Characteristics of high-power radiating imploding discharge with cold start

A qualitative model of the dynamics of a multiterawatt radiating Z-pinch with cold start and high rate of current rise is proposed. The model is used to analyze discharges with currents I ～ 2–5 MA (with dI/dt > 10¹³ A/s) through uniform or structured plasma-producing loads, including wire arrays. The most important consequence of cold start is that spatially nonuniform plasma production is prolonged to almost the entire current rise time. Under these conditions, the Ampére force begins to play a dominant role in the plasma dynamics before the plasma-producing load is completely transformed into an accelerated plasma. The results of computations of wire-array vaporization are presented. A formula is proposed for estimating the highest attainable velocity of plasma flow into a heterogeneous liner driven by the Ampére force. It is shown that local imbalance between radial motion of the produced plasma and supply of the plasma-producing substance to be ionized leads to axially nonuniform breakthrough of magnetic flux into the liner, which precedes plasma collapse. The magnetic-flux breakthrough gives rise to a chaotic azimuthal-axial plasma structure consisting of radial plasma jets of relatively small diameter, which is called a radial plasma rainstorm. The breaking-through azimuthal magnetic flux obstructs further current flow in the breakthrough region. Analyses of Z-pinch implosion based on the theory of Rayleigh-Taylor instability or the snowplow model are incorrect under the plasma-rainstorm conditions. The processes taking place in a stagnant Z-pinch include conversion of the energy carried by the current-generated magnetic field into turbulent MHD flow of the ion component of the plasma, its convective mixing with magnetic field, heating, energy transfer from ions to electrons, and emission from the plasma. Under typical experimental conditions, emission plays a key role in the energy balance in an imploding pinch. Z-pinch is modeled by an electric-circuit component that has a time-dependent nonlinear impedance and consumes the magnetic energy supplied by a generator through a magnetically insulated transmission line (MITL). The peak power reached in the circuit is comparable to the peak soft X-ray power output emitted by the pinch in terms of magnitude and timing. Optimum matching conditions are formulated for the generator-MITL-pinch circuit.     

Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

A mathematical model of the response of the semicircular canal and otolith to vestibular system rotation under gravity

A mathematical model of the system composed of two sensors, the semicircular canal and the sacculus, is suggested. The model is described by three lines of blocks, each line of which has the following structure: a biomechanical block, a mechanoelectrical transduction mechanism, and a block describing the hair cell ionic currents and membrane potential dynamics. The response of this system to various stimuli (head rotation under gravity and falling) is investigated. Identification of the model parameters was done with the experimental data obtained for the axolotl (Ambystoma tigrinum) at the Institute of Physiology, Autonomous University of Puebla, Mexico. Comparative analysis of the semicircular canal and sacculus membrane potentials is presented. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 207–220, 2005.     

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.     

Synthesis of functionalized rab GTPases by a combination of solution- or solid-phase lipopeptide synthesis with expressed protein ligation

Prenylated proteins with non-native functionalities are generally very difficult to obtain by recombinant or enzymatic means. The semisynthesis of preparative amounts of prenylated Rab guanosine triphosphatases (GTPases) from recombinant proteins and synthetic prenylated peptides depends largely on the availability of functionalised prenylated peptides corresponding to the proteins' native structure or modifications thereof. Here, we describe and compare solution-phase and solid-phase strategies for the generation of peptides corresponding to the prenylated C terminus of Rab7 GTPase. The solid-phase with utilisation of a hydrazide linker emerges as the more favourable approach. It allows a fast and practical synthesis of pure peptides and gives a high degree of flexibility in their modification. To facilitate the analysis of semisynthetic proteins, the synthesised peptides were equipped with a fluorescent group. Using the described approach, we introduced fluorophores at several different positions of the Rab7 C terminus. The position of the incorporated fluorescent groups in the peptides did not influence the protein-ligation reaction, as the generated peptides could be ligated onto thioester-tagged Rab7. However, it was found that the positioning of the fluorescent group had an influence on the functionality of the Rab7 proteins; analysis of the interaction of the semisynthetic Rab7 proteins with REP (Rab escort protein) and GDI (guanosine diphosphate dissociation inhibitor) molecules revealed that modification of the peptide side chains or of the C-terminal isoprenoid did not significantly interfere with complex formation. However, functionalisation of the C terminus was found to have an adverse effect on complex formation and stability, possibly reflecting low structural flexibility of the Rab GDI/REP molecules in the vicinity of the lipid-binding site.     

Investigation of the extraction equilibrium of ternary ion-association complexes of thallium(III) with monotetrazolium salts triphenyltetrazolium chloride and thizolyl blue

The extraction equilibrium of ternary ion-association complexes obtained during the reaction of tetrachloride complex of thallium(III) and monotetrazolium salts triphenyltetrazolium chloride (TTC) or thiazolyl blue (MTT) has been studied. The optimum conditions that are required to carry out the investigations have been found. As a result of using a developed chemical model, the constants of extraction, distribution and association, the distribution coefficients and the recovery factor of investigated ionassociates have been determined radiochemically.     

Extraction-spectrophotometric study on the vanadium(V)-2,3-dihydroxynaphthalene — iodonitrotetrazolium chloride — water — chloroform system and its analytical application

The formation of a new ternary ion-associate complex of vanadium(V) with 2,3-dihydroxynaphthalene and iodonitrotetrazolium chloride with a composition ratio of 1:2:1 is reported. The complex is quantitatively extracted from water into chloroform. The molar absorptivity (ɛ) of the extract at λ _max=340 nm is 2.5 × 10⁴ dm³/mol cm, and Beer’s law is obeyed for concentrations ranging from 0.1 to 0.9 μg/cm³ V(V). The following constants are determined: the extraction constant, the association constant, the distribution constant, and the recovery factor. The effects of foreign ions and reagents are studied. A selective and sensitive method is developed for determination of vanadium in steels.     

Asymmetric synthesis of [7]helicene-like molecules

[reaction: see text] A new approach to nonracemic [7]helicene-like molecules has been developed. Stereoselective Co(I)-mediated [2 + 2 + 2] cycloisomerization of aromatic triynes containing an asymmetric carbon atom produces [7]helicene-like scaffolds in diastereomeric ratios up to 100:0. This central-to-helical chirality transfer can be controlled by the absolute configuration at the asymmetric center and by the presence of carbon substituents.     

Determination of trace elements in the Lavender inflorescence (Lavandula angustifolia Mill.) — Lavender oil system

Bulgaria is a famous world producer of essential oils. Quality control of the lavender oils produced is an important analytical task in view of their wide use in perfumery and cosmetics, the food industry and aromatherapy. The present paper studies the relationship between the trace elements content in lavender inflorescence (Lavandula angustifolia Mill.) and in lavender oil derived from this inflorescence. Three model regions were investigated: two of them are situated far from industrial areas — the village of Zelenikovo and the town of Pavel Banya, and one region is located near the Plovdiv Non-Ferrous Metallurgical Plant. The content of the elements Cd, Cr, Cu, Fe, Mn and Pb in plants was determined after acid digestion by flame and electrothermal atomic absorption spectrometry (ETAAS). Lavender oils were analyzed directly by ETAAS. The results undoubtedly show that there is no strong correlation between the trace elements content in inflorescence and in essential oils. It might be assumed that the trace elements present and accumulated in the inflorescence do not pass in lavender oil during the production by steam distillation.