Distance Z0 Research Articles

On the nature of the Sommerfeld–Brillouin forerunners (or precursors)

We present a brief overview of Sommerfeld's forerunner signal, which occurs when a monochromatic plane-wave (frequency {\omega}={\omega}_s) suddenly arrives, at time t=0 and at normal incidence, at the surface of a dispersive dielectric medium of refractive index n({\omega}). Deep inside the dielectric host at a distance z0 from the surface, no signal arrives until t=z0/c, where c is the speed of light in vacuum. Immediately after this point, a weak but extremely high frequency signal is observed at z=z0. This so-called Sommerfeld forerunner (or precursor) is highly chirped, meaning that its frequency, which is much greater than {\omega}_s immediately after t=z0/c, declines rapidly with the passage of time. The incident light with its characteristic frequency {\omega}_s eventually arrives at t~z0/vg , where vg is the group velocity of the incident light inside the host medium. Brillouin has identified a second forerunner that occupies the interval between the end of the Sommerfeld forerunner at t~n(0)z0/c and the beginning of the steady signal. This second forerunner is commonly referred to as the Brillouin forerunner (or precursor). Given that the incident wave has a sudden start at t=0, its frequency spectrum spans the entire range of frequencies from minus infinity to infinity. Consequently, the high-frequency first forerunner cannot be considered a superoscillation, nor can the low-frequency second forerunner be regarded as a suboscillation. The goal of the present paper is to extend the Sommerfeld-Brillouin theory of precursors to bandlimited incident signals, in an effort to determine the conditions under which these precursors would continue to exist, and to answer the question as to whether or not such precursors, upon arising from a bandlimited incident signal, constitute super- or sub-oscillations.

Study of Parameter Influence on Quality on the Electromagnetic Imaging Reconstruction from the Spectrum of the Diffracted Field: Application to Reconstruction of the leakage Current of ISM Applicators

The ISM applicators generate leakage currents that can disrupt satellite TV transmission, taking into account the effects of the electromagnetic waves and those of the CEM. We are interested in these as a way to reconstitute their leakage currents, using the Micro-waves Imagery. We propose such a method of spectral analysis, which is intended to reconstruct the equivalent current distribution (position and form) to an object starting from the diffracted field spectrum by the Micro-waves Imagery. Our contribution resides in the influence of different parameters (N number of the measurement point, and the distance z0 of the measurement plane) on the reconstitution quality. This method is presented and illustrated; an algorithm of reconstructing the image of an object existing within a surrounding homogenous medium with known dielectric properties, this algorithm is developed with MATLAB. This method leads to more significant results, and quickly permits to get information about the object form.

Determining the Pivotal Plane of Fluid Lipid Membranes in Simulations

Each leaflet of a curved lipid membrane contains a surface at which the area strain vanishes, the so-called pivotal plane. Its distance z0 from the bilayer's mid-plane arises in numerous membrane structure related contexts, for instance the connection between monolayer and bilayer moduli, stress-profile moments, or area-difference elasticity theories. Experimentally, the pivotal plane is known to lie close to the glycerol backbone of a lipid, but only very few simulations have tried to locate it. Here we propose two precise methods for determining z0, both of which rely on monitoring the lipid imbalance across a curved bilayer. The first method considers the ratio of lipid number between the two leaflets of cylindrical or spherical vesicles and requires lipid flip-flop for equilibration. The second method looks at the leaflet difference across local sections cut out from a buckled membrane and is free of this limitation. Our simulations rely on two different coarse-grained lipid models. First, the generic three-bead solvent-free Cooke model, which is amenable to both methods and gives results for z0 that agree at the percent level. And second, a ten-bead representation of dimyristoylphosphocholine (DMPC) with the explicit solvent MARTINI model, which can only be analyzed with the buckling method. For the latter, the obtained value z0 = 0.850(11) nm lies about 0.4 nm inwards of the glycerol backbone, essentially in the middle of the leaflet, and is hence unexpectedly small. We attribute this to limitations of the coarse-grained description, suggesting that the location of the pivotal plane might be a novel indicator for how well lipid models capture the microscopic origins of curvature elasticity, especially the relative contributions of head and tail regions to the overall curvature modulus.

