex coloring parameter. Thus we can color the vertices of a k-tree using O(c^k) colors if c>6 such that the color sequence on any path is square......-free. It is conjectured that a similar phenomenon holds for planar graphs, so a finite number of colors are enough. We support this conjecture by showing that this number is at most 12 for outerplanar graphs. On the other hand we prove that some outerplanar graphs require at least 7 colors. Using this latter we construct...
International Nuclear Information System (INIS)
DeWitt-Morette, C.
1983-01-01
Much is expected of path integration as a quantization procedure. Much more is possible if one recognizes that path integration is at the crossroad of stochastic and differential calculus and uses the full power of both stochastic and differential calculus in setting up and computing path integrals. In contrast to differential calculus, stochastic calculus has only comparatively recently become an instrument of thought. It has nevertheless already been used in a variety of challenging problems, for instance in the quantization problem. The author presents some applications of the stochastic scheme. (Auth.)
Two dimensional simplicial paths
International Nuclear Information System (INIS)
Piso, M.I.
1994-07-01
Paths on the R 3 real Euclidean manifold are defined as 2-dimensional simplicial strips which are orbits of the action of a discrete one-parameter group. It is proven that there exists at least one embedding of R 3 in the free Z-module generated by S 2 (x 0 ). The speed is defined as the simplicial derivative of the path. If mass is attached to the simplex, the free Lagrangian is proportional to the width of the path. In the continuum limit, the relativistic form of the Lagrangian is recovered. (author). 7 refs
Simons, Jacob V., Jr.
2017-01-01
The critical path method/program evaluation and review technique method of project scheduling is based on the importance of managing a project's critical path(s). Although a critical path is the longest path through a network, its location in large projects is facilitated by the computation of activity slack. However, logical fallacies in…
A Weighted Least Squares Approach To Robustify Least Squares Estimates.
Lin, Chowhong; Davenport, Ernest C., Jr.
This study developed a robust linear regression technique based on the idea of weighted least squares. In this technique, a subsample of the full data of interest is drawn, based on a measure of distance, and an initial set of regression coefficients is calculated. The rest of the data points are then taken into the subsample, one after another,…
Moreno, Carlos J
2005-01-01
Introduction Prerequisites Outline of Chapters 2 - 8 Elementary Methods Introduction Some Lemmas Two Fundamental Identities Euler's Recurrence for Sigma(n)More Identities Sums of Two Squares Sums of Four Squares Still More Identities Sums of Three Squares An Alternate Method Sums of Polygonal Numbers Exercises Bernoulli Numbers Overview Definition of the Bernoulli Numbers The Euler-MacLaurin Sum Formula The Riemann Zeta Function Signs of Bernoulli Numbers Alternate The von Staudt-Clausen Theorem Congruences of Voronoi and Kummer Irregular Primes Fractional Parts of Bernoulli Numbers Exercises Examples of Modular Forms Introduction An Example of Jacobi and Smith An Example of Ramanujan and Mordell An Example of Wilton: t (n) Modulo 23 An Example of Hamburger Exercises Hecke's Theory of Modular FormsIntroduction Modular Group ? and its Subgroup ? 0 (N) Fundamental Domains For ? and ? 0 (N) Integral Modular Forms Modular Forms of Type Mk(? 0(N);chi) and Euler-Poincare series Hecke Operators Dirichlet Series and ...
Leamer, Micah J.
2004-01-01
Let K be a field and Q a finite directed multi-graph. In this paper I classify all path algebras KQ and admissible orders with the property that all of their finitely generated ideals have finite Groebner bases. MS
Graphs whose complement and square are isomorphic
DEFF Research Database (Denmark)
Pedersen, Anders Sune
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...
Path planning in changeable environments
Nieuwenhuisen, D.
2007-01-01
This thesis addresses path planning in changeable environments. In contrast to traditional path planning that deals with static environments, in changeable environments objects are allowed to change their configurations over time. In many cases, path planning algorithms must facilitate quick
Cepeda Carrion, Gabriel; Henseler, Jörg; Ringle, Christian M.; Roldan, Jose Luis
2016-01-01
Under the main theme “prediction-oriented modeling in business research by means of partial least squares path modeling” (PLS), the special issue presents 17 papers. Most contributions include content from presentations at the 2nd International Symposium on Partial Least Squares Path Modeling: The
International Nuclear Information System (INIS)
Rutt, H.N.
2003-01-01
The modified Bessel functions of the second kind and fractional order K 1/3 (x) and K 2/3 (x) are of importance in the calculation of the frequency spectrum of synchrotron radiation. The parameter range of interest is typically 10 -6 x10. Recently, there has been particular interest in the generation of 'terahertz' radiation, which can be coherently enhanced by many orders of magnitude when the electron bunch length is shorter than the terahertz wavelength. This requires evaluation of the Bessel functions for small values of the argument. It is shown that the series commonly used to evaluate these functions has poor convergence properties under these conditions. An alternative series is derived which has much better convergence for x1
Sando, Yusuke; Barada, Daisuke; Jackin, Boaz Jessie; Yatagai, Toyohiko
2017-07-10
This study proposes a method to reduce the calculation time and memory usage required for calculating cylindrical computer-generated holograms. The wavefront on the cylindrical observation surface is represented as a convolution integral in the 3D Fourier domain. The Fourier transformation of the kernel function involving this convolution integral is analytically performed using a Bessel function expansion. The analytical solution can drastically reduce the calculation time and the memory usage without any cost, compared with the numerical method using fast Fourier transform to Fourier transform the kernel function. In this study, we present the analytical derivation, the efficient calculation of Bessel function series, and a numerical simulation. Furthermore, we demonstrate the effectiveness of the analytical solution through comparisons of calculation time and memory usage.
Agglomerative clustering of growing squares
Castermans, Thom; Speckmann, Bettina; Staals, Frank; Verbeek, Kevin; Bender, M.A.; Farach-Colton, M.; Mosteiro, M.A.
2018-01-01
We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish
Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces
Czech Academy of Sciences Publication Activity Database
Edmunds, D. E.; Gurka, P.; Opic, Bohumír
2006-01-01
Roč. 25, č. 1 (2006), s. 73-80 ISSN 0232-2064 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized Lorentz-Zygmund spaces * logarithmic Bessel potential spaces * Hölder-continuous functions Subject RIV: BA - General Mathematics Impact factor: 0.360, year: 2006
International Nuclear Information System (INIS)
Cash, J.R.; Raptis, A.D.; Simos, T.E.
1990-01-01
An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schroedinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are given. (orig.)
On q-analogues of the Mangontarum transform for certain q-Bessel functions and some application
Directory of Open Access Journals (Sweden)
S.K.Q. Al-Omari
2016-10-01
Full Text Available Several q-analogues of certain integral transforms have been recently investigated by many authors in the recent past. In this paper, we introduce certain analogues of the so-called q-Mangontarum transform and implement the proposed variants to given classes of q-Bessel functions. The results of this paper are new and complement the previously known results of Mangontarum (2014. Some results related to q-Laplace transforms are also obtained.
Mitri, F G
2010-03-01
Acoustic scattering properties of ultrasound contrast agents are useful in extending existing or developing new techniques for biomedical imaging applications. A useful first step in this direction is to investigate the acoustic scattering of a new class of acoustic beams, known as helicoidal high-order Bessel beams, to improve the understanding of their scattering characteristics by an ultrasound contrast agent, which at present is very limited. The transverse acoustic scattering of a commercially available albuminoidal ultrasound contrast agent shell filled with air or a denser gas such as perfluoropropane and placed in a helicoidal Bessel beam of any order is examined numerically. The shell is assumed to possess an outer radius a=3.5 microns and a thickness of approximately 105 nm. Moduli of the total and resonance transverse acoustic scattering form functions are numerically evaluated in the bandwidth 0scattering of a helicoidal Bessel beam of order m1 so that the dynamics of contrast agents would be significantly altered. The main finding of the present theory is the suppression or enhancement for a particular resonance that may be used to advantage in imaging with ultrasound contrast agents for clinical applications. 2009 Elsevier B.V. All rights reserved.
Boshier, Malcolm; Ryu, Changhyun; Blackburn, Paul; Blinova, Alina; Henderson, Kevin
2014-05-01
The painted potential is a time-averaged optical dipole potential which is able to create arbitrary and dynamic two dimensional potentials for Bose Einstein condensates (BECs). This poster reports three recent experiments using this technique. First, we have realized the dc atom SQUID geometry of a BEC in a toroidal trap with two Josephson junctions. We observe Josephson effects, measure the critical current of the junctions, and find dynamic behavior that is in good agreement with the simple Josephson equations for a tunnel junction with the ideal sinusoidal current-phase relation expected for the parameters of the experiment. Second, we have used free expansion of a rotating toroidal BEC to create matter wave Bessel beams, which are of interest because perfect Bessel beams (plane waves with amplitude profiles described by Bessel functions) propagate without diffraction. Third, we have realized the basic circuit elements necessary to create complex matter wave circuits. We launch BECs at arbitrary velocity along straight waveguides, propagate them around curved waveguides and stadium-shaped waveguide traps, and split them coherently at y-junctions that can also act as switches. Supported by LANL/LDRD.
Quivers of Bound Path Algebras and Bound Path Coalgebras
Directory of Open Access Journals (Sweden)
Dr. Intan Muchtadi
2010-09-01
Full Text Available bras and coalgebras can be represented as quiver (directed graph, and from quiver we can construct algebras and coalgebras called path algebras and path coalgebras. In this paper we show that the quiver of a bound path coalgebra (resp. algebra is the dual quiver of its bound path algebra (resp. coalgebra.
Understanding and applying open-path optical sensing data
Virag, Peter; Kricks, Robert J.
1999-02-01
During the last 10 years, open-path air monitors have evolved to yield reliable and effective measurements of single and multiple compounds on a real-time basis. To many individuals within the optical remote sensing community, the attributes of open-path and its the potential uses seem unlimited. Then why has the market has been stagnant for the last few years? The reason may center on how open-path information is applied and how well the end user understands that information. We constantly try to compare open-path data to risk/health or safety levels that are based for use at a single point and for a specific averaging period often far longer than a typical open-path data point. Often this approach is perceived as putting a square peg in a round hole. This perception may be well founded, as open-path data at times may need to go through extensive data manipulation and assumptions before it can be applied. This paper will review pervious open-path monitoring programs and their success in applying the data collected. We will also look at how open-path data is being currently used, some previous pitfalls in data use, alternate methods of data interpretation, and how open-path data can be best practically applied to fit current needs.
Path Following in the Exact Penalty Method of Convex Programming.
Zhou, Hua; Lange, Kenneth
2015-07-01
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to ∞, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.
Qian, Weixian; Zhou, Xiaojun; Lu, Yingcheng; Xu, Jiang
2015-09-15
Both the Jones and Mueller matrices encounter difficulties when physically modeling mixed materials or rough surfaces due to the complexity of light-matter interactions. To address these issues, we derived a matrix called the paths correlation matrix (PCM), which is a probabilistic mixture of Jones matrices of every light propagation path. Because PCM is related to actual light propagation paths, it is well suited for physical modeling. Experiments were performed, and the reflection PCM of a mixture of polypropylene and graphite was measured. The PCM of the mixed sample was accurately decomposed into pure polypropylene's single reflection, pure graphite's single reflection, and depolarization caused by multiple reflections, which is consistent with the theoretical derivation. Reflection parameters of rough surface can be calculated from PCM decomposition, and the results fit well with the theoretical calculations provided by the Fresnel equations. These theoretical and experimental analyses verify that PCM is an efficient way to physically model light-matter interactions.
Abrams, Gene; Siles Molina, Mercedes
2017-01-01
This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...
2016-07-22
be reduced to TP in -D UDH for any . We then show that the 2-D disk hypergraph constructed in the proof of Theorem 1 can be modified to an exposed...transmission range that induces hy- peredge , i.e., (3) GAO et al.: THINNEST PATH PROBLEM 1181 Theorem 5 shows that the covered area of the path...representation of (the two hyperedges rooted at from the example given in Fig. 6 are illustrated in green and blue, respectively). step, we show in this
DEFF Research Database (Denmark)
Garud, Raghu; Karnøe, Peter
This edited volume stems from a conference held in Copenhagen that the authors ran in August of 1997. The authors, aware of the recent work in evolutionary theory and the science of chaos and complexity, challenge the sometimes deterministic flavour of this work. They are interested in uncovering...... the place of agency in these theories that take history so seriously. In the end, they are as interested in path creation and destruction as they are in path dependence. This book is compiled of both theoretical and empirical writing. It shows relatively well-known industries such as the automobile...
Reparametrization in the path integral
International Nuclear Information System (INIS)
Storchak, S.N.
