Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T02:09:52.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Nano-wrinkles, compactons, and wrinklons associated with laser-induced Rayleigh–Taylor instability: I. Bubble environment

Published online by Cambridge University Press:  06 April 2020

Stjepan Lugomer Open the ORCID record for Stjepan Lugomer [Opens in a new window]
Stjepan Lugomer*
Affiliation:
Center of Excellence for Advanced Materials and Sensing Devices, Rudjer Boskovic Institute, Bijenicka c. 54, 10000Zagreb, Croatia
*
Author for correspondence: S. Lugomer, Center of Excellence for Advanced Materials and Sensing Devices, Rudjer Boskovic Institute, Bijenicka c. 54, 10000Zagreb, Croatia. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study dynamics, structure and organization of the new paradigm of wavewrinkle structures associated with multipulse laser-induced RayleighTaylor (RT) instability in the plane of a target surface in the circumferential zone (C-zone) of the spot. Irregular target surface, variation of the fluid layer thickness and of the fluid velocity affect the nonlinearity and dispersion. The fluid layer inhomogeneity establishes local domains arranged (organized) in the «domain network». The traveling wavewrinkles become solitary waves and latter on become transformed into stationary soliton wavewrinkle patterns. Their morphology varies in the radial direction ofaussian-like spot ranging from the compacton-like solitons to the aperiodic rectangular waves (with rounded top surface) and to the periodic ones. These wavewrinkles may be successfully juxtapositioned with the exact solution of the nonlinear differential equations formulated in the KadomtsevPetviashvili sense taking into account the fluid conditions in particular domain. The cooling wave that starts at the periphery by the end of the pulse causes sudden increase of density and surface tension: the wavewrinkle structures become unstable what causes their break-up. The onset of solidification causes formation of an elastic sheet which starts to shrink generating lateral tension on the wavewrinkles. The focusing of energy at the constrained boundary causes the formation of wrinklons as the new elementary excitation of the elastic sheets.

