Modulation depth of Michelson interferometer with Gaussian beam.

Science.gov (United States)

Välikylä, Tuomas; Kauppinen, Jyrki

2011-12-20

Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.

Beam propagation factor and Kurtosis parameter of different types of flattened Gaussian beams

International Nuclear Information System (INIS)

Saghafi, S.; Forbes, G.W.; Sheppard, C.J.R.

1999-01-01

Full text: The beam propagation factor, M 2 and the Kurtosis parameter, K, are considered for three different models of flattened Gaussian beams. Plots of M 2 versus K reveal similarities between these flattened beams. In fact, for this type of beam, it is possible to predict K from the value of M 2 We also determine the values of the parameters that characterize those different types of flattened Gaussian beam modes for any given value of M 2 . Finally, once K and M 2 have been measured for any flattened beam, these equations can be used to determine the closeness of this real beam to members of the three well-known classes of flattened beams. This can facilitate the analyses of the beam and its propagation. Copyright (1999) Australian Optical Society

Time-domain least-squares migration using the Gaussian beam summation method

Science.gov (United States)

Yang, Jidong; Zhu, Hejun; McMechan, George; Yue, Yubo

2018-04-01

With a finite recording aperture, a limited source spectrum and unbalanced illumination, traditional imaging methods are insufficient to generate satisfactory depth profiles with high resolution and high amplitude fidelity. This is because traditional migration uses the adjoint operator of the forward modeling rather than the inverse operator. We propose a least-squares migration approach based on the time-domain Gaussian beam summation, which helps to balance subsurface illumination and improve image resolution. Based on the Born approximation for the isotropic acoustic wave equation, we derive a linear time-domain Gaussian beam modeling operator, which significantly reduces computational costs in comparison with the spectral method. Then, we formulate the corresponding adjoint Gaussian beam migration, as the gradient of an L2-norm waveform misfit function. An L1-norm regularization is introduced to the inversion to enhance the robustness of least-squares migration, and an approximated diagonal Hessian is used as a preconditioner to speed convergence. Synthetic and field data examples demonstrate that the proposed approach improves imaging resolution and amplitude fidelity in comparison with traditional Gaussian beam migration.

Hermite-Gaussian beams with self-forming spiral phase distribution

Science.gov (United States)

Zinchik, Alexander A.; Muzychenko, Yana B.

2014-05-01

Spiral laser beams is a family of laser beams that preserve the structural stability up to scale and rotate with the propagation. Properties of spiral beams are of practical interest for laser technology, medicine and biotechnology. Researchers use a spiral beams for movement and manipulation of microparticles. Spiral beams have a complicated phase distribution in cross section. This paper describes the results of analytical and computer simulation of Hermite-Gaussian beams with self-forming spiral phase distribution. In the simulation used a laser beam consisting of the sum of the two modes HG TEMnm and TEMn1m1. The coefficients n1, n, m1, m were varied. Additional phase depending from the coefficients n, m, m1, n1 imposed on the resulting beam. As a result, formed the Hermite Gaussian beam phase distribution which takes the form of a spiral in the process of distribution. For modeling was used VirtualLab 5.0 (manufacturer LightTrans GmbH).

A comparison on the propagation characteristics of focused Gaussian beam and fundamental Gaussian beam in vacuum

International Nuclear Information System (INIS)

Liu Shixiong; Guo Hong; Liu Mingwei; Wu Guohua

2004-01-01

Propagation characteristics of focused Gaussian beam (FoGB) and fundamental Gaussian beam (FuGB) propagating in vacuum are investigated. Based on the Fourier transform and the angular spectral analysis, the transverse component and the second-order approximate longitudinal component of the electric field are obtained in the paraxial approximation. The electric field components, the phase velocity and the group velocity of FoGB are compared with those of FuGB. The spot size of FoGB is also discussed

Ultrasonic Beam Propagation in Highly Anisotropic Materials Simulated by Multi-Gaussian Beams

International Nuclear Information System (INIS)

Jeong, Hyun Jo; Schmerr, Lester W.

2007-01-01

The necessity of nondestructively inspecting fiber-reinforced composites, austenitic steels, and other inherently anisotropic materials has stimulated considerable interest in developing beam models for anisotropic media. The properties of slowness surface play key role in the beam models based on the paraxial approximation. In this paper, we apply a modular multi-Gaussian beam (MMGB) model to study the effects of material anisotropy on ultrasonic beam profile. It is shown that the anisotropic effects of beam skew and excess beam divergence enter into the MMGB model through parameters defining the slope and curvature of the slowness surface. The overall beam profile is found when the quasi longitudinal (qL) beam propagates in the symmetry plane of a transversely isotropic gr/ep composite. Simulation results are presented to illustrate the effects of these parameters on ultrasonic beam diffraction and beam skew. The MMGB calculations are also checked by comparing the anisotropy factor and beam skew angle with other analytical solutions

Coherence of the vortex Bessel-Gaussian beam in turbulent atmosphere

Science.gov (United States)

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.

Integral momenta of vortex Bessel-Gaussian beams in turbulent atmosphere.

Science.gov (United States)

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.

Experimental Results and Numerical Simulation of the Target RCS using Gaussian Beam Summation Method

Directory of Open Access Journals (Sweden)

Ghanmi Helmi

2018-05-01

Full Text Available This paper presents a numerical and experimental study of Radar Cross Section (RCS of radar targets using Gaussian Beam Summation (GBS method. The purpose GBS method has several advantages over ray method, mainly on the caustic problem. To evaluate the performance of the chosen method, we started the analysis of the RCS using Gaussian Beam Summation (GBS and Gaussian Beam Launching (GBL, the asymptotic models Physical Optic (PO, Geometrical Theory of Diffraction (GTD and the rigorous Method of Moment (MoM. Then, we showed the experimental validation of the numerical results using experimental measurements which have been executed in the anechoic chamber of Lab-STICC at ENSTA Bretagne. The numerical and experimental results of the RCS are studied and given as a function of various parameters: polarization type, target size, Gaussian beams number and Gaussian beams width.

Polarization coupling of vector Bessel–Gaussian beams

International Nuclear Information System (INIS)

Takeuchi, Ryushi; Kozawa, Yuichi; Sato, Shunichi

2013-01-01

We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO 4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation. (paper)

Coincidence Imaging and interference with coherent Gaussian beams

Institute of Scientific and Technical Information of China (English)

CAI Yang-jian; ZHU Shi-yao

2006-01-01

we present a theoretical study of coincidence imaging and interference with coherent Gaussian beams The equations for the coincidence image formation and interference fringes are derived,from which it is clear that the imaging is due to the corresponding focusing in the two paths .The quality and visibility of the images and fringes can be high simultaneously.The nature of the coincidence imaging and interference between quantum entangled photon pairs and coherent Gaussian beams are different .The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence,a classical nature,while that with entangled photon pairs is due to the amplitude correlation a quantum nature.

Unperturbed Schelling Segregation in Two or Three Dimensions

Science.gov (United States)

Barmpalias, George; Elwes, Richard; Lewis-Pye, Andrew

2016-09-01

Schelling's models of segregation, first described in 1969 (Am Econ Rev 59:488-493, 1969) are among the best known models of self-organising behaviour. Their original purpose was to identify mechanisms of urban racial segregation. But his models form part of a family which arises in statistical mechanics, neural networks, social science, and beyond, where populations of agents interact on networks. Despite extensive study, unperturbed Schelling models have largely resisted rigorous analysis, prior results generally focusing on variants in which noise is introduced into the dynamics, the resulting system being amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory (Young in Individual strategy and social structure: an evolutionary theory of institutions, Princeton University Press, Princeton, 1998). A series of recent papers (Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012); Barmpalias et al. in: 55th annual IEEE symposium on foundations of computer science, Philadelphia, 2014, J Stat Phys 158:806-852, 2015), has seen the first rigorous analyses of 1-dimensional unperturbed Schelling models, in an asymptotic framework largely unknown in statistical mechanics. Here we provide the first such analysis of 2- and 3-dimensional unperturbed models, establishing most of the phase diagram, and answering a challenge from Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012).

Off-Axis Gaussian Beams with Random Displacement in Atmospheric Turbulence

Directory of Open Access Journals (Sweden)

Yahya Baykal

2006-10-01

Full Text Available Our recent work in which we study the propagation of the general Hermite-sinusoidal-Gaussian laser beams in wireless broadband access telecommunication systems is elaborated in this paper to cover the special case of an off-axis Gaussian beam. We mainly investigate the propagation characteristics in atmospheric turbulence of an off-axis Gaussian beam possessing Gaussian distributed random displacement parameters. Our interest is to search for different types of laser beams that will improve the performance of a wireless broadband access system when atmospheric turbulence is considered. Our formulation is based on the basic solution of the second order mutual coherence function evaluated at the receiver plane. For fixed turbulence strength, the coherence length calculated at the receiver plane is found to decrease as the variance of the random displacement is increased. It is shown that as the turbulence becomes stronger, coherence lengths due to off-axis Gaussian beams tend to approach the same value, irrespective of the variance of the random displacement. As expected, the beam spreading is found to be pronounced for larger variance of displacement parameter. Average intensity profiles when atmospheric turbulence is present are plotted for different values of the variance of the random displacement parameter of the off-axis Gaussian beam.

Mean intensity of the fundamental Bessel-Gaussian beam in turbulent atmosphere

Science.gov (United States)

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.

Coherence degree of the fundamental Bessel-Gaussian beam in turbulent atmosphere

Science.gov (United States)

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.

Random source generating far field with elliptical flat-topped beam profile

International Nuclear Information System (INIS)

Zhang, Yongtao; Cai, Yangjian

2014-01-01

Circular and rectangular multi-Gaussian Schell-model (MGSM) sources which generate far fields with circular and rectangular flat-topped beam profiles were introduced just recently (Sahin and Korotkova 2012 Opt. Lett. 37 2970; Korotkova 2014 Opt. Lett. 39 64). In this paper, a random source named an elliptical MGSM source is introduced. An analytical expression for the propagation factor of an elliptical MGSM beam is derived. Furthermore, an analytical propagation formula for an elliptical MGSM beam passing through a stigmatic ABCD optical system is derived, and its propagation properties in free space are studied. It is interesting to find that an elliptical MGSM source generates a far field with an elliptical flat-topped beam profile, being qualitatively different from that of circular and rectangular MGSM sources. The ellipticity and the flatness of the elliptical flat-topped beam profile in the far field are determined by the initial coherence widths and the beam index, respectively. (paper)

Frequency Characteristics of Surface Wave Generated by Single-Line Pulsed Laser Beam with Two Kinds of Spatial Energy Profile Models: Gaussian and Square-Like

Energy Technology Data Exchange (ETDEWEB)

Seo, Ho Geon; Kim, Myung Hwan; Choi, Sung Ho; Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)

2012-08-15

Using a single-line pulsed laser beam is well known as a useful noncontact method to generate a directional surface acoustic wave. In this method, different laser beam energy profiles produce different waveforms and frequency characteristics. In this paper, we considered two typical kinds of laser beam energy profiles, Gaussian and square-like, to find out a difference in the frequency characteristics. To achieve this, mathematical models were proposed first for Gaussian laser beam profile and square-like respectively, both of which depended on the laser beam width. To verify the theoretical models, experimental setups with a cylindrical lens and a line-slit mask were respectively designed to produce a line laser beam with Gaussian spatial energy profile and square-like. The frequency responses of the theoretical models showed good agreement with experimental results in terms of the existence of harmonic frequency components and the shift of the first peak frequencies to low.

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.

Learning from Schelling's Strategy of Conflict

OpenAIRE

Roger B. Myerson

2009-01-01

Thomas Schelling's Strategy of Conflict is a masterpiece that should be recognized as one of the most important and influential books in social theory. This paper reviews some of the important ideas in Strategy of Conflict and considers some of the broader impact that this book has had on game theory, economics, and social theory. By his emphasis on the critical importance of information and commitment in strategic dynamics, Schelling played a vital role in stimulating the development of nonc...

Influence of Turbulent Atmosphere on Polarization Properties of Stochastic Electromagnetic Pulsed Beams

International Nuclear Information System (INIS)

Ding Chao-Liang; Zhao Zhi-Guo; Li Xiao-Feng; Pan Liu-Zhan; Yuan Xiao

2011-01-01

Using the coherence theory of non-stationary fields and the characterization of stochastic electromagnetic pulsed beams, the analytical expression for the spectral degree of polarization of stochastic electromagnetic Gaussian Schell-model pulsed (GSMP) beams in turbulent atmosphere is derived and is used to study the polarization properties of stochastic electromagnetic GSMP beams propagating through turbulent atmosphere. The results of numerical calculation are given to illustrate the dependence of spectral degree of polarization on the pulse frequency, refraction index structure constant and spatial correlation length. It is shown that, compared with free-space case, in turbulent atmosphere propagation there are two positions at which the on-axis spectral degree of polarization P is equal to zero. The position change depends on the pulse frequency, refraction index structure constant and spatial correlation length. (fundamental areas of phenomenology(including applications))

Propagation of Gaussian Beams through Active GRIN Materials

International Nuclear Information System (INIS)

Gomez-Varela, A I; Flores-Arias, M T; Bao-Varela, C; Gomez-Reino, C; De la Fuente, X

2011-01-01

We discussed light propagation through an active GRIN material that exhibits loss or gain. Effects of gain or loss in GRIN materials can be phenomenologically taken into account by using a complex refractive index in the wave equation. This work examines the implication of using a complex refractive index on light propagation in an active GRIN material illuminated by a non-uniform monochromatic wave described by a Gaussian beam. We analyze how a Gaussian beam is propagated through the active material in order to characterize it by the beam parameters and the transverse irradiance distribution.

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.

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.

Propagation of flat-topped multi-Gaussian beams through a double-lens system with apertures.

Science.gov (United States)

Gao, Yanqi; Zhu, Baoqiang; Liu, Daizhong; Lin, Zunqi

2009-07-20

A general model for different apertures and flat-topped laser beams based on the multi-Gaussian function is developed. The general analytical expression for the propagation of a flat-topped beam through a general double-lens system with apertures is derived using the above model. Then, the propagation characteristics of the flat-topped beam through a spatial filter are investigated by using a simplified analytical expression. Based on the Fluence beam contrast and the Fill factor, the influences of a pinhole size on the propagation of the flat-topped multi-Gaussian beam (FMGB) through the spatial filter are illustrated. An analytical expression for the propagation of the FMGB through the spatial filter with a misaligned pinhole is presented, and the influences of the pinhole offset are evaluated.

Hermite-cosine-Gaussian laser beam and its propagation characteristics in turbulent atmosphere.

Science.gov (United States)

Eyyuboğlu, Halil Tanyer

2005-08-01

Hermite-cosine-Gaussian (HcosG) laser beams are studied. The source plane intensity of the HcosG beam is introduced and its dependence on the source parameters is examined. By application of the Fresnel diffraction integral, the average receiver intensity of HcosG beam is formulated for the case of propagation in turbulent atmosphere. The average receiver intensity is seen to reduce appropriately to various special cases. When traveling in turbulence, the HcosG beam initially experiences the merging of neighboring beam lobes, and then a TEM-type cosh-Gaussian beam is formed, temporarily leading to a plain cosh-Gaussian beam. Eventually a pure Gaussian beam results. The numerical evaluation of the normalized beam size along the propagation axis at selected mode indices indicates that relative spreading of higher-order HcosG beam modes is less than that of the lower-order counterparts. Consequently, it is possible at some propagation distances to capture more power by using higher-mode-indexed HcosG beams.

Propagation of truncated modified Laguerre-Gaussian beams

Science.gov (United States)

Deng, D.; Li, J.; Guo, Q.

2010-01-01

By expanding the circ function into a finite sum of complex Gaussian functions and applying the Collins formula, the propagation of hard-edge diffracted modified Laguerre-Gaussian beams (MLGBs) through a paraxial ABCD system is studied, and the approximate closed-form propagation expression of hard-edge diffracted MLGBs is obtained. The transverse intensity distribution of the MLGB carrying finite power can be characterized by a single bright and symmetric ring during propagation when the aperture radius is very large. Starting from the definition of the generalized truncated second-order moments, the beam quality factor of MLGBs through a hard-edged circular aperture is investigated in a cylindrical coordinate system, which turns out to be dependent on the truncated radius and the beam orders.

Theoretical and experimental study of Gaussian beam and mode propagation in over-dimensioned circular guides

International Nuclear Information System (INIS)

Crenn, J.P.

1984-06-01

A theoretical study of modes in circular hollow over-dimensioned waveguides is developed; it shows the interest of dielectric or weakly conducting wall guide use. An optical model computing the transmitted power of gaussian beams through these guides, for different types of walls, is established. The formulas obtained allow to optimize the guide and to adapt the beam. Applied to the EH 11 mode this optical model leads to new results. Systematical measurements of gaussian beam propagation in over-dimensioned guides are realised; they are concerned with beam power transmission, polarization, its structure and its radiation at the guide exit in function of the different characteristics of the beam and the guide [fr

Change in spatial coherence of light on refraction and on reflection.

Science.gov (United States)

Lahiri, Mayukh; Wolf, Emil

2013-06-01

A theory of refraction and reflection of partially coherent electromagnetic beams has been recently developed. In this paper, we apply it to study the change in spatial coherence caused by refraction and by reflection more fully. By considering a Gaussian Schell-model beam, we show that the change is, in general, dependent on the angle of incidence.

Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

Science.gov (United States)

Steely, Sidney L.

1993-01-01

The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

Gaussian beam diffraction in weakly anisotropic inhomogeneous media

Energy Technology Data Exchange (ETDEWEB)

Kravtsov, Yu.A., E-mail: kravtsov@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland); Space Research Institute, Russian Academy of Science, Moscow 117 997 (Russian Federation); Berczynski, P., E-mail: pawel.berczynski@ps.p [Institute of Physics, West Pomeranian University of Technology, Szczecin 70-310 (Poland); Bieg, B., E-mail: b.bieg@am.szczecin.p [Institute of Physics, Maritime University of Szczecin, Szczecin 70-500 (Poland)

2009-08-10

Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.

Gaussian beam diffraction in weakly anisotropic inhomogeneous media

International Nuclear Information System (INIS)

Kravtsov, Yu.A.; Berczynski, P.; Bieg, B.

2009-01-01

Combination of quasi-isotropic approximation (QIA) of geometric optics with paraxial complex geometric optics (PCGO) is suggested, which allows describing both diffraction and polarization evolution of Gaussian electromagnetic beams in weakly anisotropic inhomogeneous media. Combination QIA/PCGO reduces Maxwell equations to the system of the ordinary differential equations of the first order and radically simplifies solution of various problems, related to microwave plasma diagnostics, including plasma polarimetry, interferometry and refractometry in thermonuclear reactors. Efficiency of the method is demonstrated by the example of electromagnetic beam diffraction in a linear layer of magnetized plasma with parameters, modeling tokamak plasma in the project ITER.

Intra-cavity metamorphosis of a Gaussian beam to flat-top distribution

CSIR Research Space (South Africa)

Naidoo, Darryl

2014-02-01

Full Text Available We explore an intra-cavity beam shaping approach to generate a Gaussian distribution by the metamorphosis of a Gaussian beam into a flat-top distribution on opposing mirrors. The concept is tested external to the cavity through the use of two...

Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen.

Science.gov (United States)

Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng

2011-09-12

In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.

Visio intellectualis: Nicolás de Cusa y Schelling

Directory of Open Access Journals (Sweden)

Harald Schwaetzer

2006-11-01

Full Text Available Este trabajo pretende descubrir una proximidad sistemática entre el pensamiento de Nicolás de Cusa y el idealismo alemán, en particular, en torno a la noción de "visio intellectualis" entendida en el plano teórico del conocimiento. Pretende demostrar que lo que el Cusano piensa como "visión intelectual" acaba por no ser otra cosa que el "Yo que se contempla a sí mismo" ["selbst anschauende Ich"] en el que piensa Schelling y, así, que aquello que está en la base del pensamiento cusano y que se ha sido pensado a su manera en su tiempo, es lo mismo que fue mostrado en el tiempo de Schelling y a la manera de Schelling.

Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

Science.gov (United States)

Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

2016-06-27

We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

Effects of relativistic and channel focusing on q-Gaussian laser beam propagating in a preformed parabolic plasma channel

Energy Technology Data Exchange (ETDEWEB)

Wang, Li; Hong, Xue-Ren, E-mail: hxr_nwnu@163.com; Sun, Jian-An, E-mail: sunja@nwnu.edu.cn; Tang, Rong-An; Yang, Yang; Zhou, Wei-Jun; Tian, Jian-Min; Duan, Wen-Shan

2017-07-12

The propagation of q-Gaussian laser beam in a preformed plasma channel is investigated by means of the variational method. A differential equation for the spot size has been obtained by including the effects of relativistic self-focusing, ponderomotive self-channeling and preformed channel focusing. The propagation behaviors and their corresponding physical conditions are identified. The comparison of the propagation between q-Gaussian and Gaussian laser beams is done by theoretical and numerical analysis. It is shown that, in the same channel, the focusing power of q-Gaussian laser beam is lower than that of Gaussian laser beam, i.e., the q-Gaussian laser beam is easier to focus than Gaussian laser beam. - Highlights: • Some behaviors for Gaussian laser are also found for q-Gaussian one. • The parameter regions corresponding to different laser behaviors are given. • Influence of q on the laser propagation behavior is obvious. • The q-Gaussian laser beam is easier to focus than the Gaussian one.

Effects of relativistic and channel focusing on q-Gaussian laser beam propagating in a preformed parabolic plasma channel

International Nuclear Information System (INIS)

Wang, Li; Hong, Xue-Ren; Sun, Jian-An; Tang, Rong-An; Yang, Yang; Zhou, Wei-Jun; Tian, Jian-Min; Duan, Wen-Shan

2017-01-01

The propagation of q-Gaussian laser beam in a preformed plasma channel is investigated by means of the variational method. A differential equation for the spot size has been obtained by including the effects of relativistic self-focusing, ponderomotive self-channeling and preformed channel focusing. The propagation behaviors and their corresponding physical conditions are identified. The comparison of the propagation between q-Gaussian and Gaussian laser beams is done by theoretical and numerical analysis. It is shown that, in the same channel, the focusing power of q-Gaussian laser beam is lower than that of Gaussian laser beam, i.e., the q-Gaussian laser beam is easier to focus than Gaussian laser beam. - Highlights: • Some behaviors for Gaussian laser are also found for q-Gaussian one. • The parameter regions corresponding to different laser behaviors are given. • Influence of q on the laser propagation behavior is obvious. • The q-Gaussian laser beam is easier to focus than the Gaussian one.

Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media

Science.gov (United States)

Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai

2018-01-01

Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.

The robustness of truncated Airy beam in PT Gaussian potentials media

Science.gov (United States)

Wang, Xianni; Fu, Xiquan; Huang, Xianwei; Yang, Yijun; Bai, Yanfeng

2018-03-01

The robustness of truncated Airy beam in parity-time (PT) symmetric Gaussian potentials media is numerically investigated. A high-peak power beam sheds from the Airy beam due to the media modulation while the Airy wavefront still retain its self-bending and non-diffraction characteristics under the influence of modulation parameters. Increasing the modulation factor results in the smaller value of maximum power of the center beam, and the opposite trend occurs with the increment of the modulation depth. However, the parabolic trajectory of the Airy wavefront does not be influenced. By utilizing the unique features, the Airy beam can be used as a long distance transmission source under the PT symmetric Gaussian potentials medium.

On the exploration of effect of critical beam power on the propagation of Gaussian laser beam in collisionless magnetized plasma

Science.gov (United States)

Urunkar, T. U.; Valkunde, A. T.; Vhanmore, B. D.; Gavade, K. M.; Patil, S. D.; Takale, M. V.

2018-05-01

It is quite known that critical power of the laser plays vital role in the propagation of Gaussian laser beam in collisionless plasma. The nonlinearity in dielectric constant considered herein is due to the ponderomotive force. In the present analysis, the interval of critical beam power has been explored to sustain the competition between diffraction and self-focusing of Gaussian laser beam during propagation in collisionless magnetized plasma. Differential equation for beam-width parameter has been established by using WKB and paraxial approximations under parabolic equation approach. The effect of critical power on the propagation of Gaussian laser beam has been presented graphically and discussed.

Schellings Wesensbestimmung des Christentums in den ...

African Journals Online (AJOL)

p1243322

SW V, 214) die besonderen Wissenschaften als Darstellungen des Absoluten zu begreifen. In diesem Kosmos der Wissenschaften findet auch die. Theologie neben Jurisprudenz und Medizin ihren Ort. Sie wird von Schelling als “die erste und ...

Launching and controlling Gaussian beams from point sources via planar transformation media

Science.gov (United States)

Odabasi, Hayrettin; Sainath, Kamalesh; Teixeira, Fernando L.

2018-02-01

Based on operations prescribed under the paradigm of complex transformation optics (CTO) [F. Teixeira and W. Chew, J. Electromagn. Waves Appl. 13, 665 (1999), 10.1163/156939399X01104; F. L. Teixeira and W. C. Chew, Int. J. Numer. Model. 13, 441 (2000), 10.1002/1099-1204(200009/10)13:5%3C441::AID-JNM376%3E3.0.CO;2-J; H. Odabasi, F. L. Teixeira, and W. C. Chew, J. Opt. Soc. Am. B 28, 1317 (2011), 10.1364/JOSAB.28.001317; B.-I. Popa and S. A. Cummer, Phys. Rev. A 84, 063837 (2011), 10.1103/PhysRevA.84.063837], it was recently shown in [G. Castaldi, S. Savoia, V. Galdi, A. Alù, and N. Engheta, Phys. Rev. Lett. 110, 173901 (2013), 10.1103/PhysRevLett.110.173901] that a complex source point (CSP) can be mimicked by parity-time (PT ) transformation media. Such coordinate transformation has a mirror symmetry for the imaginary part, and results in a balanced loss/gain metamaterial slab. A CSP produces a Gaussian beam and, consequently, a point source placed at the center of such a metamaterial slab produces a Gaussian beam propagating away from the slab. Here, we extend the CTO analysis to nonsymmetric complex coordinate transformations as put forth in [S. Savoia, G. Castaldi, and V. Galdi, J. Opt. 18, 044027 (2016), 10.1088/2040-8978/18/4/044027] and verify that, by using simply a (homogeneous) doubly anisotropic gain-media metamaterial slab, one can still mimic a CSP and produce Gaussian beam. In addition, we show that a Gaussian-like beams can be produced by point sources placed outside the slab as well. By making use of the extra degrees of freedom (the real and imaginary parts of the coordinate transformation) provided by CTO, the near-zero requirement on the real part of the resulting constitutive parameters can be relaxed to facilitate potential realization of Gaussian-like beams. We illustrate how beam properties such as peak amplitude and waist location can be controlled by a proper choice of (complex-valued) CTO Jacobian elements. In particular, the beam waist

Spiral phase plates for the generation of high-order Laguerre-Gaussian beams with non-zero radial index

Science.gov (United States)

Ruffato, G.; Carli, M.; Massari, M.; Romanato, F.

2015-03-01

The work of design, fabrication and characterization of spiral phase plates for the generation of Laguerre-Gaussian (LG) beams with non-null radial index is presented. Samples were fabricated by electron beam lithography on polymethylmethacrylate layers over glass substrates. The optical response of these phase optical elements was measured and the purity of the experimental beams was investigated in terms of Laguerre-Gaussian modes contributions. The farfield intensity pattern was compared with theoretical models and numerical simulations, while the expected phase features were confirmed by interferometric analyses. The high quality of the output beams confirms the applicability of these phase plates for the generation of high-order Laguerre-Gaussian beams. A novel application consisting in the design of computer-generated holograms encoding information for light beams carrying phase singularities is shown. A numerical code based on iterative Fourier transform algorithm has been developed for the computation of the phase pattern of phase-only diffractive optical element for illumination under LG beams. Numerical analysis and preliminary experimental results confirm the applicability of these devices as high-security optical elements.

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schroedinger equation

International Nuclear Information System (INIS)

Leung Shingyu; Qian Jianliang

2010-01-01

We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.

Propagation Characteristics of High-Power Vortex Laguerre-Gaussian Laser Beams in Plasma

Directory of Open Access Journals (Sweden)

Zhili Lin

2018-04-01

Full Text Available The propagation characteristics of high-power laser beams in plasma is an important research topic and has many potential applications in fields such as laser machining, laser-driven accelerators and laser-driven inertial confined fusion. The dynamic evolution of high-power Laguerre-Gaussian (LG beams in plasma is numerically investigated by using the finite-difference time-domain (FDTD method based on the nonlinear Drude model, with both plasma frequency and collision frequency modulated by the light intensity of laser beam. The numerical algorithms and implementation techniques of FDTD method are presented for numerically simulating the nonlinear permittivity model of plasma and generating the LG beams with predefined parameters. The simulation results show that the plasma has different field modulation effects on the two exemplified LG beams with different cross-sectional patterns. The self-focusing and stochastic absorption phenomena of high-power laser beam in plasma are also demonstrated. This research also provides a new means for the field modulation of laser beams by plasma.

Tuneable Gaussian to flat-top resonator by amplitude beam shaping

CSIR Research Space (South Africa)

Ngcobo, S

2013-09-01

Full Text Available We outline a simple laser cavity comprising an opaque ring and a circular aperture that is capable of producing spatially tuneable laser modes, from a Gaussian beam to a Flat-top beam. The tuneability is achieved by varying the diameter...

Structured Laguerre-Gaussian beams for mitigation of spherical aberration in tightly focused regimes

Science.gov (United States)

Haddadi, S.; Bouzid, O.; Fromager, M.; Hasnaoui, A.; Harfouche, A.; Cagniot, E.; Forbes, A.; Aït-Ameur, K.

2018-04-01

Many laser applications utilise a focused laser beam having a single-lobed intensity profile in the focal plane, ideally with the highest possible on-axis intensity. Conventionally, this is achieved with the lowest-order Laguerre-Gaussian mode (LG00), the Gaussian beam, in a tight focusing configuration. However, tight focusing often involves significant spherical aberration due to the high numerical aperture of the systems involved, thus degrading the focal quality. Here, we demonstrate that a high-order radial LG p0 mode can be tailored to meet and in some instances exceed the performance of the Gaussian. We achieve this by phase rectification of the mode using a simple binary diffractive optic. By way of example, we show that the focusing of a rectified LG50 beam is almost insensitive to a spherical aberration coefficient of over three wavelengths, in contrast with the usual Gaussian beam for which the intensity of the focal spot is reduced by a factor of two. This work paves the way towards enhanced focal spots using structured light.

Paint stripping with high power flattened Gaussian beams

CSIR Research Space (South Africa)

Forbes, A

2009-08-01

Full Text Available In this paper the researchers present results on improved paint stripping performance with an intra-cavity generated Flattened Gaussian Beam (FGB). A resonator with suitable diffractive optical elements was designed in order to produce a single mode...

Amplitude calculations for 3D Gaussian beam migration using complex-valued traveltimes

International Nuclear Information System (INIS)

Bleistein, Norman; Gray, Samuel H

2010-01-01

Gaussian beams are often used to represent Green's functions in three-dimensional Kirchhoff-type true-amplitude migrations because such migrations made using Gaussian beams yield superior images to similar migrations using classical ray-theoretic Green's functions. Typically, the integrand of a migration formula consists of two Green's functions—each describing propagation to the image point—one from the source and the other from the receiver position. The use of Gaussian beams to represent each of these Green's functions in 3D introduces two additional double integrals when compared to a Kirchhoff migration using ray-theoretic Green's functions, thereby adding a significant computational burden. Hill (2001 Geophysics 66 1240–50) proposed a method for reducing those four integrals to two, compromising slightly on the full potential quality of the Gaussian beam representations for the sake of more efficient computation. That approach requires a two-dimensional steepest descent analysis for the asymptotic evaluation of a double integral. The method requires evaluation of the complex traveltimes of the Gaussian beams as well as the amplitudes of the integrands at the determined saddle points. In addition, it is necessary to evaluate the determinant of a certain (Hessian) matrix of second derivatives. Hill (2001 Geophysics 66 1240–50) did not report on this last part; thus, his proposed migration formula is kinematically correct but lacks correct amplitude behavior. In this paper, we derive a formula for that Hessian matrix in terms of dynamic ray tracing quantities. We also show in a simple example how the integral that we analyze here arises in a true amplitude migration formula

Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma

International Nuclear Information System (INIS)

Patil, S. D.; Takale, M. V.

2013-01-01

In the present paper, we have employed the quantum dielectric response in thermal quantum plasma to model relativistic self-focusing of Gaussian laser beam in a plasma. We have presented an extensive parametric investigation of the dependence of beam-width parameter on distance of propagation in relativistic thermal quantum plasma. We have studied the role of Fermi temperature in the phenomenon of self-focusing. It is found that the quantum effects cause much higher oscillations of beam-width parameter and better relativistic focusing of laser beam in thermal quantum plasma in comparison with that in the relativistic cold quantum plasma and classical relativistic plasma. Our computations show more reliable results in comparison to the previous works

Spot size characterization of focused non-Gaussian X-ray laser beams.

Science.gov (United States)

Chalupský, J; Krzywinski, J; Juha, L; Hájková, V; Cihelka, J; Burian, T; Vysín, L; Gaudin, J; Gleeson, A; Jurek, M; Khorsand, A R; Klinger, D; Wabnitz, H; Sobierajski, R; Störmer, M; Tiedtke, K; Toleikis, S

2010-12-20

We present a new technique for the characterization of non-Gaussian laser beams which cannot be described by an analytical formula. As a generalization of the beam spot area we apply and refine the definition of so called effective area (A(eff)) [1] in order to avoid using the full-width at half maximum (FWHM) parameter which is inappropriate for non-Gaussian beams. Furthermore, we demonstrate a practical utilization of our technique for a femtosecond soft X-ray free-electron laser. The ablative imprints in poly(methyl methacrylate) - PMMA and amorphous carbon (a-C) are used to characterize the spatial beam profile and to determine the effective area. Two procedures of the effective area determination are presented in this work. An F-scan method, newly developed in this paper, appears to be a good candidate for the spatial beam diagnostics applicable to lasers of various kinds.

Modulation Transfer Function of a Gaussian Beam Based on the Generalized Modified Atmospheric Spectrum

Directory of Open Access Journals (Sweden)

Chao Gao

2016-01-01

Full Text Available This paper investigates the modulation transfer function of a Gaussian beam propagating through a horizontal path in weak-fluctuation non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized modified atmospheric spectrum, which includes the spectral power law value of non-Kolmogorov turbulence, the finite inner and outer scales of turbulence, and other optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the inner scale of turbulence. Additionally, the increased outer scale of turbulence makes a Gaussian beam influenced more seriously by the atmospheric turbulence.

Twist phase-induced characteristics changes of a radially polarized Gaussian Schell-Model beam in a uniaxial crystal orthogonal to the optical axis

Science.gov (United States)

Cao, Pengfei; Fu, Wenyu

2017-10-01

Based on the extended Huygens-Fresnel integral formula and unified theory of coherence and polarization, we obtained the cross-spectral density matrix elements for a radially polarized partially coherent twist (RPPCT) beam in a uniaxial crystal. Moreover, compared with free space, we explore numerically the evolution properties of a RPPCT beam in a uniaxial crystal. The calculation results show that the evolution properties of a RPPCT beam in crystals are substantially different from its properties in free space. These properties in crystals are mainly determined by the twist factor and the ratio of extraordinary index to ordinary refractive index. In a uniaxial crystal, the distribution of the intensity of a RPPCT beam all exhibits non-circular symmetry, and these distributions change with twist factor and the ratio of extraordinary index to ordinary refractive index. The twist factor affects their rotation orientation angles, and the ratio of extraordinary index to ordinary refractive index impacts their twisted levels. This novel characteristics can be used for free-space optical communications, particle manipulation and nonlinear optics, where partially coherent beam with controlled profile and twist factor are required.

