Low Density Phases in a Uniformly Charged Liquid

It is well known that quantum correlations for bipartite dichotomic measurements are those of the form \({\gamma=(\langle u_i,v_j\rangle)_{i,j=1}^n}\), where the vectors u_i and v_j are in the unit ball of a real Hilbert space. In this work we study the probability of the nonlocal nature of these correlations as a function of \({\alpha=\frac{m}{n}}\), where the previous vectors are sampled according to the Haar measure in the unit sphere of \({\mathbb R^m}\). In particular, we prove the existence of an \({\alpha_0 > 0}\) such that if \({\alpha\leq \alpha_0}\), \({\gamma}\) is nonlocal with probability tending to 1 as \({n\rightarrow \infty}\), while for \({\alpha > 2}\), \({\gamma}\) is local with probability tending to 1 as \({n\rightarrow \infty}\).     

Direct evidence of two superconducting gaps in FeSe<Subscript>0.5</Subscript>Te<Subscript>0.5</Subscript>: SnS-Andreev spectroscopy and the lower critical field

We present direct measurements of the superconducting order parameter in nearly optimal FeSe Te single crystals with the critical temperature T _C ≈ 14 K. Using the intrinsic multiple Andreev reflection effect (IMARE) spectroscopy and measurements of the lower critical field, we directly determined two superconducting gaps, Δ_L ≈ 3.3?3.4 meV and Δ_S ≈ 1 meV, and their temperature dependences. We show that a twoband model fits well the experimental data. The estimated electron–boson coupling constants indicate a strong intraband and a moderate interband interaction.     

Solution of two mutually-reducible problems in electrostatics

There are two well-known problems in electrostatics whose solutions reduce to each other. One of them is that of a grounded conductor containing a cavity with given boundary . A charge distribution is specified on another surface S inside the cavity, or within the volume enclosed by S. It is required to find the charge density induced on . The other problem is that of finding “equivalent” sets of charges (producing identical external fields). Here again there are surfaces and S and the same original distributed charge as in the first problem, but the system is now in empty space and the problem is to find the charge distribution on that produces the same external field as the given distribution on S. Mutual reducibility means that it is sufficient to consider one of the two problems, say, the second. The problem examined in this paper is that of confocal ellipsoids S and and charge distributions described in terms polynomial functions of Cartesian coordinates. The method of multipole moments which leads directly to the solution (i.e., without the need to evaluate the field) is described. Analytical solutions are given for simple surface and volume charge distributions. Special and limiting cases are examined, including degenerate surfaces S and in the form of confocal elliptic cylinders. Zh. Tekh. Fiz. 67, 1–6 (April 1997)     

Fе–Co metal–carbon nanocomposite based on IR pyrolized polyvinyl alcohol

Russian Journal of Physical Chemistry A - Powders of metal–carbon nanocomposites consisting of nanosized bimetallic Fe–Co particles dispersed in a carbon matrix are obtained via the IR...     

Performance of slotted pores in particle manufacture using rotating membrane emulsification

This paper addresses the use of different slotted pores in rotating membrane emulsification technology.Pores of square and rectangular shapes were studied to understand the effect of aspect ratio (1-3.5) and their orientation on oil droplet formation.Increasing the membrane rotation speed decreased the droplet size,and the oil droplets produced were more uniform using slotted pores as compared to circular geometry.At a given rotation speed,the droplet size was mainly determined by the pore size and the fluid velocity of oil through the pore (pore fluid velocity).The ratio of droplet diameter to the equivalent diameter of the slotted pore increased with the pore fluid velocity.At a given pore fluid velocity and rotation speed,pore orientation significantly influences the droplet formation rate: horizontally disposed pores (with their longer side perpendicular to the membrane axis) generate droplets at double the rate of vertically disposed pores.This work indicates practical benefits in the use of slotted membranes over conventional methods.     

Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model

We performed an extensive numerical study of pattern formation scenarios in the two-dimensional Gray-Scott reaction-diffusion model. We concentrated on the parameter region in which there exists a strong separation of length and/or time scales. We found that the static one-dimensional autosolitons (stripes) break up into two-dimensional radially-symmetric autosolitons (spots). The traveling one-dimensional autosolitons (wave fronts) can be stable or undergo breakup. The static two-dimensional radially-symmetric autosolitons may break up and self-replicate leading to the formation of space-filling patterns of spots, wave fronts, or spatio-temporal chaos due to the competition of self-replication and annihilation of spots upon collision. Received 6 November 2000 and Received in final form 27 February 2001     

Droplet Phases in Non-local Ginzburg-Landau Models with Coulomb Repulsion in Two Dimensions

We establish the behavior of the energy of minimizers of non-local Ginzburg-Landau energies with Coulomb repulsion in two space dimensions near the onset of multi-droplet patterns. Under suitable scaling of the background charge density with vanishing surface tension the non-local Ginzburg-Landau energy becomes asymptotically equivalent to a sharp interface energy with screened Coulomb interaction. Near the onset the minimizers of the sharp interface energy consist of nearly identical circular droplets of small size separated by large distances. In the limit the droplets become uniformly distributed throughout the domain. The precise asymptotic limits of the bifurcation threshold, the minimal energy, the droplet radii, and the droplet density are obtained.     

Stability Analysis of Artificial Ice Islands by Methods of Mathematical Modeling

Doklady Mathematics - The elastic effects on an artificial ice island produced by drill impacts and the pressure of structures located on the island are numerically modeled. The problem is solved...