Keywords

Compactonslasermatter interactionnonlinear wavespartial differential equationsRayleighTaylor instabilitysolitary waveswrinklons
Type
Research Article
Information
Laser and Particle Beams , Volume 38 , Issue 2 , June 2020 , pp. 101 - 113
Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abarzhi, SI and Rosner, R (2008) Coherent structures and pattern formation in Rayleigh–Taylor turbulent mixing. Physica Scripta 78, 015401.CrossRefGoogle Scholar
Abarzhi, SI and Sreenivasan, KR (2010) Turbulent Mixing and Beyond. Royal Society Publishing. ISBN-10 085403806X, ISBN-13 978-0854038060.Google Scholar
Abarzhi, SI, Cadjan, M and Fedorov, S (2007) Stochastic model of rayleigh-Taylor turbulent mixing. Physics Letters A 371, 457–461.CrossRefGoogle Scholar
Abarzhi, SI, Gauthier, S and Sreenivasan, KR (2013 a) Turbulent Mixing and Beyond: Non-equilibrium Processes from Atomistic to Astrophysical Scales II. Royal Society Publishing. ISBN-10 1782520384, ISBN-13 978-1782520382.Google Scholar
Abarzhi, SI, Gauthier, S and Sreenivasan, KR (2013 b) Turbulent Mixing and Beyond: Non-equilibrium Processes from Atomistic to Astrophysical Scales I. Royal Society Publishing. ISBN-10 0854039864, ISBN-13: 978-0854039869.Google Scholar
Ablowitz, MJ and Clarkson, PA (1992) Cambridge Lecture. “Solitons, Nonlinear Evolution Equations and Inverse Scattering”. New York: Press Syndicate of the University of Cambridge.Google Scholar
Adem, KR and Khalique, CM (2014) Conservatioon laws and traveling wave solutions of a generalized nonlinear ZK-BBM equation. Abstract and Applied Analysis 2014, 139513.CrossRefGoogle Scholar
Adem, KR and Khalique, CM (2015) Symmetry analysis and conservation laws of a generalized two-dimensional nonlinear KP-MEW equation. Mathematical Problems in Engineering 2015, 805763.CrossRefGoogle Scholar
Aziz, F (2011) Ion-Acoustic Solitons: Analytical, Experimental and Numerical Studies (PhD Thesis). Inst. für Plasmaforshung der Universität Stuttgart, Stuttgart. Available at: https://elib.uni-stuttgart.de/bitstream/11682/1924/1/farah_phd.pdf.Google Scholar
Ben-Yakar, A and Byer, RL (2004) Femtosecond laser ablation properties of borosilicateglass. Journal of Applied Physics 96, 5316–5323.CrossRefGoogle Scholar
Berger, KM and Milewski, PA (2000) The generation and evolution of lump solitary waves in surface-tension-dominated flows. SIAM Journal on Applied Mathematics 61, 731–750.CrossRefGoogle Scholar
Bonse, J, Baudach, S, Kruger, J, Kautek, W and Lenzner, M (2002) Femtosecond laser ablation of silicon-modification thresholds and morphology. Applied Physics A 74, 19–25.CrossRefGoogle Scholar
Chakravarty, S and Kodama, Y (2009) Soliton solutions of the KP equation and application to shallow water waves. Studies in Applied Mathematics 123, 83–151.CrossRefGoogle Scholar
Deng, S and Berry, V (2015) Wrinkled, rippled and crumpled graphene: an overview of formation mechanism, electronic properties, and applications. Materials Today 19, 197–211.10.1016/j.mattod.2015.10.002CrossRefGoogle Scholar
Dimonte, G (1999) Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Physics of Plasmas 80, 2009–2015.CrossRefGoogle Scholar
Dudley, JM, Peacock, AC and Millot, G (2001) The cancellation and dispersive phase components on the fundamental optical fiber soliton; a pedagogical note. Optics Communications 193, 253–259.CrossRefGoogle Scholar
Ganguly, A and Das, A (2015) Explicit solutions and stability analysis of the (2 + 1) dimensional KP-BBM equation with dispersion effect. Communications in Nonlinear Science and Numerical Simulation 25, 102–117.CrossRefGoogle Scholar
Gorodetsky, G, Kanicki, J, Kazyaka, T and Meicher, RI (1985) Far UV pulsed laser melting of silicon. Applied Physics Letters 46, 547–549.CrossRefGoogle Scholar
Graf, S, Kunz, C, Engel, S, Derrien, TJY and Muller, F (2018) Femtosecond laser-induced periodic surface structures on fused silica: The impact of the initial substrate temperature. Materials 11, 1340.10.3390/ma11081340CrossRefGoogle ScholarPubMed
