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1

Murray, D. R., and P. Öhberg. "Matter wave focusing." Journal of Physics B: Atomic, Molecular and Optical Physics 38, no. 8 (2005): 1227–34. http://dx.doi.org/10.1088/0953-4075/38/8/012.

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2

Xu, Guochun, Hongbin Hao, Qingwei Ma, and Qinqin Gui. "An Experimental Study of Focusing Wave Generation with Improved Wave Amplitude Spectra." Water 11, no. 12 (2019): 2521. http://dx.doi.org/10.3390/w11122521.

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We experimentally investigate the generating results of space-time focusing waves based on two new wave spectra, i.e., the quasi constant wave amplitude spectrum (QCWA) and the quasi constant wave steepness spectrum (QCWS), in which amplitude and steepness for each wave component can be adjusted with fixed wave energy. The wavemaker signal consists of a theoretical wavemaker motion signal and two different auxiliary functions at two ends of the signal. By testing a series of focusing waves in a physical wave tank, we found that with given wave energy, the QCWA spectrum can produce a focusing w
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3

Smit, Pieter Bart, T. T. Janssen, and T. H. C. Herbers. "TOPOGRAPHY-INDUCED FOCUSING OF RANDOM WAVES." Coastal Engineering Proceedings 1, no. 33 (2012): 6. http://dx.doi.org/10.9753/icce.v33.waves.6.

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Refraction of narrow-band surface waves in coastal areas can result in wave-focal zones where due to interference, wave statistics vary rapidly and on similar length scales as those of individual waves. However such interference patterns, or wave coherence, are not accounted for in conventional stochastic wave models that are based on the energy balance equation or radiative transfer equation. In this work we present a quasi-coherent theory, which is an extension of the radiative transfer equation and quasi-homogeneous theory. We show that this new stochastic modelling approach can resolve rap
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4

Vogel, K., F. Gleisberg, N. L. Harshman, et al. "Optimally focusing wave packets." Chemical Physics 375, no. 2-3 (2010): 133–43. http://dx.doi.org/10.1016/j.chemphys.2010.07.002.

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5

Chen, Jinbing, and Dmitry E. Pelinovsky. "Rogue periodic waves of the focusing nonlinear Schrödinger equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2210 (2018): 20170814. http://dx.doi.org/10.1098/rspa.2017.0814.

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Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov–Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine
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6

Zhang, Zhen Fu, Xin Wu Zeng, Qing Yu Cai, and Kai Feng Han. "Numerical Simulation on Underwater Shock Wave Focusing." Applied Mechanics and Materials 105-107 (September 2011): 121–26. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.121.

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Shock wave focusing by an ellipsoidal reflector can produce higher pressure in the focal region. The focusing process of shock wave was studied by theory analyses and numerical results. Base on the experimental observation the shock wave source is equivalent to the explosion of an underwater explosive. A finite element model was set up to investigate the shock wave focusing behaviors. Both the pressure-time history and the peak pressure along the axial position were presented. The shock wave focusing process was shown. The interactions of waves in the focal region are shown. A modified EOS of
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7

Merkoune, D., J. Touboul, N. Abcha, D. Mouazé, and A. Ezersky. "Focusing wave group on a current of finite depth." Natural Hazards and Earth System Sciences 13, no. 11 (2013): 2941–49. http://dx.doi.org/10.5194/nhess-13-2941-2013.

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Abstract. Formation of freak waves resulting from the wave packets propagating in finite water depth on the background of a current is studied experimentally and numerically. In the experiment, the freak waves appear as a result of dispersion focusing of wave train excited by wave maker with modulated frequency. The space evolution of the frequency modulated train is studied in numerical simulations. We showed that in the water of finite depth, a distance of focusing increases and amplitude in the focal point decreases in comparison with infinite water depth. Experimental results are in good a
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8

Zhou, Binzhen, Kanglixi Ding, Jiahao Wang, Lei Wang, Peng Jin, and Tianning Tang. "Experimental study on the interactions between wave groups in double-wave-group focusing." Physics of Fluids 35, no. 3 (2023): 037118. http://dx.doi.org/10.1063/5.0142042.