Attenuation of laser power of a focused Gaussian beam during interaction between a laser and powder in coaxial laser cladding

International Nuclear Information System (INIS)

Liu Jichang; Li Lijun; Zhang Yuanzhong; Xie Xiaozhu

2005-01-01

The power of a focused laser beam with a Gaussian intensity profile attenuated by powder in coaxial laser cladding is investigated experimentally and theoretically, and its resolution model is developed. With some assumptions, it is concluded that the attenuation of laser power is an exponential function and is determined by the powder feed rate, particle moving speed, spraying angles and waist positions and diameters of the laser beam and powder flow, grain diameter and run of the laser beam through the powder flow. The attenuation of laser power increases with powder feed rate or run of laser beam through the powder flow. In the experiment presented, 300 W laser power from a focused Gaussian beam is attenuated by a coaxial powder flow. The experimental results agree well with the values calculated with the developed model

Optical vortex scanning inside the Gaussian beam

International Nuclear Information System (INIS)

Masajada, J; Leniec, M; Augustyniak, I

2011-01-01

We discussed a new scanning method for optical vortex-based scanning microscopy. The optical vortex is introduced into the incident Gaussian beam by a vortex lens. Then the beam with the optical vortex is focused by an objective and illuminates the sample. By changing the position of the vortex lens we can shift the optical vortex position at the sample plane. By adjusting system parameters we can get 30 times smaller shift at the sample plane compared to the vortex lens shift. Moreover, if the range of vortex shifts is smaller than 3% of the beam radius in the sample plane the amplitude and phase distribution around the phase dislocation remains practically unchanged. Thus we can scan the sample topography precisely with an optical vortex

Numerical investigations of non-collinear optical parametric chirped pulse amplification for Laguerre-Gaussian vortex beam

Science.gov (United States)

Xu, Lu; Yu, Lianghong; Liang, Xiaoyan

2016-04-01

We present for the first time a scheme to amplify a Laguerre-Gaussian vortex beam based on non-collinear optical parametric chirped pulse amplification (OPCPA). In addition, a three-dimensional numerical model of non-collinear optical parametric amplification was deduced in the frequency domain, in which the effects of non-collinear configuration, temporal and spatial walk-off, group-velocity dispersion and diffraction were also taken into account, to trace the dynamics of the Laguerre-Gaussian vortex beam and investigate its critical parameters in the non-collinear OPCPA process. Based on the numerical simulation results, the scheme shows promise for implementation in a relativistic twisted laser pulse system, which will diversify the light-matter interaction field.

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

Ultrasound beam transmission using a discretely orthogonal Gaussian aperture basis

Science.gov (United States)

Roberts, R. A.

2018-04-01

Work is reported on development of a computational model for ultrasound beam transmission at an arbitrary geometry transmission interface for generally anisotropic materials. The work addresses problems encountered when the fundamental assumptions of ray theory do not hold, thereby introducing errors into ray-theory-based transmission models. Specifically, problems occur when the asymptotic integral analysis underlying ray theory encounters multiple stationary phase points in close proximity, due to focusing caused by concavity on either the entry surface or a material slowness surface. The approach presented here projects integrands over both the transducer aperture and the entry surface beam footprint onto a Gaussian-derived basis set, thereby distributing the integral over a summation of second-order phase integrals which are amenable to single stationary phase point analysis. Significantly, convergence is assured provided a sufficiently fine distribution of basis functions is used.

Dipole saturated absorption modeling in gas phase: Dealing with a Gaussian beam

Science.gov (United States)

Dupré, Patrick

2018-01-01

With the advent of new accurate and sensitive spectrometers, cf. combining optical cavities (for absorption enhancement), the requirement for reliable molecular transition modeling is becoming more pressing. Unfortunately, there is no trivial approach which can provide a definitive formalism allowing us to solve the coupled systems of equations associated with nonlinear absorption. Here, we propose a general approach to deal with any spectral shape of the electromagnetic field interacting with a molecular species under saturation conditions. The development is specifically applied to Gaussian-shaped beams. To make the analytical expressions tractable, approximations are proposed. Finally, two or three numerical integrations are required for describing the Lamb-dip profile. The implemented model allows us to describe the saturated absorption under low pressure conditions where the broadening by the transit-time may dominate the collision rates. The model is applied to two specific overtone transitions of the molecular acetylene. The simulated line shapes are discussed versus the collision and the transit-time rates. The specific collisional and collision-free regimes are illustrated, while the Rabi frequency controls the intermediate regime. We illustrate how to recover the input parameters by fitting the simulated profiles.

Vortex beam characterization in terms of Hypergeometric- Gaussian modes

CSIR Research Space (South Africa)

Sephton, Bereneice C

2016-10-01

Full Text Available in Optics: The 100th OSA Annual Meeting and Exhibit/Laser Science XXXII , 17-21 October 2016, Rochester Riverside Convention Center, Rochester, New York United States Vortex beam characterization in terms of Hypergeometric- Gaussian modes Sephton...

Optical trapping with Super-Gaussian beams

CSIR Research Space (South Africa)

Mc

2013-04-01

Full Text Available stream_source_info McLaren1_2013.pdf.txt stream_content_type text/plain stream_size 2236 Content-Encoding UTF-8 stream_name McLaren1_2013.pdf.txt Content-Type text/plain; charset=UTF-8 JT2A.34.pdf Optics in the Life... Sciences Congress Technical Digest © 2013 The Optical Society (OSA) Optical trapping with Super-Gaussian beams Melanie McLaren, Thulile Khanyile, Patience Mthunzi and Andrew Forbes* National Laser Centre, Council for Scientific and Industrial Research...

Determination of Cross-Sectional Area of Focused Picosecond Gaussian Laser Beam

Science.gov (United States)

Ledesma, Rodolfo; Fitz-Gerald, James; Palmieri, Frank; Connell, John

2018-01-01

Measurement of the waist diameter of a focused Gaussian-beam at the 1/e(sup 2) intensity, also referred to as spot size, is key to determining the fluence in laser processing experiments. Spot size measurements are also helpful to calculate the threshold energy and threshold fluence of a given material. This work reports an application of a conventional method, by analyzing single laser ablated spots for different laser pulse energies, to determine the cross-sectional area of a focused Gaussian-beam, which has a nominal pulse width of approx. 10 ps. Polished tungsten was used as the target material, due to its low surface roughness and low ablation threshold, to measure the beam waist diameter. From the ablative spot measurements, the ablation threshold fluence of the tungsten substrate was also calculated.

Schelling og Nietzsche som kritikere af Descartes

DEFF Research Database (Denmark)

Liisberg, Sune

2008-01-01

: 'Hvad er det første for mig' - og svaret var: 'Det er jeg selv'. Cogito-argumentet, der implicerer en forudgående beslutning om at drage alt i tvivl, manifesterer således en historisk enestående 'frigørelse fra al autoritet' (Schelling). Ifølge Schelling - der ligesom Schopenhauer og Nietzsche havde...... blik for, at cogito-argumentet og dets problemer har med dets sprogbundethed at gøre - er ytringsdimensionen nu helt afgørende for cogito-argumentets meningsfuldhed, da allerede 'den blotte tanke 'Jeg er' kan forstås som en indre ytring og forudsætter et talende jeg'. Nietzsche henleder opmærksomheden...... på, at 'eftersom Descartes formulerer cogito-argumentet sprogligt, kan det ikke være nogen umiddelbar, første erkendelse'. Nietzsche antager nemlig, at Descartes selv fejlagtigt betragtede cogito-argumentet som en umiddelbar vished - altså strengt taget ikke som et argument. Men Descartes blev...

Optical propagation of the HE11 mode and Gaussian beams in hollow circular waveguides

International Nuclear Information System (INIS)

Crenn, J.P.

1993-05-01

The propagation of the HE 11 mode and Gaussian beams in hollow oversized circular waveguides is analyzed using optical theories. Different types of waveguides are considered: hollow dielectric or conducting waveguides, dielectric-lined waveguides, corrugated waveguides. General formulas are derived which give the power transmission through these different guides. The best wall materials and structures are determined from a comparison of the waveguide transmissions, at the infrared and millimeter wavelengths. The question of the coupling between the HE 11 mode and Gaussian beams is discussed and from a review of coupling coefficients derived before, an optimum value is pointed out. The problem of matching a Gaussian beam into circular waveguides in order to achieve the maximum power transmission is analyzed

Scattering of aerosol particles by a Hermite-Gaussian beam in marine atmosphere.

Science.gov (United States)

Huang, Qingqing; Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Yan, Xu; Liu, Songhua

2017-07-01

Based on the complex-source-point method and the generalized Lorenz-Mie theory, the scattering properties and polarization of aerosol particles by a Hermite-Gaussian (HG) beam in marine atmosphere is investigated. The influences of beam mode, beam width, and humidity on the scattered field are analyzed numerically. Results indicate that when the number of HG beam modes u (v) increase, the radar cross section of aerosol particles alternating appears at maximum and minimum values in the forward and backward scattering, respectively, because of the special petal-shaped distribution of the HG beam. The forward and backward scattering of aerosol particles decreases with the increase in beam waist. When beam waist is less than the radius of the aerosol particle, a minimum value is observed in the forward direction. The scattering properties of aerosol particles by the HG beam are more sensitive to the change in relative humidity compared with those by the plane wave and the Gaussian beam (GB). The HG beam shows superiority over the plane wave and the GB in detecting changes in the relative humidity of marine atmosphere aerosol. The effects of relative humidity on the polarization of the HG beam have been numerically analyzed in detail.

Temporal self-splitting of optical pulses

Science.gov (United States)

Ding, Chaoliang; Koivurova, Matias; Turunen, Jari; Pan, Liuzhan

2018-05-01

We present mathematical models for temporally and spectrally partially coherent pulse trains with Laguerre-Gaussian and Hermite-Gaussian Schell-model statistics as extensions of the standard Gaussian Schell model for pulse trains. We derive propagation formulas of both classes of pulsed fields in linearly dispersive media and in temporal optical systems. It is found that, in general, both types of fields exhibit time-domain self-splitting upon propagation. The Laguerre-Gaussian model leads to multiply peaked pulses, while the Hermite-Gaussian model leads to doubly peaked pulses, in the temporal far field (in dispersive media) or at the Fourier plane of a temporal system. In both model fields the character of the self-splitting phenomenon depends both on the degree of temporal and spectral coherence and on the power spectrum of the field.

Effect of exponential density transition on self-focusing of q-Gaussian laser beam in collisionless plasma

Science.gov (United States)

Valkunde, Amol T.; Vhanmore, Bandopant D.; Urunkar, Trupti U.; Gavade, Kusum M.; Patil, Sandip D.; Takale, Mansing V.

2018-05-01

In this work, nonlinear aspects of a high intensity q-Gaussian laser beam propagating in collisionless plasma having upward density ramp of exponential profiles is studied. We have employed the nonlinearity in dielectric function of plasma by considering ponderomotive nonlinearity. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing of q-Gaussian laser beam for various values of q is systematically carried out and compared with results Gaussian laser beam propagating in collisionless plasma having uniform density. It is found that exponential plasma density ramp causes the laser beam to become more focused and gives reasonably interesting results.

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

Science.gov (United States)

Eom, Jeongsook; Kim, Gunzung; Park, Yongwan

2018-02-01

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

Spot size characterization of focused non-Gaussian X-ray laser beams

NARCIS (Netherlands)

Chalupsky, J.; Krzywinski, J.; Juha, L.; Hajkova, V.; Cihelka, J.; Burian, T.; Vysin, L.; Gaudin, J.; Gleeson, A.; Jurek, M.; Khorsand, A. R.; Klinger, D.; Wabnitz, H.; Sobierajski, R.; Stormer, M.; Tiedtke, K.; Toleikis, S.

2010-01-01

We present a new technique for the characterization of non-Gaussian laser beams which cannot be described by an analytical formula. As a generalization of the beam spot area we apply and refine the definition of so called effective area (A(eff)) [1] in order to avoid using the full-width at half

Effects of dispersion and longitudinal chromatic aberration on the focusing of isodiffracting pulsed Gaussian light beam

International Nuclear Information System (INIS)

Deng Dongmei; Guo Hong; Han Dingan; Liu Mingwei; Li Changfu

2005-01-01

Taking into account the dispersion and the longitudinal chromatic aberration (LCA) of the material of the lens, focusing of isodiffracting pulsed Gaussian light beam through single lens is analyzed. The smaller the cycle number of the isodiffracting pulsed Gaussian light beam is, the higher the order of the material dispersion should be considered

Experimental verification of dose calculation using the simplified Monte Carlo method with an improved initial beam model for a beam-wobbling system

International Nuclear Information System (INIS)

Tansho, Ryohei; Takada, Yoshihisa; Mizutani, Shohei; Kohno, Ryosuke; Hotta, Kenji; Akimoto, Tetsuo; Hara, Yousuke

2013-01-01

A beam delivery system using a single-radius-beam-wobbling method has been used to form a conformal irradiation field for proton radiotherapy in Japan. A proton beam broadened by the beam-wobbling system provides a non-Gaussian distribution of projection angle different in two mutually orthogonal planes with a common beam central axis, at a certain position. However, the conventional initial beam model for dose calculations has been using an approximation of symmetric Gaussian angular distribution with the same variance in both planes (called here a Gaussian model with symmetric variance (GMSV)), instead of the accurate one. We have developed a more accurate initial beam model defined as a non-Gaussian model with asymmetric variance (NonGMAV), and applied it to dose calculations using the simplified Monte Carlo (SMC) method. The initial beam model takes into account the different distances of two beam-wobbling magnets from the iso-center and also the different amplitudes of kick angle given by each magnet. We have confirmed that the calculation using the SMC with NonGMAV reproduced the measured dose distribution formed in air by a mono-energetic proton beam passing through a square aperture collimator better than with the GMSV and with a Gaussian model with asymmetric variance (GMAV) in which different variances of angular distributions are used in the two mutually orthogonal planes. Measured dose distributions in a homogeneous phantom formed by a modulated proton beam passing through a range shifter and an L-shaped range compensator, were consistent with calculations using the SMC with GMAV and NonGMAV, but in disagreement with calculations using the SMC with GMSV. Measured lateral penumbrae in a lateral direction were reproduced better by calculations using the SMC with NonGMAV than by those with GMAV, when an aperture collimator with a smaller opening was used. We found that such a difference can be attributed to the non-Gaussian angular distribution of the

Bayesian electron density inference from JET lithium beam emission spectra using Gaussian processes

Science.gov (United States)

Kwak, Sehyun; Svensson, J.; Brix, M.; Ghim, Y.-C.; Contributors, JET

2017-03-01

A Bayesian model to infer edge electron density profiles is developed for the JET lithium beam emission spectroscopy (Li-BES) system, measuring Li I (2p-2s) line radiation using 26 channels with  ∼1 cm spatial resolution and 10∼ 20 ms temporal resolution. The density profile is modelled using a Gaussian process prior, and the uncertainty of the density profile is calculated by a Markov Chain Monte Carlo (MCMC) scheme. From the spectra measured by the transmission grating spectrometer, the Li I line intensities are extracted, and modelled as a function of the plasma density by a multi-state model which describes the relevant processes between neutral lithium beam atoms and plasma particles. The spectral model fully takes into account interference filter and instrument effects, that are separately estimated, again using Gaussian processes. The line intensities are inferred based on a spectral model consistent with the measured spectra within their uncertainties, which includes photon statistics and electronic noise. Our newly developed method to infer JET edge electron density profiles has the following advantages in comparison to the conventional method: (i) providing full posterior distributions of edge density profiles, including their associated uncertainties, (ii) the available radial range for density profiles is increased to the full observation range (∼26 cm), (iii) an assumption of monotonic electron density profile is not necessary, (iv) the absolute calibration factor of the diagnostic system is automatically estimated overcoming the limitation of the conventional technique and allowing us to infer the electron density profiles for all pulses without preprocessing the data or an additional boundary condition, and (v) since the full spectrum is modelled, the procedure of modulating the beam to measure the background signal is only necessary for the case of overlapping of the Li I line with impurity lines.

Application of Gaussian beam ray-equivalent model and back-propagation artificial neural network in laser diode fast axis collimator assembly.

Science.gov (United States)

Yu, Hao; Rossi, Giammarco; Braglia, Andrea; Perrone, Guido

2016-08-10

The paper presents the development of a tool based on a back-propagation artificial neural network to assist in the accurate positioning of the lenses used to collimate the beam from semiconductor laser diodes along the so-called fast axis. After training using a Gaussian beam ray-equivalent model, the network is capable of indicating the tilt, decenter, and defocus of such lenses from the measured field distribution, so the operator can determine the errors with respect to the actual lens position and optimize the diode assembly procedure. An experimental validation using a typical configuration exploited in multi-emitter diode module assembly and fast axis collimating lenses with different focal lengths and numerical apertures is reported.

Tuneable Gaussian to flat-top resonator by amplitude beam shaping using a digital laser

CSIR Research Space (South Africa)

Ngcobo, S

2014-02-01

Full Text Available In this paper we experimentally demonstrate a simple laser cavity that produces spatial tuneable laser modes from a Gaussian beam to a Flat-top beam and a Donut-beam. The laser cavity contains an opaque ring and an adjustable circular aperture...

Propagation characteristics of a Gaussian laser beam in plasma with modulated collision frequency

International Nuclear Information System (INIS)

Wang Ying; Yuan Chengxun; Zhou Zhongxiang; Gao Ruilin; Li Lei; Du Yanwei

2012-01-01

The propagation characteristics of a Gaussian laser beam in cold plasma with the electron collision frequency modulated by laser intensity are presented. The nonlinear dynamics of the ponderomotive force, which induce nonlinear self-focusing as opposed to spatial diffraction, are considered. The effective dielectric function of the Drude model and complex eikonal function are adopted in deriving coupled differential equations of the varying laser beam parameters. In the framework of ponderomotive nonlinearity, the frequency of electron collision in plasmas, which is proportional to the spatial electron density, is strongly interrelated with the laser beam propagation characteristics. Hence, the propagation properties of the laser beam and the modulated electron collision frequency distribution in plasma were studied and explained in depth. Employing this self-consistent method, the obtained simulation results approach practical conditions, which is of significance to the study of laser–plasma interactions.

High power infrared super-Gaussian beams: generation, propagation and application

CSIR Research Space (South Africa)

Du Preez, NC

2009-09-01

Full Text Available In this paper researchers present the design of a CO2 laser resonator that produces as the stable transverse mode a super–Gaussian laser beam. The resonator makes use of an intra–cavity diffractive mirror and a flat output coupler, generating...

Propagation of rotational Risley-prism-array-based Gaussian beams in turbulent atmosphere

Science.gov (United States)

Chen, Feng; Ma, Haotong; Dong, Li; Ren, Ge; Qi, Bo; Tan, Yufeng

2018-03-01

Limited by the size and weight of prism and optical assembling, Rotational Risley-prism-array system is a simple but effective way to realize high power and superior beam quality of deflecting laser output. In this paper, the propagation of the rotational Risley-prism-array-based Gaussian beam array in atmospheric turbulence is studied in detail. An analytical expression for the average intensity distribution at the receiving plane is derived based on nonparaxial ray tracing method and extended Huygens-Fresnel principle. Power in the diffraction-limited bucket is chosen to evaluate beam quality. The effect of deviation angle, propagation distance and intensity of turbulence on beam quality is studied in detail by quantitative simulation. It reveals that with the propagation distance increasing, the intensity distribution gradually evolves from multiple-petal-like shape into the pattern that contains one main-lobe in the center with multiple side-lobes in weak turbulence. The beam quality of rotational Risley-prism-array-based Gaussian beam array with lower deviation angle is better than its counterpart with higher deviation angle when propagating in weak and medium turbulent (i.e. Cn2 beam quality of higher deviation angle arrays degrades faster as the intensity of turbulence gets stronger. In the case of propagating in strong turbulence, the long propagation distance (i.e. z > 10km ) and deviation angle have no influence on beam quality.

Tight focusing of a radially polarized Laguerre–Bessel–Gaussian beam and its application to manipulation of two types of particles

International Nuclear Information System (INIS)

Nie, Zhongquan; Shi, Guang; Li, Dongyu; Zhang, Xueru; Wang, Yuxiao; Song, Yinglin

2015-01-01

The intensity distributions near the focus for radially polarized Laguerre–Bessel–Gaussian beams by a high numerical aperture objective in the immersion liquid are computed based on the vector diffraction theory. We compare the focusing properties of the radially polarized Laguerre–Bessel–Gaussian beams with those of Laguerre–Gaussian and Bessel–Gaussian modes. Furthermore, the effects of the optimally designed concentric three-zone phase filters on the intensity profiles in the focal region are examined. We further analyze the radiation forces on Rayleigh particles produced by the highly focused radially polarized Laguerre–Bessel–Gaussian beams using the specially engineered three-zone phase filters. - Highlights: • The tightly focusing of radially polarized LBG beams is examined. • The focusing performances of LBG beams are preferable over that of LG and BG modes. • A bright spot and an optical cage can be formed by special phase modulation. • These special focusing patterns can stably manipulate two types of particles

Unstable propagation of a Gaussian laser beam in a plasma waveguide

International Nuclear Information System (INIS)

Feit, M.D.; Maiden, D.E.

1976-01-01

Laser heating of long magnetically confined plasma columns to fusion temperatures requires propagation of a trapped laser beam over considerable distances. The present paper employs the parabolic approximation to the wave equation to analyze the propagation of a Gaussian beam through a plasma with a parabolic transverse density profile. Although propagation is stable in the axially uniform case, exhibiting alternate focusing and defocusing of the beam, it is unstable to small axial perturbations of certain wavelengths. In particular, an exponentially growing beam radius results from perturbations at wavelengths near that associated with the alternate focusing and defocusing mentioned above

Strong self-focusing of a cosh-Gaussian laser beam in collisionless magneto-plasma under plasma density ramp

International Nuclear Information System (INIS)

Nanda, Vikas; Kant, Niti

2014-01-01

The effect of plasma density ramp on self-focusing of cosh-Gaussian laser beam considering ponderomotive nonlinearity is analyzed using WKB and paraxial approximation. It is noticed that cosh-Gaussian laser beam focused earlier than Gaussian beam. The focusing and de-focusing nature of the cosh-Gaussian laser beam with decentered parameter, intensity parameter, magnetic field, and relative density parameter has been studied and strong self-focusing is reported. It is investigated that decentered parameter “b” plays a significant role for the self-focusing of the laser beam as for b=2.12, strong self-focusing is seen. Further, it is observed that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For b=2.12, with the increase in the value of magnetic field self-focusing effect, in case of extraordinary mode, becomes very strong under plasma density ramp. Present study may be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers. Moreover, plasma density ramp plays a vital role to enhance the self-focusing effect

Strong self-focusing of a cosh-Gaussian laser beam in collisionless magneto-plasma under plasma density ramp

Energy Technology Data Exchange (ETDEWEB)

Nanda, Vikas; Kant, Niti, E-mail: nitikant@yahoo.com [Department of Physics, Lovely Professional University, G. T. Road, Phagwara, Punjab 144411 (India)

2014-07-15

The effect of plasma density ramp on self-focusing of cosh-Gaussian laser beam considering ponderomotive nonlinearity is analyzed using WKB and paraxial approximation. It is noticed that cosh-Gaussian laser beam focused earlier than Gaussian beam. The focusing and de-focusing nature of the cosh-Gaussian laser beam with decentered parameter, intensity parameter, magnetic field, and relative density parameter has been studied and strong self-focusing is reported. It is investigated that decentered parameter “b” plays a significant role for the self-focusing of the laser beam as for b=2.12, strong self-focusing is seen. Further, it is observed that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For b=2.12, with the increase in the value of magnetic field self-focusing effect, in case of extraordinary mode, becomes very strong under plasma density ramp. Present study may be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers. Moreover, plasma density ramp plays a vital role to enhance the self-focusing effect.

Propagation of Bessel-Gaussian beams through a double-apertured fractional Fourier transform optical system.

Science.gov (United States)

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.

Aperture correction with an asymmetrically trimmed gaussian weight in SPECT with a fan-beam collimator

International Nuclear Information System (INIS)

Kamiya, Ryo; Ogawa, Koichi

2013-01-01

The aim of the study is to improve the spatial resolution of single photon emission computed tomography (SPECT) images acquired with a fan-beam collimator. The aperture angle of a hole in the fan-beam collimator depends on the position of the collimator. To correct the aperture effect in an iterative image reconstruction, an asymmetrically trimmed Gaussian weight was used for a model. To confirm the validity of our method, point source phantoms and brain phantom were used in the simulation, and we applied the method to the clinical data. The results of the simulation showed that the spatial resolution of point sources improved from about 6 to 2 pixels full width at half maximum, and the corrected point sources were isotropic. The results of the simulation with the brain phantom showed that our proposed method could improve the spatial resolution of the phantom, and our method was effective for different fan-beam collimators with different focal lengths. The results of clinical data showed that the quality of the reconstructed image was improved with our proposed method. Our proposed aperture correction method with the asymmetrically trimmed Gaussian weighting function was effective in improving the spatial resolution of SPECT images acquired with the fan-beam collimator. (author)

ECE from MAST - Gaussian beams and antenna aiming problem

Czech Academy of Sciences Publication Activity Database

Preinhaelter, Josef; Urban, Jakub; Pavlo, Pavol; Shevchenko, V.; Valovic, M.; Vahala, L.; Vahala, G.

2004-01-01

Roč. 54, suppl.C (2004), C116-C122 ISSN 0011-4626. [Symposium on Plasma Physics and Technology /21./. Praha, 14.06.2004-17.06.2004] R&D Projects: GA ČR GA202/04/0360 Institutional research plan: CEZ:AV0Z2043910 Keywords : ECEemission, Gaussian beams Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 0.292, year: 2004

Diffraction of a Gaussian beam in a three-dimensional smoothly inhomogeneous medium: an eikonal-based complex geometrical-optics approach.

Science.gov (United States)

Berczynski, Pawel; Bliokh, Konstantin Yu; Kravtsov, Yuri A; Stateczny, Andrzej

2006-06-01

We present an ab initio account of the paraxial complex geometrical optics (CGO) in application to scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of the Riccati type. This substantially simplifies the description of Gaussian beam diffraction as compared with full-wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lenslike medium, the CGO equations possess analytical solutions; otherwise, they can be readily solved numerically. As a nontrivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross section grows unboundedly; it is oriented predominantly in the azimuthal (binormal) direction and does not obey the parallel-transport law.

Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.

Science.gov (United States)

Mitri, Farid G

2015-10-01

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

The Experimental Verification of Gaussian Beam Coupling for ECH Transmission Line at 400 GHz

Directory of Open Access Journals (Sweden)

Choe Mun Seok

2017-01-01

Full Text Available We design a quasi-optical transmission line system for a 400 GHz gyrotron beam. The 400GHz Gaussian beam is injected to a corrugated waveguide bounced from a quasi-optical mirror. From detailed 2D field patterns of the output beam emitted from the corrugated waveguide, we analyze the mode contents and the source of non-ideal beam expansion

Effects of a modulated vortex structure on the diffraction dynamics of ring Airy Gaussian beams.

Science.gov (United States)

Huang, Xianwei; Shi, Xiaohui; Deng, Zhixiang; Bai, Yanfeng; Fu, Xiquan

2017-09-01

The evolution of the ring Airy Gaussian beams with a modulated vortex in free space is numerically investigated. Compared with the unmodulated vortex, the unique property is that the beam spots first break up, and then gather. The evolution of the beams is influenced by the parameters of the vortex modulation, and the splitting phenomenon gets enhanced with multiple rings becoming light spots if the modulation depth increases. The symmetric branch pattern of the beam spots gets changed when the number of phase folds increases, and the initial modulation phase only impacts the angle of the beam spots. Moreover, a large distribution factor correlates to a hollow Gaussian vortex shape and weakens the splitting and gathering trend. By changing the initial parameters of the vortex modulation and the distribution factor, the peak intensity is greatly affected. In addition, the energy flow and the angular momentum are elucidated with the beam evolution features being confirmed.

Influence of atmospheric turbulence on the energy focusability of Gaussian beams with spherical aberration

International Nuclear Information System (INIS)

Deng, Jinping; Ji, Xiaoling

2014-01-01

By using the four-dimensional (4D) computer code of the time-dependent propagation of laser beams through atmospheric turbulence, the influence of atmospheric turbulence on the energy focusability of Gaussian beams with spherical aberration is studied in detail, where the mean-squared beam width, the power in the bucket (PIB), the β parameter and the energy Strehl ratio are taken as the characteristic parameters. It is shown that turbulence results in beam spreading, and the effect of spherical aberration on the beam spreading decreases due to turbulence. Gaussian beams with negative spherical aberration are more affected by turbulence than those with positive spherical aberration. For the negative spherical aberration case, the focus position moves to the source plane due to turbulence. It is mentioned that the influence of turbulence on the energy focusability defined by a certain energy (i.e. PIB = 63%) is very heavy when the negative spherical aberration is very heavy. On the other hand, the influence of turbulence on the energy focusability defined by the energy within a given bucket radius (i.e. mean-squared beam width) is heaviest when a certain negative spherical aberration coefficient is adopted. (papers)

Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam.

Science.gov (United States)

Nicolas, F; Coëtmellec, S; Brunel, M; Allano, D; Lebrun, D; Janssen, A J E M

2005-11-01

The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by a collimated plane wave [J. Opt. Soc. Am A 19, 1537 (2002)], but also by an elliptic and astigmatic Gaussian beam when two different fractional orders are considered. Simulations and experimental results are presented.

Measurements of refractive index and size of a spherical drop from Gaussian beam scattering in the primary rainbow region

Science.gov (United States)

Yu, Haitao; Sun, Hui; Shen, Jianqi; Tropea, Cameron

2018-03-01

The primary rainbow observed when light is scattered by a spherical drop has been exploited in the past to measure drop size and relative refractive index. However, if higher spatial resolution is required in denser drop ensembles/sprays, and to avoid then multiple drops simultaneously appearing in the measurement volume, a highly focused beam is desirable, inevitably with a Gaussian intensity profile. The present study examines the primary rainbow pattern resulting when a Gaussian beam is scattered by a spherical drop and estimates the attainable accuracy when extracting size and refractive index. The scattering is computed using generalized Lorenz-Mie theory (GLMT) and Debye series decomposition of the Gaussian beam scattering. The results of these simulations show that the measurement accuracy is dependent on both the beam waist radius and the position of the drop in the beam waist.

Numerical modeling of macrodispersion in heterogeneous media: a comparison of multi-Gaussian and non-multi-Gaussian models

Science.gov (United States)

Wen, Xian-Huan; Gómez-Hernández, J. Jaime

1998-03-01

The macrodispersion of an inert solute in a 2-D heterogeneous porous media is estimated numerically in a series of fields of varying heterogeneity. Four different random function (RF) models are used to model log-transmissivity (ln T) spatial variability, and for each of these models, ln T variance is varied from 0.1 to 2.0. The four RF models share the same univariate Gaussian histogram and the same isotropic covariance, but differ from one another in terms of the spatial connectivity patterns at extreme transmissivity values. More specifically, model A is a multivariate Gaussian model for which, by definition, extreme values (both high and low) are spatially uncorrelated. The other three models are non-multi-Gaussian: model B with high connectivity of high extreme values, model C with high connectivity of low extreme values, and model D with high connectivities of both high and low extreme values. Residence time distributions (RTDs) and macrodispersivities (longitudinal and transverse) are computed on ln T fields corresponding to the different RF models, for two different flow directions and at several scales. They are compared with each other, as well as with predicted values based on first-order analytical results. Numerically derived RTDs and macrodispersivities for the multi-Gaussian model are in good agreement with analytically derived values using first-order theories for log-transmissivity variance up to 2.0. The results from the non-multi-Gaussian models differ from each other and deviate largely from the multi-Gaussian results even when ln T variance is small. RTDs in non-multi-Gaussian realizations with high connectivity at high extreme values display earlier breakthrough than in multi-Gaussian realizations, whereas later breakthrough and longer tails are observed for RTDs from non-multi-Gaussian realizations with high connectivity at low extreme values. Longitudinal macrodispersivities in the non-multi-Gaussian realizations are, in general, larger than

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

Science.gov (United States)

Zou, Defeng; Li, Xiaohui; Chai, Tong; Zheng, Hairong

2018-05-01

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

Composite optical vortices in noncollinear Laguerre–Gaussian beams and their propagation in free space

International Nuclear Information System (INIS)

Chen Ke; Liu Pusheng; Lü Baida

2008-01-01

Taking two Laguerre—Gaussian beams with topological charge l = ± 1 as an example, this paper studies the composite optical vortices formed by two noncollinear Laguerre—Gaussian beams with different phases, amplitudes, waist widths, off-axis distances, and their propagation in free space. It is shown by detailed numerical illustrative examples that the number and location of composite vortices at the waist plane are variable by varying the relative phase β, amplitude ratio η, waist width ratio ζ, or off-axis distance ratio μ. The net topological charge l net is not always equal to the sum l sum of charges of the two component beams. The motion, creation and annihilation of composite vortices take place in the free-space propagation, and the net charge during the propagation remains unchanged and equals to the net charge at the waist plane

Electron acceleration by longitudinal electric field of a gaussian laser beam

International Nuclear Information System (INIS)

Takeuchi, Satoshi; Sugihara, Ryo; Shimoda, Koichi.

1991-11-01

It is shown that the longitudinal electric field of a transverse magnetic mode of a Gaussian laser beam accelerates an electron to an ultra-relativistic energy. The electron is captured and accelerated in a length of the order of the Rayleigh range. The ultimate energy increment of the electron with a single laser beam is given by the product of transverse field intensity and the beam waist, and can be of the order of 100MeV. This fact implies that a multi-stage acceleration enables TeV-order-acceleration in a length of a few kilometers with the present state of the art. (author)

Average spreading and beam quality evolution of Gaussian array beams propagating through oceanic turbulence

International Nuclear Information System (INIS)

Zhi, Dong; Chen, Yizhu; Tao, Rumao; Ma, Yanxing; Zhou, Pu; Si, Lei

2015-01-01

The propagation properties of a radial Gaussian beam array through oceanic turbulence are studied analytically. The analytical expressions for the average intensity and the beam quality (power-in-the-bucket (PIB) and M 2 -factor) of a radial beam array in a turbulent ocean are derived based on an account of statistical optics methods, the extended Huygens-Fresnel principle, and the second order moments of the Wigner distribution function. The influences of w, ε, and χ T on the average intensity are investigated. The array divergence increases and the laser beam spreads as the salinity-induced dominant, ε decreased, and χ T increased. Further, the analytical expression of PIB and the M 2 -factor in the target plane is obtained. The changes of PIB and the M 2 -factor with three oceanic turbulence parameters indicate that the stronger turbulence with a larger w, smaller ε, and larger χ T results in the value of PIB decreasing, the value of the M 2 -factor increasing, and the beam quality degrading. (letter)

Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.

Science.gov (United States)

Sun, Dong; Zhao, Daomu

2005-08-01

By introducing the hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of the Wigner distribution function for Hermite-cosine-Gaussian beams passing through an apertured paraxial ABCD optical system are obtained. The analytical results are compared with the numerically integrated ones, and the absolute errors are also given. It is shown that the analytical results are proper and that the calculation speed for them is much faster than for the numerical results.

Gaussian representation of high-intensity focused ultrasound beams.

Science.gov (United States)

Soneson, Joshua E; Myers, Matthew R

2007-11-01

A method for fast numerical simulation of high-intensity focused ultrasound beams is derived. The method is based on the frequency-domain representation of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and assumes for each harmonic a Gaussian transverse pressure distribution at all distances from the transducer face. The beamwidths of the harmonics are constrained to vary inversely with the square root of the harmonic number, and as such this method may be viewed as an extension of a quasilinear approximation. The technique is capable of determining pressure or intensity fields of moderately nonlinear high-intensity focused ultrasound beams in water or biological tissue, usually requiring less than a minute of computer time on a modern workstation. Moreover, this method is particularly well suited to high-gain simulations since, unlike traditional finite-difference methods, it is not subject to resolution limitations in the transverse direction. Results are shown to be in reasonable agreement with numerical solutions of the full KZK equation in both tissue and water for moderately nonlinear beams.