1983-01-01
The question of the invariance of a measure in the n-dimensional path integral under the path reparametrization is considered. The non-invariance of the measure through the jacobian is suggeste. After the path integral reparametrization the representatioq for the Green's function of the Hamilton operator in terms of the path integral with the classical Hamiltonian has been obtained
Directed paths in a layered environment
International Nuclear Information System (INIS)
Alvarez, J; Janse van Rensburg, E J
2008-01-01
A polymer in a layered environment is modeled as a directed path in a layered square lattice composed of alternating A-layers of width w a and B-layers of width w b . In this paper we consider general cases of this model, where edges in the path interact with the layers, and vertices in the path interact with interfaces between adjacent layers. The phase diagram exhibits different regimes. In particular, we found that the path may be localized to one layer, be adsorbed on an interface between two layers or be delocalized across layers. We examine special aspects of the model in detail: the asymptotic regimes of the models are examined, and entropic forces on the interfaces are determined. We focus on several different cases, including models with layers of equal or similar width. More general models of layers with different but finite widths, or with one layer of infinite width, are also examined in detail. Several of these models exhibit phase behavior which relate to well-studied polymer phase behavior such as adsorption at an impenetrable wall, pinning at an interface between two immiscible solvents, steric stabilization of colloidal particles and sensitized flocculation of colloidal particles by polymers
8th International Conference on Partial Least Squares and Related Methods
Vinzi, Vincenzo; Russolillo, Giorgio; Saporta, Gilbert; Trinchera, Laura
2016-01-01
This volume presents state of the art theories, new developments, and important applications of Partial Least Square (PLS) methods. The text begins with the invited communications of current leaders in the field who cover the history of PLS, an overview of methodological issues, and recent advances in regression and multi-block approaches. The rest of the volume comprises selected, reviewed contributions from the 8th International Conference on Partial Least Squares and Related Methods held in Paris, France, on 26-28 May, 2014. They are organized in four coherent sections: 1) new developments in genomics and brain imaging, 2) new and alternative methods for multi-table and path analysis, 3) advances in partial least square regression (PLSR), and 4) partial least square path modeling (PLS-PM) breakthroughs and applications. PLS methods are very versatile methods that are now used in areas as diverse as engineering, life science, sociology, psychology, brain imaging, genomics, and business among both academics ...
DRAMAtic transforms in magic angle spinning recoupling NMR: The Bessel function pathway.
Goodman, Russell; Hancock, Jason; Siemens, Mark; Jarrell, Harold; Siminovitch, David
2005-07-01
In magic angle spinning (MAS) NMR recoupling experiments, the extraction of multiple couplings or a coupling distribution from the observed dephasing signals remains a challenging problem. At least for REDOR experiments, the REDOR transform solves this problem, enabling the simultaneous measurement of multiple dipolar couplings. Focusing on the quadrupolar dephasing observed in QUADRAMA experiments as a representative example, we demonstrate that the same analytical form used for the mathematical description of REDOR dephasing also describes the dephasing observed in a wide variety of MAS NMR recoupling experiments. This fact immediately extends REDOR transform techniques to a much broader suite of recoupling experiments than had previously been realized, including those of DRAMA, MELODRAMA and QUADRAMA. As an illustration, we use the DRAMAtic transform to provide the first inversion of a QUADRAMA dephasing signal to extract the quadrupole coupling distribution. Using a complete elliptic integral of the first kind, we further develop a novel expression for the Pake-spun powder patterns of the corresponding recoupled lineshapes. Our methods and results reinforce the central role that Bessel functions can play in simplifying the integrals that define both the dephasing signals in the time domain, and their Fourier transforms in the frequency domain.
Jiao, Li-Guang; Ho, Yew Kam
2014-05-01
The screened Coulomb potential (SCP) has been extensively used in atomic physics, nuclear physics, quantum chemistry and plasma physics. However, an accurate calculation for atomic resonances under SCP is still a challenging task for various methods. Within the complex-scaling computational scheme, we have developed a method utilizing the modified Bessel functions to calculate doubly-excited resonances in two-electron atomic systems with configuration interaction-type basis. To test the validity of our method, we have calculated S- and P-wave resonance states of the helium atom with various screening strengths, and have found good agreement with earlier calculations using different methods. Our present method can be applied to calculate high-lying resonances associated with high excitation thresholds of the He+ ion, and with high-angular-momentum states. The derivation and calculation details of our present investigation together with new results of high-angular-momentum states will be presented at the meeting. Supported by NSC of Taiwan.
Revisiting the orthogonality of Bessel functions of the first kind on an infinite interval
International Nuclear Information System (INIS)
Leon, J Ponce de
2015-01-01
The rigorous proof of the orthogonality integral ∫ 0 ∞ ρ J ν (kρ)J ν (k ′ ρ) dρ=((δ(k−k ′ ))/k), for ν>=−1, is laborious and requires the use of mathematical techniques that, probably, are unfamiliar to most physics students, even at the graduate level. In physics, we are used to the argument that it may be proved by the use of Hankel transforms. However, the logic of the matter is the opposite, i.e., the existence of the inverse Hankel transform is a consequence of the orthogonality integral. The goal of this work is to prove this integral without circular reasoning. In this paper, using elementary properties of Bessel functions, we give a simple analytical derivation of this integral for the case where ν is an integer, zero, or half-integer not less than −1/2. Then, using the asymptotic behaviour of J ν (x), we extend the result to any ν>=−1. This work is of a pedagogical nature. Therefore, to add educational value to the discussion, we do not skip the details of the calculations. (paper)
The generalized Abel-Plana formula. Applications to Bessel functions and Casimir effect
International Nuclear Information System (INIS)
Saharian, A.A.; Institute of Applied Problems in Physics NAS RA, Yerevan; Abdus Salam International Centre for Theoretical Physics, Trieste
2000-02-01
One of the most efficient methods to obtain the vacuum expectation values for the physical observables in the Casimir effect is based on using the Abel-Plana summation formula. This allows us to derive the regularized quantities in a manifestly cutoff independent way and present them in the form of strongly convergent integrals. However, the application of Abel-Plana formula, in its usual form, is restricted by simple geometries when the eigenmodes have a simple dependence on quantum numbers. The author generalized the Abel-Plana formula which essentially enlarges its application range. Based on this generalization, formulae have been obtained for various types of series over the zeros of some combinations of Bessel functions and for integrals involving these functions. It has been shown that these results generalize the special cases existing in literature. Further, the derived summation formulae have been used to summarize series arising in the mode summation approach to the Casimir effect for spherically and cylindrically symmetric boundaries. This allows us to extract the divergent parts from the vacuum expectation values for the local physical observables in a manifestly cutoff independent way. The present paper reviews these results. Some new considerations are also added. (author)
Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L
2011-01-01
The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.
Foreign Object Detection by Sub-Terahertz Quasi-Bessel Beam Imaging
Directory of Open Access Journals (Sweden)
Hyang Sook Chun
2012-12-01
Full Text Available Food quality monitoring, particularly foreign object detection, has recently become a critical issue for the food industry. In contrast to X-ray imaging, terahertz imaging can provide a safe and ionizing-radiation-free nondestructive inspection method for foreign object sensing. In this work, a quasi-Bessel beam (QBB known to be nondiffracting was generated by a conical dielectric lens to detect foreign objects in food samples. Using numerical evaluation via the finite-difference time-domain (FDTD method, the beam profiles of a QBB were evaluated and compared with the results obtained via analytical calculation and experimental characterization (knife edge method, point scanning method. The FDTD method enables a more precise estimation of the beam profile. Foreign objects in food samples, namely crickets, were then detected with the QBB, which had a deep focus and a high spatial resolution at 210 GHz. Transmitted images using a Gaussian beam obtained with a conventional lens were compared in the sub-terahertz frequency experimentally with those using a QBB generated using an axicon.
Directory of Open Access Journals (Sweden)
Peter Juhasz
2017-03-01
Full Text Available While risk management gained popularity during the last decades even some of the basic risk types are still far out of focus. One of these is path dependency that refers to the uncertainty of how we reach a certain level of total performance over time. While decision makers are careful in accessing how their position will look like the end of certain periods, little attention is given how they will get there through the period. The uncertainty of how a process will develop across a shorter period of time is often “eliminated” by simply choosing a longer planning time interval, what makes path dependency is one of the most often overlooked business risk types. After reviewing the origin of the problem we propose and compare seven risk measures to access path. Traditional risk measures like standard deviation of sub period cash flows fail to capture this risk type. We conclude that in most cases considering the distribution of the expected cash flow effect caused by the path dependency may offer the best method, but we may need to use several measures at the same time to include all the optimisation limits of the given firm
Fullwood, James; Wang, Dongxu
2018-01-01
We introduce a class of F-theory vacua whose smooth elliptic fibers admit a vanishing $j$-invariant, and construct a weak coupling limit associated with such vacua which we view as the `square' of the Sen limit. We find that while Sen's limit is naturally viewed as an orientifold theory, the universal tadpole relation which equates the D3 charge between the associated F-theory compactification and the limit we construct suggests that perhaps the limiting theory is in fact an oriented theory c...
Renaming Zagreb Streets and Squares
Directory of Open Access Journals (Sweden)
Jelena Stanić
2009-06-01
Full Text Available The paper deals with changes in street names in the city of Zagreb. Taking the Lower Town (Donji grad city area as an example, the first part of the paper analyses diachronic street name changes commencing from the systematic naming of streets in 1878. Analysis of official changes in street names throughout Zagreb’s history resulted in categorisation of five periods of ideologically motivated naming/name-changing: 1. the Croatia modernisation period, when the first official naming was put into effect, with a marked tendency towards politicisation and nationalisation of the urban landscape; 2. the period of the Kingdom of the Serbs, Croatians and Slovenians/Yugoslavia, when symbols of the new monarchy, the idea of the fellowship of the Southern Slavs, Slavenophilism and the pro-Slavic geopolitical orientation were incorporated into the street names, and when the national idea was highly evident and remained so in that process; 3. the period of the NDH, the Independent State of Croatia, with decanonisation of the tokens of the Yugoslavian monarchy and the Southern Slavic orientation, and reference to the Ustashi and the German Nazi and Italian Fascist movement; 4. the period of Socialism, embedding the ideals and heroes of the workers’ movement and the War of National Liberation into the canonical system; and, 5. the period following the democratic changes in 1990, when almost all the signs of Socialism and the Communist/Antifascist struggle were erased, with the prominent presence of a process of installing new references to early national culture and historical tradition. The closing part of the paper deals with public discussions connected with the selection of a location for a square to bear the name of the first president of independent Croatia, Franjo Tuđman. Analysis of these public polemics shows two opposing discourses: the right-wing political option, which supports a central position for the square and considers the chosen area to
Latin squares and their applications
Keedwell, A Donald
2015-01-01
Latin Squares and Their Applications Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader 'from the beginnings of the subject to the frontiers of research'. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the
semPLS: Structural Equation Modeling Using Partial Least Squares
Directory of Open Access Journals (Sweden)
Armin Monecke
2012-05-01
Full Text Available Structural equation models (SEM are very popular in many disciplines. The partial least squares (PLS approach to SEM offers an alternative to covariance-based SEM, which is especially suited for situations when data is not normally distributed. PLS path modelling is referred to as soft-modeling-technique with minimum demands regarding mea- surement scales, sample sizes and residual distributions. The semPLS package provides the capability to estimate PLS path models within the R programming environment. Different setups for the estimation of factor scores can be used. Furthermore it contains modular methods for computation of bootstrap confidence intervals, model parameters and several quality indices. Various plot functions help to evaluate the model. The well known mobile phone dataset from marketing research is used to demonstrate the features of the package.
Nonadiabatic transition path sampling
International Nuclear Information System (INIS)
Sherman, M. C.; Corcelli, S. A.
2016-01-01
Fewest-switches surface hopping (FSSH) is combined with transition path sampling (TPS) to produce a new method called nonadiabatic path sampling (NAPS). The NAPS method is validated on a model electron transfer system coupled to a Langevin bath. Numerically exact rate constants are computed using the reactive flux (RF) method over a broad range of solvent frictions that span from the energy diffusion (low friction) regime to the spatial diffusion (high friction) regime. The NAPS method is shown to quantitatively reproduce the RF benchmark rate constants over the full range of solvent friction. Integrating FSSH within the TPS framework expands the applicability of both approaches and creates a new method that will be helpful in determining detailed mechanisms for nonadiabatic reactions in the condensed-phase.
PATHS groundwater hydrologic model
Energy Technology Data Exchange (ETDEWEB)
Nelson, R.W.; Schur, J.A.
1980-04-01
A preliminary evaluation capability for two-dimensional groundwater pollution problems was developed as part of the Transport Modeling Task for the Waste Isolation Safety Assessment Program (WISAP). Our approach was to use the data limitations as a guide in setting the level of modeling detail. PATHS Groundwater Hydrologic Model is the first level (simplest) idealized hybrid analytical/numerical model for two-dimensional, saturated groundwater flow and single component transport; homogeneous geology. This document consists of the description of the PATHS groundwater hydrologic model. The preliminary evaluation capability prepared for WISAP, including the enhancements that were made because of the authors' experience using the earlier capability is described. Appendixes A through D supplement the report as follows: complete derivations of the background equations are provided in Appendix A. Appendix B is a comprehensive set of instructions for users of PATHS. It is written for users who have little or no experience with computers. Appendix C is for the programmer. It contains information on how input parameters are passed between programs in the system. It also contains program listings and test case listing. Appendix D is a definition of terms.
Squares of Random Linear Codes
DEFF Research Database (Denmark)
Cascudo Pueyo, Ignacio; Cramer, Ronald; Mirandola, Diego
2015-01-01
a positive answer, for codes of dimension $k$ and length roughly $\\frac{1}{2}k^2$ or smaller. Moreover, the convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in $k$. The proof uses random coding and combinatorial arguments, together with algebraic tools involving the precise......Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code ``typically'' fill the whole space? We give...
