Journal articles: 'Airy'

1

Suzuki, Masato, Keisaku Yamane, Takashige Omatsu, and Ryuji Morita. "Propagation-invariant vortex Airy beam whose singular point follows its main lobe." New Journal of Physics 23, no. 11 (November 1, 2021): 113043. http://dx.doi.org/10.1088/1367-2630/ac37af.

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Abstract We propose and demonstrate a novel vortex Airy beam which is a superposition of an Airy beam and its laterally sheared beam with a π/2 phase shift. This new-type of vortex Airy beam exhibits stable propagation dynamics, wherein its singular point closely follows its main lobe, unlike conventional vortex Airy beams. Notably, the orbital angular mode purity of this new vortex Airy beam is up to 10% better than that of a conventional vortex Airy beam. We anticipate that this new type of vortex Airy beam, which combines the characteristics of an optical vortex and a diffraction-free Airy beam, will facilitate new directions in applications such as microscopy, material processing and nonlinear optics.

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Liu, Jinyu, Ruiyun Jiao, Jing Wang, Zhendong Yang, and Kaiyun Zhan. "Propagation dynamics of cosh-Airy beams in Kerr nonlinear media." Journal of Nonlinear Optical Physics & Materials 28, no. 03 (September 2019): 1950030. http://dx.doi.org/10.1142/s0218863519500309.

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We investigate propagation dynamics of cosh- and cosine-Airy beams in Kerr nonlinear media. The cosh-Airy and cosine-Airy beam can be considered as a superposition of two Airy beams with different decay factors and different propagation trajectories, respectively. It is shown that the solitons shedding from cosh-Airy and cosine-Airy beams and their interaction in both in-phase and out-of-phase cases are strongly dependent on the modulation parameter associated with the cosh function. The interaction between two cosine-Airy beams can exhibit attraction or repulsion under proper interval and initial angle condition in both in-phase and out-of-phase cases.

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3

Aghili, Arman. "Some Results Involving the Airy Functions and Airy Transforms." Tatra Mountains Mathematical Publications 79, no. 2 (December 1, 2021): 13–32. http://dx.doi.org/10.2478/tmmp-2021-0017.

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Abstract In the present work, the author studied some properties of the modified Bessel’s functions and Airy functions. It is worth mentioning that the Airy functions are used in many fields of physics. They are applied in many branches of classical and quantum physics. The author also studied certain properties of the Airy transform and derived some new integral relations involving the Airy functions. Non-trivial illustrative examples are provided as well. All the results are presented in lucid and comprehensible language.

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Shao, Li, Yun-Long Wu, and Qing Ye. "Anomalous Propagation Characteristics of Airy Beam in Nonlinear Kerr Media." Crystals 11, no. 8 (July 28, 2021): 879. http://dx.doi.org/10.3390/cryst11080879.

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The propagation characteristics of a single Airy beam in nonlinear Kerr media were numerically investigated by utilizing the split-step Fourier transform method. We show that in addition to normal breathing solitons, the anomalous bound states of Airy spatial solitons can also be formed, which are similar to the states formed in the interaction between two Airy beams in nonlinear media. This quasi-equilibrium state is formed by the interaction of the main soliton beam and side lobes of Airy beam due to their different propagation trajectories in the nonlinear media. Moreover, it has been shown the Airy spatial solitons in tree structure can be formed by adjusting the initial parameters in the interaction between the Airy beam and Kerr media.

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5

Chen, Ye, Lijuan Ge, Xinglin Wang, and Ming Shen. "Collapse arrest in a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam in nonlocal nonlinear media." Communications in Theoretical Physics 74, no. 2 (February 1, 2022): 025501. http://dx.doi.org/10.1088/1572-9494/ac46a5.

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Abstract Propagation dynamics of a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam are investigated numerically in local and nonlocal nonlinear media. The self-healing and collapse of the beam crucially depend on the distribution factor b and the topological charge m. With the aid of nonlocality, a stable Airy Gaussian beam and an Airy Gaussian vortex beam with larger amplitude can be obtained, which always collapse in local nonlinear media. When the distribution factor b is large enough, the Airy Gaussian vortex beam will transfer into quasi-vortex solitons in nonlocal nonlinear media.

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6

Hakim, Lukman, and Ari Kusumastuti. "Generalisasi Fungsi Airy sebagai Solusi Analitik Persamaan Schrodinger Nonlinier." CAUCHY 2, no. 2 (May 4, 2012): 86. http://dx.doi.org/10.18860/ca.v2i2.2223.

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<p>Persamaan Schrodinger adalah persamaan diferensial parsial nonlinier yang menginterpretasikan pergerakan suatu partikel atau atom. Penelitian ini berupaya untuk memperoleh analisis konstruksi bentuk umum solusi ananalitik persamaan Schrodinger nonlinier dengan fungsi Airy. Fungsi Airy adalah solusi persamaan diferensial Airy, adapun langkah pertama adalah manipulasi bentuk persamaan Schrodinger nonlinier menjadi bentuk persamaan Airy dengan menerapkan transformasi Fourier. Dengan demikian didapatkan solusia nanalitik persamaan Airy dengan generalisasi fungsi Airy. Dan langkah selanjutnya adalah menerapkan invers dari transformasi Fourier yang digunakan untuk memdapatkan solusi analitik bagi persamaan Schrodinger nonlinier, dalam hal ini diberikan kondisi awal bilangan kompleks pada invers transformasi Fourier, yaitu. Adapun hasil dari penelitian ini adalah solusi bagi persamaan Schrodinger nonlinier ketika pangkat dari modulusnya di analisis dengan bentuk ganjil dan genap memberikan bentuk solusi yang sama.</p>

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7

Zhou, Yimin, Yiqing Xu, Xiuxiang Chu, and Guoquan Zhou. "Propagation of Cosh-Airy and Cos-Airy Beams in Parabolic Potential." Applied Sciences 9, no. 24 (December 16, 2019): 5530. http://dx.doi.org/10.3390/app9245530.

