Numerical investigation of unsteady laminar incompressible co-axial boundary layer flows

Finite difference method for analysis of laminar incompressible boundary layer flows at jet exi

Resolvent modelling of jet noise: the need for forcing models

The singular value decomposition of the mean-flow-based resolvent operator, or resolvent analysis, has proven to provide essential insights into the dynamics of various turbulent flows. In this study, we perform a resolvent analysis of a compressible turbulent jet, where the optimisation domain of the response modes is located in the acoustic field, excluding the hydrodynamic region, in order to promote acoustically efficient modes. We examine the properties of the acoustic resolvent and assess its potential for jet-noise modelling, focusing on the subsonic regime. We compare resolvent modes with SPOD modes educed from LES data. Resolvent forcing modes, consistent with previous studies, are found to contain supersonic waves associated with Mach wave radiation in the response modes. This differs from the standard resolvent in which hydrodynamic instabilities dominate. Acoustic resolvent response modes generally have better alignment with acoustic SPOD modes than standard resolvent response modes. For the optimal mode, the angle of the acoustic beam is close to that found in SPOD modes for moderate frequencies. However, there is no significant separation between the singular values of the leading and sub-optimal modes. Some suboptimal modes are furthermore shown to contain irrelevant structure for jet noise. Thus, even though it contains essential acoustic features absent from the standard resolvent approach, the SVD of the acoustic resolvent alone is insufficient to educe a low-rank model for jet noise. But because it identifies the prevailing mechanisms of jet noise, it provides valuable guidelines in the search of a forcing model (Karban $\textit{et al.}$ 2022, An empirical model of noise sources in subsonic jets. arXiv preprint arXiv:2210.01866).Comment: 24 pages, 20 figure

Quantum phase space distributions in thermofield dynamics

It is shown that the the quantum phase space distributions corresponding to a density operator $\rho$ can be expressed, in thermofield dynamics, as overlaps between the state $\mid \rho >$ and "thermal" coherent states. The usefulness of this approach is brought out in the context of a master equation describing a nonlinear oscillator for which exact expressions for the quantum phase distributions for an arbitrary initial condition are derived.Comment: 17 pages, revtex, no figures. number of pages were incorrectly stated as 3 instead of 17. No other correction

Preparation of Silica Nanoparticles and Its Beneficial Role in Cementitious Materials

Spherical silica nanoparticles (n‐SiO2) with controllable size have been synthesized using tetraethoxysilane as starting material and ethanol as solvent by sol‐gel method. Morphology and size of the particles was controlled through surfactants. Sorbitan monolaurate, sorbitain monopalmitate and sorbitain monostearate produced silica nanoparticles of varying sizes (80‐150 nm), indicating the effect of chain length of the surfactant. Increase in chain length of non‐ionic surfactant resulted in decreasing particle size of silica nanoparticles. Further, the size of silica particles was also controlled using NH3 as base catalyst. These silica nanoparticles were incorporated into cement paste and their role in accelerating the cementitious reactions was investigated. Addition of silica nanoparticles into cement paste improved the microstructure of the paste and calcium leaching is significantly reduced as n‐SiO2 reacts with calcium hydroxide and form additional calcium‐ silicate‐hydrate (C‐S‐H) gel. It was found that calcium hydroxide content in silica nanoparticles incorporated cement paste reduced ~89% at 1 day and up to ~60% at 28 days of hydration process. Synthesized silica particles and cement paste samples were characterized using scanning electron microscopy (SEM), powder X‐ray diffraction (XRD), infrared spectroscopy (IR) and thermogravimetric analysis (TGA)

Entanglement by linear SU(2) transformations: generation and evolution of quantum vortex states

We consider the evolution of a two-mode system of bosons under the action of a Hamiltonian that generates linear SU(2) transformations. The Hamiltonian is generic in that it represents a host of entanglement mechanisms, which can thus be treated in a unified way. We start by solving the quantum dynamics analytically when the system is initially in a Fock state. We show how the two modes get entangled by evolution to produce a coherent superposition of vortex states in general, and a single vortex state under certain conditions. The degree of entanglement between the modes is measured by finding the explicit analytical dependence of the Von Neumann entropy on the system parameters. The reduced state of each mode is analyzed by means of its correlation function and spatial coherence function. Remarkably, our analysis is shown to be equally as valid for a variety of initial states that can be prepared from a two-mode Fock state via a unitary transformation and for which the results can be obtained by mere inspection of the corresponding results for an initial Fock state. As an example, we consider a quantum vortex as the initial state and also find conditions for its revival and charge conjugation. While studying the evolution of the initial vortex state, we have encountered and explained an interesting situation in which the entropy of the system does not evolve whereas its wave function does. Although the modal concept has been used throughout the paper, it is important to note that the theory is equally applicable for a two-particle system in which each particle is represented by its bosonic creation and annihilation operators.Comment: 6 figure

Exact time evolution and master equations for the damped harmonic oscillator

Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath preparations. Exact non-stationary Liouville operators can be found only for particular preparations. Three physically meaningful examples are examined. An exact new master equation is derived for thermal initial conditions. Second, the Liouville operator governing the time-evolution of equilibrium correlations is obtained. Third, factorizing initial conditions are studied. Additionally, one can show that there are approximate Liouville operators independent of the initial preparation describing the long time dynamics under appropriate conditions. The general form of these approximate master equations is derived and the coefficients are determined for special cases of the bath spectral density including the Ohmic, Drude and weak coupling cases. The connection with earlier work is discussed.Comment: to be published in Phys. Rev.

Quantum interference in optical fields and atomic radiation

We discuss the connection between quantum interference effects in optical beams and radiation fields emitted from atomic systems. We illustrate this connection by a study of the first- and second-order correlation functions of optical fields and atomic dipole moments. We explore the role of correlations between the emitting systems and present examples of practical methods to implement two systems with non-orthogonal dipole moments. We also derive general conditions for quantum interference in a two-atom system and for a control of spontaneous emission. The relation between population trapping and dark states is also discussed. Moreover, we present quantum dressed-atom models of cancellation of spontaneous emission, amplification on dark transitions, fluorescence quenching and coherent population trapping.Comment: To be published in Journal of Modern Optics Special Issue on Quantum Interferenc

Pulse Control of Decoherence with Population Decay

The pulse control of decoherence in a qubit interacting with a quantum environment is studied with focus on a general case where decoherence is induced by both pure dephasing and population decay. To observe how the decoherence is suppressed by periodic pi pulses, we present a simple method to calculate the time evolution of a qubit under arbitrary pulse sequences consisting of bit-flips and/or phase-flips. We examine the effectiveness of the two typical sequences: bb sequence consisting of only bit-flips, and bp sequence consisting of both bit- and phase-flips. It is shown that the effectiveness of the pulse sequences depends on a relative strength of the two decoherence processes especially when a pulse interval is slightly shorter than qubit-environment correlation times. In the short-interval limit, however, the bp sequence is always more effective than, or at least as effective as, the bb sequence.Comment: 11 pages, 7 figure

Dynamics of Dissipative Quantum Systems--from Path Integrals to Master Equations

The path integral approach offers not only an exact expression for the non- equilibrium dynamics of dissipative quantum systems, but is also a convenient starting point for perturbative treatments. An alternative way to explore the influence of friction in the quantum realm is based on master equations which require, however, in one or the other aspect approximations. Here it is discussed under which conditions and limitations Markovian master equations can be derived from exact path integrals thus providing a firm basis for their applicability.Comment: 10 pages, 1 figur