Liquid mixing time and gas distribution in aerated multiple-impeller stirred tanks

Gas-liquid fluid dynamics and mass transfer are crucial aspects of aerobic fermentation and robust methodologies for their determination in industrial bioreactors are expected to provide significant improvements in many production processes. In this work, a gas-liquid stirred tank of high aspect ratio, that replicates the geometry of typical industrial aerated fermenters, is investigated. In particular, the liquid phase homogenization dynamics and the gas phase spatial distribution are determined. The selected methodology is based on the analysis of the conductivity measurements obtained by Electrical Resistance Tomography. The gas-liquid flow regimes and the mixing time are identified at various gas flow rates and impeller speeds, thus covering different gas-liquid regimes. Data col lected with vertical and horizontal arrangements of the electrodes allow to obtain a tailed picture of the equipment working mode and to gain insight into the gas-liquid flow dynamics under optically inaccessible conditions. Quantitative evaluation of the bility of the collected data is attempted by comparing the results obtained with the tical and horizontal arrangements in the same locations

Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result

In this paper we prove that any multi-resolution analysis of \Lc^2(\R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author.Comment: Submitted to Journal Mathematical Physisc

Biochemical correlates of cardiac hypertrophy. I. Experimental model; changes in heart weight, RNA content, and nuclear RNA polymerase activity

Cardiac hypertrophy occurred in mature rats after producing supravalvular aortic stenosis with a specially designed silver clip. For 2 weeks following this procedure, heart weight, body weight, and RNA content of the myocardium were serially determined. Heart weight and RNA content increased within 24 hours of aortic banding, reaching a maximal level in 2 days and remaining elevated during the 2 weeks of observation. Nuclei were isolated and purified from heart muscle homogenates, and changes in RNA polymerase activity following aortic banding were determined. The nearest neighbor frequency of the bases of the RNA synthesized by the polymerase from nuclear preparations was identical in both the banded animals and the sham-operated controls. Both groups could thus be compared on the basis of the enzyme assay. RNA polymerase activity in nuclei from the hearts of banded rats rose rapidly when compared with the activity in sham-operated rats; peak values were reached on the second day, the earliest detectable change being around 12 hours. The increase in RNA polymerase activity represents one of the earliest biochemical events that take place in the myocardium following aortic banding

Emergent Classicality via Commuting Position and Momentum Operators

Any account of the emergence of classicality from quantum theory must address the fact that the quantum operators representing positions and momenta do not commute, whereas their classical counterparts suffer no such restrictions. To address this, we revive an old idea of von Neumann, and seek a pair of commuting operators $X,P$ which are, in a specific sense, "close" to the canonical non-commuting position and momentum operators, $x,p$. The construction of such operators is related to the problem of finding complete sets of orthonormal phase space localized states, a problem severely limited by the Balian-Low theorem. Here these limitations are avoided by restricting attention to situations in which the density matrix is reasonably decohered (i.e., spread out in phase space).Comment: To appear in Proceedings of the 2008 DICE Conferenc

Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects

We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of Berry-phase terms for the semiclassical dynamics and the quantization rule. For electromagnetic perturbations, we recover the orbital magnetization energy and the anomalous velocity purely within a single-band picture without invoking inter-band couplings. For deformations in crystals, besides a deformation potential, we obtain a Berry-phase term in the Lagrangian due to lattice tracking, which gives rise to new terms in the expressions for the wave-packet velocity and the semiclassical force. For multiple-valued displacement fields surrounding dislocations, this term manifests as a Berry phase, which we show to be proportional to the Burgers vector around each dislocation.Comment: 12 pages, RevTe

Surfaces containing a family of plane curves not forming a fibration

We complete the classification of smooth surfaces swept out by a 1-dimensional family of plane curves that do not form a fibration. As a consequence, we characterize manifolds swept out by a 1-dimensional family of hypersurfaces that do not form a fibration.Comment: Author's post-print, final version published online in Collect. Mat

Orthogonal localized wave functions of an electron in a magnetic field

We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.Comment: RevTex, 18 pages, 5 ps fi

Factorizations and Physical Representations

A Hilbert space in M dimensions is shown explicitly to accommodate representations that reflect the prime numbers decomposition of M. Representations that exhibit the factorization of M into two relatively prime numbers: the kq representation (J. Zak, Phys. Today, {\bf 23} (2), 51 (1970)), and related representations termed $q_{1}q_{2}$ representations (together with their conjugates) are analysed, as well as a representation that exhibits the complete factorization of M. In this latter representation each quantum number varies in a subspace that is associated with one of the prime numbers that make up M

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte

Predicting the glomerular filtration rate in bariatric surgery patients

BACKGROUND/AIMS: Identifying the best method to estimate the glomerular filtration rate (GFR) in bariatric surgery patients has important implications for the clinical care of obese patients and research into the impact of obesity and weight reduction on kidney health. We therefore performed such an analysis in patients before and after surgical weight loss. METHODS: Fasting measured GFR (mGFR) by plasma iohexol clearance before and after bariatric surgery was obtained in 36 severely obese individuals. Estimated GFR was calculated using the Modification of Diet in Renal Disease equation, the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation using serum creatinine only, the CKD-EPI equation using serum cystatin C only and a recently derived equation that uses both serum creatinine and cystatin C (CKD-EPIcreat-cystC) and then compared to mGFR. RESULTS: Participants were primarily middle-aged white females with a mean baseline body mass index of 46 ± 9, serum creatinine of 0.81 ± 0.24 mg/dl and mGFR of 117 ± 40 ml/min. mGFR had a stronger linear relationship with inverse cystatin C before (r = 0.28, p = 0.09) and after (r = 0.38, p = 0.02) surgery compared to the inverse of creatinine (before: r = 0.26, p = 0.13; after: r = 0.11, p = 0.51). mGFR fell by 17 ± 35 ml/min (p = 0.007) following surgery. The CKD-EPIcreat-cystC was unquestionably the best overall performing estimating equation before and after surgery, revealing very little bias and a capacity to estimate mGFR within 30% of its true value over 80% of the time. This was true whether or not mGFR was indexed for body surface area. CONCLUSIONS: In severely obese bariatric surgery patients with normal kidney function, cystatin C is more strongly associated with mGFR than is serum creatinine. The CKD-EPIcreat-cystC equation best predicted mGFR both before and after surgery