Huang, Y, Liu, S and Zhu, H (2011) A ripple microstructure formation on a uniform-melted material surface by ns laser pulses. Physics Procedia 22, 442–448.CrossRefGoogle Scholar
Infeld, E, Senatorski, A and Skorupski, AA (1994) Decay of Kadomtsev-Petviashvili solitons. Physical Review Letters 72, 1345.CrossRefGoogle ScholarPubMed
Infeld, E, Senatorski, A and Skorupski, AA (1995) Numerical simulations of Kadomtsev-Petviashvili soliton interactions. Physical Review E 51, 3183.CrossRefGoogle ScholarPubMed
Israwi, S (2010) Variable depth KdV equations and generalizations to more nonlinear regimes. ESAIM: Mathematical Modelling and Numerical Analysis 44, 347–370.CrossRefGoogle Scholar
Kao, C-Y and Kodama, Y (2012) Numerical study of the KP equation for non-periodic waves. Mathematics and Computers in Simulation 82, 1185.CrossRefGoogle Scholar
Kuriakose, VC and Porsezian, K (2010) Elements of optical solitons: An overview. Resonance 15, 643–666.CrossRefGoogle Scholar
Li, S and Song, M (2014) Compacton-like wave and kink-like wave solutions of the generalized KP-MEW (2,2) equation. Physica Scripta 89, 035202.CrossRefGoogle Scholar
Liu, C and Dodin, IY (2015) Nonlinear frequency shift of electrostatic waves in general collisionless plasma: Unifying theory of fluid kinetic nonlinearities. Physics of Plasmas 22, 082117.CrossRefGoogle Scholar
Liu, Y, Jiang, MQ, Yang, GW, Guan, YJ and Dai, LH (2011) Surface rippling on bulk metallic glass under nanosecond pulse laser ablation. Applied Physics Letters 99, 191902.CrossRefGoogle Scholar
Lugomer, S (2007) Micro-fluid dynamics via laser-matter interactions: Vortex filament structures, helical instability, reconnection, merging, and undulation. Physics Letters A 361, 87–97.CrossRefGoogle Scholar
Lugomer, S (2016) Laser generated Richtmyer-Meshkov instability and nonlinear wave paradigm in turbulent mixing: I. Central region of Gaussian spot. Laser and Particle Beams 34, 687–704.CrossRefGoogle Scholar
Lugomer, S (2017) Laser generated Richtmyer-Meshkov instability and nonlinear wave paradigm in turbulent mixing: II. Near-Central region of Gaussian spot. Laser and Particle Beams 35, 210–225.CrossRefGoogle Scholar
Lugomer, S, Maksimovic, A, Farkas, B, Geretovzsky, Z, Toth, AL, Zolnai, Z and Barsonyi, I (2011) Multipulse irradiation of silicon by femtosecond laser pulses: Variation of surface morphology. Applied Surface Science 258, 3589–3597.CrossRefGoogle Scholar
Lugomer, S, Maksimovic, A, Geretovzsky, Z and Sorenyi, T (2013) Nonlinear waves generated on liquid silicon layer by femtosecond laser pulses. Applied Surface Science 285, 588–599.CrossRefGoogle Scholar
Meng, L, Geng, D, Yu, G, Dou, R-F, Nie, R-C and He, L (2013) Hierarchy of graphene wrinkles induced by thermal strain engineering. Applied Physics Letters 103, 251610.CrossRefGoogle Scholar
Oikawa, M and Tsuji, H (2006) Oblique interactions of weakly nonlinear long waves in dispersive systems. Fluid Dynamics Research 38, 868–898.CrossRefGoogle Scholar
Pandian, A, Stellingwerf, RF and Abarzhi, SI (2017) Effect of wave interference on nonilinear dynamics of RM flows. Physics of Fluids 2, 073903.CrossRefGoogle Scholar
Park, Y, Chai, JS, Chai, T, Lee, MJ, Jia, Q, Park, M, Lee, H and Park, BH (2014) Configuration of ripple domains and their topological defects formed under local mechanical stress on hexagonal monolayer graphene. Scientific Reports 5, 9350.Google Scholar
Reif, J, Varlamova, O, Varlamov, S and Beestehorn, M (2011) The role of asymmetric excitation in self-organized nanostructure formation upon fs laser irradiation. Applied Physics A 104, 969–973.CrossRefGoogle Scholar
Rosenau, P (2000) Compact and noncompact dispesrive patterns. Physics Letters A 275, 193–203.CrossRefGoogle Scholar
Rosenau, P (2005) What is a compacton. Notices of the AMS 52, 738–739.Google Scholar
Rosenau, P and Hyman, JM (1993) Compactons: Solitons with finite wavelength. Physical Review Letters 70, 564–567.CrossRefGoogle ScholarPubMed