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The analytical expressions of one-dimensional cosh-Airy and cos-Airy beams in the parabolic potential are derived in the general and the phase transition points. The expression in the phase transition point shows a symmetric Gaussian intensity profile and is independent of any Airy features, which is completely different from that in the general point. The intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are periodic and have the same period. The effects of the transverse displacement, the cosh factor, and the cosine factor on these periodic behaviors are also investigated. The direction of self-acceleration reverses every half-period. The phase transition point is also the inversion point of the intensity distribution, which indicates that the intensity distributions before and after the phase transition point are mirror symmetrical. The periodic behaviors of the normalized intensity, the center of gravity, and the effective beam size of the cosh-Airy and cos-Airy beams in the parabolic potential are attractive and well displayed. The results obtained here may have potential applications in particle manipulation, signal processing, and so on.

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8

Deng, Suhui, Liusong Yuan, Peiwei Cheng, Yuhao Wang, and Mingping Liu. "Enhancement of image quality in planar Airy light-sheet microscopy via subtraction method." Journal of Optics 24, no. 2 (January 4, 2022): 025301. http://dx.doi.org/10.1088/2040-8986/ac4437.

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Abstract The use of propagation-invariant Airy beams enables a light-sheet microscopy with a large field-of-view. Without relying upon two-photon excitation or deconvolution-based processing to eliminate out-of focus blur caused by the side lobes, here, we present how the subtraction method is applied to enhance the image quality in digital scanned light-sheet microscopy with Airy beam. In the proposed method, planar Airy beam with the symmetric transversal structure is used to excite the sample. A hollow Airy beam with zero intensity at the focal plane is created, which is mainly used to excite the out-of-focus signal. By scanning the sample twice with the normal planar Airy beam and the hollow Airy beam, digital post-processing of the obtained images by subtraction allows for the rejection of out-of-focus blur and improves the optical sectioning, the axial resolution and the intensity distribution uniformity of the light-sheet microscopy.

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9

Wu, Fuping, Yuanfei Hui, Zhiwei Cui, and Ju Wang. "Reflection Characteristics of Airy Beams Impinging on Graphene-Substrate Surfaces." International Journal of Optics 2022 (January 3, 2022): 1–10. http://dx.doi.org/10.1155/2022/5319174.

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In this work, we analytically and numerically investigate the reflection characteristics of the airy beams impinging on graphene-substrate surfaces. The explicit analytical expressions for the electric and magnetic field components of the airy beams reflected from a graphene-substrate interface are derived. The local-field amplitude, Poynting vector, and spin and orbital angular momentum of the reflected airy beams with different graphene structure and beam parameters are presented and discussed. The results show that the reflection properties of the airy beams can be flexibly tuned by modulating the Fermi energy of the graphene and have a strong dependence on the incident angle and polarization state. These results may have potential applications in the modulation of airy beams and precise measurement of graphene structure parameters.

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10

Guo, Yong, Yangrui Huang, Jin Li, Luwei Wang, Zhigang Yang, Jinyuan Liu, Xiao Peng, Wei Yan, and Junle Qu. "Deep Penetration Microscopic Imaging with Non-Diffracting Airy Beams." Membranes 11, no. 6 (May 26, 2021): 391. http://dx.doi.org/10.3390/membranes11060391.

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We report a deep penetration microscopic imaging method with a non-diffracting Airy beam. The direct mapping of volume imaging in free space shows that the axial imaging range of the Airy beam is approximately 4 times that of the traditional Gaussian beam along the axial direction while maintaining a narrow lateral width. Benefiting from its non-diffracting property, the microscopic imaging with Airy beam illumination can acquire image structures through turbid medium and capture a volumetric image in a single frame. We demonstrate the penetration ability of the Airy microscopic imaging through a strongly scattering environment with 633 nm and 780 nm lasers. The performances of the volumetric imaging method were evaluated using HeLa cells and isolated mouse kidney tissue. The thick sample was scanned layer by layer in the Gaussian mode, however, in the Airy mode, the three-dimensional (3D) structure information was projected onto a two-dimensional (2D) image, which vastly increased the volume imaging speed. To show the characteristics of the Airy microscope, we performed dynamic volumetric imaging on the isolated mouse kidney tissue with two-photon.

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11

Hadasz, Leszek, and Błażej Ruba. "Airy Structures for Semisimple Lie Algebras." Communications in Mathematical Physics 385, no. 3 (June 24, 2021): 1535–69. http://dx.doi.org/10.1007/s00220-021-04142-7.

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AbstractWe give a complete classification of Airy structures for finite-dimensional simple Lie algebras over $${\mathbb {C}}$$ C , and to some extent also over $${\mathbb {R}}$$ R , up to isomorphisms and gauge transformations. The result is that the only algebras of this type which admit any Airy structures are $$\mathfrak {sl}_2$$ sl 2 , $$\mathfrak {sp}_4$$ sp 4 and $$\mathfrak {sp}_{10}$$ sp 10 . Among these, each admits exactly two non-equivalent Airy structures. Our methods apply directly also to semisimple Lie algebras. In this case it turns out that the number of non-equivalent Airy structures is countably infinite. We have derived a number of interesting properties of these Airy structures and constructed many examples. Techniques used to derive our results may be described, broadly speaking, as an application of representation theory in semiclassical analysis.

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12

Chen, Weijun, Cheng Lian, and Yuang Luo. "Interaction of Airy beams modeled by the fractional nonlinear cubic-quintic Schrödinger equation." Physica Scripta 96, no. 12 (November 24, 2021): 125256. http://dx.doi.org/10.1088/1402-4896/ac36ec.