Implementation of Bessel's method for solar eclipses prediction in the WRF-ARW model
Directory of Open Access Journals (Sweden)
A. Montornès
2016-05-01
Full Text Available Solar eclipses are predictable astronomical events that abruptly reduce the incoming solar radiation into the Earth's atmosphere, which frequently results in non-negligible changes in meteorological fields. The meteorological impacts of these events have been analyzed in many studies since the late 1960s. The recent growth in the solar energy industry has greatly increased the interest in providing more detail in the modeling of solar radiation variations in numerical weather prediction (NWP models for the use in solar resource assessment and forecasting applications. The significant impact of the recent partial and total solar eclipses that occurred in the USA (23 October 2014 and Europe (20 March 2015 on solar power generation have provided additional motivation and interest for including these astronomical events in the current solar parameterizations.Although some studies added solar eclipse episodes within NWP codes in the 1990s and 2000s, they used eclipse parameterizations designed for a particular case study. In contrast to these earlier implementations, this paper documents a new package for the Weather Research and Forecasting–Advanced Research WRF (WRF-ARW model that can simulate any partial, total or hybrid solar eclipse for the period 1950 to 2050 and is also extensible to a longer period. The algorithm analytically computes the trajectory of the Moon's shadow and the degree of obscuration of the solar disk at each grid point of the domain based on Bessel's method and the Five Millennium Catalog of Solar Eclipses provided by NASA, with a negligible computational time. Then, the incoming radiation is modified accordingly at each grid point of the domain.This contribution is divided in three parts. First, the implementation of Bessel's method is validated for solar eclipses in the period 1950–2050, by comparing the shadow trajectory with values provided by NASA. Latitude and longitude are determined with a bias lower than 5
Uchugonova, Aisada; Breunig, Hans Georg; Batista, Ana; König, Karsten
2015-11-01
We report a virus-free optical approach to human cell reprogramming into induced pluripotent stem cells with low-power nanoporation using ultrashort Bessel-shaped laser pulses. Picojoule near-infrared sub-20 fs laser pulses at a high 85 MHz repetition frequency are employed to generate transient nanopores in the membrane of dermal fibroblasts for the introduction of four transcription factors to induce the reprogramming process. In contrast to conventional approaches which utilize retro- or lentiviruses to deliver genes or transcription factors into the host genome, the laser method is virus-free; hence, the risk of virus-induced cancer generation limiting clinical application is avoided.
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Neves, J. S.; Opic, Bohumír
2010-01-01
Roč. 32, č. 3 (2010), s. 201-228 ISSN 0926-2601 R&D Projects: GA ČR GA201/05/2033; GA ČR GA201/08/0383 Institutional research plan: CEZ:AV0Z10190503 Keywords : slowly varying functions * Lorentz-Karamata spaces * Rearrangement-invariant Banach function spaces * Bessel potentials * (fractional) Sobolev-type spaces * Hölder-type spaces * Zygmund-type spaces Subject RIV: BA - General Mathematics Impact factor: 0.853, year: 2010 http://link.springer.com/article/10.1007%2Fs11118-009-9148-2
Yamasaki, K.; Fujisawa, A.; Nagashima, Y.
2017-09-01
It is a critical issue to find the best set of fitting function bases in mode structural analysis of two dimensional images like plasma emission profiles. The paper proposes a method to optimize a set of the bases in the case of Fourier-Bessel function series, using their orthonormal property, for more efficient and precise analysis. The method is applied on a tomography image of plasma emission obtained with the Maximum-likelihood expectation maximization method in a linear cylindrical device. The result demonstrates the excellency of the method that realizes the smaller residual error and minimum Akaike information criterion using smaller number of fitting function bases.
Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E
2010-11-08
Gradient forces on double negative (DNG) spherical dielectric particles are theoretically evaluated for v-th Bessel beams supposing geometrical optics approximations based on momentum transfer. For the first time in the literature, comparisons between these forces for double positive (DPS) and DNG particles are reported. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a DNG particle may not reverse sign when the relative refractive index n goes from |n|>1 to |n|<1, thus revealing new and interesting trapping properties.
Shortest Paths and Vehicle Routing
DEFF Research Database (Denmark)
Petersen, Bjørn
This thesis presents how to parallelize a shortest path labeling algorithm. It is shown how to handle Chvátal-Gomory rank-1 cuts in a column generation context. A Branch-and-Cut algorithm is given for the Elementary Shortest Paths Problem with Capacity Constraint. A reformulation of the Vehicle...... Routing Problem based on partial paths is presented. Finally, a practical application of finding shortest paths in the telecommunication industry is shown....
Square-root measurement for pure states
International Nuclear Information System (INIS)
Huang Siendong
2005-01-01
Square-root measurement is a very useful suboptimal measurement in many applications. It was shown that the square-root measurement minimizes the squared error for pure states. In this paper, the least squared error problem is reformulated and a new proof is provided. It is found that the least squared error depends only on the average density operator of the input states. The properties of the least squared error are then discussed, and it is shown that if the input pure states are uniformly distributed, the average probability of error has an upper bound depending on the least squared error, the rank of the average density operator, and the number of the input states. The aforementioned properties help explain why the square-root measurement can be effective in decoding processes
36 CFR 910.67 - Square guidelines.
2010-07-01
... 36 Parks, Forests, and Public Property 3 2010-07-01 2010-07-01 false Square guidelines. 910.67... GUIDELINES AND UNIFORM STANDARDS FOR URBAN PLANNING AND DESIGN OF DEVELOPMENT WITHIN THE PENNSYLVANIA AVENUE DEVELOPMENT AREA Glossary of Terms § 910.67 Square guidelines. Square Guidelines establish the Corporation's...
Directory of Open Access Journals (Sweden)
Jamie Waters
2014-09-01
Full Text Available This project uses Newton’s Second Law of Motion, Euler’s method, basic physics, and basic calculus to model the flight path of a rocket. From this, one can find the height and velocity at any point from launch to the maximum altitude, or apogee. This can then be compared to the actual values to see if the method of estimation is a plausible. The rocket used for this project is modeled after Bullistic-1 which was launched by the Society of Aeronautics and Rocketry at the University of South Florida.
Mehhtz, Peter
2005-01-01
JPF is an explicit state software model checker for Java bytecode. Today, JPF is a swiss army knife for all sort of runtime based verification purposes. This basically means JPF is a Java virtual machine that executes your program not just once (like a normal VM), but theoretically in all possible ways, checking for property violations like deadlocks or unhandled exceptions along all potential execution paths. If it finds an error, JPF reports the whole execution that leads to it. Unlike a normal debugger, JPF keeps track of every step how it got to the defect.
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Wolfowitz,Paul
2006-01-01
Paul Wolfowitz, President of the World Bank, discussed Singapore's remarkable progress along the road from poverty to prosperity which has also been discovered by many other countries in East Asia and around the world. He spoke of how each country must find its own path for people to pursue the same dreams of the chance to go to school, the security of a good job, and the ability to provide a better future for their children. Throughout the world, and importantly in the developing world, ther...
International Nuclear Information System (INIS)
Niv, A.; Biener, G.; Kleiner, V.; Hasman, E.
2004-01-01
Full Text:Propagation-invariant scalar fields have been extensively studied both theoretically and experimentally, since they were proposed by Durnin et al. These fields were employed in applications such as optical tweezers and for transport and guiding of microspheres. Although there has recently been considerable theoretical interest in propagation-invariant vectorial beams, experimental studies of such beams have remained somewhat limited. One of the most interesting types of propagation-invariant vectorial beam is the linearly polarized axially symmetric beam (LPASB) [l]. Recently, we introduced and experimentally demonstrated propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry based on quantized Pancharatnam-Berry phase optical elements (QPBOEs) [21 and an axicon. QP-BOEs utilize the geometric phase that accompanies space-variant polarization manipulations to achieve a desired phase modification [31. To test our approach we formed QPBOEs with different polarization orders as computer-generated space-variant sub wavelength gratings upon GaAs wafers for use with 10.6 micron laser radiation. The resultant beams were also transmitted through a polarizer that produced a unique propagation-invariant scalar beam. This beam has a propeller-shaped intensity pattern that can be rotated by simple rotation of the polarizer. We therefore have demonstrated the formation of a vectorial Bessel beam by using simple, lightweight thin elements and exploited that beam to perform a controlled rotation of a propeller-shaped intensity pattern that can be suitable for optical tweezers
Energy Technology Data Exchange (ETDEWEB)
Balakin, A. A., E-mail: balakin.alexey@yandex.ru; Mironov, V. A.; Skobelev, S. A., E-mail: sk.sa1981@gmail.com [Russian Academy of Sciences, Institute of Applied Physics (Russian Federation)
2017-01-15
The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.
International Nuclear Information System (INIS)
Connolly, T.J.; Hansen, U.; Jaek, W.; Beckurts, K.H.
1979-01-01
In examing the world nuclear energy paths, the following assumptions were adopted: the world economy will grow somewhat more slowly than in the past, leading to reductions in electricity demand growth rates; national and international political impediments to the deployment of nuclear power will gradually disappear over the next few years; further development of nuclear power will proceed steadily, without serious interruption but with realistic lead times for the introduction of advanced technologies. Given these assumptions, this paper attempts a study of possible world nuclear energy developments, disaggregated on a regional and national basis. The scenario technique was used and a few alternative fuel-cycle scenarios were developed. Each is an internally consistent model of technically and economically feasible paths to the further development of nuclear power in an aggregate of individual countries and regions of the world. The main purpose of this modeling exercise was to gain some insight into the probable international locations of reactors and other nuclear facilities, the future requirements for uranium and for fuel-cycle services, and the problems of spent-fuel storage and waste management. The study also presents an assessment of the role that nuclear power might actually play in meeting future world energy demand
World University Ranking Systems: An Alternative Approach Using Partial Least Squares Path Modelling
Jajo, Nethal K.; Harrison, Jen
2014-01-01
University rankings are key drivers in national and institutional strategic planning. The increase in the number of university ranking systems and the diversity of methods and indicators used by these systems necessitate the development of an index that can measure a university's performance in all these systems at once. This article presents…
International Nuclear Information System (INIS)
Liu Yingling
2008-01-01
The recent policy tools have also consolidated and advanced traditional renewable energy industries, including hydropower and solar thermal panels, where China has already been a world leader. The technologies are comparatively simple and low-cost, and the country has developed fairly strong construction, manufacturing and installation industries for both sources. They are still dominant in China's renewable energy use, and are expected to see continuous strong growth. Hydropower accounts for about two-thirds of China's current renewable energy use. It has grown by over 8 per cent annually from 2002 to 2006, and installed capacity will reach 190 GW by 2010 and 300 GW by 2020. China also has nearly two-thirds of the world's solar hot water capacity: more than one in every ten households bathe in water heated by the sun. Such solar thermal has witnessed 20-25 per cent annual growth in recent years, with installed capacity rising from 35 million square metres in 2000 to 100 million square metres by the end of 2006. The government aims for 150 million square metres by 2010 and double that figure by 2020. A more optimistic prediction envisages 800 million square metres installed capacity by 2030, which would mean that more than half of all Chinese households would be using solar energy for water heating. Renewable energy has become a strategic industry in China. The country has more than 50 domestic wind turbine manufacturers, over 15 major solar cell manufacturers and roughly 50 companies constructing, expanding or planning for polysilicon production lines, the key components for solar PV systems. Those two industries together employ some 80,000 people. The country also has thousands of hydropower manufacturers and engineering and design firms. More than a thousand solar water heater manufacturers throughout the country - and associated design, installation and service providers - provide some 600,000 jobs. As renewable industries are scaled up, costs will come down
Acoustics of finite asymmetric exotic beams: Examples of Airy and fractional Bessel beams
Mitri, F. G.
2017-12-01
The purpose of this investigation is to examine the properties of finite asymmetric exotic scalar (acoustic) beams with unusual properties using the angular spectrum decomposition in plane waves. Such beams possess intrinsic uncommon characteristics that make them attractive from the standpoint of particle manipulation, handling and rotation, and possibly other applications in particle clearing and separation. Assuming a specific apodization function at the acoustic source, the angular spectrum function is calculated and used to synthesize the radiated pressure field (i.e., excluding evanescent waves that decay away from the source) in the forward direction of wave motion (i.e., away from the source). Moreover, a generalized hybrid method combining the angular spectrum approach with the multipole expansion formalism in spherical coordinates is developed, which is applicable to any finite beam of arbitrary wavefront. The improved approach allows adequate computation of the resonance scattering, radiation force, and spin torque components on an object of arbitrary shape, located on or off the axis of the incident beam in space. Considering the illustrative example of a viscous fluid sphere submerged in a non-viscous liquid and illuminated by finite asymmetric beams such as the Airy and the Bessel vortex beam with fractional order, numerical computations for the scattering, radiation force, and torque components are performed with an emphasis on the distance from the source, the arbitrary location of the particle ,and the asymmetric nature of the incident field. Moreover, beamforming calculations are presented with supplementary animations for the pressure field distribution in space, with an emphasis on the intrinsic properties of the selected beams. The numerical predictions illustrate the scattering, radiation force, and spin torque properties depending on the beam parameters and the distance separating the sphere from the source. This study provides a generalized
Twin edge colorings of certain square graphs and product graphs
Directory of Open Access Journals (Sweden)
R Rajarajachozhan
2016-04-01
Full Text Available A twin edge $k\\!$-coloring of a graph $G$ is a proper edge $k$-coloring of $G$ with the elements of $\\mathbb{Z}_k$ so that the induced vertex $k$-coloring, in which the color of a vertex $v$ in $G$ is the sum in $\\mathbb{Z}_k$ of the colors of the edges incident with $v,$ is a proper vertex $k\\!$-coloring. The minimum $k$ for which $G$ has a twin edge $k\\!$-coloring is called the twin chromatic index of $G.$ Twin chromatic index of the square $P_n^2,$ $n\\ge 4,$ and the square $C_n^2,$ $n\\ge 6,$ are determined. In fact, the twin chromatic index of the square $C_7^2$ is $\\Delta+2,$ where $\\Delta$ is the maximum degree. Twin chromatic index of $C_m\\,\\Box\\,P_n$ is determined, where $\\Box$ denotes the Cartesian product. $C_r$ and $P_r$ are, respectively, the cycle, and the path on $r$ vertices each.
