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The present numerical study concerns the steady two‐dimensional laminar mixed convection flow of Newtonian fluid over a heated horizontal plate of finite length at a zero angle of attack for large Peclet and small Prandtl and Richardson numbers. The plate is located in a horizontal channel of finite height. Buoyancy induces a uniform hydrostatic pressure jump at the trailing edge and across the thermal wake, which is compensated by a perturbation of the outer potential flow according to the Kutta condition. Counter‐intuitively, the total lift force acting on the plate points in the opposite direction compared to the buoyancy force. The numerical solution obtained with the Finite Element solver FEniCS is compared to an analytical boundary‐layer solution from the literature. For small values of the Richardson number (Ri), an excellent agreement between the numerical and analytical solutions is observed. When Ri exceeds a certain threshold, the flow separates near the leading edge at the lower side of the plate. For some narrow intervals of Ri, three co‐existing solutions of the governing equations are found, which differ by the size of the separation bubble. The flow separation can be suppressed by bending the leading edge. [ABSTRACT FROM AUTHOR]

An inverse problem is solved for identifying unknown force loadings on the inner surface of a finite‐length hollow cylinder using the variational method of homogeneous solutions. The problem is considered within the axisymmetric formulation, and the radial and axial displacements of the outer surface of the cylinder are used as the auxiliary data for solving the inverse problem. The accessible surfaces of the cylinder (the end‐faces and the outer surface) are assumed to be free of force loading. By making use of the variational method of homogeneous solutions, the problem is reduced to an infinite system of linear algebraic equations. The solution is verified numerically and its stability with respect to small errors in the input data is analyzed. [ABSTRACT FROM AUTHOR]

Analytical solutions were derived to predict transient change of intra‐particle concentration inside cylindrical pellets with finite length immersed in an infinitely large medium. After the derivation of steady‐state concentration by eigenfunction expansion, a transient solution was obtained by the separation of variables. Effects of the Thiele modulus (Φ) and aspect ratio of the pellet (H/R) were studied by calculating the average intra‐particle concentration at a stationary state. The effectiveness factor (η) was also affected by H/R and Φ, since irreversible first order kinetics was assumed. As Biot number (Bi) increased, both intra‐particle concentration and η increased due to the decrease of the mass transfer resistance of the surrounding film. Good agreement between analytical and numerical solutions was confirmed for both steady‐state and transient solution by comparing the analytical results with the numerical solutions by finite element method. To extend the results to a batch reactor with finite volume, Duhamel's theorem was applied by assuming time‐dependent boundary conditions to reflect the change in bulk concentration as a function of time. A method was proposed to measure intra‐particle diffusivity for batch adsorber by setting Φ = 0. To investigate the effect of H/R, η could be included in material balance of batch, continuously stirred tank reactor (CSTR), and fixed bed reactors to predict reactor performance assuming a pseudo‐steady state. First‐order reaction by egg‐shell catalysts as well as nonlinear reaction with two reactants could be solved numerically assuming finite cylindrical pellets. By solving coupled differential equations of material and energy balances, dynamic catalysis was confirmed from the enhancement of conversion, assuming forced oscillation of inlet temperature in CSTR. [ABSTRACT FROM AUTHOR]

A circular coil equipped with magnetic core of finite length and constant permeability is difficult to analyse by traditional analytical methods in consequence of the complicated boundary conditions. The difficulties can be overcome by using the truncated region eigenfunction expansion method, and with the aid of a special source function K(z) introduced in the work, this method can be simplified remarkably and concise expressions of the inductance of coils with magnetic cores are obtained. In addition, the calculations can be extended readily to a pair of coaxial coils with magnetic cores of finite length and different permeability. The eigenvalues and inversions of matrices are implemented numerically in the solving process, while most of calculations are accomplished by analytic integrations and matrix algebra, by which the deduced expressions are quite suitable for numerical evaluations. The proposed method is verified by the numerical results compared with those of finite‐element method simulations, from which it is confirmed that the proposed method is much faster and more memory efficient. [ABSTRACT FROM AUTHOR]

