A three-dimensional simulation of transition and early turbulence in a time-developing mixing layer

The physics of the transition and early turbulence regimes in the time developing mixing layer was investigated. The sensitivity of the mixing layer to the disturbance field of the initial condition is considered. The growth of the momentum thickness, the mean velocity profile, the turbulence kinetic energy, the Reynolds stresses, the anisotropy tensor, and particle track pictures of computations are all examined in an effort to better understand the physics of these regimes. The amplitude, spectrum shape, and random phases of the initial disturbance field were varied. A scheme of generating discrete orthogonal function expansions on some nonuniform grids was developed. All cases address the early or near field of the mixing layer. The most significant result shows that the secondary instability of the mixing layer is produced by spanwise variations in the straining field of the primary vortex structures

Certain aspects of the H-ion concentration of the soils of a central Indiana river bluff

In a recent paper, Cain and Friesner (3) found that there was a relation between topography and the hydrogen-ion concentration of the soil. This work was done on certain hills in the Sycamore creek region, Morgan county, Indiana, where it was found that the acidity was greater on the hilltops and less in the intervening ravines, so that curves representing the degree of acidity of the soil at different points on a line crossing the hills were roughly parallel with the topography. The average acidity on three ridge tops was pH 5.3, while the adjacent ravine bottoms were practically neutral, averaging pH 6.9. The consistently greater acidity of the ridge tops and upper slopes seems to play a significant part in the distribution of certain plants found only in such situations, viz., Vaccinium vacillans, Gaylussacia baccata, Polytrichum juniperinum, etc. Since these ridges studied in the Sycamore creek region were only about one hundred feet high, it was thought desirable to investigate some river hills which rise about 250 feet above their immediate bases

Quantum Network Theory of Computing with Respect to Entangled Flux Qubits and External Perturbation

In this work, we attempt to show the differences between traditional qubit-based spintronic methodology for quantum computation and the possible ballistic quantum network implementations. Flux qubits can be considered topologically similar to the persistent currents possessed as the angular momentum in Aharonov-Bohm loops, which can be coupled and thus entangled together. Since entanglement is guaranteed for coupled quantum networks, starting from a point-contacted situation, we first investigate how varying the degree of entanglement strength can affect the superposition of the four possible states for two isolated flux qubits being brought together. In general, the superposition is destroyed once the degree of entanglement is altered from the point-contact situation. However, we show that for a specific network with maximum entanglement, a Bell state situation can be produced. We then examine the effects of varying the external perturbation strength on the readout capability in quantum networks by changing the coupling strength through the cross-sectional area ratio. From the analysis of our results, we are persuaded to believe that two universally accepted components for quantum computing are not valid in the quantum network approach: the need of a weak perturbation for measurement of computational results and the requirement of fixed entanglement among qubits. We show there is an interplay between the strength of the entanglement and that of the external perturbation for high-fidelity classical readouts

Thevenin Equivalence in Disorderless Quantum Networks

We outline the procedure of extending the Thévenin equivalence principle for classical electric circuits to reducing Aharonov-Bohm-based quantum networks into equivalent models. With examples, we show from first principles how the requirements are related to the electron band structure\u27s Fermi level and the lattice spacing of the network. Quantum networks of varying degrees of coupling strength from four basic classifications of single and double entangled loops sharing symmetry and highly correlated band structures are used to demonstrate the concept. We show the limitations of how the principle may be applied. Several classes of examples are given and their equivalent forms are shown

Electron Transport Through Two Irreducibly-Coupled Aharonov-Bohm Rings with Applications to Nanostructure Quantum Computing Circuits

We investigated several classes of two coupled Aharonov-Bohm rings that share a finite center common path, where the phase of the electron wave function can be modulated by two distinct magnetic fluxes. The coupling is similar to two coupled atoms. The behavior of charge accumulation along the center common path or, equivalently, the bonding and anti-bonding of the two rings can be achieved as the two applied fluxes are varied. Thus, when three external terminals are connected to such coupled rings, the behavior of the electron transport is divided into several classes, depending on the number of atoms in each ring and the locations of the terminals. The results are presented here. The applicable electron wave computing circuits are discussed. In particular, a half-adder construction is shown here by employing the symmetric and anti-symmetric properties of the transmission of a given terminal when the sign of the flux is changed. The analogy of two coupled rings with respect to two spins allows one to make a further connection with traditional spintronics-based schemes

Scaling Relations and the Role of Bond-Charge to the Electron Transmission through Two Coupled Aharonov-Bohm Rings

Electron transport and the exact scaling relations for two irreducibly coupled Aharonov-Bohm (AB) rings with two external terminals attached are investigated. In coupled AB rings, a center common path exists where the phase of the electron wave function can be modulated by two applied fluxes simultaneously. The two coupled rings can be considered as two coupled atoms where Fermi level crossings exist not only between bonding states but also between bonding and anti-bonding states when the applied flux is varied in one of the two cases studied. We show that when the smallest atomic-sized coupled rings are scaled up any odd number of times, an identical electron transmission is preserved. When two terminals are attached to isolated coupled AB rings, there is a further redistribution of bond-charge stored within the center common path. The shift of the electron charge distribution to favor one end of the common path is accompanied by the redistribution of the two partial waves that traverse through the two arms from the input to the output terminal. The flux can control which arm the electron traverses through more favorably, and hence, the center path behaves like a flux-controlled charge reservoir for the electron transport. The unbalanced charge in the entire structure creates a space-charge effect much like a p-n junction. The paradox of the delocalization of the electron wave when two AB rings are coupled and the subsequent localization effect of the electron transport in a quantum network are described