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Nonlinear interactions in wave-group focusing are regarded as one of the main mechanisms in the generation of destructive extreme waves. In real seas, the wideband bimodal state is a typical configuration, containing interactions within a single wave group and between different wave groups. The former has been well uncovered under the assumption of narrow bandwidth, but the latter is poorly understood. In this paper, physical experiments are conducted to reveal the physics of double-wave-group focusing considering various energy distributions. Superposed wavemaker signals generated by the iter
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9

Liu, Mao, Haijie Yu, and Ben Wang. "Tuning and controlling antiplane shear wave propagation in elastic membranes." AIP Advances 12, no. 8 (2022): 085319. http://dx.doi.org/10.1063/5.0103469.

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In this paper, a rotary-focusing device for the antiplane shear wave is constructed to control and guide elastic wave energy transmission in elastic membranes. The designed device can cloak the antiplane shear waves outside the device and has a rotary-focusing effect on the shear waves energy inside the device in a membrane. The multilayered isotropic material properties of the rotary-focusing device are derived based on the transformation and rotary medium method, and a rotation parameter to guide the propagating trajectories of the antiplane shear waves is introduced. The efficiency of the r
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10

Vines, R. E., Shin-ichiro Tamura, and J. P. Wolfe. "Surface Acoustic Wave Focusing and Induced Rayleigh Waves." Physical Review Letters 74, no. 14 (1995): 2729–32. http://dx.doi.org/10.1103/physrevlett.74.2729.

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11

Vines, R. E., Shin-ichiro Tamura, and J. P. Wolfe. "Surface Acoustic Wave Focusing and Induced Rayleigh Waves." Physical Review Letters 75, no. 9 (1995): 1873. http://dx.doi.org/10.1103/physrevlett.75.1873.

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12

CHAMPEAUX, S., T. PASSOT, and P. L. SULEM. "Alfvén-wave filamentation." Journal of Plasma Physics 58, no. 4 (1997): 665–90. http://dx.doi.org/10.1017/s0022377897006119.

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Transverse focusing or filamentation of weakly nonlinear Alfvén waves propagating in a dispersive medium is studied using an amplitude-equation formalism. Special attention is devoted to the small-β regime, where kinetic effects are weak and Alfvén-wave trains are unstable to convective filamentation. It is shown that, according to their initial duration, focusing wave packets can collapse in a finite distance or, conversely, the focusing can be arrested by the development of magnetosonic waves, which in both cases may lead to the formation of sharp acoustic fronts. This effect, which dominate
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13

Hayashi, Takahiro, Koichiro Kawashima, Zongqi Sun, and Joseph L. Rose. "Guided Wave Focusing Mechanics in Pipe." Journal of Pressure Vessel Technology 127, no. 3 (2005): 317–21. http://dx.doi.org/10.1115/1.1990209.

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Guided waves can be used in pipe inspection over long distances. Presented in this paper is a beam focusing technique to improve the S∕N ratio of the reflection from a tiny defect. Focusing is accomplished by using nonaxisymmetric waveforms and subsequent time delayed superposition at a specific point in a pipe. A semianalytical finite element method is used to present wave structure in the pipe. Focusing potential is also studied with various modes and frequencies.
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14

WATANABE, Yasunori, and Takashi OGUMA. "WAVE PACKET FOCUSING UNIFORM CURRENT." Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 77, no. 2 (2021): I_31—I_36. http://dx.doi.org/10.2208/kaigan.77.2_i_31.

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15

Aktosun, Tuncay, and James H. Rose. "Wave focusing on the line." Journal of Mathematical Physics 43, no. 7 (2002): 3717–45. http://dx.doi.org/10.1063/1.1483894.

