Localized S-inversion of time-domain electromagnetic data

Journal ArticleInterpretation of time-domain electromagnetic (TDEM) data over inhomogeneous geological structures is a challenging problem of geophysical exploration. The most widely used approach of interpreting TDEM data is based on the smooth 1-D layered resistivity inversion. We have developed an effective technique of fast TDEM inversion based on thin-sheet conductance approximation that we call S-inversion. In this paper we extend the S-inversion technique, approximating the conductivity cross-section by adding a local inhomogeneous disk with an excess conductance 1S to the horizontal conductive thin sheet used in S-inversion. Localized S-inversion determines the distribution of this excess conductance as a function of a depth and a horizontal coordinate. This new method takes into account the limited horizontal extent of the inhomogeneities, localizing inversion. The numerical modeling results and inversion of practical TDEM data demonstrate that the method resolves local geological targets better than traditional 1-D inversion and original S-inversion. The method can be applied to interpret both ground and airborne TDEM data sets

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

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

Three-dimensional structure of Mach cones in monolayer complex plasma

Structure of Mach cones in a crystalline complex plasma has been studied experimentally using an intensity sensitive imaging, which resolved particle motion in three dimensions. This revealed a previously unknown out-of-plane cone structure, which appeared due to excitation of the vertical wave mode. The complex plasma consisted of micron sized particles forming a monolayer in a plasma sheath of a gas discharge. Fast particles, spontaneously moving under the monolayer, created Mach cones with multiple structures. The in-plane cone structure was due to compressional and shear lattice waves.Comment: Accepted for publication in Physical Review Letter

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.Comment: 14 page

Group classification of (1+1)-Dimensional Schr\"odinger Equations with Potentials and Power Nonlinearities

We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$ $\gamma$ is a real non-zero constant. We construct all the possible inequivalent potentials for which these equations have non-trivial Lie symmetries using a combination of algebraic and compatibility methods. The proposed approach can be applied to solving group classification problems for a number of important classes of differential equations arising in mathematical physics.Comment: 10 page