This study presents an efficient method for modelling the proximity effect in complex conductor systems. This method is based on a discretisation partial element equivalent circuit (DPEEC) scheme in combination with artificial neural network (ANN). Circuit parameters of a conductor system are obtained with DPEEC at low frequency. ANN trained with the low‐frequency parameters is employed to predict proximity effect at high frequencies. The proposed method significantly improves the calculation efficiency in both time and memory consuming. The method is validated by comparing with the result obtained by MoM‐SO. Case studies of closely‐spaced cables with different configurations are analysed. It is applied to evaluate the lightning current in typical cable installations. The comparison among different configurations reveals that the proximity effect leads to uneven current distribution in cables. Cable modelling without considering the proximity effect could lead to significant errors in transient current analysis. [ABSTRACT FROM AUTHOR]

This article deals with free vibration analysis of thick nanocomposite laminated curved panels with finite length resting on two-parameter elastic foundations, based on the three-dimensional elasticity theory. The main objective of this research paper is to present a 3D elasticity solution for free vibration analysis of thick laminated curved panels with continuously graded carbon nanotube-reinforced sheets. The structure is supported by an elastic foundation with Winkler's (normal) and Pasternak's (shear) coefficients. The volume fractions of oriented, straight single-walled carbon nanotubes are assumed to be a three-parameter power-law distribution which is graded in the radial direction of the panels. An equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. The convergence of the method is demonstrated and comparisons are made between the present results and results reported by well-known references and have confirmed accuracy and efficiency of the present approach. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated curved panels. POLYM. COMPOS., 38:E563-E576, 2017. © 2016 Society of Plastics Engineers [ABSTRACT FROM AUTHOR]

This paper addresses the development of a method to simulate and analyze unsteady flows of incompressible and inviscid fluids in rectangular channels. Mathematically, the flow problem formulates as Euler equations in terms of the stream function and vorticity. The normal velocity and the vorticity are given at the inlet of the channel, and only the normal velocity is specified at the outlet. The particle‐spectral method describes the vorticity field change in a Lagrangian sense by dynamics of marker particles and an Eulerian description of the velocity field using the global Galerkin approximation. The method involves the subdivision of flow domain on rectangular cells; the approximation of vorticity distribution in cells by least‐squares method; Galerkin coefficients calculation using analytical integration on space variables. For time integration, the five‐stage Runge‐Kutta method of the third accuracy order and the sixth one of symplecticity with adaptive step size control uses. The extension of the particle‐spectral approach comprises algorithms for fluid flows qualitative analysis jointly with the time simulation of unsteady flows. This includes the trajectories of marker particles calculation, computing the particle's residence time in the channel, kinetic energy dynamics, and algorithms for analyzing the dynamics and mixing of vortex patches. Test calculations based on reference solutions showed the effectiveness and good accuracy of the particle‐spectral approach. Using the developed method the dynamics of one and two initial vortex patches in the channel were investigated. We found the final state of their long‐time dynamics is time‐periodic or quasi‐periodic movements. The application of qualitative analysis algorithms demonstrates these final states produce a chaotic scattering of fluid particles in the flow‐through zone of the channel. [ABSTRACT FROM AUTHOR]

Real-valued shift-orthogonal finite-length sequences are sequences in which the side lobes of the aperiodic autocorrelation function become 0, except for the endpoints of the shift to both sides, and can be applied in pulse compression radar and spread spectrum communications. In this paper, a fast correlation algorithm for efficiently calculating the periodic correlation function is discussed for real-valued shift-orthogonal finite-length sequences with length M=2ν+1. For input data, including a real-valued shift-orthogonal finite-length sequence over a certain range, the value of the aperiodic correlation function is found in a certain shift range. Based on the synthesis of this sequence by the convolution of ν+1 partial sequences, the correlation processing is broken down into correlation processing of the ν+1 stages of partial sequences. As a result, the number of multiplications and the number of additions can be suppressed on the order Mlog2M. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(9): 18– 30, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20301 [ABSTRACT FROM AUTHOR]

