Rectangular Step Research Articles

2-Dimensional electron gas under strong magnetic fields: Properties near abrupt edges

According to mechanism of electron confinement within the plane, the effective confinement barriers at system edges can be classified as smooth and abrupt. Here, less studied abrupt barriers will be investigated. For simple finite rectangular step barriers, Landau level bending in the step vicinity exhibits pronounced structures in the form of electron dispersion plateaus above the barrier tops, accompanied by regions with a substantial reduction of energy gaps between neighbouring Landau branches [1].The enhanced density of electron states should be observable in optical and nuclear spin relaxation phenomena. Distortions of electron wave functions, consisting in systematical lagging of electron center of mass behind the orbital center are described. Diamagnetic current density, and in particular, development of diamagnetic edge channels as a function of the position of the Fermi level of the 2-dimensional electron gas (2DEG) is investigated. Total currents along the individual edges are found to be quantized. From the Kubo formula, very simple expressions for Hall conductivity have been derived for a general confinement barrier. Application to a system with a simple rectangular confinement elucidates the problem of space distribution of the current throughout the Hall bar. Total deviation of the Hall conductivity from the integer values is found to be given by the product of two factors. The geometrical factor is inversely proportional to the sample width. The edge factor is proportional to the derivative of the electron dispersion relation at the Fermi level and in this way it relates the Hall conductivity deviation to the shape of the confinement barrier. The deviations have been evaluated for several channel widths and found to be in qualitative agreement with recent experimental results for quantum wires.

Squeezing for the one-mode electromagnetic-field oscillator with δ-kicked frequency

Squeezing phenomenon is analysed for the non-stationary forced harmonic oscillator which is perturbed parametrically by very short pulses. The energy of the oscillator, distribution function and the squeezing coefficients as well as some other values are calculated for the models of δ-pulses, rectangular steps and some others types of time-dependence of the frequency of the oscillator.

LANDAU LEVEL GAP REDUCTION AT ABRUPT EDGES

For an electron localized near a finite rectangular step potential under strong magnetic field we found a profound local reduction of the gap between neighboring Landau levels.1,2 We investigate under what conditions the effect persists when the barrier gets smoother. The conclusion is that to get a substantial gap reduction the barrier gradient has to be larger than ħw c /a L (a L is the magnetic length). The sensitivity of the gap reduction is illustrated using tilted and multiple step barriers and finite stripe configurations.

Application of the Spectral Multidomain Method to the Navier-Stokes Equations

An application of the spectral multidomain method to the two-dimensional, time-dependent, incompressible Navier-Stokes equations is presented. The governing equations are discretized on a non-staggered, stretched mesh with a mixed finite difference/Chebyshev method and are integrated by a time-splitting procedure. The accuracy of the multidomain method is demonstrated for two different channel flow configurations, one with a backward-facing step and the other with a rectangular step. The method is then applied to the investigation of the effects of an isolated, two-dimensional roughness element on the spatial development of instability waves in boundary layers.

Graded action potentials generated by differentiated human neuroblastoma cells.

Stimulus-dependent impulses and resting membrane parameters of human SH-SY5Y neuroblastoma cells, induced to differentiate by retinoic acid, were investigated with tight-seal recording techniques. Mean resting potential was -53 mV, mean input resistance 2.1 G omega, mean capacitance 14 pF, and mean time constant 30 ms. Rectangular current steps induced clearly stimulus-dependent impulses, with stronger current steps causing impulses of larger amplitude. The degree of impulse variability differed significantly among different cells. The current thresholds for impulse generation ranged from 35 to 100 pA for 10 ms current steps. With longer current steps, thresholds below 10 pA were recorded. In response to 0.5-1 s long current steps, most cells generated only a single impulse, but a few cells generated two impulses. When two impulses were generated, the interval between the impulses decreased with increasing stimulus strength. Whole-cell currents were recorded under voltage-clamp conditions. Voltage-activated, tetrodotoxin-sensitive Na+ currents and 'delayed rectifier' K+ currents were recorded. The degree of impulse variability was correlated to the maximum Na+ current density. Cells with large Na+ currents showed little impulse variability, while a marked variability was recorded in cells with intermediate or small Na+ currents. Cells which generated more than one impulse in response to prolonged stimuli belonged to the group with large Na+ currents. Spontaneous impulse-currents were recorded from cell-attached membrane patches on intact cells. Also these impulses showed a large variability in amplitude: In each of five cells analysed, the peak-to-peak amplitude varied by a factor larger than 1.7.

