Exact analytical expressions for the potential of electrical double layer interactions for a sphere-plate system.

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.

Analytical expressions for the FM and AM responses of an integrated laser-modulator

The need for low-chirp and compact transmitters for high-bit-rate optical links has led to the development of integrated laser electroabsorption modulators (ILM). We have investigated feedback effects inducing frequency chirp by developing a model treating the ILM as a whole and obtained analytical expressions of the FM and AM responses. The variation of the frequency chirp with the residual facet reflectivity of the modulator section is calculated. The model predicts the unusual peak in the measured frequency responses and has been used to define design rules.

Power analysis applying the instantaneous complex power analytical expressions on a RL symmetrical three-phase system

This paper enhances some concepts of the Instantaneous Complex Power Theory by analyzing the analytical expressions for voltages, currents and powers developed on a symmetrical RL three-phase system, during the transient caused by a sinusoidal voltage excitation. The powers delivered to an ideal inductor will be interpreted, allowing a deep insight in the power phenomenon by analyzing the voltages in each element of the circuit. The results can be applied to the understanding of non-linear systems subject to sinusoidal voltage excitation and distorted currents.

Analytical Closed-Form Expressions for Harmonic Distortion Corresponding to Novel Switching Sequences for Neutral-Point-Clamped Inverters

Analytical closed-form expressions for harmonic distortion factors corresponding to various pulsewidth modulation (PWM) techniques for a two-level inverter have been reported in the literature. This paper derives such analytical closed-form expressions, pertaining to centered space-vector PWM (CSVPWM) and eight different advanced bus-clamping PWM (ABCPWM) schemes, for a three-level neutral-point-clamped (NPC) inverter. These ABCPWM schemes switch each phase at twice the nominal switching frequency in certain intervals of the line cycle while clamping each phase to one of the dc terminals over certain other intervals. The harmonic spectra of the output voltages, corresponding to the eight ABCPWM schemes, are studied and compared experimentally with that of CSVPWM over the entire modulation range. The measured values of weighted total harmonic distortion (WTHD) of the line voltage V-WTHD are used to validate the analytical closed-form expressions derived. The analytical expressions, pertaining to two of the ABCPWM methods, are also validated by measuring the total harmonic distortion (THD) in the line current I-THD on a 2.2-kW constant volts-per-hertz induction motor drive.

Analytical solution of the laminar mean flow wave equation in a lined or unlined two-dimensional rectangular duct

The prediction of the sound attenuation in lined ducts with sheared mean flow has been a topic of research for many years. This involves solving the sheared mean flow wave equation, satisfying the relevant boundary condition. As far as the authors' knowledge goes, this has always been done using numerical techniques. Here, an analytical solution is presented for the wave propagation in two-dimensional rectangular lined ducts with laminar mean flow. The effect of laminar mean flow is studied for both the downstream and the upstream wave propagation. The attenuation values predicted for the laminar mean flow case are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.

Analytic expressions for the constitutive parameters of magnetoelectric metamaterials

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling. © 2010 The American Physical Society.

Simple and accurate analytical model of planar grids and high-impedance surfaces, comprising metal strips or patches

Simple analytical formulas are introduced for the grid impedance of electrically dense arrays of square patches and for the surface impedance of high-impedance surfaces based on the dense arrays of metal strips or square patches over ground planes. Emphasis is on the oblique-incidence excitation. The approach is based on the known analytical models for strip grids combined with the approximate Babinet principle for planar grids located at a dielectric interface. Analytical expressions for the surface impedance and reflection coefficient resulting from our analysis are thoroughly verified by full-wave simulations and compared with available data in open literature for particular cases. The results can be used in the design of various antennas and microwave or millimeter wave devices which use artificial impedance surfaces and artificial magnetic conductors (reflect-array antennas, tunable phase shifters, etc.), as well as for the derivation of accurate higher-order impedance boundary conditions for artificial (high-) impedance surfaces. As an example, the propagation properties of surface waves along the high-impedance surfaces are studied.

Analytical Study of Light Propagation in Highly Nonlinear Media

The present dissertation is devoted to the construction of exact and approximate analytical solutions of the problem of light propagation in highly nonlinear media. It is demonstrated that for many experimental conditions, the problem can be studied under the geometrical optics approximation with a sufficient accuracy. Based on the renormalization group symmetry analysis, exact analytical solutions of the eikonal equations with a higher order refractive index are constructed. A new analytical approach to the construction of approximate solutions is suggested. Based on it, approximate solutions for various boundary conditions, nonlinear refractive indices and dimensions are constructed. Exact analytical expressions for the nonlinear self-focusing positions are deduced. On the basis of the obtained solutions a general rule for the single filament intensity is derived; it is demonstrated that the scaling law (the functional dependence of the self-focusing position on the peak beam intensity) is defined by a form of the nonlinear refractive index but not the beam shape at the boundary. Comparisons of the obtained solutions with results of experiments and numerical simulations are discussed.

Simple analytical expression for vector hypernuclear asymmetry in nonmesonic decay ofΛ 5He andΛ 12C

We present general explicit expressions for a shell-model calculation of the vector hypernuclear parameter in nonmesonic weak decay. We use a widely accepted effective coupling Hamiltonian involving the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω, K*). In contrast to the approximated formula widely used in the literature, we correctly treat the contribution of transitions originated from single-proton states beyond the s-shell. Exact and simple analytical expressions are obtained for the particular cases of Λ 5He and Λ 12C, within the one-pion-exchange model. Numerical computations of the asymmetry parameter, aΛ, are presented. Our results show a qualitative agreement with other theoretical estimates but also a contradiction with recent experimental determinations. Our simple analytical formulas provide a guide in searching the origin of such discrepancies, and they will be useful for helping to solve the hypernuclear weak decay puzzle.

Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions

Using an analytical model to design liquid crystal microlenses

We have developed new analytical expressions for designing liquid crystal (LC) microlenses. These equations are based on a novel equivalent electric circuit and can be used to create an optimum design for the LC lenses in which the lens diameter ranges from a few micrometers to several millimeters. Thus far, only experimental studies have been conducted on the LC lenses. The analytical expressions developed in this letter depend on various manufacturing parameters and can be used to design lenses with specific focal lengths and a parabolic phase profile. The required driving scheme (modal or hole-patterned) can be predicted. The LC microlenses were manufactured and electrooptically characterized: the measurements were compared using an analytical approach.

Modeling multivariate autoregressive conditional heteroskedasticity with the double smooth transition conditional correlation GARCH Model

In this paper, we propose a multivariate GARCH model with a time-varying conditional correlation structure. The new double smooth transition conditional correlation (DSTCC) GARCH model extends the smooth transition conditional correlation (STCC) GARCH model of Silvennoinen and Teräsvirta (2005) by including another variable according to which the correlations change smoothly between states of constant correlations. A Lagrange multiplier test is derived to test the constancy of correlations against the DSTCC-GARCH model, and another one to test for another transition in the STCC-GARCH framework. In addition, other specification tests, with the aim of aiding the model building procedure, are considered. Analytical expressions for the test statistics and the required derivatives are provided. Applying the model to the stock and bond futures data, we discover that the correlation pattern between them has dramatically changed around the turn of the century. The model is also applied to a selection of world stock indices, and we find evidence for an increasing degree of integration in the capital markets.

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.