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Abstract We investigate theoretically and numerically the interaction of Airy beams modeled by fractional nonlinear cubic-quintic Schrödinger equation. By considering fractional diffraction effect, when the initial beam interval between the two Airy beams is large enough, it is found that two in-phase Airy beams attract and repel each other, and two out-of-phase beams repel each other. This is different from the interaction of two Airy beams with large interval in standard nonlinear Schrödinger equation, where the two beams display a weak interaction. For smaller interval, single breathing soliton and symmetric breathing soliton pairs are formed in the in-phase and out-of-phase cases, respectively. As the Lévy index decreases, for the single breathing soliton, the oscillation becomes stronger, the mean peak intensity increases, and the soliton width decreases, for the symmetric breathing soliton pair, the width becomes narrower, and the repulsion between the two Airy components becomes stronger. Besides, the quintic defocusing strength will modulate the interaction of Airy beams. When the strength coefficient increases, the width of the breathing soliton formed in the in-phase case becomes wider, the repulsion between the two beams in the out-of-phase case increases, as well as the width of the soliton pair becomes wider. The work may provide new control methods on the interaction of Airy beams.

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13

Bouchard, Vincent, Paweł Ciosmak, Leszek Hadasz, Kento Osuga, Błażej Ruba, and Piotr Sułkowski. "Super Quantum Airy Structures." Communications in Mathematical Physics 380, no. 1 (October 13, 2020): 449–522. http://dx.doi.org/10.1007/s00220-020-03876-0.

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Abstract We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations. Furthermore, we present various examples of super quantum Airy structures, both finite-dimensional—which include well known superalgebras and super Frobenius algebras, and whose classification scheme we also discuss—as well as infinite-dimensional, that arise in the realm of vertex operator super algebras.

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Khairurrijal, Khairurrijal, Fatimah A. Noor, Mikrajuddin Abdullah, and Sukirno Sukirno. "Simulation of Electron Transmittance and Tunneling Current in a Metal-Oxide- Semiconductor Capacitor with a High-K Dielectric Stack of HfO2 and SiO2 Using Exponential- and Airy-Wavefunction Approaches and a Transfer Matrix Method." Indonesian Journal of Physics 20, no. 2 (November 3, 2016): 27–32. http://dx.doi.org/10.5614/itb.ijp.2009.20.2.2.

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Analytical expressions of electron transmittance and tunneling current in a metal-oxide-semiconductor (MOS) capacitor with a high dielectric constant (high-K) oxide stack of HfO2 and SiO2 and a negative bias applied to the metal gate were derived. Exponential- and Airy-wavefunction approaches were employed in deriving analytically the electron transmittance and tunneling current. A numerical approach based on a transfer matrix method was used as a standard to evaluate the analytical approaches. It was found that the transmittances obtained under the exponential- and Airy-wavefunction approaches and the TMM are matching for low electron energies, while for higher energies only the transmittances calculated by employing the Airy- wavefunction approach is the same as those computed by using the TMM. It was also found that the tunneling currents calculated by using the exponential- and the Airy-wavefunction approaches and the TMM are equal for low oxide voltages (lower than 0.5 V), while for higher oxide voltages only the tunneling currents computed under the Airy-wavefunction approach fit those obtained under the TMM. Therefore, the Airy-wavefunction approach provides a better analytical model to tunneling processes in the MOS capacitor.

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Habibi, Forouzan, and Mohammad Moradi. "Evaluation of nonlinear behavior of Airy, cos-Airy, and cosh-Airy beams with and without optical vortex." Journal of Optics 24, no. 4 (March 17, 2022): 045507. http://dx.doi.org/10.1088/2040-8986/ac4e5e.

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Abstract In this study, we investigate Airy, cos-Airy, and cosh-Airy beam lasers with optical vortex (OV). Then, taking into account the Fourier transform, we examine and compare the propagation of these beams in a strong nonlinear system. The results indicate that by changing the input power p 0 and the parameters b and propagation length, the location of OV displaces. It is shown that nonlinearity is one of the parameters that control OV in optical systems used in these types of lasers. An important property in these beams is their direction variation due to the change in the mentioned parameters, which can be used in applications such as beam switching.

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FERNANDEZ, RAHUL N., and V. S. VARADARAJAN. "MATRIX AIRY FUNCTIONS FOR COMPACT LIE GROUPS." International Journal of Mathematics 20, no. 08 (August 2009): 945–77. http://dx.doi.org/10.1142/s0129167x09005595.

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The classical Airy function has been generalized by Kontsevich to a function of a matrix argument, which is an integral over the space of skew-hermitian matrices of a unitary-invariant exponential kernel. In this paper, the Kontsevich integral is further generalized to integrals over the Lie algebra of an arbitrary connected compact Lie group, using exponential kernels invariant under the group. The (real) polynomial defining this kernel is said to have the Airy property if the integral defines a function of moderate growth. A very general sufficient criterion for a polynomial to have the Airy property is given. It is shown that an invariant polynomial on the Lie algebra has the Airy property if its restriction to a Cartan subalgebra has the Airy property. This result is used to evaluate these invariant integrals completely and explicitly on the hermitian matrices, obtaining formulae that contain those of Kontsevich as special cases.

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Marinha, Marcelo Diniz Santa, Danian S. Oliveira, Paulo Eduardo Miranda Cunha, and Luiz Gallisa Guimarães. "DISCRETE AIRY BEAM PROPAGATION IN DEEP OCEANS." Revista Brasileira de Geofísica 36, no. 4 (December 21, 2018): 1. http://dx.doi.org/10.22564/rbgf.v36i4.1969.

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ABSTRACT. In this work, based on the theory of modal propagation of acoustic energy in deep oceans and using the analogy between acoustics and quantum mechanics, we show that it is possible the existence of almost dispersionless Airy beams propagation at great distances with simultaneous wave packet shape preservation.Keywords: Normal modes, wave propagation, ocean acoustics, Airy beam.RESUMO. Neste trabalho, baseado na teoria de propagação da energia acústica por modos em oceanos profundos, mostraremos que é possível a existência de feixes de Airy que se propagam em grandes distâncias, com pouca dispersão da energia acústica e preservação de sua formaPalavras-chave: Modos normais, propagação de ondas, acústica oceanográfica, feixe de Airy.

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Chen, Rui-Pin, and Khian-Hooi Chew. "Far-field properties of a vortex Airy beam." Laser and Particle Beams 31, no. 1 (November 27, 2012): 9–15. http://dx.doi.org/10.1017/s0263034612000729.

