Firm corruption in the presence of an auditor

This paper develops a framework to explore firm corruption taking account of interaction with an auditor. The basic idea is that an auditor can provide auditing and other (consultancy) services. The extent of the other services depends on firm profitability. Hence auditor profitability can increase with firm corruption that may provide an incentive to collude in corrupt practices. This basic idea is developed using a game theoretic framework. It is shown that a multiplicity of equilibria exist from stable corruption, through auditor controlled corruption, via multiple equilibria to honesty on behalf of both actors. Following the development of the model various policy options are highlighted that show the difficulty of completely removing corrupt practices

Reply on `comment on our paper `Single two-level ion in an anharmonic-oscillator trap: Time evolution of the Q function and population inversion ''

We show here that the model Hamiltonian used in our paper for ion vibrating in a q-analog harmonic oscillator trap and interacting with a classical single-mode light field is indeed obtained by replacing the usual bosonic creation and annihilation operators of the harmonic trap model by their q-deformed counterparts. The approximations made in our paper amount to using for the ion-laser interaction in a q-analog harmonic oscillator trap, the operator F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon A}, which is analogous to the corresponding operator for ion in a harmonic oscillator trap that is $F=exp{-(|\epsilon|^2 /2)}exp{i\epsilon a^{\dagger }}exp{i\epsilon a}$. In our article we do not claim to have diagonalized the operator, $F_q = exp{i \epsilon (A^{\dagger}+A)}$, for which the basis states |g,m> and |e,m> are not analytic vectors.Comment: Revtex, 4pages. To be Published in Physical Review A59, NO.4(April 99

A critical layer model for turbulent pipe flow

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating modes, permitting comparison of our results to experimental data, and identify the steady component of the velocity field that varies only in the wall-normal direction as the turbulent mean profile. The "optimal" forcing shape, that gives the largest velocity response, is assumed to lead to modes that will be dominant and hence observed in turbulent pipe flow. An investigation of the most amplified velocity response at a given wavenumber-frequency combination reveals critical layer-like behaviour reminiscent of the neutrally stable solutions of the Orr-Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely a wall layer that scales with $R^{+1/2}$ and a critical layer, where the propagation velocity is equal to the local mean velocity, that scales with $R^{+2/3}$ in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall.Comment: Submitted to the Journal of Fluid Mechanics and currently under revie

On the design of optimal compliant walls for turbulence control

This paper employs the theoretical framework developed by Luhar et al. (J. Fluid Mech., 768, 415-441) to consider the design of compliant walls for turbulent skin friction reduction. Specifically, the effects of simple spring-damper walls are contrasted with the effects of more complex walls incorporating tension, stiffness and anisotropy. In addition, varying mass ratios are tested to provide insight into differences between aerodynamic and hydrodynamic applications. Despite the differing physical responses, all the walls tested exhibit some important common features. First, the effect of the walls (positive or negative) is greatest at conditions close to resonance, with sharp transitions in performance across the resonant frequency or phase speed. Second, compliant walls are predicted to have a more pronounced effect on slower-moving structures because such structures generally have larger wall-pressure signatures. Third, two-dimensional (spanwise constant) structures are particularly susceptible to further amplification. These features are consistent with many previous experiments and simulations, suggesting that mitigating the rise of such two-dimensional structures is essential to designing performance-improving walls. For instance, it is shown that further amplification of such large-scale two-dimensional structures explains why the optimal anisotropic walls identified by Fukagata et al. via DNS (J. Turb., 9, 1-17) only led to drag reduction in very small domains. The above observations are used to develop design and methodology guidelines for future research on compliant walls

Production of nuclei and antinuclei in pp and Pb-Pb collisions with ALICE at the LHC

We present first results on the production of nuclei and antinuclei such as (anti)deuterons, (anti)tritons, (anti)3He and (anti)4He in pp collisions at \s = 7 TeV and Pb-Pb collisions at \sNN = 2.76 TeV. These particles are identified using their energy loss (dE/dx) information in the Time Projection Chamber of the ALICE experiment. The Inner Tracking System gives a precise determination of the event vertex, by which primary and secondary particles are separated. The high statistics of over 360 million events for pp and 16 million events for Pb-Pb collisions give a significant number of light nuclei and antinuclei (Pb-Pb collisions: \sim30,000 anti-deuterons($\bar{d}$) and \sim4 anti-alpha($\bar{^4He}$)). The predictions of various particle ratios from the THERMUS model is also discussed.Comment: 4 pages, 5 figures, parallel talk at Quark Matter 2011, May 23rd-28th 2011, Annecy, Franc