I. Singular perturbation problems involving singular points and turning points. II. On the averaged Lagrangian technique for nonlinear dispersive waves

In Part I a class of linear boundary value problems is considered which is a simple model of boundary layer theory. The effect of zeros and singularities of the coefficients of the equations at the point where the boundary layer occurs is considered. The usual boundary layer techniques are still applicable in some cases and are used to derive uniform asymptotic expansions. In other cases it is shown that the inner and outer expansions do not overlap due to the presence of a turning point outside the boundary layer. The region near the turning point is described by a two-variable expansion. In these cases a related initial value problem is solved and then used to show formally that for the boundary value problem either a solution exists, except for a discrete set of eigenvalues, whose asymptotic behaviour is found, or the solution is non-unique. A proof is given of the validity of the two-variable expansion; in a special case this proof also demonstrates the validity of the inner and outer expansions.

Nonlinear dispersive wave equations which are governed by variational principles are considered in Part II. It is shown that the averaged Lagrangian variational principle is in fact exact. This result is used to construct perturbation schemes to enable higher order terms in the equations for the slowly varying quantities to be calculated. A simple scheme applicable to linear or near-linear equations is first derived. The specific form of the first order correction terms is derived for several examples. The stability of constant solutions to these equations is considered and it is shown that the correction terms lead to the instability cut-off found by Benjamin. A general stability criterion is given which explicitly demonstrates the conditions under which this cut-off occurs. The corrected set of equations are nonlinear dispersive equations and their stationary solutions are investigated. A more sophisticated scheme is developed for fully nonlinear equations by using an extension of the Hamiltonian formalism recently introduced by Whitham. Finally the averaged Lagrangian technique is extended to treat slowly varying multiply-periodic solutions. The adiabatic invariants for a separable mechanical system are derived by this method.

Computational microscopy: turning megapixels into gigapixels

The layout of a typical optical microscope has remained effectively unchanged over the past century. Besides the widespread adoption of digital focal plane arrays, relatively few innovations have helped improve standard imaging with bright-field microscopes. This thesis presents a new microscope imaging method, termed Fourier ptychography, which uses an LED to provide variable sample illumination and post-processing algorithms to recover useful sample information. Examples include increasing the resolution of megapixel-scale images to one gigapixel, measuring quantitative phase, achieving oil-immersion quality resolution without an immersion medium, and recovering complex three dimensional sample structure.

No turning back: Indonesia, illegal fishing

Despite official legislation, Indonesia is yet to institute processes to curb illegal, unreported and unregulated (IUU) fishing.

Development of a turning mid turbine frame with embedded design-part II: Unsteady measurements

© 2014 by ASME. This paper, the second of two parts, presents a new setup for the two-stage two-spool facility located at the Institute for Thermal Turbomachinery and Machine Dynamics (ITTM) of Graz University of Technology. The rig was designed to reproduce the flow behavior of a transonic turbine followed by a counter-rotating low pressure stage such as those in high bypass aero-engines. The meridional flow path of the machine is characterized by a diffusing S-shaped duct between the two rotors. The role of wide chord vanes placed into the mid turbine frame is to lead the flow towards the low pressure (LP) rotor with appropriate swirl. Experimental and numerical investigations performed on this setup showed that the wide chord struts induce large wakes and extended secondary flows at the LP inlet flow. Moreover, large deterministic fluctuations of pressure, which may cause noise and blade vibrations, were observed downstream of the LP rotor. In order to minimize secondary vortices and to damp the unsteady interactions, the mid turbine frame was redesigned to locate two zero-lift splitters into each vane passage. While in the first part of the paper the design process of the splitters and the time-averaged flow field were presented, in this second part the measurements performed by means of a fast response probe will support the explanation of the time-resolved field. The discussion will focus on the comparison between the baseline case (without splitters) and the embedded design.

