Superposition Of Potentials Research Articles

Adiabaticity and diabaticity in strong-field ionization

If the photon energy is much less than the electron binding energy, ionization of an atom by a strong optical field is often described in terms of electron tunneling through the potential barrier resulting from the superposition of the atomic potential and the potential associated with the instantaneous electric component of the optical field. In the strict tunneling regime, the electron response to the optical field is said to be adiabatic, and nonadiabatic effects are assumed to be negligible. Here, we investigate to what degree this terminology is consistent with a language based on the so-called adiabatic representation. This representation is commonly used in various fields of physics. For electronically bound states, the adiabatic representation yields discrete potential energy curves that are connected by nonadiabatic transitions. When applying the adiabatic representation to optical strong-field ionization, a conceptual challenge is that the eigenstates of the instantaneous Hamiltonian form a continuum; i.e., there are no discrete adiabatic states. This difficulty can be overcome by applying an analytic-continuation technique. In this way, we obtain a rigorous classification of adiabatic states and a clear characterization of (non)adiabatic and (non)diabatic ionization dynamics. Moreover, we distinguish two different regimes within tunneling ionization and explain the dependence of the ionization probability on the pulse envelope.

Fundamental Theories on a Combined Energy Cycle of Electrostatic Induction Hydrogen Electrolytic Cell and Fuel Cell to Produce Fully Sustainable Hydrogen Energy

A hydrogen electrolyzer for decomposition of chemically stable compound H2O is essentially an electronic device that uses manly electrostatic-to-chemical energy conversion to produce a stoichiometric H2+1/2O2 fuel. To achieve a breakthrough in the practical hydrogen electrolytic cell, we demonstrate the electrostatic induction potential superposed electrolyzer. This system works on the mechanism in which, on the theoretical base, power used is 20% of the total electrical energy required, while the remaining 80% can be provided by the electrostatic energy free of power. Because H2O is placed in its decomposition state in the electrostatic field where no current flows, the decomposition voltage is identified as a barrier potential that electrolytic current must overcome by expending the major part of the total system power. The potential superposition method for supplying energy to the cell was found to avoid the barrier potential effect within the laws of thermodynamics. Combining a fuel cell for producing power from pure H2 and O2 of stoichiometric ratio with this type of hydrogen electrolytic cell in a closed energy cycle can achieve a highly positive H2 balance.

On the spectrum of the superposition of separated potentials.

Suppose that $V(x)$ is an exponentially localized potential and $L$ is a constantcoefficient differential operator. A method for computingthe spectrum of $L+V(x-x_1) + ... + V(x-x_N)$ given that one knows the spectrum of$L+V(x)$ is described. The method is functional theoretic in nature anddoes not rely heavily on any special structure of $L$ or $V$ apart fromthe exponential localization. The result is aimed at applications involvingthe existence and stability of multi-pulses in partial differential equations.

Theoretical Analysis of a Non-Symmetric Polarization-Maintaining Single-Mode Fiber for Sensor Applications

An asymmetric polarization-maintaining single-mode fiber with one side-hole being incorporated into the fiber cladding has been investigated analytically in this work for potential pressure measurements. The material birefringence of the fiber is calculated using a thermo-elastic displacement potential method through the superposition of sectional displacement potentials. The results obtained are generic and are thus applicable to any one-hole fiber structures, should the hole diameter or position vary in the fiber cladding, or the fiber hole be empty or filled in with any material. This enables the analysis to be applied more widely in a range of optical fiber sensor applications.

Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type

Solitons in the model of nonlinear photonic crystals with the transverse structure based on two-dimensional (2D) quadratic- or rhombic-shaped Kronig-Penney (KP) lattices are studied by means of numerical methods. The model can also applies to a Bose-Einstein condensate (BEC) trapped in a superposition of linear and nonlinear 2D periodic potentials. The analysis is chiefly presented for the self-repulsive nonlinearity, which gives rise to several species of stable fundamental gap solitons, dipoles, four-peak complexes, and vortices in two finite bandgaps of the underlying spectrum. Stable solitons with complex shapes are found, in particular, in the second bandgap of the KP lattice with the rhombic structure. The stability of the localized modes is analyzed in terms of eigenvalues of small perturbations, and tested in direct simulations. Depending on the value of the KP's duty cycle (DC, i.e., the ratio of the void's width to the lattice period), an internal stability boundary for the solitons and vortices may exist inside of the first bandgap. Otherwise, the families of the localized modes are entirely stable or unstable in the bandgaps. With the self-attractive nonlinearity, only unstable solitons and vortices are found in the semi-infinite gap.