Optimization of the geometrical stability in square ring laser gyroscopes
International Nuclear Information System (INIS)
Santagata, R; Beghi, A; Cuccato, D; Belfi, J; Beverini, N; Virgilio, A Di; Ortolan, A; Porzio, A; Solimeno, S
2015-01-01
Ultra-sensitive ring laser gyroscopes are regarded as potential detectors of the general relativistic frame-dragging effect due to the rotation of the Earth. Our project for this goal is called GINGER (gyroscopes in general relativity), and consists of a ground-based triaxial array of ring lasers aimed at measuring the rotation rate of the Earth with an accuracy of 10 −14 rad s −1 . Such an ambitious goal is now within reach, as large-area ring lasers are very close to the required sensitivity and stability. However, demanding constraints on the geometrical stability of the optical path of the laser inside the ring cavity are required. Thus, we have begun a detailed study of the geometry of an optical cavity in order to find a control strategy for its geometry that could meet the specifications of the GINGER project. As the cavity perimeter has a stationary point for the square configuration, we identify a set of transformations on the mirror positions that allows us to adjust the laser beam steering to the shape of a square. We show that the geometrical stability of a square cavity strongly increases by implementing a suitable system to measure the mirror distances, and that the geometry stabilization can be achieved by measuring the absolute lengths of the two diagonals and the perimeter of the ring. (paper)
International Nuclear Information System (INIS)
Kostroun, V.O.
1980-01-01
Theoretical expressions for the angular and spectral distributions of synchrotron radiation involve modified Bessel functions of fractional order and the integral ∫sup(infinitely)sub(x)Ksub(ν)(eta)d eta. A simple series expression for these quantities which can be evaluated numerically with hand-held programmable calculators is presented. (orig.)
Square pulse linear transformer driver
Directory of Open Access Journals (Sweden)
A. A. Kim
2012-04-01
Full Text Available The linear transformer driver (LTD technological approach can result in relatively compact devices that can deliver fast, high current, and high-voltage pulses straight out of the LTD cavity without any complicated pulse forming and pulse compression network. Through multistage inductively insulated voltage adders, the output pulse, increased in voltage amplitude, can be applied directly to the load. The usual LTD architecture [A. A. Kim, M. G. Mazarakis, V. A. Sinebryukhov, B. M. Kovalchuk, V. A. Vizir, S. N Volkov, F. Bayol, A. N. Bastrikov, V. G. Durakov, S. V. Frolov, V. M. Alexeenko, D. H. McDaniel, W. E. Fowler, K. LeCheen, C. Olson, W. A. Stygar, K. W. Struve, J. Porter, and R. M. Gilgenbach, Phys. Rev. ST Accel. Beams 12, 050402 (2009PRABFM1098-440210.1103/PhysRevSTAB.12.050402; M. G. Mazarakis, W. E. Fowler, A. A. Kim, V. A. Sinebryukhov, S. T. Rogowski, R. A. Sharpe, D. H. McDaniel, C. L. Olson, J. L. Porter, K. W. Struve, W. A. Stygar, and J. R. Woodworth, Phys. Rev. ST Accel. Beams 12, 050401 (2009PRABFM1098-440210.1103/PhysRevSTAB.12.050401] provides sine shaped output pulses that may not be well suited for some applications like z-pinch drivers, flash radiography, high power microwaves, etc. A more suitable power pulse would have a flat or trapezoidal (rising or falling top. In this paper, we present the design and first test results of an LTD cavity that generates such a type of output pulse by including within its circular array a number of third harmonic bricks in addition to the main bricks. A voltage adder made out of a square pulse cavity linear array will produce the same shape output pulses provided that the timing of each cavity is synchronized with the propagation of the electromagnetic pulse.
Directory of Open Access Journals (Sweden)
Paul Ballonoff
2017-12-01
Full Text Available A theory of cultural structures predicts the objects observed by anthropologists. We here define those which use kinship relationships to define systems. A finite structure we call a partially defined quasigroup (or pdq, as stated by Definition 1 below on a dictionary (called a natural language allows prediction of certain anthropological descriptions, using homomorphisms of pdqs onto finite groups. A viable history (defined using pdqs states how an individual in a population following such history may perform culturally allowed associations, which allows a viable history to continue to survive. The vector states on sets of viable histories identify demographic observables on descent sequences. Paths of vector states on sets of viable histories may determine which histories can exist empirically.
Propagators and path integrals
Energy Technology Data Exchange (ETDEWEB)
Holten, J.W. van
1995-08-22
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role of world-line reparametrization invariance of the classical action and the implementation of the corresponding BRST-symmetry in the quantum theory are discussed. The presence of classical world-line supersymmetry is shown to lead to an unwanted doubling of states for massive spin-1/2 particles. The origin of this phenomenon is traced to a `hidden` topological fermionic excitation. A different formulation of the pseudo-classical mechanics using a bosonic representation of {gamma}{sub 5} is shown to remove these extra states at the expense of losing manifest supersymmetry. (orig.).
Directory of Open Access Journals (Sweden)
Li Jian
2016-01-01
Full Text Available The world has entered the information age, all kinds of information technologies such as cloud technology, big data technology are in rapid development, and the “Internet plus” appeared. The main purpose of “Internet plus” is to provide an opportunity for the further development of the enterprise, the enterprise technology, business and other aspects of factors combine. For enterprises, grasp the “Internet plus” the impact of the market economy will undoubtedly pave the way for the future development of enterprises. This paper will be on the innovation path of the enterprise management “Internet plus” era tied you study, hope to be able to put forward some opinions and suggestions.
Weighted conditional least-squares estimation
International Nuclear Information System (INIS)
Booth, J.G.
1987-01-01
A two-stage estimation procedure is proposed that generalizes the concept of conditional least squares. The method is instead based upon the minimization of a weighted sum of squares, where the weights are inverses of estimated conditional variance terms. Some general conditions are given under which the estimators are consistent and jointly asymptotically normal. More specific details are given for ergodic Markov processes with stationary transition probabilities. A comparison is made with the ordinary conditional least-squares estimators for two simple branching processes with immigration. The relationship between weighted conditional least squares and other, more well-known, estimators is also investigated. In particular, it is shown that in many cases estimated generalized least-squares estimators can be obtained using the weighted conditional least-squares approach. Applications to stochastic compartmental models, and linear models with nested error structures are considered
Energy Technology Data Exchange (ETDEWEB)
Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, Viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)
2016-04-29
The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.
International Nuclear Information System (INIS)
Mignemi, S.; Štrajn, R.
2016-01-01
The definition of path integrals in one- and two-dimensional Snyder space is discussed in detail both in the traditional setting and in the first-order formalism of Faddeev and Jackiw. - Highlights: • The definition of the path integral in Snyder space is discussed using phase space methods. • The same result is obtained in the first-order formalism of Faddeev and Jackiw. • The path integral formulation of the two-dimensional Snyder harmonic oscillator is outlined.
Sets of Mutually Orthogonal Sudoku Latin Squares
Vis, Timothy; Petersen, Ryan M.
2009-01-01
A Latin square of order "n" is an "n" x "n" array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is c ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9…
The Square Light Clock and Special Relativity
Galli, J. Ronald; Amiri, Farhang
2012-01-01
A thought experiment that includes a square light clock is similar to the traditional vertical light beam and mirror clock, except it is made up of four mirrors placed at a 45[degree] angle at each corner of a square of length L[subscript 0], shown in Fig. 1. Here we have shown the events as measured in the rest frame of the square light clock. By…
Distribution of squares modulo a composite number
Aryan, Farzad
2015-01-01
In this paper we study the distribution of squares modulo a square-free number $q$. We also look at inverse questions for the large sieve in the distribution aspect and we make improvements on existing results on the distribution of $s$-tuples of reduced residues.
Some Theoretical Essences of Lithuania Squares Formation
Directory of Open Access Journals (Sweden)
Gintautas Tiškus
2016-04-01
Full Text Available In the Lithuanian acts of law and in the scientific literature there are no clear criteria and notions to define a square. The unbuilt city space places or the gaps between buildings are often defined as the squares, which do not have clear limits or destination. The mandatory attributes of the place which is called the square are indicated in the article, the notion of square is defined. The article deals with Lithuanian squares theme, analyses the differences between representation and representativeness. The article aims to indicate an influence of city environmental context and monument in the square on its function. The square is an independent element of city plan structure, but it is not an independent element of city spatial structure. The space and environment of the square are related to each other not only by physical, aesthetical relations, but as well as by causalities, which may be named as the essences of squares’ formation. The interdisciplinary discourse analysis method is applied in the article.
Entrywise Squared Transforms for GAMP Supplementary Material
DEFF Research Database (Denmark)
2016-01-01
Supplementary material for a study on Entrywise Squared Transforms for Generalized Approximate Message Passing (GAMP). See the README file for the details.......Supplementary material for a study on Entrywise Squared Transforms for Generalized Approximate Message Passing (GAMP). See the README file for the details....
Lagrange’s Four-Square Theorem
Directory of Open Access Journals (Sweden)
Watase Yasushige
2015-02-01
Full Text Available This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23].
Two Generations of Path Dependence
DEFF Research Database (Denmark)
Madsen, Mogens Ove
Even if there is no fully articulated and generally accepted theory of Path Dependence it has eagerly been taken up across a wide range of social sciences - primarily coming from economics. Path Dependence is most of all a metaphor that offers reason to believe, that some political, social...
Chromatic roots and hamiltonian paths
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
Mitri, F G; Fellah, Z E A
2011-08-01
The present investigation examines the instantaneous force resulting from the interaction of an acoustical high-order Bessel vortex beam (HOBVB) with a rigid sphere. The rigid sphere case is important in fluid dynamics applications because it perfectly simulates the interaction of instantaneous sound waves in a reduced gravity environment with a levitated spherical liquid soft drop in air. Here, a closed-form solution for the instantaneous force involving the total pressure field as well as the Bessel beam parameters is obtained for the case of progressive, stationary and quasi-stationary waves. Instantaneous force examples for progressive waves are computed for both a fixed and a movable rigid sphere. The results show how the instantaneous force per unit cross-sectional surface and unit pressure varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere's radius), the half-cone angle β and the order m of the HOBVB. It is demonstrated here that the instantaneous force is determined only for (m,n) = (0,1) (where n is the partial-wave number), and vanishes for m>0 because of symmetry. In addition, the instantaneous force and normalized amplitude velocity results are computed and compared with those of a rigid immovable (fixed) sphere. It is shown that they differ significantly for ka values below 5. The proposed analysis may be of interest in the analysis of instantaneous forces on spherical particles for particle manipulation, filtering, trapping and drug delivery. The presented solutions may also serve as a method for comparison to other solutions obtained by strictly numerical or asymptotic approaches. Copyright © 2011 Elsevier B.V. All rights reserved.
BIOMECHANICS. Why the seahorse tail is square.
Porter, Michael M; Adriaens, Dominique; Hatton, Ross L; Meyers, Marc A; McKittrick, Joanna
2015-07-03
Whereas the predominant shapes of most animal tails are cylindrical, seahorse tails are square prisms. Seahorses use their tails as flexible grasping appendages, in spite of a rigid bony armor that fully encases their bodies. We explore the mechanics of two three-dimensional-printed models that mimic either the natural (square prism) or hypothetical (cylindrical) architecture of a seahorse tail to uncover whether or not the square geometry provides any functional advantages. Our results show that the square prism is more resilient when crushed and provides a mechanism for preserving articulatory organization upon extensive bending and twisting, as compared with its cylindrical counterpart. Thus, the square architecture is better than the circular one in the context of two integrated functions: grasping ability and crushing resistance. Copyright © 2015, American Association for the Advancement of Science.
Hard paths, soft paths or no paths? Cross-cultural perceptions of water solutions
Wutich, A.; White, A. C.; White, D. D.; Larson, K. L.; Brewis, A.; Roberts, C.
2014-01-01
In this study, we examine how development status and water scarcity shape people's perceptions of "hard path" and "soft path" water solutions. Based on ethnographic research conducted in four semi-rural/peri-urban sites (in Bolivia, Fiji, New Zealand, and the US), we use content analysis to conduct statistical and thematic comparisons of interview data. Our results indicate clear differences associated with development status and, to a lesser extent, water scarcity. People in the two less developed sites were more likely to suggest hard path solutions, less likely to suggest soft path solutions, and more likely to see no path to solutions than people in the more developed sites. Thematically, people in the two less developed sites envisioned solutions that involve small-scale water infrastructure and decentralized, community-based solutions, while people in the more developed sites envisioned solutions that involve large-scale infrastructure and centralized, regulatory water solutions. People in the two water-scarce sites were less likely to suggest soft path solutions and more likely to see no path to solutions (but no more likely to suggest hard path solutions) than people in the water-rich sites. Thematically, people in the two water-rich sites seemed to perceive a wider array of unrealized potential soft path solutions than those in the water-scarce sites. On balance, our findings are encouraging in that they indicate that people are receptive to soft path solutions in a range of sites, even those with limited financial or water resources. Our research points to the need for more studies that investigate the social feasibility of soft path water solutions, particularly in sites with significant financial and natural resource constraints.