A real-valued shift-orthogonal finite-length sequence is a sequence for which the side-lobe of the aperiodic autocorrelation function is zero except at the two ends. It is effectively used in spread-spectrum communications and other applications. This type of sequence can be synthesized by using element sequences of adequate lengths. Consequently, fast correlation processing can be realized by dividing the process for each element sequence. A problem in this sequence is that the round-off error of its real values has an effect on the correlation characteristics. Therefore, this paper investigates the effect of the round-off error on integrated correlation processing and divided correlation processing. In the former, the mean-square error of the correlation output is inversely proportional to the sequence length. In the latter, it is the sum of the mean-square errors of the element sequences, which are inversely proportional to the respective sequence lengths. Thus, we see that the error of shorter element sequences should be reduced in the latter method in order to speed up correlation processing. This paper considers in particular a method by which the mean-square error is reduced without significantly enlarging the circuit scale. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(6): 1–12, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10152 [ABSTRACT FROM AUTHOR]

The authors study the performance of protograph low-density parity-check (LDPC) codes over two-dimensional (2D) intersymbol interference (ISI) channels in this study. To begin with, the authors propose a modified version of finite-length (FL) extrinsic information transfer (EXIT) algorithm so as to facilitate the convergence analysis of protograph codes. Exploiting the FL-EXIT analyses, the authors observe that the protograph codes optimised for 1D ISI channels, e.g. the 1D ISI protograph code, cannot maintain their advantages in the 2D-ISI scenarios. To address this problem, the authors develop a simple design scheme for constructing a family of rate-compatible improved protograph (RCIP) codes particularly for 2D-ISI channels, which not only outperform the 1D-ISI protograph code, but also are superior to the regular column-weight-3 code and optimised irregular LDPC codes in terms of the convergence speed and error performance. More importantly, such RCIP codes benefit from relatively lower error-floor as well as linear encoding and fast decoding. Thanks to these advantages, the proposed RCIP codes stand out as better alternatives in comparison with other error-correction codes for ultra-high-density data storage systems. [ABSTRACT FROM AUTHOR]

In this paper, the authors study the performance of finite-length repeat-accumulate (RA) codes in the waterfall region. Utilising density evolution technique, the authors present estimation algorithms to predict the error performance of finite-length RA codes over binary memoryless channels. Through comparison with numerical results, the authors show that the finite-length performance of RA codes can be closely estimated by using authors' proposed approach. [ABSTRACT FROM AUTHOR]

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Subsurface physical barriers have been recognized as effective in mitigating seawater intrusion in coastal aquifers, although mainly 2D (cross‐sectional) barrier effects have been considered. In this study, impermeable barriers with finite shore‐parallel lengths are investigated through 3D numerical simulation, thereby extending previous analyses. Two scenarios are considered: (a) barrier‐only and (b) barrier‐well systems; and three available barrier types are analyzed and compared: (1) subsurface dam, (2) cutoff wall, and (3) fully penetrating barrier. Barrier location, length, and height are investigated, and barrier effectiveness is evaluated from seawater volumes, seawater wedge toe positions, and maximum safe pumping rates. In the barrier‐only system, a better performance in preventing seawater intrusion was achieved by cutoff walls rather than subsurface dams. Finite‐length subsurface dams may slightly enhance seawater extent along parts of the coastline that are beyond the dam's length. Cutoff walls performed best when located at relatively small distances from the coast in the barrier‐only system, whereas with a well at 450 m from the shoreline, the subsurface dam located at a critical distance from the sea (i.e., 300 m in the current study) performed optimally (from the tested cases) and was superior to cutoff walls in terms of the maximum safe pumping rate. A fully penetrating barrier outperformed cutoff walls and subsurface dams, as expected. Our investigation indicates that subsurface barrier design should consider the effect of the shore‐parallel length, because barrier benefits may otherwise be significantly overestimated. Key Points: Partially/fully penetrating impermeable barrier of finite‐length analyzed in 3D coastal aquifer, with/without pumping wellSubsurface dams reduced less seawater wedge volume than cutoff walls due to slightly enhanced seawater extent beyond the dam lengthSubsurface dams allowed larger maximum safe pumping rates than cutoff walls [ABSTRACT FROM AUTHOR]