Orbital angular momentum mode of Gaussian beam induced by atmospheric turbulence

Science.gov (United States)

Cheng, Mingjian; Guo, Lixin; Li, Jiangting; Yan, Xu; Dong, Kangjun

2018-02-01

Superposition theory of the spiral harmonics is employed to numerical study the transmission property of the orbital angular momentum (OAM) mode of Gaussian beam induced by atmospheric turbulence. Results show that Gauss beam does not carry OAM at the source, but various OAM modes appear after affected by atmospheric turbulence. With the increase of atmospheric turbulence strength, the smaller order OAM modes appear firstly, followed by larger order OAM modes. The beam spreading of Gauss beams in the atmosphere enhance with the increasing topological charge of the OAM modes caused by atmospheric turbulence. The mode probability density of the OAM generated by atmospheric turbulence decreases, and peak position gradually deviate from the Gauss beam spot center with the increase of the topological charge. Our results may be useful for improving the performance of long distance laser digital spiral imaging system.

Gaussian beam profile shaping apparatus, method therefore and evaluation thereof

International Nuclear Information System (INIS)

Dickey, F.M.; Holswade, S.C.; Romero, L.A.

1999-01-01

A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system. 27 figs

Evaluation of the influence of double and triple Gaussian proton kernel models on accuracy of dose calculations for spot scanning technique.

Science.gov (United States)

Hirayama, Shusuke; Takayanagi, Taisuke; Fujii, Yusuke; Fujimoto, Rintaro; Fujitaka, Shinichiro; Umezawa, Masumi; Nagamine, Yoshihiko; Hosaka, Masahiro; Yasui, Keisuke; Omachi, Chihiro; Toshito, Toshiyuki

2016-03-01

The main purpose in this study was to present the results of beam modeling and how the authors systematically investigated the influence of double and triple Gaussian proton kernel models on the accuracy of dose calculations for spot scanning technique. The accuracy of calculations was important for treatment planning software (TPS) because the energy, spot position, and absolute dose had to be determined by TPS for the spot scanning technique. The dose distribution was calculated by convolving in-air fluence with the dose kernel. The dose kernel was the in-water 3D dose distribution of an infinitesimal pencil beam and consisted of an integral depth dose (IDD) and a lateral distribution. Accurate modeling of the low-dose region was important for spot scanning technique because the dose distribution was formed by cumulating hundreds or thousands of delivered beams. The authors employed a double Gaussian function as the in-air fluence model of an individual beam. Double and triple Gaussian kernel models were also prepared for comparison. The parameters of the kernel lateral model were derived by fitting a simulated in-water lateral dose profile induced by an infinitesimal proton beam, whose emittance was zero, at various depths using Monte Carlo (MC) simulation. The fitted parameters were interpolated as a function of depth in water and stored as a separate look-up table. These stored parameters for each energy and depth in water were acquired from the look-up table when incorporating them into the TPS. The modeling process for the in-air fluence and IDD was based on the method proposed in the literature. These were derived using MC simulation and measured data. The authors compared the measured and calculated absolute doses at the center of the spread-out Bragg peak (SOBP) under various volumetric irradiation conditions to systematically investigate the influence of the two types of kernel models on the dose calculations. The authors investigated the difference

Extended wavelet transformation to digital holographic reconstruction: application to the elliptical, astigmatic Gaussian beams.

Science.gov (United States)

Remacha, Clément; Coëtmellec, Sébastien; Brunel, Marc; Lebrun, Denis

2013-02-01

Wavelet analysis provides an efficient tool in numerous signal processing problems and has been implemented in optical processing techniques, such as in-line holography. This paper proposes an improvement of this tool for the case of an elliptical, astigmatic Gaussian (AEG) beam. We show that this mathematical operator allows reconstructing an image of a spherical particle without compression of the reconstructed image, which increases the accuracy of the 3D location of particles and of their size measurement. To validate the performance of this operator we have studied the diffraction pattern produced by a particle illuminated by an AEG beam. This study used mutual intensity propagation, and the particle is defined as a chirped Gaussian sum. The proposed technique was applied and the experimental results are presented.

Self-focusing and self-defocusing of elliptically shaped Gaussian laser beams in plasmas

Energy Technology Data Exchange (ETDEWEB)

Nayyar, V P; Soni, V S [Punjabi Univ., Patiala (India). Dept. of Physics

1979-02-14

This paper presents a study of the self-focusing and self-defocusing of elliptically shaped Gaussian laser beams in collisional and collisionless plasmas. The non-linear dependence of the dielectric constant inside a collisional plasma is due to inhomogeneous heating of energy carriers and in a collisionless plasma it is due to the ponderomotive force. It is found that the beam gets focused at different points in different planes, exhibiting the effect of astigmatism. In certain power regions considered, the beam either converges or defocuses in both the directions, while in some other regions of the power spectrum one dimension of the beam focuses while the other defocuses. The beam also propagates in an oscillatory waveguide.

Linac beam core modeling from wire-scanner data

International Nuclear Information System (INIS)

Law, A.G.

1977-08-01

This study introduces mathematical modeling of accelerator beams from data collected by wire scanners. Details about a beam core D(x,x',y,y') are examined in several situations: (a) for a discretization of the projection into xy-space, a maximum-entropy solution and a minimum-norm solution are developed and discussed, (b) for undiscretized xy-subspace, a two-dimensional Gaussian approximation D(x,.,y,.) = a exp [α(x-x 0 ) 2 + β(x-x 0 )(y-y 0 ) + γ(y-y 0 ) 2 ] is obtained by least squares, and (c) for four-dimensional space, the fit of a single Gaussian to data from a succession of wire scanners is investigated

Numerical simulation of Gaussian beam scattering by complex particles of arbitrary shape and structure

International Nuclear Information System (INIS)

Han, Y.P.; Cui, Z.W.; Gouesbet, G.

2012-01-01

An efficient numerical method based on the surface integral equations is introduced to simulate the scattering of Gaussian beam by complex particles that consist of an arbitrarily shaped host particle and multiple internal inclusions of arbitrary shape. In particular, the incident focused Gaussian beam is described by the Davis fifth-order approximate expressions in combination with rotation defined by Euler angles. The established surface integral equations are discretized with the method of moments, where the unknown equivalent electric and magnetic currents induced on the surfaces of the host particle and the internal inclusions are expanded using the Rao-Wilton-Glisson (RWG) basis functions. The resultant matrix equations are solved by using the parallel conjugate gradient method. The proposed numerical method is validated and its capability illustrated in several characteristic examples.

Type I parametric down conversion of highly focused Gaussian beams in finite length crystals

International Nuclear Information System (INIS)

Jeronimo-Moreno, Yasser; Jáuregui, R

2014-01-01

This paper presents a study of the correlations in wave vector space of photon pairs generated by type I spontaneous parametric down conversion using a Gaussian pump beam. The analysis covers both moderate focused and highly focused regimes, paying special attention to the angular spectrum and the conditional angular spectrum. Simple analytic expressions are derived that allow a detailed study of the dependence of these spectra on the waist of the source and the length of the nonlinear crystal. These expressions are in good agreement with numerical expectations and reported experimental results. They are used to make a systematic search of optimization parameters that improve the feasibility of using highly focused Gaussian beams to generate idler and signal photons with predetermined mean values and spread of their transverse wave vectors. (papers)

Three-dimensional propagation and absorption of high frequency Gaussian beams in magnetoactive plasmas

International Nuclear Information System (INIS)

Nowak, S.; Orefice, A.

1994-01-01

In today's high frequency systems employed for plasma diagnostics, power heating, and current drive the behavior of the wave beams is appreciably affected by the self-diffraction phenomena due to their narrow collimation. In the present article the three-dimensional propagation of Gaussian beams in inhomogeneous and anisotropic media is analyzed, starting from a properly formulated dispersion relation. Particular attention is paid, in the case of electromagnetic electron cyclotron (EC) waves, to the toroidal geometry characterizing tokamak plasmas, to the power density evolution on the advancing wave fronts, and to the absorption features occurring when a beam crosses an EC resonant layer

Generation of tunable chain of three-dimensional optical bottle beams via focused multi-ring hollow Gaussian beam.

Science.gov (United States)

Philip, Geo M; Viswanathan, Nirmal K

2010-11-01

We report here the generation of a chain of three-dimensional (3-D) optical bottle beams by focusing a π-phase shifted multi-ring hollow Gaussian beam (HGB) using a lens with spherical aberration. The rings of the HGB of suitable radial (k(r)) and axial (k(z)) wave vectors are generated using a double-negative axicon chemically etched in the optical fiber tips. Moving the lens position with respect to the fiber tip results in variation of the semi-angle of the cones of wave vectors of the HGBs and their diameter, using which we demonstrate tunability in the size and the periodicity of the 3-D optical bottle beams over a wide range, from micrometers to millimeters. The propagation characteristics of the beams resulting from focusing of single- and multi-ring HGBs and resulting in a quasi-non-diffracting beam and a chain of 3-D optical bottle beams, respectively, are simulated using only the input beam parameters and are found to agree well with experimental results.

Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam

CSIR Research Space (South Africa)

Romero, J

2012-08-01

Full Text Available -1 Journal of Optics August 2012/ Vol. 14. No 8 Orbital angular momentum correlations with a phase- flipped Gaussian mode pump beam J Romero1,2, D Giovannini1, M G McLaren3,4, E J Galvez5, A Forbes3,4 and M J Padgett1 1 School of Physics...

Integral superposition of paraxial Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

Czech Academy of Sciences Publication Activity Database

Červený, V.; Pšenčík, Ivan

2015-01-01

Roč. 25, - (2015), s. 109-155 ISSN 2336-3827 Institutional support: RVO:67985530 Keywords : integral superposition of paraxial Gaussian beams * inhomogeneous anisotropic media * S waves in weakly anisotropic media Subject RIV: DC - Siesmology, Volcanology, Earth Structure

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

International Nuclear Information System (INIS)

Ji, Xiaoling; Deng, Jinping

2014-01-01

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration. - Highlights: • In weak turbulence scintillations can be suppressed using positive spherical aberration. • In weak turbulence scintillations may be very large due to negative spherical aberration. • The effect of spherical aberration on scintillations is less with increasing of turbulence

Effect of spherical aberration on scintillations of Gaussian beams in atmospheric turbulence

Energy Technology Data Exchange (ETDEWEB)

Ji, Xiaoling, E-mail: jiXL100@163.com; Deng, Jinping

2014-07-18

The effect of spherical aberration on scintillations of Gaussian beams in weak, moderate and strong turbulence is studied using numerical simulation method. It is found that the effect of the negative spherical aberration on the on-axis scintillation index is quite different from that of the positive spherical aberration. In weak turbulence, the positive spherical aberration results in a decrease of the on-axis scintillation index on propagation, but the negative spherical aberration results in an increase of the on-axis scintillation index when the propagation distance is not large. In particular, in weak turbulence the negative spherical aberration may cause peaks of the on-axis scintillation index, and the peaks disappear in moderate and strong turbulence, which is explained in physics. The strong turbulence leads to less discrepancy among scintillations of Gaussian beams with and without spherical aberration. - Highlights: • In weak turbulence scintillations can be suppressed using positive spherical aberration. • In weak turbulence scintillations may be very large due to negative spherical aberration. • The effect of spherical aberration on scintillations is less with increasing of turbulence.

SU-D-BRC-01: An Automatic Beam Model Commissioning Method for Monte Carlo Simulations in Pencil-Beam Scanning Proton Therapy

Energy Technology Data Exchange (ETDEWEB)

Qin, N; Shen, C; Tian, Z; Jiang, S; Jia, X [UT Southwestern Medical Ctr, Dallas, TX (United States)

2016-06-15

Purpose: Monte Carlo (MC) simulation is typically regarded as the most accurate dose calculation method for proton therapy. Yet for real clinical cases, the overall accuracy also depends on that of the MC beam model. Commissioning a beam model to faithfully represent a real beam requires finely tuning a set of model parameters, which could be tedious given the large number of pencil beams to commmission. This abstract reports an automatic beam-model commissioning method for pencil-beam scanning proton therapy via an optimization approach. Methods: We modeled a real pencil beam with energy and spatial spread following Gaussian distributions. Mean energy, and energy and spatial spread are model parameters. To commission against a real beam, we first performed MC simulations to calculate dose distributions of a set of ideal (monoenergetic, zero-size) pencil beams. Dose distribution for a real pencil beam is hence linear superposition of doses for those ideal pencil beams with weights in the Gaussian form. We formulated the commissioning task as an optimization problem, such that the calculated central axis depth dose and lateral profiles at several depths match corresponding measurements. An iterative algorithm combining conjugate gradient method and parameter fitting was employed to solve the optimization problem. We validated our method in simulation studies. Results: We calculated dose distributions for three real pencil beams with nominal energies 83, 147 and 199 MeV using realistic beam parameters. These data were regarded as measurements and used for commission. After commissioning, average difference in energy and beam spread between determined values and ground truth were 4.6% and 0.2%. With the commissioned model, we recomputed dose. Mean dose differences from measurements were 0.64%, 0.20% and 0.25%. Conclusion: The developed automatic MC beam-model commissioning method for pencil-beam scanning proton therapy can determine beam model parameters with

Doppler-shifted neutral beam line shape and beam transmission

International Nuclear Information System (INIS)

Kamperschroer, J.H.; Grisham, L.R.; Kokatnur, N.; Lagin, L.J.; Newman, R.A.; O'Connor, T.E.; Stevenson, T.N.; von Halle, A.

1994-04-01

Analysis of Doppler-shifted Balmer-α line emission from the TFTR neutral beam injection systems has revealed that the line shape is well approximated by the sum of two Gaussians, or, alternatively, by a Lorentzian. For the sum of two Gaussians, the broad portion of the distribution contains 40% of the beam power and has a divergence five times that of the narrow part. Assuming a narrow 1/e- divergence of 1.3 degrees (based on fits to the beam shape on the calorimeter), the broad part has a divergence of 6.9 degrees. The entire line shape is also well approximated by a Lorentzian with a half-maximum divergence of 0.9 degrees. Up to now, fusion neutral beam modelers have assumed a single Gaussian velocity distribution, at the extraction plane, in each direction perpendicular to beam propagation. This predicts a beam transmission efficiency from the ion source to the calorimeter of 97%. Waterflow calorimetry data, however, yield a transmission efficiency of ∼75%, a value in rough agreement with predictions of the Gaussian or Lorentzian models presented here. The broad wing of the two Gaussian distribution also accurately predicts the loss in the neutralizer. An average angle of incidence for beam loss at the exit of the neutralizer is 2.2 degrees, rather than the 4.95 degrees subtended by the center of the ion source. This average angle of incidence, which is used in computing power densities on collimators, is shown to be a function of beam divergence

Tabulated square-shaped source model for linear accelerator electron beam simulation.

Science.gov (United States)

Khaledi, Navid; Aghamiri, Mahmood Reza; Aslian, Hossein; Ameri, Ahmad

2017-01-01

Using this source model, the Monte Carlo (MC) computation becomes much faster for electron beams. The aim of this study was to present a source model that makes linear accelerator (LINAC) electron beam geometry simulation less complex. In this study, a tabulated square-shaped source with transversal and axial distribution biasing and semi-Gaussian spectrum was investigated. A low energy photon spectrum was added to the semi-Gaussian beam to correct the bremsstrahlung X-ray contamination. After running the MC code multiple times and optimizing all spectrums for four electron energies in three different medical LINACs (Elekta, Siemens, and Varian), the characteristics of a beam passing through a 10 cm × 10 cm applicator were obtained. The percentage depth dose and dose profiles at two different depths were measured and simulated. The maximum difference between simulated and measured percentage of depth doses and dose profiles was 1.8% and 4%, respectively. The low energy electron and photon spectrum and the Gaussian spectrum peak energy and associated full width at half of maximum and transversal distribution weightings were obtained for each electron beam. The proposed method yielded a maximum computation time 702 times faster than a complete head simulation. Our study demonstrates that there was an excellent agreement between the results of our proposed model and measured data; furthermore, an optimum calculation speed was achieved because there was no need to define geometry and materials in the LINAC head.

Beam shape coefficients calculation for an elliptical Gaussian beam with 1-dimensional quadrature and localized approximation methods

Science.gov (United States)

Wang, Wei; Shen, Jianqi

2018-06-01

The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.

Die trinitarische Spekulation und göttliche Freiheit beim späten Schelling

Czech Academy of Sciences Publication Activity Database

Landa, Ivan

-, č. 3 (2011), s. 74-86 ISSN 0010-3713 R&D Projects: GA AV ČR(CZ) KJB900090902 Institutional research plan: CEZ:AV0Z90090514 Keywords : trinity * freedom * God * Schelling * Hegel Subject RIV: AA - Philosophy ; Religion

Theoretical study of the attenuation of a gaussian beam penetrating into a dielectric circular wave guide

International Nuclear Information System (INIS)

Crenn, J.P.

1981-07-01

It is proposed to draw up an approximate formula directly giving the attenuation of a gaussian beam penetrating into a superdimensioned dielectric circular wave guide. This formula is derived from optical laws, i.e. Fresnel's formulae of the reflexion of a wave on a dielectric to which a correcting term due to diffraction has been added. The results given by this formula are compared with the existing results, based on the breakdown of a gaussian beam into propagation modes, thereby enabling their validity and the field of use to be checked. An application is then made to the wave guides that will be employed in the infrared interferometer fitted in JET [fr

Direction-dependent waist-shift-difference of Gaussian beam in a multiple-pass zigzag slab amplifier and geometrical optics compensation method.

Science.gov (United States)

Li, Zhaoyang; Kurita, Takashi; Miyanaga, Noriaki

2017-10-20

Zigzag and non-zigzag beam waist shifts in a multiple-pass zigzag slab amplifier are investigated based on the propagation of a Gaussian beam. Different incident angles in the zigzag and non-zigzag planes would introduce a direction-dependent waist-shift-difference, which distorts the beam quality in both the near- and far-fields. The theoretical model and analytical expressions of this phenomenon are presented, and intensity distributions in the two orthogonal planes are simulated and compared. A geometrical optics compensation method by a beam with 90° rotation is proposed, which not only could correct the direction-dependent waist-shift-difference but also possibly average the traditional thermally induced wavefront-distortion-difference between the horizontal and vertical beam directions.

Scattering of Gaussian beam by a spherical particle with a spheroidal inclusion

International Nuclear Information System (INIS)

Zhang Huayong; Liao Tongqing

2011-01-01

A generalized Lorenz-Mie theory framework (GLMT) is applied to the study of Gaussian beam scattering by a spherical particle with an embedded spheroid at the center. By virtue of a transformation between the spherical and spheroidal vector wave functions, a theoretical procedure is developed to deal with the boundary conditions. Numerical results of the normalized differential scattering cross section are presented.

Levy-Student processes for a stochastic model of beam halos

Energy Technology Data Exchange (ETDEWEB)

Petroni, N. Cufaro [Department of Mathematics, University of Bari, and INFN Sezione di Bari, via E. Orabona 4, 70125 Bari (Italy)]. E-mail: cufaro@ba.infn.it; De Martino, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); De Siena, S. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy); Illuminati, F. [Department of Physics, University of Salerno, and INFN Sezione di Napoli (gruppo di Salerno), Via S. Allende, I-84081 Baronissi (SA) (Italy)

2006-06-01

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.

Levy-Student processes for a stochastic model of beam halos

International Nuclear Information System (INIS)

Petroni, N. Cufaro; De Martino, S.; De Siena, S.; Illuminati, F.

2006-01-01

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the stochastic mechanics which produces time reversal invariant diffusion processes. In this paper we analyze the consequences of introducing the generalized Student laws, namely non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will analyze this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) stochastic model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. In the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams

Aperture averaging and BER for Gaussian beam in underwater oceanic turbulence

Science.gov (United States)

Gökçe, Muhsin Caner; Baykal, Yahya

2018-03-01

In an underwater wireless optical communication (UWOC) link, power fluctuations over finite-sized collecting lens are investigated for a horizontally propagating Gaussian beam wave. The power scintillation index, also known as the irradiance flux variance, for the received irradiance is evaluated in weak oceanic turbulence by using the Rytov method. This lets us further quantify the associated performance indicators, namely, the aperture averaging factor and the average bit-error rate (). The effects on the UWOC link performance of the oceanic turbulence parameters, i.e., the rate of dissipation of kinetic energy per unit mass of fluid, the rate of dissipation of mean-squared temperature, Kolmogorov microscale, the ratio of temperature to salinity contributions to the refractive index spectrum as well as system parameters, i.e., the receiver aperture diameter, Gaussian source size, laser wavelength and the link distance are investigated.

Ghost reflections of Gaussian beams in anamorphic optical systems with an application to Michelson interferometer.

Science.gov (United States)

Abd El-Maksoud, Rania H

2016-02-20

In this paper, a methodology is developed to model and analyze the effect of undesired (ghost) reflections of Gaussian beams that are produced by anamorphic optical systems. The superposition of these beams with the nominal beam modulates the nominal power distribution at the recording plane. This modulation may cause contrast reduction, veiling parts of the nominal image, and/or the formation of spurious interference fringes. The developed methodology is based on synthesizing the beam optical paths into nominal and ghost optical beam paths. Similar to the nominal beam, we present the concept that each ghost beam is characterized by a beam size, wavefront radius of curvature, and Gouy phase in the paraxial regime. The nominal and ghost beams are sequentially traced through the system and formulas for estimating the electric field magnitude and phase of each ghost beam at the recording plane are presented. The effective electric field is the addition of the individual nominal and ghost electric fields. Formulas for estimating Gouy phase, the shape of the interference fringes, and the central interference order are introduced. As an application, the theory of the formation of the interference fringes by Michelson interferometer is presented. This theory takes into consideration the ghost reflections that are formed by the beam splitter. To illustrate the theory and to show its wide applicability, simulation examples that include a Mangin mirror, a Michelson interferometer, and a black box optical system are provided.

Uniform versus Gaussian Beams: A Comparison of the Effects of Diffraction, Obscuration, and Aberations.

Science.gov (United States)

1985-12-16

balancing is discussed for the two types of beams. Zernike polynomials representing balanced primary aberration for uniform and Gaussian annular beams...plotted on a logarithmic scale (Figs. 3c and 3d ). The positions of maxima and minima and the correspond- ing irradiance and encircled-power values are...aberration 2 4 (representing a term in the expansion of the aberration in terms of a set of " Zernike " polynomials which are orthonormal over the amplitude

Analytic methods to find beating transitions of asymmetric Gaussian beams in GNLS equations

Science.gov (United States)

Ianetz, David; Schiff, Jeremy

2018-01-01

In a simple model of propagation of asymmetric Gaussian beams in nonlinear waveguides, described by a reduction to ordinary differential equations of generalized nonlinear Schrödinger equations with cubic-quintic (CQ) and saturable (SAT) nonlinearities and a graded-index profile, the beam widths exhibit two different types of beating behavior, with transitions between them. We present an analytic model to explain these phenomena, which originate in a 1:1 resonance in a 2 degree-of-freedom Hamiltonian system. We show how small oscillations near a fixed point close to 1:1 resonance in such a system can be approximated using an integrable Hamiltonian and, ultimately, a single first order differential equation. In particular, the beating transitions can be located from coincidences of roots of a pair of quadratic equations, with coefficients determined (in a highly complex manner) by the internal parameters and initial conditions of the original system. The results of the analytic model agree with the numerics of the original system over large parameter ranges, and allow new predictions that can be verified directly. In the CQ case, we identify a band of beam energies for which there is only a single beating transition (as opposed to 0 or 2) as the eccentricity is increased. In the SAT case, we explain the sudden (dis)appearance of beating transitions for certain values of the other parameters as the grade-index is changed.

Laguerre Gaussian beam multiplexing through turbulence

CSIR Research Space (South Africa)

Trichili, A

2014-08-17

Full Text Available We analyze the effect of atmospheric turbulence on the propagation of multiplexed Laguerre Gaussian modes. We present a method to multiplex Laguerre Gaussian modes using digital holograms and decompose the resulting field after encountering a...

Self-Focusing of Quadruple Gaussian Laser Beam in an Inhomogenous Magnetized Plasma with Ponderomotive Non-Linearity: Effect of Linear Absorption

International Nuclear Information System (INIS)

Aggarwal, Munish; Vij, Shivani; Kant, Niti

2015-01-01

The propagation of quadruple Gaussian laser beam in a plasma characterized by axial inhomogeneity and nonlinearity due to ponderomotive force in the paraxial ray approximation is investigated. An appropriate expression for the nonlinear dielectric constant has been developed in the presence of external magnetic field, with linear absorption and due to saturation effects for arbitrary large intensity. The effects of different types of plasma axial inhomogeneities on self-focusing of laser beam have been studied with the typical laser and plasma parameters. Self-focusing of quadruple Gaussian laser beam in the presence of externally applied magnetic field and saturating parameter is found significantly improved in the case of extraordinary mode. Our results reveal that initially converging beam shows oscillatory convergence whereas initially diverging beam shows oscillatory divergence. The beam is more focussed at lower intensity in both cases viz. extraordinary and ordinary mode. (paper)

Density Transition Based Self-Focusing of cosh-Gaussian Laser Beam in Plasma with Linear Absorption

International Nuclear Information System (INIS)

Kant, Niti; Wani, Manzoor Ahmad

2015-01-01

Density transition based self-focusing of cosh-Gaussian laser beam in plasma with linear absorption has been studied. The field distribution in the plasma is expressed in terms of beam width parameter, decentered parameter, and linear absorption coefficient. The differential equation for the beam width parameter is solved by following Wentzel–Kramers–Brillouin (WKB) and paraxial approximation through parabolic wave equation approach. The behaviour of beam width parameter with dimensionless distance of propagation is studied at optimum values of plasma density, decentered parameter and with different absorption levels in the medium. The results reveal that these parameters can affect the self-focusing significantly. (paper)

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate.

Science.gov (United States)

Kotlyar, Victor V; Almazov, Anton A; Khonina, Svetlana N; Soifer, Victor A; Elfstrom, Henna; Turunen, Jari

2005-05-01

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

A pintura em Schelling e o problema da imagem = The painting in Schelling and the problem of image

Directory of Open Access Journals (Sweden)

Barros, Fernando Ribeiro de Moraes

2010-01-01

Full Text Available O propósito geral deste artigo consiste em mostrar, a partir de hipóteses globais de interpretação da natureza e da arte, o lugar da pintura na filosofia de F. W. J. v. Schelling. Submetendo a obra pictórica a condições teórico-especulativas inovadoras, a ponderação schellinguiana impele-nos, não raro, a um tratamento diferenciado do visível. Por isso, a título de exercício de reflexão, espera-se igualmente indicar que tal caracterização da pintura ecoa e antecipa, ao longe, questões levantadas pela filosofia contemporânea – em especial, pela fenomenologia – a respeito da imagem

A Gaussian mixture copula model based localized Gaussian process regression approach for long-term wind speed prediction

International Nuclear Information System (INIS)

Yu, Jie; Chen, Kuilin; Mori, Junichi; Rashid, Mudassir M.

2013-01-01

Optimizing wind power generation and controlling the operation of wind turbines to efficiently harness the renewable wind energy is a challenging task due to the intermittency and unpredictable nature of wind speed, which has significant influence on wind power production. A new approach for long-term wind speed forecasting is developed in this study by integrating GMCM (Gaussian mixture copula model) and localized GPR (Gaussian process regression). The time series of wind speed is first classified into multiple non-Gaussian components through the Gaussian mixture copula model and then Bayesian inference strategy is employed to incorporate the various non-Gaussian components using the posterior probabilities. Further, the localized Gaussian process regression models corresponding to different non-Gaussian components are built to characterize the stochastic uncertainty and non-stationary seasonality of the wind speed data. The various localized GPR models are integrated through the posterior probabilities as the weightings so that a global predictive model is developed for the prediction of wind speed. The proposed GMCM–GPR approach is demonstrated using wind speed data from various wind farm locations and compared against the GMCM-based ARIMA (auto-regressive integrated moving average) and SVR (support vector regression) methods. In contrast to GMCM–ARIMA and GMCM–SVR methods, the proposed GMCM–GPR model is able to well characterize the multi-seasonality and uncertainty of wind speed series for accurate long-term prediction. - Highlights: • A novel predictive modeling method is proposed for long-term wind speed forecasting. • Gaussian mixture copula model is estimated to characterize the multi-seasonality. • Localized Gaussian process regression models can deal with the random uncertainty. • Multiple GPR models are integrated through Bayesian inference strategy. • The proposed approach shows higher prediction accuracy and reliability

Inspection of commercial optical devices for data storage using a three Gaussian beam microscope interferometer

International Nuclear Information System (INIS)

Flores, J. Mauricio; Cywiak, Moises; Servin, Manuel; Juarez P, Lorenzo

2008-01-01

Recently, an interferometric profilometer based on the heterodyning of three Gaussian beams has been reported. This microscope interferometer, called a three Gaussian beam interferometer, has been used to profile high quality optical surfaces that exhibit constant reflectivity with high vertical resolution and lateral resolution near λ. We report the use of this interferometer to measure the profiles of two commercially available optical surfaces for data storage, namely, the compact disk (CD-R) and the digital versatile disk (DVD-R). We include experimental results from a one-dimensional radial scan of these devices without data marks. The measurements are taken by placing the devices with the polycarbonate surface facing the probe beam of the interferometer. This microscope interferometer is unique when compared with other optical measuring instruments because it uses narrowband detection, filters out undesirable noisy signals, and because the amplitude of the output voltage signal is basically proportional to the local vertical height of the surface under test, thus detecting with high sensitivity. We show that the resulting profiles, measured with this interferometer across the polycarbonate layer, provide valuable information about the track profiles, making this interferometer a suitable tool for quality control of surface storage devices

Analyzing the Propagation Behavior of a Gaussian Laser Beam through Seawater and Comparing with Atmosphere

Directory of Open Access Journals (Sweden)

F Dabbagh Kashani

2013-12-01

Full Text Available Study of the beam propagation behavior through oceanic media is a challenging subject. In this paper, based on generalized Collins integral, the mean irradiance profile of Gaussian laser beam propagation through ocean is investigated. Power In Special Bucket (PIB is calculated. Using analytical expressions and calculating seawater transmission, the effects of absorption and scattering on beam propagation are studied. Based on these formulae, propagation in ocean and atmosphere are compared. The effects of some optical and environmental specifications, such as divergence angle and chlorophyll concentration in seawater on beam propagation by using mean irradiance, PIB and analytical formula of oceanic transmission are studied. The calculated results are shown graphically.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle.

Science.gov (United States)

Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu

2006-07-10

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.

Entry limitations and heterogeneous tolerances in a Schelling-like segregation model

International Nuclear Information System (INIS)

Radi, Davide; Gardini, Laura

2015-01-01

In this paper we consider a Schelling-type segregation model with two groups of agents that differ in some aspects, such as religion, political affiliation or color of skin. The first group is identified as the local population, while the second group is identified as the newcomers, whose members want to settle down in the city or country, or more generally a system, already populated by members of the local population. The members of the local population have a limited tolerance towards newcomers. On the contrary, some newcomers, but not all of them, may stand the presence of any amount of members of the local population. The heterogeneous, and partially limited, levels of tolerance trigger an entry and exit dynamics into and from the system of the members of the two groups based on their satisfaction with the number of members of the other group into the system. This entry/exit dynamics is described by a continuous piecewise-differentiable map in two dimensions. The dynamics of the model is characterized by smooth bifurcations as well as by border collision bifurcations. A combination of analytical results and numerical analysis are the main tools used to describe the quite complicated local and global dynamics of the model. The investigation reveals that two factors are the main elements that preclude integration. The first one is a low level of tolerance of the members of the two populations. The second one is an excessive and unbalanced level of tolerance between the two populations. In this last case, to facilitate the integration between members of the two groups, we impose an entry-limitation policy represented by the imposition of a maximum number of newcomers allowed to enter the system. The investigation of the dynamics reveals that the entry-limitation policy is useful to promote integration as it limits the negative effects due to excessive and unbalanced levels of tolerance.

Measurement of the broadening and depolarization of a Gaussian beam to transmit in fog water

International Nuclear Information System (INIS)

Serrano, G.; Reynoso, E; Davila, J. A.

2012-01-01

In this paper, we develop a controlled experimental environment in the laboratory, a waterproof camera where it will introduce artificial fog and become a beam of linearly polarized Gaussian laser light, creating sprawl, broadening and depolarization is studied with a system capable of measuring such phenomena. Most studies on dispersion have focused on the lobes of backscattering, however the correct conditions with the incident light beam a substantial fraction of light is scattered in the forward direction forming a widened light lobe. With this light lobe formed could be studied with extreme precision many factors such as the existence of single or multiple scattering and the amount by which this is carried out. This is of great importance in the estimation of lidar returns because these foundations can learn important information such as extinction and backscatter coefficients, particulate pollutants in the atmosphere and thus understand the operation model of nature. (Author)

Bayesian modelling of the emission spectrum of the Joint European Torus Lithium Beam Emission Spectroscopy system.

Science.gov (United States)

Kwak, Sehyun; Svensson, J; Brix, M; Ghim, Y-C

2016-02-01

A Bayesian model of the emission spectrum of the JET lithium beam has been developed to infer the intensity of the Li I (2p-2s) line radiation and associated uncertainties. The detected spectrum for each channel of the lithium beam emission spectroscopy system is here modelled by a single Li line modified by an instrumental function, Bremsstrahlung background, instrumental offset, and interference filter curve. Both the instrumental function and the interference filter curve are modelled with non-parametric Gaussian processes. All free parameters of the model, the intensities of the Li line, Bremsstrahlung background, and instrumental offset, are inferred using Bayesian probability theory with a Gaussian likelihood for photon statistics and electronic background noise. The prior distributions of the free parameters are chosen as Gaussians. Given these assumptions, the intensity of the Li line and corresponding uncertainties are analytically available using a Bayesian linear inversion technique. The proposed approach makes it possible to extract the intensity of Li line without doing a separate background subtraction through modulation of the Li beam.

Functional Dual Adaptive Control with Recursive Gaussian Process Model

International Nuclear Information System (INIS)

Prüher, Jakub; Král, Ladislav

2015-01-01

The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)

Gaussian Mixture Model of Heart Rate Variability

Science.gov (United States)

Costa, Tommaso; Boccignone, Giuseppe; Ferraro, Mario

2012-01-01

Heart rate variability (HRV) is an important measure of sympathetic and parasympathetic functions of the autonomic nervous system and a key indicator of cardiovascular condition. This paper proposes a novel method to investigate HRV, namely by modelling it as a linear combination of Gaussians. Results show that three Gaussians are enough to describe the stationary statistics of heart variability and to provide a straightforward interpretation of the HRV power spectrum. Comparisons have been made also with synthetic data generated from different physiologically based models showing the plausibility of the Gaussian mixture parameters. PMID:22666386

A Simple Model for Nonlinear Confocal Ultrasonic Beams

Science.gov (United States)

Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen

2007-01-01

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.

Walk-off reduction, using an external optical plate and Bessel–Gaussian interaction

International Nuclear Information System (INIS)

Mansouri, Masoume; Askarbioki, Mohsen; Ghavami Sabouri, Saeed; Khorsandi, Alireza

2015-01-01

To reduce the walk-off angle of the extraordinary third-harmonic ultraviolet wave at 355 nm generated by type II KTiOPO 4 and type I β-BaB 2 O 4 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. (paper)

Walk-off reduction, using an external optical plate and Bessel-Gaussian interaction

Science.gov (United States)

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.

Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam

NARCIS (Netherlands)

Nicolas, F.; Coëtmellec, S.; Brunel, M.; Allano, D.; Lebrun, D.; Janssen, A.J.E.M.

2005-01-01

The authors have studied the diffraction pattern produced by a particle field illuminated by an elliptic and astigmatic Gaussian beam. They demonstrate that the bidimensional fractional Fourier transformation is a mathematically suitable tool to analyse the diffraction pattern generated not only by

GPU-Powered Modelling of Nonlinear Effects due to Head-On Beam-Beam Interactions in High-Energy Hadron Colliders.

