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Some Representations of Unified Voigt functions

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Acta Mathematica Sinica,English Series 2005年第4期21卷 865-868页

作者： M.KAMARUJJAMA DineshSINGH Department of Applied Mathematics Z.H.College of Engg.and Tech.Aligarh Muslim UniversityAligarh-202002India

The authors derive a set of unified representations of the Voigt functions in terms of familiar special functions of Mathematical Physics. Some deductions from these representations are also considered.

关键词： Voigt functions bessel functions Confluent hypergeometric function Laguerre and Hermite polynomials

Self-accelerating and self-breathing bessel-like beams along arbitrary trajectories

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Chinese Optics Letters 2013年第11期11卷 42-45页

作者：赵娟莹张鹏邓冬梅楼慈波宋道红刘京郊陈志刚 School of Optoelectronics Beijing Institute of Technology Department of Physics and Astronomy San Francisco State University NSF Nanoscale Science and Engineering Center University of California Laboratory of Nanophotonic Functional Materials and Devices South China Normal University The MOE Key Laboratory of Weak Light Nonlinear Photonics and TEDA Applied Physics School Nankai University

We theoretically and experimentally study self-accelerating and self-breathing bessel-like beams that fol- low arbitrary trajectories, including hyperbolic, hyperbolic secant, and three-dimensional （3D） spiraling trajectories. The beams have an overall bessel-like profile in transverse dimensions; however, the intensity of their central main lobe breathes while traveling along a curved trajectory. Such beams can be readily generated experimentally through appropriate phase modulation of the optical wavefront. The beams con- tribute to the design of new families of self-accelerating beams.

关键词： bessel functions Laser beams Phase modulation Three dimensional

Spiral spectrum of Airy-Schell beams through non-Kolmogorov turbulence

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Chinese Optics Letters 2016年第4期14卷 54-58页

作者：朱云章里程张逸新 School of IoT Engineering Jiangnan University School of Science Jiangnan University

Based on the geometrical optics approximation, we analyze the effects of non-Kolmogorov turbulence on the spiral spectrum of the orbital angular momentum （OAM） of Airy-Schell beams. Our numerical results of Airy-Schell beams on the horizontal path show that the beam spreading due to diffraction is smaller for shorter wavelengths, a smaller OAM quantum number, a larger radius of the main ring, and a higher arbitrary trans- verse scale in weak turbulence. The oscillation frequency of the mode probability density of Airy-Schell beams in the radial direction is much lower than that of Hankel-bessel beams. The mode probability densities of Airy-Schell and HankM-bessel beams are remarkably dependent on the wavelength and OAM quantum num- ber. In order to improve the mode probability density, Airy-Schell beams with shorter wavelengths and lower OAM quantum numbers may be the better choice, which is diametrically opposite to Hankel-bessel beams. Our research provides a reasonable basis for selecting light sources and precise tracking.

关键词： bessel functions Geometrical optics Laser beams Light sources Probability Quantum theory Spectrum analysis Turbulence Turbulence models

Numerical analysis of non-isothermal viscous jet with peripheral heat transfer

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International Journal of Modeling, Simulation, and Scientific Computing 2016年第3期7卷 50-73页

作者： Sulagna Chatterjee Trisha Sen Anindya Mitra Department of Chemical Engineering Heritage Institute of Technology Kolkata 700107India Department of Chemical Engineering IIT Bombay Mumbai 400076India Department of Chemical Engineering University of Waterloo ON N2L 3G1 Canada

A fluid jet ejected from micron size nozzle is a commonly occurring phenomenon in biomedical engineering,printing technology and micro-fluidic applications.Disintegration of a jet into drops occurs due to disturbances induced by external sources.This work explores the various sources of perturbation and their effect on jet disintegration through numerical simulation of a two-dimensional non-isothermal model.The mathematical approach uses a novel technique to combine analytical solutions for the energy balance equation in the radial direction to solve the complete two dimensional problem.The two dimensional energy balance equation is simultaneously solved together with the axi-symmetric Navier–Stokes equations using the slender-jet approximation to predict jet velocity.The energy balance takes into account of peripheral heat transfer to the environment through analytical expressions derived from radial approximations.The model helps in understanding the factors in dynamic temperature variations that eventually render the jet unstable.The distinguishing aspect of this work is the analysis of the effect of a periodic thermal perturbation applied at any point in the domain of a progressive jet,a situation typically encountered in thermal inkjet printers and not considered previously.Results presented for non-isothermal jets which are both stationary and moving illustrate the effect of jet velocity in propagation of perturbation and subsequent drop formation.The major contribution of this numerical study is that it provides an insight on novel ways of controlling droplet formation in bubble jet printers.This study demonstrates that thermal disturbance propagating from periodic heating can be manipulated to shape the droplets and control their breakage point along the jet.

