Two-dimensional Tunnel Research Articles

Transonic turbine vane tests in a new miniature cascade facility

A new two-dimensional mini-cascade blow-down tunnel, with eight vane passages of only 20 mm true chord, 15 mm pitch, and 40 mm span, has been developed for testing gas turbine nozzle guide vane profiles at transonic exit Mach numbers ( M) and realistic Reynolds numbers ( Re) with a quick turnaround and high accuracy. The small size of the cascade has many advantages. Vane profiles can be tested at adjustable engine representative Re at room temperature with exit static pressures above atmospheric and Re and M can be independently varied. The mass flow is small and the long run times (>3 min) allow downstream traversing with a three-hole miniature probe. The inaccuracies inherent in the traditional method of mounting the vanes/blades on pegs in the Schlieren windows have been eliminated by accurately computer numerical control (CNC) machining the whole cascade of vanes integral with the tunnel side walls, with re-usable, plug-in Schlieren windows. Cascades of new test vane profiles are quickly machined and tested, with a fast turn-around for comparative studies. A new Schlieren photography lens arrangement is demonstrated, which captures numerous flow visualization images per run directly into a digital SLR camera. Lower-than-atmospheric exhaust pressures were achieved by using a long exhaust designed to maximize exit flow dynamic pressure recovery using the self-ejector pumping effect. Exhaust pressures as low as 0.7 bar were achieved using the self-pumping exhaust, allowing M up to 1.6 with 3 bar inlet pressure and an exhaust at atmospheric pressure. An analytical model is developed for the mildly supersonic exit flow condition and validated against experimental data. Excellent agreement is achieved. Results presented for a typical transonic cascade show that the tunnel performs well in the subsonic and low supersonic region, but, as the exit M increases, shock-wave reflections from the free jet boundary, seen on the Schlieren, cause non-periodicity. Deep in the cascade, the flow is still periodic and can be used for investigations of loss and shock boundary-layer interaction. Interestingly, if the downstream pressure is reduced further to give even higher (but unrealistic) M, the cascade becomes axially supersonic and excellent periodicity is restored. Schlieren results are compared with computational fluid dynamics (CFD) simulations of the tunnel flow, and the loss measurements are validated against measurements conducted using a large-scale cascade at Göttingen.

Effect of Rashba spin–orbit coupling on the spin-polarized transport in ferromagnet/semiconductor double tunnel junctions

Considering the Rashba spin–orbit interaction in the semiconductor, we study theoretically the spin-polarized transport in a two-dimensional ferromagnetic semiconductor double tunnel junctions by a quantum-mechanical approach. It is found that the transmission coefficient shows typical resonant transmission properties and the Rashba spin–orbit coupling has great different influences on the transmission coefficients of electrons with spin-up and down and tunnelling magnetoresistance (TMR). More importantly, the TMR is significantly enhanced by increasing the spin–orbit coupling, which is very useful for the designing of magnetic digital and memory sensor.

Two-Dimensional Tunneling Effects on the Leakage Current of MOSFETs With Single Dielectric and High-$\kappa$ Gate Stacks

The gate leakage currents of single-gate silicon-on- insulator (SOI) n-type MOSFETs are investigated, assuming direct tunneling as the leakage mechanism and using either a 1-D Schrodinger-Poisson-based approach coupled to the conventional drift-diffusion transport model or a full quantum mechanical treatment. The first approach consists of calculating the transmission probability through the dielectric material along straight lines connecting the transistor channel to the gate. The second method is based on a 2-D Schrodinger-Poisson solver, where carriers are injected into the device from the source, drain, and gate contacts. The simulated structures have a physical gate length of 32 nm. The channel is isolated from the gate contact by a dielectric layer with an equivalent oxide thickness of 1.2 nm. This layer is composed of either pure SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> or a high-kappa SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stack. Irrespective of the dielectric material, the leakage currents calculated with the 1-D approach are about one order of magnitude smaller at low gate voltages and converge toward the same value as the channel potential barrier decreases. The difference is caused by the diffraction of the electron waves at both edges of the gate contact. This peculiar 2-D behavior of the gate leakage currents, as well as the limit of the 1-D model, is discussed in this paper for various dielectric configurations.

