Global exact controllability of 1d Schrödinger equations with a polarizability term

We consider a quantum particle in a 1d interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with respect to the control), we prove global exact controllability in a suitable space for arbitrary potential and arbitrary dipole moment. This term is relevant both from the mathematical and physical points of view. The proof uses tools from the bilinear setting and a perturbation argument.     

Critical properties of the double-frequency sine-Gordon model with applications

We study the properties of the double-frequency sine-Gordon model in the vicinity of the Ising quantum phase transition displayed by this model. Using a mapping onto a generalized lattice quantum Ashkin–Teller model, we obtain critical and nearly-off-critical correlation functions of various operators. We discuss applications of the double-sine-Gordon model to one-dimensional physical systems, like spin chains in a staggered external field and interacting electrons in a staggered potential.     

Photochemical transformations of 7-dehydrocholesterol

Russian Journal of Applied Chemistry - Photochemical transformations of 7-dehydrocholesterol were performed with a two-lamp experimental circulation installation equipped with a ferrioxalate...     

New DNA Methylation Inhibitors Based on 1,2,4-Triazole Thioether Derivatives

New 4-substituted 4H-1,2,4-triazole-3-thiol derivatives were synthesized by introducing benzylsulfanylethyl groups in the 5-position of the heterocycle. Alkylation of the thiol group provides additional pharmacophore thioether, carboxamide, carboxyl, and hydroxyethyl fragments. Regardless of the nature of the substituents in the position 5 aminomethylation and cyanoethylation proceed at the N₂ atom. The synthesized compounds were studied for anti-tumor activity and the effect on the methylation level of tumor DNA.     

Zero-modes and thermodynamics of disordered spin-1/2 ladders

The influence of non-magnetic doping on the thermodynamic properties of two-leg S = 1/2 spin ladders is studied in this paper. It is shown that, for a weak interchain coupling, the problem can be mapped onto a model of random mass Dirac (Majorana) fermions. We investigate in detail the structure of the fermionic states localized at an individual mass kink (zero-modes) in the framework of a generalized Dirac model. The low-temperature thermodynamic properties are dominated by these zero-modes. We use the single-fermion density of states, known to exhibit the Dyson singularity in the zero-energy limit, to construct the thermodynamics of the spin ladder. In particular, we find that the magnetic susceptibility χ diverges at T → 0 as 1/T ln²(1/T), and the specific heat behaves as C 1/ln³(1/T). The predictions on magnetic susceptibility are consistent with the most recent results of quantum Monte Carlo simulations on doped ladders with randomly distributed impurities. We also calculate the average staggered magnetic susceptibility induced in the system by such defects.     

Experimental investigation of preset electrostatic fields in a quasi-electrode system

We describe the results of implementation and breadboard investigations of the method for obtaining constant electric fields of a preset form in a quasi-electrode system. We have constructed a prototype (12 cm in diameter and 30 cm in length) with 36 filamentary electrodes fed with potentials from divider systems with azimuthal distribution laws corresponding to cosθ′, cos2θ′, and cos3θ′ laws with the maximal voltages up to ±2.4 kV. As a result, the electric dipole, quadrupole, and sextupole fields are formed. These fields are analyzed for a 2D cross section of the prototype by physical simulation on a specially developed device with conducting paper. The distributions of the families of equipotential curves measured using the bridge circuit are considered and the strengths of the three types of electric fields are calculated. The results indicate the attainment of all predicted fields with preset parameters and a working area of the aperture of ≥84%. Some other favorable features are also outlined and a number of technical recommendations for producing such fields are given.     

Bounded point derivations on R(x) and approximation with simultaneous interpolation

Translated from Matematicheskii Zametki, Vol. 49, No. 3, pp. 66–72, March, 1991.     

An optical study of high-pressure water-jet dynamics

This paper considers the results of an optical study of high-speed fluid jets ejected from a nozzle at 400 MPa. The objective was to study two-phase flows under extreme conditions and to analyze the possibility of the optimization of the device design. The process of a high-speed water jet as it exits the focusing tube of the Flow WaterJet Mach3 abrasive cutting machine, along with its development, and the state of the stationary flow are considered. The shadow method was used to investigate the initial stage of high-speed water-jet formation, as well as the jet-head dynamics during the first 200–400 µs after ejection at 400 MPa. A Photron FASTCAM SA5 high-speed camera with a frame rate of one million shots per second and an exposure time of 1 [mu]s and a FLIR SC7000 infrared thermal camera with a frame rate of 400 shot/s and an exposure time of 1 ms were employed in order to study the jet-formation process. The spatiotemporal characteristics of the jet-development process were analyzed. The jet velocity and the starting jet head acceleration were measured by post-processing of digital images.     

Light-controlled reorientation of nematic liquid crystal driven by an electric field

The joint influence of optical and (quasi-)static electric fields on the orientation of liquid crystal gives rise to peculiar effects. In this article we report on the generation of transient domains in liquid crystals, which are an order of magnitude larger than the size of the optical field profile. The formation of such a domain is due to the fact that the initially present optical field reverses the pre-tilt, and the voltage that is then applied gives rise to an amplification of the tilt angle. The resulting reorientation of the director strongly depends on the starting conditions of the preliminary present optical field. We demonstrate different switching conditions, depending on the relation between the incident angle of the beam and the pre-tilt angle. The resulting refractive index profiles give rise to lensing effects.