The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory (LST). To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number (based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow) and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations (PSE). At Mach 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At Mach 4.5 and Mach 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear layer. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher Mach number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wave numbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at Mach 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes

Bubbling and bistability in two parameter discrete systems

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.Comment: LaTeX v2.09, 14 pages with 4 PNG figure

Light-cone gauge Hamiltonian for AdS_4 x CP^3 superstring

It is developed the phase-space formulation for the Type IIA superstring on the AdS_4 x CP^3 background in the kappa-symmetry light-cone gauge for which the light-like directions are taken from the D=3 Minkowski boundary of AdS_4. After fixing bosonic light-cone gauge the superstring Hamiltonian is expressed as a function of the transverse physical variables and in the quadratic approximation corresponds to the light-cone gauge-fixed IIA superstring in flat space.Comment: 12 pages, LaTeX; v2 minor improvements of the text, misprints corrected, reference added; v3: missing terms in Eqs.(8),(53) and (56) adde

Introduction to dynamical horizons in numerical relativity

This paper presents a quasi-local method of studying the physics of dynamical black holes in numerical simulations. This is done within the dynamical horizon framework, which extends the earlier work on isolated horizons to time-dependent situations. In particular: (i) We locate various kinds of marginal surfaces and study their time evolution. An important ingredient is the calculation of the signature of the horizon, which can be either spacelike, timelike, or null. (ii) We generalize the calculation of the black hole mass and angular momentum, which were previously defined for axisymmetric isolated horizons to dynamical situations. (iii) We calculate the source multipole moments of the black hole which can be used to verify that the black hole settles down to a Kerr solution. (iv) We also study the fluxes of energy crossing the horizon, which describes how a black hole grows as it accretes matter and/or radiation. We describe our numerical implementation of these concepts and apply them to three specific test cases, namely, the axisymmetric head-on collision of two black holes, the axisymmetric collapse of a neutron star, and a non-axisymmetric black hole collision with non-zero initial orbital angular momentum.Comment: 20 pages, 16 figures, revtex4. Several smaller changes, some didactic content shortene

Holographic Dual of Linear Dilaton Black Hole in Einstein-Maxwell-Dilaton-Axion Gravity

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SL(2, R)$_L$$\times$SL(2, R)$_R$ Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.Comment: 15 pages, no figure, published versio

Bioremediation of Penicillin-Contaminated Poultry Faecal Waste using Betalactamase-Producing Bacteria

The widespread use of antibiotics in poultry farming has led to the contamination of the environment with antibiotic residues, posing significant risks to human health and contributing to the development of antibiotic resistance. In this study, we aimed to isolate betalactamase-producing bacteria from poultry faecal waste samples obtained from local poultry processing industries in Namakkal, Tamilnadu, India. The potential isolates were further characterized for betalactamase enzyme activity and their ability to degrade penicillin, a commonly used antibiotic in the poultry industry. Twenty poultry faecal waste samples were collected from regular poultry waste dumping sites. Microorganisms were isolated from these samples using the serial dilution and plating method on nutrient agar media. The isolated bacterial colonies were purified to obtain pure cultures for further analysis. The betalactamase-producing isolates were identified using the iodometric tube method, and four out of ten isolates showed positive results for betalactamase activity. These positive isolates were subjected to enzyme assay, and isolate 10 exhibited the highest enzyme activity with a concentration of 43U/ml, followed by isolate 7 with 30.5U/ml of enzyme. The potential betalactamase-producing isolate 10 was selected for its application in the degradation of penicillin in poultry faecal waste. The faecal waste samples were collected from the antibiotic-contaminated area of a poultry farm. After the addition of separated crude enzyme (5ml of 100U), the faecal sample was incubated for 15 days under specific conditions. HPLC analysis revealed a significant degradation of penicillin in the test sample treated with the betalactamase enzyme, with a degradation percentage of 48.6%. The results of this study indicate that betalactamase-producing bacteria can effectively degrade penicillin in poultry faecal waste. This bioremediation approach presents a potential solution to reduce antibiotic pollution in the environment and mitigate the risk of antibiotic resistance. Further research and application of such enzymatic degradation methods could contribute to sustainable and eco-friendly waste management practices in the poultry industry

Hidden Conformal Symmetry of the Reissner-Nordstr{\o}m Black Holes

Motivated by recent progresses in the holographic descriptions of the Kerr and Reissner-Nordstr{\o}m (RN) black holes, we explore the hidden conformal symmetry of nonextremal uplifted 5D RN black hole by studying the near horizon wave equation of a massless scalar field propagating in this background. Similar to the Kerr black hole case, this hidden symmetry is broken by the periodicity of the associated angle coordinate in the background geometry, but the results somehow testify the dual CFT description of the nonextremal RN black holes. The duality is further supported by matching of the entropies and absorption cross sections calculated from both CFT and gravity sides.Comment: 14 pages, no figur