Optimal Paths in Gliding Flight
Wolek, Artur
Underwater gliders are robust and long endurance ocean sampling platforms that are increasingly being deployed in coastal regions. This new environment is characterized by shallow waters and significant currents that can challenge the mobility of these efficient (but traditionally slow moving) vehicles. This dissertation aims to improve the performance of shallow water underwater gliders through path planning. The path planning problem is formulated for a dynamic particle (or "kinematic car") model. The objective is to identify the path which satisfies specified boundary conditions and minimizes a particular cost. Several cost functions are considered. The problem is addressed using optimal control theory. The length scales of interest for path planning are within a few turn radii. First, an approach is developed for planning minimum-time paths, for a fixed speed glider, that are sub-optimal but are guaranteed to be feasible in the presence of unknown time-varying currents. Next the minimum-time problem for a glider with speed controls, that may vary between the stall speed and the maximum speed, is solved. Last, optimal paths that minimize change in depth (equivalently, maximize range) are investigated. Recognizing that path planning alone cannot overcome all of the challenges associated with significant currents and shallow waters, the design of a novel underwater glider with improved capabilities is explored. A glider with a pneumatic buoyancy engine (allowing large, rapid buoyancy changes) and a cylindrical moving mass mechanism (generating large pitch and roll moments) is designed, manufactured, and tested to demonstrate potential improvements in speed and maneuverability.
Around and Beyond the Square of Opposition
Béziau, Jean-Yves
2012-01-01
aiThe theory of oppositions based on Aristotelian foundations of logic has been pictured in a striking square diagram which can be understood and applied in many different ways having repercussions in various fields: epistemology, linguistics, mathematics, psychology. The square can also be generalized in other two-dimensional or multi-dimensional objects extending in breadth and depth the original theory of oppositions of Aristotle. The square of opposition is a very attractive theme which has been going through centuries without evaporating. Since 10 years there is a new growing interest for
Partial update least-square adaptive filtering
Xie, Bei
2014-01-01
Adaptive filters play an important role in the fields related to digital signal processing and communication, such as system identification, noise cancellation, channel equalization, and beamforming. In practical applications, the computational complexity of an adaptive filter is an important consideration. The Least Mean Square (LMS) algorithm is widely used because of its low computational complexity (O(N)) and simplicity in implementation. The least squares algorithms, such as Recursive Least Squares (RLS), Conjugate Gradient (CG), and Euclidean Direction Search (EDS), can converge faster a
Perfect discretization of path integrals
International Nuclear Information System (INIS)
Steinhaus, Sebastian
2012-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Perfect discretization of path integrals
Steinhaus, Sebastian
2012-05-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.
Elmo bumpy square plasma confinement device
Owen, L.W.
1985-01-01
The invention is an Elmo bumpy type plasma confinement device having a polygonal configuration of closed magnet field lines for improved plasma confinement. In the preferred embodiment, the device is of a square configuration which is referred to as an Elmo bumpy square (EBS). The EBS is formed by four linear magnetic mirror sections each comprising a plurality of axisymmetric assemblies connected in series and linked by 90/sup 0/ sections of a high magnetic field toroidal solenoid type field generating coils. These coils provide corner confinement with a minimum of radial dispersion of the confined plasma to minimize the detrimental effects of the toroidal curvature of the magnetic field. Each corner is formed by a plurality of circular or elliptical coils aligned about the corner radius to provide maximum continuity in the closing of the magnetic field lines about the square configuration confining the plasma within a vacuum vessel located within the various coils forming the square configuration confinement geometry.
Quantized kernel least mean square algorithm.
Chen, Badong; Zhao, Songlin; Zhu, Pingping; Príncipe, José C
2012-01-01
In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the "redundant" data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.
Anomalous structural transition of confined hard squares.
Gurin, Péter; Varga, Szabolcs; Odriozola, Gerardo
2016-11-01
Structural transitions are examined in quasi-one-dimensional systems of freely rotating hard squares, which are confined between two parallel walls. We find two competing phases: one is a fluid where the squares have two sides parallel to the walls, while the second one is a solidlike structure with a zigzag arrangement of the squares. Using transfer matrix method we show that the configuration space consists of subspaces of fluidlike and solidlike phases, which are connected with low probability microstates of mixed structures. The existence of these connecting states makes the thermodynamic quantities continuous and precludes the possibility of a true phase transition. However, thermodynamic functions indicate strong tendency for the phase transition and our replica exchange Monte Carlo simulation study detects several important markers of the first order phase transition. The distinction of a phase transition from a structural change is practically impossible with simulations and experiments in such systems like the confined hard squares.
The inverse square law of gravitation
International Nuclear Information System (INIS)
Cook, A.H.
1987-01-01
The inverse square law of gravitation is very well established over the distances of celestial mechanics, while in electrostatics the law has been shown to be followed to very high precision. However, it is only within the last century that any laboratory experiments have been made to test the inverse square law for gravitation, and all but one has been carried out in the last ten years. At the same time, there has been considerable interest in the possibility of deviations from the inverse square law, either because of a possible bearing on unified theories of forces, including gravitation or, most recently, because of a possible additional fifth force of nature. In this article the various lines of evidence for the inverse square law are summarized, with emphasis upon the recent laboratory experiments. (author)
Parand, K.; Nikarya, M.
2017-11-01
In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.
Four new topological indices based on the molecular path code.
Balaban, Alexandru T; Beteringhe, Adrian; Constantinescu, Titus; Filip, Petru A; Ivanciuc, Ovidiu
2007-01-01
The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.
Applications of square-related theorems
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
Power Efficient Division and Square Root Unit
DEFF Research Database (Denmark)
Liu, Wei; Nannarelli, Alberto
2012-01-01
Although division and square root are not frequent operations, most processors implement them in hardware to not compromise the overall performance. Two classes of algorithms implement division or square root: digit-recurrence and multiplicative (e.g., Newton-Raphson) algorithms. Previous work....... The proposed unit is compared to similar solutions based on the digit-recurrence algorithm and it is compared to a unit based on the multiplicative Newton-Raphson algorithm....
An Introduction to Path Analysis
Wolfe, Lee M.
1977-01-01
The analytical procedure of path analysis is described in terms of its use in nonexperimental settings in the social sciences. The description assumes a moderate statistical background on the part of the reader. (JKS)
Probabilistic simulation of fermion paths
International Nuclear Information System (INIS)
Zhirov, O.V.
1989-01-01
Permutation symmetry of fermion path integral allows (while spin degrees of freedom are ignored) to use in its simulation any probabilistic algorithm, like Metropolis one, heat bath, etc. 6 refs., 2 tabs
Formal language constrained path problems
Energy Technology Data Exchange (ETDEWEB)
Barrett, C.; Jacob, R.; Marathe, M.
1997-07-08
In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvable efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.
Perfect discretization of path integrals
Steinhaus, Sebastian
2011-01-01
In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discu...
Kiselev, A
2003-01-01
Two new families of exact solutions of the wave equation u sub x sub x + u sub y sub y + u sub z sub z - c sup - sup 2 u sub t sub t = 0 generalizing Bessel-Gauss pulses and Bateman-Hillion relatively undistorted progressive waves, respectively are presented. In each of these families new simple solutions describing localized wave propagation are found. The approach is based on a kind of separation of variables. (letter to the editor)
Kim, Jongki; Jeong, Yoonseob; Lee, Sejin; Ha, Woosung; Shin, Jeon-Soo; Oh, Kyunghwan
2012-02-15
Highly efficient Bessel-like beam generation was achieved based on a new all-fiber method that implements Fourier transformation of a micro annular aperture along a concatenated composite optical fiber. The beam showed unique characteristics of tilted washboard optical potential in the transverse plane and sustained a nondiffracting length over 400 μm along the axial direction. Optical trapping of multiple dielectric particles and living Jurkat cells were successfully demonstrated along the axial direction of the beam in the water.
Path integrals on curved manifolds
International Nuclear Information System (INIS)
Grosche, C.; Steiner, F.
1987-01-01
A general framework for treating path integrals on curved manifolds is presented. We also show how to perform general coordinate and space-time transformations in path integrals. The main result is that one has to subtract a quantum correction ΔV ∝ ℎ 2 from the classical Lagrangian L, i.e. the correct effective Lagrangian to be used in the path integral is L eff = L-ΔV. A general prescription for calculating the quantum correction ΔV is given. It is based on a canonical approach using Weyl-ordering and the Hamiltonian path integral defined by the midpoint prescription. The general framework is illustrated by several examples: The d-dimensional rotator, i.e. the motion on the sphere S d-1 , the path integral in d-dimensional polar coordinates, the exact treatment of the hydrogen atom in R 2 and R 3 by performing a Kustaanheimo-Stiefel transformation, the Langer transformation and the path integral for the Morse potential. (orig.)
Path-based Queries on Trajectory Data
DEFF Research Database (Denmark)
Krogh, Benjamin Bjerre; Pelekis, Nikos; Theodoridis, Yannis
2014-01-01
In traffic research, management, and planning a number of path-based analyses are heavily used, e.g., for computing turn-times, evaluating green waves, or studying traffic flow. These analyses require retrieving the trajectories that follow the full path being analyzed. Existing path queries cannot...... sufficiently support such path-based analyses because they retrieve all trajectories that touch any edge in the path. In this paper, we define and formalize the strict path query. This is a novel query type tailored to support path-based analysis, where trajectories must follow all edges in the path...... a specific path by only retrieving data from the first and last edge in the path. To correctly answer strict path queries existing network-constrained trajectory indexes must retrieve data from all edges in the path. An extensive performance study of NETTRA using a very large real-world trajectory data set...
Completely automated open-path FT-IR spectrometry.
Griffiths, Peter R; Shao, Limin; Leytem, April B
2009-01-01
Atmospheric analysis by open-path Fourier-transform infrared (OP/FT-IR) spectrometry has been possible for over two decades but has not been widely used because of the limitations of the software of commercial instruments. In this paper, we describe the current state-of-the-art of the hardware and software that constitutes a contemporary OP/FT-IR spectrometer. We then describe advances that have been made in our laboratory that have enabled many of the limitations of this type of instrument to be overcome. These include not having to acquire a single-beam background spectrum that compensates for absorption features in the spectra of atmospheric water vapor and carbon dioxide. Instead, an easily measured "short path-length" background spectrum is used for calculation of each absorbance spectrum that is measured over a long path-length. To accomplish this goal, the algorithm used to calculate the concentrations of trace atmospheric molecules was changed from classical least-squares regression (CLS) to partial least-squares regression (PLS). For calibration, OP/FT-IR spectra are measured in pristine air over a wide variety of path-lengths, temperatures, and humidities, ratioed against a short-path background, and converted to absorbance; the reference spectrum of each analyte is then multiplied by randomly selected coefficients and added to these background spectra. Automatic baseline correction for small molecules with resolved rotational fine structure, such as ammonia and methane, is effected using wavelet transforms. A novel method of correcting for the effect of the nonlinear response of mercury cadmium telluride detectors is also incorporated. Finally, target factor analysis may be used to detect the onset of a given pollutant when its concentration exceeds a certain threshold. In this way, the concentration of atmospheric species has been obtained from OP/FT-IR spectra measured at intervals of 1 min over a period of many hours with no operator intervention.
Statistical mechanics of directed models of polymers in the square lattice
Rensburg, J V
2003-01-01
Directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature. These are idealized geometric directed lattice models introduced to study phase behaviour in polymers, and include Dyck paths, partially directed paths, directed trees and directed vesicles models. Directed models are closely related to models studied in the combinatorics literature (and are often exactly solvable). They are also simplified versions of a number of statistical mechanics models, including the self-avoiding walk, lattice animals and lattice vesicles. The exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models, and this will be explored in this review. The combinatorial nature of directed lattice path models makes a study using generating function approaches most natural. In contrast, the statistical mechanics approach would introduce...
Extracting the invariant model from the feedback paths of digital hearing aids
DEFF Research Database (Denmark)
Ma, Guilin; Gran, Fredrik; Jacobsen, Finn
2011-01-01
environments given a specific type of hearing aids. Based on this observation, a feedback path model that consists of an invariant model and a variant model is proposed. A common-acoustical-pole and zero model-based approach and an iterative least-square search-based approach are used to extract the invariant...... model from a set of impulse responses of the feedback paths. A hybrid approach combining the two methods is also proposed. The general properties of the three methods are studied using artificial datasets, and the methods are cross-validated using the measured feedback paths. The results show...
Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I
2016-04-01
Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it
Path integration on hyperbolic spaces
Energy Technology Data Exchange (ETDEWEB)
Grosche, C [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
1991-11-01
Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S{sub 1} {approx equal} SO (n,1)/SO(n) and S{sub 2} {approx equal} SU(n,1)/S(U(1) x U(n)) in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E{sub O} = h{sup 2} /8m(m{sub {alpha}} +2m{sub 2} {alpha}){sup 2} (m {alpha} and m{sub 2}{alpha} denote the dimension of the root subspace corresponding to the roots {alpha} and 2{alpha}, respectively). I also discuss the case, where a constant magnetic field on H{sup n} is incorporated. (orig.).