FE/BE coupling for an acoustic fluid–structure interaction problem. Residual a posteriori error estimates

SUMMARYIn this paper, we developed an a posteriori error analysis of a coupling of finite elements and boundary elements for a fluid–structure interaction problem in two and three dimensions. This problem is governed by the acoustic and the elastodynamic equations in time‐harmonic vibration. Our methods combined integral equations for the exterior fluid and FEMs for the elastic structure. It is well‐known that because of the reduction of the boundary value problem to boundary integral equations, the solution is not unique in general. However, because of superposition of various potentials, we consider a boundary integral equation that is uniquely solvable and avoids the irregular frequencies of the negative Laplacian operator of the interior domain. In this paper, two stable procedures were considered; one is based on the nonsymmetric formulation and the other is based on a symmetric formulation. For both formulations, we derived reliable residual a posteriori error estimates. From the estimators we computed local error indicators that allowed us to develop an adaptive mesh refinement strategy. For the two‐dimensional case we performed an adaptive algorithm on triangles, and for the three‐dimensional case we used hanging nodes on hexahedrons. Numerical experiments underline our theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.

On the solution of the relativistic quasipotential equation for the superposition of a local potential and of the sum of nonlocal separable quasipotentials

A solution has been found for the finite-difference quasipotential equation with the total quasi-potential that describes the interaction of two relativistic spinless particles of unequal mass. The total interaction, which is the superposition of a local potential and of the sum of nonlocal separable quasi-potentials, is centrally symmetric, does not depend on energy, and admits existence of true bound states. The treatment has been performed in the context of the relativistic quasipotential approach to quantum field theory. Exact expressions for the phase shift increments have been found and their properties have been investigated, the conditions for existence of bound states have been determined, and a generalization of the Levinson theorem is given.

An alternative approach of Kirsch-Kress method for reconstructing the shape of a sound-soft obstacle from several incident fields

The inverse problem we consider is to reconstruct the shape of a plane acoustically sound-soft obstacle from the knowledge of the far-field patterns for several incident fields. An alternatively iterative procedure is proposed based on the numerical method which was developed by Kirsch and Kress. For several incident fields, a computational technique with its corresponding iterative method is presented to reduce the amount of computation by the superposition of the single-layer potential and of the far-field equation. Numerical examples show that the methods give accurate numerical approximations in relatively few iterations for several incoming waves.

Self-potential investigations of a gravel bar in a restored river corridor

Abstract. Self-potentials (SP) are sensitive to water fluxes and concentration gradients in both saturated and unsaturated geological media, but quantitative interpretations of SP field data may often be hindered by the superposition of different source contributions and time-varying electrode potentials. Self-potential mapping and close to two months of SP monitoring on a gravel bar were performed to investigate the origins of SP signals at a restored river section of the Thur River in northeastern Switzerland. The SP mapping and subsequent inversion of the data indicate that the SP sources are mainly located in the upper few meters in regions of soil cover rather than bare gravel. Wavelet analyses of the time-series indicate a strong, but non-linear influence of water table and water content variations, as well as rainfall intensity on the recorded SP signals. Modeling of the SP response with respect to an increase in the water table elevation and precipitation indicate that the distribution of soil properties in the vadose zone has a very strong influence. We conclude that the observed SP responses on the gravel bar are more complicated than previously proposed semi-empiric relationships between SP signals and hydraulic head or the thickness of the vadose zone. We suggest that future SP monitoring in restored river corridors should either focus on quantifying vadose zone processes by installing vertical profiles of closely spaced SP electrodes or by installing the electrodes within the river to avoid signals arising from vadose zone processes and time-varying electrochemical conditions in the vicinity of the electrodes.

