Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p = p(\epsilon)$. For linear EOS $p = \kappa \epsilon$ we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS ($\kappa=1$) we obtain ''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Supersonic dislocations observed in a plasma crystal

Experimental results on the dislocation dynamics in a two-dimensional plasma crystal are presented. Edge dislocations were created in pairs in lattice locations where the internal shear stress exceeded a threshold and then moved apart in the glide plane at a speed higher than the sound speed of shear waves, $C_T$. The experimental system, a plasma crystal, allowed observation of this process at an atomistic (kinetic) level. The early stage of this process is identified as a stacking fault. At a later stage, supersonically moving dislocations generated shear-wave Mach cones

Comment on "Control landscapes are almost always trap free: a geometric assessment"

We analyze a recent claim that almost all closed, finite dimensional quantum systems have trap-free (i.e., free from local optima) landscapes (B. Russell et.al. J. Phys. A: Math. Theor. 50, 205302 (2017)). We point out several errors in the proof which compromise the authors' conclusion. Interested readers are highly encouraged to take a look at the "rebuttal" (see Ref. [1]) of this comment published by the authors of the criticized work. This "rebuttal" is a showcase of the way the erroneous and misleading statements under discussion will be wrapped up and injected in their future works, such as R. L. Kosut et.al, arXiv:1810.04362 [quant-ph] (2018).Comment: 6 pages, 1 figur

Coupling of non-crossing wave modes in a two-dimensional plasma crystal

We report an experimental observation of coupling of the transverse vertical and longitudinal in-plane dust-lattice wave modes in a two-dimensional complex plasma crystal in the absence of mode crossing. A new large diameter rf plasma chamber was used to suspend the plasma crystal. The observations are confirmed with molecular-dynamics simulations. The coupling manifests itself in traces of the transverse vertical mode appearing in the measured longitudinal spectra and vice versa. We calculate the expected ratio of the trace to the principal mode with a theoretical analysis of the modes in a crystal with finite temperature and find good agreement with the experiment and simulations.Comment: 4 figures, 5 pages, accepted for publication in PRL Nov 201

Diffusive transport of adsorbed n-alkanes along e-beam irradiated plane surfaces and nanopillars

Diffusion of adsorbed n-alkanes was studied by means of electron beam induced deposition (EBID) technique. Carbon ring-like and pillar-like deposits were produced on bulk and thin substrates in a scanning electron microscope (SEM) operated in a “spot” mode. Residual nalkanes used as a precursor gas were delivered to the beam interaction region (BIR) via surface diffusion. The model of adsorbate diffusion along a heterogeneous surface with different diffusion coefficients D1 and D2 outside and inside the BIR, respectively, was proposed to explain the measured deposition rates. The estimates for diffusion coefficients ranging from ~1x10-10 to ~1x10-7 cm2s-1 at room temperature on surfaces with different roughness were obtained. These estimates most likely should be attributed to n-decane molecules expected to play the key role in the deposition process. Clusters of polymerized molecules produced by irradiation were assumed to act as effective traps hampering surface diffusion. For high D1/D2 ratios the deposition rates were found to be practically independent of the substrate material and initial roughness

Observation of particle pairing in a two-dimensional plasma crystal

The observation is presented of naturally occurring pairing of particles and their cooperative drift in a two-dimensional plasma crystal. A single layer of plastic microspheres was suspended in the plasma sheath of a capacitively coupled rf discharge in argon at a low pressure of 1 Pa. The particle dynamics were studied by combining the top-view and side-view imaging of the suspension. Cross analysis of the particle trajectories allowed us to identify naturally occurring metastable pairs of particles. The lifetime of pairs was long enough for their reliable identification.Comment: 5 pages, 4 figure

Rigorous 3D inversion of marine CSEM data based on the integral equation method

Journal ArticleMarine controlled-source electromagnetic (MCSEM) surveys have become an important part of offshore petroleum exploration. However, due to enormous computational difficulties with full 3D inversion, practical interpretation of MCSEM data is still a very challenging problem. We present a new approach to 3D inversion of MCSEM data based on rigorous integral-equation (IE) forward modeling and a new IE representation of the sensitivity (Fréchet derivative matrix) of observed data to variations in sea-bottom conductivity. We develop a new form of the quasi-analytical approximation for models with variable background conductivity (QAVB) and apply this form for more efficient Fréchet derivative calculations. This approach requires just one forward modeling on every iteration of the regularized gradient-type inversion algorithm, which speeds up the computations significantly. We also use a regularized focusing inversion method, which provides a sharp boundary image of the petroleum reservoir. The methodology is tested on a 3D inversion of the synthetic EM data representing a typical MCSEM survey conducted for offshore petroleum exploration