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AbstractAnalytical far-field expressions for the transverse electric mode and transverse electric magnetic mode terms, and the energy flux distributions of vortex Airy beams are derived based on the vector angular spectrum of the beam and the stationary phase method. The physical pictures of vortex Airy beams from the vectorial structure are illustrated and the energy flux distributions are demonstrated in far-field. The influences of the beam parameters, especially the exponential factor, on the energy flux distributions of vortex Airy beams and its transverse electric mode and transverse electric magnetic mode terms are discussed. This work provides a new understanding of the propagation behaviors and applications of a vortex Airy beam.

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Britto, A. L. M., Ashok K. Das, and J. Frenkel. "Fermion propagator in an external potential and generalized Airy functions." Modern Physics Letters A 32, no. 32 (October 12, 2017): 1750171. http://dx.doi.org/10.1142/s0217732317501711.

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We study the behavior of the fermion propagator in an external time-dependent potential in 0 + 1 dimension. We show that, when the potential has up to quadratic terms in time, the propagator can be expressed in terms of generalized Airy functions (or standard Airy functions depending on the exact time dependence). We study various properties of these new generalized functions which reduce to the standard Airy functions in a particular limit.

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Belteki, Daniel. "Trust in Glass: Negotiating the Purchase of the Object Glass for the Airy Transit Circle." Journal for the History of Astronomy 51, no. 4 (November 2020): 401–22. http://dx.doi.org/10.1177/0021828620968631.

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The Airy Transit Circle of the Royal Observatory, Greenwich is one of the most important instruments in the history of astronomy, navigation and time distribution. However, there has been very little research done on the history of the instrument. This article examines how the purchase of the object glass for the Airy Transit Circle involved active negotiations between George Biddell Airy and three different opticians: Georg Merz, Noel Paymal Lerebours, and William Simms. The article also shows the involvement of John Herschel and Richard Sheepshanks in Airy’s decision making process. By highlighting the presence of these individuals, the article shows how Airy’s trust and distrust in different instrument makers influenced his choice of supplier for the object glass of the Airy Transit Circle.

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Kulakov, Sergey V., Gennady V. Kulak, and Oleg V. Shakin. "Acousto-optical modulation of airy light beams in crystals." Journal of Physics: Conference Series 2373, no. 6 (December 1, 2022): 062010. http://dx.doi.org/10.1088/1742-6596/2373/6/062010.

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Abstract The non-collinear diffraction of Airy light beams on ultrasound in the regime of weak and strong acousto-optical (AO) interaction is investigated. Expressions are obtained for the complex amplitudes of diffracted waves in the general case of an anisotropic medium. It is shown that with an increase in the dimensionless parameter of the Airy beam, the efficiency of Bragg diffraction decreases. At the same time, however, the shape of the modulation curve remains unchanged. It is established that the greatest efficiency of anisotropic Bragg diffraction is achieved for a case when the diffracted Airy beam propagates along the front of the ultrasonic wave. It is shown that the efficiency of AO diffraction of Airy beam on an amplitude-modulated wave is determined by the diffraction efficiencies of constant components in a diffracted beam.

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Liu, Jinyu, and Kun Liang. "Interaction of Airy beams in photorefractive media." Modern Physics Letters B 32, no. 27 (September 27, 2018): 1850323. http://dx.doi.org/10.1142/s0217984918503232.

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We investigate numerical interactions between two Airy beams with different relative phases in photorefractive (PR) nonlinear media in one transverse dimension. It is shown that solitons and soliton pairs are generated that are not accelerating, although the incident beams exhibit acceleration property. When the relative phase is very small, the attraction between the two Airy beams is strengthened and their propagation behavior is similar to that in in-phase case, where the two Airy beams attract each other and the main lobes can fuse into one single breathing soliton, secondary lobes can generate soliton pairs with symmetric intensity distribution. While the relative phase is close to [Formula: see text], these beams present out-phase propagation with strong repulsive effect. Their interaction properties are sensitive to both the interval and relative phase between the two Airy beams.

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Yang, Donghui, Zhou Yu, Zheng-Da Hu, Wenhai Wang, and Yun Zhu. "Bi-Photon Entangled Airy Beams through Unstable Oceanic Turbulence." Journal of Marine Science and Engineering 10, no. 11 (October 31, 2022): 1604. http://dx.doi.org/10.3390/jmse10111604.

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Orbital angular momentum (OAM) carried by bi-photon entangled Airy beams in unstable oceanic turbulence is theoretically investigated. The analytical expression of the spatial coherence radius of a spherical wave in the unstable stratification oceanic turbulence is derived to obtain the relative detection probability of bi-photon entangled Airy beams. The relative detection probability of OAM carried by bi-photon entangled Airy beams acquires significant enhancements—up to 62% compared to the same measurement for the single photon system over a distance of 100 m. Lower-order bi-photon entangled Airy beams with larger wavelengths, and main ring radius are less affected by oceanic turbulence. A larger main ring radius also contributes to reducing the fluctuations in detection probability. Oceanic turbulence dominated by salinity fluctuations induces more adverse effects on the OAM, as well as a stronger strength of the turbulence.

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Fan, Junjie. "Airy function solution of two classes of nonlinear evolution equations." Pacific International Journal 5, no. 2 (June 30, 2022): 88–91. http://dx.doi.org/10.55014/pij.v5i2.172.

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In this paper , we study the problem of constructing the new solutions of the mKdV equation and STO equation. By using the Airy equation and its solution, the new solutions of mKdV equation and STO equation are constructed. First of all, through function transformation, mKdV equation and STO equation can be turned into Airy function to solve. Then, construct the solution of mKdV equation and STO equation by using the solution of Airy function. Finally, analyze the properties of these solutions with the help of symbolic computation system: Mathematica.

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Blaya, Salvador, Edmundo Lopez-Sola, Pablo Acebal, and Luis Carretero. "Theoretical Analysis of Airy–Gauss Bullets Obtained by Means of High Aperture Binary Micro Zonal Plate." Micromachines 13, no. 2 (February 10, 2022): 279. http://dx.doi.org/10.3390/mi13020279.