Determining the pivotal plane of fluid lipid membranes in simulations.

Each leaflet of a curved lipid membrane contains a surface at which the area strain vanishes, the so-called pivotal plane. Its distance z0 from the bilayer's midplane arises in numerous contexts, for instance the connection between monolayer and bilayer moduli, stress-profile moments, or area-difference elasticity theories. Here, we propose two precise methods for determining the location of the pivotal plane in computer simulations, both of which rely on monitoring the lipid imbalance across a curved bilayer. The first method considers the ratio of lipid number between the two leaflets of cylindrical or spherical vesicles; it hence requires lipid flip-flop for equilibration. The second method looks at the leaflet difference across local sections cut out from a buckled membrane; this observable equilibrates even in the absence of flip-flop. We apply our methods to two different coarse-grained lipid models, the generic three-bead solvent-free Cooke model and a ten-bead representation of dimyristoylphosphocholine with the explicit solvent MARTINI model. The Cooke model is amenable to both methods and gives results that agree at the percent level. Using it, we also show that the pivotal plane moves outward as lipid curvature becomes more positive. The MARTINI model can only be analyzed with the buckling method; the obtained value z0 = 0.850(11) nm lies about 0.4 nm inwards of the glycerol backbone and is hence unexpectedly small. We attribute this to limitations of the coarse-grained description, suggesting that the location of the pivotal plane might be a good indicator for how well lipid models capture the microscopic origins of curvature elasticity. Finally, we also show that the pivotal plane position itself moves as the membrane is bent. The leading correction is linear in curvature, dependent on the Poisson ratio, and can matter when analyzing experimental results obtained from highly curved inverse hexagonal phases.

Changes of skewness and sharpness of partially coherent decentered annular beams on propagation

Changes of skewness and sharpness of partially coherent decentered annular beams (PCDA beams) on propagation both in free space and in oceanic turbulence are studied. Based on the Wigner distribution function, the analytical expressions for the skewness parameter A and the kurtosis parameter K of PCDA beams are derived. The analytical expression for the oceanic turbulence parameter T′ related to K is also derived, and characteristics of T′ are examined. It is found that the behaviors of A and K in oceanic turbulence are quite different from those in free space. In free space, the mass of the intensity distribution may move from one side of the centroid position axis yc to another side at a certain propagation distance z0, and z0 is independent of the correlation parameter τ. The mass of the intensity distribution is concentrated on one side of yc on propagation only for a poorly coherent beam in free space, but it is always this situation for different value of τ when oceanic turbulence is not weak. In free space, it takes a leptokurtic profile in the far field, and a Gaussian profile appears only for a poorly coherent beam. However, in oceanic turbulence it always reaches a Gaussian profile for different value of τ in the far field.

Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model

We calculate the Gaussian curvature modulus kappa of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value kappa/kappa = -1.04 +/- 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce kappa(m)/kappa(m) = -0.98 +/- 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z0 of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K(0m). By also analyzing the lateral stress profile sigma0(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K(0m) and kappa through the first and second moment of sigma0(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.

E-FIELD EXTRACTION FROM H-NEAR-FIELD IN TIME-DOMAIN BY USING PWS METHOD

A novel technique of the electric- or E-fleld extraction from the magnetic- or H-near-fleld in time-domain is reported. This technique is based on the use of the Maxwell-Ampere relation associated to the plane wave spectrum (PWS) transform. It is useful for the E-near-fleld computations and measurements which are practically complicated in time-domain in particular, for the EMC applications. The considered EM-fleld radiation is generated by a set of electric dipoles excited by an ultra-short duration current having frequency bandwidth of about 10-GHz. The presented EM- fleld calculation technique is carried out by taking into account the evanescent wave efiects. In the flrst step, the time-dependent H-fleld data mapped in 2-D plan placed at the height z0 above the radiating devices are transposed in frequency-dependent data through the fast Fourier transform. In order to respect the near-fleld approach, the arbitrary distance z0 between the EM-fleld mapping plan and radiating source plan should be below one-sixth of the excitation signal minimal wavelength. In the second step, one applies the PWS transform to the obtained frequency-data. Then, through the Maxwell-Ampere relation, one can extract the E-fleld from the calculated PWS of the H-fleld. In the last step, the inverse fast Fourier transform of the obtained E- fleld gives the expected time-dependent results. The relevance of the proposed technique was conflrmed by considering a set of flve dipole sources placed arbitrarily in the horizontal plan equated by z = 0 and excited by a pulse current having amplitude of 50mA and half-width of about 0.6ns. As expected, by using the Hx, Hy and Hz 2-D data calculated with Matlab in the rectangular plan placed at z0 = 3mm and z0 = 5mm above the radiating source, it was demonstrated that

