In this experimental study, the ablative Richtmyer–Meshkov (RM) and the Rayleigh–Taylor (RT) instabilities were generated by the laser pulse of Gaussian-like power profile. The initial multi-modal perturbation, the inhomogeneous momentum transfer and different Atwood numbers generate different shapes of spikes and bubbles in the central region (CR) and the near-central region (NCR) of the spot. A one-dimensional Gaussian-like power profile causes the formation of the wavy-like rows of aperiodic spikes. The periodic spike segments inside the rows appear due to locally coherent flow. In the NCR, the mushroom-shape spikes tend to the organization on the isotropic square and the anisotropic rhombic lattices. The increase of the lattice periods two, three, or four times indicates formation of superstructures. The growth of sharp asymmetric RM/RT spikes in the CR is fast, uncorrelated and linear, while the growth of the symmetric mushroom-shape ones in the NCR is slow, correlated, and nonlinear.

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The 3D Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) instabilities induced by a laser pulse of the Gaussian-like power profile on a metal surface in a ‘covered target configuration’ environment evolve into complex fluid dynamics with the new paradigm of wave-vortex phenomena in turbulent mixing. Such a RM instability (RMI)/RT instability (RTI) environment is generated in a semiconfined configuration (SCC) of the experiment which causes the extended vapor/plasma lifetime and fast multiple reshocks that strike the density interface. The Gaussian power profile causes different circular regions with a different momentum transfer, different Atwood number and different RMI/RTI morphology. In the central region (CR) of the Gaussian-like spot, where the momentum transfer and Atwood number are maximal, the oscillatory field of reshocks causes the separation of small and large bubbles, the growth of bubble penetration depth and of bubble size by the formation of bubble pairs inside the cluster and their merging. Discrete merging jumps give rise to larger bubbles in the process which can be represented by the ‘Lindenmayer tree’.

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surface superheating on a ns time scale is connected with the formation of a spinodal fluid which decomposes into a gaseous phase through microexplosions, generating vortex filament structures on the vaporizing surface. Vortex filaments associated with the Reynolds number Reϳ10 3 -10 4 are organized into regular, quasiregular, or chaotic structures. Homotopic operations transfer these structures into irreducible ones of a simple closed-loop type, showing that all of them are embedded in a three-dimensional torus either as a vortex ring ͑unknotted knot͒, as a cloverleaf ͑trefoil knotted knot͒, or as Hopf links ͑knotted knot͒. ͓S0163-1829͑96͒08432-9͔The paper deals with experimental evidence of generation and organization of vortex filaments in the explosive decomposition of a spinodal fluid ͑liquid Ta͒ into a gaseous phase on the time scale р10 ns. Spinodal fluid 1,2 is generated during surface superheating of metals in high-power, short-timescale laser-metal interactions when the surface layer behaves as a dielectric. 3 It thus, becomes transparent enabling a deep volume absorption of a laser beam. 3 The vapor pressure above the surface prevents boiling, and causes superheating of the liquid metal. 1,3 The calculations of Grosse 4 ͑based on the van der Waals theory͒ have shown that superheating may in principle occur for all metals, but that the spinodal curve for some of them is flat rather than cusplike. However, for refractory metals ͑Ti, Ta, Mo, etc.͒ the cusp is large, and superheating may reach even 10 3 -10 4 K. The system is pushed into a metastable region of a thermodynamic diagram, where thermal conductivity k→0, and specific heat Cp→ϱ. 1,2 Since fluctuations play a crucial role in the metastable phase, the system is not stable, and exists only for a short time, after which it decomposes into a gaseous phase through microexplosions of surface bubbles, characteristic of the onset of ''volume'' boiling. As usually assumed, this transition occurs at QӍ10 8 W/cm 2 .The transition from planar to ''volume'' boiling is not a well-elucidated problem from the aspect of the phase diagram, nor from the aspect of surface dynamics and the corresponding surface morphology. Ultrafast cooling after pulse termination causes the surface morphology to stay permanently frozen, thus enabling a posteriori analysis.Recent studies of these problems on metals, 5 semiconductors, 6 and superconductor ceramics 7,8 shed more light on superheating on a ns time scale. In spite of the difference in the absorption process and the superheating ͑sur-face or subsurface͒ in these materials, the surface morphology associated with fully developed volume boiling is the same. The most intriguing aspect relates to the onset of volume boiling ͑not fully developed͒ associated with the reach spectrum of dynamic phenomena, and generation of a strange morphology. 5 Our studies with a Q-switched Nd:YAG ͑yttrium aluminum garnet͒ laser, with 10 ns at half width at half-maximum, at a spot size ϳ3 -4 mm, QӍ10 7 W/cm 2 performed on small samples ϳ1ϫ1ϫ0,05...

