Arbitrary Width Research Articles

Holomorphic operator families on a manifold with edge

We construct specific holomorphic families of operators on a manifold \(M\) with edge \(Y\) that have the order reducing property between weighted spaces \(H^{s,\gamma }(M)\) for arbitrary weights \(\gamma \) varying in a prescribed compact interval and for all complex parameters in a strip parallel to the imaginary axis of arbitrary finite width. These operator functions are constructed as parameter-dependent elliptic elements of the edge calculus, here without additional conditions of trace and potential type. They play a role as operator-valued Mellin symbols in the higher corners pseudo-differential calculus.

Spatial coherence measurement of polychromatic light with modified Young’s interferometer

Partial spatial coherence is a fundamental concept in optical systems. Theoretically, the normalized mutual coherence function gives a quantitative measure for partial spatial coherence regardless of the spectral nature of the radiation. For narrowband light the degree of spatial coherence can be measured in terms of the fringe modulation in the classic Young's two-pinhole interferometer. Though not commonly appreciated, with polychromatic radiation this is not the case owing to the wavelength dependence of diffraction. In this work we show that with a modified two-beam interferometer containing an achromatic Fresnel transformer the degree of spatial coherence is again related to the visibility of intensity fringes in Young's experiment for any polychromatic light. This result, which is demonstrated both theoretically and experimentally, thus restores the usefulness of the two-pinhole interferometer in the measurement of the spatial coherence of light beams of arbitrary spectral widths.

Unified asymptotic description of Gaussian pulse propagation of arbitrary initial pulse width in a Lorentz-type gain medium

An asymptotic approach is utilized in order to obtain a unified description of the propagated field dynamics due to an input Gaussian-modulated harmonic wave of arbitrary initial pulse width in a linear, causally dispersive gain medium, described by the single resonance Lorentz model. The asymptotic method of analysis is applied on the unified, exact integral representation of the propagated field, which is characterized by a unified complex phase function that depends upon the input field and gain medium parameters as well as upon the propagation distance in the medium. In order to apply the asymptotic method, an analysis of the evolution of the saddle point locations, which depend upon the dispersive properties of the gain medium, the temporal width, and the carrier frequency of the input Gaussian pulse as well as upon the propagation distance and of the topography of the real part of the unified phase function in the complex ω plane, must be performed. Upon the subsequent numerical application of the asymptotic method, the predictions of the unified asymptotic approach are found to be in exceptional agreement with the respective results of a purely numerical experiment for all considered initial pulse widths and lead to a unified model of Gaussian pulse propagation in a gain Lorentzian medium. According to this model, the propagated field is composed of pulse components, each being due to the asymptotic contribution of a respective relevant saddle point of the unified phase function. The instantaneous angular frequency of oscillation and the stationary point(s) of the envelope of each such pulse component are then obtained from the real and imaginary parts, respectively, of the corresponding relevant saddle point as it evolves in the complex ω plane. This theoretical approach may then yield particularly useful physical insights into attosecond pulse propagation.

Inductances and attenuation constant for a thin-film superconducting coplanar waveguide resonator

The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide resonator consisting of a current-carrying central conductor, adjacent slots, and ground planes that return the current. The analysis focuses on films of thickness d obeying d<2λ (λ is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length Λ=2λ2/d. Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small Λ. Exact results for arbitrary Λ are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.

Eddy currents and magnetic moments of planar rings of arbitrary width

We analyze the response of a metallic ring to an applied time-harmonic and spatially uniform magnetic field. The self-consistent current distribution and magnetic moment are compared with that from an equivalent LR circuit model and the range of parameters (size, frequency and conductivity) for the model applicability is analyzed. The circuit model does not perform quantitatively well in the parameter region with high magnetic moment and low losses that is important for metamaterial design. We show that scaling of the magnetic response is conveniently described by a single parameter which combines size, conductivity, and frequency.