CERN Document Server

Furuseth, Sondre

2017-01-01

The performance of high-energy circular hadron colliders, as the Large Hadron Collider, is limited by beam-beam interactions. The strongly nonlinear force between the two opposing beams causes diverging Hamiltonians and resonances, which can lead to a reduction of the lifetime of the beams. The nonlinearity makes the effect of the force difficult to study analytically, even at first order. Numerical models are therefore needed to evaluate the overall effect of different configurations of the machines. This report discusses results from an implementation of the weak-strong model, studying the effects of head-on beam-beam interactions. The assumptions has been shown to be valid for configurations where the growth and losses of the beam are small. The tracking has been done using an original code which applies graphic cards to reduce the computation time. The bunches in the beams have been modelled cylindrically symmetrical, based on a Gaussian distribution in three dimensions. This choice fits well with bunches...

Analytical calculations of intense Gaussian laser beam propagating in plasmas with relativistic collision correction

International Nuclear Information System (INIS)

Wang Ying; Yuan Chengxun; Gao Ruilin; Zhou Zhongxiang

2012-01-01

Theoretical investigations of a Gaussian laser beam propagating in relativistic plasmas have been performed with the WKB method and complex eikonal function. We consider the relativistic nonlinearity induced by intense laser beam, and present the relativistically generalized forms of the plasma frequency and electron collision frequency in plasmas. The coupled differential equations describing the propagation variations of laser beam are derived and numerically solved. The obtained simulation results present the similar variation tendency with experiments. By changing the plasma density, we theoretically analyze the feasibility of using a plasmas slab of a fixed thickness to compress the laser beam-width and acquire the focused laser intensity. The present work complements the relativistic correction of the electron collision frequency with reasonable derivations, promotes the theoretical approaching to experiments and provides effective instructions to the practical laser-plasma interactions.

Acoustic radiation force on a double-layer microsphere by a Gaussian focused beam

International Nuclear Information System (INIS)

Wu, Rongrong; Cheng, Kaixuan; Liu, Jiehui; Mao, Yiwei; Gong, Xiufen; Liu, Xiaozhou

2014-01-01

A new model for calculating the radiation force on double-layer microsphere is proposed based on the ray acoustics approach. The axial acoustic radiation force resulting from a focused Gaussian beam incident on spherical shells immersed in water is examined theoretically in relation to its thickness and the contents of its double-layer. The attenuation both in the water and inside the sphere is considered in this method, which cannot be ignored while the high frequency ultrasonic is used. Results of numerical calculations are presented for fat and low density polyethylene materials, with the hollow region filled with animal oil, water, or air. These results show how the acoustic impedance and the sound velocity of both layers, together with the thickness of the shell, affect the acoustic radiation force.

Fundamentals of negative refractive index optical trapping: forces and radiation pressures exerted by focused Gaussian beams using the generalized Lorenz-Mie theory.

Science.gov (United States)

Ambrosio, Leonardo A; Hernández-Figueroa, Hugo E

2010-11-04

Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised.

Evolution of a Gaussian laser beam in warm collisional magnetoplasma

Energy Technology Data Exchange (ETDEWEB)

Jafari, M. J.; Jafari Milani, M. R., E-mail: mrj.milani@gmail.com [Plasma Physics Research School, NSTRI, Tehran (Iran, Islamic Republic of); Niknam, A. R. [Laser and Plasma Research Institute, Shahid Beheshti University, G.C., Tehran (Iran, Islamic Republic of)

2016-07-15

In this paper, the spatial evolution of an intense circularly polarized Gaussian laser beam propagated through a warm plasma is investigated, taking into account the ponderomotive force, Ohmic heating, external magnetic field, and collisional effects. Using the momentum transfer and energy equations, both modified electron temperature and electron density in plasma are obtained. By introducing the complex dielectric permittivity of warm magnetized plasma and using the complex eikonal function, coupled differential equations for beam width parameter are established and solved numerically. The effects of polarization state of laser and magnetic field on the laser spot size evolution are studied. It is observed that in case of the right-handed polarization, an increase in the value of external magnetic field causes an increase in the strength of the self-focusing, especially in the higher values, and consequently, the self-focusing occurs in shorter distance of propagation. Moreover, the results demonstrate the existence of laser intensity and electron temperature ranges where self-focusing can occur, while the beam diverges outside of these regions; meanwhile, in these intervals, there exists a turning point for each of intensity and temperature in which the self-focusing process has its strongest strength. Finally, it is found that the self-focusing effect can be enhanced by increasing the plasma frequency (plasma density).

Influence of light absorption on relativistic self-focusing of Gaussian laser beam in cold quantum plasma

Science.gov (United States)

Patil, S. D.; Valkunde, A. T.; Vhanmore, B. D.; Urunkar, T. U.; Gavade, K. M.; Takale, M. V.

2018-05-01

When inter particle distance is comparable to the de Broglies wavelength of charged particles, quantum effects in plasmas are unavoidable. We have exploited an influence of light absorption on self-focusing of Gaussian laser beam in cold quantum plasma by considering relativistic nonlinearity. Nonlinear differential equation governing beam-width parameter has been established by using parabolic equation approach under paraxial and WKB approximations. The effect of light absorption on variation of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. It is found that light absorption plays vital role in weakening the relativistic self-focusing of laser beam during propagation in cold quantum plasma and gives reasonably interesting results.

Measurement of the orbital angular momentum density of Bessel beams by projection into a Laguerre–Gaussian basis

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...

Wigner functions for evanescent waves.

Science.gov (United States)

Petruccelli, Jonathan C; Tian, Lei; Oh, Se Baek; Barbastathis, George

2012-09-01

We propose phase space distributions, based on an extension of the Wigner distribution function, to describe fields of any state of coherence that contain evanescent components emitted into a half-space. The evanescent components of the field are described in an optical phase space of spatial position and complex-valued angle. Behavior of these distributions upon propagation is also considered, where the rapid decay of the evanescent components is associated with the exponential decay of the associated phase space distributions. To demonstrate the structure and behavior of these distributions, we consider the fields generated from total internal reflection of a Gaussian Schell-model beam at a planar interface.

Beam-beam depolarization in SPEAR and PEP

International Nuclear Information System (INIS)

Montague, B.W.

1977-01-01

In this note some approximate estimates are made of depolarization due to beam-beam forces in SPEAR and PEP, using the results of a calculation by Kondratenko. The model assumes head-on collisions between bunches of Gaussian distribution in the transverse directions; the force on the weak-beam particle is taken to be a δ-function at the interaction point. 1 ref

Transmission characteristics of Bessel-Gaussian vortex beams propagating along both longitudinal and transverse directions in a subway tunnel

Science.gov (United States)

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.

Modeling Non-Gaussian Time Series with Nonparametric Bayesian Model.

Science.gov (United States)

Xu, Zhiguang; MacEachern, Steven; Xu, Xinyi

2015-02-01

We present a class of Bayesian copula models whose major components are the marginal (limiting) distribution of a stationary time series and the internal dynamics of the series. We argue that these are the two features with which an analyst is typically most familiar, and hence that these are natural components with which to work. For the marginal distribution, we use a nonparametric Bayesian prior distribution along with a cdf-inverse cdf transformation to obtain large support. For the internal dynamics, we rely on the traditionally successful techniques of normal-theory time series. Coupling the two components gives us a family of (Gaussian) copula transformed autoregressive models. The models provide coherent adjustments of time scales and are compatible with many extensions, including changes in volatility of the series. We describe basic properties of the models, show their ability to recover non-Gaussian marginal distributions, and use a GARCH modification of the basic model to analyze stock index return series. The models are found to provide better fit and improved short-range and long-range predictions than Gaussian competitors. The models are extensible to a large variety of fields, including continuous time models, spatial models, models for multiple series, models driven by external covariate streams, and non-stationary models.

Tight focusing properties of linearly polarized Gaussian beam with a pair of vortices

Energy Technology Data Exchange (ETDEWEB)

Chen, Ziyang [Department of Physics, Zhejiang University, Hangzhou 310027 (China); College of Information Science and Engineering, Institute of Optics and Photonics, Huaqiao University, Xiamen, Fujian 361021 (China); Pu, Jixiong [College of Information Science and Engineering, Institute of Optics and Photonics, Huaqiao University, Xiamen, Fujian 361021 (China); Zhao, Daomu, E-mail: zhaodaomu@yahoo.com [Department of Physics, Zhejiang University, Hangzhou 310027 (China)

2011-07-25

The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical-aperture are studied on the basis of vector Debye integral. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges. For incident beam with a pair of vortices with opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane. -- Highlights: → The properties of a pair of vortices focused by a high numerical-aperture are studied. → It is shown that the focusing vortices with equal topological charges move toward and rotate. → It is shown that the focusing vortices with opposite topological charges move toward each other, annihilate and revive.

Superresolution beams

CSIR Research Space (South Africa)

Ngcobo, S

2011-11-01

Full Text Available The transformation of a Gaussian beam (GB) into a symmetrical higher order TEMp0 Laguerre Gaussian beam (LGB) intensity distribution of which is further rectified and transformed into a Gaussian intensity distribution in the plane of a converging...

Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

Czech Academy of Sciences Publication Activity Database

Červený, V.; Pšenčík, Ivan

2016-01-01

Roč. 26 (2016), s. 131-153 ISSN 2336-3827 R&D Projects: GA ČR(CZ) GA16-05237S Institutional support: RVO:67985530 Keywords : elastodynamic Green function * inhomogeneous anisotropic media * integral superposition of Gaussian beams Subject RIV: DC - Siesmology, Volcanology, Earth Structure

Selective excitation of higher-radial-order Laguerre-Gaussian beams using a solid-state digital laser

CSIR Research Space (South Africa)

Bell, Teboho

2017-01-01

Full Text Available Filter (LF) was introduced to only transmit 1064 nm and block the 808 nm pump. The laser beam was transmitted out of the cavity through an output coupler mirror (M3 on Figure 1) and was 1:1 relay imaged using two 125 mm lenses (L3 and L4) to a Photon...; Published December 30, 2016 Citation: Bell T, Ngcobo S (2016) Selective Excitation of Higher-radial-order Laguerre-Gaussian Beams Using a Solid-state Digital Laser. J Laser Opt Photonics 3: 144. doi: 10.4172/2469-410X.1000144 Copyright: © 2016 Bell T, et...

Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data

Directory of Open Access Journals (Sweden)

Ji Hoon Ryoo

2017-08-01

Full Text Available As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.

Diffusion weighted imaging in patients with rectal cancer: Comparison between Gaussian and non-Gaussian models.

Directory of Open Access Journals (Sweden)

Georgios C Manikis

Full Text Available The purpose of this study was to compare the performance of four diffusion models, including mono and bi-exponential both Gaussian and non-Gaussian models, in diffusion weighted imaging of rectal cancer.Nineteen patients with rectal adenocarcinoma underwent MRI examination of the rectum before chemoradiation therapy including a 7 b-value diffusion sequence (0, 25, 50, 100, 500, 1000 and 2000 s/mm2 at a 1.5T scanner. Four different diffusion models including mono- and bi-exponential Gaussian (MG and BG and non-Gaussian (MNG and BNG were applied on whole tumor volumes of interest. Two different statistical criteria were recruited to assess their fitting performance, including the adjusted-R2 and Root Mean Square Error (RMSE. To decide which model better characterizes rectal cancer, model selection was relied on Akaike Information Criteria (AIC and F-ratio.All candidate models achieved a good fitting performance with the two most complex models, the BG and the BNG, exhibiting the best fitting performance. However, both criteria for model selection indicated that the MG model performed better than any other model. In particular, using AIC Weights and F-ratio, the pixel-based analysis demonstrated that tumor areas better described by the simplest MG model in an average area of 53% and 33%, respectively. Non-Gaussian behavior was illustrated in an average area of 37% according to the F-ratio, and 7% using AIC Weights. However, the distributions of the pixels best fitted by each of the four models suggest that MG failed to perform better than any other model in all patients, and the overall tumor area.No single diffusion model evaluated herein could accurately describe rectal tumours. These findings probably can be explained on the basis of increased tumour heterogeneity, where areas with high vascularity could be fitted better with bi-exponential models, and areas with necrosis would mostly follow mono-exponential behavior.

Self-focusing of a Hermite-cosh Gaussian laser beam in a magnetoplasma with ramp density profile

International Nuclear Information System (INIS)

Nanda, Vikas; Kant, Niti; Wani, Manzoor Ahmad

2013-01-01

The early and strong self-focusing of a Hermite-cosh-Gaussian laser beam in magnetoplasma in the presence of density ramp has been observed. Focusing and de-focusing nature of the Hermite-cosh-Gaussian laser beam with decentered parameter and magnetic field has been studied, and strong self-focusing is reported. It is investigated that decentered parameter 'b' plays a significant role for the self-focusing of the laser beam and is very sensitive as in case of extraordinary mode. For mode indices, m = 0, 1, 2, and b = 4.00, 3.14, and 2.05, strong self-focusing is observed. Similarly in case of ordinary mode, for m = 0, 1, 2 and b = 4.00, 3.14, 2.049, respectively, strong self-focusing is reported. Further, it is seen that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For mode indices m = 0, 1, and 2, diffraction term becomes more dominant over nonlinear term for decentered parameter b=0. For selective higher values of decentered parameter in case of mode indices m=0, 1, and 2, self-focusing effect becomes strong for extraordinary mode. Also increase in the value of magnetic field enhances the self-focusing ability of the laser beam, which is very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers

Self-focusing of a Hermite-cosh Gaussian laser beam in a magnetoplasma with ramp density profile

Energy Technology Data Exchange (ETDEWEB)

Nanda, Vikas; Kant, Niti; Wani, Manzoor Ahmad [Department of Physics, Lovely Professional University, Phagwara 144411, Punjab (India)

2013-11-15

The early and strong self-focusing of a Hermite-cosh-Gaussian laser beam in magnetoplasma in the presence of density ramp has been observed. Focusing and de-focusing nature of the Hermite-cosh-Gaussian laser beam with decentered parameter and magnetic field has been studied, and strong self-focusing is reported. It is investigated that decentered parameter 'b' plays a significant role for the self-focusing of the laser beam and is very sensitive as in case of extraordinary mode. For mode indices, m = 0, 1, 2, and b = 4.00, 3.14, and 2.05, strong self-focusing is observed. Similarly in case of ordinary mode, for m = 0, 1, 2 and b = 4.00, 3.14, 2.049, respectively, strong self-focusing is reported. Further, it is seen that extraordinary mode is more prominent toward self-focusing rather than ordinary mode of propagation. For mode indices m = 0, 1, and 2, diffraction term becomes more dominant over nonlinear term for decentered parameter b=0. For selective higher values of decentered parameter in case of mode indices m=0, 1, and 2, self-focusing effect becomes strong for extraordinary mode. Also increase in the value of magnetic field enhances the self-focusing ability of the laser beam, which is very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, and x-ray lasers.

Coherent mode decomposition using mixed Wigner functions of Hermite-Gaussian beams.

Science.gov (United States)

Tanaka, Takashi

2017-04-15

A new method of coherent mode decomposition (CMD) is proposed that is based on a Wigner-function representation of Hermite-Gaussian beams. In contrast to the well-known method using the cross spectral density (CSD), it directly determines the mode functions and their weights without solving the eigenvalue problem. This facilitates the CMD of partially coherent light whose Wigner functions (and thus CSDs) are not separable, in which case the conventional CMD requires solving an eigenvalue problem with a large matrix and thus is numerically formidable. An example is shown regarding the CMD of synchrotron radiation, one of the most important applications of the proposed method.

Cylindrical particle manipulation and negative spinning using a nonparaxial Hermite-Gaussian light-sheet beam

Science.gov (United States)

Mitri, F. G.

2016-10-01

Based on the angular spectrum decomposition method (ASDM), a nonparaxial solution for the Hermite-Gaussian (HG m ) light-sheet beam of any order m is derived. The beam-shape coefficients (BSCs) are expressed in a compact form and computed using the standard Simpson’s rule for numerical integration. Subsequently, the analysis is extended to evaluate the longitudinal and transverse radiation forces as well as the spin torque on an absorptive dielectric cylindrical particle in 2D without any restriction to a specific range of frequencies. The dynamics of the cylindrical particle are also examined based on Newton’s second law of motion. The numerical results show that a Rayleigh or Mie cylindrical particle can be trapped, pulled or propelled in the optical field depending on its initial position in the cross-sectional plane of the HG m light-sheet. Moreover, negative or positive axial spin torques can arise depending on the choice of the non-dimensional size parameter ka (where k is the wavenumber and a is the radius of the cylinder) and the location of the absorptive cylinder in the beam. This means that the HG m light-sheet beam can induce clockwise or anti-clockwise rotations depending on its shift from the center of the cylinder. In addition, individual vortex behavior can arise in the cross-sectional plane of wave propagation. The present analysis presents an analytical model to predict the optical radiation forces and torque induced by a HG m light-sheet beam on an absorptive cylinder for applications in optical light-sheet tweezers, optical micro-machines, particle manipulation and opto-fluidics to name a few areas of research.

Excitation of a plasma wave by a right-handed Gaussian EM beam

International Nuclear Information System (INIS)

Sodha, M.S.; Patheja, B.L.; Sharma, R.P.

1979-01-01

This paper presents an investigation of the excitation of an electron plasma wave in a hot collisionless magnetoplasma by a right-handed Gaussian EM beam (pump wave) when the plasma wave and the pump wave are propagating along the static magnetic field. On account of the Gaussian intensity distribution of the pump wave, pondermotive force becomes finite and the electrons are redistributed. This redistribution is highly dependent on whether ω/sub c/>2ω 0 or ω/sub c/ 0 , where ω/sub c/ is the electron cyclotron frequency and ω 0 is the pump-wave frequency. The modified background electron density leads to coupling between the plasma wave and the pump wave. When the initial power of the pump wave is greater than the critical power for self-focusing, oscillatory self-focusing of the pump wave occurs and the coupling of the two waves are modified. Moreover, the effect of changing the intensity of the magnetic field affects the self-focusing of the pump wave, and the plasma-wave excitation is accordingly affected

Acceleration of on-axis and ring-shaped electron beams in wakefields driven by Laguerre-Gaussian pulses

Energy Technology Data Exchange (ETDEWEB)

Zhang, Guo-Bo [College of Science, National University of Defense Technology, Changsha 410073 (China); Key Laboratory for Laser Plasmas (MOE) and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Chen, Min, E-mail: minchen@sjtu.edu.cn, E-mail: yanyunma@126.com; Luo, Ji; Zeng, Ming; Yuan, Tao; Yu, Ji-Ye; Yu, Lu-Le; Weng, Su-Ming [Key Laboratory for Laser Plasmas (MOE) and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240 (China); Ma, Yan-Yun, E-mail: minchen@sjtu.edu.cn, E-mail: yanyunma@126.com [College of Science, National University of Defense Technology, Changsha 410073 (China); Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240 (China); Yu, Tong-Pu [College of Science, National University of Defense Technology, Changsha 410073 (China); Sheng, Zheng-Ming [Key Laboratory for Laser Plasmas (MOE) and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China); Collaborative Innovation Center of IFSA (CICIFSA), Shanghai Jiao Tong University, Shanghai 200240 (China); SUPA, Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom)

2016-03-14

The acceleration of electron beams with multiple transverse structures in wakefields driven by Laguerre-Gaussian pulses has been studied through three-dimensional (3D) particle-in-cell simulations. Under different laser-plasma conditions, the wakefield shows different transverse structures. In general cases, the wakefield shows a donut-like structure and it accelerates the ring-shaped hollow electron beam. When a lower plasma density or a smaller laser spot size is used, besides the donut-like wakefield, a central bell-like wakefield can also be excited. The wake sets in the center of the donut-like wake. In this case, both a central on-axis electron beam and a ring-shaped electron beam are simultaneously accelerated. Further, reducing the plasma density or laser spot size leads to an on-axis electron beam acceleration only. The research is beneficial for some potential applications requiring special pulse beam structures, such as positron acceleration and collimation.

Extended Linear Models with Gaussian Priors

DEFF Research Database (Denmark)

Quinonero, Joaquin

2002-01-01

In extended linear models the input space is projected onto a feature space by means of an arbitrary non-linear transformation. A linear model is then applied to the feature space to construct the model output. The dimension of the feature space can be very large, or even infinite, giving the model...... a very big flexibility. Support Vector Machines (SVM's) and Gaussian processes are two examples of such models. In this technical report I present a model in which the dimension of the feature space remains finite, and where a Bayesian approach is used to train the model with Gaussian priors...... on the parameters. The Relevance Vector Machine, introduced by Tipping, is a particular case of such a model. I give the detailed derivations of the expectation-maximisation (EM) algorithm used in the training. These derivations are not found in the literature, and might be helpful for newcomers....

Calculating emittance for Gaussian and Non-Gaussian distributions by the method of correlations for slits

International Nuclear Information System (INIS)

Tan, Cheng-Yang; Fermilab

2006-01-01

One common way for measuring the emittance of an electron beam is with the slits method. The usual approach for analyzing the data is to calculate an emittance that is a subset of the parent emittance. This paper shows an alternative way by using the method of correlations which ties the parameters derived from the beamlets to the actual parameters of the parent emittance. For parent distributions that are Gaussian, this method yields exact results. For non-Gaussian beam distributions, this method yields an effective emittance that can serve as a yardstick for emittance comparisons

Modeling text with generalizable Gaussian mixtures

DEFF Research Database (Denmark)

Hansen, Lars Kai; Sigurdsson, Sigurdur; Kolenda, Thomas

2000-01-01

We apply and discuss generalizable Gaussian mixture (GGM) models for text mining. The model automatically adapts model complexity for a given text representation. We show that the generalizability of these models depends on the dimensionality of the representation and the sample size. We discuss...

Gaussian beam-to-slab waveguide coupler by graded index photonic crystal lens

International Nuclear Information System (INIS)

Bahari, B; Abrishamian, M S

2013-01-01

In this numerical study, a Gaussian beam-to-slab waveguide coupler for both modes of TM and TE has been studied. For this purpose, a concrete structure is suggested, in which the graded index photonic crystal lens and the slab waveguide are in the same structure composed of Si material, and can be fabricated with a single-step lithography process. For maximum power coupling, half-holes have been used as an input matching layer. Power coupling of 80% over a 450 nm bandwidth for the TM mode, and 60% over a 180 nm bandwidth for the TE mode is achieved. (paper)

A note on moving average models for Gaussian random fields

DEFF Research Database (Denmark)

Hansen, Linda Vadgård; Thorarinsdottir, Thordis L.

The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy...... basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result...

Optimal multicopy asymmetric Gaussian cloning of coherent states

International Nuclear Information System (INIS)

Fiurasek, Jaromir; Cerf, Nicolas J.

2007-01-01

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward

Optimal multicopy asymmetric Gaussian cloning of coherent states

Science.gov (United States)

Fiurášek, Jaromír; Cerf, Nicolas J.

2007-05-01

We investigate the asymmetric Gaussian cloning of coherent states which produces M copies from N input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.

Area of isodensity contours in Gaussian and non-Gaussian fields

International Nuclear Information System (INIS)

Ryden, B.S.

1988-01-01

The area of isodensity contours in a smoothed density field can be measured by the contour-crossing statistic N1, the number of times per unit length that a line drawn through the density field pierces an isodensity contour. The contour-crossing statistic distinguishes between Gaussian and non-Gaussian fields and provides a measure of the effective slope of the power spectrum. The statistic is easy to apply and can be used on pencil beams and slices as well as on a three-dimensional field. 10 references

The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems

International Nuclear Information System (INIS)

Trappe, Neil; Murphy, J Anthony; Withington, Stafford

2003-01-01

Gaussian beam mode analysis (GBMA) offers a more intuitive physical insight into how light beams evolve as they propagate than the conventional Fresnel diffraction integral approach. In this paper we illustrate that GBMA is a computationally efficient, alternative technique for tracing the evolution of a diffracting coherent beam. In previous papers we demonstrated the straightforward application of GBMA to the computation of the classical diffraction patterns associated with a range of standard apertures. In this paper we show how the GBMA technique can be expanded to investigate the effects of aberrations in the presence of diffraction by introducing the appropriate phase error term into the propagating quasi-optical beam. We compare our technique to the standard diffraction integral calculation for coma, astigmatism and spherical aberration, taking - for comparison - examples from the classic text 'Principles of Optics' by Born and Wolf. We show the advantages of GBMA for allowing the defocusing of an aberrated image to be evaluated quickly, which is particularly important and useful for probing the consequences of astigmatism and spherical aberration

The Gaussian beam mode analysis of classical phase aberrations in diffraction-limited optical systems

Science.gov (United States)

Trappe, Neil; Murphy, J. Anthony; Withington, Stafford

2003-07-01

Gaussian beam mode analysis (GBMA) offers a more intuitive physical insight into how light beams evolve as they propagate than the conventional Fresnel diffraction integral approach. In this paper we illustrate that GBMA is a computationally efficient, alternative technique for tracing the evolution of a diffracting coherent beam. In previous papers we demonstrated the straightforward application of GBMA to the computation of the classical diffraction patterns associated with a range of standard apertures. In this paper we show how the GBMA technique can be expanded to investigate the effects of aberrations in the presence of diffraction by introducing the appropriate phase error term into the propagating quasi-optical beam. We compare our technique to the standard diffraction integral calculation for coma, astigmatism and spherical aberration, taking—for comparison—examples from the classic text 'Principles of Optics' by Born and Wolf. We show the advantages of GBMA for allowing the defocusing of an aberrated image to be evaluated quickly, which is particularly important and useful for probing the consequences of astigmatism and spherical aberration.

Model selection for Gaussian kernel PCA denoising

DEFF Research Database (Denmark)

Jørgensen, Kasper Winther; Hansen, Lars Kai

2012-01-01

We propose kernel Parallel Analysis (kPA) for automatic kernel scale and model order selection in Gaussian kernel PCA. Parallel Analysis [1] is based on a permutation test for covariance and has previously been applied for model order selection in linear PCA, we here augment the procedure to also...... tune the Gaussian kernel scale of radial basis function based kernel PCA.We evaluate kPA for denoising of simulated data and the US Postal data set of handwritten digits. We find that kPA outperforms other heuristics to choose the model order and kernel scale in terms of signal-to-noise ratio (SNR...

Revisiting non-Gaussianity from non-attractor inflation models

Science.gov (United States)

Cai, Yi-Fu; Chen, Xingang; Namjoo, Mohammad Hossein; Sasaki, Misao; Wang, Dong-Gang; Wang, Ziwei

2018-05-01

Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition—such as in the case of smooth transition or some sharp transition scenarios—the Script O(1) local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.

IBS for non-gaussian distributions

International Nuclear Information System (INIS)

Fedotov, A.; Sidorin, A.O.; Smirnov, A.V.

2010-01-01

In many situations distribution can significantly deviate from Gaussian which requires accurate treatment of IBS. Our original interest in this problem was motivated by the need to have an accurate description of beam evolution due to IBS while distribution is strongly affected by the external electron cooling force. A variety of models with various degrees of approximation were developed and implemented in BETACOOL in the past to address this topic. A more complete treatment based on the friction coefficient and full 3-D diffusion tensor was introduced in BETACOOL at the end of 2007 under the name 'local IBS model'. Such a model allowed us calculation of IBS for an arbitrary beam distribution. The numerical benchmarking of this local IBS algorithm and its comparison with other models was reported before. In this paper, after briefly describing the model and its limitations, they present its comparison with available experimental data.

Comment on “Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma” [Phys. Plasmas 20, 072703 (2013)

International Nuclear Information System (INIS)

Habibi, M.; Ghamari, F.

2014-01-01

Patil and Takale in their recent article [Phys. Plasmas 20, 072703 (2013)], by evaluating the quantum dielectric response in thermal quantum plasma, have modeled the relativistic self-focusing of Gaussian laser beam in a plasma. We have found that there are some important shortcomings and fundamental mistakes in Patil and Takale [Phys. Plasmas 20, 072703 (2013)] that we give a brief description about them and refer readers to important misconception about the use of the Fermi temperature in quantum plasmas, appearing in Patil and Takale [Phys. Plasmas 20, 072703 (2013)

Characterization and monitoring of transverse beam tails

International Nuclear Information System (INIS)

Seeman, J.T.; Decker, F.J.; Hsu, I.; Young, C.

1991-05-01

Low emittance electron beams accelerated to high energy in a linac experience transverse effects (wakefield, filamentation, optics) which produce non-Gaussian projected transverse beam distributions. Characterizations of the beam shapes are difficult because the shapes are asymmetric and change with betatron phase. In this note several methods to describe beam distributions are discussed including an accelerator physics model of these tails. The uses of these characterizations in monitoring the beam emittances in the SLC are described in this paper. First, two dimensional distributions from profile monitor screens are reviewed showing correlated tails. Second, a fitting technique for non-Gaussian one dimensional distributions is used to extract the core from the tail areas. Finally, a model for tail propagation in the linac is given. 3 refs., 6 figs

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...

Gaussian cloning of coherent states with known phases

International Nuclear Information System (INIS)

Alexanian, Moorad

2006-01-01

The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadratic in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier

Beam-beam limit in e+e- circular colliders

International Nuclear Information System (INIS)

Ohmi, K.; Tawada, M.; Kamada, S.; Oide, K.; Cai, Y.; Qiang, J.

2004-01-01

Beam-beam effects limit the luminosity of circular colliders. Once the bunch population exceeds a threshold, the luminosity increases at a slower rate. This phenomenon is called the beam-beam limit. Onset of the beam-beam limit has been analyzed with various simulation methods based on the weak-strong and strong-strong models. We have observed that an incoherent phenomenon is mainly concerned in the beam-beam limit. The simulation have shown that equilibrium distributions of the two colliding beams are distorted from Gaussians when the luminosity is limited. The beam-beam limit is estimated to be ξ∼0.1 for a B factory with damping time of several thousand turns

Analytical investigation on domain of decentered parameter for self-focusing of Hermite-cosh-Gaussian laser beam in collisional plasma

Science.gov (United States)

Valkunde, Amol T.; Patil, Sandip D.; Vhanmore, Bandopant D.; Urunkar, Trupti U.; Gavade, Kusum M.; Takale, Mansing V.; Fulari, Vijay J.

2018-03-01

In the present paper, an analytically investigated domain of decentered parameter and its effect on the self-focusing of Hermit-cosh-Gaussian (HChG) laser beams in a collisional plasma have been studied theoretically. The nonlinearity in the dielectric constant of plasma arising due to the nonuniform heating of carriers along the wavefront of the laser beam has been employed in the present investigation. The nonlinear differential equation of beam width parameter for various laser modes of HChG beam is obtained by following the standard Akhamanov's parabolic equation approach under Wentzel-Kramers-Brillouin and paraxial approximations. The analytical treatment has enabled us to define three distinct regions: self-focusing, self-trapping and defocusing, which are presented graphically.

Linear velocity fields in non-Gaussian models for large-scale structure

Science.gov (United States)

Scherrer, Robert J.

1992-01-01

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.

Enhanced relativistic self-focusing of Hermite-cosh-Gaussian laser beam in plasma under density transition

International Nuclear Information System (INIS)

Nanda, Vikas; Kant, Niti

2014-01-01

Enhanced and early relativistic self-focusing of Hermite-cosh-Gaussian (HChG) beam in the plasmas under density transition has been investigated theoretically using Wentzel-Kramers-Brillouin and paraxial ray approximation for mode indices m=0, 1, and 2. The variation of beam width parameter with normalized propagation distance for m=0, 1, and 2 is reported, and it is observed that strong self-focusing occurs as the HChG beam propagates deeper inside the nonlinear medium as spot size shrinks due to highly dense plasmas and the results are presented graphically. A comparative study between self-focusing of HChG beam in the presence and absence of plasmas density transition is reported. The dependency of beam width parameter on the normalized propagation distance for different values of decentered parameter “b” has also been presented graphically. For m=0 and 1, strong self-focusing is reported for b=1.8, and for m=2 and b=1.8, beam gets diffracted. The results obtained indicate the dependency of the self-focusing of the HChG beam on the selected values of decentered parameter. Moreover, proper selection of decentered parameter results strong self-focusing of HChG beam. Stronger self-focusing of laser beam is observed due to the presence of plasma density transition which might be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, etc

Enhanced relativistic self-focusing of Hermite-cosh-Gaussian laser beam in plasma under density transition

Energy Technology Data Exchange (ETDEWEB)

Nanda, Vikas; Kant, Niti, E-mail: nitikant@yahoo.com [Department of Physics, Lovely Professional University, Phagwara 144411, Punjab (India)

2014-04-15

Enhanced and early relativistic self-focusing of Hermite-cosh-Gaussian (HChG) beam in the plasmas under density transition has been investigated theoretically using Wentzel-Kramers-Brillouin and paraxial ray approximation for mode indices m=0, 1, and 2. The variation of beam width parameter with normalized propagation distance for m=0, 1, and 2 is reported, and it is observed that strong self-focusing occurs as the HChG beam propagates deeper inside the nonlinear medium as spot size shrinks due to highly dense plasmas and the results are presented graphically. A comparative study between self-focusing of HChG beam in the presence and absence of plasmas density transition is reported. The dependency of beam width parameter on the normalized propagation distance for different values of decentered parameter “b” has also been presented graphically. For m=0 and 1, strong self-focusing is reported for b=1.8, and for m=2 and b=1.8, beam gets diffracted. The results obtained indicate the dependency of the self-focusing of the HChG beam on the selected values of decentered parameter. Moreover, proper selection of decentered parameter results strong self-focusing of HChG beam. Stronger self-focusing of laser beam is observed due to the presence of plasma density transition which might be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, etc.

Diffraction study of duty-cycle error in ferroelectric quasi-phase-matching gratings with Gaussian beam illumination

Science.gov (United States)

Dwivedi, Prashant Povel; Kumar, Challa Sesha Sai Pavan; Choi, Hee Joo; Cha, Myoungsik

2016-02-01

Random duty-cycle error (RDE) is inherent in the fabrication of ferroelectric quasi-phase-matching (QPM) gratings. Although a small RDE may not affect the nonlinearity of QPM devices, it enhances non-phase-matched parasitic harmonic generations, limiting the device performance in some applications. Recently, we demonstrated a simple method for measuring the RDE in QPM gratings by analyzing the far-field diffraction pattern obtained by uniform illumination (Dwivedi et al. in Opt Express 21:30221-30226, 2013). In the present study, we used a Gaussian beam illumination for the diffraction experiment to measure noise spectra that are less affected by the pedestals of the strong diffraction orders. Our results were compared with our calculations based on a random grating model, demonstrating improved resolution in the RDE estimation.

Circular motion of particles suspended in a Gaussian beam with circular polarization validates the spin part of the internal energy flow

DEFF Research Database (Denmark)

Angelsky, O. V.; Bekshaev, A. Ya.; Maksimyak, P. P.

2012-01-01

switching to the right (left) circular polarization, the particles performed spinning motion in agreement with the angular momentum imparted by the field, but they were involved in an orbital rotation around the beam axis as well, which in previous works [Y. Zhao et al, Phys. Rev. Lett. 99, 073901 (2007......Non-spherical dielectric microparticles were suspended in a water-filled cell and exposed to a coherent Gaussian light beam with controlled state of polarization. When the beam polarization is linear, the particles were trapped at certain off-axial position within the beam cross section. After...... of inhomogeneously polarized paraxial beams [A. Bekshaev et al, J. Opt. 13, 053001 (2011)]....

Comparison of non-Gaussian and Gaussian diffusion models of diffusion weighted imaging of rectal cancer at 3.0 T MRI.

Science.gov (United States)

Zhang, Guangwen; Wang, Shuangshuang; Wen, Didi; Zhang, Jing; Wei, Xiaocheng; Ma, Wanling; Zhao, Weiwei; Wang, Mian; Wu, Guosheng; Zhang, Jinsong

2016-12-09

Water molecular diffusion in vivo tissue is much more complicated. We aimed to compare non-Gaussian diffusion models of diffusion-weighted imaging (DWI) including intra-voxel incoherent motion (IVIM), stretched-exponential model (SEM) and Gaussian diffusion model at 3.0 T MRI in patients with rectal cancer, and to determine the optimal model for investigating the water diffusion properties and characterization of rectal carcinoma. Fifty-nine consecutive patients with pathologically confirmed rectal adenocarcinoma underwent DWI with 16 b-values at a 3.0 T MRI system. DWI signals were fitted to the mono-exponential and non-Gaussian diffusion models (IVIM-mono, IVIM-bi and SEM) on primary tumor and adjacent normal rectal tissue. Parameters of standard apparent diffusion coefficient (ADC), slow- and fast-ADC, fraction of fast ADC (f), α value and distributed diffusion coefficient (DDC) were generated and compared between the tumor and normal tissues. The SEM exhibited the best fitting results of actual DWI signal in rectal cancer and the normal rectal wall (R 2  = 0.998, 0.999 respectively). The DDC achieved relatively high area under the curve (AUC = 0.980) in differentiating tumor from normal rectal wall. Non-Gaussian diffusion models could assess tissue properties more accurately than the ADC derived Gaussian diffusion model. SEM may be used as a potential optimal model for characterization of rectal cancer.