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We theoretically analyze the methodology for obtaining vectorial three-dimensional bullets, concretely Airy–Gauss bullets. To do this, binary micro zonal plates (BZP) were designed in order to obtain different Airy–Gauss bullets with sub-diffraction main lobe width. Following the vectorial diffraction theory, among the electrical field, we extend the theory to the magnetic field, and thus we analyze several properties such as the Poynting vector and the energy of Airy–Gauss vectorial bullets generated by illuminating the designed BZP with a temporal Gaussian circular polarized pulses.

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BERTOLA, M., and M. CAFASSO. "THE GAP PROBABILITIES OF THE TACNODE, PEARCEY AND AIRY POINT PROCESSES, THEIR MUTUAL RELATIONSHIP AND EVALUATION." Random Matrices: Theory and Applications 02, no. 02 (April 2013): 1350003. http://dx.doi.org/10.1142/s2010326313500032.

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We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard Tracy–Widom distribution, while the numerator is the Fredholm determinant of a very explicit kernel constructed with Airy functions and exponentials. The formula allows us to apply the theory of numerical evaluation of Fredholm determinants and thus produce numerical results for the gap probabilities. In particular we investigate numerically how, in different regimes, the Pearcey process degenerates to the Airy one, and the tacnode degenerates to the Pearcey and Airy ones.

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LI, Y. T., and R. WONG. "GLOBAL ASYMPTOTICS OF STIELTJES–WIGERT POLYNOMIALS." Analysis and Applications 11, no. 05 (September 2013): 1350028. http://dx.doi.org/10.1142/s0219530513500280.

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Asymptotic formulas are derived for the Stieltjes–Wigert polynomials Sn(z; q) in the complex plane as the degree n grows to infinity. One formula holds in any disc centered at the origin, and the other holds outside any smaller disc centered at the origin; the two regions together cover the whole plane. In each region, the q-Airy function Aq(z) is used as the approximant. For real x > 1/4, a limiting relation is also established between the q-Airy function Aq(x) and the ordinary Airy function Ai (x) as q → 1.

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Jin, Long, and Xingqiang Zhang. "Propagation Properties of Airy Beam through Periodic Slab System with Negative Index Materials." International Journal of Optics 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/9478483.

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Based on light transfer matrix and electric field vector equation, the evolution of Airy beam propagating in periodic slab system with three negative index materials (NIMs) and its transmission mechanism are investigated. The intensity profiles on emergent surface of periodic slab system and side view of Airy beam propagating in each right handed material (RHM) and double negative material (DNM) unit including lossless and losses DNMs are discussed. It is revealed that the self-recovery Airy beam can be achieved in long distance by using lossless periodic slab system as long as the negative refractive index nl=-nr and each unit length L=Z. As to losses slab system contained DNMs, the smaller the collision frequencies are, the better the Airy beam quality is formed. It is expected that the proposed manner of beam transmission and corresponding conclusions can be useful for extension applications of optical control, especially for optical communication and optical encryption technique.

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Ansari, Alireza, and Mohammad Rasool Masomi. "Some integral identities for products of Airy functions using integral transforms." Asian-European Journal of Mathematics 11, no. 03 (May 3, 2018): 1850046. http://dx.doi.org/10.1142/s1793557118500468.

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In this paper, using the integral identities of Bessel functions, we obtain new integral identities for the products of Airy functions. We get various integrals involving the Widder potential, the Fourier sine and cosine transforms of the products of Airy functions in terms of some special functions.

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Berezhnoy, Yu A., and A. S. Molev. "Airy minima in 4He +28Si elastic and inelastic scattering." Modern Physics Letters A 35, no. 19 (May 14, 2020): 2050159. http://dx.doi.org/10.1142/s021773232050159x.

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We present the results of the [Formula: see text]-matrix description of the [Formula: see text] elastic and inelastic scattering differential cross-sections between 40 and 240 MeV with allocation of Airy minima of various orders. The first-order Airy minima have been unambiguously identified in the differential cross-sections for elastic scattering and inelastic scattering to the first [Formula: see text] state of [Formula: see text] at energies [Formula: see text] MeV, and the second-order Airy minima — at [Formula: see text] MeV. The angular positions of these minima obey an inverse dependence on energy. The intensities of nuclear refraction and absorption also obey the same energy dependence.

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31

Sinha, Anjana, Rajkumar Roychoudhury, and Y. P. Varshni. "Supersymmetric modified Airy-function method and its application to the Schrödinger potential V(x) = x6 − 3x2." Canadian Journal of Physics 74, no. 1-2 (January 1, 1996): 39–42. http://dx.doi.org/10.1139/p96-007.

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A supersymmetric version of the modified Airy-function method is developed. Explicit calculations for eigenvalues are obtained for the Schrödinger potential V(x) = x6 − 3x2. Comparison is made with exact numerical results as well as those of the Wentzel–Kramers–Brillouin (WKB), supersymmetric WKB (SWKB), and modified Airy-function approximation methods.

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Every, A. G., M. Pluta, and W. Grill. "Interference of non-aligned Airy diffraction patterns in transmission acoustic microscopy images of crystals." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2064 (September 23, 2005): 3847–62. http://dx.doi.org/10.1098/rspa.2005.1545.

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This paper describes interference effects present in narrow band transmission acoustic microscopy images of crystals that arise from the superposition of pairs of non-aligned but symmetry equivalent Airy diffraction patterns. In the cases we examine, these Airy patterns are associated with folded portions of the slow transverse (ST) sheet of the acoustic wave surface of cubic crystals intersecting in the {110} symmetry planes. Each set of Airy fringes is inclined in the (001) observation plane to its overlapping counterpart, giving rise to curved Moiré-like fringes. Also, because of tilting of the two portions of the wave surface in opposite directions out of the (001) plane, each composite Airy fringe breaks up along its length into a large number of narrow, regularly spaced fringes, in a manner akin to wedge diffraction. We present calculations of these effects in GaAs and Ge, based on the elastodynamic Green's function, , for the infinitely extended anisotropic elastic continuum. A measured time-gated diffraction image is presented for GaAs, which is in good agreement with calculation.