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16

Wang, Weizhi, Arun Kamath, Csaba Pakozdi, and Hans Bihs. "Investigation of Focusing Wave Properties in a Numerical Wave Tank with a Fully Nonlinear Potential Flow Model." Journal of Marine Science and Engineering 7, no. 10 (2019): 375. http://dx.doi.org/10.3390/jmse7100375.

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Nonlinear wave interactions and superpositions among the different wave components and wave groups in a random sea sometimes produce rogue waves with extremely large wave heights that appear unexpectedly. A good understanding of the generation and evolution of such extreme wave events is of great importance for the analysis of wave forces on marine structures. A fully nonlinear potential flow (FNPF) model is proposed in the presented paper to investigate the different factors that influence the wave focusing location, focusing time and focusing wave height in a numerical wave tank. Those facto
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17

Ermanyuk, E. V., N. D. Shmakova, and J. B. Flór. "Internal wave focusing by a horizontally oscillating torus." Journal of Fluid Mechanics 813 (January 26, 2017): 695–715. http://dx.doi.org/10.1017/jfm.2016.871.

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This paper presents an experimental study on internal waves emitted by a horizontally oscillating torus in a linearly stratified fluid. Two internal wave cones are generated with the kinetic energy focused at the apices of the cones above and below the torus where the wave amplitude is maximal. Their motion is measured via tracking of distortions of horizontal fluorescein dye planes created prior to the experiments and illuminated by a vertical laser sheet. The distortion of the dye planes gives a direct access to the Lagrangian displacement of local wave amplitudes and slopes, and in particul
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18

BÜHLER, OLIVER, and CAROLINE J. MULLER. "Instability and focusing of internal tides in the deep ocean." Journal of Fluid Mechanics 588 (September 24, 2007): 1–28. http://dx.doi.org/10.1017/s0022112007007410.

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The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation.As part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simp
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19

Li, Chi-Yu, Ruey-Syan Shih, and Wen-Kai Weng. "Investigation of Ocean-Wave-Focusing Characteristics Induced by a Submerged Crescent-Shaped Plate for Long-Crested Waves." Water 12, no. 2 (2020): 509. http://dx.doi.org/10.3390/w12020509.

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The need for renewable energy has gained importance with growing concerns about climate change. Wave energy has attracted considerable attention owing to its sustainability potential. Reflection, refraction, diffraction, and shoaling of waves occur when waves propagate through a submerged structure. These mechanics, when properly utilized, can be employed to focus waves to a specific location and also to increase wave heights, by which wave energy is usually represented, for planning and designing wave farms. Wave focusing induced by a submerged crescent-shaped plate for different wave conditi
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20

Sun, Zongqi, Li Zhang, and Joseph L. Rose. "Flexural Torsional Guided Wave Mechanics and Focusing in Pipe." Journal of Pressure Vessel Technology 127, no. 4 (2005): 471–78. http://dx.doi.org/10.1115/1.2065587.

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Theoretical work on flexural torsional guided waves in pipe is presented along with angular profile experimental justification. Combined with previous work on flexural longitudinal modes and axisymmetric longitudinal and torsional modes, this work now forms a framework of nonaxisymmetric guided wave mechanics in pipe. Pipe inspection experiments are also carried out by flexural torsional wave focusing to demonstrate the advantages of the focusing technique.
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21

DONATO, A. N., D. H. PEREGRINE, and J. R. STOCKER. "The focusing of surface waves by internal waves." Journal of Fluid Mechanics 384 (April 10, 1999): 27–58. http://dx.doi.org/10.1017/s0022112098003917.