Deformation of Nonlinear Waves on a Rectangular Step

ABSTRACTA numerical model for nonlinear wave propagation over a rectangular step is formulated by utilizing the boundary element method. The computation by this model gives a more realistic wave profile than that of linear wave theory. The model is used for study of the formation of higher harmonic components in the process of wave propagation over the step. In comparison with the results of laboratory experiments, the model gives good estimation of the amplitudes of the second and third harmonic components, and gives a over-prediction of the first harmonic component. Reflection and transmission coefficients are calculated by including these harmonic components in the computation of wave height. The model yields the coefficients in good agreement with the experimental results.In addition to the analysis of harmonic components, the energy loss in the process of wave propagation over the step was experimentally investigated. A Fiber Laser Velocimeter is used to measure the water particle velocity at about f...

Detailed comparison of two approximate methods for the solution of the scalar wave equation for a rectangular optical waveguide

Two approximate methods for the determination of the fundamental mode of an optical waveguide with rectangular core cross section and step refractive-index profiles are presented and analyzed thoroughly. Both methods are based on Galerkin's method. The first method uses Hermite-Gauss basis functions and the second uses the guided and nonguided slab waveguide solutions as basis functions. The results are compared with results from an accurate circular harmonic analysis. Both methods provide values of the normalized propagation constant with errors less than 0.1% for practical rectangular single-mode waveguides. The slab waveguide method is the fastest, and even when only one slab waveguide mode is used the propagation constant for the fundamental mode can be calculated with an error of less than 1%. The slab waveguide method also gives very accurate results for the propagation constant for higher order modes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Role of an inwardly rectifying potassium current in rabbit ventricular action potential.

1. Whole-cell voltage-clamp measurements were made of the time- and voltage-dependent properties of the inwardly rectifying background potassium current IK1, in single myocytes from rabbit ventricle. The main goal of these experiments was to define the role of IK1 in the plateau and repolarization phases of the action potential (AP). 2. Action potentials from single ventricular myocytes were used as the command signals for voltage-clamp measurements. In these 'action potential voltage-clamp' experiments, IK1 was isolated from other membrane currents by taking the difference between control currents and currents in K(+)-free bathing solution. The results show that IK1 is small during the plateau, but then rapidly increases during repolarization and declines in early diastole. 3. Evidence of an important functional role for IK1 in AP repolarization was obtained by comparing the magnitude of IK1 and the rate of change of membrane potential (dVm/dt) in the same cell during the AP. The time courses of IK1 and dVm/dt during the AP were closely correlated, indicating that IK1 was the principal current responsible for final repolarization. 4. Rectangular voltage-clamp steps were used to study time- and voltage-dependent changes in IK1 at membrane potentials corresponding to the repolarization phase of the AP. 'Slow' relaxations or tail currents, lasting 100-300 ms, were consistently recorded when the cell was repolarized to potentials in the range -30 to -70 mV, following depolarizations between +10 and -10 mV. 5. The close correlation between the magnitude of the steady-state IK1 (in an external K+ concentration of 5.4 mM), which was outward for membrane potentials in the range -30 to -70 mV, and the magnitude of the tail currents, suggests that they resulted from a slow increase, or reactivation, of IK1. 6. The component of the slow tails due to reactivation of IK1 can be separated from a previously described component due to Na(+)-Ca2+ exchange since the IK1 component: (i) does not depend on the presence of the calcium current, ICa; (ii) can be recorded when internal EGTA (5 mM) suppresses large changes in [Ca2+]i; (iii) does not depend on the Na+ electrochemical gradient; (iv) is abolished in K(+)-free external solution; and (v) is not present in rabbit atrial myocytes, in which IK1 is very small. 7. The time- and voltage-dependent properties of IK1 revealed by these tail current experiments suggest that the measured magnitude of IK1 will be dependent on the voltage-clamp protocol.(ABSTRACT TRUNCATED AT 400 WORDS)

Propagation of plane surface waves over a rectangular step with overhang and over a partially capped rectangular trench

Propagation of plane surface waves over a rectangular step with overhang and over a partially capped rectangular trench

Impulses and resting membrane properties of small cultured rat hippocampal neurons.