A Coupled Reservoir/Wellbore Model for Calculating Pressure and Inflow Profile Along a Horizontal Well with Stinger Completion

Pressure and the flow distribution are not uniform due to the pressure drawdown in a horizontal wellbore, thus reducing the effectiveness of the toe of the well and increasing the tendency for water and gas coning at the heel. Completions have been proposed to combat this effect using a stinger that extends from the heel into the horizontal section. A comprehensive three-dimensional, anisotropic reservoir/wellbore coupling model based on the equivalent wellbore radius model and the principle of potential superposition was developed. The model is capable of handling the problem of pressure distribution and inflow profile in stinger completion. The optimal length of the stinger is obtained by solving the coupling model. For the given example, optimum stinger length is about a third of the length of the horizontal section. In this situation, the difference between the pressure along the wellbore is smaller and the reservoir influx takes a U-shaped distribution.

Localization of Cold Atoms in State-Dependent Optical Lattices via a Rabi Pulse

We propose a novel realization of Anderson localization in nonequilibrium states of ultracold atoms in an optical lattice. A Rabi pulse transfers part of the population to a different internal state with infinite effective mass. These frozen atoms create a quantum superposition of different disorder potentials, localizing the mobile atoms. For weakly interacting mobile atoms, Anderson localization is obtained. The localization length increases with increasing disorder and decreasing interaction strength, contrary to the expectation for equilibrium localization.

Low Operating Bias and Matched Input−Output Characteristics in Graphene Logic Inverters

We developed a simple and novel method to fabricate complementary-like logic inverters based on ambipolar graphene field-effect transistors (FETs). We found that the top gate stacks (with both the metal and oxide layers) can be simply prepared with only one-step deposition process and show high capacitive efficiency. By employing such a top gate as the operating terminal, the operating bias can be lowered within 2 V. In addition, the complementary p- and n-type FET pairs can be also simply fulfilled through potential superposition effect from the drain bias. The inverters can be operated, with up to 4-7 voltage gains, in both the first and third quadrants due to the ambipolarity of graphene FETs. For the first time, a match between the input and output voltages is achieved in graphene logic devices, indicating the potential in direct cascading of multiple devices for future nanoelectronic applications.

Debundling of carbon single-walled nanotubes at oxidation of bromine ions

An electrochemical method of modification of carbon single-walled nanotubes at anodic polarization in aqueous solutions of potassium bromide is proposed. Bundles of nanotubes disperse under superposition of anodic potentials without damage of structure of individual nanotubes as revealed by cyclic voltammetry, electron microscopy, and small-angle X-ray scattering. On the basis of elemental and thermogravimetric analyses data obtained for the initial and processed samples, the mechanism of nanotube modification is proposed for potassium bromide electrolysis in aqueous solution.

Phase of the transmission amplitude for a quantum dot embedded in the arm of an electronic Mach-Zehnder interferometer

We investigate an electronic Mach-Zehnder interferometer with high visibility in the quantum Hall regime. The superposition of the electrostatic potentials from a quantum point contact (QPC) and the residual disorder potential from doping impurities frequently results in the formation of inadvertent quantum dots (QDs) in one arm of the interferometer. This gives rise to resonances in the QPC transmission characteristics. While crossing the QD resonance in energy, the interferometer gains a phase shift of $\ensuremath{\pi}$ in the interference pattern.

Observation and Measurement of Negative Differential Resistance on PtSi Schottky Junctions on Porous Silicon

Nanosize porous Si is made by two step controlled etching of Si. The first etching step is carried on the Si surface and the second is performed after deposition of 75 Å of platinum on the formed surface. A platinum silicide structure with a size of less than 25 nm is formed on the porous Si surface, as measured with an Atomic Forced Microscope (AFM). Differential resistance curve as a function of voltage in 77 K and 100 K shows a negative differential resistance and indicates the effect of quantum tunneling. In general form, the ratio of maximum to minimum tunneling current (PVR) and the number of peaks in I–V curves reduces by increasing the temperature. However, due to accumulation of carriers behind the potential barrier and superposition of several peaks, it is observed that the PVR increases at 100 K and the maximum PVR at 100 K is 189.6.