Analysis of the axial distribution of a tightly focused beam with different polarizations

The paper analyzes an axial distribution of the tightly focused laser beam with different polarizations. The beam is presented as a superposition of the vortex phase functions. An analytical solution for the each component of the electric field is obtained for the incident beam narrowed by a ring aperture of arbitrary width. Approximate analytical estimates for the axial distribution in elementary functions have been obtained also. This makes to easily analyze the nature of the intensity along the optical axis. The influence of weighted superposition of vortex phase functions in the incident beam and the type of polarization on the relative contributions of the different components of the electric field in the focal region of the optical axis is numerically investigated.

Numerical interactions between compactons and kovatons of the Rosenau–Pikovsky [formula omitted] equation

A numerical study of the nonlinear wave solutions of the Rosenau–Pikovsky K(cos) equation is presented. This equation supports at least two kinds of solitary waves with compact support: compactons of varying amplitude and speed both bounded and kovatons which have the maximum compacton amplitude but arbitrary width. A new Padé numerical method is used to simulate the propagation and, with small artificial viscosity added, the interaction between these kind of solitary waves. Several numerically induced phenomena that appear while propagating these compact travelling waves are discussed quantitatively, including self-similar forward and backward wavepackets. The collisions of compactons and kovatons show new phenomena such as the inversion of compactons and the generation of pairwise ripples decomposing into small compacton–anticompacton pairs.

New approach to pulse propagation in nonlinear dispersive optical media

We develop an intuitive approach for studying propagation of optical pulses through nonlinear dispersive media. Our new approach is based on the impulse response of linear systems, but we extend the impulse response function using a self-consistent time-transformation approach so that it can be applied to nonlinear media as well. Numerical calculations based on our new approach show excellent agreement with the generalized nonlinear Schrodinger equation in the specific case of the Kerr nonlinearity in both the normal and anomalous dispersion regimes. An important feature of our approach is that it works directly with the electric field associated with an optical pulse and can be applied to pulses of arbitrary width. Numerical calculations performed using single-cycle optical pulses show that our results agree with those obtained with the finite-difference time-domain technique using considerably more computing resources.

Geodesic acoustic mode excitation by a spatially broad energetic particle beam

Global radial eigenmodes of energetic-particle-induced geodesic acoustic mode are systematically studied, and their properties are found to depend on the nonuniformities of both the geodesic acoustic mode continuous spectrum and the energetic particle (EP) radial density profile. For a broad EP drive, the eigenmode equation valid for arbitrary EP drift orbit width is derived, and the excited energetic-particle-induced geodesic acoustic mode is shown to be strongly coupled to the geodesic acoustic mode continuous spectrum; resulting in a finite drive threshold in EP density. The cross-scale couplings between micro-, meso-, and macro-scales, discussed in this work, are mediated by the EP dynamics and have many interesting similarities with complex behaviors, expected in burning plasmas of fusion interest.

Microscopic Model for Feshbach Interacting Fermions in an Optical Lattice with Arbitrary Scattering Length and Resonance Width

We numerically study the problem of two fermions in a three-dimensional optical lattice interacting via a zero-range Feshbach resonance and display the dispersions of the bound states as a two-particle band structure with unique features compared to typical single-particle band structures. We show that the exact two-particle solutions of a projected Hamiltonian may be used to define an effective two-channel, few-band model for the low-energy, low-density physics of many fermions at arbitrary s-wave scattering length. Our method applies to resonances of any width and can be adapted to multichannel situations or higher-ℓ pairing. In strong contrast to usual Hubbard physics, we find that pair hopping is significantly altered by strong interactions and the presence of the lattice, and the lattice induces multiple molecular bound states.

Influence of correlations in a flat distribution of impurity ions on the mobility of two-dimensional electrons at low temperatures

The temperature dependences of the electrical resistivity of degenerate two-dimensional electrons in scattering by impurity ions in heterostructures with a spacer of arbitrary width have been investigated using the AlxGa1 − xAs/GaAs heterostructure as an example. Correlations in the arrangement of impurity ions have been taken into account in the model of hard spheres on a plane.