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The surface current generated by internal waves in the ocean affects surface gravity waves. The propagation of short surface waves is studied using both simple ray theory for linear waves and a fully nonlinear numerical potential solver. Attention is directed to the case of short waves with initially uniform wavenumber, as may be generated by a strong gust of wind. In general, some of the waves are focused by the surface current and in these regions the waves steepen and may break. Comparisons are made between ray theory and the more accurate solutions. For ray theory, the occurrence of focusi
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22

Georgieva, M., A. Shivarova, and I. Urdev†. "Self-focusing of surface waves in a cylindrical plasma waveguide." Journal of Plasma Physics 52, no. 3 (1994): 391–407. http://dx.doi.org/10.1017/s0022377800027215.

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Self-consistent nonlinear changes of plasma parameters and characteristics of electromagnetic guided waves are studied with regard to the effect of self- focusing and waveguided channel formation in a cylindrical plasma waveguide. Besides the nonlinearity due to the ponderomotive force action usually involved, ionization nonlinearity specified for different regimes of particle loss mechanisms is considered. An azimuthally symmetric electromagnetic surface wave is the guided mode that forms and sustains the wave channel.The nonlinear dispersion law and the nonlinear changes in the wave field di
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23

Jeon, Wooyoung, Sunho Park, Gyu-Mok Jeon, and Jong-Chun Park. "Computational Study on Rogue Wave and Its Application to a Floating Body." Applied Sciences 12, no. 6 (2022): 2853. http://dx.doi.org/10.3390/app12062853.

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A rogue wave is a huge wave that is generated by wave energy focusing. Rogue waves can cause critical damage to ships and offshore platforms due to their great wave energy and unpredictability. In this paper, to generate a rogue wave, a bull’s-eye wave, which is a focusing of multi-directional waves, was simulated in a numerical wave tank. A multi-directional wave generating boundary was developed using OpenFOAM, which is an open-source computational fluid dynamics (CFD) library. The wave height and profile of the generated rogue wave were compared to those of the regular wave. In addition, th
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24

Liu, Dianyong, Yuxiang Ma, Guohai Dong, and Marc Perlin. "Detuning and wave breaking during nonlinear surface wave focusing." Ocean Engineering 113 (February 2016): 215–23. http://dx.doi.org/10.1016/j.oceaneng.2015.12.048.

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25

Zhang, Haiming, Aifeng Tao, Junhao Tu, Junwei Su, and Shuya Xie. "The Focusing Waves Induced by Bragg Resonance with V-Shaped Undulating Bottom." Journal of Marine Science and Engineering 9, no. 7 (2021): 708. http://dx.doi.org/10.3390/jmse9070708.

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Intensive wave reflection occurs when the wavelengths of the incident waves and bottom undulations are in a 2:1 ratio. Existing studies have included the Bragg resonance phenomenon of waves passing over a continuous undulating bottom parallel to and oblique to the shoreline. More generally, the Bragg resonance mechanism is used as a means of coastal protection, rather than wave power generation. To focus the wave energy in a specific area, here, we propose sinusoidal sandbars of a horizontal V-shaped pattern, which is formed by two continuous undulating bottoms inclined at an angle to each oth
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26

IBRAHIM, SLIM. "GEOMETRIC-OPTICS FOR NONLINEAR CONCENTRATING WAVES IN FOCUSING AND NON-FOCUSING TWO GEOMETRIES." Communications in Contemporary Mathematics 06, no. 01 (2004): 1–23. http://dx.doi.org/10.1142/s0219199704001239.

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With the methods used in [1] and [4], we prove that in the absence of focus, nonlinear geometrical optics of the critical wave equation with variable coefficients, is reduced to linear geometrical optics combined with wave operators for the critical wave equation with coefficients fixed on concentrating points. On the odd-dimensional spheres, we prove that passing through a focus is generated by a modified scattering operator.
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27

Sadin, D. V., B. V. Belyaev, and V. A. Davidchuk. "EFFECT OF RELAXATION PROCESSES ON THE SHOCK WAVE FOCUSING IN A GAS SUSPENSION CLOUD." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 66 (2020): 121–31. http://dx.doi.org/10.17223/19988621/66/10.