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Zhao, Yuefeng, Yinghe Wang, Qian Chen, Pujuan Ma, Yangjian Cai, and Chunhao Liang. "Enhancing the Self-Healing Ability of a Partially Coherent Airy Beam via Fourier Processing: Numerical Investigation." Photonics 10, no. 2 (January 30, 2023): 143. http://dx.doi.org/10.3390/photonics10020143.

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Almost all of the beams under propagation are believed to suffer severe distortion when the source coherence deteriorates, due to the optical diffraction. This implies that low-coherence beams have poor self-healing ability, but were found to be robust against the turbulence, distortion, scattering, etc. In this letter, we first prove numerically that partially coherent Airy beams (PCABs), generated via Fourier processing, have better self-healing ability than that of conventional fully coherent Airy beams. Moreover, as the source coherence deteriorates and the propagation distance increases, the self-healing ability is found to increase. We believe that such PCABs may find Airy beam-related applications in adverse environments, such as particle trapping in biological tissues.

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Adekanye, Oluwaseye, and Talitha Washington. "Numerical comparison of nonstandard schemes for the Airy equation." International Journal of Applied Mathematical Research 6, no. 4 (November 19, 2017): 141. http://dx.doi.org/10.14419/ijamr.v6i4.8490.

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This paper considers the Airy ordinary differential equation (ODE) and different ways it can be discretized. We first consider a standard discretization using the central difference scheme. We then consider two difference schemes which were created using a nonstandard methodology. Finally, we compare the different schemes and how well they approximate solutions to the Airy ODE.

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Aitken, E. "A REVISION OF GENTIANELLA, COMASTOMA AND GENTIANOPSIS (GENTIANACEAE) IN NEPAL." Edinburgh Journal of Botany 64, no. 2 (July 2007): 253–68. http://dx.doi.org/10.1017/s0960428607000935.

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AbstractThe genus Gentianella in Nepal is revised and five species are recognized: G. angustiflora Harry Sm., G. azurea (Bunge) Holub, G. glanduligera Airy Shaw, G. lowndesii Harry Sm. and G. moorcroftiana (Wall. ex G.Don) Airy Shaw. Gentianella maddenii (C.B.Clarke) Airy Shaw, usually treated as a distinct species, is placed in synonymy of G. moorcroftiana. The genus Comastoma in Nepal is revised, four species are recognized and one new combination is made: C. falcatum (Turcz. ex Kar. & Kir.) Toyok., C. pedunculatum (D.Don) Holub, C. stellariifolium (Franch.) Holub and C. urnigerum (E.Aitken & D.G.Long) E.Aitken comb. nov. The genus Gentianopsis in Nepal is revised and three species are recognized: G. contorta (Royle) Ma, G. paludosa (Hook.) Ma and G. vvedenskyi (Grossh.) Pissjauk.

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36

Yuce, C. "Self-accelerating matter waves." Modern Physics Letters B 29, no. 28 (October 19, 2015): 1550171. http://dx.doi.org/10.1142/s0217984915501717.

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The free particle Schrödinger equation admits a nontrivial self-accelerating Airy wave packet solution. Recently, the Airy beams that freely accelerate in space was experimentally realized in photonics community. Here, we present self-accelerating waves for the Bose–Einstein condensate in a time-dependent harmonic oscillator potential. We show that parity and time reversal symmetries for self-accelerating waves are spontaneously broken.

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Benjamin, Stefanie, Paige P. Schneider, and Derek H. Alderman. "Film Tourism Event Longevity: Lost in Mayberry." Tourism Review International 16, no. 2 (November 1, 2012): 139–50. http://dx.doi.org/10.3727/154427212x13485031583939.

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The purpose of this study is to examine a US festival widely known for attracting television fan tourists, build a traveler profile or typology of festival goers, and reflect on how the behavioral segmentation of these tourists may affect the longevity of the film tourism event and the broader planning of the destination community. Specifically, this study examines the Mayberry Days Festival, an annual event held in Mount Airy, North Carolina. Mount Airy is the birthplace and boyhood home of actor, Andy Griffith, whose television series (The Andy Griffith Show) was set in the fictional hamlet of Mayberry. Online survey invitation cards were distributed during the 2010 Mayberry Days Festival to gather data on the sociodemographic characteristics, motivations, perceptions, and economic impact of the attendee to comprehend how sustainable the Mayberry Days Festival will be for Mount Airy. Results suggest that visitors are drawn to Mount Airy for a variety of reasons and that The Andy Griffith Show is not necessarily the main motivator. It is important for the town's tourism promoters not to get “lost in Mayberry” as they plan for alternative marketing and attraction development in the future.

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Ozturk, Ali. "Characterization of the Tungsten-Steel Functionally Graded Cylinder in Elastic Region." Solid State Phenomena 263 (September 2017): 67–71. http://dx.doi.org/10.4028/www.scientific.net/ssp.263.67.

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This paper presents how to derive Airy stress function to obtain the thermal stresses in a tungsten-steel functionally graded solid cylinder with fixed ends in elastic region. Once Airy stress function is derived, the thermal stresses can be found due to the related equations. There is uniform heat generation inside the tungsten-steel functionally graded solid cylinder. Material properties of the functionally graded cylinder (FGC) are assumed to vary radially according to a parabolic form and assumed to be independent of the temperature. These properties are yield strength, modulus of elasticity, coefficient of thermal conduction and coefficient of thermal expansion (CTE). Poisson’s ratio is assumed to be constant as an average value between tungsten’s and steel’s. Airy stress function is derived in terms of these properties to characterize the FGC entirely.

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Keluskar, Yugesh C., Megha M. Navada, Chaitanya S. Jage, and Navin G. Singhaniya. "Implementation of Airy function using Graphics Processing Unit (GPU)." ITM Web of Conferences 32 (2020): 03052. http://dx.doi.org/10.1051/itmconf/20203203052.