We studied the self‐organization (SO) of small‐size (D = 90 nm), medium‐size (220 nm), and large‐size (450 nm) colloidal silica nanoparticles in Langmuir‐Blodgett layers induced by a focused Ga+ ion beam with energy of 30 keV. The ion irradiation induces SO into various types of clusters as the result of particle charging and heating, Coulomb repulsion and motion on the substrate surface, as well as of particle ‐ particle and particle ‐ substrate interaction. These processes show a great difference of the underlying dynamics and of the characteristics of SO pattern, depending on the particle size and on the ion fluence. The two dimensional (2D) pattern of the small‐size particles is transformed into “infinite” chain‐cluster, while the pattern of medium‐size particles is transformed into a number of short separated chain‐clusters. The pattern of large‐size particles is mostly unchanged, but shows particle melting and buckling, which at higher fluences passes into ion beam‐induced sputtering (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Dynamics and organization of laser-generated three-dimensional (3D) Richtmyer–Meshkov (RMI) and Rayleigh–Taylor instabilities (RMI and RTI) on metal target in the semiconfined configuration are different in the central region (CR) (Lugomer, 2016), near central region (NCR) (Lugomer, 2017) and the near periphery region (NPR) of the Gaussian-like spot. The RMI/RTI in the NPR evolve from the shock and series of reshocks associated with lateral expansion and increase of the vapor density, decrease of the Atwood number and momentum transfer. Scanning electron micrographs show irregular (chaotic) web of the base-plane walls, and mushroom spikes on its nodal points with disturbed two-dimensional (2D) lattice organization. Lattice disturbance is caused by the incoherent wavy motion of background fluid due to fast reshocks, which after series of reflections change their strength and direction. Reconstruction of the disturbed lattice reveals rectangular lattice of mushroom spikes with p2mm symmetry. The splitting (bifurcation) of mushroom diameter distribution on the large and small mushroom spikes increases with radial distance from the center of Gaussian-like spot. Dynamics of their evolution is represented by the orbits or stable periods in 2D phase space. The constant mushroom diameter – stable circulation or the stable periodic orbits – are the limit cycles between the unstable spiral orbits. Those with increasing periods represent supercritical Hopf bifurcation, while those leading to decrease and disappearance represent subcritical Hopf bifurcation. The empirical models of RMI, although predict dependence of the growth rate on radial distance (distance the reshocks travel to reach the interface), show many limitations. More appropriate interpretation of the simultaneous growth and lattice organization of small and large spikes give the fundamental model based on the interference of the perturbation modes depending on their amplitude, relative phase, and the symmetry. The late-time instability in the base-plane evolves into line solitons, vortex filaments and wave–vortex structures with chaotic rather than stochastic features.

The dynamic properties of the molecular model proposed by Maier-Saupe t, 'MS) for nematic liquid crystals are investigated. It is shown that the model predicts diffusive optic soft modes, describing nematic-order-parameter fluctuations which condense at the isotropicnematic stability limit. Since the MS Hamiltonian in its usual form does not exhibit the full symmetry of the high-tempexature phase, no symmetry-recovering Goldstone mode is predicted. A rotationally invariant form of the Maier-Saupe Hamiltonian, on the other hand, predicts the existence of tv' different diffusive optic soft modes in.the nematic phase, in addition to a doubly degenerate '*magnon" mode which is the Goldstone mode of the isotropicnematic transition.