"On the Collander equation": protein partitioning in polymer/polymer aqueous two-phase systems

Distribution coefficients of randomly selected proteins were measured in aqueous two-phase systems (ATPSs) formed by different combinations of Dextran-75 (Dex), Ficoll-70, polyethylene glycol-8000 (PEG), hydroxypropyl starch-100 (PES), and Ucon50HB5100 (Ucon, a random copolymer of ethylene glycol and propylene glycol) at particular polymer concentrations, all containing 0.15M NaCl in 0.01 M phosphate buffer, pH 7.4. Most of the proteins in the PEG-Ucon system precipitated at the interface. In the other ATPSs, namely, PES-PEG, PES-Ucon, Ficoll-PEG, Ficoll-Ucon, and in Dex-PEG and Dex-Ucon described earlier the distribution coefficients for the proteins were correlated according to the solvent regression equation: lnKi=aiolnKo+bio, where Ki and Ko are the distribution coefficients for any protein in the ith and oth two-phase systems. Coefficients aio and bio are constants, the values of which depend upon the particular compositions of the two-phase systems under comparison.     

Applications of symmetry to problem solving

Symmetry is an important mathematical concept which plays an extremely important role as a problem-solving technique. Nevertheless, symmetry is rarely used in secondary school in solving mathematical problems. Several investigations demonstrate that secondary school mathematics teachers are not aware enough of the importance of this elegant problem-solving tool. In this paper we present examples of problems from several branches of mathematics that can be solved using different types of symmetry. Teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems are discussed.     

Short-wave sectioned free-electron masers with Bragg resonators based on the traveling and quasi-critical wave coupling

We consider the possibility of implementation of a free-electron maser with a two-mirror resonator composed of modified and conventional Bragg mirrors, operated in the short-wave part of the millimeter-wave range. The use of a modified Bragg mirror based on the traveling and quasicritical wave coupling at the input of the interaction space permits the transverse-index selection of modes. Amplification of the synchronous co-propagating wave by an electron beam is reached mainly in the regular part of the resonator. Even slight reflections from the conventional output Bragg cavity, which directly couples the co- and counter-propagating traveling waves, turn out to be sufficient for generation of self-excited oscillations. It is shown that the new scheme of a free electron maser ensures the oscillation frequency stabilization with respect to the electron-energy variation. With the optimal choice of the parameters, the oscillation frequency is close to the cutoff frequency of a quasi-critical wave excited in the modified Bragg structure.     

Acoustic field outside a cylindrical region excited from inside

We present the results of numerical calculation of the acoustic field distribution in a structure consisting of three cylindrically symmetrical, infinitely long coaxial regions with identical constant density. The media in the inner and outer regions have the same sound velocity which is different from that in the intermediate region. In the inner region, a harmonic pressure source is located. Expressions for the acoustic fields in each region are derived and the field distribution in the outer region is determined. The numerical analysis is performed at the distances corresponding to the near field of the source. Characteristic features of the field structure as a function of the source frequency, the sizes of the system, and the acoustic parameters of the medium are determined. The results obtained can be used in geophysical prospecting for characterization of boreholes, in acoustic logging of wells, and in the problems of noise control near industrial and power plants.     

Solution of time-convolutionary Maxwell’s equations using parameter-dependent Krylov subspace reduction

We suggest a new algorithm for the solution of the time domain Maxwell equations in dispersive media. After spacial discretization we obtain a large system of time-convolution equations. Then this system is projected onto a small subspace consisting of the Laplace domain solutions for a preselected set of Laplace parameters. This approach is a generalization of the rational Krylov subspace approach for the solution of non-dispersive Maxwell’s systems. We show that the projected system preserves such properties of the initial system as stability and passivity. As an example we consider the 3D quasistationary induced polarization problem with the Cole–Cole conductivity model important for geophysical oil exploration. Our numerical experiments show that the introduction of the induced polarization does not have significant effect on convergence.     

Chaotic mixing and transport in a meandering jet flow

Mixing and transport of passive particles are studied in a simple kinematic model of a meandering jet flow motivated by the problem of lateral mixing and transport in the Gulf Stream. We briefly discuss a model stream function, Hamiltonian advection equations, stationary points, and bifurcations. The phase portrait of the chosen model flow in the moving reference frame consists of a central eastward jet, chains of northern and southern circulations, and peripheral westward currents. Under a periodic perturbation of the meander's amplitude, the topology of the phase space is complicated by the presence of chaotic layers and chains of oscillatory and ballistic islands with sticky boundaries immersed into a stochastic sea. Typical chaotic trajectories of advected particles are shown to demonstrate a complicated behavior with long flights in both the directions of motion intermittent with trapping in the circulation cells being stuck to the boundaries of vortex cores and resonant islands. Transport is asymmetric in the sense that mixing between the circulations and the peripheral currents is, in general, different from mixing between the circulations and the jet. The transport properties are characterized by probability distribution functions (PDFs) of durations and lengths of flights. Both the PDFs exhibit at their tails power-law decay with different values of exponents.     

Automated pulling of large-diameter alkali halide scintillation single crystals from the melt

Principles of a new high-productivity automated method for pulling large-diameter alkali halide crystals are described. On the stage of radial growth, the melt geometry is varied continuously by its level elevation in the conical crucible due to feeding by the melted raw material controlled by a lifting electrocontact probe. The melt level is stable when the crystal is grown in height. An automated system to control the crystal diameter has been developed using time intervals between feeding operations as the controlling parameter. This system allows control over the crystal diameter to an accuracy better than 1% over the range from 400 to 450 mm at the pulling rate from 6 to 6.5 mm/h. The method is used to produce scintillation alkali halide single crystals on an industrial scale.     

Aqueous biphasic systems formed by nonionic polymers I. Effects of inorganic salts on phase separation

The effect of salts KSCN, KI, KBr, KCl, KClO₄, KF, K₂SO₄ and NH₄Cl, LiCl, NaCl, KCl, CsCl on the binodials of the phase diagrams for aqueous biphasic dextranpolyvinylpyrrolidone, dextran-polyvinyl alcohol, dextran-ficoll and dextran-polyethylene glycol systems was studied. It is established that the K-salts present at the concentrations of 0.1 and 0.5 mol/kg alter the binodials of the phase diagrams for the above systems. The effect of a salt is found to be related to the lyotropy of the salt quantified by the salt molal surface tension increment. It is assumed that phase separation in an aqueous polymer biphasic system is affected by the presence of a salt mainly due to the effect of the salt on the structure and/or state of water in the system.     

Dissipation effect on chaos onset in a two-resonance overlap case

The problem of two-resonance interaction is considered in the dissipative case. A strange attractor is shown to appear under certain conditions. Hierarchy substructures are obtained when the strange attractor degenerates.