Non-gaussian turbulence

Energy Technology Data Exchange (ETDEWEB)

Hoejstrup, J [NEG Micon Project Development A/S, Randers (Denmark); Hansen, K S [Denmarks Technical Univ., Dept. of Energy Engineering, Lyngby (Denmark); Pedersen, B J [VESTAS Wind Systems A/S, Lem (Denmark); Nielsen, M [Risoe National Lab., Wind Energy and Atmospheric Physics, Roskilde (Denmark)

1999-03-01

The pdf`s of atmospheric turbulence have somewhat wider tails than a Gaussian, especially regarding accelerations, whereas velocities are close to Gaussian. This behaviour is being investigated using data from a large WEB-database in order to quantify the amount of non-Gaussianity. Models for non-Gaussian turbulence have been developed, by which artificial turbulence can be generated with specified distributions, spectra and cross-correlations. The artificial time series will then be used in load models and the resulting loads in the Gaussian and the non-Gaussian cases will be compared. (au)

Gaussian density matrices: Quantum analogs of classical states

International Nuclear Information System (INIS)

Mann, A.; Revzen, M.

1993-01-01

We study quantum analogs of clasical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space. (orig.)

GaussianCpG: a Gaussian model for detection of CpG island in human genome sequences.

Science.gov (United States)

Yu, Ning; Guo, Xuan; Zelikovsky, Alexander; Pan, Yi

2017-05-24

As crucial markers in identifying biological elements and processes in mammalian genomes, CpG islands (CGI) play important roles in DNA methylation, gene regulation, epigenetic inheritance, gene mutation, chromosome inactivation and nuclesome retention. The generally accepted criteria of CGI rely on: (a) %G+C content is ≥ 50%, (b) the ratio of the observed CpG content and the expected CpG content is ≥ 0.6, and (c) the general length of CGI is greater than 200 nucleotides. Most existing computational methods for the prediction of CpG island are programmed on these rules. However, many experimentally verified CpG islands deviate from these artificial criteria. Experiments indicate that in many cases %G+C is human genome. We analyze the energy distribution over genomic primary structure for each CpG site and adopt the parameters from statistics of Human genome. The evaluation results show that the new model can predict CpG islands efficiently by balancing both sensitivity and specificity over known human CGI data sets. Compared with other models, GaussianCpG can achieve better performance in CGI detection. Our Gaussian model aims to simplify the complex interaction between nucleotides. The model is computed not by the linear statistical method but by the Gaussian energy distribution and accumulation. The parameters of Gaussian function are not arbitrarily designated but deliberately chosen by optimizing the biological statistics. By using the pseudopotential analysis on CpG islands, the novel model is validated on both the real and artificial data sets.

Designing Fresnel microlenses for focusing astigmatic multi-Gaussian beams by using fractional order Fourier transforms

International Nuclear Information System (INIS)

Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P

2011-01-01

According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.

Application Of Shared Gamma And Inverse-Gaussian Frailty Models ...

African Journals Online (AJOL)

Shared Gamma and Inverse-Gaussian Frailty models are used to analyze the survival times of patients who are clustered according to cancer/tumor types under Parametric Proportional Hazard framework. The result of the ... However, no evidence is strong enough for preference of either Gamma or Inverse Gaussian Frailty.

Bayesian modeling of JET Li-BES for edge electron density profiles using Gaussian processes

Science.gov (United States)

Kwak, Sehyun; Svensson, Jakob; Brix, Mathias; Ghim, Young-Chul; JET Contributors Collaboration

2015-11-01

A Bayesian model for the JET lithium beam emission spectroscopy (Li-BES) system has been developed to infer edge electron density profiles. The 26 spatial channels measure emission profiles with ~15 ms temporal resolution and ~1 cm spatial resolution. The lithium I (2p-2s) line radiation in an emission spectrum is calculated using a multi-state model, which expresses collisions between the neutral lithium beam atoms and the plasma particles as a set of differential equations. The emission spectrum is described in the model including photon and electronic noise, spectral line shapes, interference filter curves, and relative calibrations. This spectral modeling gets rid of the need of separate background measurements for calculating the intensity of the line radiation. Gaussian processes are applied to model both emission spectrum and edge electron density profile, and the electron temperature to calculate all the rate coefficients is obtained from the JET high resolution Thomson scattering (HRTS) system. The posterior distributions of the edge electron density profile are explored via the numerical technique and the Markov chain Monte Carlo (MCMC) samplings. See the Appendix of F. Romanelli et al., Proceedings of the 25th IAEA Fusion Energy Conference 2014, Saint Petersburg, Russia.

Spatial superpositions of Gaussian beams

CSIR Research Space (South Africa)

Naidoo, Darryl

2014-02-01

Full Text Available . At the plane of the lens we obtain a multi-ringed beam with a central intensity maximum which develops into a multi-ringed beam with a central null at the focal plane of the lens. The interesting feature of this beam is that it possesses two focal spots...

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing.

Science.gov (United States)

Mitri, F G; Fellah, Z E A

2014-01-01

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z(R). Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere's resonance frequencies for kw₀≤1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force. Copyright © 2013 Elsevier B.V. All rights reserved.

Probabilistic wind power forecasting with online model selection and warped gaussian process

International Nuclear Information System (INIS)

Kou, Peng; Liang, Deliang; Gao, Feng; Gao, Lin

2014-01-01

Highlights: • A new online ensemble model for the probabilistic wind power forecasting. • Quantifying the non-Gaussian uncertainties in wind power. • Online model selection that tracks the time-varying characteristic of wind generation. • Dynamically altering the input features. • Recursive update of base models. - Abstract: Based on the online model selection and the warped Gaussian process (WGP), this paper presents an ensemble model for the probabilistic wind power forecasting. This model provides the non-Gaussian predictive distributions, which quantify the non-Gaussian uncertainties associated with wind power. In order to follow the time-varying characteristics of wind generation, multiple time dependent base forecasting models and an online model selection strategy are established, thus adaptively selecting the most probable base model for each prediction. WGP is employed as the base model, which handles the non-Gaussian uncertainties in wind power series. Furthermore, a regime switch strategy is designed to modify the input feature set dynamically, thereby enhancing the adaptiveness of the model. In an online learning framework, the base models should also be time adaptive. To achieve this, a recursive algorithm is introduced, thus permitting the online updating of WGP base models. The proposed model has been tested on the actual data collected from both single and aggregated wind farms

State of the art atmospheric dispersion modelling. Should the Gaussian plume model still be used?

Energy Technology Data Exchange (ETDEWEB)

Richter, Cornelia [Gesellschaft fuer Anlagen- und Reaktorsicherheit (GRS) gGmbH, Koeln (Germany)

2016-11-15

For regulatory purposes with respect to licensing and supervision of airborne releases of nuclear installations, the Gaussian plume model is still in use in Germany. However, for complex situations the Gaussian plume model is to be replaced by a Lagrangian particle model. Now the new EU basic safety standards for protection against the dangers arising from exposure to ionising radiation (EU BSS) [1] asks for a realistic assessment of doses to the members of the public from authorised practices. This call for a realistic assessment raises the question whether dispersion modelling with the Gaussian plume model is an adequate approach anymore or whether the use of more complex models is mandatory.

An approximate fractional Gaussian noise model with computational cost

KAUST Repository

Sørbye, Sigrunn H.

2017-09-18

Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.

Direct Importance Estimation with Gaussian Mixture Models

Science.gov (United States)

Yamada, Makoto; Sugiyama, Masashi

The ratio of two probability densities is called the importance and its estimation has gathered a great deal of attention these days since the importance can be used for various data processing purposes. In this paper, we propose a new importance estimation method using Gaussian mixture models (GMMs). Our method is an extention of the Kullback-Leibler importance estimation procedure (KLIEP), an importance estimation method using linear or kernel models. An advantage of GMMs is that covariance matrices can also be learned through an expectation-maximization procedure, so the proposed method — which we call the Gaussian mixture KLIEP (GM-KLIEP) — is expected to work well when the true importance function has high correlation. Through experiments, we show the validity of the proposed approach.

Perturbative Gaussianizing transforms for cosmological fields

Science.gov (United States)

Hall, Alex; Mead, Alexander

2018-01-01

Constraints on cosmological parameters from large-scale structure have traditionally been obtained from two-point statistics. However, non-linear structure formation renders these statistics insufficient in capturing the full information content available, necessitating the measurement of higher order moments to recover information which would otherwise be lost. We construct quantities based on non-linear and non-local transformations of weakly non-Gaussian fields that Gaussianize the full multivariate distribution at a given order in perturbation theory. Our approach does not require a model of the fields themselves and takes as input only the first few polyspectra, which could be modelled or measured from simulations or data, making our method particularly suited to observables lacking a robust perturbative description such as the weak-lensing shear. We apply our method to simulated density fields, finding a significantly reduced bispectrum and an enhanced correlation with the initial field. We demonstrate that our method reconstructs a large proportion of the linear baryon acoustic oscillations, improving the information content over the raw field by 35 per cent. We apply the transform to toy 21 cm intensity maps, showing that our method still performs well in the presence of complications such as redshift-space distortions, beam smoothing, pixel noise and foreground subtraction. We discuss how this method might provide a route to constructing a perturbative model of the fully non-Gaussian multivariate likelihood function.

A technique for simultaneous detection of individual vortex states of Laguerre-Gaussian beams transmitted through an aqueous suspension of microparticles

Science.gov (United States)

Khonina, S. N.; Karpeev, S. V.; Paranin, V. D.

2018-06-01

A technique for simultaneous detection of individual vortex states of the beams propagating in a randomly inhomogeneous medium is proposed. The developed optical system relies on the correlation method that is invariant to the beam wandering. The intensity distribution formed at the optical system output does not require digital processing. The proposed technique based on a multi-order phase diffractive optical element (DOE) is studied numerically and experimentally. The developed detection technique is used for the analysis of Laguerre-Gaussian vortex beams propagating under conditions of intense absorption, reflection, and scattering in transparent and opaque microparticles in aqueous suspensions. The performed experimental studies confirm the relevance of the vortex phase dependence of a laser beam under conditions of significant absorption, reflection, and scattering of the light.

Interaction of Airy–Gaussian beams in saturable media

International Nuclear Information System (INIS)

Zhou Meiling; Peng Yulian; Chen Chidao; Chen Bo; Peng Xi; Deng Dongmei

2016-01-01

Based on the nonlinear Schrödinger equation, the interactions of the two Airy–Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy–Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy–Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. (paper)

Propagation of a general-type beam through a truncated fractional Fourier transform optical system.

Science.gov (United States)

Zhao, Chengliang; Cai, Yangjian

2010-03-01

Paraxial propagation of a general-type beam through a truncated fractional Fourier transform (FRT) optical system is investigated. Analytical formulas for the electric field and effective beam width of a general-type beam in the FRT plane are derived based on the Collins formula. Our formulas can be used to study the propagation of a variety of laser beams--such as Gaussian, cos-Gaussian, cosh-Gaussian, sine-Gaussian, sinh-Gaussian, flat-topped, Hermite-cosh-Gaussian, Hermite-sine-Gaussian, higher-order annular Gaussian, Hermite-sinh-Gaussian and Hermite-cos-Gaussian beams--through a FRT optical system with or without truncation. The propagation properties of a Hermite-cos-Gaussian beam passing through a rectangularly truncated FRT optical system are studied as a numerical example. Our results clearly show that the truncated FRT optical system provides a convenient way for laser beam shaping.

American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution

DEFF Research Database (Denmark)

Stentoft, Lars Peter

In this paper we propose a feasible way to price American options in a model with time varying volatility and conditional skewness and leptokurtosis using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk neutral dynamics can be obtained in this model, we interpret...... properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model outperforms the Gaussian case for pricing options on three large US stocks as well as a major index...

Improved Expectation Maximization Algorithm for Gaussian Mixed Model Using the Kernel Method

Directory of Open Access Journals (Sweden)

Mohd Izhan Mohd Yusoff

2013-01-01

Full Text Available Fraud activities have contributed to heavy losses suffered by telecommunication companies. In this paper, we attempt to use Gaussian mixed model, which is a probabilistic model normally used in speech recognition to identify fraud calls in the telecommunication industry. We look at several issues encountered when calculating the maximum likelihood estimates of the Gaussian mixed model using an Expectation Maximization algorithm. Firstly, we look at a mechanism for the determination of the initial number of Gaussian components and the choice of the initial values of the algorithm using the kernel method. We show via simulation that the technique improves the performance of the algorithm. Secondly, we developed a procedure for determining the order of the Gaussian mixed model using the log-likelihood function and the Akaike information criteria. Finally, for illustration, we apply the improved algorithm to real telecommunication data. The modified method will pave the way to introduce a comprehensive method for detecting fraud calls in future work.

Color Texture Segmentation by Decomposition of Gaussian Mixture Model

Czech Academy of Sciences Publication Activity Database

Grim, Jiří; Somol, Petr; Haindl, Michal; Pudil, Pavel

2006-01-01

Roč. 19, č. 4225 (2006), s. 287-296 ISSN 0302-9743. [Iberoamerican Congress on Pattern Recognition. CIARP 2006 /11./. Cancun, 14.11.2006-17.11.2006] R&D Projects: GA AV ČR 1ET400750407; GA MŠk 1M0572; GA MŠk 2C06019 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : texture segmentation * gaussian mixture model * EM algorithm Subject RIV: IN - Informatics, Computer Science Impact factor: 0.402, year: 2005 http://library.utia.cas.cz/separaty/historie/grim-color texture segmentation by decomposition of gaussian mixture model.pdf

Spatio-Temporal Data Analysis at Scale Using Models Based on Gaussian Processes

Energy Technology Data Exchange (ETDEWEB)

Stein, Michael [Univ. of Chicago, IL (United States)

2017-03-13

Gaussian processes are the most commonly used statistical model for spatial and spatio-temporal processes that vary continuously. They are broadly applicable in the physical sciences and engineering and are also frequently used to approximate the output of complex computer models, deterministic or stochastic. We undertook research related to theory, computation, and applications of Gaussian processes as well as some work on estimating extremes of distributions for which a Gaussian process assumption might be inappropriate. Our theoretical contributions include the development of new classes of spatial-temporal covariance functions with desirable properties and new results showing that certain covariance models lead to predictions with undesirable properties. To understand how Gaussian process models behave when applied to deterministic computer models, we derived what we believe to be the first significant results on the large sample properties of estimators of parameters of Gaussian processes when the actual process is a simple deterministic function. Finally, we investigated some theoretical issues related to maxima of observations with varying upper bounds and found that, depending on the circumstances, standard large sample results for maxima may or may not hold. Our computational innovations include methods for analyzing large spatial datasets when observations fall on a partially observed grid and methods for estimating parameters of a Gaussian process model from observations taken by a polar-orbiting satellite. In our application of Gaussian process models to deterministic computer experiments, we carried out some matrix computations that would have been infeasible using even extended precision arithmetic by focusing on special cases in which all elements of the matrices under study are rational and using exact arithmetic. The applications we studied include total column ozone as measured from a polar-orbiting satellite, sea surface temperatures over the

A comparison of the Gaussian Plume models of Pasquill and Smith

International Nuclear Information System (INIS)

Barker, C.D.

1978-03-01

The Gaussian Plume models of Pasquill and Smith are compared over the full range of atmospheric stability for both short and continuous releases of material. For low level releases the two models compare well (to within a factor of approximately 2) except for very unstable conditions. The agreement between the two models for high level sources is not so good. It is concluded that the two Gaussian models are cheap and simple to use, but may require experimental verification in specific applications. (author)

Schelling, von Neumann, and the Event that Didn’t Occur

Directory of Open Access Journals (Sweden)

Alexander J. Field

2014-02-01

Full Text Available Thomas Schelling was recognized by the Nobel Prize committee as a pioneer in the application of game theory and rational choice analysis to problems of politics and international relations. However, although he makes frequent references in his writings to this approach, his main explorations and insights depend upon and require acknowledgment of its limitations. One of his principal concerns was how a country could engage in successful deterrence. If the behavioral assumptions that commonly underpin game theory are taken seriously and applied consistently, however, nuclear adversaries are almost certain to engage in devastating conflict, as John von Neumann forcefully asserted. The history of the last half century falsified von Neumann’s prediction, and the “event that didn’t occur” formed the subject of Schelling’s Nobel lecture. The answer to the question “why?” is the central concern of this paper.

SU-F-T-138: Commissioning and Evaluating Dose Computation Models for a Dedicated Proton Line Scanning Beam Nozzle in Eclipse Treatment Planning System

Energy Technology Data Exchange (ETDEWEB)

Tsai, P [Chang Gung Memorial Hospital, Proton and Radiation Therapy Center, Tao-yuan, Taiwan (China); Chang Gung University, Taoyuan, Taiwan (China); Huang, H; Cai, S; Chen, H; Wu, S; Wu, T; Lee, S; Yeh, C; Wu, T [Chang Gung Memorial Hospital, Proton and Radiation Therapy Center, Tao-yuan, Taiwan (China); Lee, C [Chang Gung University, Taoyuan, Taiwan (China)

2016-06-15

Purpose: In this study, we present an effective method to derive low dose envelope of the proton in-air spot fluence at beam positions other than the isocenter to reduce amount of measurements required for planning commission. Also, we demonstrate commissioning and validation results of this method to the Eclipse treatment planning system (version 13.0.29) for a Sumitomo dedicated proton line scanning beam nozzle. Methods: The in-air spot profiles at five beam-axis positions (±200, ±100 and 0 mm) were obtained in trigger mode using a MP3 Water tank (PTW-Freiburg) and a pinpoint ionization chamber (model 31014, PTW-Freiburg). Low dose envelope (below 1% of the center dose) of the spot profile at isocenter was obtained by repeated point measurements to minimize dosimetry uncertainty. The double Gaussian (DG) model was used to fit and obtain optimal σ1, σ2 and their corresponding weightings through our in-house MATLAB (Mathworks) program. σ1, σ2 were assumed to expand linearly along the beam axis from a virtual source position calculated by back projecting fitted sigmas from the single Gaussian (SG) model. Absolute doses in water were validated using an Advanced Markus chamber at the depth of 2cm with Pristine Peak (BP) R90d ranging from 5–32 cm for 10×10 cm2 scanned fields. The field size factors were verified with square fields from 2 to 20 cm at 2cm and before BP depth. Results: The absolute dose outputs were found to be within ±3%. For field size factor, the agreement between calculated and measurement were within ±2% at 2cm and ±3% before BP, except for the field size below 2×2 cm2. Conclusion: The double Gaussian model was found to be sufficient for characterizing the Sumitomo dedicated proton line scanning nozzle. With our effective double Gaussian fitting method, we are able to save significant proton beam time with acceptable output accuracy.

On beam models and their paraxial approximation

Science.gov (United States)

Waters, W. J.; King, B.

2018-01-01

We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak laser pulse backgrounds.

Measurement of Gaussian laser beam radius using the knife-edge technique: improvement on data analysis

International Nuclear Information System (INIS)

Araujo, Marcos A. de; Silva, Rubens; Lima, Emerson de; Pereira, Daniel P.; Oliveira, Paulo C. de

2009-01-01

We revisited the well known Khosrofian and Garetz inversion algorithm [Appl. Opt.22, 3406-3410 (1983)APOPAI0003-6935] that was developed to analyze data obtained by the application of the traveling knife-edge technique. We have analyzed the approximated fitting function that was used for adjusting their experimental data and have found that it is not optimized to work with a full range of the experimentally-measured data. We have numerically calculated a new set of coefficients, which makes the approximated function suitable for a full experimental range, considerably improving the accuracy of the measurement of a radius of a focused Gaussian laser beam

Multiple Reflections and Fresnel Absorption of Gaussian Laser Beam in an Actual 3D Keyhole during Deep-Penetration Laser Welding

Directory of Open Access Journals (Sweden)

Xiangzhong Jin

2012-01-01

Full Text Available In deep penetration laser welding, a keyhole is formed in the material. Based on an experimentally obtained bending keyhole from low- and medium-speed laser penetration welding of glass, the keyhole profiles in both the symmetric plane are determined by polynomial fitting. Then, a 3D bending keyhole is reconstructed under the assumption of circular cross-section of the keyhole at each keyhole depth. In this paper, the behavior of focused Gaussian laser beam in the keyhole is analyzed by tracing a ray of light using Gaussian optics theory, the Fresnel absorption and multiple reflections in the keyhole are systematically studied, and the laser intensities absorbed on the keyhole walls are calculated. Finally, the formation mechanism of the keyhole is deduced.

Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies.

Science.gov (United States)

Savitsky, Terrance; Vannucci, Marina; Sha, Naijun

2011-02-01

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations to the response. The modeling approach we describe incorporates Gaussian processes in a generalized linear model framework to obtain a class of nonparametric regression models where the covariance matrix depends on the predictors. We consider, in particular, continuous, categorical and count responses. We also look into models that account for survival outcomes. We explore alternative covariance formulations for the Gaussian process prior and demonstrate the flexibility of the construction. Next, we focus on the important problem of selecting variables from the set of possible predictors and describe a general framework that employs mixture priors. We compare alternative MCMC strategies for posterior inference and achieve a computationally efficient and practical approach. We demonstrate performances on simulated and benchmark data sets.

Perturbative corrections for approximate inference in gaussian latent variable models

DEFF Research Database (Denmark)

Opper, Manfred; Paquet, Ulrich; Winther, Ole

2013-01-01

Expectation Propagation (EP) provides a framework for approximate inference. When the model under consideration is over a latent Gaussian field, with the approximation being Gaussian, we show how these approximations can systematically be corrected. A perturbative expansion is made of the exact b...... illustrate on tree-structured Ising model approximations. Furthermore, they provide a polynomial-time assessment of the approximation error. We also provide both theoretical and practical insights on the exactness of the EP solution. © 2013 Manfred Opper, Ulrich Paquet and Ole Winther....

Supervised Gaussian mixture model based remote sensing image ...

African Journals Online (AJOL)

Using the supervised classification technique, both simulated and empirical satellite remote sensing data are used to train and test the Gaussian mixture model algorithm. For the purpose of validating the experiment, the resulting classified satellite image is compared with the ground truth data. For the simulated modelling, ...

Coherent beam combination of fiber lasers with a strongly confined waveguide: numerical model.

Science.gov (United States)

Tao, Rumao; Si, Lei; Ma, Yanxing; Zhou, Pu; Liu, Zejin

2012-08-20

Self-imaging properties of fiber lasers in a strongly confined waveguide (SCW) and their application in coherent beam combination (CBC) are studied theoretically. Analytical formulas are derived for the positions, amplitudes, and phases of the N images at the end of an SCW, which is important for quantitative analysis of waveguide CBC. The formulas are verified with experimental results and numerical simulation of a finite difference beam propagation method (BPM). The error of our analytical formulas is less than 6%, which can be reduced to less than 1.5% with Goos-Hahnchen penetration depth considered. Based on the theoretical model and BPM, we studied the combination of two laser beams based on an SCW. The effects of the waveguide refractive index and Gaussian beam waist are studied. We also simulated the CBC of nine and 16 fiber lasers, and a single beam without side lobes was achieved.

Influence of laser beam profile on electromagnetically induced absorption

International Nuclear Information System (INIS)

Cuk, S. M.; Radonjic, M.; Krmpot, A. J.; Nikolic, S. N.; Grujic, Z. D.; Jelenkovic, B. M.

2010-01-01

We compared, experimentally and theoretically, Hanle electromagnetically induced absorption (EIA) obtained using Gaussian and Π-shaped laser beams 3 mm in diameter. The study was done by measuring the transmission of a laser locked to the F g =2→F e =3 transition at the D 2 line of 87 Rb in a vacuum cell. EIA linewidths obtained for the two laser profiles were significantly different in the range of laser intensities 1-4 mW/cm 2 . EIA with the Π-shaped laser beam has a broad intensity maximum and linewidths larger than those obtained with the Gaussian beam profile. We also studied Hanle EIA by measuring the transmission of selected segments of the entire laser beam by placing a small movable aperture in front of the detector. Waveforms so obtained in Hanle EIA resonances were strongly influenced both by the radial distance of the transmitted segment from the beam center and by the radial profile of the laser beam. We show that outer regions of Gaussian beam, and central regions of the Π-shaped beam generate the narrowest lines. The different behaviors of EIA owing to different beam profiles revealed by both theory and experiment indicate the importance of the radial profile of the laser beam for proper modeling of coherent effects in alkali metal vapors.

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

Science.gov (United States)

Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet

2015-01-01

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating

An approximate fractional Gaussian noise model with computational cost

KAUST Repository

Sø rbye, Sigrunn H.; Myrvoll-Nilsen, Eirik; Rue, Haavard

2017-01-01

Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood

Interaction of Airy-Gaussian beams in saturable media

Science.gov (United States)

Zhou, Meiling; Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Deng, Dongmei

2016-08-01

Based on the nonlinear Schrödinger equation, the interactions of the two Airy-Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy-Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy-Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Province Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), and the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province, China. CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.

Fractional Gaussian noise: Prior specification and model comparison

KAUST Repository

Sørbye, Sigrunn Holbek

2017-07-07

Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.

Fractional Gaussian noise: Prior specification and model comparison

KAUST Repository

Sø rbye, Sigrunn Holbek; Rue, Haavard

2017-01-01

Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function of fGn are characterised by the Hurst exponent (H), which, in Bayesian contexts, typically has been assigned a uniform prior on the unit interval. This paper argues why a uniform prior is unreasonable and introduces the use of a penalised complexity (PC) prior for H. The PC prior is computed to penalise divergence from the special case of white noise and is invariant to reparameterisations. An immediate advantage is that the exact same prior can be used for the autocorrelation coefficient ϕ(symbol) of a first-order autoregressive process AR(1), as this model also reflects a flexible version of white noise. Within the general setting of latent Gaussian models, this allows us to compare an fGn model component with AR(1) using Bayes factors, avoiding the confounding effects of prior choices for the two hyperparameters H and ϕ(symbol). Among others, this is useful in climate regression models where inference for underlying linear or smooth trends depends heavily on the assumed noise model.

Gaussian discriminating strength

Science.gov (United States)

Rigovacca, L.; Farace, A.; De Pasquale, A.; Giovannetti, V.

2015-10-01

We present a quantifier of nonclassical correlations for bipartite, multimode Gaussian states. It is derived from the Discriminating Strength measure, introduced for finite dimensional systems in Farace et al., [New J. Phys. 16, 073010 (2014), 10.1088/1367-2630/16/7/073010]. As the latter the new measure exploits the quantum Chernoff bound to gauge the susceptibility of the composite system with respect to local perturbations induced by unitary gates extracted from a suitable set of allowed transformations (the latter being identified by posing some general requirements). Closed expressions are provided for the case of two-mode Gaussian states obtained by squeezing or by linearly mixing via a beam splitter a factorized two-mode thermal state. For these density matrices, we study how nonclassical correlations are related with the entanglement present in the system and with its total photon number.

Gaussian entanglement distribution via satellite

Science.gov (United States)

Hosseinidehaj, Nedasadat; Malaney, Robert

2015-02-01

In this work we analyze three quantum communication schemes for the generation of Gaussian entanglement between two ground stations. Communication occurs via a satellite over two independent atmospheric fading channels dominated by turbulence-induced beam wander. In our first scheme, the engineering complexity remains largely on the ground transceivers, with the satellite acting simply as a reflector. Although the channel state information of the two atmospheric channels remains unknown in this scheme, the Gaussian entanglement generation between the ground stations can still be determined. On the ground, distillation and Gaussification procedures can be applied, leading to a refined Gaussian entanglement generation rate between the ground stations. We compare the rates produced by this first scheme with two competing schemes in which quantum complexity is added to the satellite, thereby illustrating the tradeoff between space-based engineering complexity and the rate of ground-station entanglement generation.

Topology in two dimensions. IV - CDM models with non-Gaussian initial conditions

Science.gov (United States)

Coles, Peter; Moscardini, Lauro; Plionis, Manolis; Lucchin, Francesco; Matarrese, Sabino; Messina, Antonio

1993-02-01

The results of N-body simulations with both Gaussian and non-Gaussian initial conditions are used here to generate projected galaxy catalogs with the same selection criteria as the Shane-Wirtanen counts of galaxies. The Euler-Poincare characteristic is used to compare the statistical nature of the projected galaxy clustering in these simulated data sets with that of the observed galaxy catalog. All the models produce a topology dominated by a meatball shift when normalized to the known small-scale clustering properties of galaxies. Models characterized by a positive skewness of the distribution of primordial density perturbations are inconsistent with the Lick data, suggesting problems in reconciling models based on cosmic textures with observations. Gaussian CDM models fit the distribution of cell counts only if they have a rather high normalization but possess too low a coherence length compared with the Lick counts. This suggests that a CDM model with extra large scale power would probably fit the available data.

Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Science.gov (United States)

Borges, G. M.; Ferreira, A. S.; da Silva, M. A. A.; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.

2012-09-01

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e.g., fractional Brownian motion, Lévy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation σt which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

Directory of Open Access Journals (Sweden)

Elias D. Nino-Ruiz

2018-03-01

Full Text Available In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.

Thermally induced diffraction losses for a Gaussian pump beam and optimization of the mode-to-pump ratio in an end-pumped Nd:GdVO4 laser

International Nuclear Information System (INIS)

Wang, Y T; Li, W J; Pan, L L; Yu, J T; Zhang, R H

2013-01-01

The analytical model of thermally induced diffraction losses for a Gaussian pump beam are derived as functions of the mode-to-pump ratio and pump power in end-pumped Nd-doped lasers considering the energy transfer upconversion effects. The mode-to-pump ratio is optimized based on it. The results show that the optimum mode-to-pump ratio with the thermally induced diffraction losses is less than 0.65, and it is less than the results in which the thermally induced diffraction losses are neglected. The theoretical model is applied to a diode-end-pumped Nd:GdVO 4 laser operating at 1342 nm, and the theoretical calculations are in good agreement with the experimental results. (paper)

The behavior of the instantaneous Poynting vector of symmetrical laser beams

CSIR Research Space (South Africa)

Litvin, IA

2012-06-01

Full Text Available the radiation energy contained within the divergence angle of a Gaussian beam and the be- havior of the beam width during propagation. We have shown a connection between the behavior of the IPV at the beam waist plane and a well-known property of Gaussian... beams, namely the decreasing of the divergence of a Gaussian beam with an increase in the beam width. We have investigated the behavior of the IPV of paraxial BBs in detail and have shown that in the region of the ?double shadow? [21, 22] the BB car...

Modeling Choices in Nuclear Warfighting: Two Classroom Simulations on Escalation and Retaliation

Science.gov (United States)

Schofield, Julian

2013-01-01

Two classroom simulations--"Superpower Confrontation" and "Multipolar Asian Simulation"--are used to teach and test various aspects of the Borden versus Brodie debate on the Schelling versus Lanchester approach to nuclear conflict modeling and resolution. The author applies a Schelling test to segregate high from low empathic…

Schelling contra Jacobi. La posibilidad de un sistema de la libertad

Directory of Open Access Journals (Sweden)

Hernán Guerrero Troncoso

2016-08-01

Full Text Available Este artículo intenta mostrar cómo el examen del supuesto panteísmo del sistema de Spinoza, que abre las Investigaciones filosóficas sobre la esencia de la libertad humana de Schelling, presenta no solo su propia posición ante la polémica del panteísmo, sino que también implica una discusión con el pensamiento moderno, en particular en lo que se refiere al lugar, función e implicancias de la noción de sistema y su relación con la libertad. Una exposición del análisis crítico de Jacobi de la historia de la filosofía occidental —en el que afirma que el sistema no es compatible con el conocimiento de lo incondicionado— permitirá iluminar los términos en los que se plantea este diálogo del pensador de Leonberg con la tradición.

Generalized beam quality factor of aberrated truncated Gaussian laser beams

CSIR Research Space (South Africa)

Mafusire, C

2011-07-01

Full Text Available with a quadratic refractive index profile, a change in the beam quality factor can be used to infer the pre- sence of aberrations and thereby study the media of interest. For these reasons, among others, research into the beam qual- ity factor... very much like a normal lens (without the rotational symmetry associated with defocus) since the beam quality factor is calculated in the principal axes. With y-astigmatism, the lenslike behavior does not take place in the principal axes where...

Generation of ultra-long pure magnetization needle and multiple spots by phase modulated doughnut Gaussian beam

Science.gov (United States)

Udhayakumar, M.; Prabakaran, K.; Rajesh, K. B.; Jaroszewicz, Z.; Belafhal, Abdelmajid; Velauthapillai, Dhayalan

2018-06-01

Based on vector diffraction theory and inverse Faraday effect (IFE), the light induced magnetization distribution of a tightly focused azimuthally polarized doughnut Gaussian beam superimposed with a helical phase and modulated by an optimized multi belt complex phase filter (MBCPF) is analysed numerically. It is noted that by adjusting the radii of different rings of the complex phase filter, one can achieve many novel magnetization focal distribution such as sub wavelength scale (0.29λ) and super long (52.2λ) longitudinal magnetic probe suitable for all optical magnetic recording and the formation of multiple magnetization chain with four, six and eight sub-wavelength spherical magnetization spots suitable for multiple trapping of magnetic particles are achieved.

Contaminant dispersion prediction and source estimation with integrated Gaussian-machine learning network model for point source emission in atmosphere

International Nuclear Information System (INIS)

Ma, Denglong; Zhang, Zaoxiao

2016-01-01

Highlights: • The intelligent network models were built to predict contaminant gas concentrations. • The improved network models coupled with Gaussian dispersion model were presented. • New model has high efficiency and accuracy for concentration prediction. • New model were applied to indentify the leakage source with satisfied results. - Abstract: Gas dispersion model is important for predicting the gas concentrations when contaminant gas leakage occurs. Intelligent network models such as radial basis function (RBF), back propagation (BP) neural network and support vector machine (SVM) model can be used for gas dispersion prediction. However, the prediction results from these network models with too many inputs based on original monitoring parameters are not in good agreement with the experimental data. Then, a new series of machine learning algorithms (MLA) models combined classic Gaussian model with MLA algorithm has been presented. The prediction results from new models are improved greatly. Among these models, Gaussian-SVM model performs best and its computation time is close to that of classic Gaussian dispersion model. Finally, Gaussian-MLA models were applied to identifying the emission source parameters with the particle swarm optimization (PSO) method. The estimation performance of PSO with Gaussian-MLA is better than that with Gaussian, Lagrangian stochastic (LS) dispersion model and network models based on original monitoring parameters. Hence, the new prediction model based on Gaussian-MLA is potentially a good method to predict contaminant gas dispersion as well as a good forward model in emission source parameters identification problem.

Contaminant dispersion prediction and source estimation with integrated Gaussian-machine learning network model for point source emission in atmosphere

Energy Technology Data Exchange (ETDEWEB)

Ma, Denglong [Fuli School of Food Equipment Engineering and Science, Xi’an Jiaotong University, No.28 Xianning West Road, Xi’an 710049 (China); Zhang, Zaoxiao, E-mail: zhangzx@mail.xjtu.edu.cn [State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, No.28 Xianning West Road, Xi’an 710049 (China); School of Chemical Engineering and Technology, Xi’an Jiaotong University, No.28 Xianning West Road, Xi’an 710049 (China)

2016-07-05

Highlights: • The intelligent network models were built to predict contaminant gas concentrations. • The improved network models coupled with Gaussian dispersion model were presented. • New model has high efficiency and accuracy for concentration prediction. • New model were applied to indentify the leakage source with satisfied results. - Abstract: Gas dispersion model is important for predicting the gas concentrations when contaminant gas leakage occurs. Intelligent network models such as radial basis function (RBF), back propagation (BP) neural network and support vector machine (SVM) model can be used for gas dispersion prediction. However, the prediction results from these network models with too many inputs based on original monitoring parameters are not in good agreement with the experimental data. Then, a new series of machine learning algorithms (MLA) models combined classic Gaussian model with MLA algorithm has been presented. The prediction results from new models are improved greatly. Among these models, Gaussian-SVM model performs best and its computation time is close to that of classic Gaussian dispersion model. Finally, Gaussian-MLA models were applied to identifying the emission source parameters with the particle swarm optimization (PSO) method. The estimation performance of PSO with Gaussian-MLA is better than that with Gaussian, Lagrangian stochastic (LS) dispersion model and network models based on original monitoring parameters. Hence, the new prediction model based on Gaussian-MLA is potentially a good method to predict contaminant gas dispersion as well as a good forward model in emission source parameters identification problem.