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Special mathematical functions are an integral part of Fractional Calculus, one of them is the Airy function. But it’s a gruelling task for the processor as well as system that is constructed around the function when it comes to evaluating the special mathematical functions on an ordinary Central Processing Unit (CPU). The Parallel processing capabilities of a Graphics processing Unit (GPU) hence is used. In this paper GPU is used to get a speedup in time required, with respect to CPU time for evaluating the Airy function on its real domain. The objective of this paper is to provide a platform for computing the special functions which will accelerate the time required for obtaining the result and thus comparing the performance of numerical solution of Airy function using CPU and GPU.

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Zhang, Jinggui, Yuanjiang Xiang, Yongfan Li, Dajun Lei, and Lifu Zhang. "Role of anomalous self-steepening in controlling self-accelerating Airy pulses in nonlinear metamaterials." Journal of Nonlinear Optical Physics & Materials 25, no. 01 (March 2016): 1650010. http://dx.doi.org/10.1142/s0218863516500107.

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The additional dispersive magnetic permeability in metamaterials (MMs) described by the Drude model is able to generate the anomalous self-steepening (SS) effect which can be positive, negative even zero. This provides more great flexibility for us to control ultrashort pulse propagation, when compared with the corresponding case in naturally positive-index materials (PIMs). In this paper, we theoretically investigate the self-accelerating control of Airy pulse through such anomalous SS effect in MMs with a cubic nonlinearity. The emphasis is given to the counterintuitive dynamical behavior different from those in PIMs. It is shown that positive SS in MMs acts to promote the self-acceleration of such pulse and the corresponding spectral features exhibits a broad redshifted behaviors, as it does in PIMs; while the negative SS gives rise to the appearance of the opposite situation. That is to say, the self-acceleration of Airy pulse will be delayed through broadening the spectrum toward blue side. Meanwhile, the effect of the specific truncation coefficient imposed on Airy pulses in MMs also be discussed under the roles of positive and negative SS, respectively. Our findings show that the SS effect in MMs can provide a more powerful tool in controlling the self-accelerating of Airy pulse when compared with the corresponding case in PIMs.

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41

Canh, Le Van, Ho Le Huy Phuc, and Nguyen Hoang Phuong. "Airy-based static limit analysis of structures using stabilized radial point interpolation method." HO CHI MINH CITY OPEN UNIVERSITY JOURNAL OF SCIENCE - ENGINEERING AND TECHNOLOGY 12, no. 1 (March 22, 2022): 65–78. http://dx.doi.org/10.46223/hcmcoujs.tech.en.12.1.2020.2022.

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This paper presents a novel formulation for static limit analysis of structures, for which the Airy stress function is approximated using stabilized Radial Point Interpolation Mesh-free method (RPIM). The stress field is determined as second-order derivatives of the Airy function, and the equilibrium equations are automatically satisfied a priori. The so-called Stabilized Conforming Nodal Integration (SCNI) is employed to ensure a present method is truly a mesh-free approach, meaning that all constraints in problems are only enforced at nodes. With the use of the Airy function, SCNI, and Second-Order Cone Programming (SOCP), the size of the resulting problem is kept to be minimum. Several benchmark problems having arbitrary geometries and boundary conditions are investigated. The obtained numerical solutions are compared with those available in other studies to perform the computational aspect of the proposed method.

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Telford, Ian R. H., Kanchana Pruesapan, Peter C. van Welzen, and Jeremy J. Bruhl. "Molecular data consistently recover a 'Queensland clade' of Synostemon Phyllanthaceae, Phyllantheae) with distinctive floral morphology." Australian Systematic Botany 27, no. 6 (2014): 450. http://dx.doi.org/10.1071/sb14034.

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Molecular analysis of the newly reinstated genus Synostemon F.Muell. (Phyllanthaceae, Phyllantheae), using ITS sequence data from the now densely sampled genus, confirmed that the previously recognised ‘Queensland clade’ consists of Synostemon albiflorus (F.Muell. ex Müll.Arg.) Airy Shaw, S. sphenophyllus Airy Shaw, Sauropus podenzanae (S.Moore) Airy Shaw and the undescribed Synostemon spinescens, sp. nov. ined., the latter being validated here as S. spinosus I.Telford & J.J.Bruhl. Morphological synapomorphies for the clade are as follows: linear, apiculate anthers that are connivent but only basally connate, and thickened, clavate, recurved stigmas. A new combination is provided under Synostemon for Sauropus podenzanae as Synostemon podenzanae (S.Moore) I.Telford & Pruesapan and Sauropus convallarioides J.T.Hunter & J.J.Bruhl is formally placed in synonymy under Synostemon sphenophyllus. Descriptions, distributional data and notes on ecology and conservation status are provided for these species. Phyllanthus albiflorus F.Muell. ex Müll.Arg., the basionym of Synostemon albiflorus, is lectotypified.

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Uddin, M. Nazim, M. Oliur Rahman, and M. Atiqur Rahman. "New records of three species and a genus of the Euphorbiaceae for Bangladesh." Bangladesh Journal of Plant Taxonomy 25, no. 1 (June 27, 2018): 93–99. http://dx.doi.org/10.3329/bjpt.v25i1.37185.

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Three species belonging to two genera of the family Euphorbiaceae are beingreported here as new records for Bangladesh, viz., Cleidiocarpon laurinum Airy Shaw, Euphorbia pycnostegia Boiss. and Euphorbia repens K. Koch. The genus Cleidiocarpon Airy Shaw is also a new generic record for Bangladesh. One cultivated species, Acalypha wilkesiana Muell.-Arg., is reported as addition to the account of the Euphorbiaceae of Bangladesh. Description and photographs of these species are provided.Bangladesh J. Plant Taxon. 25(1): 93-99, 2018 (June)

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MIDDAY, MRINMOY, JAYANTA GHOSH, and DEBABRATA MAITY. "Taxonomic circumscription, new synonym and lectotypification of Saxifraga umbellulata (Saxifragaceae)." Phytotaxa 480, no. 1 (January 15, 2021): 97–102. http://dx.doi.org/10.11646/phytotaxa.480.1.11.