1. The impulses and resting membrane parameters of small (soma diameter less than 10 microM) cultured hippocampal neurons from rat embryos were studied with the tight-seal whole-cell recording technique. 2. Mean resting potential was -47 mV, mean input resistance 3.3 G omega, mean capacitance 11 pF, and mean time constant 33 ms. 3. Rectangular suprathreshold current steps elicited regenerative potential responses. The amplitude and time course of the responses were clearly stimulus dependent: stronger current steps caused impulses of larger amplitude. 4. The current threshold was very low: rheobase current was less than 15 pA. 5. The potential response depended on the preceding holding potential, responses from more negative potentials showing sharper peaks than those from more positive potentials. 6. Spontaneous impulses with pre-potentials similar to synaptically induced events were recorded from several cells. The amplitude of the spontaneous impulses varied similarly to that of the stimulus-induced responses.

Dilational viscoelasticity of fluid interfaces: The diffusion model for transient processes

The functional form of the surface dilational modulus is determined by considering the subsurface concentration changes produced by the diffusion process consequent to a non-periodic (rectangular step) perturbation of surface area (local equilibrium between surface and subsurface is assumed). The mathematical treatment is intended to present a straightforward demonstration that the same (unique) physical quantity, i.e. the dilational modulus, governs both harmonic and transient surface processes. The results definitely show that this modulus is an intrinsic physical property of a diffusive system, independent of the type of surface disturbance (within the linearity approximation).

Smoothing of Silica Glass Surfaces by Ion Implantation

Enhancement of surface smoothness during ion implantation in rectangularly patterned silica glasses has been observed by scanning electron microscopy. The smoothness of the silica glass surface is significantly improved with increasing ion dose. The efficiency of ion beam smoothing strongly depends on the energy of the incident ion and ion species, whereas it depends weakly on dose rate and temperature. The efficiency of smoothing on the ion energy indicates a maximum when the range of the incident ion corresponds to the height of the rectangular step. Viscous flow is found to be a dominant process from analysis of the change in the surface profile.

Improving the characteristics of rectangular waveguide branchings by cylindrical obstacles

The scattering matrix of a transition between one or two parallel rectangular waveguides and a larger rectangular waveguide which contains two metallic or dielectric cylinders is investigated by means of the orthogonal expansion method. Mathematical programming is applied in order to improve the characteristics of the branchings. Reflection at a rectangular step discontinuity can be reduced by 30 dB using metallic or dielectric obstacles. Using Teflon cylinders, coupling of a transition can be reduced by 40 dB without debasing reflection. Physical interpretations are given with the help of field patterns.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Tangent simple systems method applied to a precise study of viscoelastic behaviour of human blood

The tangent simple systems (TSS) method, proposed in (1), is applied in order to study the viscoelastic behaviour of human blood in transient flow for a rectangular low shear rate step. The tangent simple systems which were used are Maxwell liquids. These systems allow one to obtain plots of variations of instantaneous values of viscosity coefficient mu, elasticity modulus G and retardation time tau = mu/G of the studied blood samples, as a function of flow duration. Variations of both parameters mu and G versus time are represented by two exponential functions which involve three couples of parameters (mu o, mu infinity), (Go, G infinity) and (tau mu, tau G). These parameters can be considered as the characteristics of each blood sample. Another representation of the results, called the dual rheogram, is also indicated. The dual rheogram enables one to follow the evolution of the blood structure. Several examples of application of the TSS method to normal blood sample and to suspensions of artificially modified red blood cells (RBC) are given.

Kinetics and transient times of fluorescence optical sensors (optodes) for blood gas analysis (O2, CO2, pH).