The Gaussian atmospheric transport model and its sensitivity to the joint frequency distribution and parametric variability.

Science.gov (United States)

Hamby, D M

2002-01-01

Reconstructed meteorological data are often used in some form of long-term wind trajectory models for estimating the historical impacts of atmospheric emissions. Meteorological data for the straight-line Gaussian plume model are put into a joint frequency distribution, a three-dimensional array describing atmospheric wind direction, speed, and stability. Methods using the Gaussian model and joint frequency distribution inputs provide reasonable estimates of downwind concentration and have been shown to be accurate to within a factor of four. We have used multiple joint frequency distributions and probabilistic techniques to assess the Gaussian plume model and determine concentration-estimate uncertainty and model sensitivity. We examine the straight-line Gaussian model while calculating both sector-averaged and annual-averaged relative concentrations at various downwind distances. The sector-average concentration model was found to be most sensitive to wind speed, followed by horizontal dispersion (sigmaZ), the importance of which increases as stability increases. The Gaussian model is not sensitive to stack height uncertainty. Precision of the frequency data appears to be most important to meteorological inputs when calculations are made for near-field receptors, increasing as stack height increases.

Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers.

Science.gov (United States)

Wang, Tiansi; Zhang, Chong; Aleksov, Aleksandar; Salama, Islam; Kar, Aravinda

2017-04-01

Phased array ultrasonic transducers enable modulating the focal position of the acoustic waves, and this capability is utilized in many applications, such as medical imaging and non-destructive testing. This type of transducers also provides a mechanism to generate tilted wavefronts in acousto-optic deflectors to deflect laser beams for high precision advanced laser material processing. In this paper, a theoretical model is presented for the diffraction of ultrasonic waves emitted by several phased array transducers into an acousto-optic medium such as TeO 2 crystal. A simple analytic expression is obtained for the distribution of the ultrasonic displacement field in the crystal. The model prediction is found to be in good agreement with the results of a numerical model that is based on a non-paraxial multi-Gaussian beam (NMGB) model. Published by Elsevier B.V.

Beam profile effects on NPB [neutral particle beam] performance

International Nuclear Information System (INIS)

LeClaire, R.J. Jr.

1988-03-01

A comparison of neutral particle beam brightness for various neutral beam profiles indicates that the widely used assumption of a Gaussian profile may be misleading for collisional neutralizers. An analysis of available experimental evidence shows that lower peaks and higher tails, compared to a Gaussian beam profile, are observed out of collisional neutralizers, which implies that peak brightness is over estimated, and for a given NPB platform-to-target range, the beam current (power), dwell time or some combination of such engagement parameters would have to be altered to maintain a fixed dose on target. Based on the present analysis, this factor is nominally about 2.4 but may actually be as low as 1.8 or as high as 8. This is an important consideration in estimating NPB constellation performance in SDI engagement contexts. 2 refs., 6 figs

A summary of some beam-beam models

International Nuclear Information System (INIS)

Chao, A.W.

1989-01-01

Two categories of theoretical models for the beam-beam interaction are reviewed: the linear-lens models and the single-resonance models. In a linear-lens model, the beam-beam force is linearized and represented by a localized linear lens. Analyses of incoherent single particle effects can be performed exactly in these models by using matrix techniques. Although the results do not agree with the experimental observations in many respects, the linear-lens models constitute a starting point of our understanding of the beam-beam interaction. In the single-resonance models, one is concerned with the possible incoherent instabilities as the betatron tune of some of the particles is close to a certain rational number. It is assumed in these models that one and only one such rational number dominates the single-particle beam-beam effects. It is found that static single resonances cannot explain many of the experimental results. Some attempts have been made to modify the static single-resonance theory by including some mechanisms for diffusive tune fluctuations or periodic tune modulations. These modified single-resonance models have met only with some limited qualitative success. 21 refs., 13 figs

Fitting non-gaussian Models to Financial data: An Empirical Study

Directory of Open Access Journals (Sweden)

Pablo Olivares

2011-04-01

Full Text Available In this paper are presented some experiences about the modeling of financial data by three classes of models as alternative to Gaussian Linear models. Dynamic Volatility, Stable L'evy and Diffusion with Jumps models are considered. The techniques are illustrated with some examples of financial series on currency, futures and indexes.

Two kinds of Airy-related beams

International Nuclear Information System (INIS)

Xu, Yiqing; Zhou, Guoquan; Zhang, Lijun; Ru, Guoyun

2015-01-01

Two kinds of Airy-related beams are introduced in this manuscript. The normalized intensity distribution in the x-direction of the two kinds of Airy-related beams is close to that of the Gaussian beam. The normalized intensity distribution in the y-direction of the two kinds of Airy-related beams is close to that of the second-order and the third-order elegant Hermite–Gaussian beams, respectively. Analytical expressions of the two kinds of Airy-related beams passing through an ABCD paraxial optical system are derived. The beam propagation factors for the two kinds of Airy-related beams are 1.933 and 2.125, respectively. Analytical expressions of the beam half widths and the kurtosis parameters of the two kinds of Airy-related beams passing through an ABCD paraxial optical system are also presented. As a numerical example, the propagation properties of the two kinds of Airy-related beams are demonstrated in free space. Moreover, the comparison between the two kinds of Airy-related beams and their corresponding elegant Hermite–Gaussian beams along the two transverse directions are performed in detail. Upon propagation, the former kind of Airy-related beam will evolve from the central bright beam into the dark hollow beam. Contrarily, the latter kind of Airy-related beam will evolve from the dark hollow beam into the central bright beam. These two kinds of Airy-related beams can be used to describe specially distributed beams. (paper)

Receiver design for SPAD-based VLC systems under Poisson-Gaussian mixed noise model.

Science.gov (United States)

Mao, Tianqi; Wang, Zhaocheng; Wang, Qi

2017-01-23

Single-photon avalanche diode (SPAD) is a promising photosensor because of its high sensitivity to optical signals in weak illuminance environment. Recently, it has drawn much attention from researchers in visible light communications (VLC). However, existing literature only deals with the simplified channel model, which only considers the effects of Poisson noise introduced by SPAD, but neglects other noise sources. Specifically, when an analog SPAD detector is applied, there exists Gaussian thermal noise generated by the transimpedance amplifier (TIA) and the digital-to-analog converter (D/A). Therefore, in this paper, we propose an SPAD-based VLC system with pulse-amplitude-modulation (PAM) under Poisson-Gaussian mixed noise model, where Gaussian-distributed thermal noise at the receiver is also investigated. The closed-form conditional likelihood of received signals is derived using the Laplace transform and the saddle-point approximation method, and the corresponding quasi-maximum-likelihood (quasi-ML) detector is proposed. Furthermore, the Poisson-Gaussian-distributed signals are converted to Gaussian variables with the aid of the generalized Anscombe transform (GAT), leading to an equivalent additive white Gaussian noise (AWGN) channel, and a hard-decision-based detector is invoked. Simulation results demonstrate that, the proposed GAT-based detector can reduce the computational complexity with marginal performance loss compared with the proposed quasi-ML detector, and both detectors are capable of accurately demodulating the SPAD-based PAM signals.

'The formula that killed Wall Street': the Gaussian copula and modelling practices in investment banking.

Science.gov (United States)

MacKenzie, Donald; Spears, Taylor

2014-06-01

Drawing on documentary sources and 114 interviews with market participants, this and a companion article discuss the development and use in finance of the Gaussian copula family of models, which are employed to estimate the probability distribution of losses on a pool of loans or bonds, and which were centrally involved in the credit crisis. This article, which explores how and why the Gaussian copula family developed in the way it did, employs the concept of 'evaluation culture', a set of practices, preferences and beliefs concerning how to determine the economic value of financial instruments that is shared by members of multiple organizations. We identify an evaluation culture, dominant within the derivatives departments of investment banks, which we call the 'culture of no-arbitrage modelling', and explore its relation to the development of Gaussian copula models. The article suggests that two themes from the science and technology studies literature on models (modelling as 'impure' bricolage, and modelling as articulating with heterogeneous objectives and constraints) help elucidate the history of Gaussian copula models in finance.

Performance of monitoring networks estimated from a Gaussian plume model

International Nuclear Information System (INIS)

Seebregts, A.J.; Hienen, J.F.A.

1990-10-01

In support of the ECN study on monitoring strategies after nuclear accidents, the present report describes the analysis of the performance of a monitoring network in a square grid. This network is used to estimate the distribution of the deposition pattern after a release of radioactivity into the atmosphere. The analysis is based upon a single release, a constant wind direction and an atmospheric dispersion according to a simplified Gaussian plume model. A technique is introduced to estimate the parameters in this Gaussian model based upon measurements at specific monitoring locations and linear regression, although this model is intrinsically non-linear. With these estimated parameters and the Gaussian model the distribution of the contamination due to deposition can be estimated. To investigate the relation between the network and the accuracy of the estimates for the deposition, deposition data have been generated by the Gaussian model, including a measurement error by a Monte Carlo simulation and this procedure has been repeated for several grid sizes, dispersion conditions, number of measurements per location, and errors per single measurement. The present technique has also been applied for the mesh sizes of two networks in the Netherlands, viz. the Landelijk Meetnet Radioaciviteit (National Measurement Network on Radioactivity, mesh size approx. 35 km) and the proposed Landelijk Meetnet Nucleaire Incidenten (National Measurement Network on Nuclear Incidents, mesh size approx. 15 km). The results show accuracies of 11 and 7 percent, respectively, if monitoring locations are used more than 10 km away from the postulated accident site. These figures are based upon 3 measurements per location and a dispersion during neutral weather with a wind velocity of 4 m/s. For stable weather conditions and low wind velocities, i.e. a small plume, the calculated accuracies are at least a factor 1.5 worse.The present type of analysis makes a cost-benefit approach to the

X-ray beam-shaping via deformable mirrors: surface profile and point spread function computation for Gaussian beams using physical optics.

Science.gov (United States)

Spiga, D

2018-01-01

X-ray mirrors with high focusing performances are commonly used in different sectors of science, such as X-ray astronomy, medical imaging and synchrotron/free-electron laser beamlines. While deformations of the mirror profile may cause degradation of the focus sharpness, a deliberate deformation of the mirror can be made to endow the focus with a desired size and distribution, via piezo actuators. The resulting profile can be characterized with suitable metrology tools and correlated with the expected optical quality via a wavefront propagation code or, sometimes, predicted using geometric optics. In the latter case and for the special class of profile deformations with monotonically increasing derivative, i.e. concave upwards, the point spread function (PSF) can even be predicted analytically. Moreover, under these assumptions, the relation can also be reversed: from the desired PSF the required profile deformation can be computed analytically, avoiding the use of trial-and-error search codes. However, the computation has been so far limited to geometric optics, which entailed some limitations: for example, mirror diffraction effects and the size of the coherent X-ray source were not considered. In this paper, the beam-shaping formalism in the framework of physical optics is reviewed, in the limit of small light wavelengths and in the case of Gaussian intensity wavefronts. Some examples of shaped profiles are also shown, aiming at turning a Gaussian intensity distribution into a top-hat one, and checks of the shaping performances computing the at-wavelength PSF by means of the WISE code are made.

Learning non-Gaussian Time Series using the Box-Cox Gaussian Process

OpenAIRE

Rios, Gonzalo; Tobar, Felipe

2018-01-01

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model general non-Gaussian data with complex correlation structure, GPs can be paired with an expressive covariance kernel and then fed into a nonlinear transformation (or warping). However, overparametrising the kernel and the warping is known to, respectively, hin...

Intra-cavity generation of superpositions of Laguerre-Gaussian beams

CSIR Research Space (South Africa)

Naidoo, Darryl

2012-01-01

Full Text Available In this paper we demonstrate experimentally the intra-cavity generation of a coherent superposition of Laguerre–Gaussian modes of zero radial order but opposite azimuthal order. The superposition is created with a simple intra-cavity stop...

Random wandering of laser beams with orbital angular momentum during propagation through atmospheric turbulence.

Science.gov (United States)

Aksenov, Valerii P; Kolosov, Valeriy V; Pogutsa, Cheslav E

2014-06-10

The propagation of laser beams having orbital angular momenta (OAM) in the turbulent atmosphere is studied numerically. The variance of random wandering of these beams is investigated with the use of the Monte Carlo technique. It is found that, among various types of vortex laser beams, such as the Laguerre-Gaussian (LG) beam, modified Bessel-Gaussian beam, and hypergeometric Gaussian beam, having identical initial effective radii and OAM, the LG beam occupying the largest effective volume in space is the most stable one.

Current algorithms for computed electron beam dose planning

International Nuclear Information System (INIS)

Brahme, A.

1985-01-01

Two- and sometimes three-dimensional computer algorithms for electron beam irradiation are capable of taking all irregularities of the body cross-section and the properties of the various tissues into account. This is achieved by dividing the incoming broad beams into a number of narrow pencil beams, the penetration of which can be described by essentially one-dimensional formalisms. The constituent pencil beams are most often described by Gaussian, experimentally or theoretically derived distributions. The accuracy of different dose planning algorithms is discussed in some detail based on their ability to take the different physical interaction processes of high energy electrons into account. It is shown that those programs that take the deviations from the simple Gaussian model into account give the best agreement with experimental results. With such programs a dosimetric relative accuracy of about 5% is generally achieved except in the most complex inhomogeneity configurations. Finally, the present limitations and possible future developments of electron dose planning are discussed. (orig.)

Graphical Gaussian models with edge and vertex symmetries

DEFF Research Database (Denmark)

Højsgaard, Søren; Lauritzen, Steffen L

2008-01-01

We introduce new types of graphical Gaussian models by placing symmetry restrictions on the concentration or correlation matrix. The models can be represented by coloured graphs, where parameters that are associated with edges or vertices of the same colour are restricted to being identical. We...... study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates. We identify conditions for restrictions on the concentration and correlation matrices being equivalent. This is for example the case when symmetries are generated by permutation...

XDGMM: eXtreme Deconvolution Gaussian Mixture Modeling

Science.gov (United States)

Holoien, Thomas W.-S.; Marshall, Philip J.; Wechsler, Risa H.

2017-08-01

XDGMM uses Gaussian mixtures to do density estimation of noisy, heterogenous, and incomplete data using extreme deconvolution (XD) algorithms which is compatible with the scikit-learn machine learning methods. It implements both the astroML and Bovy et al. (2011) algorithms, and extends the BaseEstimator class from scikit-learn so that cross-validation methods work. It allows the user to produce a conditioned model if values of some parameters are known.

Generation of Laguerre-Gaussian Beams Using a Diode Pumped Solid-State Digital Laser

CSIR Research Space (South Africa)

Bell, Teboho

2015-10-01

Full Text Available The solid state digital laser was used in generation of Laguerre-Gaussian modes, LGpl, of different orders. This work demonstrates that we can generate high-order Laguerre-Gaussian modes with high purity using a digital laser....

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

Science.gov (United States)

Guo, Yongfeng; Shen, Yajun; Tan, Jianguo

2016-09-01

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

Science.gov (United States)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

A symplectic coherent beam-beam model

International Nuclear Information System (INIS)

Furman, M.A.

1989-05-01

We consider a simple one-dimensional model to study the effects of the beam-beam force on the coherent dynamics of colliding beams. The key ingredient is a linearized beam-beam kick. We study only the quadrupole modes, with the dynamical variables being the 2nd-order moments of the canonical variables q, p. Our model is self-consistent in the sense that no higher order moments are generated by the linearized beam-beam kicks, and that the only source of violation of symplecticity is the radiation. We discuss the round beam case only, in which vertical and horizontal quantities are assumed to be equal (though they may be different in the two beams). Depending on the values of the tune and beam intensity, we observe steady states in which otherwise identical bunches have sizes that are equal, or unequal, or periodic, or behave chaotically from turn to turn. Possible implications of luminosity saturation with increasing beam intensity are discussed. Finally, we present some preliminary applications to an asymmetric collider. 8 refs., 8 figs

Application of Gaussian cubature to model two-dimensional population balances

Directory of Open Access Journals (Sweden)

Bałdyga Jerzy

2017-09-01

Full Text Available In many systems of engineering interest the moment transformation of population balance is applied. One of the methods to solve the transformed population balance equations is the quadrature method of moments. It is based on the approximation of the density function in the source term by the Gaussian quadrature so that it preserves the moments of the original distribution. In this work we propose another method to be applied to the multivariate population problem in chemical engineering, namely a Gaussian cubature (GC technique that applies linear programming for the approximation of the multivariate distribution. Examples of the application of the Gaussian cubature (GC are presented for four processes typical for chemical engineering applications. The first and second ones are devoted to crystallization modeling with direction-dependent two-dimensional and three-dimensional growth rates, the third one represents drop dispersion accompanied by mass transfer in liquid-liquid dispersions and finally the fourth case regards the aggregation and sintering of particle populations.

Mode conversion efficiency to Laguerre-Gaussian OAM modes using spiral phase optics.

Science.gov (United States)

Longman, Andrew; Fedosejevs, Robert

2017-07-24

An analytical model for the conversion efficiency from a TEM 00 mode to an arbitrary Laguerre-Gaussian (LG) mode with null radial index spiral phase optics is presented. We extend this model to include the effects of stepped spiral phase optics, spiral phase optics of non-integer topological charge, and the reduction in conversion efficiency due to broad laser bandwidth. We find that through optimization, an optimal beam waist ratio of the input and output modes exists and is dependent upon the output azimuthal mode number.

Improvement of Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size.

Science.gov (United States)

Ma, Haotong; Liu, Zejin; Jiang, Pengzhi; Xu, Xiaojun; Du, Shaojun

2011-07-04

We propose and demonstrate the improvement of conventional Galilean refractive beam shaping system for accurately generating near-diffraction-limited flattop beam with arbitrary beam size. Based on the detailed study of the refractive beam shaping system, we found that the conventional Galilean beam shaper can only work well for the magnifying beam shaping. Taking the transformation of input beam with Gaussian irradiance distribution into target beam with high order Fermi-Dirac flattop profile as an example, the shaper can only work well at the condition that the size of input and target beam meets R(0) ≥ 1.3 w(0). For the improvement, the shaper is regarded as the combination of magnifying and demagnifying beam shaping system. The surface and phase distributions of the improved Galilean beam shaping system are derived based on Geometric and Fourier Optics. By using the improved Galilean beam shaper, the accurate transformation of input beam with Gaussian irradiance distribution into target beam with flattop irradiance distribution is realized. The irradiance distribution of the output beam is coincident with that of the target beam and the corresponding phase distribution is maintained. The propagation performance of the output beam is greatly improved. Studies of the influences of beam size and beam order on the improved Galilean beam shaping system show that restriction of beam size has been greatly reduced. This improvement can also be used to redistribute the input beam with complicated irradiance distribution into output beam with complicated irradiance distribution.

An integrated numerical model for the prediction of Gaussian and billet shapes

International Nuclear Information System (INIS)

Hattel, J.H.; Pryds, N.H.; Pedersen, T.B.

2004-01-01

Separate models for the atomisation and the deposition stages were recently integrated by the authors to form a unified model describing the entire spray-forming process. In the present paper, the focus is on describing the shape of the deposited material during the spray-forming process, obtained by this model. After a short review of the models and their coupling, the important factors which influence the resulting shape, i.e. Gaussian or billet, are addressed. The key parameters, which are utilized to predict the geometry and dimension of the deposited material, are the sticking efficiency and the shading effect for Gaussian and billet shape, respectively. From the obtained results, the effect of these parameters on the final shape is illustrated

Application of the Gaussian beam summation method to the study of the ultrasonic wave propagation in a turbulent medium

International Nuclear Information System (INIS)

Fiorina, D.

1998-01-01

Some systems for the control and the surveillance of fast reactors are based on the characteristics of the ultrasonic wave propagation. We present here the results of a numerical and experimental study of ultrasonic propagation in a thermal turbulent medium. A numerical model, based on the technique of superposition of discrete Fourier modes for representing isotropic and homogeneous turbulence and on the Gaussian beam summation method for calculating the acoustic field, has been implemented in order to study the propagation of a point source wave in a bidimensional turbulent medium. Our model is based on the following principle: the medium is represented by a great number of independent realizations of a turbulent field and for each of them we calculate the acoustic field in a deterministic way. Statistics over a great number of realizations enable us to access to the different quantities of the distorted acoustic field: variance of the time of flight fluctuations, scintillation index and intensity probability density function. In the case of small fluctuations, the results for these three quantities are in a good agreement with analytical solutions. When the level of the fluctuations grows, the model predicts correct evolutions. However, a great sensitivity to the location of a receiver in the vicinity of a caustic has been proved. Calculations in the temporal domain have also been performed. They give an illustration of the possible effects of the turbulence on an impulsion signal. An experimental device, fitted with thermocouples and acoustic transducers, has been used to study the ultrasonic propagation in turbulent water. The different measures permitted to characterize the turbulent field and to get aware of the effect of the turbulence on the acoustic propagation. The acoustical measures agree well with the analytical solution of Chernov and Rytov. They are show the importance of the knowledge of the real spectrum of the fluctuations and the limitations of

On the representation of the diffracted field of Hermite-Gaussian modes in an alien basis and the young diffraction principle

International Nuclear Information System (INIS)

Smirnov, V.N.; Strokovskii, G.A.

1994-01-01

An analytical form of expansion coefficients of a diffracted field for an arbitrary Hermite-Gaussian beam in an alien Hermite-Gaussian basis is obtained. A possible physical interpretation of the well-known Young phenomenological diffraction principle and experiments on diffraction of Hermite-Gaussian beams of the lowest types (n = 0 - 5) from half-plane are discussed. The case of nearly homogenous expansion corresponding to misalignment and mismatch of optical systems is also analyzed. 7 refs., 2 figs

Doughnut laser beam as an incoherent superposition of two petal beams

CSIR Research Space (South Africa)

Litvin, IA

2014-02-01

Full Text Available Laguerre–Gaussian beams with a nonzero azimuthal index are known to carry orbital angular momentum (OAM), and are routinely created external to laser cavities. The few reports of obtaining such beams from laser cavities suffer from inconclusive...

Generation of shape-invariant flat-top laser beams

CSIR Research Space (South Africa)

Ait-Ameur, K

2015-02-01

Full Text Available A great number of laser applications need in place of the usual Gaussian beam a flat-top intensity profile in the focal plane of a focusing lens. In general the transformation of the laser beam from the Gaussian to the flat-top shape is made by a...

White Gaussian Noise - Models for Engineers

Science.gov (United States)

Jondral, Friedrich K.

2018-04-01

This paper assembles some information about white Gaussian noise (WGN) and its applications. It starts from a description of thermal noise, i. e. the irregular motion of free charge carriers in electronic devices. In a second step, mathematical models of WGN processes and their most important parameters, especially autocorrelation functions and power spectrum densities, are introduced. In order to proceed from mathematical models to simulations, we discuss the generation of normally distributed random numbers. The signal-to-noise ratio as the most important quality measure used in communications, control or measurement technology is accurately introduced. As a practical application of WGN, the transmission of quadrature amplitude modulated (QAM) signals over additive WGN channels together with the optimum maximum likelihood (ML) detector is considered in a demonstrative and intuitive way.

Evaluation of Gaussian approximations for data assimilation in reservoir models

KAUST Repository

Iglesias, Marco A.

2013-07-14

The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior distribution and data from the reservoir dynamics, together with a forward model connecting the space of geological parameters to the data space. Since the posterior distribution quantifies the uncertainty in the geologic parameters of the reservoir, the characterization of the posterior is fundamental for the optimal management of reservoirs. Unfortunately, due to the large-scale highly nonlinear properties of standard reservoir models, characterizing the posterior is computationally prohibitive. Instead, more affordable ad hoc techniques, based on Gaussian approximations, are often used for characterizing the posterior distribution. Evaluating the performance of those Gaussian approximations is typically conducted by assessing their ability at reproducing the truth within the confidence interval provided by the ad hoc technique under consideration. This has the disadvantage of mixing up the approximation properties of the history matching algorithm employed with the information content of the particular observations used, making it hard to evaluate the effect of the ad hoc approximations alone. In this paper, we avoid this disadvantage by comparing the ad hoc techniques with a fully resolved state-of-the-art probing of the Bayesian posterior distribution. The ad hoc techniques whose performance we assess are based on (1) linearization around the maximum a posteriori estimate, (2) randomized maximum likelihood, and (3) ensemble Kalman filter-type methods. In order to fully resolve the posterior distribution, we implement a state-of-the art Markov chain Monte Carlo (MCMC) method that scales well with respect to the dimension of the parameter space, enabling us to study realistic forward models, in two space dimensions, at a high level of grid refinement. Our

Dynamical chaos and beam-beam models

International Nuclear Information System (INIS)

Izrailev, F.M.

1990-01-01

Some aspects of the nonlinear dynamics of beam-beam interaction for simple one-dimensional and two-dimensional models of round and flat beams are discussed. The main attention is paid to the stochasticity threshold due to the overlapping of nonlinear resonances. The peculiarities of a round beam are investigated in view of using the round beams in storage rings to get high luminosity. 16 refs.; 7 figs

Parametric estimation of covariance function in Gaussian-process based Kriging models. Application to uncertainty quantification for computer experiments

International Nuclear Information System (INIS)

Bachoc, F.

2013-01-01

The parametric estimation of the covariance function of a Gaussian process is studied, in the framework of the Kriging model. Maximum Likelihood and Cross Validation estimators are considered. The correctly specified case, in which the covariance function of the Gaussian process does belong to the parametric set used for estimation, is first studied in an increasing-domain asymptotic framework. The sampling considered is a randomly perturbed multidimensional regular grid. Consistency and asymptotic normality are proved for the two estimators. It is then put into evidence that strong perturbations of the regular grid are always beneficial to Maximum Likelihood estimation. The incorrectly specified case, in which the covariance function of the Gaussian process does not belong to the parametric set used for estimation, is then studied. It is shown that Cross Validation is more robust than Maximum Likelihood in this case. Finally, two applications of the Kriging model with Gaussian processes are carried out on industrial data. For a validation problem of the friction model of the thermal-hydraulic code FLICA 4, where experimental results are available, it is shown that Gaussian process modeling of the FLICA 4 code model error enables to considerably improve its predictions. Finally, for a meta modeling problem of the GERMINAL thermal-mechanical code, the interest of the Kriging model with Gaussian processes, compared to neural network methods, is shown. (author) [fr

Tachyon mediated non-Gaussianity

International Nuclear Information System (INIS)

Dutta, Bhaskar; Leblond, Louis; Kumar, Jason

2008-01-01

We describe a general scenario where primordial non-Gaussian curvature perturbations are generated in models with extra scalar fields. The extra scalars communicate to the inflaton sector mainly through the tachyonic (waterfall) field condensing at the end of hybrid inflation. These models can yield significant non-Gaussianity of the local shape, and both signs of the bispectrum can be obtained. These models have cosmic strings and a nearly flat power spectrum, which together have been recently shown to be a good fit to WMAP data. We illustrate with a model of inflation inspired from intersecting brane models.

Speech Enhancement by MAP Spectral Amplitude Estimation Using a Super-Gaussian Speech Model

Directory of Open Access Journals (Sweden)

Lotter Thomas

2005-01-01

Full Text Available This contribution presents two spectral amplitude estimators for acoustical background noise suppression based on maximum a posteriori estimation and super-Gaussian statistical modelling of the speech DFT amplitudes. The probability density function of the speech spectral amplitude is modelled with a simple parametric function, which allows a high approximation accuracy for Laplace- or Gamma-distributed real and imaginary parts of the speech DFT coefficients. Also, the statistical model can be adapted to optimally fit the distribution of the speech spectral amplitudes for a specific noise reduction system. Based on the super-Gaussian statistical model, computationally efficient maximum a posteriori speech estimators are derived, which outperform the commonly applied Ephraim-Malah algorithm.

Complex space source theory of partially coherent light wave.

Science.gov (United States)

Seshadri, S R

2010-07-01

The complex space source theory is used to derive a general integral expression for the vector potential that generates the extended full Gaussian wave in terms of the input value of the vector potential of the corresponding paraxial beam. The vector potential and the fields are assumed to fluctuate on a time scale that is large compared to the wave period. The Poynting vector in the propagation direction averaged over a wave period is expressed in terms of the cross-spectral density of the fluctuating vector potential across the input plane. The Schell model is assumed for the cross-spectral density. The radiation intensity distribution and the power radiated are determined. The effect of spatial coherence on the radiation intensity distribution and the radiated power are investigated for different values of the physical parameters. Illustrative numerical results are provided to bring out the effect of spatial coherence on the propagation characteristics of the fluctuating light wave.

Intra-beam Scattering Theory and RHIC Experiments

International Nuclear Information System (INIS)

Wei, J.; Fedotov, A.; Fischer, W.; Malitsky, N.; Parzen, G.; Qiang, J.

2005-01-01

Intra-beam scattering is the leading mechanism limiting the luminosity in heavy-ion storage rings like the Relativistic Heavy Ion Collider (RHIC). The multiple Coulomb scattering among the charged particles causes transverse emittance growth and longitudinal beam de-bunching and beam loss, compromising machine performance during collision. Theoretically, the original theories developed by Piwinski, Bjorken, and Mtingwa only describe the rms beam size growth of an unbounded Gaussian distribution. Equations based on the Fokker-Planck approach are developed to further describe the beam density profile evolution and beam loss. During the 2004 RHIC heavy-ion operation, dedicated IBS experiments were performed to bench-mark the rms beam size growth, beam loss, and profile evolution both for a Gaussian-like and a longitudinal hollow beam. This paper summarizes the IBS theory and discusses the experimental bench-marking results

Propagation of a laser beam in a plasma

Science.gov (United States)

Chapman, J. M.; Kevorkian, J.; Steinhauer, L. C.; Vagners, J.

1975-01-01

This paper shows that for a nonabsorbing medium with a prescribed index of refraction, the effects of beam stability, line focusing, and beam distortion can be predicted from simple ray optics. When the paraxial approximation is used, diffraction effects are examined for Gaussian, Lorentzian, and square beams. Most importantly, it is shown that for a Gaussian beam, diffraction effects can be included simply by adding imaginary solutions to the paraxial ray equations. Also presented are several procedures to extend the paraxial approximation so that the solution will have a domain of validity of greater extent.

Kinect Posture Reconstruction Based on a Local Mixture of Gaussian Process Models.

Science.gov (United States)

Liu, Zhiguang; Zhou, Liuyang; Leung, Howard; Shum, Hubert P H

2016-11-01

Depth sensor based 3D human motion estimation hardware such as Kinect has made interactive applications more popular recently. However, it is still challenging to accurately recognize postures from a single depth camera due to the inherently noisy data derived from depth images and self-occluding action performed by the user. In this paper, we propose a new real-time probabilistic framework to enhance the accuracy of live captured postures that belong to one of the action classes in the database. We adopt the Gaussian Process model as a prior to leverage the position data obtained from Kinect and marker-based motion capture system. We also incorporate a temporal consistency term into the optimization framework to constrain the velocity variations between successive frames. To ensure that the reconstructed posture resembles the accurate parts of the observed posture, we embed a set of joint reliability measurements into the optimization framework. A major drawback of Gaussian Process is its cubic learning complexity when dealing with a large database due to the inverse of a covariance matrix. To solve the problem, we propose a new method based on a local mixture of Gaussian Processes, in which Gaussian Processes are defined in local regions of the state space. Due to the significantly decreased sample size in each local Gaussian Process, the learning time is greatly reduced. At the same time, the prediction speed is enhanced as the weighted mean prediction for a given sample is determined by the nearby local models only. Our system also allows incrementally updating a specific local Gaussian Process in real time, which enhances the likelihood of adapting to run-time postures that are different from those in the database. Experimental results demonstrate that our system can generate high quality postures even under severe self-occlusion situations, which is beneficial for real-time applications such as motion-based gaming and sport training.

Fractional statistics in 2+1 dimensions through the Gaussian model

International Nuclear Information System (INIS)

Murthy, G.

1986-01-01

The free massless field in 2+1 dimensions is written as an ''integral'' over free massless fields in 1+1 dimensions. Taking the operators with fractional dimension in the Gaussian model as a springboard we construct operators with fractional statistics in the former theory

Evaluation of Distance Measures Between Gaussian Mixture Models of MFCCs

DEFF Research Database (Denmark)

Jensen, Jesper Højvang; Ellis, Dan P. W.; Christensen, Mads Græsbøll

2007-01-01

In music similarity and in the related task of genre classification, a distance measure between Gaussian mixture models is frequently needed. We present a comparison of the Kullback-Leibler distance, the earth movers distance and the normalized L2 distance for this application. Although...

Semiparametric Gaussian copula models : Geometry and efficient rank-based estimation

NARCIS (Netherlands)

Segers, J.; van den Akker, R.; Werker, B.J.M.

2014-01-01

We propose, for multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically efficient estimator for the Euclidean copula parameter. This estimator is defined as a one-step update of a rank-based pilot estimator in the direction of

Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates

Directory of Open Access Journals (Sweden)

Marcus C. Christiansen

2013-10-01

Full Text Available In the actuarial literature, it has become common practice to model future capital returns and mortality rates stochastically in order to capture market risk and forecasting risk. Although interest rates often should and mortality rates always have to be non-negative, many authors use stochastic diffusion models with an affine drift term and additive noise. As a result, the diffusion process is Gaussian and, thus, analytically tractable, but negative values occur with positive probability. The argument is that the class of Gaussian diffusions would be a good approximation of the real future development. We challenge that reasoning and study the asymptotics of diffusion processes with affine drift and a general noise term with corresponding diffusion processes with an affine drift term and an affine noise term or additive noise. Our study helps to quantify the error that is made by approximating diffusive interest and mortality rate models with Gaussian diffusions and affine diffusions. In particular, we discuss forward interest and forward mortality rates and the error that approximations cause on the valuation of life insurance claims.

Linking network usage patterns to traffic Gaussianity fit

NARCIS (Netherlands)

de Oliveira Schmidt, R.; Sadre, R.; Melnikov, Nikolay; Schönwälder, Jürgen; Pras, Aiko

Gaussian traffic models are widely used in the domain of network traffic modeling. The central assumption is that traffic aggregates are Gaussian distributed. Due to its importance, the Gaussian character of network traffic has been extensively assessed by researchers in the past years. In 2001,

Nonclassicality by Local Gaussian Unitary Operations for Gaussian States

Directory of Open Access Journals (Sweden)

Yangyang Wang

2018-04-01

Full Text Available A measure of nonclassicality N in terms of local Gaussian unitary operations for bipartite Gaussian states is introduced. N is a faithful quantum correlation measure for Gaussian states as product states have no such correlation and every non product Gaussian state contains it. For any bipartite Gaussian state ρ A B , we always have 0 ≤ N ( ρ A B < 1 , where the upper bound 1 is sharp. An explicit formula of N for ( 1 + 1 -mode Gaussian states and an estimate of N for ( n + m -mode Gaussian states are presented. A criterion of entanglement is established in terms of this correlation. The quantum correlation N is also compared with entanglement, Gaussian discord and Gaussian geometric discord.

Transfer of non-Gaussian quantum states of mechanical oscillator to light

Science.gov (United States)

Filip, Radim; Rakhubovsky, Andrey A.

2015-11-01

Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

Science.gov (United States)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

Discrimination of numerical proportions: A comparison of binomial and Gaussian models.