In this study, by exploiting the properties of finite-length polar codes, the authors introduce a physical layer encryption scheme to make secure (from a computational security perspective) and efficient communication between a sender (Alice) and a legitimate receiver (Bob) against both active and passive attacks, simultaneously. To prevent active attacks, two techniques are considered: (i) a novel method is introduced to keep the generator matrix of polar code secret from an active attacker (Oscar); (ii) a proper joint polar encoding/encryption algorithm based on the hidden generator matrix is introduced. Two additional strategies are considered against passive attacks: (i) a new method is introduced to partition the bit-channels into good and bad bit-channels and then the scrambled information bits are transmitted over those bit-channels that are good for Bob but bad for a passive attacker (Eve); (ii) the secret key cryptography is implemented at the physical layer, such that Eve cannot decode the eavesdropped data without the knowledge of the secret key shared between the authorised parties. Besides, this study discusses efficiency analysis results consisting key size, error performance and computational complexity of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a real-valued orthogonal periodic sequence of a period N=2ν derived from a real-valued shift-orthogonal finite-length sequence of length M=2ν+1. This paper also explains the principle of a fast correlation algorithm that efficiently executes periodic correlation processing for this real-valued orthogonal periodic sequence. The sidelobe of an aperiodic autocorrelation function for a real-valued shift-orthogonal finite-length sequence (length of M) is 0 except for the right and left ends of the shift. If the subsequent sequence of first values repeatedly overlap the final values of this sequence, a real-valued orthogonal periodic sequence of a period N=M-1 can be obtained. A real-valued orthogonal periodic sequence of a period N=2ν generated from real-valued shift-orthogonal finite-length sequence of length M=2ν+1 is obtained by convoluting partial sequences and based on that controls the number of multiplications and the number of additions to increment on the order of Nlog2N without using fast Fourier transformation. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(10): 18–28, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20294 [ABSTRACT FROM AUTHOR]

Effects of edge disorder on thermoelectric performance of graphene nanoribbons (GNRs) were investigated through computational simulations based on the non-equilibrium Green's function method combined with the tight-binding method. We found that the thermoelectric power factor PF can be optimized by adjusting the length, Lg, of GNRs with edge disorder concentration Cd. For example, PF of zigzag-edged GNRs with a Cd of 10 % at room temperature and at the Fermi energy shows a maximum value of 33 mW/(m K2) at Lg = 210 nm. Both the maximum PF and optimum Lg decrease with increasing Cd. The maximum PF is theoretically explained in terms of the crossover from the ballistic transport regime to the Anderson's localization regime. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In present-day land and marine controlled-source electromagnetic (CSEM) surveys, electromagnetic fields are commonly generated using wires that are hundreds of metres long. Nevertheless, simulations of CSEM data often approximate these sources as point dipoles. Although this is justified for sufficiently large source-receiver distances, many real surveys include frequencies and distances at which the dipole approximation is inaccurate. For 1D layered media, electromagnetic (EM) fields for point dipole sources can be computed using well-known quasi-analytical solutions and fields for sources of finite length can be synthesized by superposing point dipole fields. However, the calculation of numerous point dipole fields is computationally expensive, requiring a large number of numerical integral evaluations. We combine a more efficient representation of finite-length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media. We thus obtain a formulation that requires fewer numerical integrations than the superposition of dipole fields, permits source and receiver placement at any depth within the layer stack and can also easily be integrated into 3D modelling algorithms. Complex source geometries, such as wires bent due to surface obstructions, can be simulated by segmenting the wire and computing the responses for each segment separately. We first describe our finite-length wire expressions and then present 1D and 3D examples of EM fields due to finite-length sources for typical land and marine survey geometries and discuss differences to point dipole fields. [ABSTRACT FROM AUTHOR]

The earth-return impedance and capacitance formulas of a finite parallel multiconductor with arbitrary positions have proposed. A comparison with measured results has proved that the accurancy of the impedance formula is satisfactory. By applying the formulas, the characteristics of the finite line parameters such as a propagation constant and a characteristics impedance are investigated in comparison with those given by the conventional assumption of an infinite line. The impedance of the infinite line is greater and the capacitance is smaller than those of the line. The difference increases as the line length and source frequency decrease, and the height, radius and separation distance increase. According to the foregoing, the attenuation constant and the characteristic impedance of the infinite line are greater and the propagation velocity is smaller than those of the finite line. [ABSTRACT FROM AUTHOR]

