Effects of Hall Currents and Gyroviscosity on the Stability of a Finitely Conducting Rotating Viscous Plasma of Variable Density

The Rayleigh-Taylor instability of an incompressible viscous, finitely conducting, rotating plasma of variable density has been investigated in the presence of the effects of Hall currents and finite ion Larmor radius. The proper solution for a semi-infinité plasma layer having exponentially varying density in the vertical direction has been obtained by making use of a variational principle which is shown to characterize the problem. The dispersion relation has been solved numerically. It is found that gyroviscosity, viscosity and coriolis forces have stabilizing influence whereas Hall currents and resistivity have a destabilizing influence.     

Higher order number concentration structure factors for binary alloys

We introduce higher order number-concentration structure factors. Explicit forms for the long wavelength limits of the third order structure factors are given and their variation with concentration is examined for Na-K alloy.     

Multistrange baryon production in Au-Au collisions at sqrt[s(NN)]=130 GeV

The transverse mass spectra and midrapidity yields for Xis and Omegas are presented. For the 10% most central collisions, the (-)Xi(+)/h(-) ratio increases from the Super Proton Synchrotron to the Relativistic Heavy Ion Collider energies while the Xi(-)/h(-) stays approximately constant. A hydrodynamically inspired model fit to the Xi spectra, which assumes a thermalized source, seems to indicate that these multistrange particles experience a significant transverse flow effect, but are emitted when the system is hotter and the flow is smaller than values obtained from a combined fit to pi, K, p, and Lambdas.     

An embedded 3(2) pair of nonlinear methods for solving first order initial-value ordinary differential systems

In this paper, we present two families of second-order and third-order explicit methods for numerical integration of initial-value problems of ordinary differential equations. Firstly, a family of second-order methods with two free parameters is derived by considering a suitable rational approximation to the theoretical solution of the problem at some grid points. Imposing that the principal term of the local truncation error of this family vanishes, we obtain an expression for one of the parameters in terms of the other. With this approach, a new one-parameter family of third-order methods is obtained. By selecting any 3(2) pair of second and third order methods, they can be implemented as an embedded type method, thus leading to a variable step-size formulation. We have considered one 3(2) pair of second and third order methods and made a comparison of numerical results with several ode solvers which are currently used in practice. The comparison of numerical results shows that the embedded 3(2) pair outperforms the methods considered for comparison.     

New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations

We present a three-step two-parameter family of derivative free methods with seventh-order of convergence for solving systems of nonlinear equations numerically. The proposed methods require evaluation of two central divided differences and inversion of only one matrix per iteration. As a result, the proposed family is more efficient as compared with the existing methods of same order. Numerical examples show that the proposed methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations.     

Convection in Hele-Shaw cell with parametric excitation

The linear stability of a thin vertical fluid layer heated from below is considered. Here the gravitational field consists of two parts: a constant part and a time-dependent part varying periodically. The time-dependent part has been expressed in Fourier series. The effect of gravity modulation on the fluid layer is examined. Using an asymptotic analysis the convective threshold has been determined. Some comparisons are made with the known results.     

Multiphase electropatterning of cells and biomaterials

Tissues formed by cells encapsulated in hydrogels have uses in biotechnology, cell-based assays, and tissue engineering. We have previously presented a 3D micropatterning technique that rapidly localizes live cells within hydrogels using dielectrophoretic (DEP) forces, and have demonstrated the ability to modulate tissue function through the control of microscale cell architecture. A limitation of this method is the requirement that a single biomaterial must simultaneously harbor biological properties that support cell survival and function and material properties that permit efficient dielectrophoretic patterning. Here, we resolve this issue by forming multiphase tissues consisting of microscale tissue sub-units in a 'local phase' biomaterial, which, in turn, are organized by DEP forces in a separate, mechanically supportive 'bulk phase' material. We first define the effects of medium conductivity on the speed and quality of DEP cell patterning. As a case study, we then produce multiphase tissues with microscale architecture that combine high local hydrogel conductivity for enhanced survival of sensitive liver progenitor cells with low bulk conductivity required for efficient DEP micropatterning. This approach enables an expanded range of studies examining the influence of 3D cellular architecture on diverse cell types, and in the future may improve the biological function of inhomogeneous tissues assembled from a variety of modular tissue sub-units.     

Gravitational Instability of a Thermally Conducting Plasma in an Oblique Magnetic Field

The combined influence of the effects of Hall currents, magnetic resistivity and viscosity have been studied on the gravitational instability of a thermally conducting homogeneous unbounded plasma in an oblique magnetic field. The solution has been obtained through the normal mode technique and the dispersion relation has been derived. It is shown that the Jeans' criterion for gravitational instability remains unchanged. Solving numerically the dispersion relation, the dependence of the growth rate of the gravitational unstable mode on the considered physical effects has been obtained for an astrophysical situation. For conditions prevailing in the magnetized collapsing clouds, the numerical calculations for the plot of growth rate against wave number has been obtained for several values of the parameters characterizing Hall currents magnetic resistivity viscosity thermal conductivity. It is found that magnetic resistivity and thermal conductivity have destabilizing influence while viscosity has stabilizing influence on the instability of the plasma of disturbance m(ϱ) = 9 × 10⁻³ kg.     

Integrating density functional theory and chemical ionization mass spectrometry techniques to assess benzophenone derivatives in food packaging: implications for enhancing food quality and safety

Benzophenone and related derivatives are widely used as photoinitiators for food packaging to cure inks or lacquers with ultraviolet (UV) light on cardboard and paper. However, there are concerns about the potential health risks of their migration into food. Knowing the physical and chemical properties of benzophenone and its derivatives could play a significant role in their quantification and analysis using chemical ionization mass spectrometry (CI-MS) methods. These parameters are evaluated using B3LYP/6-311++** density functional theory (DFT) implemented on Gaussian code. Ion–molecule chemistry through the selection of reagent ions, reaction energetics and kinetics, thermodynamic stability, and reactivity of molecules deemed to foster VOC identification and quantification via CI-MS techniques. The VOCs under study are expected to undergo exothermic reactions from H₃O⁺, NH₄⁺, NO⁺, and O₂⁺ ions, except endothermic proton transfer from NH₄⁺ to 2-hydroxy-4-methoxybenzophenone and 2,3,4-trihydroxy benzophenone. These compounds possess less proton affinities than NH₃ and are least stable in their protonated forms. The DFT computed properties provide the basis for developing reliable and accurate methods to detect and measure the presence of benzophenone and its derivatives in packaging materials and food products.     

Pinchings and Norms of Scaled Triangular Matrices

Suppose U is an upper-triangular matrix, and D a nonsingular diagonal matrix whose diagonal entries appear in nondescending order of magnitude down the diagonal. It is proved that $$|D^{-1}UD|ge|U|$$ for any matrix norm that is reduced by a pinching. In addition to known examples -weakly unitarily invariant norms - we show that any matrix norm defined by $$| A |^{underline{underline {{rm def}}} } mathop {max }limits_{x ne 0,y ne 0} {{{mathop{rm Re}nolimits} (x^*Ay)} over {phi (x)psi (y)}},$$ where θ (.) and y (.) are two absolute vector norms, has this property. This includes l p operator norms as a special case.