On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub 0. At values of the radius above a sub 0 all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up

Boundary-layer receptivity due to a wall suction and control of Tollmien-Schlichting waves

A numerical study of the generation of Tollmien-Schlichting (T-S) waves due to the interaction between a small free-stream disturbance and a small localized suction slot on an otherwise flat surface was carried out using finite difference methods. The nonlinear steady flow is of the viscous-inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier-Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of T-S waves generated by the interaction between the free-stream disturbance and the suction slot, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T-S waves and the demonstration of the possible active control of the growth of T-S waves

The three-dimensional flow past a rapidly rotating circular cylinder

The high Reynolds number (Re) flow past a rapidly rotating circular cylinder is investigated. The rotation rate of the cylinder is allowed to vary (slightly) along the axis of the cylinder, thereby provoking three-dimensional flow disturbances, which are shown to involve relatively massive (O(Re)) velocity perturbations to the flow away from the cylinder surface. Additionally, three integral conditions, analogous to the single condition determined in two dimensions by Batchelor, are derived, based on the condition of periodicity in the azimuthal direction

Identification of roots from grass swards using PCR-RFLP and FFLP of the plastid trnL (UAA) intron

BACKGROUND: The specific associations between plant roots and the soil microbial community are key to understanding nutrient cycling in grasslands, but grass roots can be difficult to identify using morphology alone. A molecular technique to identify plant species from root DNA would greatly facilitate investigations of the root rhizosphere. RESULTS: We show that trnL PCR product length heterogeneity and a maximum of two restriction digests can separate 14 common grassland species. The RFLP key was used to identify root fragments at least to genus level in a field study of upland grassland community diversity. Roots which could not be matched to known types were putatively identified by comparison of the nuclear ribosomal ITS sequence to the GenBank database. Ten taxa were identified among almost 600 root fragments. Additionally, we have employed capillary electrophoresis of fluorescent trnL PCR products (fluorescent fragment length polymorphism, FFLP) to discriminate all taxa identified at the field site. CONCLUSION: We have developed a molecular database for the identification of some common grassland species based on PCR-RFLP of the plastid transfer RNA leucine (trnL) UAA gene intron. This technique will allow fine-scale studies of the rhizosphere, where root identification by morphology is unrealistic and high throughput is desirable

Weak Value in Wave Function of Detector

A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the realization of the weak measurement by the optical polarization and obtain the weak value for any pre- and post-selections. This formula automatically includes the interference effect which is necessary to yields the weak value as an outcome of the weak measurement.Comment: 3 pages, no figures, Published in Journal of the Physical Society of Japa

On the Origins of Three-Dimensionality And Unsteadiness in the Laminar Separation Bubble

We analyse the three-dimensional non-parallel instability mechanisms responsible for transition to turbulence in regions of recirculating steady laminar two-dimensional incompressible separation bubble ®ow in a twofold manner. First, we revisit the problem of Tollmien{Schlichting (TS)-like disturbances and we demonstrate, for the ­ rst time for this type of ®ow, excellent agreement between the parabolized stabil- ity equation results and those of independently performed direct numerical simula- tions. Second, we perform a partial-derivative eigenvalue problem stability analysis by discretizing the two spatial directions on which the basic ®ow depends, precluding TS-like waves from entering the calculation domain. A new two-dimensional set of global ampli­ ed instability modes is thus discovered. In order to prove earlier topo- logical conjectures about the ®ow structural changes occurring prior to the onset of bubble unsteadiness, we reconstruct the total ®ow­ eld by linear superposition of the steady two-dimensional basic ®ow and the new most-ampli­ ed global eigenmodes. In the parameter range investigated, the result is a bifurcation into a three-dimensional ®ow­ eld in which the separation line remains una¬ected while the primary reattach- ment line becomes three dimensional, in line with the analogous result of a multitude of experimental observations

Indistinguishable Particles in Quantum Mechanics: An Introduction

In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This is, for electrons, the Pauli Exclusion Principle, or in general, the Symmetrization Postulate. Then, we introduce fermions and bosons and the distributions respectively describing their statistical behaviour in indistinguishable situations. Following that, we discuss the spin-statistics connection, as well as alternative statistics and experimental evidence for all these results, including the use of bunching and antibunching of particles emerging from a beam splitter as a signature for some bosonic or fermionic states.Comment: To appear in Contemp. Phy

Inelastic collapse of a randomly forced particle

We consider a randomly forced particle moving in a finite region, which rebounds inelastically with coefficient of restitution r on collision with the boundaries. We show that there is a transition at a critical value of r, r_c\equiv e^{-\pi/\sqrt{3}}, above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of r_c is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion.Comment: 4 pages, REVTEX, 2 EPS figures, uses multicol.sty and epsf.st