Construction and characterization of non-uniform local interpolating polynomial splines

This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are rational, our approach provides spline interpolants having low, and sometimes minimum degree.Thanks to its generality, the proposed framework also allows us to recover uniform local interpolating splines previously proposed in the literature, to generalize them to the non-uniform case, and to complete families of arbitrary support width. Furthermore it provides new local interpolating polynomial splines with prescribed smoothness and polynomial reproduction properties.

Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles

Surface scatter effects from residual optical fabrication errors can severely degrade optical performance. The total integrated scatter (TIS) from a given mirror surface is determined by the ratio of the spatial frequency band-limited "relevant" root-mean-square surface roughness to the wavelength of light. For short-wavelength (extreme-ultraviolet/x-ray) applications, even state-of-the-art optical surfaces can scatter a significant fraction of the total reflected light. In this paper we first discuss how to calculate the band-limited relevant roughness from surface metrology data, then present parametric plots of the TIS for optical surfaces with arbitrary roughness, surface correlation widths, and incident angles. Surfaces with both Gaussian and ABC or K-correlation power spectral density functions have been modeled. These parametric TIS predictions provide insight that is useful in determining realistic optical fabrication tolerances necessary to satisfy specific optical performance requirements.

Nonadiabatic atomic ionization by intense subcycle laser pulses

The atomic photoionization by a subcycle linearly polarized laser pulse is studied with numerical solutions of the time-dependent Schr\odinger equation for a hydrogenlike atom. In this regime, the presumption for the adiabatic ionization theories that atoms are ionized directly from an initial bound state to the continuum state will fail. The nonadiabatic ionization channels turn out to play important roles: the bound electrons can climb up the energy ladder and get ionized from a certain bound state other than the original one. This process leaves significant fingerprints in carrier-envelope-phase-sensitive phenomena like total ionization yield and momentum asymmetry of the photoelectrons. For the modeling of subcycle pulses, the inconsistency of the popular vector potential definition is noticed and a modified version with an analytic envelope is presented that is capable of describing pulses with arbitrary pulse width.

An exact solution to the Helmholtz equation for a quasi-Gaussian beam in the form of a superposition of two sources and sinks with complex coordinates

An exact solution to the Helmholtz equation is proposed. The solution describes a quasi-Gaussian beam with an arbitrary width and has the form of a superposition of sources and sinks with complex coordinates. It is shown that such a beam always lacks a component that propagates against the principal propagation direction. In addition, when the diameter of the beam exceeds the wavelength, the beam becomes directional in the broad sense: the radiation condition is satisfied with respect to the beam waist plane. For the beam under study, expressions for the angular spectrum and the spherical harmonic expansion coefficients are derived.

ACCURATE REPRESENTATION OF EXCITATION AND LOADING FOR ARBITRARILY SHAPED ANTENNAS COMPOSED OF CONDUCTING SURFACES IN THE METHOD OF MOMENTS

In this work, a new method is introduced to model the excitation and loading for antennas composed of arbitrarily shaped conducting surfaces treated by the elctric fleld integral equation method described by Raw-Wilton-Glisson (RWG). Instead of using a single non-boundary edge to represent a zero-width exciting gap according to the conventional method, the proposed method uses either single or multiple pairs of facing boundary edges to form a real gap of arbitrary shape and width. The new method has many advantages over the conventional (zero-width) source/load representation considering the ∞exibility in shaping the gap to flt the antenna surface and the accuracy of the obtained results especially for the antenna input impedance and the input current distribution. The new method is described mathematically in detail. Modifled basis functions are described for the gap source/load. Numerical results are obtained to investigate the dependence of the antenna input impedance and the current distribution along the gap length on the gap width, the geometrical shape of the gap and the surface segmentation resolution along the gap length.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Structural and electronic properties of a single C chain doped zigzag AlN nanoribbon