Three-dimensional level-curve scanning based on intersection of laser lines

A dimensional measurement system that also tracks object movements is presented here. The method directly yields the level curves of an object. It is an extension of collimation methods, coupled with the use of structured lighting with features formed from several luminous planes intersecting in a single line. This line defines a set of points of the space at a fixed distance Z0 from the measuring head. The locus of the points of the object where the lighting is reduced to a single line is the level curve sought. The introduction of an asymmetry into the lighting structure permits one to determine the direction as well as an approximate value of the value of the distance to the level curve from a point on the illuminated object. The experiments performed permit one to evaluate the performance of such a system, and suggest future applications.

Dynamic Plate Thickness of ERA Sandwiches against Shaped Charge Jets

AbstractThe equation for the dynamic plate thickness is derived as a function of standoff distance Z0, jet tip velocity vj0, cutoff velocity vjc, plate velocities vPI and NATO angle of the ERA sandwich. The dynamic thickness is presented as functions of the different parameters for the front plate – flying against the shaped charge jet – and the rear plate – flying with the shaped charge jet. But the dynamic thickness is only one of the reduction factors of ERA sandwiches.

Adhesive contact based on the Lennard-Jones potential: a correction to the value of the equilibrium distance as used in the potential.

A Lennard-Jones type surface law is commonly used in adhesive contact modeling; however, one of its parameters, namely the equilibrium distance z0, is not well defined. In this paper, a self-consistent method is used to derive the Lennard-Jones surface law from the interatomic Lennard-Jones potential. The parameters of the surface law are directly related to the material lattice parameter and surface energy, and the equilibrium distance z0 values are obtained for various materials. The effect of using the z0 proposed in the present work is demonstrated via the study of adhesive contact behavior for a single sphere and a flat surface, as well as the contact between planar rough surfaces. For pull-off force prediction of the contact between a single sphere and a flat surface, the error of using the z0 suggested in previous studies could be as large as 10% at intermediate ranges of a dimensionless adhesion parameter. For the contact between planar rough surfaces, the error of using the previously proposed z0 is larger for smoother cases, and the prediction of pull-off force could be different by as much as a factor of 5.

Generalization of the Leveque problem for mass transfer in swirling flows in the entrance region of a cylindrical section

parameters. However, in contrast to axial non-swirling flows, the comparison [4] of experimental data [1–4] for various set-ups and flow regimes did not reveal the generalized character of Eq. (1) for swirling flows. To verify the applicability of Eq. (1) to mass transfer in swirling flows, we consider the problem of mass transfer from a swirling flow to a microelectrode flash mounted with the wall of a cylindrical tube of radius R (corresponding measurements were reported, e.g., in [4]). In order to simplify the mathematical formulation of the problem, we examine only axisymmetrically developed flow regimes (turbulent pulsations and threedimensional effects are ignored). Let the distance z0 from the entrance of the cylindrical section to the microelectrode be so small that the boundary layer developed in this length is thin (its thickness δ ! R) and Sh cReSc, Re Ud ν -------. = =

Coil-to-Flower Transition of a Polymer Chain Pinned near a Stepwise External Potential: Finite Size Effects

We study the behavior of a polymer chain near a stepwise external potential u. The exact partition function of the chain tethered at a distance z0 away from this interface is analyzed in a Landau framework. In this model, there exists a conformational coil-to-flower transition. Here the flower has a strongly stretched stem from the grafting point toward the interface and, on top of it, a crown composed of the remaining segments in a (perturbed) coil conformation. The classical behavior of binodal and spinodal states of the system is identified. A phase diagram in the z0 vs u coordinates is presented with a line of first-order phase transitions ending at a critical point at z0 = 0. In this last point, the transition is referred to as the rolling transition. Particular attention is payed to small systems, i.e., to systems near the critical point. This region is relevant for relatively short polymer chains and small values of the external field.