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Saxifraga umbellulata Hook & Thomson (1857:71), an Eastern Himalayan member of the genus Saxifraga Linnaeus (1753:398) (Saxifragaceae) was described based on specimens collected from the Sikkim Himalaya. The species was characterized by having a brown, densely glandular stem; many basal, very thick, fleshy (leathery), glabrous or sparsely setose-ciliate leaves, forming a rosette; few to several, erect, yellow flowers in a terminal subumbellate inflorescence. At present, the species is distributed in Nepal, India (Sikkim), Bhutan and China (Tibet) (Pan et al. 2001, Maity et al. 2018). Later Marquand and Airy Shaw described S. umbellulata f. pectinata Marquand & Airy Shaw in Marquand (1929:183) (Fig. 1) based on a few specimens, collected by F. Kingdon Ward from Pasum Lake in Tibet (Xizang), China, with cartilaginous setose-ciliate margin of basal leaves and yellow flowers. Pan (1992) raised this taxon to the rank of variety as S. umbellulata var. pectinata (C.Marquand & Airy Shaw) Pan (1992:165). Until now the variety has been accepted taxonomically.

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45

Khonina, S., A. Porfirev, S. Fomchenkov, A. Larkin, and A. Savelyev-Trofimov. "Generation of closely located light spots using specular Airy laser beams." Computer Optics 41, no. 5 (2017): 661–69. http://dx.doi.org/10.18287/2412-6179-2017-41-5-661-669.

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We conduct a comparative numerical study of the formation of closely located light spots in the focal plane of diffraction gratings and binary optical elements matched with Hermite-Gaussian modes and specular Airy beams. It is shown that while gratings allow a set of uniform focal spots to be generated with high accuracy, the resulting pattern quickly deteriorates when displaced from the focal plane. Due to their modal properties, Hermite-Gaussian beams are low-sensitive to defocusing, but produce focal spots different in size and intensity. Specular Airy beams offer a trade-off solution - they produce a more uniform intensity pattern of light spots than the Hermite-Gaussian modes, at the same time showing a lower sensitivity to defocusing. Experiments with a tunable laser have confirmed the above-mentioned advantages of the specular Airy beams in comparison with the Hermite-Gaussian modes, also showing good spectral stability of the manufactured diffraction optics.

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Xu, Ancheng. "Image system analysis of human eye wave-front aberration on the basis of HSS." Modern Physics Letters B 31, no. 19-21 (July 27, 2017): 1740036. http://dx.doi.org/10.1142/s021798491740036x.

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Hartmann–Shack sensor (HSS) has been used in objective measurement of human eye wave-front aberration, but the research on the effects of sampling point size on the accuracy of the result has not been reported. In this paper, point spread function (PSF) of the whole system mathematical model was obtained via measuring the optical imaging system structure of human eye wave-front aberration measurement. The impact of Airy spot size on the accuracy of system was analyzed. Statistics study show that the geometry of Airy spot size of the ideal light source sent from eye retina formed on the surface of HSS is far smaller than the size of the HSS sample point image used in the experiment. Therefore, the effect of Airy spot on the precision of the system can be ignored. This study theoretically and experimentally justifies the reliability and accuracy of human eye wave-front aberration measurement based on HSS.

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Zhou, Yuan, Feng Lin, Chao Tan, and Xi Quan Fu. "Scaling of Diffraction Range for Propagation Characteristics of the Finite Energy Airy Beam on the Analogy of its Main Lobe and Gaussian Beam." Advanced Materials Research 710 (June 2013): 390–94. http://dx.doi.org/10.4028/www.scientific.net/amr.710.390.

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In this paper, by analyzing the main lobe of the Airy beam and its fitting Gaussian beam, we define the Rayleigh range of Airy beam based on the width of FEABs main lobe for scaling the propagation characteristic of the Airy beam. The similar diffraction-free distance of FEAB (here, the width of the main lobe expanding to times) can be scaled by Rayleigh range, but it is from infinite (Pure non-diffraction beam) to one Rayleigh range (the same with Gaussian beam) when decay factor is from 0 to 1. On the contrary, although the FEAB with smaller decay factor () can propagate more Rayleigh ranges keeping diffraction-free, the effective energy in the main lobe is low by studying the power in the bucket (PIB). If more energy needing in the main lobe, the FEAB need bigger decay factor () will become more similar with Gaussian beam which can propagate about one Rayleigh range.

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48

Edwin, Royer. "Airy view." Physics World 7, no. 9 (September 1994): 20. http://dx.doi.org/10.1088/2058-7058/7/9/21.

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49

Shinn. "Airy Nothings." Fourth Genre: Explorations in Nonfiction 17, no. 2 (2015): 85. http://dx.doi.org/10.14321/fourthgenre.17.2.0085.

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50

Henrich-Franke, Christian. "Airy Curtains." East Central Europe 41, no. 2-3 (December 3, 2014): 158–79. http://dx.doi.org/10.1163/18763308-04103001.

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After the Second World War, the infrastructural connections between the Western and the Eastern part of Europe were subsequently cut. The sealing of the passages through the Iron Curtain did not, however, succeed entirely. One increasingly important breach was generated by radio frequencies, which carried broadcasting programs, for example, from Radio Free Europe, straight across the Iron Curtain. This paper analyses the negotiations on the broadcasting map of Europe by focusing on the broadcasting conference of Geneva 1974/75, which moved the “Airy Curtains” much more westward. Three factors explain the Eastern European success. First, Eastern European delegations followed a coordinated strategy in contrast to the Western European ones. Second, the hierarchical ussr leadership made sure that the Eastern European countries stuck to their strategy, whereas Western European countries preferred to depend on themselves. Third, the Eastern bloc let politics and politicians rule, while in Western Europe, to the contrary, frequency allocation was a battle that was largely fought by technicians. The gap between the “political East” and the “technical West” was an important advantage for the East. Focus in this article is put on the radio stations which were situated in Berlin because the city was an important bridgehead for Western broadcasters on socialist territory.

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Journal articles on the topic 'Airy'

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