The effects of a single C-chain on the structural and electronic properties of the H terminated zigzag AlN nanoribbons (ZAlNNRs) have been investigated systemically by using the first-principles. The results show that in perfect 7-ZAlNNR for example, the states of the lowest unoccupied conduction band (LUCB) and the highest occupied valence band (HOVB) at zone boundary Z are edge states their charges are localized at edge Al and N atoms, respectively. Introducing a single C-chain and changing its position lead to the LUCB and HOVB getting closer with each other. Similar to the edge states existing in perfect ZAlNNR, the flat dispersion border states also exist in a single C-chain decorated ZAlNNR, but their charges are localized at border C–N and C–Al for LUCB and HOVB, respectively. Furthermore, for N z -ZAlNNR-C( n) with ribbon width N z = 2, 3, 4, 5, 6, 7 and 10, only N z -ZAlNNR-C(1) has a direct band gap, while the other N z -ZAlNNR-C( n) has an indirect band gap. Variation of the band gap with C-chain position n shows that, for N z -ZAlNNR-C( n) of arbitrary width N z , the N z -ZAlNNR-C(1) and N z -ZAlNNR-C(2) have nearly identical the minimum band gap of 0.132 eV and nearly identical the maximum band gap of 1 eV, respectively, except the maximum band gap of 0.63 eV for 2-ZAlNNR-C(2) because it belongs to the group of C-chain substituting the right edge Al–N chain, the band gap of this group decreases linearly with increasing ribbon width N z . For 3-, 4-, 5-, 6-, 7- and 10-ZAlNNR-C( n), the band gap decreases successively for C-chain position n from 2 to 3, 4, 5, 6, 7 and 10, respectively.

A mathematical model of spit growth and barrier elongation: Application to Fire Island Inlet (USA) and Badreveln Spit (Sweden)

A mathematical model of spit growth and barrier elongation adjacent to an inlet (of arbitrary width), supplied by sediment coming from longshore sediment transport, was developed based on the spit growth model proposed by Kraus (1999). The fundamental governing equation is the conservation equation for sand, where the width of the spit is assumed constant during growth. The portion of the longshore sediment transport feeding the spit has been estimated based on the ratio between the depth of the inlet channel and the depth of active longshore transport. Sediment transport from the channel due to the inlet flow, as well as other sinks of sand (e.g., dredging), are taken into account. Measured data on spit elongation at Fire Island Inlet, United States, and at Badreveln Spit, Sweden, were used to validate the model. The simulated results agree well with the measured data at both study sites, where spit growth at Fire Island was restricted by the inlet flow and the growth at Badreveln Spit was unrestricted. The model calculation for Fire Island Inlet indicates that the dredging to maintain channel navigation is the major reason for the stable period observed from 1954 to 1994 at the Fire Island barrier. The average annual net longshore transport rate at the eastern side of the Fire Island inlet obtained in this study was about 220,000 m 3/yr, of which approximately 165,000 m 3/yr (75% of the net longshore transport) is deposited in the inlet feeding the spit growth, whereas the remaining portion (25%) is bypassed downdrift through the ebb shoal complex.

A Digital CMOS Parallel Counter Architecture Based on State Look-Ahead Logic

We present a high-speed wide-range parallel counter that achieves high operating frequencies through a novel pipeline partitioning methodology (a counting path and state look-ahead path), using only three simple repeated CMOS-logic module types: an initial module generates anticipated counting states for higher significant bit modules through the state look-ahead path, simple D-type flip-flops, and 2-bit counters. The state look-ahead path prepares the counting path's next counter state prior to the clock edge such that the clock edge triggers all modules simultaneously, thus concurrently updating the count state with a uniform delay at all counting path modules/stages with respect to the clock edge. The structure is scalable to arbitrary N-bit counter widths (2-to-2N range) using only the three module types and no fan-in or fan-out increase. The counter's delay is comprised of the initial module access time (a simple 2-bit counting stage), one three-input and-gate delay, and a D-type flip-flop setup-hold time. We implemented our proposed counter using a 0.15-μ m TSMC digital cell library and verified maximum operating speeds of 2 and 1.8 GHz for 8- and 17-bit counters, respectively. Finally, the area of a sample 8-bit counter was 78 125 μ m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (510 transistors) and consumed 13.89 mW at 2 GHz.