A plateau structure in the tunnelling spectrum as a manifestation of a new tunnelling mechanism in multi-dimensional barrier systems

In recent years a new description has been developed for tunnelling in multi-dimensional systems based on complexified stable–unstable manifolds of periodic saddles. The complexified stable–unstable manifolds guide complex-classical tunnelling trajectories over the energetic barrier (Takahashi and Ikeda 2003 J. Phys. A: Math. Gen. 36 7953). In this paper it is claimed, based on theoretical analysis and numerical evidence, that the tunnelling mechanism due to complexified stable–unstable manifolds is associated with a characteristic plateau feature in the tunnelling spectrum. An analysis of a particular two-dimensional barrier tunnelling model shows that the plateau feature is obtained by a fully quantum-mechanical computation, and that the complex-semiclassical theory successfully reproduces this feature. Moreover, an analytical theory based upon Melnikov's method is developed and used to clarify quantitatively how the tunnelling mechanism due to the complexified stable–unstable manifolds leads to the formation of the plateau structure; in particular, it is shown that the classical action along the complexified stable manifold controls the height of the plateau. The analysis presented here is based on a particular model, but the main claims should hold for any system with multi-dimensional barrier tunnelling because of the universality of the underlying mechanism.

Flow field of self-excited rotationally oscillating equilateral triangular cylinder

Abstract This paper studies the flow field of a particular fluid-structure interaction phenomenon—the continuous angular oscillation of a centrally pivoted equilateral triangular cylinder (prism), under uniform two-dimensional incompressible flow. Dye flow visualization of a 30 cm long and 10 cm wide cylinder in a two-dimensional water tunnel was conducted. Under a uniform incoming flow of 7.5 cm/s, the cylinder oscillated continuously after an initial perturbation. On the windward side of the cylinder, a vortex was formed at the sharp edges of the cylinder during the initial phase, whereas on the leeward side, the flow stayed attached. The phase-averaged particle image velocimetry (PIV) measurements are also presented. PIV results show the interchange of flow patterns from that over a flat plate to flow past a sharp edge and vice versa.

Calculation of the kinetics of the photochemical reaction of hydrogen atom transfer in a molecular crystal

The rate constant for the tunneling bimolecular reaction of hydrogen atom transfer in the condensed phase was calculated. For the fluorene-acridine (T1) system embedded into a fluorene molecular crystal, two-dimensional tunneling amplitudes were determined by numerically solving the Schrodinger equation and a complete calculation of the kinetic characteristics of the reaction was performed within the frame of the Fermi golden rule with consideration given to the quantization of energy levels of reactants and products and the phonon spectrum of the crystal. Sections of a PES that was calculated with regard to the interaction of the chemical subsystem with the crystalline environment were calculated by means of a previously described method. The experimentally observed kinetic characteristics were satisfactorily reproduced over a temperature range of 30 K < T < 300 K by adjusting the phonon spectrum parameters within 20% of the values obtained in their independent calculations. The proposed interpretation of the low-temperature kinetics of the process differs from that based on the earlier asymptotic estimate. The fundamental problems that arise when the Fermi golden rule is applied to the treatment of hydrogen atom transfer at low temperatures are discussed.

Probing the Electronic Properties of Self-Organized Poly(3-dodecylthiophene) Monolayers by Two-Dimensional Scanning Tunneling Spectroscopy Imaging at the Single Chain Scale

Regioregular poly(3-dodecylthiophene) films self-organized on highly oriented pyrolytic graphite have been investigated by scanning tunneling microscopy and two-dimensional scanning tunneling spectroscopy (STS). Simulated spectra in very good agreement with the experimental data have been obtained by a method combining ab initio and semiempirical approaches, which allows a careful discussion of the polymer electronic states. From the experimental data, with the support of modeling, it is shown that the STS spectra give a direct access to the polymer semiconducting band gap without noticeable charge-transfer effects from the substrate. Spectroscopic images are achieved at the single chain scale, which allows scrutinizing the electronic consequences of chain folds and pi-stacking effects through spectroscopic contrasts. While chain folds do not locally increase the polymer band gap more than a few tens of millielectonvolt, a striking widening of the STS conductance gap is observed in the case of electronic tunneling through two interacting polymer layers. Scenarios based on nonplanar configuration of thiophene cycles within the second layer or variations of the charge screening effects are proposed to explain this phenomenon.

Low energy dynamics of two-dimensional lateral tunnel junctions

We report on the low temperature tunneling characteristics of two-dimensional lateral tunnel junctions (2DLTJs) consisting of two coplanar two-dimensional electron systems separated by an in-plane tunnel barrier. The tunneling conductance of the 2DLTJ exhibits a characteristic dip at small voltages—consistent with the phenomenon of zero-bias anomaly in low-dimensional tunnel junctions—and a broad conductance peak at the Coulombic energy scale. The conductance peak remains robust under magnetic fields well into the quantum Hall regime. We identify the broad conductance maxima as the signature of the pseudogap in the tunneling density of states below the characteristic Coulomb interaction energy of the 2DLTJ.

