Temperature development in the leakage flow of screw extruders

Temperature distribution at the exit of the leakage gap is of interest for a number of problems. For the calculation of temperatures, the leakage flow may be considered to be a pure drag flow to a good approximation. In the Newtonian case, thermal development length may be expressed in terms of gap height as L ≈ 3/8Pe ·δ ;usually this is less than the available gap length. Pe is the Peclet number and δ the height of leakage gap. Therefore the existing flow may be considered fully developed. For power law fluids, numerical calculations lead to results of the same order. Martin's results therefore may be applied to the flow at the exit of the leakage gap

AN EVALUATION OF THE NON-LINEAR VISCOELASTIC PROPERTIES OF THE HEALING MEDIAL COLLATERAL LIGAMENT

Injuries to knee ligaments are frequent, demanding an increased understanding of the healing process. Clinically, the injured medial collateral ligament (MCL) has been found to heal without surgical intervention. However, laboratory studies have shown that, even one year after injury, the biomechanical properties, biochemical composition, and histomorphological appearance of the healing MCL remains suboptimal. While research has focused on the changes in mechanical properties (i.e. stress-strain behavior) of the healed MCL, studies on its viscoelastic properties are limited. Yet, this knowledge is critical to determine the overall kinetic response of the knee joint.The quasi-linear viscoelastic (QLV) theory proposed by Professor Y.C. Fung has been frequently used to model the viscoelastic properties of the MCL. This theory was developed based on an idealized step-elongation during a stress relaxation test. As this is experimentally impossible, the constants of the theory may not be representative when they are determine based on experiments that utilize finite strain rates. Thus, the overall objectives of this dissertation were to 1) develop and validate a novel experimental and analytical approach that accounts for finite strain rates and provides an accurate determination of the viscoelastic properties of the normal MCL, 2) apply this new approach to describe the viscoelastic behavior of the healing MCL, and 3) to determine whether the new approach can describe the response of the MCL to harmonic oscillations.This work demonstrated that a newly developed approach could be utilized to determine the constants of the quasi-linear viscoelastic theory and successfully describe the viscoelastic behavior of both the normal and healing MCLs. Interestingly, the healing ligaments display a lower initial slope of the stress-strain curve and a greater propensity to dissipate energy, suggesting other structures within the knee would have to play a compensatory role in knee function. It was also found that the mechanisms governing the viscoelastic response of the MCL to harmonic oscillations may not be the same as that which governs stress relaxation behavior. Thus, a more general theory may be necessary to describe both phenomena

Viscoelastic spectrum analysis and the identification of a fung viscoelastic material

Despite its many limitations, the Fung “quasi-linear viscoelastic” constitutive model continues to serve as a workhorse of the biomechanics community. A central challenge in applying the model is that it requires a specific form for the relaxation spectrum that is difficult to relate to easily obtained experimental spectra such as a generalized Maxwell relaxation spectrum. Here, we present a simple and general technique for obtaining a from relaxation data a viscoelastic spectrum appropriate to the Fung model. We apply the model to identify several biomaterials that are modeled reasonably by a Fung model, and many more that are not

Spectrum of the non-commutative spherical well

We give precise meaning to piecewise constant potentials in non-commutative quantum mechanics. In particular we discuss the infinite and finite non-commutative spherical well in two dimensions. Using this, bound-states and scattering can be discussed unambiguously. Here we focus on the infinite well and solve for the eigenvalues and eigenfunctions. We find that time reversal symmetry is broken by the non-commutativity. We show that in the commutative and thermodynamic limits the eigenstates and eigenfunctions of the commutative spherical well are recovered and time reversal symmetry is restored

Microscopic mechanism for experimentally observed anomalous elasticity of DNA in 2D

By exploring a recent model [Palmeri, J., M. Manghi, and N. Destainville. 2007. Phys. Rev. Lett. 99:088103] where DNA bending elasticity, described by the wormlike chain model, is coupled to base-pair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic force microscopy (AFM) experiments [Wiggins, P. A., et al. 2006. Nature Nanotech. 1:137-141]. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by AFM.Comment: To appear in Biophys. J. 8 pages, supplementary information included (7 pages

Spectroscopic properties of a two-level atom interacting with a complex spherical nanoshell

Frequency shifts, radiative decay rates, the Ohmic loss contribution to the nonradiative decay rates, fluorescence yields, and photobleaching of a two-level atom radiating anywhere inside or outside a complex spherical nanoshell, i.e. a stratified sphere consisting of alternating silica and gold concentric spherical shells, are studied. The changes in the spectroscopic properties of an atom interacting with complex nanoshells are significantly enhanced, often more than two orders of magnitude, compared to the same atom interacting with a homogeneous dielectric sphere. The detected fluorescence intensity can be enhanced by 5 or more orders of magnitude. The changes strongly depend on the nanoshell parameters and the atom position. When an atom approaches a metal shell, decay rates are strongly enhanced yet fluorescence exhibits a well-known quenching. Rather contra-intuitively, the Ohmic loss contribution to the nonradiative decay rates for an atomic dipole within the silica core of larger nanoshells may be decreasing when the silica core - inner gold shell interface is approached. The quasistatic result that the radial frequency shift in a close proximity of a spherical shell interface is approximately twice as large as the tangential frequency shift appears to apply also for complex nanoshells. Significantly modified spectroscopic properties (see computer program (pending publication of this manuscript) freely available at http://www.wave-scattering.com) can be observed in a broad band comprising all (nonresonant) optical and near-infrared wavelengths.Comment: 20 pages plus 63 references and 11 figures, plain LaTex, for more information see http://www.wave-scattering.com (color of D sphere in figures 2-6 altered, minor typos corrected.

The Single-Particle density of States, Bound States, Phase-Shift Flip, and a Resonance in the Presence of an Aharonov-Bohm Potential

Both the nonrelativistic scattering and the spectrum in the presence of the Aharonov-Bohm potential are analyzed. The single-particle density of states (DOS) for different self-adjoint extensions is calculated. The DOS provides a link between different physical quantities and is a natural starting point for their calculation. The consequences of an asymmetry of the S matrix for the generic self-adjoint extension are examined. I. Introduction II. Impenetrable flux tube and the density of states III. Penetrable flux tube and self-adjoint extensions IV. The S matrix and scattering cross sections V. The Krein-Friedel formula and the resonance VI. Regularization VII. The R --> 0 limit and the interpretation of self-adjoint extensions VIII. Energy calculations IX. The Hall effect in the dilute vortex limit X. Persistent current of free electrons in the plane pierced by a flux tube XI. The 2nd virial coefficient of nonrelativistic interacting anyons XII. Discussion of the results and open questionsComment: 68 pages, plain latex, 7 figures, 3 references and one figure added plus a few minor text correction