Path integration on hyperbolic spaces
International Nuclear Information System (INIS)
Grosche, C.
1991-11-01
Quantum mechanics on the hyperbolic spaces of rank one is discussed by path integration technique. Hyperbolic spaces are multi-dimensional generalisation of the hyperbolic plane, i.e. the Poincare upper half-plane endowed with a hyperbolic geometry. We evalute the path integral on S 1 ≅ SO (n,1)/SO(n) and S 2 ≅ SU(n,1)/S[U(1) x U(n)] in a particular coordinate system, yielding explicitly the wave-functions and the energy spectrum. Futhermore we can exploit a general property of all these spaces, namely that they can be parametrized by a pseudopolar coordinate system. This allows a separation in path integration over spheres and an additional path integration over the remaining hyperbolic coordinate, yielding effectively a path integral for a modified Poeschl-Teller potential. Only continuous spectra can exist in all the cases. For all the hyperbolic spaces of rank one we find a general formula for the largest lower bound (zero-point energy) of the spectrum which is given by E O = h 2 /8m(m α +2m 2 α) 2 (m α and m 2 α denote the dimension of the root subspace corresponding to the roots α and 2α, respectively). I also discuss the case, where a constant magnetic field on H n is incorporated. (orig.)
Non-spill control squared cascade
International Nuclear Information System (INIS)
Kai, Tsunetoshi; Inoue, Yoshiya; Oya, Akio; Suemori, Nobuo.
1974-01-01
Object: To reduce a mixed loss thus enhancing separating efficiency by the provision of a simple arrangement wherein a reflux portion in a conventional spill control squared cascade is replaced by a special stage including centrifugal separators. Structure: Steps in the form of a square cascade, in which a plurality of centrifugal separators are connected by pipe lines, are accumulated in multistage fashion to form a squared cascade. Between the adjoining steps is disposed a special stage including a centrifugal separator which receives both lean flow from the upper step and rich flow from the lower step. The centrifugal separator in the special stage has its rich side connected to the upper step and its lean side connected to the lower step. Special stages are each disposed at the upper side of the uppermost step and at the lower side of the lowermost step. (Kamimura, M.)
Least Squares Data Fitting with Applications
DEFF Research Database (Denmark)
Hansen, Per Christian; Pereyra, Víctor; Scherer, Godela
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data....... In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working...... with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis...
Good Filtrations and the Steinberg Square
DEFF Research Database (Denmark)
Kildetoft, Tobias
that tensoring the Steinberg module with a simple module of restricted highest weight gives a module with a good filtration. This result was first proved by Andersen when the characteristic is large enough. In this dissertation, generalizations of those results, which are joint work with Daniel Nakano......, the socle completely determines how a Steinberg square decomposes. The dissertation also investigates the socle of the Steinberg square for a finite group of Lie type, again providing formulas which describe how to find the multiplicity of a simple module in the socle, given information about...
Rathore, Kavita; Bhattacharjee, Sudeep; Munshi, Prabhat
2017-06-01
A tomographic method based on the Fourier transform is used for characterizing a microwave plasma in a multicusp (MC), in order to obtain 2D distribution of plasma emissions, plasma (electron) density (Ne) and temperature (Te). The microwave plasma in the MC is characterized as a function of microwave power, gas pressure, and axial distance. The experimentally obtained 2D emission profiles show that the plasma emissions are generated in a circular ring shape. There are usually two bright rings, one at the plasma core and another near the boundary. The experimental results are validated using a numerical code that solves Maxwell's equations inside a waveguide filled with a plasma in a magnetic field, with collisions included. It is inferred that the dark and bright circular ring patterns are a result of superposition of Bessel modes (TE11 and TE21) of the wave electric field inside the plasma filled MC, which are in reasonable agreement with the plasma emission profiles. The tomographically obtained Ne and Te profiles indicate higher densities in the plasma core (˜1010 cm-3) and enhanced electron temperature in the ECR region (˜13 eV), which are in agreement with earlier results using a Langmuir probe and optical emission spectroscopy (OES) diagnostics.
Jafari, Seyed Hamed; Gauthier, Robert C.
2015-02-01
Maxwell's wave equations can be solved using different techniques in order to extract optical properties of a variety of dielectric structures. For structures that contain an extended axis which serve for the reference for cylindrical symmetry, we have shown that an expansion of the fields and inverse of the relative dielectric profile using a simplified and complete set of basis functions of Fourier-Bessel terms provide access to an eigenvalue formulation from which the eigen-states can be computed. We review the steps used to convert Maxwell's equation into an eigenvalue formulation, and then proceed to discuss several applications of the technique. For cylindrically symmetric structures, the computational technique provides a significantly reduced matrix order to be populated. New target structure for the presentation consists of cylindrical space slot channel waveguide in which the channel extends in azimuthal (ϕ) direction. The channel is provided by considering the etching of external side walls of "Bragg fiber". The configuration is similar to a structure that can support whispering-gallery modes, except that the modes highest field locations are within the ambient medium of the channel. Optical properties of this structure can be best examined through ?? field component which is discontinuous by ratio of relative dielectric constants when passing air-Bragg interfaces. The ability to select Bragg dielectric properties and to introduce non-uniformities in Bragg plane spacing provides access to tuning slot channel waveguide properties and design several novel configurations.
Wang, Xiaohui; Song, Yingxiong
2018-02-01
By exploiting the non-Kolmogorov model and Rytov approximation theory, a propagation model of Bessel-Gaussian vortex beams (BGVB) propagating in a subway tunnel is derived. Based on the propagation model, a model of orbital angular momentum (OAM) mode probability distribution is established to evaluate the propagation performance when the beam propagates along both longitudinal and transverse directions in the subway tunnel. By numerical simulations and experimental verifications, the influences of the various parameters of BGVB and turbulence on the OAM mode probability distribution are evaluated, and the results of simulations are consistent with the experimental statistics. The results verify that the middle area of turbulence is more beneficial for the vortex beam propagation than the edge; when the BGVB propagates along the longitudinal direction in the subway tunnel, the effects of turbulence on the OAM mode probability distribution can be decreased by selecting a larger anisotropy parameter, smaller coherence length, larger non-Kolmogorov power spectrum coefficient, smaller topological charge number, deeper subway tunnel, lower train speed, and longer wavelength. When the BGVB propagates along the transverse direction, the influences can be also mitigated by adopting a larger topological charge number, less non-Kolmogorov power spectrum coefficient, smaller refractive structure index, shorter wavelength, and shorter propagation distance.
Thériault, Gabrielle; Cottet, Martin; Castonguay, Annie; McCarthy, Nathalie; De Koninck, Yves
2014-01-01
Two-photon microscopy has revolutionized functional cellular imaging in tissue, but although the highly confined depth of field (DOF) of standard set-ups yields great optical sectioning, it also limits imaging speed in volume samples and ease of use. For this reason, we recently presented a simple and retrofittable modification to the two-photon laser-scanning microscope which extends the DOF through the use of an axicon (conical lens). Here we demonstrate three significant benefits of this technique using biological samples commonly employed in the field of neuroscience. First, we use a sample of neurons grown in culture and move it along the z-axis, showing that a more stable focus is achieved without compromise on transverse resolution. Second, we monitor 3D population dynamics in an acute slice of live mouse cortex, demonstrating that faster volumetric scans can be conducted. Third, we acquire a stereoscopic image of neurons and their dendrites in a fixed sample of mouse cortex, using only two scans instead of the complete stack and calculations required by standard systems. Taken together, these advantages, combined with the ease of integration into pre-existing systems, make the extended depth-of-field imaging based on Bessel beams a strong asset for the field of microscopy and life sciences in general.
Path Integrals in Quantum Mechanics
International Nuclear Information System (INIS)
Louko, J
2005-01-01
Jean Zinn-Justin's textbook Path Integrals in Quantum Mechanics aims to familiarize the reader with the path integral as a calculational tool in quantum mechanics and field theory. The emphasis is on quantum statistical mechanics, starting with the partition function Tr exp(-β H) and proceeding through the diffusion equation to barrier penetration problems and their semiclassical limit. The 'real time' path integral is defined via analytic continuation and used for the path-integral representation of the nonrelativistic S-matrix and its perturbative expansion. Holomorphic and Grassmannian path integrals are introduced and applied to nonrelativistic quantum field theory. There is also a brief discussion of path integrals in phase space. The introduction includes a brief historical review of path integrals, supported by a bibliography with some 40 entries. As emphasized in the introduction, mathematical rigour is not a central issue in the book. This allows the text to present the calculational techniques in a very readable manner: much of the text consists of worked-out examples, such as the quartic anharmonic oscillator in the barrier penetration chapter. At the end of each chapter there are exercises, some of which are of elementary coursework type, but the majority are more in the style of extended examples. Most of the exercises indeed include the solution or a sketch thereof. The book assumes minimal previous knowledge of quantum mechanics, and some basic quantum mechanical notation is collected in an appendix. The material has a large overlap with selected chapters in the author's thousand-page textbook Quantum Field Theory and Critical Phenomena (2002 Oxford: Clarendon). The stand-alone scope of the present work has, however, allowed a more focussed organization of this material, especially in the chapters on, respectively, holomorphic and Grassmannian path integrals. In my view the book accomplishes its aim admirably and is eminently usable as a textbook
International Nuclear Information System (INIS)
Canright, G.S.
1992-01-01
I offer a pedagogical review of the homotopy arguments for fractional statistics in two dimensions. These arguments arise naturally in path-integral language since they necessarily consider the properties of paths rather than simply permutations. The braid group replaces the permutation group as the basic structure for quantum statistics; hence properties of the braid group on several surfaces are briefly discussed. Finally, the question of multiple (real-space) occupancy is addressed; I suggest that the ''traditional'' treatment of this question (ie, an assumption that many-anyon wavefunctions necessarily vanish for multiple occupancy) needs reexamination
Isomorphisms and traversability of directed path graphs
Broersma, Haitze J.; Li, Xueliang; Li, X.
1998-01-01
The concept of a line digraph is generalized to that of a directed path graph. The directed path graph $\\forw P_k(D)$ of a digraph $D$ is obtained by representing the directed paths on $k$ vertices of $D$ by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in $D$
Self-diffusion of particles interacting through a square-well or square-shoulder potential
Wilbertz, H.; Michels, J.; Beijeren, H. van; Leegwater, J.A.
1988-01-01
The diffusion coefficient and velocity autocorrelation function for a fluid of particles interacting through a square-well or square-shoulder potential are calculated from a kinetic theory similar to the Davis-Rice-Sengers theory and the results are compared to those of computer simulations. At low
Multiples least-squares reverse time migration
Zhang, Dongliang; Zhan, Ge; Dai, Wei; Schuster, Gerard T.
2013-01-01
To enhance the image quality, we propose multiples least-squares reverse time migration (MLSRTM) that transforms each hydrophone into a virtual point source with a time history equal to that of the recorded data. Since each recorded trace is treated
Least-squares variance component estimation
Teunissen, P.J.G.; Amiri-Simkooei, A.R.
2007-01-01
Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible because it works with a user-defined weight
Square root approximation to the poisson channel
Tsiatmas, A.; Willems, F.M.J.; Baggen, C.P.M.J.
2013-01-01
Starting from the Poisson model we present a channel model for optical communications, called the Square Root (SR) Channel, in which the noise is additive Gaussian with constant variance. Initially, we prove that for large peak or average power, the transmission rate of a Poisson Channel when coding
Latin square three dimensional gage master
Jones, Lynn L.
1982-01-01
A gage master for coordinate measuring machines has an nxn array of objects distributed in the Z coordinate utilizing the concept of a Latin square experimental design. Using analysis of variance techniques, the invention may be used to identify sources of error in machine geometry and quantify machine accuracy.
Time Scale in Least Square Method
Directory of Open Access Journals (Sweden)
Özgür Yeniay
2014-01-01
Full Text Available Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.
Group-wise partial least square regression
Camacho, José; Saccenti, Edoardo
2018-01-01
This paper introduces the group-wise partial least squares (GPLS) regression. GPLS is a new sparse PLS technique where the sparsity structure is defined in terms of groups of correlated variables, similarly to what is done in the related group-wise principal component analysis. These groups are
Clar sextets in square graphene antidot lattices
DEFF Research Database (Denmark)
Petersen, Rene; Pedersen, Thomas Garm; Jauho, Antti-Pekka
2011-01-01
A periodic array of holes transforms graphene from a semimetal into a semiconductor with a band gap tuneable by varying the parameters of the lattice. In earlier work only hexagonal lattices have been treated. Using atomistic models we here investigate the size of the band gap of a square lattice...
Deformation analysis with Total Least Squares
Directory of Open Access Journals (Sweden)
M. Acar
2006-01-01
Full Text Available Deformation analysis is one of the main research fields in geodesy. Deformation analysis process comprises measurement and analysis phases. Measurements can be collected using several techniques. The output of the evaluation of the measurements is mainly point positions. In the deformation analysis phase, the coordinate changes in the point positions are investigated. Several models or approaches can be employed for the analysis. One approach is based on a Helmert or similarity coordinate transformation where the displacements and the respective covariance matrix are transformed into a unique datum. Traditionally a Least Squares (LS technique is used for the transformation procedure. Another approach that could be introduced as an alternative methodology is the Total Least Squares (TLS that is considerably a new approach in geodetic applications. In this study, in order to determine point displacements, 3-D coordinate transformations based on the Helmert transformation model were carried out individually by the Least Squares (LS and the Total Least Squares (TLS, respectively. The data used in this study was collected by GPS technique in a landslide area located nearby Istanbul. The results obtained from these two approaches have been compared.