Nonlinear resonant tunneling in low-dimensional systems in a magnetic field: Energy dispersion

We study two-dimensional to two-dimensional (2D–2D) tunneling between two electron layers separated by a wide barrier in an in-plane magnetic field B. The electron gases are separately in equilibrium with their chemical potentials displaced by the bias energy V. We show for a general electronic structure that the tunneling current shows a “fish-like” domain shape on the Δ k - V plane where Δ k ∝ B is the B-induced wave number displacement. The domain shape is determined by the Fermi energies and wave numbers. The boundaries between the high-, low-, and zero-current regions are sharp, representing the high differential conductance and are made of a combination of regular, inverted, and shifted energy-dispersion curves. This result is also valid for 2D–1D and 1D–1D tunneling. The observed data for the 2D–2D tunneling currents as well as the differential conductance in GaAs/Al x Ga 1 - x As double quantum wells yield good agreement with the predicted domain shape.

Interaction Effects and Pseudogap in Two-Dimensional Lateral Tunnel Junctions

Tunneling characteristics of a two-dimensional lateral tunnel junction are reported. A pseudogap on the order of Coulomb energy is detected in the tunneling density of states (TDOS) when two identical two-dimensional electron systems are laterally separated by a thin energy barrier. The Coulombic pseudogap remains robust well into the quantum Hall regime until it is overshadowed by the cyclotron gap in the TDOS. The pseudogap is modified by the in-plane magnetic field, demonstrating a nontrivial effect of the in-plane magnetic field on the electron-electron interaction.

Two-Dimensional Simulation of Quantum Tunneling across Barrier with Surface Roughness

We present two-dimensional simulation of quantum tunneling across a potential barrier with surface roughness using quantum lattice–gas automata. The impact of the nonuniformity of the barrier thickness on the transmission coefficient is discussed by comparing the results of one- and two-dimensional tunneling simulations. The dependence of the transmission coefficient on the parallel momentum of the incident electron is also investigated, and it is demonstrated that the scattering by the surface roughness on the incident side of the interface causes the violation of the parallel momentum conservation. We discuss the effect of the obtained results on the gate current modeling for the scaled metal–oxide–semiconductor field-effect transistors.

Application of a photogrammetric technique to a model tunnel

Close range photogrammetric technique (digital imaging process) is a useful non-intrusive method for studying deformation patterns imposing no constraints on the material. In this study, the close range photogrammetric technique for a laboratory two-dimensional model tunnel test using the multi-sized rod material was introduced and consequently, the displacement and strain data were provided to compare with the finite element analysis. The close photogrammetric technique with a linear strain theory showed a remarkable agreement with the physical model data.

Nest excavation in ants: group size effects on the size and structure of tunneling networks.

Collective digging activity was studied in the ant Messor sancta Forel in laboratory conditions and with a two dimensional set-up. We analyzed the digging dynamics and topology of tunneling networks excavated by groups of workers ranging from 50 to 200 individuals over 3 days. In all conditions, the dynamics of excavated sand volume were clearly non-linear. Excavation began with an exponential growth and after 3 days reached a saturation phase in which activity was almost totally stopped. The final volume of sand excavated was positively correlated with the number of workers. At the end of the experiments, the two-dimensional tunneling networks were mapped onto planar graphs where the vertices represent small chambers or intersections between tunnels and the edges represent tunnels. We found that all the networks belonged to a same topological family and exhibited several striking invariants such as the distribution of vertex degree that follows a power law. When increasing the number of ants, some changes occurred in the network structure, mainly an increase in the number of edges and vertices, and the progressive emergence of enlarged and highly connected vertices.

A bonded-particle model for rock

A numerical model for rock is proposed in which the rock is represented by a dense packing of non-uniform-sized circular or spherical particles that are bonded together at their contact points and whose mechanical behavior is simulated by the distinct-element method using the two- and three-dimensional discontinuum programs PFC2D and PFC3D. The microproperties consist of stiffness and strength parameters for the particles and the bonds. Damage is represented explicitly as broken bonds, which form and coalesce into macroscopic fractures when load is applied. The model reproduces many features of rock behavior, including elasticity, fracturing, acoustic emission, damage accumulation producing material anisotropy, hysteresis, dilation, post-peak softening and strength increase with confinement. These behaviors are emergent properties of the model that arise from a relatively simple set of microproperties. A material-genesis procedure and microproperties to represent Lac du Bonnet granite are presented. The behavior of this model is described for two- and three-dimensional biaxial, triaxial and Brazilian tests and for two-dimensional tunnel simulations in which breakout notches form in the region of maximum compressive stress. The sensitivity of the results to microproperties, including particle size, is investigated. Particle size is not a free parameter that only controls resolution; instead, it affects the fracture toughness and thereby influences damage processes (such as notch formation) in which damage localizes at macrofracture tips experiencing extensile loading.

