SELF-SIMILAR PROPERTIES AND LEADING BALANCE SCALING STRUCTURE OF WALL-BOUNDED TURBULENT FLOWS

Wall-bounded turbulent flows are ubiquitous in numerous technological applications, and thus much effort has been devoted to investigate their properties. Scaling analyses involving the application multiple-scale approaches are effectively used to explore parameters (Reynolds, Prandtl numbers) dependent scaling behaviors of these flows. The objective of this dissertation research is to firstly extend the analysis of self-similar behaviors on the inertial domain as admitted by the mean dynamics in wall-bounded turbulent flows (WBTF). It then mathematically and physically characterizes the existence of a leading order balance structure in both the kinetic energy and passive scalar transport budgets, and subsequently uses this leading balance structure for scaling purposes. Recent evidence indicates that, at sufficiently high Reynolds number, a number of the statistical measures of wall-turbulence exhibit self-similar behaviors on an interior inertial domain. Experimental measurements in the Flow Physics Facility at the University of New Hampshire have been acquired, and well-resolved streamwise velocity measurements up to high Reynolds number are used to investigate three measures of self-similarity in turbulent boundary layers, and compare their behaviors with those revealed through analysis of the mean momentum equation. The measures include the Kullback-Leibler divergence (KLD), the logarithmic decrease of even statistical moments, and the so-called diagnostic plot. The findings indicate that the approximately constant KLD profiles and the approximately logarithmic moment profiles follow the same scaling but reside interior to the bounds of the self-similar inertial domain associated with the mean dynamics. Conversely, the bounds of the self-similar region on the diagnostic plot correspond closely to the theoretically estimated bounds. Multiple-scale analysis involving the consideration of the relative magnitude of terms in the governing equation is applied to kinetic energy budgets for fully developed turbulent flow in pipes and channels, and in the zero-pressure gradient turbulent boundary layer. These analyses are based on available high-quality numerical simulation data. The mean kinetic energy budget is analytically verified to exhibit the same four-layer structure as the mean momentum equation, while the turbulence budget only shows either a two- or three-layer structure depending on channel/pipe versus boundary layer flow. A distinct four-layer structure is observed in position and size for the total kinetic energy budget. Here the width of the third layer, which is located in the inertia domain of the mean dynamics, is mathematically reasoned to scale with $\delta^+-\sqrt{\delta^+}$ at finite Reynolds number. Like the velocity field, the passive scalar field equation in WBTF can also be quantified in terms of its leading balance structure. Both the mean scalar and scalar variance equations with constant heat generation for fully-developed turbulent channel are explored. A similar four-layer structure is found using the same methodology. Both the Reynolds number and Prandtl number dependent scaling of the layer thickness is empirically quantified with available DNS data and verified through rigorous scaling analysis. The analysis also indicates that the mean scalar equation can be cast into an invariant form that properly reflects the local dominant physical mechanism, which uncovers the governing effect of a small and constant parameter on an underlying scaling layer hierarchy. There exists a linear region in the distribution of the inner-normalized widths of this layer hierarchy. Like the momentum equation, analysis indicates that this region coincides with where the mean scalar profile exhibits a logarithmic increase and leads to a distinct expression for the scalar log law. The scalar variance equation manifests itself like the total kinetic energy budget with a distinctive four-layer structure, in which the third layer size has a special scaling under the effects of both Reynolds number and Prandtl Number. The underlying causes of the difference between the K{\\u27a}rm{\\u27a}n constant and the scalar K{\\u27a}rm{\\u27a}n constant, i.e., $k_\theta \u3ek$, are also investigated and clarified

Towards Dual-functional Radar-Communication Systems: Optimal Waveform Design

We focus on a dual-functional multi-input-multi-output (MIMO) radar-communication (RadCom) system, where a single transmitter communicates with downlink cellular users and detects radar targets simultaneously. Several design criteria are considered for minimizing the downlink multi-user interference. First, we consider both the omnidirectional and directional beampattern design problems, where the closed-form globally optimal solutions are obtained. Based on these waveforms, we further consider a weighted optimization to enable a flexible trade-off between radar and communications performance and introduce a low-complexity algorithm. The computational costs of the above three designs are shown to be similar to the conventional zero-forcing (ZF) precoding. Moreover, to address the more practical constant modulus waveform design problem, we propose a branch-and-bound algorithm that obtains a globally optimal solution and derive its worst-case complexity as a function of the maximum iteration number. Finally, we assess the effectiveness of the proposed waveform design approaches by numerical results.Comment: 13 pages, 10 figures. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

A Novel Multifunction Digital Chip Design Based on CMOS Technology

The realization of an analog-to-digital-conversion chip has great significance in the applications of electronic products. By considering mature time–number digitization, a new multifunction digital chip with a long time delay was designed in this study on the basis of the principle of analog-to-time conversion (ATC) and the realization of long time delay. With additional resistance, capacitance, and transistors, this chip can easily realize ATC, monostable triggers, Schmitt triggers, and multivibrators. The circuit composition of this chip was analyzed, and every module design was introduced. According to the simulation result of Hspice and CSMC 2P2M CMOS (Complementary Metal Oxide Semiconductor) process database, the chip layout (1mm2) design was accomplished by using CSMC 2P2M CMOS technology. Finally, the designed chip was applied in multiproject wafer flow. The flow test demonstrated that this new chip can meet design goal and is applicable to various digital integrated chip designs as an IP (intellectual property) core

Analyticity and the NcN_c counting rule of SS matrix poles

By studying $\pi\pi$ scattering amplitudes in the large $N_c$ limit, we clarify the $N_c$ dependence of the $S$ matrix pole position. It is demonstrated that analyticity and the $N_c$ counting rule exclude the existence of $S$ matrix poles with ${\cal M}, \Gamma\sim O(1)$. Especially the properties of $\sigma$ and $f_0(980)$ with respect to the $1/N_c$ expansion are discussed. We point out that in general tetra-quark resonances do not exist.Comment: This paper replaces hep-ph/0412175. The latter is withdraw

Synthesis of Bio-inspired μ-oxo Heterobimetallic Nonheme Complexes

University of Minnesota Ph.D. dissertation.July 2017. Major: Chemistry. Advisor: Lawrence Que. 1 computer file (PDF); xxvi, 204 pages.Enzymes with dinuclear metallocofactors perform versatile functions in nature. In their catalytic cycles, the two metal ions are often connected through a bridging ligand with resulting cooperative effects. Oxo-bridged heterobimetallic species stand out and act as crucial intermediates in various bimetallic active sites. For decades different approaches have been investigated to prepare synthetic μ-oxo heterobimetallic molecules. However, the synthetic strategies either have difficulties in selectively binding the two metals at specific sites while avoiding mixtures and homodinuclear side products, or require complicated unsymmetrical ligand synthesis. This thesis explores a way of quantitatively obtaining μ-oxo heterobimetallic nonheme complexes from the inner sphere electron transfer reaction between ¬nonheme oxoiron(IV) species and a reducing metal salt. Specifically, two types of molecules with Fe–O–Cr and Fe–O–Mn cores are prepared, and based on thorough spectroscopic characterization their structures have been identified. The effect of the Fe coordination ligand to the Fe–O–Cr core is discussed in detail. The Fe–O–Mn species are among the very few synthetic complexes with Fe/Mn bimetallic center, and their structures and reactivities have been compared with the Fe/Mn intermediates in Class Ic RNR. This research has given rise to an alternative way of synthesizing μ-oxo heterobimetallic nonheme complexes with convenience and high efficiency