Science.gov (United States)

Raidvee, Aire; Lember, Jüri; Allik, Jüri

2017-01-01

Observers discriminated the numerical proportion of two sets of elements (N = 9, 13, 33, and 65) that differed either by color or orientation. According to the standard Thurstonian approach, the accuracy of proportion discrimination is determined by irreducible noise in the nervous system that stochastically transforms the number of presented visual elements onto a continuum of psychological states representing numerosity. As an alternative to this customary approach, we propose a Thurstonian-binomial model, which assumes discrete perceptual states, each of which is associated with a certain visual element. It is shown that the probability β with which each visual element can be noticed and registered by the perceptual system can explain data of numerical proportion discrimination at least as well as the continuous Thurstonian-Gaussian model, and better, if the greater parsimony of the Thurstonian-binomial model is taken into account using AIC model selection. We conclude that Gaussian and binomial models represent two different fundamental principles-internal noise vs. using only a fraction of available information-which are both plausible descriptions of visual perception.

BEAMS3D Neutral Beam Injection Model

Energy Technology Data Exchange (ETDEWEB)

Lazerson, Samuel

2014-04-14

With the advent of applied 3D fi elds in Tokamaks and modern high performance stellarators, a need has arisen to address non-axisymmetric effects on neutral beam heating and fueling. We report on the development of a fully 3D neutral beam injection (NBI) model, BEAMS3D, which addresses this need by coupling 3D equilibria to a guiding center code capable of modeling neutral and charged particle trajectories across the separatrix and into the plasma core. Ionization, neutralization, charge-exchange, viscous velocity reduction, and pitch angle scattering are modeled with the ADAS atomic physics database [1]. Benchmark calculations are presented to validate the collisionless particle orbits, neutral beam injection model, frictional drag, and pitch angle scattering effects. A calculation of neutral beam heating in the NCSX device is performed, highlighting the capability of the code to handle 3D magnetic fields.

Bayes factor between Student t and Gaussian mixed models within an animal breeding context

Directory of Open Access Journals (Sweden)

García-Cortés Luis

2008-07-01

Full Text Available Abstract The implementation of Student t mixed models in animal breeding has been suggested as a useful statistical tool to effectively mute the impact of preferential treatment or other sources of outliers in field data. Nevertheless, these additional sources of variation are undeclared and we do not know whether a Student t mixed model is required or if a standard, and less parameterized, Gaussian mixed model would be sufficient to serve the intended purpose. Within this context, our aim was to develop the Bayes factor between two nested models that only differed in a bounded variable in order to easily compare a Student t and a Gaussian mixed model. It is important to highlight that the Student t density converges to a Gaussian process when degrees of freedom tend to infinity. The twomodels can then be viewed as nested models that differ in terms of degrees of freedom. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling of the complex model (Student t mixed model. The performance of this Bayes factor was tested under simulation and on a real dataset, using the deviation information criterion (DIC as the standard reference criterion. The two statistical tools showed similar trends along the parameter space, although the Bayes factor appeared to be the more conservative. There was considerable evidence favoring the Student t mixed model for data sets simulated under Student t processes with limited degrees of freedom, and moderate advantages associated with using the Gaussian mixed model when working with datasets simulated with 50 or more degrees of freedom. For the analysis of real data (weight of Pietrain pigs at six months, both the Bayes factor and DIC slightly favored the Student t mixed model, with there being a reduced incidence of outlier individuals in this population.

On the thermodynamic properties of the generalized Gaussian core model

Directory of Open Access Journals (Sweden)

B.M.Mladek

2005-01-01

Full Text Available We present results of a systematic investigation of the properties of the generalized Gaussian core model of index n. The potential of this system interpolates via the index n between the potential of the Gaussian core model and the penetrable sphere system, thereby varying the steepness of the repulsion. We have used both conventional and self-consistent liquid state theories to calculate the structural and thermodynamic properties of the system; reference data are provided by computer simulations. The results indicate that the concept of self-consistency becomes indispensable to guarantee excellent agreement with simulation data; in particular, structural consistency (in our approach taken into account via the zero separation theorem is obviously a very important requirement. Simulation results for the dimensionless equation of state, β P / ρ, indicate that for an index-value of 4, a clustering transition, possibly into a structurally ordered phase might set in as the system is compressed.

Non-Gaussianity from inflation: theory and observations

Science.gov (United States)

Bartolo, N.; Komatsu, E.; Matarrese, S.; Riotto, A.

2004-11-01

This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.

Wavelength-independent laser beam shaping

CSIR Research Space (South Africa)

Degama, MP

2010-07-01

Full Text Available This paper presents a beam shaping device namely, a Diffractive Optical Element (DOE), which is used to change a beam having a Gaussian intensity profile into a beam with a uniform intensity profile. The DOE used in this work was fabricated from Zn...

Gaussian Process Regression Model in Spatial Logistic Regression

Science.gov (United States)

Sofro, A.; Oktaviarina, A.

2018-01-01

Spatial analysis has developed very quickly in the last decade. One of the favorite approaches is based on the neighbourhood of the region. Unfortunately, there are some limitations such as difficulty in prediction. Therefore, we offer Gaussian process regression (GPR) to accommodate the issue. In this paper, we will focus on spatial modeling with GPR for binomial data with logit link function. The performance of the model will be investigated. We will discuss the inference of how to estimate the parameters and hyper-parameters and to predict as well. Furthermore, simulation studies will be explained in the last section.

Soft Sensor Modeling Based on Multiple Gaussian Process Regression and Fuzzy C-mean Clustering

Directory of Open Access Journals (Sweden)

Xianglin ZHU

2014-06-01

Full Text Available In order to overcome the difficulties of online measurement of some crucial biochemical variables in fermentation processes, a new soft sensor modeling method is presented based on the Gaussian process regression and fuzzy C-mean clustering. With the consideration that the typical fermentation process can be distributed into 4 phases including lag phase, exponential growth phase, stable phase and dead phase, the training samples are classified into 4 subcategories by using fuzzy C- mean clustering algorithm. For each sub-category, the samples are trained using the Gaussian process regression and the corresponding soft-sensing sub-model is established respectively. For a new sample, the membership between this sample and sub-models are computed based on the Euclidean distance, and then the prediction output of soft sensor is obtained using the weighting sum. Taking the Lysine fermentation as example, the simulation and experiment are carried out and the corresponding results show that the presented method achieves better fitting and generalization ability than radial basis function neutral network and single Gaussian process regression model.

Maximum Correntropy Criterion Kalman Filter for α-Jerk Tracking Model with Non-Gaussian Noise

Directory of Open Access Journals (Sweden)

Bowen Hou

2017-11-01

Full Text Available As one of the most critical issues for target track, α -jerk model is an effective maneuver target track model. Non-Gaussian noises always exist in the track process, which usually lead to inconsistency and divergence of the track filter. A novel Kalman filter is derived and applied on α -jerk tracking model to handle non-Gaussian noise. The weighted least square solution is presented and the standard Kalman filter is deduced firstly. A novel Kalman filter with the weighted least square based on the maximum correntropy criterion is deduced. The robustness of the maximum correntropy criterion is also analyzed with the influence function and compared with the Huber-based filter, and, moreover, the kernel size of Gaussian kernel plays an important role in the filter algorithm. A new adaptive kernel method is proposed in this paper to adjust the parameter in real time. Finally, simulation results indicate the validity and the efficiency of the proposed filter. The comparison study shows that the proposed filter can significantly reduce the noise influence for α -jerk model.

Statistical imitation system using relational interest points and Gaussian mixture models

CSIR Research Space (South Africa)

Claassens, J

2009-11-01

Full Text Available The author proposes an imitation system that uses relational interest points (RIPs) and Gaussian mixture models (GMMs) to characterize a behaviour. The system's structure is inspired by the Robot Programming by Demonstration (RDP) paradigm...

Revealing the radial modes in vortex beams

CSIR Research Space (South Africa)

Sephton, Bereneice C

2016-10-01

Full Text Available Light beams that carry orbital angular momentum are often approximated by modulating an initial beam, usually Gaussian, with an azimuthal phase variation to create a vortex beam. Such vortex beams are well defined azimuthally, but the radial profile...

Markov chain modeling of evolution of strains in reinforced concrete flexural beams

Directory of Open Access Journals (Sweden)

Anoop, M. B.

2012-09-01

Full Text Available From the analysis of experimentally observed variations in surface strains with loading in reinforced concrete beams, it is noted that there is a need to consider the evolution of strains (with loading as a stochastic process. Use of Markov Chains for modeling stochastic evolution of strains with loading in reinforced concrete flexural beams is studied in this paper. A simple, yet practically useful, bi-level homogeneous Gaussian Markov Chain (BLHGMC model is proposed for determining the state of strain in reinforced concrete beams. The BLHGMC model will be useful for predicting behavior/response of reinforced concrete beams leading to more rational design.A través del análisis de la evolución de la deformación superficial observada experimentalmente en vigas de hormigón armado al entrar en carga, se constata que dicho proceso debe considerarse estocástico. En este trabajo se estudia la utilización de cadenas de Markov para modelizar la evolución estocástica de la deformación de vigas flexotraccionadas. Se propone, para establecer el estado de deformación de estas, un modelo con distribución gaussiana tipo cadena de Markov homogénea de dos niveles (BLHGMC por sus siglas en inglés, cuyo empleo resulta sencillo y práctico. Se comprueba la utilidad del modelo BLHGMC para prever el comportamiento de estos elementos, lo que determina a su vez una mayor racionalidad a la hora de su cálculo y diseño

Inverse Gaussian model for small area estimation via Gibbs sampling

African Journals Online (AJOL)

We present a Bayesian method for estimating small area parameters under an inverse Gaussian model. The method is extended to estimate small area parameters for finite populations. The Gibbs sampler is proposed as a mechanism for implementing the Bayesian paradigm. We illustrate the method by application to ...

A model of non-Gaussian diffusion in heterogeneous media

Science.gov (United States)

Lanoiselée, Yann; Grebenkov, Denis S.

2018-04-01

Recent progress in single-particle tracking has shown evidence of the non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. Similar behavior has also been observed in granular materials, turbulent flows, gels and colloidal suspensions, suggesting that this is a general feature of diffusion in complex media. A possible interpretation of this phenomenon is that a tracer explores a medium with spatio-temporal fluctuations which result in local changes of diffusivity. We propose and investigate an ergodic, easily interpretable model, which implements the concept of diffusing diffusivity. Depending on the parameters, the distribution of displacements can be either flat or peaked at small displacements with an exponential tail at large displacements. We show that the distribution converges slowly to a Gaussian one. We calculate statistical properties, derive the asymptotic behavior and discuss some implications and extensions.

The Gaussian copula model for the joint deficit index for droughts

Science.gov (United States)

Van de Vyver, H.; Van den Bergh, J.

2018-06-01

The characterization of droughts and their impacts is very dependent on the time scale that is involved. In order to obtain an overall drought assessment, the cumulative effects of water deficits over different times need to be examined together. For example, the recently developed joint deficit index (JDI) is based on multivariate probabilities of precipitation over various time scales from 1- to 12-months, and was constructed from empirical copulas. In this paper, we examine the Gaussian copula model for the JDI. We model the covariance across the temporal scales with a two-parameter function that is commonly used in the specific context of spatial statistics or geostatistics. The validity of the covariance models is demonstrated with long-term precipitation series. Bootstrap experiments indicate that the Gaussian copula model has advantages over the empirical copula method in the context of drought severity assessment: (i) it is able to quantify droughts outside the range of the empirical copula, (ii) provides adequate drought quantification, and (iii) provides a better understanding of the uncertainty in the estimation.

Entanglement concentration for two-mode Gaussian states in non-inertial frames

International Nuclear Information System (INIS)

Di Noia, Maurizio; Giraldi, Filippo; Petruccione, Francesco

2017-01-01

Entanglement creation and concentration by means of a beam splitter (BS) is analysed for a generic two-mode bipartite Gaussian state in a relativistic framework. The total correlations, the purity and the entanglement in terms of logarithmic negativity are analytically studied for observers in an inertial state and in a non-inertial state of uniform acceleration. The dependence of entanglement on the BS transmissivity due to the Unruh effect is analysed in the case when one or both observers undergo uniform acceleration. Due to the Unruh effect, depending on the initial Gaussian state parameters and observed accelerations, the best condition for entanglement generation limited to the two modes of the observers in their regions is not always a balanced beam splitter, as it is for the inertial case. (paper)

Transverse wakefield effects in the two-beam accelerator

International Nuclear Information System (INIS)

Selph, F.; Sessler, A.

1986-01-01

Transverse wakefield effects in the high-gradient accelerating structure of the two-beam accelerator (TBA) are analyzed theoretically using three different models. The first is a very simple two-particle model, the second is for a beam with uniform charge distribution, constant betatron wavelength, and a linear wake approximation. Both of these models give analytic scaling laws. The third model has a Gaussian beam (represented by 11 superparticles), energy variation across the bunch, acceleration, variation of betatron focusing with energy, and variation of the wakefield from linearity. The three models are compared, and the third model is used to explore the wakefield effects when accelerator parameters such as energy, energy spread, injection energy, accelerating gradient, and betatron wavelength are varied. Also explored are the sensitivity of the beam to the wakefield profile to the longitudinal charge distribution. Finally, in consideration of wakefield effects, possible parameters of a TBA are presented. (orig./HSI)

Variational Gaussian approximation for Poisson data

Science.gov (United States)

Arridge, Simon R.; Ito, Kazufumi; Jin, Bangti; Zhang, Chen

2018-02-01

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence from the posterior distribution to the approximation, or equivalently maximizing the lower bound for the model evidence. We derive an explicit expression for the lower bound, and show the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization that penalizes also the covariance. Then we develop an efficient alternating direction maximization algorithm for solving the optimization problem, and analyze its convergence. We discuss strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an application of the lower bound, we discuss hierarchical Bayesian modeling for selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

Influence of beam divergence on form-factor in X-ray diffraction radiation

International Nuclear Information System (INIS)

Sergeeva, D.Yu.; Tishchenko, A.A.; Strikhanov, M.N.

2015-01-01

Diffraction radiation from divergent beam is considered in terms of radiation in UV and X-ray range. Scedastic form of Gaussian distribution of the particle in the bunch, i.e. Gaussian distribution with changing dispersion has been used, which is more adequate for description of divergent beams than often used Gaussian distribution with constant dispersion. Both coherent and incoherent form-factors are taken into account. The conical diffraction effect in diffraction radiation is proved to make essential contribution in spectral-angular characteristics of radiation from a divergent beam

Infrared maritime target detection using a probabilistic single Gaussian model of sea clutter in Fourier domain

Science.gov (United States)

Zhou, Anran; Xie, Weixin; Pei, Jihong; Chen, Yapei

2018-02-01

For ship targets detection in cluttered infrared image sequences, a robust detection method, based on the probabilistic single Gaussian model of sea background in Fourier domain, is put forward. The amplitude spectrum sequences at each frequency point of the pure seawater images in Fourier domain, being more stable than the gray value sequences of each background pixel in the spatial domain, are regarded as a Gaussian model. Next, a probability weighted matrix is built based on the stability of the pure seawater's total energy spectrum in the row direction, to make the Gaussian model more accurate. Then, the foreground frequency points are separated from the background frequency points by the model. Finally, the false-alarm points are removed utilizing ships' shape features. The performance of the proposed method is tested by visual and quantitative comparisons with others.

Generation of vector beams using a double-wedge depolarizer: Non-quantum entanglement

Science.gov (United States)

Samlan, C. T.; Viswanathan, Nirmal K.

2016-07-01

Propagation of horizontally polarized Gaussian beam through a double-wedge depolarizer generates vector beams with spatially varying state of polarization. Jones calculus is used to show that such beams are maximally nonseparable on the basis of even (Gaussian)-odd (Hermite-Gaussian) mode parity and horizontal-vertical polarization state. The maximum nonseparability in the two degrees of freedom of the vector beam at the double wedge depolarizer output is verified experimentally using a modified Sagnac interferometer and linear analyser projected interferograms to measure the concurrence 0.94±0.002 and violation of Clauser-Horne-Shimony-Holt form of Bell-like inequality 2.704±0.024. The investigation is carried out in the context of the use of vector beams for metrological applications.

Annular beam shaping and optical trepanning

Science.gov (United States)

Zeng, Danyong

Percussion drilling and trepanning are two laser drilling methods. Percussion drilling is accomplished by focusing the laser beam to approximately the required diameter of the hole, exposing the material to one or a series of laser pulses at the same spot to melt and vaporize the material. Drilling by trepanning involves cutting a hole by rotating a laser beam with an optical element or an x-y galvo-scanner. Optical trepanning is a new laser drilling method using an annular beam. The annular beams allow numerous irradiance profiles to supply laser energy to the workpiece and thus provide more flexibility in affecting the hole quality than a traditional circular laser beam. Heating depth is important for drilling application. Since there are no good ways to measure the temperature inside substrate during the drilling process, an analytical model for optical trepanning has been developed by considering an axisymmetric, transient heat conduction equation, and the evolutions of the melting temperature isotherm, which is referred to as the melt boundary in this study, are calculated to investigate the influences of the laser pulse shapes and intensity profiles on the hole geometry. This mathematical model provides a means of understanding the thermal effect of laser irradiation with different annular beam shapes. To take account of conduction in the solid, vaporization and convection due to the melt flow caused by an assist gas, an analytical two-dimensional model is developed for optical trepanning. The influences of pulse duration, laser pulse length, pulse repetition rate, intensity profiles and beam radius are investigated to examine their effects on the recast layer thickness, hole depth and taper. The ray tracing technique of geometrical optics is employed to design the necessary optics to transform a Gaussian laser beam into an annular beam of different intensity profiles. Such profiles include half Gaussian with maximum intensities at the inner and outer

Interactive Gaussian Graphical Models for Discovering Depth Trends in ChemCam Data

Science.gov (United States)

Oyen, D. A.; Komurlu, C.; Lanza, N. L.

2018-04-01

Interactive Gaussian graphical models discover surface compositional features on rocks in ChemCam targets. Our approach visualizes shot-to-shot relationships among LIBS observations, and identifies the wavelengths involved in the trend.

Stochastic cluster algorithms for discrete Gaussian (SOS) models

International Nuclear Information System (INIS)

Evertz, H.G.; Hamburg Univ.; Hasenbusch, M.; Marcu, M.; Tel Aviv Univ.; Pinn, K.; Muenster Univ.; Solomon, S.

1990-10-01

We present new Monte Carlo cluster algorithms which eliminate critical slowing down in the simulation of solid-on-solid models. In this letter we focus on the two-dimensional discrete Gaussian model. The algorithms are based on reflecting the integer valued spin variables with respect to appropriately chosen reflection planes. The proper choice of the reflection plane turns out to be crucial in order to obtain a small dynamical exponent z. Actually, the successful versions of our algorithm are a mixture of two different procedures for choosing the reflection plane, one of them ergodic but slow, the other one non-ergodic and also slow when combined with a Metropolis algorithm. (orig.)

Ground states and formal duality relations in the Gaussian core model

NARCIS (Netherlands)

Cohn, H.; Kumar, A.; Schürmann, A.

2009-01-01

We study dimensional trends in ground states for soft-matter systems. Specifically, using a high-dimensional version of Parrinello-Rahman dynamics, we investigate the behavior of the Gaussian core model in up to eight dimensions. The results include unexpected geometric structures, with surprising

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State Space Models

NARCIS (Netherlands)

Koopman, S.J.; Lucas, A.; Scharth, M.

2015-01-01

We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer

Gaussian Process-Mixture Conditional Heteroscedasticity.

Science.gov (United States)

Platanios, Emmanouil A; Chatzis, Sotirios P

2014-05-01

Generalized autoregressive conditional heteroscedasticity (GARCH) models have long been considered as one of the most successful families of approaches for volatility modeling in financial return series. In this paper, we propose an alternative approach based on methodologies widely used in the field of statistical machine learning. Specifically, we propose a novel nonparametric Bayesian mixture of Gaussian process regression models, each component of which models the noise variance process that contaminates the observed data as a separate latent Gaussian process driven by the observed data. This way, we essentially obtain a Gaussian process-mixture conditional heteroscedasticity (GPMCH) model for volatility modeling in financial return series. We impose a nonparametric prior with power-law nature over the distribution of the model mixture components, namely the Pitman-Yor process prior, to allow for better capturing modeled data distributions with heavy tails and skewness. Finally, we provide a copula-based approach for obtaining a predictive posterior for the covariances over the asset returns modeled by means of a postulated GPMCH model. We evaluate the efficacy of our approach in a number of benchmark scenarios, and compare its performance to state-of-the-art methodologies.

Gaussian random bridges and a geometric model for information equilibrium

Science.gov (United States)

Mengütürk, Levent Ali

2018-03-01

The paper introduces a class of conditioned stochastic processes that we call Gaussian random bridges (GRBs) and proves some of their properties. Due to the anticipative representation of any GRB as the sum of a random variable and a Gaussian (T , 0) -bridge, GRBs can model noisy information processes in partially observed systems. In this spirit, we propose an asset pricing model with respect to what we call information equilibrium in a market with multiple sources of information. The idea is to work on a topological manifold endowed with a metric that enables us to systematically determine an equilibrium point of a stochastic system that can be represented by multiple points on that manifold at each fixed time. In doing so, we formulate GRB-based information diversity over a Riemannian manifold and show that it is pinned to zero over the boundary determined by Dirac measures. We then define an influence factor that controls the dominance of an information source in determining the best estimate of a signal in the L2-sense. When there are two sources, this allows us to construct information equilibrium as a functional of a geodesic-valued stochastic process, which is driven by an equilibrium convergence rate representing the signal-to-noise ratio. This leads us to derive price dynamics under what can be considered as an equilibrium probability measure. We also provide a semimartingale representation of Markovian GRBs associated with Gaussian martingales and a non-anticipative representation of fractional Brownian random bridges that can incorporate degrees of information coupling in a given system via the Hurst exponent.

Gaussian limit of compact spin systems

International Nuclear Information System (INIS)

Bellissard, J.; Angelis, G.F. de

1981-01-01

It is shown that the Wilson and Wilson-Villain U(1) models reproduce, in the low coupling limit, the gaussian lattice approximation of the Euclidean electromagnetic field. By the same methods it is also possible to prove that the plane rotator and the Villain model share a common gaussian behaviour in the low temperature limit. (Auth.)

Treatment of non-Gaussian tails of multiple Coulomb scattering in track fitting with a Gaussian-sum filter

International Nuclear Information System (INIS)

Strandlie, A.; Wroldsen, J.

2006-01-01

If any of the probability densities involved in track fitting deviate from the Gaussian assumption, it is plausible that a non-linear estimator which better takes the actual shape of the distribution into account can do better. One such non-linear estimator is the Gaussian-sum filter, which is adequate if the distributions under consideration can be approximated by Gaussian mixtures. The main purpose of this paper is to present a Gaussian-sum filter for track fitting, based on a two-component approximation of the distribution of angular deflections due to multiple scattering. In a simulation study within a linear track model the Gaussian-sum filter is shown to be a competitive alternative to the Kalman filter. Scenarios at various momenta and with various maximum number of components in the Gaussian-sum filter are considered. Particularly at low momenta the Gaussian-sum filter yields a better estimate of the uncertainties than the Kalman filter, and it is also slightly more precise than the latter

An efficient and accurate method for calculating nonlinear diffraction beam fields

Energy Technology Data Exchange (ETDEWEB)

Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)

2016-04-15

This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.

Non-gaussianity versus nonlinearity of cosmological perturbations.

Science.gov (United States)

Verde, L

2001-06-01

Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

Consistency checks in beam emission modeling for neutral beam injectors

International Nuclear Information System (INIS)

Punyapu, Bharathi; Vattipalle, Prahlad; Sharma, Sanjeev Kumar; Baruah, Ujjwal Kumar; Crowley, Brendan

2015-01-01

In positive neutral beam systems, the beam parameters such as ion species fractions, power fractions and beam divergence are routinely measured using Doppler shifted beam emission spectrum. The accuracy with which these parameters are estimated depend on the accuracy of the atomic modeling involved in these estimations. In this work, an effective procedure to check the consistency of the beam emission modeling in neutral beam injectors is proposed. As a first consistency check, at a constant beam voltage and current, the intensity of the beam emission spectrum is measured by varying the pressure in the neutralizer. Then, the scaling of measured intensity of un-shifted (target) and Doppler shifted intensities (projectile) of the beam emission spectrum at these pressure values are studied. If the un-shifted component scales with pressure, then the intensity of this component will be used as a second consistency check on the beam emission modeling. As a further check, the modeled beam fractions and emission cross sections of projectile and target are used to predict the intensity of the un-shifted component and then compared with the value of measured target intensity. An agreement between the predicted and measured target intensities provide the degree of discrepancy in the beam emission modeling. In order to test this methodology, a systematic analysis of Doppler shift spectroscopy data obtained on the JET neutral beam test stand data was carried out

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)

Gaussian process regression analysis for functional data

CERN Document Server

Shi, Jian Qing

2011-01-01

Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables.Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dime

Computer simulation of electron beams. II. Low-cost beam-current reconstruction

International Nuclear Information System (INIS)

de Wolf, D.A.

1985-01-01

Reconstruction of current density in electron beams is complicated by distortion of phase space which can require very fine discretization of the beam into trajectories. An efficient discretization of phase space is exploited, using conservation of charge and current in hypertriangle patches, to reconstruct the current density by fitting Gaussians through the distorted hypertriangles. Advantages and limitations are discussed

Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

KAUST Repository

Yan, Yuan; Genton, Marc G.

2017-01-01

Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.

Gaussian likelihood inference on data from trans-Gaussian random fields with Matérn covariance function

KAUST Repository

Yan, Yuan

2017-07-13

Gaussian likelihood inference has been studied and used extensively in both statistical theory and applications due to its simplicity. However, in practice, the assumption of Gaussianity is rarely met in the analysis of spatial data. In this paper, we study the effect of non-Gaussianity on Gaussian likelihood inference for the parameters of the Matérn covariance model. By using Monte Carlo simulations, we generate spatial data from a Tukey g-and-h random field, a flexible trans-Gaussian random field, with the Matérn covariance function, where g controls skewness and h controls tail heaviness. We use maximum likelihood based on the multivariate Gaussian distribution to estimate the parameters of the Matérn covariance function. We illustrate the effects of non-Gaussianity of the data on the estimated covariance function by means of functional boxplots. Thanks to our tailored simulation design, a comparison of the maximum likelihood estimator under both the increasing and fixed domain asymptotics for spatial data is performed. We find that the maximum likelihood estimator based on Gaussian likelihood is overall satisfying and preferable than the non-distribution-based weighted least squares estimator for data from the Tukey g-and-h random field. We also present the result for Gaussian kriging based on Matérn covariance estimates with data from the Tukey g-and-h random field and observe an overall satisfactory performance.

Self-reconstruction of diffraction-free and accelerating laser beams in scattering media

International Nuclear Information System (INIS)

Ersoy, T.; Yalizay, B.; Akturk, S.

2012-01-01

We experimentally investigate propagation of laser beams with different intensity profiles in highly scattering media. We generate transverse laser amplitude profiles with Gaussian, Bessel and Airy function envelopes. We then propagate these beams through optical phantoms formed with variable density intralipid solutions. At the sample exit, we compare change in maximum intensities, as well as beam profile reconstruction. We show that self-reconstruction properties of Bessel and Airy beams bring about slower decrease in maximum intensity with increasing scatterer density. On the other hand, the beam profiles deteriorate faster, as compared to reference Gaussian beams. Slower decrease in the intensity can be attributed to the wavevector spectra providing a continuous flow of energy to the beam center, while beam deterioration is linked to total beam volume in the scattering medium. These results show that beam shaping methods can significantly enhance delivery of intense light deeper into turbid media, but this enhancement is compromised by stronger speckling of beam profiles. -- Highlights: ► We experimentally investigate propagation of shaped laser beams in turbid media. ► Peak intensity of Bessel and Airy beams decrease slower with increasing scatterer. ► Shaped beam profiles deteriorate faster, as compared to reference Gaussian beams. ► Shaped beam profiles can enhance applications of lasers inscattering media.

Investigation of non-Gaussian effects in the Brazilian option market

Science.gov (United States)

Sosa-Correa, William O.; Ramos, Antônio M. T.; Vasconcelos, Giovani L.

2018-04-01

An empirical study of the Brazilian option market is presented in light of three option pricing models, namely the Black-Scholes model, the exponential model, and a model based on a power law distribution, the so-called q-Gaussian distribution or Tsallis distribution. It is found that the q-Gaussian model performs better than the Black-Scholes model in about one third of the option chains analyzed. But among these cases, the exponential model performs better than the q-Gaussian model in 75% of the time. The superiority of the exponential model over the q-Gaussian model is particularly impressive for options close to the expiration date, where its success rate rises above ninety percent.

Imprint of primordial non-Gaussianity on dark matter halo profiles

Energy Technology Data Exchange (ETDEWEB)

Dizgah, Azadeh Moradinezhad; Dodelson, Scott; Riotto, Antonio

2013-09-01

We study the impact of primordial non-Gaussianity on the density profile of dark matter halos by using the semi-analytical model introduced recently by Dalal {\\it et al.} which relates the peaks of the initial linear density field to the final density profile of dark matter halos. Models with primordial non-Gaussianity typically produce an initial density field that differs from that produced in Gaussian models. We use the path-integral formulation of excursion set theory to calculate the non-Gaussian corrections to the peak profile and derive the statistics of the peaks of non-Gaussian density field. In the context of the semi-analytic model for halo profiles, currently allowed values for primordial non-Gaussianity would increase the shapes of the inner dark matter profiles, but only at the sub-percent level except in the very innermost regions.

On the use of magnetic buckets for ion beam profile tailoring

International Nuclear Information System (INIS)

MacGill, R. A.; Vizir, A.; Brown, I. G.

2000-01-01

Magnetic multipole plasma confinement geometries employing permanent magnet ''buckets'' are used extensively for a range of laboratory plasma applications. Among the several consequences for plasma confinement is the important result that the plasma can acquire a more-or-less flat density profile, which when embodied in an ion source, can also lead to a flat profile for the extracted ion beam. For many applications a uniform ion beam current density profile is quite advantageous, for example, for carrying out large-area ion implantation. There are, however, inherent limitations on the extent to which this approach to beam ''homogenization'' can be utilized, and even for a perfectly flat profile in the immediate postextraction region, the beam will evolve toward Gaussian as it propagates downstream. Here we describe the rare-earth permanent magnet bucket that we have incorporated into our broad-beam vacuum arc ion source, and its effect on the beam profile at the extractor and downstream. The experimental results are compared with a simple model for the beam profile evolution with axial distance. We find that the beam loses memory of its initially flat profile and relaxes to a more-or-less Gaussian shape in a relatively short axial distance ∼w/4θ, where w is the initial width of the flat beam profile and θ is the beamlet divergence half angle. (c) 2000 American Institute of Physics

Clustering gene expression time series data using an infinite Gaussian process mixture model.

Science.gov (United States)

McDowell, Ian C; Manandhar, Dinesh; Vockley, Christopher M; Schmid, Amy K; Reddy, Timothy E; Engelhardt, Barbara E

2018-01-01

Transcriptome-wide time series expression profiling is used to characterize the cellular response to environmental perturbations. The first step to analyzing transcriptional response data is often to cluster genes with similar responses. Here, we present a nonparametric model-based method, Dirichlet process Gaussian process mixture model (DPGP), which jointly models data clusters with a Dirichlet process and temporal dependencies with Gaussian processes. We demonstrate the accuracy of DPGP in comparison to state-of-the-art approaches using hundreds of simulated data sets. To further test our method, we apply DPGP to published microarray data from a microbial model organism exposed to stress and to novel RNA-seq data from a human cell line exposed to the glucocorticoid dexamethasone. We validate our clusters by examining local transcription factor binding and histone modifications. Our results demonstrate that jointly modeling cluster number and temporal dependencies can reveal shared regulatory mechanisms. DPGP software is freely available online at https://github.com/PrincetonUniversity/DP_GP_cluster.

Clustering gene expression time series data using an infinite Gaussian process mixture model.

Directory of Open Access Journals (Sweden)

Ian C McDowell

2018-01-01

Full Text Available Transcriptome-wide time series expression profiling is used to characterize the cellular response to environmental perturbations. The first step to analyzing transcriptional response data is often to cluster genes with similar responses. Here, we present a nonparametric model-based method, Dirichlet process Gaussian process mixture model (DPGP, which jointly models data clusters with a Dirichlet process and temporal dependencies with Gaussian processes. We demonstrate the accuracy of DPGP in comparison to state-of-the-art approaches using hundreds of simulated data sets. To further test our method, we apply DPGP to published microarray data from a microbial model organism exposed to stress and to novel RNA-seq data from a human cell line exposed to the glucocorticoid dexamethasone. We validate our clusters by examining local transcription factor binding and histone modifications. Our results demonstrate that jointly modeling cluster number and temporal dependencies can reveal shared regulatory mechanisms. DPGP software is freely available online at https://github.com/PrincetonUniversity/DP_GP_cluster.

Interconversion of pure Gaussian states requiring non-Gaussian operations

Science.gov (United States)

Jabbour, Michael G.; García-Patrón, Raúl; Cerf, Nicolas J.

2015-01-01

We analyze the conditions under which local operations and classical communication enable entanglement transformations between bipartite pure Gaussian states. A set of necessary and sufficient conditions had been found [G. Giedke et al., Quant. Inf. Comput. 3, 211 (2003)] for the interconversion between such states that is restricted to Gaussian local operations and classical communication. Here, we exploit majorization theory in order to derive more general (sufficient) conditions for the interconversion between bipartite pure Gaussian states that goes beyond Gaussian local operations. While our technique is applicable to an arbitrary number of modes for each party, it allows us to exhibit surprisingly simple examples of 2 ×2 Gaussian states that necessarily require non-Gaussian local operations to be transformed into each other.

Model-independent test for scale-dependent non-Gaussianities in the cosmic microwave background.

Science.gov (United States)

Räth, C; Morfill, G E; Rossmanith, G; Banday, A J; Górski, K M

2009-04-03

We present a model-independent method to test for scale-dependent non-Gaussianities in combination with scaling indices as test statistics. Therefore, surrogate data sets are generated, in which the power spectrum of the original data is preserved, while the higher order correlations are partly randomized by applying a scale-dependent shuffling procedure to the Fourier phases. We apply this method to the Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background and find signatures for non-Gaussianities on large scales. Further tests are required to elucidate the origin of the detected anomalies.

Performance modeling and analysis of parallel Gaussian elimination on multi-core computers

Directory of Open Access Journals (Sweden)

Fadi N. Sibai

2014-01-01

Full Text Available Gaussian elimination is used in many applications and in particular in the solution of systems of linear equations. This paper presents mathematical performance models and analysis of four parallel Gaussian Elimination methods (precisely the Original method and the new Meet in the Middle –MiM– algorithms and their variants with SIMD vectorization on multi-core systems. Analytical performance models of the four methods are formulated and presented followed by evaluations of these models with modern multi-core systems’ operation latencies. Our results reveal that the four methods generally exhibit good performance scaling with increasing matrix size and number of cores. SIMD vectorization only makes a large difference in performance for low number of cores. For a large matrix size (n ⩾ 16 K, the performance difference between the MiM and Original methods falls from 16× with four cores to 4× with 16 K cores. The efficiencies of all four methods are low with 1 K cores or more stressing a major problem of multi-core systems where the network-on-chip and memory latencies are too high in relation to basic arithmetic operations. Thus Gaussian Elimination can greatly benefit from the resources of multi-core systems, but higher performance gains can be achieved if multi-core systems can be designed with lower memory operation, synchronization, and interconnect communication latencies, requirements of utmost importance and challenge in the exascale computing age.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

Science.gov (United States)

Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi

2006-07-10

On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

Making tensor factorizations robust to non-gaussian noise.

Energy Technology Data Exchange (ETDEWEB)

Chi, Eric C. (Rice University, Houston, TX); Kolda, Tamara Gibson

2011-03-01

Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of independent and identically distributed (i.i.d.) Gaussian noise. We demonstrate that this loss function can be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization (MM) algorithm for fitting a CP model using our proposed loss function (CPAL1) and compare its performance to the workhorse algorithm for fitting CP models, CP alternating least squares (CPALS).