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In this paper, the interaction of a plane shock wave in air with a cylindrical region of a gas suspension and the effect of relaxation processes for various particle sizes on the refraction and focusing of the shock wave are studied. In the course of numerical modeling, the Euler approach is used to describe non-equilibrium motion of the gas and dispersed phases. A second order accuracy method in space and time is used. Verification of the method through test problems by comparing with exact solutions and calculations of other authors confirms a capability of detecting shock wave refraction ef
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28

Mukherjee, Joydeep, and A. Roy Chowdhury. "Self-focusing of Nonlinear Waves in a Relativistic Plasma with Positive and Negative Ions." Australian Journal of Physics 47, no. 6 (1994): 773. http://dx.doi.org/10.1071/ph940773.

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We have analysed the phenomenon of self-focusing of nonlinear waves in a relativistic plasma consisting of both positive and negative ions, which are assumed to be hot. We also consider the effect of the inertia of the relativistic electron by treating it dynamically. A modified form of reductive perturbation is used to deduce a nonlinear Schr�dinger equation describing the purely spatial variation of the nonlinear wave. Self-focusing of the wave can be ascertained by analysing the transversal stability of the solitary wave. It is shown that the zones of stability of the wave may become wider
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29

Infeld, E. "Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas." Journal of Plasma Physics 33, no. 2 (1985): 171–82. http://dx.doi.org/10.1017/s0022377800002415.

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The Zakharov-Kuznetsov equation describing Korteweg–de Vries waves and solitons in a strong, uniform magnetic field is rederived taking space stretching to be isotropic. This equation is then used to investigate nonlinear waves and solitons for long-wave instabilities. A solid angle of instability develops around the plane perpendicular to the magnetic field. For weakly nonlinear waves this angle is very narrow: widening as the amplitude of the nonlinear wave is increased. The soliton wave is unstable for all directions other than parallel to the field. Previous results of other authors, limit
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30

SHRIRA, VICTOR I., and WILLIAM A. TOWNSEND. "Inertia-gravity waves beyond the inertial latitude. Part 1. Inviscid singular focusing." Journal of Fluid Mechanics 664 (October 15, 2010): 478–509. http://dx.doi.org/10.1017/s0022112010003812.

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The paper is concerned with analytical study of inertia-gravity waves in rotating density-stratified ideal fluid confined in a spherical shell. It primarily aims at clarifying the possible role of these motions in deep ocean mixing. Recently, it was found that on the ‘non-traditional’ β-plane inertia-gravity internal waves can propagate polewards beyond their inertial latitude, where the wave frequency equals the local Coriolis parameter, by turning into subinertial modes trapped in the narrowing waveguides around the local minima of buoyancy frequency N. The behaviour of characteristics was e
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31

Li Yong-Feng, Zhang Jie-Qiu, Qu Shao-Bo, et al. "Circularly polarized wave reflection focusing metasurfaces." Acta Physica Sinica 64, no. 12 (2015): 124102. http://dx.doi.org/10.7498/aps.64.124102.

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32

Murashige, Sunao, and Takeshi Kinoshita. "Fundamental Studies on Ocean Wave Focusing." Journal of the Society of Naval Architects of Japan 1990, no. 168 (1990): 183–92. http://dx.doi.org/10.2534/jjasnaoe1968.1990.168_183.

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33

Apazidis, N., S. Sembian, and M. Liverts. "Supersonic jet by blast wave focusing." Physics of Fluids 33, no. 12 (2021): 126101. http://dx.doi.org/10.1063/5.0068309.

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34

Kim, Gunho, Carlos M. Portela, Paolo Celli, Antonio Palermo, and Chiara Daraio. "Poroelastic microlattices for underwater wave focusing." Extreme Mechanics Letters 49 (November 2021): 101499. http://dx.doi.org/10.1016/j.eml.2021.101499.