Saco, PM and Kumar, P (2002) Kinematic dispersion in stream networks 1. Coupling hydraulics and network geometry. Water Resources Research 38, doi:10.1029/2001WR000695.CrossRefGoogle Scholar
Snell, J, Sivapalan, M and Bates, B (2004) Nonlinear kinematic dispersion in channel network response and scale effects: Application of the meta-channel concept. Advances in Water Resources 27, 141–154.CrossRefGoogle Scholar
Song, M and Liu, Z (2012) Periodic wave solutions and their limits for the generalized KP-BBM equation. Journal of Applied Mathematics 363879, 2012.Google Scholar
Tofeldt, O and Ryden, NJ (2017) Zero-group velocity modes in plates with continuous material variation through thickness. Journal of the Acoustical Society of America 141, 3302–3311.CrossRefGoogle Scholar
Tran, DV, Lam, YC, Zheng, HY, Murukeshan, VM, Chai, JC and Hardt, DE (2005) Femtosecond Laser Processing of Crystalline Si. Available at: https://dspace.mit.edu/handle/1721.1/7449.Google Scholar
Trtica, MS, Gakovic, BM, Radak, BB, Batani, D, Desai, T and Bussoli, M (2007) Periodic surface structures on crystalline Si created by 532 nm ps Nd:YAG laser pulse. Applied Surface Science 254, 1377–1381.CrossRefGoogle Scholar
Tsibidis, GD, Barberoglou, M, Loukakos, PA, Stratakis, E and Fotakis, C (2012) Dynamics of ripple formation on silicon surfaces by ultrafast laser pulses in subablation aconditions. Physical Review B 86, 115316.CrossRefGoogle Scholar
Vandeparre, H, Pinerua, M, Brau, F, Roman, B, Bico, J, Gaz, C, Bao, W, Lau, CN, Reis, PM and Damman, P (2011) Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains. Physical Review Letters 106, 224301.CrossRefGoogle ScholarPubMed
Varlamova, O, Costache, F, Ratzke, M and Reif, J (2007) Control parameters in patern formation upon fs laser anlation. Applied Surface Science 253, 7932–7936.CrossRefGoogle Scholar
Wai, PKA, Chen, HH and Lee, YC (1989) Radiations by solitons at the zero group-dispersion wavelength of single-mode optical fibers. Physical Review A 41, 426–439.CrossRefGoogle Scholar
Wang, J and Guo, C (2005) Ultrafast dynamics of fs laser-induced periodiic surface pattern formation on metals. Applied Physics Letters 87, 251914.CrossRefGoogle Scholar
Wazwaz, A-M (2005) The tanh method and the sine-cosine method for solving the KP-MEW equation. International Journal of Computer Mathematics 82, 235–246.CrossRefGoogle Scholar
Yang, G (2012) Laser Ablation in Liquids: Principles and Applications in the Preparation of Nanomaterials. Singapore: Pan Stanford Publishing Pte, Ltd.CrossRefGoogle Scholar
Zabusky, NJ, Lugomer, S and Zhang, S (2005) Micro-fluid dynamics via laser metal surface interactions: Wave-vortex interpretation of emerging multiscale coherent structurres. Fluid Dynamics Research 36, 291.CrossRefGoogle Scholar
Zhong, L, Tang, S, Li, D and Zhao, H (2014) Compacton, peakon, cuspon, loop solutions and smooth solitons for the generalized KP-MEW equation. Computers and Mathematics with Applications 68, 1775–1786.CrossRefGoogle Scholar
Zhou, Y (2017 a) Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. I. Physics Reports 720–722, 1–136.Google Scholar
Zhou, Y (2017 b) Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Physics Reports 723–725, 1–160.Google Scholar
Zhou, Y and Cabot, WH (2019) Time-depemdent study of anisotropy in Rayleigh-taylor instability induced turbulent flows with avariety of density ratios. Physics of Fluids 31, 084106.CrossRefGoogle Scholar
Zhou, Y, Cabot, WH and Thornber, B (2016) Asymptotic behavior of the mixed mass in Rayleigh-Taylor and Richtmayer-Meshkov instability induced flows. Physics of Plasmas 23, 052712.CrossRefGoogle Scholar
Zhou, Y, Clark, T, Clark, DF, Glendinning, S, Skiner, MA, Hantington, CF, Huricane, OA, Dimits, AM and Remington, BA (2019) Turbulent Mixing and transition crirteria of flows induced by hydrodynamic instabilities. Physics of Plasmas 26, 080901.CrossRefGoogle Scholar
Supplementary material: File

Lugomer supplementary material

Lugomer supplementary material

Download Lugomer supplementary material(File)
File 106 KB