Thin films flowing down inverted substrates: Three dimensional flow

We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three dimensional setting. In the previous work (Phys. Fluids, {\bf 22}, 052105 (2010)), we considered two dimensional flow, finding formation of surface waves whose properties within the implemented long wave model depend on a single parameter, $D=(3Ca)^{1/3}\cot\alpha$, where $Ca$ is the capillary number and $\alpha$ is the inclination angle. In the present work we consider fully 3D setting and discuss the influence of the additional dimension on stability properties of the flow. In particular, we concentrate on the coupling between the surface instability and the transverse (fingering) instabilities of the film front. We furthermore consider these instabilities in the setting where fluid viscosity varies in the transverse direction. It is found that the flow pattern strongly depends on the inclination angle and the viscosity gradient

Algebraic Model for scattering in three-s-cluster systems. I. Theoretical Background

A framework to calculate two-particle matrix elements for fully antisymmetrized three-cluster configurations is presented. The theory is developed for a scattering situation described in terms of the Algebraic Model. This means that the nuclear many-particle state and its asymptotic behaviour are expanded in terms of oscillator states of the intra-cluster coordinates. The Generating Function technique is used to optimize the calculation of matrix elements. In order to derive the dynamical equations, a multichannel version of the Algebraic Model is presented.Comment: 20 pages, 1 postscript figure, submitted to Phys. Rev.

Probability representation and quantumness tests for qudits and two-mode light states

Using tomographic-probability representation of spin states, quantum behavior of qudits is examined. For a general j-qudit state we propose an explicit formula of quantumness witnetness whose negative average value is incompatible with classical statistical model. Probability representations of quantum and classical (2j+1)-level systems are compared within the framework of quantumness tests. Trough employing Jordan-Schwinger map the method is extended to check quantumness of two-mode light states.Comment: 5 pages, 2 figures, PDFLaTeX, Contribution to the 11th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'09), June 22-26, 2009, Olomouc, Czech Republi

Quantum State Tomography Using Successive Measurements

We describe a quantum state tomography scheme which is applicable to a system described in a Hilbert space of arbitrary finite dimensionality and is constructed from sequences of two measurements. The scheme consists of measuring the various pairs of projectors onto two bases --which have no mutually orthogonal vectors--, the two members of each pair being measured in succession. We show that this scheme implies measuring the joint quasi-probability of any pair of non-degenerate observables having the two bases as their respective eigenbases. The model Hamiltonian underlying the scheme makes use of two meters initially prepared in an arbitrary given quantum state, following the ideas that were introduced by von Neumann in his theory of measurement.Comment: 12 Page

Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics

Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability representation. The problem of SIC-POVM existence is formulated in terms of symbols of operators associated with a star-product quantization scheme. We show that SIC-POVMs (if they do exist) must obey general rules of the star product, and, starting from this fact, we derive new relations on SIC-projectors. The case of qubits is considered in detail, in particular, the relation between the SIC probability representation and other probability representations is established, the connection with mutually unbiased bases is discussed, and comments to the Lie algebraic structure of SIC-POVMs are presented.Comment: 22 pages, 1 figure, LaTeX, partially presented at the Workshop "Nonlinearity and Coherence in Classical and Quantum Systems" held at the University "Federico II" in Naples, Italy on December 4, 2009 in honor of Prof. Margarita A. Man'ko in connection with her 70th birthday, minor misprints are corrected in the second versio

Nucleon-nucleon interaction in the JJ-matrix inverse scattering approach and few-nucleon systems

The nucleon-nucleon interaction is constructed by means of the $J$-matrix version of inverse scattering theory. Ambiguities of the interaction are eliminated by postulating tridiagonal and quasi-tridiagonal forms of the potential matrix in the oscillator basis in uncoupled and coupled waves, respectively. The obtained interaction is very accurate in reproducing the $NN$ scattering data and deuteron properties. The interaction is used in the no-core shell model calculations of $^3$H and $^4$He nuclei. The resulting binding energies of $^3$H and $^4$He are very close to experimental values.Comment: Text is revised, new figures and references adde

Non-equilibrium raft-like membrane domains under continuous recycling

We present a model for the kinetics of spontaneous membrane domain (raft) assembly that includes the effect of membrane recycling ubiquitous in living cells. We show that the domains have a broad power-law distribution with an average radius that scales with the 1/4 power of the domain lifetime when the line tension at the domain edges is large. For biologically reasonable recycling and diffusion rates the average domain radius is in the tens of nm range, consistent with observations. This represents one possible link between signaling (involving rafts) and traffic (recycling) in cells. Finally, we present evidence that suggests that the average raft size may be the same for all scale-free recycling schemes.Comment: 8 pages, 5 figure

Inverse spin-s portrait and representation of qudit states by single probability vectors

Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j+1)(4j+1)-dimensional probability vector whose components are labeled by spin projections and points on the sphere. Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j+3) simplex, with the boundary being illustrated for qubits (j=1/2) and qutrits (j=1). A relation to the (2j+1)^2- and (2j+1)(2j+2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.Comment: 23 pages, 4 figures, PDF LaTeX, submitted to the Journal of Russian Laser Researc

Heat treatment forming a dissipative metal base in wear-resistant chromium-alloyed cast iron

The maximum abrasive wear resistance is provided by a metal base from metastable retained austenite and martensite. Such a microstructure of 260Kh16M2 and 250Kh25MFT chromium cast irons with different types of Cr 7 C 3 and Cr 23 C 6 , carbides is created by high-temperature quenching with heating to temperatures of 1125-1170 °C and cooling in oil or air. Austenite is transformed to disperse martensite on the working surface as a result of the impact of abrasive particles during operation. Together with carbides, it provides a high hardening level and a high working capacity of the secondary microstructure of the cast irons. © 2018 Author(s)