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35

Wang, Zhenyu, Z. X. Li, Ruifang Wang, et al. "Spin-wave focusing induced skyrmion generation." Applied Physics Letters 117, no. 22 (2020): 222406. http://dx.doi.org/10.1063/5.0029401.

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36

Lubow, Stephen H. "A wave focusing model for starbursts." Astrophysical Journal 328 (May 1988): L3. http://dx.doi.org/10.1086/185148.

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37

Watanabe, Yasunori, Yosuke Tsuda, and Ayumi Saruwatari. "Wave packet focusing in shallow water." Coastal Engineering Journal 62, no. 2 (2020): 336–49. http://dx.doi.org/10.1080/21664250.2020.1756033.

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38

Berg, Richard E. "Heat‐wave focusing by concave relectors." Physics Teacher 28, no. 1 (1990): 56–57. http://dx.doi.org/10.1119/1.2342934.

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39

Ramm, A. G., and S. Gutman. "Computational method for acoustic wave focusing." International Journal of Computing Science and Mathematics 1, no. 1 (2007): 1. http://dx.doi.org/10.1504/ijcsm.2007.013760.

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40

Smirnov, N. N., O. G. Penyazkov, K. L. Sevrouk, V. F. Nikitin, L. I. Stamov, and V. V. Tyurenkova. "Detonation onset following shock wave focusing." Acta Astronautica 135 (June 2017): 114–30. http://dx.doi.org/10.1016/j.actaastro.2016.09.014.

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41

Ishikawa, Katsuji. "Automatic focusing apparatus using ultrasonic wave." Journal of the Acoustical Society of America 78, no. 1 (1985): 284. http://dx.doi.org/10.1121/1.392513.

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42

Hosseini, S. H. R., O. Onodera, and K. Takayama. "Focusing of Converging Cylindrical Shock Wave." REVIEW OF HIGH PRESSURE SCIENCE AND TECHNOLOGY 7 (1998): 927–29. http://dx.doi.org/10.4131/jshpreview.7.927.

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43

Gowda, Vinay R., Mohammadreza F. Imani, Timothy Sleasman, and David R. Smith. "Efficient Holographic Focusing Metasurface." Electronics 10, no. 15 (2021): 1837. http://dx.doi.org/10.3390/electronics10151837.

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We present the design and experimental demonstration of an efficient holographic metasurface aperture that focuses microwaves in the Fresnel zone. The proposed circular structure consists of two stacked plates with their periphery terminated in a conductive layer. Microwaves are injected into the bottom plate, which forms the feed layer, and are coupled to the top holographic metasurface layer via an annular ring. This coupling results in an inward traveling cylindrical wave in the top layer, which serves as the reference wave for a hologram. The radiating elements consist of a slot pair with
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44

Zhuang, Ze-Peng, Rui Chen, Zhi-Bin Fan, Xiao-Ning Pang, and Jian-Wen Dong. "High focusing efficiency in subdiffraction focusing metalens." Nanophotonics 8, no. 7 (2019): 1279–89. http://dx.doi.org/10.1515/nanoph-2019-0115.

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AbstractVector beams with phase modulation in a high numerical aperture system are able to break through the diffraction limit. However, the implementation of such a device requires a combination of several discrete bulky optical elements, increasing its complexity and possibility of the optical loss. Dielectric metalens, an ultrathin and planar nanostructure, has a potential to replace bulky optical elements, but its optimization with full-wave simulations is time-consuming. In this paper, an accurate and efficient theoretical model of planar metalens is developed. Based on this model, a twof
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45

Menachof, David A., and Anthony Damian. "Mergers and alliances in the liner shipping industry: an historical perspective." Journal of Transportation Management 10, no. 2 (1998): 44–56. http://dx.doi.org/10.22237/jotm/901929900.