Fountain codes were introduced to provide high reliability and scalability and low complexities for networks such as the Internet. Luby-transform (LT) codes, which are the first realisation of Fountain codes, achieve the capacity of the binary erasure channel (BEC) asymptotically and universally. Most previous work on single-layer Fountain coding targets the design via the right degree distribution. The left degree distribution of an LT code is left as a Poisson to protect the universality. For finite lengths, this is no longer an issue; thus, the author's focus is on designing better codes for the BEC at practical lengths. Their left degree shaping provides codes outperforming LT codes and all other competing schemes in the literature. At a bit error rate of 10-7 and packet length k = 256, their scheme provides a realised rate of 0.6 which is 23.5% higher than that of Sorensen et al.'s decreasing-ripple-size scheme. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the effect of finite boundary on the stress intensity factor of an internal semi-elliptical crack in a pressurized finite-length thick-walled cylinder . The three-dimensional finite element method, in conjunction with the weight function method, is used for computing the stress intensity factor at the deepest and surface points of an axial semi-elliptical crack in a cylinder. The transition aspect ratios, the aspect ratios in which the maximum stress intensity factor translates from the deepest to the surface points of the crack, are calculated for different relative depths and cylinder lengths. The results show that the stress intensity factor increases as the cylinder length decreases, especially at the corner point of the crack compared with the deepest point. The major advantage of this paper is that a closed-form expression is extracted for the stress intensity factor at the surface point of a semi-elliptical crack, which experiences higher changes due to the effect of the finite boundary of the cylinder. [ABSTRACT FROM AUTHOR]

The problem of the buckling of finite length externally constrained thin circular cylinders is solved to yield a generalized eigenvalue problem with constraint conditions. The solution is based on an inverse iteration procedure in which the non-linear complementary equation is solved by a non-smooth version of Newton's method that saves computer time and space when compared to a linear complementary algorithm. The numerical results show that the method proposed is effective and that the critical buckling load of the constrained cylinder is almost independent of the length of the cylinder, unlike the critical load of free (unconstrained) thin cylinders. In the direction of its axis, the shell is discretized by finite strips which circumferentially use straight bar and beam displacement functions. It is proved that when the widths of the strips approach zero, the geometrical relationships used in this paper approach those of Koiter–Sanders cylindrical shell theory. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For numerous applications in the field of signal processing, it is desired to design a compact window that can simultaneously concentrate maximum energy in finite time interval and frequency band. Although zero‐order discrete prolate spheroidal sequence (DPSS) meets this requirement, it is of infinite support. Limiting this sequence to finite support no longer guarantees the optimality property. This study aims at designing a discrete finite length window that can maximise the energy simultaneously in narrow time interval and frequency band. A multi‐objective optimisation approach is adopted to obtain the upper bound of maximum achievable time and frequency domain energy concentrations for finite length sequences. The optimal sequence thus obtained is termed as the optimal window with finite support (OWFS), and its various associated properties are discussed. It is shown analytically that as the support of OWFS approaches infinity, it converges to zero‐order DPSS. In order to illustrate its optimality, the compactness of the proposed OWFS is compared with those of various window functions. Extending the proposed OWFS, this study also discusses the formulation and associated properties of the zero‐order periodic DPSS. Further, the closed form expression for the upper bound of achievable time and frequency domain energy concentrations is also derived. [ABSTRACT FROM AUTHOR]

This paper investigates the radiation and propagation of electromagnetic fields in a uniformly bent section of a rib waveguide connected with the straight section when guided modes are incident from the straight section. The analysis is based on a method in which fields in uniformly bent sections are expressed in terms of a spectral integral of eigenmodes with continuous eigenvalues. Fields propagated along a uniformly curved slab waveguide with finite-length also are analysed in detail using the same method for a full numerical investigation of mode transmission and mode conversion characteristics for the slab waveguide structure where two straight waveguides are connected via one finite-length, uniformly curved section. [ABSTRACT FROM AUTHOR]

This paper presents analytically electromagnetic fields radiated from finite-length transmission-lines. The method is based on the fact that the measured power patterns radiated from the finite-length transmission line are the same as that measured for the coupling, which is phenomenon when a plane wave excites a transmission line. Under the hypothesis, reciprocity is assumed between the radiation and the coupling. The power radiated from the finite-length transmission line, which is received by the measuring antenna, is obtained by the use of a circuit-concept approach, the transmission-line equation for the coupling. By comparing the computed values with the measured ones, the reciprocity between them is verified. A discussion is also made on the model with a bend, in addition to the straight line, to confirm the validity. As a result, the fields radiated from the finite-length transmission line are determined from the power received by the antenna. [ABSTRACT FROM AUTHOR]

