Phenol degradation using 20, 300 and 520 kHz ultrasonic reactors with hydrogen peroxide, ozone and zero valent metals

The extent of phenol degradation by the advanced oxidation process in the presence of zero valent iron (ZVI) and zero valent copper (ZVC) was studied using 20, 300 and 520 kHz ultrasonic (US) reactors. Quantification of hydrogen peroxide has also been performed with an aim of investigating the efficacy of different sonochemical reactors for hydroxyl radical production. It has been observed that the 300 kHz sonochemical reactor has the maximum efficacy for hydroxyl radical production. Phenol degradation studies clearly indicate that degradation of phenol is intensified in the presence of the catalyst and hydrogen peroxide, which can be attributed to enhanced production of hydroxyl radicals in the system. Experimental data shows that with ZVI, when the reaction was subjected to 300 kHz, complete phenol removal and 37% TOC mineralization was achieved within 25 min, whereas, in the case of 20 kHz US treatment no phenol was detected after 45 min and 39% TOC mineralization was observed. This novel study also investigated the use of zero valent copper (ZVC) and results showed that with 20, 300 and 520 kHz ultrasonic rectors, phenol removal was 10–98%, however, the maximum TOC mineralization achieved was only 26%. A comparative study between hydrogen peroxide and ozone as a suitable oxidant for Fenton-like reactions in conjunction with zero valent catalysts showed that an integrated approach of US/Air/ZVC/H2O2 system works better than US/ZVC/O3 (the ZOO process)

Root asymptotics of spectral polynomials for the Lame operator

The study of polynomial solutions to the classical Lam\'e equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr\"odinger equation with finite gap potential given by the Weierstrass $\wp$-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.Comment: final version, to appear in Commun. Math. Phys.; 13 pages, 3 figures, LaTeX2

Engineering multiple levels of specificity in an RNA viral vector

Synthetic molecular circuits could provide powerful therapeutic capabilities, but delivering them to specific cell types and controlling them remains challenging. An ideal "smart" viral delivery system would enable controlled release of viral vectors from "sender" cells, conditional entry into target cells based on cell-surface proteins, conditional replication specifically in target cells based on their intracellular protein content, and an evolutionarily robust system that allows viral elimination with drugs. Here, combining diverse technologies and components, including pseudotyping, engineered bridge proteins, degrons, and proteases, we demonstrate each of these control modes in a model system based on the rabies virus. This work shows how viral and protein engineering can enable delivery systems with multiple levels of control to maximize therapeutic specificity

Solvable relativistic quantum dots with vibrational spectra

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum is roughly equidistant and where a fine-tuning of the levels is mediated by PT-symmetric interactions composed of imaginary delta functions which mimic creation/annihilation processes.Comment: Int. Worskhop "Pseudo-Hermitian Hamiltonians in Quantum Physics III" (June 20 - 22, 2005, Koc Unversity, Istanbul(http://home.ku.edu.tr/~amostafazadeh/workshop/workshop.htm) a part of talk (9 pages

Nonlocal symmetries of Riccati and Abel chains and their similarity reductions

We study nonlocal symmetries and their similarity reductions of Riccati and Abel chains. Our results show that all the equations in Riccati chain share the same form of nonlocal symmetry. The similarity reduced $N^{th}$ order ordinary differential equation (ODE), $N=2, 3,4,...$, in this chain yields $(N-1)^{th}$ order ODE in the same chain. All the equations in the Abel chain also share the same form of nonlocal symmetry (which is different from the one that exist in Riccati chain) but the similarity reduced $N^{th}$ order ODE, $N=2, 3,4,$, in the Abel chain always ends at the $(N-1)^{th}$ order ODE in the Riccati chain. We describe the method of finding general solution of all the equations that appear in these chains from the nonlocal symmetry.Comment: Accepted for publication in J. Math. Phy

Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation

We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere and hyperbolic double-well potential are investigated by this method

The Pseudothreshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes

The values at pseudothreshold of two loop sunrise master amplitudes with arbitrary masses are obtained by solving a system of differential equations. The expansion at pseudothreshold of the amplitudes is constructed and some lowest terms are explicitly presented.Comment: 1+22 pages, Latex, no figures, changes in Eq.(41),(44),(47

Lagrangian Formalism for nonlinear second-order Riccati Systems: one-dimensional Integrability and two-dimensional Superintegrability

The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are nonnatural and the forces are not derivable from a potential. The constant value $E$ of a preserved energy function can be used as an appropriate parameter for characterizing the behaviour of the solutions of these two systems. In the second part the existence of two--dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figuresComment: 25 pages, 7 figure

The Threshold Expansion of the 2-loop Sunrise Selfmass Master Amplitudes

The threshold behavior of the master amplitudes for two loop sunrise self-mass graph is studied by solving the system of differential equations, which they satisfy. The expansion at the threshold of the master amplitudes is obtained analytically for arbitrary masses.Comment: 1+18 pages, Latex, no figures, as in Journal reference with more changes in Eq.(31),(42),(45

Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of bifurcations "touch-and-go" replaced by "island-chain