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This article chronicles the history of mergers and alliances in the liner shipping industry during the past century before focusing on the latest wave of mergers to hit the industry Each merger wave in the liner shipping industry generally coincided with merger waves from the general industrial world. The incentive for each wave of mergers seemed to be different, with the most recent wave focusing on synergy between the merging companies. The reduction of competing firms through mergers has implications for the shipper and these are also examined.
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46

Smirnov, Nickolay, and Valeriy Nikitin. "Three-dimensional simulation of combustion, detonation and deflagration to detonation transition processes." MATEC Web of Conferences 209 (2018): 00003. http://dx.doi.org/10.1051/matecconf/201820900003.

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The paper presents results of numerical and experimental investigation of mixture ignition and detonation onset in shock wave reflected from inside a wedge. Contrary to existing opinion of shock wave focusing being the mechanism for detonation onset in reflection from a wedge or cone, it was demonstrated that along with the main scenario there exists a transient one, under which focusing causes ignition and successive flame acceleration bringing to detonation onset far behind the reflected shock wave. Several different flow scenarios manifest in reflection of shock waves all being dependent on
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47

Fuscaldo, Walter, Santi C. Pavone, Davide Comite, et al. "Design criteria of X-wave launchers for millimeter-wave applications." International Journal of Microwave and Wireless Technologies 11, no. 9 (2019): 939–47. http://dx.doi.org/10.1017/s175907871900062x.

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AbstractBessel-beam launchers are promising and established technologies for focusing applications at microwaves. Their use in time-domain leads to the definition of a new class of devices, namely, the X-wave launchers. In this work, we discuss the focusing features of such devices with a specific interest at millimeter waves. The spatial resolutions of such systems are described under a rigorous mathematical framework to derive novel operating conditions for designing X-wave launchers. These criteria might be particularly appealing for specific millimeter-wave applications. In particular, it
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48

Beckebanze, F., C. Brouzet, I. N. Sibgatullin, and L. R. M. Maas. "Damping of quasi-two-dimensional internal wave attractors by rigid-wall friction." Journal of Fluid Mechanics 841 (February 26, 2018): 614–35. http://dx.doi.org/10.1017/jfm.2018.107.

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The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto ‘wave attractors’. For small-amplitude internal waves, the projection of energy onto higher wavenumbers by geometric focusing can be balanced by viscous dissipation at high wavenumbers. Contrary to what was previously suggested, viscous dissipation in interior shear layers may not be sufficient to explain the experiments on wave attractors in the classical quasi-two-dimensional trapezoidal laboratory set-ups. Applying
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49

MAAS, LEO R. M. "Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids." Journal of Fluid Mechanics 437 (June 22, 2001): 13–28. http://dx.doi.org/10.1017/s0022112001004074.

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Rotating fluids support waves. These inertial waves propagate obliquely through the fluid, with an angle that is fixed with respect to the rotation axis. Upon reflection, their wavelength is unchanged only when the wall obeys the local reflectional symmetry, that is, when it is either parallel or perpendicular to the rotation axis. For internal gravity waves in a density-stratified fluid, sloping boundaries thus break the symmetry of ray paths, in a two-dimensional container, predicting their focusing upon attractors: particular paths onto which the wave rays, and hence the energy, converge, a
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50

Pelinovsky, E., E. Shurgalina, and N. Chaikovskaya. "The scenario of a single freak wave appearance in deep water – dispersive focusing mechanism framework." Natural Hazards and Earth System Sciences 11, no. 1 (2011): 127–34. http://dx.doi.org/10.5194/nhess-11-127-2011.

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Abstract. One of the possible mechanisms of the emergence of freak waves in deep water, based on the dispersive focusing of unidirectional wave packets is analysed. This mechanism is associated with the frequency dispersion of water waves and manifested in the interference of many spectral components, moving with different velocities. Formation of a single freak wave in a random wind wave field is considered in the frame of linear theory. The characteristic lifetime of an abnormal wave in the framework of this mechanism for typical conditions is approximately two minutes, thus, a rapid effect
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