We study the electronic properties of hydrogenated carbon nanotubes under an electric field based on the density functional theory with effective screening medium method. We find that, screening against the external electric field strongly depends on local atomic arrangement due to the inhomogeneous charge distribution arising from the bond alternation induced by the H-terminated C atoms at the edge region. Besides the screening arising from the bond alternation, unusual electric field screening occurs at the vicinity of the edge C atomic site in zigzag nanotubes. We also find that the energy gap between the highest occupied and the lowest unoccupied states of armchair and zigzag nanotubes oscillates in triple and double periodicity, respectively, in their units with respect to the length. The electric field induces the charge redistribution in which the charge accumulation and depletion only occur around the H-terminated C atoms situated near the ends of the nanotubes. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A linear induction motor (LIM) has a much larger mechanical clearance than the conventional rotating-type induction motor and the magnetic path of its primary core is not closed. The effect of stationary pulsating magneto-motive force (mmf) is not taken into account in the analysis based on Fourier transformation, where it is assumed that the primary current is represented by a sinusoidal current of finite length. This assumption holds only when the winding is of single-layer type and the numbers of slots and phases are very large. The pulsating mmf penetrates the secondary conductor and primary core over the full length of the LIM inducing the eddy current in the secondary conductor which increases the secondary copper loss considerably.

The article presents an analytical problem of conventional LIM theories based on a sinusoidal primary current sheet model with finite length. The secondary conductor of the LIM does not consist of a winding and therefore its electromagnetic characteristics must be analyzed by electromagnetic theory. In this analysis, the primary mmf has to be represented by an equivalent current sheet. For an infinitely long LIM with many slots and multiphase windings, it is possible to assume that the primary mmf is distributed sinusoidally.

Here, we theoretically analyze the mutual coupling between two finite-length thin wire chirostrip antennas. These antennas are defined as thin wires printed on grounded substrate made of chiral materials which exhibit electromagnetic handedness. Chiral materials are circular polarization (CP) birefrin gent and are described by the constituitive relations D = ε c E + iξ cB and H = iξcE + B/μc, with ξ 011(1 E, as material parameters. Mutual coupling for broadside, collinear, and echelon configurations for these antennas is investigated, and it is shown that introducing chirality in the substrate can, under certain circumstances, modify the mutual coupling between the chi- rostrip antennas. [ABSTRACT FROM AUTHOR]

Low-lying electronic terms of the hydrocarbons [C] ( q = 1,3...9) were calculated within CASSCF approach. The [C] are H-terminated finite fragment of zigzag carbon nanotube (7,0) containing q cyclacene units. Each [C] with odd q has D point symmetry. All systems [C] with arbitrary n and q have a specific set of the one-electron states characterized by the exponential decay along the cylinder axis that has been estimated within the Huckel model. These MOs are localized near bases of the cylinder and they are frontier in all systems [C]. By hypothesis, the low-lying electronic terms of the hydrocarbons [C] ( q = 1,3...9) are defined by four quasi-degenerate MOs e′, e″, which were included in the active space CASSCF. Low-lying electronic terms possess tier structure and systems with various q have the same order of states. The distance between tiers tends to asymptotic limit with increasing q. In this case, states in each tier become quasi-degenerate. The lowest tier consists of close set of states A, A, A, and each is characterized by single occupation of the localized MOs. Ground state of [C] is singlet; values of splitting are well described by Heisenberg hamiltonaian. The calculation results can be interpreted as reducing interaction of states localized on opposite cylinder bases with increasing fragment length. According to CASSCF, this interaction reduces exponentially in exact accordance with the similar characteristics of the localized MOs. There is a reason to believe that the value of splitting decreases less rapidly with increasing q if level of calculation is improved. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 [ABSTRACT FROM AUTHOR]