On a Generalized Squared Gaussian Diffusion Model for Option Valuation

Directory of Open Access Journals (Sweden)

Edeki S.O.

2017-01-01

Full Text Available In financial mathematics, option pricing models are vital tools whose usefulness cannot be overemphasized. Modern approaches and modelling of financial derivatives are therefore required in option pricing and valuation settings. In this paper, we derive via the application of Ito lemma, a pricing model referred to as Generalized Squared Gaussian Diffusion Model (GSGDM for option pricing and valuation. Same approach can be considered via Stratonovich stochastic dynamics. We also show that the classical Black-Scholes, and the square root constant elasticity of variance models are special cases of the GSGDM. In addition, general solution of the GSGDM is obtained using modified variational iterative method (MVIM.

Scalable Gaussian Processes and the search for exoplanets

CERN Multimedia

CERN. Geneva

2015-01-01

Gaussian Processes are a class of non-parametric models that are often used to model stochastic behavior in time series or spatial data. A major limitation for the application of these models to large datasets is the computational cost. The cost of a single evaluation of the model likelihood scales as the third power of the number of data points. In the search for transiting exoplanets, the datasets of interest have tens of thousands to millions of measurements with uneven sampling, rendering naive application of a Gaussian Process model impractical. To attack this problem, we have developed robust approximate methods for Gaussian Process regression that can be applied at this scale. I will describe the general problem of Gaussian Process regression and offer several applicable use cases. Finally, I will present our work on scaling this model to the exciting field of exoplanet discovery and introduce a well-tested open source implementation of these new methods.

Study of the Hollow Waveguides Physical Parameters Determined the Beam Shape Conservation of the Delivered Radiation

International Nuclear Information System (INIS)

Ben-David, M.; Inberg, A.; Katzir, A.; Croitoru, N.

1999-01-01

The modification of the laser source beam quality is one of the important factors effect the delivery of laser radiation by a waveguide. In this paper the results of input radiation coupling, radius of bending, length, cross section diameter, waveguide internal wall roughness and coupling lens focal length influence on the beam shape delivered from the flexible hollow waveguides are presented. The conditions for which the beam shape is near to that of the source were found. A theoretical model for the radiation propagation gives quantitative representation of relation between attenuation, beam profile, divergence and above indicated parameters was developed. In this model was supposed that the guiding is produced by multiple incidences on a metal (silver) layer and a dielectric (silver iodine) over layer, by refraction and reflection. The propagation of the rays was calculated using the physical laws of the geometrical optics. For the scattering calculations a random distribution of roughness centers on dielectric layer surface was considered. It was also supposed that the value of the cross section internal diameter (ID=d) was much larger than the transmitted wavelength. The experimental results have shown that losses due to absorption of the propagated radiation in the guiding layers, mainly (AgI), generate satellites of the laser source delivered fundamental Gaussian beam. Increasing of the hollow waveguide internal diameter decreases the attenuation and increases the deviation of beam shape from Gaussian. Off center coupling produce decreasing of the fundamental mode height and generation of the coupled Gaussian beam satellites. The waveguide internal wall roughness produce losses of the coupled radiation and beam profile deviations from that of the laser source. A good correspondence between the theoretical and experimental results obtained

Interference of Multi-Mode Gaussian States and "non Appearance" of Quantum Correlations

Science.gov (United States)

Olivares, Stefano

2012-01-01

We theoretically investigate bilinear, mode-mixing interactions involving two modes of uncorrelated multi-mode Gaussian states. In particular, we introduce the notion of "locally the same states" (LSS) and prove that two uncorrelated LSS modes are invariant under the mode mixing, i.e. the interaction does not lead to the birth of correlations between the outgoing modes. We also study the interference of orthogonally polarized Gaussian states by means of an interferometric scheme based on a beam splitter, rotators of polarization and polarization filters.

Levy-Student distributions for halos in accelerator beams

International Nuclear Information System (INIS)

Cufaro Petroni, Nicola; De Martino, Salvatore; De Siena, Silvio; Illuminati, Fabrizio

2005-01-01

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of stochastic mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Schroedinger-like (SL) equation. The space charge effects have been introduced in recent papers by coupling this S-L equation with the Maxwell equations. We analyze the space-charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self-consistent solutions are related to the (external and space-charge) potentials both when we suppose that the external field is harmonic (constant focusing), and when we a priori prescribe the shape of the stationary solution. We then proceed to discuss a few other ideas by introducing generalized Student distributions, namely, non-Gaussian, Levy infinitely divisible (but not stable) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non-Gaussian) Levy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws and in the case (b) the discontinuities of the Levy-Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams

Spin-orbit beams for optical chirality measurement

Science.gov (United States)

Samlan, C. T.; Suna, Rashmi Ranjan; Naik, Dinesh N.; Viswanathan, Nirmal K.

2018-01-01

Accurate measurement of chirality is essential for the advancement of natural and pharmaceutical sciences. We report here a method to measure chirality using non-separable states of light with geometric phase-gradient in the circular polarization basis, which we refer to as spin-orbit beams. A modified polarization Sagnac interferometer is used to generate spin-orbit beams wherein the spin and orbital angular momentum of the input Gaussian beam are coupled. The out-of-phase interference between counter-propagating Gaussian beams with orthogonal spin states and lateral-shear or/and linear-phase difference between them results in spin-orbit beams with linear and azimuthal phase gradient. The spin-orbit beams interact efficiently with the chiral medium, inducing a measurable change in the center-of-mass of the beam, using the polarization rotation angle and hence the chirality of the medium are accurately calculated. Tunable dynamic range of measurement and flexibility to introduce large values of orbital angular momentum for the spin-orbit beam, to improve the measurement sensitivity, highlight the techniques' versatility.

Gaussian Mixture Random Coefficient model based framework for SHM in structures with time-dependent dynamics under uncertainty

Science.gov (United States)

Avendaño-Valencia, Luis David; Fassois, Spilios D.

2017-12-01

The problem of vibration-based damage diagnosis in structures characterized by time-dependent dynamics under significant environmental and/or operational uncertainty is considered. A stochastic framework consisting of a Gaussian Mixture Random Coefficient model of the uncertain time-dependent dynamics under each structural health state, proper estimation methods, and Bayesian or minimum distance type decision making, is postulated. The Random Coefficient (RC) time-dependent stochastic model with coefficients following a multivariate Gaussian Mixture Model (GMM) allows for significant flexibility in uncertainty representation. Certain of the model parameters are estimated via a simple procedure which is founded on the related Multiple Model (MM) concept, while the GMM weights are explicitly estimated for optimizing damage diagnostic performance. The postulated framework is demonstrated via damage detection in a simple simulated model of a quarter-car active suspension with time-dependent dynamics and considerable uncertainty on the payload. Comparisons with a simpler Gaussian RC model based method are also presented, with the postulated framework shown to be capable of offering considerable improvement in diagnostic performance.

Three dimensional δf simulations of beams in the SSC

International Nuclear Information System (INIS)

Koga, J.; Tajima, T.; Machida, S.

1993-01-01

A three dimensional δf strong-strong algorithm has been developed to apply to the study of such effects as space charge and beam-beam interaction phenomena in the Superconducting Super Collider (SSC). The algorithm is obtained from the merging of the particle tracking code Simpsons used for 3 dimensional space charge effects and a δf code. The δf method is used to follow the evolution of the non-gaussian part of the beam distribution. The advantages of this method are twofold. First, the Simpsons code utilizes a realistic accelerator model including synchrotron oscillations and energy ramping in 6 dimensional phase space with electromagnetic fields of the beams calculated using a realistic 3 dimensional field solver. Second, the beams are evolving in the fully self-consistent strong-strong sense with finite particle fluctuation noise is greatly reduced as opposed to the weak-strong models where one beam is fixed

Three dimensional [delta]f simulations of beams in the SSC

Energy Technology Data Exchange (ETDEWEB)

Koga, J.; Tajima, T. (Texas Univ., Austin, TX (United States). Inst. for Fusion Studies); Machida, S. (Superconducting Super Collider Lab., Dallas, TX (United States))

1993-02-01

A three dimensional [delta]f strong-strong algorithm has been developed to apply to the study of such effects as space charge and beam-beam interaction phenomena in the Superconducting Super Collider (SSC). The algorithm is obtained from the merging of the particle tracking code Simpsons used for 3-dimensional space charge effects and a [delta]f code. The [delta]f method is used to follow the evolution of the non-gaussian part of the beam distribution. The advantages of this method are twofold. First, the Simpsons code utilizes a realistic accelerator model including synchrotron oscillations and energy ramping in 6-dimensional phase space with electromagnetic fields of the beams calculated using a realistic 3-dimensional field solver. Second, the beams are evolving in the fully self-consistent strong-strong sense where finite particle fluctuation noise is greatly reduced as opposed to the weak-strong models where one beam is fixed.

Three dimensional {delta}f simulations of beams in the SSC

Energy Technology Data Exchange (ETDEWEB)

Koga, J.; Tajima, T. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies; Machida, S. [Superconducting Super Collider Lab., Dallas, TX (United States)

1993-02-01

A three dimensional {delta}f strong-strong algorithm has been developed to apply to the study of such effects as space charge and beam-beam interaction phenomena in the Superconducting Super Collider (SSC). The algorithm is obtained from the merging of the particle tracking code Simpsons used for 3-dimensional space charge effects and a {delta}f code. The {delta}f method is used to follow the evolution of the non-gaussian part of the beam distribution. The advantages of this method are twofold. First, the Simpsons code utilizes a realistic accelerator model including synchrotron oscillations and energy ramping in 6-dimensional phase space with electromagnetic fields of the beams calculated using a realistic 3-dimensional field solver. Second, the beams are evolving in the fully self-consistent strong-strong sense where finite particle fluctuation noise is greatly reduced as opposed to the weak-strong models where one beam is fixed.

Three dimensional δf simulations of beams in the SSC

International Nuclear Information System (INIS)

Koga, J.; Tajima, T.

1993-02-01

A three dimensional δf strong-strong algorithm has been developed to apply to the study of such effects as space charge and beam-beam interaction phenomena in the Superconducting Super Collider (SSC). The algorithm is obtained from the merging of the particle tracking code Simpsons used for 3-dimensional space charge effects and a δf code. The δf method is used to follow the evolution of the non-gaussian part of the beam distribution. The advantages of this method are twofold. First, the Simpsons code utilizes a realistic accelerator model including synchrotron oscillations and energy ramping in 6-dimensional phase space with electromagnetic fields of the beams calculated using a realistic 3-dimensional field solver. Second, the beams are evolving in the fully self-consistent strong-strong sense where finite particle fluctuation noise is greatly reduced as opposed to the weak-strong models where one beam is fixed

Propagation of partially coherent fields through planar dielectric boundaries using angle-impact Wigner functions I. Two dimensions.

Science.gov (United States)

Petruccelli, Jonathan C; Alonso, Miguel A

2007-09-01

We examine the angle-impact Wigner function (AIW) as a computational tool for the propagation of nonparaxial quasi-monochromatic light of any degree of coherence past a planar boundary between two homogeneous media. The AIWs of the reflected and transmitted fields in two dimensions are shown to be given by a simple ray-optical transformation of the incident AIW plus a series of corrections in the form of differential operators. The radiometric and leading six correction terms are studied for Gaussian Schell-model fields of varying transverse width, transverse coherence, and angle of incidence.

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)

Integrating a street-canyon model with a regional Gaussian dispersion model for improved characterisation of near-road air pollution

Science.gov (United States)

Fallah-Shorshani, Masoud; Shekarrizfard, Maryam; Hatzopoulou, Marianne

2017-03-01

The development and use of dispersion models that simulate traffic-related air pollution in urban areas has risen significantly in support of air pollution exposure research. In order to accurately estimate population exposure, it is important to generate concentration surfaces that take into account near-road concentrations as well as the transport of pollutants throughout an urban region. In this paper, an integrated modelling chain was developed to simulate ambient Nitrogen Dioxide (NO2) in a dense urban neighbourhood while taking into account traffic emissions, the regional background, and the transport of pollutants within the urban canopy. For this purpose, we developed a hybrid configuration including 1) a street canyon model, which simulates pollutant transfer along streets and intersections, taking into account the geometry of buildings and other obstacles, and 2) a Gaussian puff model, which resolves the transport of contaminants at the top of the urban canopy and accounts for regional meteorology. Each dispersion model was validated against measured concentrations and compared against the hybrid configuration. Our results demonstrate that the hybrid approach significantly improves the output of each model on its own. An underestimation appears clearly for the Gaussian model and street-canyon model compared to observed data. This is due to ignoring the building effect by the Gaussian model and undermining the contribution of other roads by the canyon model. The hybrid approach reduced the RMSE (of observed vs. predicted concentrations) by 16%-25% compared to each model on its own, and increased FAC2 (fraction of predictions within a factor of two of the observations) by 10%-34%.

A practical guide to handling laser diode beams

CERN Document Server

Sun, Haiyin

2015-01-01

This book offers the reader a practical guide to the control and characterization of laser diode beams.  Laser diodes are the most widely used lasers, accounting for 50% of the global laser market.  Correct handling of laser diode beams is the key to the successful use of laser diodes, and this requires an in-depth understanding of their unique properties. Following a short introduction to the working principles of laser diodes, the book describes the basics of laser diode beams and beam propagation, including Zemax modeling of a Gaussian beam propagating through a lens.  The core of the book is concerned with laser diode beam manipulations: collimating and focusing, circularization and astigmatism correction, coupling into a single mode optical fiber, diffractive optics and beam shaping, and manipulation of multi transverse mode beams.  The final chapter of the book covers beam characterization methods, describing the measurement of spatial and spectral properties, including wavelength and linewidth meas...

Modelling and control of dynamic systems using gaussian process models

CERN Document Server

Kocijan, Juš

2016-01-01

This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior know...

Non-Gaussian halo assembly bias

International Nuclear Information System (INIS)

Reid, Beth A.; Verde, Licia; Dolag, Klaus; Matarrese, Sabino; Moscardini, Lauro

2010-01-01

The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f NL , offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ∼ 23% and ∼ 48% for galaxies at z = 1 selected by stellar mass and star formation rate, respectively

Gaussian free turbulence: structures and relaxation in plasma models

International Nuclear Information System (INIS)

Gruzinov, A.V.

1993-01-01

Free-turbulent relaxation in two-dimensional MHD, the degenerate Hasegawa-Mima equation and a two-dimensional microtearing model are studied. The Gibbs distributions of these three systems can be completely analyzed, due to the special structure of their invariants and due to the existence of ultraviolet catastrophe. The free-turbulent field is seen to be a sum of a certain coherent structure (statistical attractor) and Gaussian random noise. Two-dimensional current layers are shown to be statistical attractors in 2D MHD. (author)

The Gaussian streaming model and convolution Lagrangian effective field theory

Energy Technology Data Exchange (ETDEWEB)

Vlah, Zvonimir [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA 94306 (United States); Castorina, Emanuele; White, Martin, E-mail: zvlah@stanford.edu, E-mail: ecastorina@berkeley.edu, E-mail: mwhite@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States)

2016-12-01

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.

Prediction of Geological Subsurfaces Based on Gaussian Random Field Models

Energy Technology Data Exchange (ETDEWEB)

Abrahamsen, Petter

1997-12-31

During the sixties, random functions became practical tools for predicting ore reserves with associated precision measures in the mining industry. This was the start of the geostatistical methods called kriging. These methods are used, for example, in petroleum exploration. This thesis reviews the possibilities for using Gaussian random functions in modelling of geological subsurfaces. It develops methods for including many sources of information and observations for precise prediction of the depth of geological subsurfaces. The simple properties of Gaussian distributions make it possible to calculate optimal predictors in the mean square sense. This is done in a discussion of kriging predictors. These predictors are then extended to deal with several subsurfaces simultaneously. It is shown how additional velocity observations can be used to improve predictions. The use of gradient data and even higher order derivatives are also considered and gradient data are used in an example. 130 refs., 44 figs., 12 tabs.

Childhood malnutrition in Egypt using geoadditive Gaussian and latent variable models.

Science.gov (United States)

Khatab, Khaled

2010-04-01

Major progress has been made over the last 30 years in reducing the prevalence of malnutrition amongst children less than 5 years of age in developing countries. However, approximately 27% of children under the age of 5 in these countries are still malnourished. This work focuses on the childhood malnutrition in one of the biggest developing countries, Egypt. This study examined the association between bio-demographic and socioeconomic determinants and the malnutrition problem in children less than 5 years of age using the 2003 Demographic and Health survey data for Egypt. In the first step, we use separate geoadditive Gaussian models with the continuous response variables stunting (height-for-age), underweight (weight-for-age), and wasting (weight-for-height) as indicators of nutritional status in our case study. In a second step, based on the results of the first step, we apply the geoadditive Gaussian latent variable model for continuous indicators in which the 3 measurements of the malnutrition status of children are assumed as indicators for the latent variable "nutritional status".

Gaussian vs non-Gaussian turbulence: impact on wind turbine loads

DEFF Research Database (Denmark)

Berg, Jacob; Natarajan, Anand; Mann, Jakob

2016-01-01

taking into account the safety factor for extreme moments. Other extreme load moments as well as the fatigue loads are not affected because of the use of non-Gaussian turbulent inflow. It is suggested that the turbine thus acts like a low-pass filter that averages out the non-Gaussian behaviour, which......From large-eddy simulations of atmospheric turbulence, a representation of Gaussian turbulence is constructed by randomizing the phases of the individual modes of variability. Time series of Gaussian turbulence are constructed and compared with its non-Gaussian counterpart. Time series from the two...

Case studies in Gaussian process modelling of computer codes

International Nuclear Information System (INIS)

Kennedy, Marc C.; Anderson, Clive W.; Conti, Stefano; O'Hagan, Anthony

2006-01-01

In this paper we present a number of recent applications in which an emulator of a computer code is created using a Gaussian process model. Tools are then applied to the emulator to perform sensitivity analysis and uncertainty analysis. Sensitivity analysis is used both as an aid to model improvement and as a guide to how much the output uncertainty might be reduced by learning about specific inputs. Uncertainty analysis allows us to reflect output uncertainty due to unknown input parameters, when the finished code is used for prediction. The computer codes themselves are currently being developed within the UK Centre for Terrestrial Carbon Dynamics

Legendre Duality of Spherical and Gaussian Spin Glasses

Energy Technology Data Exchange (ETDEWEB)

Genovese, Giuseppe, E-mail: giuseppe.genovese@math.uzh.ch [Universität Zürich, Institut für Mathematik (Switzerland); Tantari, Daniele, E-mail: daniele.tantari@sns.it [Scuola Normale Superiore di Pisa, Centro Ennio de Giorgi (Italy)

2015-12-15

The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model.

Legendre Duality of Spherical and Gaussian Spin Glasses

International Nuclear Information System (INIS)

Genovese, Giuseppe; Tantari, Daniele

2015-01-01

The classical result of concentration of the Gaussian measure on the sphere in the limit of large dimension induces a natural duality between Gaussian and spherical models of spin glass. We analyse the Legendre variational structure linking the free energies of these two systems, in the spirit of the equivalence of ensembles of statistical mechanics. Our analysis, combined with the previous work (Barra et al., J. Phys. A: Math. Theor. 47, 155002, 2014), shows that such models are replica symmetric. Lastly, we briefly discuss an application of our result to the study of the Gaussian Hopfield model

An example of enhancement of a non-classical feature of a light beam by mixing with another classical light beam using a beam splitter

International Nuclear Information System (INIS)

Prakash, Hari; Mishra, Devendra Kumar

2005-01-01

We present here an example where a non-classical feature of a light beam is enhanced simply by mixing with another classical coherent light beam using a beam splitter. This non-classical feature is amplitude-squared squeezing of a Gaussian light beam expressed by a negative value of Y e or a negative value of the normalized quantity W e which can become more negative on enhancement. Here, these values comprise the density, annihilation and creation operators, respectively

MCEM algorithm for the log-Gaussian Cox process

OpenAIRE

Delmas, Celine; Dubois-Peyrard, Nathalie; Sabbadin, Regis

2014-01-01

Log-Gaussian Cox processes are an important class of models for aggregated point patterns. They have been largely used in spatial epidemiology (Diggle et al., 2005), in agronomy (Bourgeois et al., 2012), in forestry (Moller et al.), in ecology (sightings of wild animals) or in environmental sciences (radioactivity counts). A log-Gaussian Cox process is a Poisson process with a stochastic intensity depending on a Gaussian random eld. We consider the case where this Gaussian random eld is ...

Quasi-ideal dynamics of vortex solitons embedded in flattop nonlinear Bessel beams.

Science.gov (United States)

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.

Poisson-Gaussian Noise Reduction Using the Hidden Markov Model in Contourlet Domain for Fluorescence Microscopy Images

Science.gov (United States)

Yang, Sejung; Lee, Byung-Uk

2015-01-01

In certain image acquisitions processes, like in fluorescence microscopy or astronomy, only a limited number of photons can be collected due to various physical constraints. The resulting images suffer from signal dependent noise, which can be modeled as a Poisson distribution, and a low signal-to-noise ratio. However, the majority of research on noise reduction algorithms focuses on signal independent Gaussian noise. In this paper, we model noise as a combination of Poisson and Gaussian probability distributions to construct a more accurate model and adopt the contourlet transform which provides a sparse representation of the directional components in images. We also apply hidden Markov models with a framework that neatly describes the spatial and interscale dependencies which are the properties of transformation coefficients of natural images. In this paper, an effective denoising algorithm for Poisson-Gaussian noise is proposed using the contourlet transform, hidden Markov models and noise estimation in the transform domain. We supplement the algorithm by cycle spinning and Wiener filtering for further improvements. We finally show experimental results with simulations and fluorescence microscopy images which demonstrate the improved performance of the proposed approach. PMID:26352138

High-Order Local Pooling and Encoding Gaussians Over a Dictionary of Gaussians.

Science.gov (United States)

Li, Peihua; Zeng, Hui; Wang, Qilong; Shiu, Simon C K; Zhang, Lei

2017-07-01

Local pooling (LP) in configuration (feature) space proposed by Boureau et al. explicitly restricts similar features to be aggregated, which can preserve as much discriminative information as possible. At the time it appeared, this method combined with sparse coding achieved competitive classification results with only a small dictionary. However, its performance lags far behind the state-of-the-art results as only the zero-order information is exploited. Inspired by the success of high-order statistical information in existing advanced feature coding or pooling methods, we make an attempt to address the limitation of LP. To this end, we present a novel method called high-order LP (HO-LP) to leverage the information higher than the zero-order one. Our idea is intuitively simple: we compute the first- and second-order statistics per configuration bin and model them as a Gaussian. Accordingly, we employ a collection of Gaussians as visual words to represent the universal probability distribution of features from all classes. Our problem is naturally formulated as encoding Gaussians over a dictionary of Gaussians as visual words. This problem, however, is challenging since the space of Gaussians is not a Euclidean space but forms a Riemannian manifold. We address this challenge by mapping Gaussians into the Euclidean space, which enables us to perform coding with common Euclidean operations rather than complex and often expensive Riemannian operations. Our HO-LP preserves the advantages of the original LP: pooling only similar features and using a small dictionary. Meanwhile, it achieves very promising performance on standard benchmarks, with either conventional, hand-engineered features or deep learning-based features.

Influence of wind speed on free space optical communication performance for Gaussian beam propagation through non Kolmogorov strong turbulence

International Nuclear Information System (INIS)

Deng Peng; Yuan Xiuhua; Zeng Yanan; Zhao Ming; Luo Hanjun

2011-01-01

In free-space optical communication links, atmospheric turbulence causes fluctuations in both the intensity and the phase of the received signal, affecting link performance. Most theoretical treatments have been described by Kolmogorov's power spectral density model through weak turbulence with constant wind speed. However, several experiments showed that Kolmogorov theory is sometimes incomplete to describe atmospheric turbulence properly, especially through the strong turbulence with variable wind speed, which is known to contribute significantly to the turbulence in the atmosphere. We present an optical turbulence model that incorporates into variable wind speed instead of constant value, a non-Kolmogorov power spectrum that uses a generalized exponent instead of constant standard exponent value 11/3, and a generalized amplitude factor instead of constant value 0.033. The free space optical communication performance for a Gaussian beam wave of scintillation index, mean signal-to-noise ratio , and mean bit error rate , have been derived by extended Rytov theory in non-Kolmogorov strong turbulence. And then the influence of wind speed variations on free space optical communication performance has been analyzed under different atmospheric turbulence intensities. The results suggest that the effects of wind speed variation through non-Kolmogorov turbulence on communication performance are more severe in many situations and need to be taken into account in free space optical communication. It is anticipated that this work is helpful to the investigations of free space optical communication performance considering wind speed under severe weather condition in the strong atmospheric turbulence.

Quality factor of aberrated gaussian laser beams

CSIR Research Space (South Africa)

Mafusire, C

2010-09-01

Full Text Available 15 20 25 30 35 M 4 © CSIR 2010 www.csir.co.za Conclusion • Laser beam quality depends on - y-Astigmatism - y-Coma - x-Coma - y-Triangular astigmatism - x-Triangular astigmatism - Spherical aberration...

Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives

NARCIS (Netherlands)

Durbin, J.; Koopman, S.J.M.

1998-01-01

The analysis of non-Gaussian time series using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Monte Carlo Markov chain methods are not employed. Non-Gaussian

Fast uncertainty reduction strategies relying on Gaussian process models

International Nuclear Information System (INIS)

Chevalier, Clement

2013-01-01

This work deals with sequential and batch-sequential evaluation strategies of real-valued functions under limited evaluation budget, using Gaussian process models. Optimal Stepwise Uncertainty Reduction (SUR) strategies are investigated for two different problems, motivated by real test cases in nuclear safety. First we consider the problem of identifying the excursion set above a given threshold T of a real-valued function f. Then we study the question of finding the set of 'safe controlled configurations', i.e. the set of controlled inputs where the function remains below T, whatever the value of some others non-controlled inputs. New SUR strategies are presented, together with efficient procedures and formulas to compute and use them in real world applications. The use of fast formulas to recalculate quickly the posterior mean or covariance function of a Gaussian process (referred to as the 'kriging update formulas') does not only provide substantial computational savings. It is also one of the key tools to derive closed form formulas enabling a practical use of computationally-intensive sampling strategies. A contribution in batch-sequential optimization (with the multi-points Expected Improvement) is also presented. (author)

New deconvolution method for microscopic images based on the continuous Gaussian radial basis function interpolation model.

Science.gov (United States)

Chen, Zhaoxue; Chen, Hao

2014-01-01

A deconvolution method based on the Gaussian radial basis function (GRBF) interpolation is proposed. Both the original image and Gaussian point spread function are expressed as the same continuous GRBF model, thus image degradation is simplified as convolution of two continuous Gaussian functions, and image deconvolution is converted to calculate the weighted coefficients of two-dimensional control points. Compared with Wiener filter and Lucy-Richardson algorithm, the GRBF method has an obvious advantage in the quality of restored images. In order to overcome such a defect of long-time computing, the method of graphic processing unit multithreading or increasing space interval of control points is adopted, respectively, to speed up the implementation of GRBF method. The experiments show that based on the continuous GRBF model, the image deconvolution can be efficiently implemented by the method, which also has a considerable reference value for the study of three-dimensional microscopic image deconvolution.

Segmenting Continuous Motions with Hidden Semi-markov Models and Gaussian Processes

Directory of Open Access Journals (Sweden)

Tomoaki Nakamura

2017-12-01

Full Text Available Humans divide perceived continuous information into segments to facilitate recognition. For example, humans can segment speech waves into recognizable morphemes. Analogously, continuous motions are segmented into recognizable unit actions. People can divide continuous information into segments without using explicit segment points. This capacity for unsupervised segmentation is also useful for robots, because it enables them to flexibly learn languages, gestures, and actions. In this paper, we propose a Gaussian process-hidden semi-Markov model (GP-HSMM that can divide continuous time series data into segments in an unsupervised manner. Our proposed method consists of a generative model based on the hidden semi-Markov model (HSMM, the emission distributions of which are Gaussian processes (GPs. Continuous time series data is generated by connecting segments generated by the GP. Segmentation can be achieved by using forward filtering-backward sampling to estimate the model's parameters, including the lengths and classes of the segments. In an experiment using the CMU motion capture dataset, we tested GP-HSMM with motion capture data containing simple exercise motions; the results of this experiment showed that the proposed GP-HSMM was comparable with other methods. We also conducted an experiment using karate motion capture data, which is more complex than exercise motion capture data; in this experiment, the segmentation accuracy of GP-HSMM was 0.92, which outperformed other methods.

Gaussian processes for machine learning.

Science.gov (United States)

Seeger, Matthias

2004-04-01

Gaussian processes (GPs) are natural generalisations of multivariate Gaussian random variables to infinite (countably or continuous) index sets. GPs have been applied in a large number of fields to a diverse range of ends, and very many deep theoretical analyses of various properties are available. This paper gives an introduction to Gaussian processes on a fairly elementary level with special emphasis on characteristics relevant in machine learning. It draws explicit connections to branches such as spline smoothing models and support vector machines in which similar ideas have been investigated. Gaussian process models are routinely used to solve hard machine learning problems. They are attractive because of their flexible non-parametric nature and computational simplicity. Treated within a Bayesian framework, very powerful statistical methods can be implemented which offer valid estimates of uncertainties in our predictions and generic model selection procedures cast as nonlinear optimization problems. Their main drawback of heavy computational scaling has recently been alleviated by the introduction of generic sparse approximations.13,78,31 The mathematical literature on GPs is large and often uses deep concepts which are not required to fully understand most machine learning applications. In this tutorial paper, we aim to present characteristics of GPs relevant to machine learning and to show up precise connections to other "kernel machines" popular in the community. Our focus is on a simple presentation, but references to more detailed sources are provided.

Beam conditioner for free electron lasers and synchrotrons

International Nuclear Information System (INIS)

Liu, H.; Neil, G.R.

1998-01-01

A focused optical has been used to introduce an optical pulse, or electromagnetic wave, collinear with the electron beam in a free electron laser or synchrotron thereby adding an axial field component that accelerates the electrons on the radial outside of the distribution of electrons in the electron beam. This invention consists of using the axial electrical component of a TEM 10 mode Gaussian beam in vacuum to condition the electron beam and speed up the outer electrons in the beam. The conditioning beam should possess about the same diameter as the electron beam. The beam waist of the conditioning wave must be located around the entrance of the undulator longitudinally to have a net energy exchange between the electrons in the outer part of the distribution and the conditioning wave owing to the natural divergence of a Gaussian beam. By accelerating the outer electrons, the outer and core electrons are caused to stay in phase. This increases the fraction of the electron beam energy that is converted to light thereby improving the efficiency of conversion of energy to light and therefore boosting the power output of the free electron laser and synchrotron. 4 figs

Modelling Inverse Gaussian Data with Censored Response Values: EM versus MCMC

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R. S. Sparks

2011-01-01

Full Text Available Low detection limits are common in measure environmental variables. Building models using data containing low or high detection limits without adjusting for the censoring produces biased models. This paper offers approaches to estimate an inverse Gaussian distribution when some of the data used are censored because of low or high detection limits. Adjustments for the censoring can be made if there is between 2% and 20% censoring using either the EM algorithm or MCMC. This paper compares these approaches.

Gaussian-windowed frame based method of moments formulation of surface-integral-equation for extended apertures

Energy Technology Data Exchange (ETDEWEB)

Shlivinski, A., E-mail: amirshli@ee.bgu.ac.il [Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105 (Israel); Lomakin, V., E-mail: vlomakin@eng.ucsd.edu [Department of Electrical and Computer Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0407 (United States)

2016-03-01

Scattering or coupling of electromagnetic beam-field at a surface discontinuity separating two homogeneous or inhomogeneous media with different propagation characteristics is formulated using surface integral equation, which are solved by the Method of Moments with the aid of the Gabor-based Gaussian window frame set of basis and testing functions. The application of the Gaussian window frame provides (i) a mathematically exact and robust tool for spatial-spectral phase-space formulation and analysis of the problem; (ii) a system of linear equations in a transmission-line like form relating mode-like wave objects of one medium with mode-like wave objects of the second medium; (iii) furthermore, an appropriate setting of the frame parameters yields mode-like wave objects that blend plane wave properties (as if solving in the spectral domain) with Green's function properties (as if solving in the spatial domain); and (iv) a representation of the scattered field with Gaussian-beam propagators that may be used in many large (in terms of wavelengths) systems.

Loop corrections to primordial non-Gaussianity

Science.gov (United States)

Boran, Sibel; Kahya, E. O.

2018-02-01

We discuss quantum gravitational loop effects to observable quantities such as curvature power spectrum and primordial non-Gaussianity of cosmic microwave background (CMB) radiation. We first review the previously shown case where one gets a time dependence for zeta-zeta correlator due to loop corrections. Then we investigate the effect of loop corrections to primordial non-Gaussianity of CMB. We conclude that, even with a single scalar inflaton, one might get a huge value for non-Gaussianity which would exceed the observed value by at least 30 orders of magnitude. Finally we discuss the consequences of this result for scalar driven inflationary models.

tgp: An R Package for Bayesian Nonstationary, Semiparametric Nonlinear Regression and Design by Treed Gaussian Process Models

Directory of Open Access Journals (Sweden)

Robert B. Gramacy

2007-06-01

Full Text Available The tgp package for R is a tool for fully Bayesian nonstationary, semiparametric nonlinear regression and design by treed Gaussian processes with jumps to the limiting linear model. Special cases also implemented include Bayesian linear models, linear CART, stationary separable and isotropic Gaussian processes. In addition to inference and posterior prediction, the package supports the (sequential design of experiments under these models paired with several objective criteria. 1-d and 2-d plotting, with higher dimension projection and slice capabilities, and tree drawing functions (requiring maptree and combinat packages, are also provided for visualization of tgp objects.

Topological transformation of fractional optical vortex beams using computer generated holograms

Science.gov (United States)

Maji, Satyajit; Brundavanam, Maruthi M.

2018-04-01

Optical vortex beams with fractional topological charges (TCs) are generated by the diffraction of a Gaussian beam using computer generated holograms embedded with mixed screw-edge dislocations. When the input Gaussian beam has a finite wave-front curvature, the generated fractional vortex beams show distinct topological transformations in comparison to the integer charge optical vortices. The topological transformations at different fractional TCs are investigated through the birth and evolution of the points of phase singularity, the azimuthal momentum transformation, occurrence of critical points in the transverse momentum and the vorticity around the singular points. This study is helpful to achieve better control in optical micro-manipulation applications.

Gaussian entanglement revisited

Science.gov (United States)

Lami, Ludovico; Serafini, Alessio; Adesso, Gerardo

2018-02-01

We present a novel approach to the separability problem for Gaussian quantum states of bosonic continuous variable systems. We derive a simplified necessary and sufficient separability criterion for arbitrary Gaussian states of m versus n modes, which relies on convex optimisation over marginal covariance matrices on one subsystem only. We further revisit the currently known results stating the equivalence between separability and positive partial transposition (PPT) for specific classes of Gaussian states. Using techniques based on matrix analysis, such as Schur complements and matrix means, we then provide a unified treatment and compact proofs of all these results. In particular, we recover the PPT-separability equivalence for: (i) Gaussian states of 1 versus n modes; and (ii) isotropic Gaussian states. In passing, we also retrieve (iii) the recently established equivalence between separability of a Gaussian state and and its complete Gaussian extendability. Our techniques are then applied to progress beyond the state of the art. We prove that: (iv) Gaussian states that are invariant under partial transposition are necessarily separable; (v) the PPT criterion is necessary and sufficient for separability for Gaussian states of m versus n modes that are symmetric under the exchange of any two modes belonging to one of the parties; and (vi) Gaussian states which remain PPT under passive optical operations can not be entangled by them either. This is not a foregone conclusion per se (since Gaussian bound entangled states do exist) and settles a question that had been left unanswered in the existing literature on the subject. This paper, enjoyable by both the quantum optics and the matrix analysis communities, overall delivers technical and conceptual advances which are likely to be useful for further applications in continuous variable quantum information theory, beyond the separability problem.