Development of a turning mid turbine frame with embedded design-part I: Design and steady measurements

© 2014 by ASME. The paper presents a new setup for the two-stage two-spool facility located at the Institute for Thermal Turbomachinery and Machine Dynamics (ITTM) of Graz University of Technology. The rig was designed in order to simulate the flow behavior of a transonic turbine followed by a counter-rotating low pressure (LP) stage like the spools of a modern high bypass aeroengine. The meridional flow path of the machine is characterized by a diffusing S-shaped duct between the two rotors. The role of turning struts placed into the mid turbine frame is to lead the flow towards the LP rotor with appropriate swirl. Experimental and numerical investigations performed on the setup over the last years, which were used as baseline for this paper, showed that wide chord vanes induce large wakes and extended secondary flows at the LP rotor inlet flow. Moreover, unsteady interactions between the two turbines were observed downstream of the LP rotor. In order to increase the uniformity and to decrease the unsteady content of the flow at the inlet of the LP rotor, the mid turbine frame was redesigned with two zero-lifting splitters embedded into the strut passage. In this first part of the paper the design process of the splitters and its critical points are presented, while the time-averaged field is discussed by means of five-hole probe measurements and oil flow visualizations. The comparison between the baseline case and the embedded design configuration shows that the new design is able to reduce the flow gradients downstream of the turning struts, providing a more suitable inlet condition for the low pressure rotor. The improvement in the flow field uniformity is also observed downstream of the turbine and it is, consequently, reflected in an enhancement of the LP turbine performance. In the second part of this paper the influence of the embedded design on the time-resolved field is investigated.

Ultrafast photo-induced turning of magnetization and its relaxation dynamics in GaMnAs

We report that, by linearly polarized pumping of different wavelengths, Kerr transients appear at zero magnetic field only in the case when GaMnAs samples are initialized at 3 K by first applying a 0.8 Tesla field and then returning to zero field. We find that, instead of magnetization precession, the near-band gap excitation induces a coherent out-of-plane turning of magnetization, which shows very long relaxation dynamics with no precession. When photon energy increases, the peak value of the Kerr transient increases, but it decays rapidly to the original slow transient seen under the near-band-gap excitation.

The wave function evolution of an exciton in a bilayer system: Turning on a static in-plane electric field

The time evolution of the ground state wave function of an exciton in an ideal bilayer system is investigated within the framework of the effective-mass approximation. All of the moduli squared of the ground state wave functions evolve with time as cosine functions after an in-plane electric field is applied to the bilayer system. The variation amplitude and period of the modulus squared of the ground state wave function increase with the in-plane electric field F-r for a fixed in-plane relative coordinate r and fixed separation d between the electron and hole layers. Moreover, the variation amplitude and period of the modulus squared of the ground state wave function increase with the separation d for a fixed r and fixed in-plane electric field. Additionally, the modulus squared of the ground state wave function decreases as r increases at a given time t for fixed values of d and F-r. (c) 2007 American Institute of Physics.

Properties and turning of intraband optical absorption in InxGa1-xAs/GaAs self-assembled quantum dot superlattice

We investigated properties of intraband absorption in In-x Ga1-xAs quantum dots (QDs) superlattice. Energy levels in conduction band in QDs were calculated for a cone-shaped quantum dot associated with coupling between QDs in the framework of the effective-mass envelope-function theory. Theoretical results demonstrated that energy levels in conduction band were greatly affected by the vertical coupling between quantum dots, which can be used to modify transition wavelength by adjusting the space layer thickness. Intraband transition is really sensitive to normal incidence and the absorption peak intensity is dependent on the polarization. A satisfying agreement is found between theoretical and experimental values. This result opens up prospects for the fabrication of QDs infrared detectors, which work at atmospheric windows.

Evidences of the intertidal red alga Grateloupia turuturu in turning Vibrio parahaemolyticus into non-culturable state in the presence of light

Grateloupia turuturu, previously known as Grateloupia doryphora, has been widely reported to be an invasive algal species. There are no studies to relate the impact of its existence on its surrounding environment. In this paper, we present our results to show that about 70% of individuals collected from the field could turn Vibrio parahaemolyticus into non-culturable state on both selective (TCBS) and non-selective (2216E) culture medium in 24 h in the presence of light in live algal culture. Total bacteria counts on TCBS and 2216E plates dropped from the initial 565 (174) and 1192 (60) cfu ml(-1) respectively to zero in 24 h. This effect disappeared when the alga was grown in darkness. The same effect was not found in two other intertidal macroalgae Laminaria japonica and Palmaria palmata. Further tests showed that the settlement ability of bacteria in seawater was impaired significantly in the presence of this alga in comparison with three other algal species. (c) 2006 Elsevier B.V. All rights reserved.

open source spirituality: turning the world upside down

Sermon preached at Boston University School of Theology during Wednesday Chapel on October 24, 2007