Optimistic semi-supervised least squares classification
DEFF Research Database (Denmark)
Krijthe, Jesse H.; Loog, Marco
2017-01-01
The goal of semi-supervised learning is to improve supervised classifiers by using additional unlabeled training examples. In this work we study a simple self-learning approach to semi-supervised learning applied to the least squares classifier. We show that a soft-label and a hard-label variant ...
Iterative methods for weighted least-squares
Energy Technology Data Exchange (ETDEWEB)
Bobrovnikova, E.Y.; Vavasis, S.A. [Cornell Univ., Ithaca, NY (United States)
1996-12-31
A weighted least-squares problem with a very ill-conditioned weight matrix arises in many applications. Because of round-off errors, the standard conjugate gradient method for solving this system does not give the correct answer even after n iterations. In this paper we propose an iterative algorithm based on a new type of reorthogonalization that converges to the solution.
The Grid Method in Estimating the Path Length of a Moving Animal
Reddingius, J.; Schilstra, A.J.; Thomas, G.
1983-01-01
(1) The length of a path covered by a moving animal may be estimated by counting the number of times the animal crosses any line of a grid and applying a conversion factor. (2) Some factors are based on the expected distance through a randomly crossed square; another on the expected crossings of a
Least-squares model-based halftoning
Pappas, Thrasyvoulos N.; Neuhoff, David L.
1992-08-01
A least-squares model-based approach to digital halftoning is proposed. It exploits both a printer model and a model for visual perception. It attempts to produce an 'optimal' halftoned reproduction, by minimizing the squared error between the response of the cascade of the printer and visual models to the binary image and the response of the visual model to the original gray-scale image. Conventional methods, such as clustered ordered dither, use the properties of the eye only implicitly, and resist printer distortions at the expense of spatial and gray-scale resolution. In previous work we showed that our printer model can be used to modify error diffusion to account for printer distortions. The modified error diffusion algorithm has better spatial and gray-scale resolution than conventional techniques, but produces some well known artifacts and asymmetries because it does not make use of an explicit eye model. Least-squares model-based halftoning uses explicit eye models and relies on printer models that predict distortions and exploit them to increase, rather than decrease, both spatial and gray-scale resolution. We have shown that the one-dimensional least-squares problem, in which each row or column of the image is halftoned independently, can be implemented with the Viterbi's algorithm. Unfortunately, no closed form solution can be found in two dimensions. The two-dimensional least squares solution is obtained by iterative techniques. Experiments show that least-squares model-based halftoning produces more gray levels and better spatial resolution than conventional techniques. We also show that the least- squares approach eliminates the problems associated with error diffusion. Model-based halftoning can be especially useful in transmission of high quality documents using high fidelity gray-scale image encoders. As we have shown, in such cases halftoning can be performed at the receiver, just before printing. Apart from coding efficiency, this approach
Mathematical Construction of Magic Squares Utilizing Base-N Arithmetic
O'Brien, Thomas D.
2006-01-01
Magic squares have been of interest as a source of recreation for over 4,500 years. A magic square consists of a square array of n[squared] positive and distinct integers arranged so that the sum of any column, row, or main diagonal is the same. In particular, an array of consecutive integers from 1 to n[squared] forming an nxn magic square is…
DiversePathsJ: diverse shortest paths for bioimage analysis.
Uhlmann, Virginie; Haubold, Carsten; Hamprecht, Fred A; Unser, Michael
2018-02-01
We introduce a formulation for the general task of finding diverse shortest paths between two end-points. Our approach is not linked to a specific biological problem and can be applied to a large variety of images thanks to its generic implementation as a user-friendly ImageJ/Fiji plugin. It relies on the introduction of additional layers in a Viterbi path graph, which requires slight modifications to the standard Viterbi algorithm rules. This layered graph construction allows for the specification of various constraints imposing diversity between solutions. The software allows obtaining a collection of diverse shortest paths under some user-defined constraints through a convenient and user-friendly interface. It can be used alone or be integrated into larger image analysis pipelines. http://bigwww.epfl.ch/algorithms/diversepathsj. michael.unser@epfl.ch or fred.hamprecht@iwr.uni-heidelberg.de. Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.
Spreading paths in partially observed social networks
Onnela, Jukka-Pekka; Christakis, Nicholas A.
2012-03-01
Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using static, structurally realistic social networks as platforms for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Although partial observation inflates the length of the shortest path, the stochastic nature of the spreading process also frequently derails the dynamic path from the shortest path. We find that the partially observed shortest path does not necessarily give an inflated estimate of the length of the process path; in fact, partial observation may, counterintuitively, make the path seem shorter than it actually is.
Spreading paths in partially observed social networks.
Onnela, Jukka-Pekka; Christakis, Nicholas A
2012-03-01
Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a network, and the other is the typical constraint of only partially observing a network. Using static, structurally realistic social networks as platforms for simulations, we juxtapose three distinct paths: (1) the stochastic path taken by a simulated spreading process from source to target; (2) the topologically shortest path in the fully observed network, and hence the single most likely stochastic path, between the two nodes; and (3) the topologically shortest path in a partially observed network. In a sampled network, how closely does the partially observed shortest path (3) emulate the unobserved spreading path (1)? Although partial observation inflates the length of the shortest path, the stochastic nature of the spreading process also frequently derails the dynamic path from the shortest path. We find that the partially observed shortest path does not necessarily give an inflated estimate of the length of the process path; in fact, partial observation may, counterintuitively, make the path seem shorter than it actually is.
Regularization by truncated total least squares
DEFF Research Database (Denmark)
Hansen, Per Christian; Fierro, R.D; Golub, G.H
1997-01-01
The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use...... schemes for relativistic hydrodynamical equations. Such an approximate Riemann solver is presented in this paper which treats all waves emanating from an initial discontinuity as themselves discontinuous. Therefore, jump conditions for shocks are approximately used for rarefaction waves. The solver...... is easy to implement in a Godunov scheme and converges rapidly for relativistic hydrodynamics. The fast convergence of the solver indicates the potential of a higher performance of a Godunov scheme in which the solver is used....
Total least squares for anomalous change detection
Theiler, James; Matsekh, Anna M.
2010-04-01
A family of subtraction-based anomalous change detection algorithms is derived from a total least squares (TLSQ) framework. This provides an alternative to the well-known chronochrome algorithm, which is derived from ordinary least squares. In both cases, the most anomalous changes are identified with the pixels that exhibit the largest residuals with respect to the regression of the two images against each other. The family of TLSQbased anomalous change detectors is shown to be equivalent to the subspace RX formulation for straight anomaly detection, but applied to the stacked space. However, this family is not invariant to linear coordinate transforms. On the other hand, whitened TLSQ is coordinate invariant, and special cases of it are equivalent to canonical correlation analysis and optimized covariance equalization. What whitened TLSQ offers is a generalization of these algorithms with the potential for better performance.
Constrained least squares regularization in PET
International Nuclear Information System (INIS)
Choudhury, K.R.; O'Sullivan, F.O.
1996-01-01
Standard reconstruction methods used in tomography produce images with undesirable negative artifacts in background and in areas of high local contrast. While sophisticated statistical reconstruction methods can be devised to correct for these artifacts, their computational implementation is excessive for routine operational use. This work describes a technique for rapid computation of approximate constrained least squares regularization estimates. The unique feature of the approach is that it involves no iterative projection or backprojection steps. This contrasts with the familiar computationally intensive algorithms based on algebraic reconstruction (ART) or expectation-maximization (EM) methods. Experimentation with the new approach for deconvolution and mixture analysis shows that the root mean square error quality of estimators based on the proposed algorithm matches and usually dominates that of more elaborate maximum likelihood, at a fraction of the computational effort
Classical square-plus-triangle well fluid
International Nuclear Information System (INIS)
Boghdadi, M.
1984-01-01
A simplified model for the intermolecular-potential function which consists of a hard core and a square-plus-triangle well is proposed. The square width is taken to be lambda 1 -1 and the triangle width is lambda 2 -lambda 1 , where the diameter of the molecules is assumed to be epsilon. Under the restriction that the area under the potential well should be equal to 0.5epsilon, which has its own reason, it is shown that the appropriate choice of lambda 1 and lambda 2 that best mimics the Lennard-Jones (LJ) cut-off results is 1.15 and 1.85 respectively. With this choice for lambda 1 and lambda 2 , the proposed model is effective and satisfactory
Dancoff Correction in Square and Hexagonal Lattices
Energy Technology Data Exchange (ETDEWEB)
Carlvik, I
1966-11-15
This report presents the results of a series of calculations of Dancoff corrections for square and hexagonal rod lattices. The tables cover a wide range of volume ratios and moderator cross sections. The results were utilized for checking the approximative formula of Sauer and also the modification of Bonalumi to Sauer's formula. The modified formula calculates the Dancoff correction with an accuracy of 0.01 - 0.02 in cases of practical interest. Calculations have also been performed on square lattices with an empty gap surrounding the rods. The results demonstrate the error involved in treating this kind of geometry by means of homogenizing the gap and the moderator. The calculations were made on the Ferranti Mercury computer of AB Atomenergi before it was closed down. Since then FORTRAN routines for Dancoff corrections have been written, and a subroutine DASQHE is included in the report.
Elastic least-squares reverse time migration
Feng, Zongcai; Schuster, Gerard T.
2016-01-01
Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.
Elastic least-squares reverse time migration
Feng, Zongcai
2016-09-06
Elastic least-squares reverse time migration (LSRTM) is used to invert synthetic particle-velocity data and crosswell pressure field data. The migration images consist of both the P- and Svelocity perturbation images. Numerical tests on synthetic and field data illustrate the advantages of elastic LSRTM over elastic reverse time migration (RTM). In addition, elastic LSRTM images are better focused and have better reflector continuity than do the acoustic LSRTM images.
Natural convective heat transfer from square cylinder
Energy Technology Data Exchange (ETDEWEB)
Novomestský, Marcel, E-mail: marcel.novomestsky@fstroj.uniza.sk; Smatanová, Helena, E-mail: helena.smatanova@fstroj.uniza.sk; Kapjor, Andrej, E-mail: andrej.kapjor@fstroj.uniza.sk [University of Žilina, Faculty of Mechanical Engineering, Department of Power Engineering, Univerzitná 1, 010 26 Žilina (Slovakia)
2016-06-30
This article is concerned with natural convective heat transfer from square cylinder mounted on a plane adiabatic base, the cylinders having an exposed cylinder surface according to different horizontal angle. The cylinder receives heat from a radiating heater which results in a buoyant flow. There are many industrial applications, including refrigeration, ventilation and the cooling of electrical components, for which the present study may be applicable.
Least Squares Problems with Absolute Quadratic Constraints
Directory of Open Access Journals (Sweden)
R. Schöne
2012-01-01
Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
RCS Leak Rate Calculation with High Order Least Squares Method
International Nuclear Information System (INIS)
Lee, Jeong Hun; Kang, Young Kyu; Kim, Yang Ki
2010-01-01
As a part of action items for Application of Leak before Break(LBB), RCS Leak Rate Calculation Program is upgraded in Kori unit 3 and 4. For real time monitoring of operators, periodic calculation is needed and corresponding noise reduction scheme is used. This kind of study was issued in Korea, so there have upgraded and used real time RCS Leak Rate Calculation Program in UCN unit 3 and 4 and YGN unit 1 and 2. For reduction of the noise in signals, Linear Regression Method was used in those programs. Linear Regression Method is powerful method for noise reduction. But the system is not static with some alternative flow paths and this makes mixed trend patterns of input signal values. In this condition, the trend of signal and average of Linear Regression are not entirely same pattern. In this study, high order Least squares Method is used to follow the trend of signal and the order of calculation is rearranged. The result of calculation makes reasonable trend and the procedure is physically consistence
A least-squares computational ''tool kit''
International Nuclear Information System (INIS)
Smith, D.L.
1993-04-01
The information assembled in this report is intended to offer a useful computational ''tool kit'' to individuals who are interested in a variety of practical applications for the least-squares method of parameter estimation. The fundamental principles of Bayesian analysis are outlined first and these are applied to development of both the simple and the generalized least-squares conditions. Formal solutions that satisfy these conditions are given subsequently. Their application to both linear and non-linear problems is described in detail. Numerical procedures required to implement these formal solutions are discussed and two utility computer algorithms are offered for this purpose (codes LSIOD and GLSIOD written in FORTRAN). Some simple, easily understood examples are included to illustrate the use of these algorithms. Several related topics are then addressed, including the generation of covariance matrices, the role of iteration in applications of least-squares procedures, the effects of numerical precision and an approach that can be pursued in developing data analysis packages that are directed toward special applications
Advancing Astrophysics with the Square Kilometre Array
Fender, Rob; Govoni, Federica; Green, Jimi; Hoare, Melvin; Jarvis, Matt; Johnston-Hollitt, Melanie; Keane, Evan; Koopmans, Leon; Kramer, Michael; Maartens, Roy; Macquart, Jean-Pierre; Mellema, Garrelt; Oosterloo, Tom; Prandoni, Isabella; Pritchard, Jonathan; Santos, Mario; Seymour, Nick; Stappers, Ben; Staveley-Smith, Lister; Tian, Wen Wu; Umana, Grazia; Wagg, Jeff; Bourke, Tyler L; AASKA14
2015-01-01
In 2014 it was 10 years since the publication of the comprehensive ‘Science with the Square Kilometre Array’ book and 15 years since the first such volume appeared in 1999. In that time numerous and unexpected advances have been made in the fields of astronomy and physics relevant to the capabilities of the Square Kilometre Array (SKA). The SKA itself progressed from an idea to a developing reality with a baselined Phase 1 design (SKA1) and construction planned from 2017. To facilitate the publication of a new, updated science book, which will be relevant to the current astrophysical context, the meeting "Advancing Astrophysics with the Square Kilometre Array" was held in Giardina Naxos, Sicily. Articles were solicited from the community for that meeting to document the scientific advances enabled by the first phase of the SKA and those pertaining to future SKA deployments, with expected gains of 5 times the Phase 1 sensitivity below 350 MHz, about 10 times the Phase 1 sensitivity above 350 MHz and with f...