If two transmission lines such as microstrip lines are set in the neighborhood, a coupling or crosstalk phenomenon may be generated between them. When the coupling level is low, the phenomenon can be considered as a coupling of external fields by one transmission line to the other transmission line; a set of nonhomogeneous differential equations with regard to a line voltage and current holds approximately. The fields can be obtained by estimating vector potentials of currents on the line section and the terminals in terms of a terminal voltage and current of the line concerned. Thus, a solution to the equations can be obtained in expression of a four-port network. Estimation of the coupling between microstrip lines is made by applying the terminal conditions to the expression. To confirm the theory, an experiment has been conducted; the experimental results are in good agreement with the theory. © 1998 Scripta Technica, Electr Eng Jpn, 123(2): 8–15, 1998 [ABSTRACT FROM AUTHOR]

The study on the hydraulic properties of coastal aquifers has significant implications both in hydrological sciences and environmental engineering. Although many analytical solutions are available, most of them are based on the same basic assumption that assumes aquifers extend landward semi‐infinitely, which does not necessarily reflect the reality. In this study, the general solutions for a leaky confined coastal aquifer have been developed that consider both finitely landward constant‐head and no‐flow boundaries. The newly developed solutions were then used to examine theoretically the joint effects of leakage and aquifer length on hydraulic head fluctuations within the leaky confined aquifer, and the validity of using the simplified solution, which assumes the aquifer is semi‐infinite. The results illustrated that the use of the simplified solution may cause significant errors, depending on joint effects of leakage and aquifer length. A dimensionless characteristic parameter was then proposed as an index for judging the applicability of the simplified solution. In addition, practical application of the general solution for the constant‐head inland boundary was used to characterize the hydraulic properties of a leaky confined aquifer using the data collected from a field site at the Seine River estuary, France, and the versatility of the general solution was further justified. [ABSTRACT FROM AUTHOR]

Auroral field‐aligned currents (FACs) have an intrinsic complexity caused by the superposition of contributions from a broad spectrum of scales and diversity of locations. The complex FAC systems are investigated by using the multiscale minimum variance analysis. This technique provides a scale based decomposition of the FAC systems by identifying the constituting FAC elements as well as their structure. At the basis, the analysis exploits the scale dependence of the eigenvalues of the magnetic field variance matrix. The scale decomposition along the transversal (latitudinal) direction results from the scale derivative of the maximum eigenvalue. The complementary information from the scale derivative of the minimum eigenvalue helps to infer the full structure of each FAC element by providing estimates of the FAC length (longitudinal) scale. The scale derivative of minimum and maximum eigenvalues are used to identify FAC signatures associated to different types of aurora (e.g., highly extended, finite arcs, gradient regions) as well as to characterize the influence of the crossing location with respect to the FAC structures (e.g., near edge crossings). The multiscale analysis is applied to simulated FACs and to spacecraft observations made by the Swarm mission. The use with real world data illustrates the power of this analysis, whose full benefits for magnetosphere‐ionosphere coupling investigations are yet to be explored. Plain Language Summary: The analysis in this work applies to magnetic field observations from satellites crossing above the aurora. The complexity of auroral displays relates to complex currents that flow along the Earth main magnetic field. These currents are observed as a perturbation magnetic field. The added contributions from currents of different spatial scales, locations and life‐times lead to complex signatures of the field‐aligned currents. The analysis here traces this complexity by a decomposition of the measured magnetic field perturbation into discrete current elements. The aim is to decompose the magnetic field observations into the constituent discrete elements and to characterize their respective structures. The analysis is applied to Swarm observations whereas the ground optical observations provide a qualitative cross‐check to the analysis. Key Points: Single‐spacecraft decomposition of complex field‐aligned current (FAC) systems associated to finite length (east‐west) auroral structuresEstimation of the geometric structure of finite FACs by the transversal and longitudinal scalesIdentification of FAC signatures associated to finite FACs like the crossings near the eastward/westward edges of longitudinally extended FACs [ABSTRACT FROM AUTHOR]

A new asymptotic high-frequency solution is presented for the problem of diffraction of acoustic waves emanating from a ring source by a cylindrical impedance rod of finite length. This problem is described by a modified Wiener-Hopf equation of the third kind which can be solved approximately. The solution involves two infinite sets of constants satisfying two infinite systems of linear algebraic equations. [ABSTRACT FROM AUTHOR]