关键词： Nonlinear viscous microjets bessel functions heat transfer Navier-Stokes slender jet approximation

Scattering of an unpolarized bessel beam by spheres

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Chinese Optics Letters 2010年第12期8卷 1195-1198页

作者：马秀波李恩邦 College of Precision Instrument and Optoelectronics Engineering Tianjin University

The scattering process of an unpolarized bessel beam through spherical scatterers is investigated. We derive the analytical solutions of scattered fields of x-and y-polarized bessel beams using a sphere, after which the dimensionless scattering function for an unpolarized bessel beam is obtained. The dimensionless scattering function is applicable to spherical scatterers of any size on the beam axis or near it. Through numerical simulations, we demonstrate that extreme points exist in the direction or neighboring direction of the conical angle for spherical scatterers on the beam axis, whereas the existence of extreme points depends on the ratio between the spherical scatterers size and central spot size of the bessel beam.

关键词： bessel functions Laser beams Optical waveguides Spheres

Detailing Losses in the M/M/1/1 Transient Loss System

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Acta Mathematicae Applicatae Sinica 2018年第2期34卷 373-385页

作者： Pierpaolo FERRANTE National Workers Compensation Authority (INAIL) Department of Occupational and Environmental Medicine Epidemiology and Hygiene (DiMEILA)

This paper is aimed at investigating the transient losses in the M/M/1/1 Erlang loss system. We evaluate the explicit form of the probability distribution of the number of losses in the time interval [0, t） and provide two alternative representations： one based on the iterated derivatives of hyperbolic sinus and cosine and the other on the spherical modified bessel function of the second kind. The mathematical structures of the transient loss rate and of the transient probability of losing all customers are described and several analytical properties are derived.

关键词： transient losses transient loss rate Erlang bessel functions

On the cutoff law of laser induced high harmonic spectra

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Frontiers of physics 2015年第2期10卷 91-96页

作者： Dong-Sheng Guo Chao Yu Jingtao Zhang Ju Gao Zhi-Wei Sun Zhenrong Sun State Key Laboratory of Precision Spectroscopy Department of Physics East China Normal University Shanghai 200062 China School of Physics Peking University Beijing 100871 China State Key Laboratory of High-field Laser Physics Shanghai Institute of Optical and Fine Mechanics Chinese Academy of Sciences Shanghai 201800 China jingpin Opto-Electronic Co. Jiangsu FOHO Science Park Fenhu Town Wujiang 215211 China Key Laboratory of Microgravity Institute of Mechanics Chinese Academy of Sciences Beijing 100190 China

The currently well accepted cutoff law for laser induced high harmonic spectra predicts the cutoff energy as a linear combination of two interaction energies, the ponderomotive energy Up and the atomic biding energy Ip, with coefficients 3.17 and 1.32, respectively. Even though, this law has been there for twenty years or so, the background information for these two constants, such as how they relate to fundamental physics and mathematics constants, is still unknown. This simple fact, keeps this cutoff law remaining as an empirical one. Based on the cutoff property of bessel functions and the Einstein photoelectric law in the multiphoton case, we show these two coefficients are algebraic constants, 9 - 4√2 ≈ 3.34 and 2√2-1≈1.83, respectively. A recent spectra calculation and an experimental measurement support the new cutoff law.

关键词： high harmonic generation cutoff law strong laser physics nonperturbative quantumelectrodynamics bessel functions Einstein photoelectric effect.

Boundedness of Iterated Spherical Average on α-Modulation Spaces

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Chinese Annals of Mathematics,Series B 2021年第5期42卷 721-736页

作者： Qiang HUANG Xiaomei WU Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina College of Data Science Jiaxing UniversityJiaxing 314001ZhejiangChina

For the iteration of spherical average(A_(1))^(N)and the Laplace operator△,we consider the boundedness of the operator△(A_(1))^(N) on theα-modulation spaces M^(s,α)_(p,q).The authors obtain some sufficient and necessary conditions to ensure the boundedness on theα-modulation spaces.The main theorems significantly improve some known results.

关键词： Spherical average α-Modulation spaces bessel functions

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

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Chinese Optics Letters 2006年第10期4卷 559-562页

作者：张逸新王高刚 School of Science Southern Yangtze UniversityWuxi 214036 School of Communication and Control Engineering Southern Yangtze UniversityWuxi 214036

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function, and Gaussian approximation for the product of Gaussian function and bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.

关键词： Atmospheric turbulence bessel functions Coherent light Polynomials Refractive index