International Nuclear Information System (INIS)
Qin, Shitong; Li, Renxian; Yang, Ruiping; Ding, Chunying
2017-01-01
The interaction of an axicon-generated vector Bessel beam (AGVBB) with a homogeneous sphere is investigated in the framework of generalized Lorenz-Mie theory (GLMT). An analytical expression of beam shape coefficients (BSCs) is derived using angular spectrum decomposition method (ASDM), and the scattering coefficients are expanded using Debye series (DSE) in order to isolate the contribution of single scattering process. The internal and near-surface electric fields are numerically analyzed, and the effect of beam location, polarization, order of beam, half-cone angle, and scattering process (namely Debye mode p) are mainly discussed. Numerical results show that a curve formed by extreme peaks can be observed, and the electric fields can be locally enhanced after the interaction of AGVBBs with the particle. Internal and near-surface fields, especially its local enhancement, are very sensitive to the beam parameters, including polarization, order, half-cone angle, etc. The internal fields can also be enhanced by various scattering process (or Debye mode p). Such results have important applications in various fields, including particle sizing, optical tweezers, etc. - Highlights: • Debye series is employed to the analysis of internal and near-surface fields for a sphere illuminated by a vector Bessel beam. • Analytical expressions of BSCs for vector Bessel beams with selected polarizations are derived using ASDM. • The local enhancement of internal and near-surface fields is investigated. • The polarization, order, half-cone angle of the beam affect the local enhancement. • The local enhancement of internal fields is sensitive to the scattering process.
Directory of Open Access Journals (Sweden)
CoÅkun Deniz
Full Text Available Common recipe for the Lengthening Pendulum (LP involves some change of variables to give a relationship with the Besselâs equation. In this work, semiclassical MAF (Modified Airy Function solution of the LP is being obtained by first transforming the related Besselâs equation into the normal form via the suggested change of independent variable just as one of our recent work regarding the JWKB solution of the LP in (Deniz, 2017. MAF approximation of the first order Bessel Functions (Î½Â =Â 1 of both type along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (Î½Â =Â 0 and 2 by the recursion relations. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is small, MAF solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined via the use of MAF applicability criterion given in the literature. As a result, the semiclassical MAF method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully just as our previous work regarding the JWKB solution of the LP. Interestingly, we have very accurate results in the entire domain except for xâ0. PACS: 02.30.Hq, 02.30.Mv, 03.65.Sq, 03.65.-w, 45.05.+x, 45.10.-b, Keywords: Method of Modified Airy Function (MAF, Semiclassical approximation, Linear differential equations, Initial value problems, The lengthening pendulum
International Nuclear Information System (INIS)
Qin Hong; Phillips, Cynthia K.; Davidson, Ronald C.
2007-01-01
The susceptibility tensor of a hot, magnetized plasma is conventionally expressed in terms of infinite sums of products of Bessel functions. For applications where the particle's gyroradius is larger than the wavelength, such as alpha particle dynamics interacting with lower-hybrid waves, and the focusing of charged particle beams using a solenoidal field, the infinite sums converge slowly. In this paper, a new derivation of the plasma susceptibility tensor is presented which exploits a symmetry in the particle's orbit to simplify the integration along the unperturbed trajectories. As a consequence, the infinite sums appearing in the conventional expression are replaced by definite double integrals over one gyroperiod, and the cyclotron resonances of all orders are captured by a single term. Furthermore, the double integrals can be carried out and expressed in terms of Bessel functions of complex order, in agreement with expressions deduced previously using the Newburger sum rule. From this new formulation, it is straightforward to derive the asymptotic form of the full hot plasma susceptibility tensor for a gyrotropic but otherwise arbitrary plasma distribution in the large gyroradius limit. These results are of more general importance in the numerical evaluation of the plasma susceptibility tensor. Instead of using the infinite sums occurring in the conventional expression, it is only necessary to evaluate the Bessel functions once according to the new expression, which has significant advantages, especially when the particle's gyroradius is large and the conventional infinite sums converge slowly. Depending on the size of the gyroradius, the computational saving enabled by this representation can be several orders-of-magnitude
Stochastic control with rough paths
International Nuclear Information System (INIS)
Diehl, Joscha; Friz, Peter K.; Gassiat, Paul
2017-01-01
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Stochastic control with rough paths
Energy Technology Data Exchange (ETDEWEB)
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Path modeling and process control
DEFF Research Database (Denmark)
Høskuldsson, Agnar; Rodionova, O.; Pomerantsev, A.
2007-01-01
and having three or more stages. The methods are applied to a process control of a multi-stage production process having 25 variables and one output variable. When moving along the process, variables change their roles. It is shown how the methods of path modeling can be applied to estimate variables...... be performed regarding the foreseeable output property y, and with respect to an admissible range of correcting actions for the parameters of the next stage. In this paper the basic principles of path modeling is presented. The mathematics is presented for processes having only one stage, having two stages...... of the next stage with the purpose of obtaining optimal or almost optimal quality of the output variable. An important aspect of the methods presented is the possibility of extensive graphic analysis of data that can provide the engineer with a detailed view of the multi-variate variation in data....
Hierarchical path planning and control of a small fixed-wing UAV: Theory and experimental validation
Jung, Dongwon
2007-12-01
Recently there has been a tremendous growth of research emphasizing control of unmanned aerial vehicles (UAVs) either in isolation or in teams. As a matter of fact, UAVs increasingly find their way into military and law enforcement applications (e.g., reconnaissance, remote delivery of urgent equipment/material, resource assessment, environmental monitoring, battlefield monitoring, ordnance delivery, etc.). This trend will continue in the future, as UAVs are poised to replace the human-in-the-loop during dangerous missions. Civilian applications of UAVs are also envisioned such as crop dusting, geological surveying, search and rescue operations, etc. In this thesis we propose a new online multiresolution path planning algorithm for a small UAV with limited on-board computational resources. The proposed approach assumes that the UAV has detailed information of the environment and the obstacles only in its vicinity. Information about far-away obstacles is also available, albeit less accurately. The proposed algorithm uses the fast lifting wavelet transform (FLWT) to get a multiresolution cell decomposition of the environment, whose dimension is commensurate to the on-board computational resources. A topological graph representation of the multiresolution cell decomposition is constructed efficiently, directly from the approximation and detail wavelet coefficients. Dynamic path planning is sequentially executed for an optimal path using the A* algorithm over the resulting graph. The proposed path planning algorithm is implemented on-line on a small autopilot. Comparisons with the standard D*-lite algorithm are also presented. We also investigate the problem of generating a smooth, planar reference path from a discrete optimal path. Upon the optimal path being represented as a sequence of cells in square geometry, we derive a smooth B-spline path that is constrained inside a channel that is induced by the geometry of the cells. To this end, a constrained optimization
Factorization-algebraization-path integration
International Nuclear Information System (INIS)
Inomata, A.; Wilson, R.
1986-01-01
The authors review the method of factorization proposed by Schroedinger of a quantum mechanical second-order linear differential equation into a product of two first-order differential operators, often referred to as ladder operators, as well as the modifications made to Schroedinger's method by Infeld and Hull. They then review the group theoretical treatments proposed by Miller of the Schroedinger-Infeld-Hull factorizations and go on to demonstrate the application of dynamical symmetry to path integral calculations. 30 references
CERN. Geneva
2017-01-01
Join the path of code linting and discover how it can help you reach higher levels of programming enlightenment. Today we will cover how to embrace code linters to offload cognitive strain on preserving style standards in your code base as well as avoiding error-prone constructs. Additionally, I will show you the journey ahead for integrating several code linters in the programming tools your already use with very little effort.
Career path for operations personnel
International Nuclear Information System (INIS)
Asher, J.A.
1985-01-01
This paper explains how selected personnel can now obtain a Bachelor of Science degree in Physics with a Nuclear Power Operations option. The program went into effect the Fall of 1984. Another program was worked out in 1982 whereby students attending the Nuclear Operators Training Program could obtain an Associates of Science degree in Mechanical Engineering Technology at the end of two years of study. This paper presents tables and charts which describe these programs and outline the career path for operators
Conditionally solvable path integral problems
International Nuclear Information System (INIS)
Grosche, C.
1995-05-01
Some specific conditionally exactly solvable potentials are discussed within the path integral formalism. They generalize the usually known potentials by the incorporation of a fractional power behaviour and strongly anharmonic terms. We find four different kinds of such potentials, the first is related to the Coulomb potential, the second is an anharmonic confinement potential, and the third and the fourth are related to the Manning-Rosen potential. (orig.)
Path integrals in curvilinear coordinates
International Nuclear Information System (INIS)
Prokhorov, L.V.
1984-01-01
Integration limits are studied for presenting the path integral curvilinear coordinates. For spherical (and topoloqically equivalent) coordinates it is shown that in formulas involving classical action in the exponent integration over all variables should be carried out within infinite limits. Another peculiarity is associated with appearance of the operator q which provides a complete definition of the wave functions out of the physical region. arguments are given upporting the validity of the cited statament in the general case
Lax-pair operators for squared-sum and squared-difference eigenfunctions
International Nuclear Information System (INIS)
Ichikawa, Yoshihiko; Iino, Kazuhiro.
1984-10-01
Inter-relationship between various representations of the inverse scattering transformation is established by examining eigenfunctions of Lax-pair operators of the sine-Gordon equation and the modified Korteweg-de Vries equation. In particular, it is shown explicitly that there exists Lax-pair operators for the squared-sum and squared-difference eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation. (author)
International Nuclear Information System (INIS)
Exner, P.; Kolerov, G.I.
1981-01-01
Properties of the subset of polygonal paths in the Hilbert space H of paths referring to a d-dimensional quantum-mechanical system are examined. Using the reproduction kernel technique we prove that each element of H is approximated by polygonal paths uniformly with respect to the ''norm'' of time-interval partitions. This result will be applied in the second part of the present paper to prove consistency of the uniform polygonal-path extension of the Feynman maps [ru
Path Integrals in Quantum Mechanics
International Nuclear Information System (INIS)
Chetouani, L
2005-01-01
By treating path integrals the author, in this book, places at the disposal of the reader a modern tool for the comprehension of standard quantum mechanics. Thus the most important applications, such as the tunnel effect, the diffusion matrix, etc, are presented from an original point of view on the action S of classical mechanics while having it play a central role in quantum mechanics. What also emerges is that the path integral describes these applications more richly than are described traditionally by differential equations, and consequently explains them more fully. The book is certainly of high quality in all aspects: original in presentation, rigorous in the demonstrations, judicious in the choice of exercises and, finally, modern, for example in the treatment of the tunnel effect by the method of instantons. Moreover, the correspondence that exists between classical and quantum mechanics is well underlined. I thus highly recommend this book (the French version being already available) to those who wish to familiarize themselves with formulation by path integrals. They will find, in addition, interesting topics suitable for exploring further. (book review)
Nonperturbative path integral expansion II
International Nuclear Information System (INIS)
Kaiser, H.J.
1976-05-01
The Feynman path integral representation of the 2-point function for a self-interacting Bose field is investigated using an expansion ('Path Integral Expansion', PIE) of the exponential of the kinetic term of the Lagrangian. This leads to a series - illustrated by a graph scheme - involving successively a coupling of more and more points of the lattice space commonly employed in the evaluation of path integrals. The values of the individual PIE graphs depend of course on the lattice constant. Two methods - Pade approximation and Borel-type extrapolation - are proposed to extract information about the continuum limit from a finite-order PIE. A more flexible PIE is possible by expanding besides the kinetic term a suitably chosen part of the interaction term too. In particular, if the co-expanded part is a mass term the calculation becomes only slightly more complicated than in the original formulation and the appearance of the graph scheme is unchanged. A significant reduction of the number of graphs and an improvement of the convergence of the PIE can be achieved by performing certain sums over an infinity of graph elements. (author)
Distribution definition of path integrals
International Nuclear Information System (INIS)
Kerler, W.
1979-01-01
By starting from quantum mechanics it turns out that a rather general definition of quantum functional integrals can be given which is based on distribution theory. It applies also to curved space and provides clear rules for non-linear transformations. The refinements necessary in usual definitions of path integrals are pointed out. Since the quantum nature requires special care with time sequences, it is not the classical phase space which occurs in the phase-space form of the path integral. Feynman's configuration-space form only applies to a highly specialized situation, and therefore is not a very advantageous starting point for general investigations. It is shown that the commonly used substitutions of variables do not properly account for quantum effects. The relation to the traditional ordering problem is clarified. The distribution formulation has allowed to treat constrained systems directly at the quantum level, to complete the path integral formulation of the equivalence theorem, and to define functional integrals also for space translation after the transition to fields. (orig.)