Propagation of sound through a sheared flow

Sound generated in a moving fluid must propagate through a shear layer in order to be measured by a fixed instrument. These propagation effects were evaluated for noise sources typically associated with single and co-flowing subsonic jets and for subcritical flow over airfoils in such jets. The techniques for describing acoustic propagation fall into two categories: geometric acoustics and wave acoustics. Geometric acoustics is most convenient and accurate for high frequency sound. In the frequency range of interest to the present study (greater than 150 Hz), the geometric acoustics approach was determined to be most useful and practical

Leo

The purpose of this project was to understand how information is gathered about stars, constellations, and galaxies, specifically the constellation Leo. Information gathered for this project includes how a star\u27s position can be used to calculate the length of the year and how the mass and spectral type of a specific star can show when the star will die. This is a project for the Natural Sciences Poster Session at Parkland Colleg

A study of ingestion and dispersion of engine exhaust products in trailing vortex systems

Analysis has been made of the ingestion and dispersion of engine exhaust products into the trailing vortex system of supersonic aircraft flying in the stratosphere. The rate of mixing between the supersonic jet and the co-flowing supersonic stream was found to be an order of magnitude less than would be expected on the basis of subsonic eddy-viscosity results. The length of the potential core was 66 nozzle exit radii so that the exhaust gases remain at elevated temperatures and concentrations over much longer distances than previsously estimated. Ingestion started at the end of the potential core and all hot gas from the engine was ingested into the trailing vortex within two core lengths. Comparison between the buoyancy calculations for the supersonic case with nondimensionalized subsonic aircraft contrail data on wake spreading showed good agreement. Velocity and temperature profiles have been specified at various stages of the wake, and the analysis in this report can be used to predict variations of concentrations of species such as nitrogen oxides under conditions of chemical reaction

Power spectra methods for a stochastic description of diffusion on deterministically growing domains

A central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity. Generally, the mathematical treatments of biological systems have used continuum, mean-field hypotheses for their constituent parts, which ignores any sources of intrinsic stochastic effects. In this paper we consider a stochastic space-jump process as a description of diffusion, i.e., particles are able to undergo a random walk on a discretized domain. By developing analytical Fourier methods we are able to probe this probabilistic framework, which gives us insight into the patterning potential of diffusive systems. Further, an alternative description of domain growth is introduced, with which we are able to rigorously link the mean-field and stochastic descriptions. Finally, through combining these ideas, it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean-field steady state

Stochastic reaction & diffusion on growing domains: understanding the breakdown of robust pattern formation

Many biological patterns, from population densities to animal coat markings, can be thought of as heterogeneous spatiotemporal distributions of mobile agents. Many mathematical models have been proposed to account for the emergence of this complexity, but, in general, they have consisted of deterministic systems of differential equations, which do not take into account the stochastic nature of population interactions. One particular, pertinent criticism of these deterministic systems is that the exhibited patterns can often be highly sensitive to changes in initial conditions, domain geometry, parameter values, etc. Due to this sensitivity, we seek to understand the effects of stochasticity and growth on paradigm biological patterning models. In this paper, we extend spatial Fourier analysis and growing domain mapping techniques to encompass stochastic Turing systems. Through this we find that the stochastic systems are able to realize much richer dynamics than their deterministic counterparts, in that patterns are able to exist outside the standard Turing parameter range. Further, it is seen that the inherent stochasticity in the reactions appears to be more important than the noise generated by growth, when considering which wave modes are excited. Finally, although growth is able to generate robust pattern sequences in the deterministic case, we see that stochastic effects destroy this mechanism for conferring robustness. However, through Fourier analysis we are able to suggest a reason behind this lack of robustness and identify possible mechanisms by which to reclaim it

Influence of stochastic domain growth on pattern nucleation for diffusive systems with internal noise

Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport. However, self-organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity, as illustrated by the behavior of the French-flag model in response to intrinsic noise and Turing’s model when subjected to fluctuations in initial conditions. Domain growth is known to be a stabilizing factor for the latter, though the interaction of intrinsic noise and domain growth is underexplored, even in the simplest of biophysical settings. Previously, we developed analytical Fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems. In this paper we extend our analysis to encompass stochastically growing domains. This form of growth can be used only to link the meso- and macroscopic domains as the “box-splitting” form of growth on the microscopic scale has an ill-defined thermodynamic limit. The extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain, while stochastically controlling the length of each discretized compartment. Due to the dependence of diffusion on the domain discretization, we find that the description of diffusion cannot be uniquely derived. We apply these analytical methods to two justified descriptions, where it is shown that, under certain conditions, diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium, without additional kinetics. Finally, a logistically growing domain is considered. Not only does this show that we can deal with nonmonotonic descriptions of stochastic growth, but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary “on average.

Theoretical and experimental study of supersonic mixing of turbulent dissimilar streams

Molecular weight effects on rate of turbulent mixing of dissimilar supersonic gas stream

Continuous quantum non-demolition measurement of Fock states of a nanoresonator using feedback-controlled circuit QED

We propose a scheme for the quantum non-demolition (QND) measurement of Fock states of a nanomechanical resonator via feedback control of a coupled circuit QED system. A Cooper pair box (CPB) is coupled to both the nanoresonator and microwave cavity. The CPB is read-out via homodyne detection on the cavity and feedback control is used to effect a non-dissipative measurement of the CPB. This realizes an indirect QND measurement of the nanoresonator via a second-order coupling of the CPB to the nanoresonator number operator. The phonon number of the Fock state may be determined by integrating the stochastic master equation derived, or by processing of the measurement signal.Comment: 5 pages, 3 figure

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases

Non-linear effects on Turing patterns: time oscillations and chaos.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, Turing patterns oscillate in time, a phenomenon which is expected to occur only in a three morphogen system. When varying a single parameter, a series of bifurcations lead to period doubling, quasi-periodic and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examined the Turing conditions for obtaining a diffusion driven instability and discovered that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. All this results demonstrates the limitations of the linear analysis for reaction-diffusion systems