A Physical and Numerical Investigation on the Stability of Shallow Tunnels in Strain Softening Media

The behaviour up to failure of shallow underground openings is discussed on the basis of some laboratory, small-scale model tests and of finite element simulation. The experimental results are first illustrated. They were obtained from two-dimensional (plane strain) and three-dimensional tunnel models tested under standard gravity conditions. Then, the phenomenon of strain localisation that characterizes the medium surrounding the model tunnels is discussed, recalling two alternative approaches for its numerical interpretation. On this basis, a finite element procedure for strain softening analyses is outlined and applied to the simulation of the tests in both two- and three-dimensional conditions. The comparison between experimental and numerical results leads to some conclusions on the influence of strain localisation on the overall behaviour of shallow tunnels and on the stability of their headings.

Two-dimensional tunnel bifurcations

Two possible types of two-dimensional tunnel bifurcations have been studied in frames of the «quantum tunneling with dissipation» science. Quantum oscillations near bifurcation point have been revealed in case оf parallel tunnel transition for interacting particles. Also, the chaotic regime near the critical effective temperature in case of antiparallel tunnel transfer has been revealed.

Two-dimensional tunnel correlations with dissipation

Tunneling of two particles in synchronous and asynchronous regimes is studied in the framework of dissipative quantum tunneling. The critical temperature T_c corresponding to a bifurcation of the underbarrier trajectory is determined. The effect of a heat bath local mode on the probability of two-dimensional tunneling transfer is also investigated. At certain values of the parameters, the degeneracy of antiparallel tunneling trajectories is important. Thus, four, six, twelve, etc., pairs of the trajectories should be taken into account (a cascade of bifurcations). For the parallel particle tunneling the bifurcation resembles phase transition of a first kind, while for the antiparallel transfer it behaves as second order phase transition. The proposed theory allows for the explanation of experimental data on quantum fluctuations in two-proton tunneling in porphyrins near the critical temperature.

Evidence of two-dimensional macroscopic quantum tunneling of a current-biased dc SQUID.

The escape probability out of the superconducting state of a hysteretic dc SQUID has been measured at different values of the applied magnetic flux. At low temperatures, the escape current and the width of the probability distribution are temperature independent but they depend on flux. Experimental results do not fit the usual one-dimensional macroscopic quantum tunneling (MQT) law but are perfectly accounted for by the two-dimensional MQT behavior as we propose here. Near zero flux, our data confirms the recent MQT observation in a dc SQUID [Phys. Rev. Lett. 89, 98301 (2002)]].

Imaging simulation of near‐field optical scanning microscope: Comparison between dielectric probe and metal‐coated aperture probe

AbstractIn this paper, a simulation code for a two‐dimensional photon scanning tunneling microscope (PSTM) is created by using the boundary element method based on the guided‐mode extracted integral equation. Imaging simulation is carried out for the cases of a dielectric probe or a metal‐coated probe and observation objects that are multiple dielectrics or metals. In the simulation, the transmission coefficient of the guided mode in a collection mode probe with an incident TE wave (s polarization) and the reflection coefficient of the illumination mode for the incident fundamental TE mode are derived. By a probe scan, the relationship between the output image and the observation object is studied. It is shown that the output image contrast decreases and the effect of interference pattern increases with a metal‐coated aperture probe, whereas the image characteristics on the output image are improved relative to those obtained with a dielectric probe. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(10): 7–16, 2002; Published online in Wiley InterScienc (www.interscience.wiley.com). DOI 10.1002/ecjb.10050

Design of a Quadruped Robot for Motion with Quasistatic Force Constraints

This paper presents a novel design of a four-legged “spider” robot capable of moving in a wide range of two-dimensional tunnels. The robot moves in a quasistatic manner, by stably bracing itself against the tunnel walls while moving its free parts to the next position. The design has been strongly influenced by the recent immobilization theory of Rimon and Burdick (1998a, 1998b). The theory dictates the minimum number of limbs such a mechanism can have, as well as the curvature of the mechanism footpads. The class of tunnel geometries dictates other key parameters of the robot, such as limb dimensions and number of degrees of freedom of each limb. We review the relevant components of the immobilization theory and describe its implications for the robot design. Then we describe our choice of other key design parameters of the robot. The spider-like robot will move under a worst-case assumption of slippery tunnel walls, and we also describe a locomotion strategy for the robot under this assumption. Finally, we describe an immobilization-based control algorithm for executing the motion strategy. The robot has been built, and experiments verifying its robustness with respect to leg-placement errors are described.