Scale-up criteria of square tank surface aerator

Oxygen transfer rate and the corresponding power requirement to operate the rotor are vital for design and scale-up of surface aerators. Present study develops simulation or scale-up criterion correlating the oxygen transsimulation fer coefficient and power number along with a parameter governing theoretical power per unit volume (X, which is defined as equal to (FR1/3)-R-4/3, where F and R are impellers' Fronde and Reynolds number, respectively). Based on such scale-up criteria, design considerations are developed to save energy requirements while designing square tank surface aerators. It has been demonstrated that energy can be saved substantially if the aeration tanks are run at relatively higher input powers. It is also demonstrated that smaller sized tanks are more energy conservative and economical when compared to big sized tanks, while aerating the same volume of water, and at the same time by maintaining a constant input power in all the tanks irrespective of their size. An example illustrating how energy can be reduced while designing different sized aerators is given. The results presented have a wide application in biotechnology and bioengineering areas with a particular emphasis on the design of appropriate surface aeration systems.

Scale-up criteria of square tank surface aerator

Oxygen transfer rate and the corresponding power requirement to operate the rotor are vital for design and scale-up of surface aerators. Present study develops simulation or scale-up criterion correlating the oxygen transsimulation fer coefficient and power number along with a parameter governing theoretical power per unit volume (X, which is defined as equal to (FR1/3)-R-4/3, where F and R are impellers' Fronde and Reynolds number, respectively). Based on such scale-up criteria, design considerations are developed to save energy requirements while designing square tank surface aerators. It has been demonstrated that energy can be saved substantially if the aeration tanks are run at relatively higher input powers. It is also demonstrated that smaller sized tanks are more energy conservative and economical when compared to big sized tanks, while aerating the same volume of water, and at the same time by maintaining a constant input power in all the tanks irrespective of their size. An example illustrating how energy can be reduced while designing different sized aerators is given. The results presented have a wide application in biotechnology and bioengineering areas with a particular emphasis on the design of appropriate surface aeration systems.

Self-assembly of a nanoscopic platinum(II) double square cage

Self-assembly of a rigid tripyridyl linker with a bidentate 90 degrees Pt(II) acceptor yielded a somewhat unusual double square cage, representing the first example of Pt(II) cage of such shape. Multinuclear NMR as well as single-crystal structure analysis characterized the cage.

Self-assembly of a nanoscopic platinum(II) double square cage

Self-assembly of a rigid tripyridyl linker with a bidentate 90 degrees Pt(II) acceptor yielded a somewhat unusual double square cage, representing the first example of Pt(II) cage of such shape. Multinuclear NMR as well as single-crystal structure analysis characterized the cage.

On the maximal rate of non-square STBCs from complex orthogonal designs

A Linear Processing Complex Orthogonal Design (LPCOD) is a p x n matrix epsilon, (p >= n) in k complex indeterminates x(1), x(2),..., x(k) such that (i) the entries of epsilon are complex linear combinations of 0, +/- x(i), i = 1,..., k and their conjugates, (ii) epsilon(H)epsilon = D, where epsilon(H) is the Hermitian (conjugate transpose) of epsilon and D is a diagonal matrix with the (i, i)-th diagonal element of the form l(1)((i))vertical bar x(1)vertical bar(2) + l(2)((i))vertical bar x(2)vertical bar(2)+...+ l(k)((i))vertical bar x(k)vertical bar(2) where l(j)((i)), i = 1, 2,..., n, j = 1, 2,...,k are strictly positive real numbers and the condition l(1)((i)) = l(2)((i)) = ... = l(k)((i)), called the equal-weights condition, holds for all values of i. For square designs it is known. that whenever a LPCOD exists without the equal-weights condition satisfied then there exists another LPCOD with identical parameters with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1. This implies that the maximum possible rate for square LPCODs without the equal-weights condition is the same as that or square LPCODs with equal-weights condition. In this paper, this result is extended to a subclass of non-square LPCODs. It is shown that, a set of sufficient conditions is identified such that whenever a non-square (p > n) LPCOD satisfies these sufficient conditions and do not satisfy the equal-weights condition, then there exists another LPCOD with the same parameters n, k and p in the same complex indeterminates with l(1)((i)) = l(2)((i)) = ... = l(k)((i)) = 1.