Energy eigenvalues of spherical symmetric potentials with relativistic corrections: analytic results

Based on the investigation of the asymptotic behaviour of the polarization loop function for charged n scalar particles in an external gauge field, we determine the interaction Hamiltonian including the relativistic corrections. The energy eigenvalues of spherical symmetric potentials for two-particle bound state systems with relativistic corrections are analytically derived. The energy spectra of linear and funnel potentials with orbital and radial excitations are determined. The energy spectrum of a superposition of Coulomb and Yukawa potentials is also determined. Our result shows that the energy spectrum with the relativistic corrections for the linear, harmonic oscillator and funnel potentials is smaller than the upper boundaries for the energy spectrum established in the framework of the spinless Salpeter equation for the orbital and radial excited states. The relativistic corrections to the energy spectrum of a superposition of the attractive Coulomb potential and the Yukawa (exponentially screened Coulomb) potentials are very small.

Understanding the Effect of Corners: Adsorption of Fluids in Three Different Shapes of Nanopores

AbstractAdsorption of nitrogen, hydrogen and methane in square and rectangular nanopores of various sizes has been studied by grand canonical Monte Carlo simulations (GCMC). By comparison of three kinds of potential models, it was found that the site‐site model was more rational, which was therefore used in the work. Adsorption behavior of fluids in square, rectangular and cylindrical pores at T=77 K was compared. Prewetting was found in the corners of the square and rectangular pores, which is absent in the cylindrical pores. Adsorption of hydrogen and methane in the three kinds of pores was compared. Among them, the adsorption uptake of hydrogen in the square pore is highest, especially at low pressures, because the effect of potential superposition in the "corners" makes an important contribution to hydrogen adsorption. The results indicate that the presence of corners has a profound effect upon the adsorption and phase behavior of fluids at low pressures.

Electrical resistance characterization of insulating membrane with multipore

The insulating membranes with micropores are increasingly required for the electrochemical sensing of microfluid around pores with high sensitivity. To characterize the electrical resistance of fabricated insulating membranes with microscaled-multipore by impedance spectroscopy was introduced in this article. The potential distribution and resistance under a weak electric field were investigated with respect to the dimension and configuration of pores by using FEM simulation. The simulation results demonstrated that the equipotential lines around multipore are superposed in dependence of the configuration and dimension of pores, thus the electrical resistance of multipore is determined by the degree of potential superposition around pores.

A fast and accurate analysis of the interacting cracks in linear elastic solids

This paper presents a fast and accurate solution for crack interaction problems in infinite- and half- plane solids. The new solution is based on the method of complex potentials developed by Muskhelishvili for the analysis of plane linear elasticity, and it is formulated through three steps. First, the problem is decomposed into a set of basic problems, and for each sub-problem, there is only one crack in the solid. Next, after a crack-dependent conformal mapping, the modified complex potentials associated with the sub-problems are expanded into Laurent’s series with unknown coefficients, which in turn provides a mechanism to exactly implement in the form of Fourier series the boundary condition in each sub-problem. Finally, taking into account the crack interaction via a perturbation approach, an iterative algorithm based on fast Fourier transforms (FFT) is developed to solve the unknown Fourier coefficients, and the solution of the whole problem is readily obtained with the superposition of the complex potentials in each sub-problem. The performance of the proposed method is fully investigated by comparing with benchmark results in the literatures, and superb accuracy and efficiency is observed in all situations including patterns where cracks are closely spaced. Also, the new method is able to cope with interactions among a large number of cracks, and this capability is demonstrated by a calculation of effective moduli of an elastic solid with thousands of randomly-spaced cracks.

A new method for prediction of productivity of fractured horizontal wells based on non-steady flow

Hydraulic fracturing technologies of horizontal well are important ways to develop oil-gas field with low permeability. Productivity forecast of fractured horizontal wells is a difficult problem of hydraulic fracturing technologies. Basing on non-steady flow of fractures fluid during production, applying potential function principles, superposition principle and mathematical method for solving, coupling of seepage flow in the formation and pipe flow in the well bore, a new model on multi-fracture interference productivity forecast of fractured horizontal well is established in this article. The results indicate the coincidence rate between this model and practice is high. The pressure loss in the horizontal well bore has definite influence on the production status of fractured horizontal wells. The productions of different fractures in horizontal well bore are unequal, the productions of outer fractures are higher than middle fractures ; the pressure in the well bore shows an uneven distribution, the pressure declines gradually from finger tip to heel end. Asymmetry of fractures may make productivity of fractured horizontal wells decline. The conclusions are instructive in designing fractured horizontal well for low permeability reservoir.