Oxygen measurements with optical sensors (O2 optodes) (Lubbers and Opitz, 1983; Opitz and Lubbers, 1984) are based on fluorescence quenching of certain indicator molecules by molecular oxygen in a diffusion-controlled collisional process (Vaughan and Weber, 1970; Knopp and Longmuir, 1972). The functional dependence follows Stern-Volmer’s equation (Stern and Volmer, 1919) : S (P O2) = S0/ (1+KηPO2), where K is overall quenching constant, PO2, oxygen partial pressure, and S and So, relative fluorescence intensity in the presence and absence of oxygen, respectively. Since fluorescence optical sensors incorporate membrane-protected indicator layers, an exponential time course of the PO2 within these layers can be assumed (Jost, 1960), if a rectangular PO2 step, ΔP O2 = PO2″ − PO2′, is induced in front of the sensor membrane. Insertion of this time course into the hyperbolic calibration curve brings about asymmetrical kinetics of reversible reactions with different transient times, e.g. to 90% of final value (t90): $$\begin{matrix}t_{90,02}^{\downarrow }={{k}^{-1}}\cdot \log \left( 10-\left( 9\cdot k\cdot \Delta P{{O}_{2}} \right)/\left( 1+k\cdot P{{O}_{2}}\prime\prime \right) \right) \\t_{90,02}^{\uparrow }={{k}^{-1}}\cdot \log \left( 10+\left( 9\cdot k\cdot \Delta P{{O}_{2}} \right)/\left( 1+k\cdot P{{O}_{2}}\prime\right) \right) \\\end{matrix}$$ (4.1) where k−1 ~ D02/12, D02, oxygen diffusion coefficient and, 1, thickness of the sensor membrane.KeywordsStep HeightRelative Fluorescence IntensityTransient TimeSensor MembraneOxygen Diffusion CoefficientThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Dynamics of Gas-Lubricated Slider Bearings in Magnetic Recording Disk Files—Part II: Numerical Simulation

This two part paper presents the experimental observation and numerical simulation of the dynamic response of self-acting gas-lubricated slider bearings used to maintain the sub-micron spacings between the Read/Write transducers and the rotating disks in magnetic recording disk files. In this Part II, a factored implicit finite difference scheme is used to integrate the Reynolds lubrication equation, which describes the isothermal compressible fluid flow within the bearing region, and a fourth order Runge-Kutta method is used to solve the equations of motion, which describe the slider dynamics. Using this numerical model, the theoretical slider response due to a rectangular step in the disk surface is obtained. Excellent correlation is observed between theory and experiment. Results are presented to illustrate the effects of step size, step location, and surface velocity on the dynamic performance of slider bearings.

Dynamics of Gas-Lubricated Slider Bearings in Magnetic Recording Disk Files—Part I: Experimental Observation

This two part paper presents the experimental observation and numerical simulation of the dynamic response of self-acting gas-lubricated slider bearings used to maintain the sub-micron spacings between the Read/Write transducers and the rotating disks in magnetic recording disk files. In this Part I, a novel laser Doppler interferometric technique is used to measure the transient motions of the R/W head as it encounters an artificially introduced crater-like surface imperfection and a sputtered rectangular step.

Patch and whole-cell voltage clamp of single mammalian visceral and vascular smooth muscle cells

Dispersal of the constituent cells of mammalian visceral and vascular smooth muscles has permitted recordings both of membrane currents under whole-cell voltage clamp, and of currents through single ionic channels using the patch-clamp technique. A rectangular depolarizing step applied to a single cell under voltage clamp yielded a net inward current followed by a net outward current in normal physiological solution. In isolated, 'inside-out' patches of cell membrane a calcium- and potential-sensitive K channel (100 pS conductance) and a calcium-insensitive, potential-sensitive K+ channel (50 pS conductance) with slow kinetics have so far been identified and characterized.

Scattering of atomic beams off a single surface step: An exact solution

The scattering of atomic beams off a single rectangular step on a planar hard-wall surface is calculated exactly using the Wiener-Hopf technique. The diffuse scattering consists of a sharp peak around the specular direction which is due to interference effects between the two surface levels and which oscillates in magnitude with incident angle. A second part then describes a smooth background scattering which strongly depends on the actual shape of the step whereas the former does not. Since the step is an infinitely extended defect a finite part of the incident atoms is scattered into the peak around specular, in contrast to the case of a compact scattering object, where only an infinitesimal part is removed from the specular beam.

Image potential for stepped and corrugated surfaces.

The classical image potential is derived for a nonplanar conducting surface. A general formulation is given for first-order deformations of an arbitrary shape. Detailed formulas are presented for a variety of rectangular step and terrace configurations including corrugations. It is shown that ions and electrons are always attracted to the elevated part of the surface. Potential-energy minima and hence bound states parallel to the surface can exist on a track or terrace. Classical trajectories are calculated in some special cases and compared to the plane conductor. The effects produced by these nonplanar surfaces on ion angular distributions are also discussed.