Site characterization model using least-square support vector machine and relevance vector machine based on corrected SPT data (N-c)

Statistical learning algorithms provide a viable framework for geotechnical engineering modeling. This paper describes two statistical learning algorithms applied for site characterization modeling based on standard penetration test (SPT) data. More than 2700 field SPT values (N) have been collected from 766 boreholes spread over an area of 220 sqkm area in Bangalore. To get N corrected value (N,), N values have been corrected (Ne) for different parameters such as overburden stress, size of borehole, type of sampler, length of connecting rod, etc. In three-dimensional site characterization model, the function N-c=N-c (X, Y, Z), where X, Y and Z are the coordinates of a point corresponding to N, value, is to be approximated in which N, value at any half-space point in Bangalore can be determined. The first algorithm uses least-square support vector machine (LSSVM), which is related to aridge regression type of support vector machine. The second algorithm uses relevance vector machine (RVM), which combines the strengths of kernel-based methods and Bayesian theory to establish the relationships between a set of input vectors and a desired output. The paper also presents the comparative study between the developed LSSVM and RVM model for site characterization. Copyright (C) 2009 John Wiley & Sons,Ltd.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Electronic structure of square planar CuO46− clusters

The results of spin-polarized MSXagr calculations show that the ground state of the CuO 4 6– cluster is essentially non-magnetic in spite of odd number of electrons in the system for short Cu–O distances (1.90 Å) as found in the highT c superconductors. This arises due to the fact that the unpaired electron resides in a molecular orbital with primarily oxygen 3s character. The stability of this molecular orbital is found to be sensitive to the cluster geometry and thus, increase in Cu–O distance (as well as other changes affecting oxygen-oxygen distance) tend to favour a magnetic state. From these calculations we have also estimated the Coulomb correlation strength within the Cu 3d to be about 5.3 eV.

Variational calculation for the spin-(1/2 Heisenberg antiferromagnet on a square lattice

The ground-state properties of the spin-(1/2 Heisenberg antiferromagnet on a square lattice are studied by using a simple variational wave function that interpolates continuously between the Néel state and short-range resonating-valence-bond states. Exact calculations of the variational energy for small systems show that the state with the lowest energy has long-range antiferromagnetic order. The staggered magnetization in this state is approximately 70% of its maximum possible value. The variational estimate of the ground-state energy is substantially lower than the value obtained for the nearest-neighbor resonating-valence-bond wave function.

Mean square displacements of hydrogen interstitial and its neighbours in the intermetallic compound Fe0.5Ti0.5

A Green's function technique is used in the scattering matrix formalism to compute the mean square displacement of hydrogen and deuterium interstitials in the intermetallic compound Fe0.5Ti0.5 for low hydrogen/deuterium concentration. The mean square amplitudes of the metal atoms surrounding the interstitial are found to be smaller than those for the host crystal. This anomalous effect is due to the stiffening of the lattice by the dissolved hydrogen or deuterium at low concentration. This type of effect is experimentally observed in the case of NbHx at low hydrogen concentration.

Spiral states in the square-lattice Hubbard model

We present a variety of physical implications of a mean-field theory for spiral spin-density-wave states in the square-lattice Hubbard model for small deviations from half filling. The phase diagram with the paramagnetic metal, two spiral (semimetallic) states, and ferromagnet is calculated. The momentum distribution function and the (quasiparticle) density of states are discussed. There is a significant broadening of the quasiparticle bands when the antiferromagnetic insulator is doped. The evolution of the Fermi surface and the variation of the plasma frequency and a charge-stiffness constant with U/t and δ are calculated. The connection to results based on the Schwinger-boson-slave-fermion formalism is made.

Mean-field results of the multiple-band extended Hubbard model for the square-planar CuO2 lattice

We obtain metal-insulator phase diagrams at half-filling for the five-band extended Hubbard model of the square-planar CuO2 lattice treated within a Hartree-Fock mean-field approximation, allowing for spiral spin-density waves. We indicate the existence of an insulating phase (covalent insulator) characterized by strong covalency effects, not identified in the earlier Zaanen-Sawatzky-Allen phase diagram. While the insulating phase is always antiferromagnetic, we also obtain an antiferromagnetic metallic phase for a certain range of interaction parameters. Performing a nonperturbative calculation of J(eff), the in-plane antiferromagnetic interaction is presented as a function of the parameters in the model. We also calculate the band gap and magnetic moments at various sites and discuss critically the contrasting interpretation of the electronic structure of high-T(c) materials arising from photoemission and neutron-scattering experiments.

Probing potential energy surfaces in confined systems: behavior of mean-square displacement in zeolites

Time evolution of mean-squared displacement based on molecular dynamics for a variety of adsorbate-zeolite systems is reported. Transition from ballistic to diffusive behavior is observed for all the systems. The transition times are found to be system dependent and show different types of dependence on temperature. Model calculations on a one-dimensional system are carried out which show that the characteristic length and transition times are dependent on the distance between the barriers, their heights, and temperature. In light of these findings, it is shown that it is possible to obtain valuable information about the average potential energy surface sampled under specific external conditions.