First-order coil-to-flower transition of a polymer chain pinned near a stepwise external potential: Numerical, analytical, and scaling analysis

A polymer chain near a penetrable interface is studied in the Gaussian model, in the lattice random walk model and by a scaling analysis. The interface is modeled as an external potential u of a Heaviside step-function form. One end of the chain is fixed at a distance z0 away from this interface. When the end point is fixed in the high potential region, a first-order coil-to-flower transition takes place upon variation of the distance z0. Here, the flower has a strongly stretched stem from the grafting point towards the interface and, on top of it, a crown composed of the remaining segments in a (perturbed) coil conformation. The coil-to-flower transition is analyzed in terms of the Landau free energy. The order parameter is taken to be related to the fraction of segments residing in the energetically favorable region. Exact analytical expressions for the Landau function are obtained in the Gaussian model for any distances z0 and potential strength u. A phase diagram in the z0 versus u coordinates is constructed. It contains a line of the first-order phase transitions (binodal line) ending at a critical point z0=u=0, and two spinodal lines. Numerical results are obtained for several chain lengths in the lattice random walk model demonstrating the effects of finite extensibility on the position of the transition point. Excluded volume effects are analyzed within the scaling approach.

Landau quantized 2D nonlocal Bernstein mode magnetoplasmon coupling with surface and bulk phonons

We have examined the collective modes of a two-dimensional (2D) Landau-quantized magnetoplasma in a planar quantum well, including nonlocal 2D Bernstein modes, in interaction with surface and bulk optical phonons. The system considered is a 2D sheet of nonlocal electron magnetoplasma embedded in a semi-infinite semiconductor medium with optical phonons. We analyze the longitudinal collective mode spectrum as a function of distance z0 of the 2D sheet from the bounding surface of the semiconductor. In particular, the 2D magnetoplasma/Bernstein modes couple preferentially to the bulk LO phonon deep in the medium, whereas in the vicinity of the surface they couple preferentially to the surface phonon. The study is carried out by employing the spatially inhomogeneous inverse dielectric function of the combined system of planar quantum well plasma and semi-infinite semiconductor in position representation to obtain the coupled mode dispersion relation which we analyze to determine the dependence of the modes on wave number as well as on z0.

Forward projection of transient signals obtained from a fiber-optic pressure sensor

An analytical/experimental approach is presented to reconstruct the space–time pressure field in a plane and forward project the resultant space–time pressure field using tomographic and wave vector time-domain methods. Transient pressure signals from an underwater ultrasonic planar transducer are first measured using a line fiber-optic pressure sensor which is scanned across a plane at a fixed distance z0 from the transducer. The resulting spatial line integrals in the plane are time-dependent signals which are first used to reconstruct the space–time pressure field in the plane via simply implemented tomographic methods. These signals are then used to forward project the space–time pressure field to arbitrary planes employing a wave vector time-domain method. Verification of the method is first presented using synthetic signals and the impulse response approach. An experimental verification of the approach is then presented using an ultrasonic planar transducer. The results of the projected and experimental fields are compared at various distances for synthetic signals and experimental data. Good correlation is found between the calculated, projected, and experimental data.

Penetration Cutoff Velocities of Shaped Charge Jets

AbstractThe maximum depth of penetration, Pmax, of a shaped charge jet can theoretically be calculated from 5 quantities for the purely continuous, or for the initially continuous and then particulated, or for the fully particulated penetrating jet. These quantities are the distance Z0 of the target plate from the virtual origin, the value of γ (i.e. the square root of the ratio of target to jet density), the jet tip velocity vj,0 the efficient residual velocity vj,min, and the particulation time tp.Instead of calculating the individual values of vj,min for the individual depths of penetration Pexp at various standoff distances, this quantity can quite simply be read from the standoff diagram by means of the penetration cutoff lines‐ a so‐called Standoff/Cutoff‐diagram ‐, using the experimentally determined depth of penetration Pexp. The penetration cutoff lines are lines which start at the virtual origin and which represent the ideal increment in depth of penetration per jet velocity interval in the standoff diagram, the abscissas of this line corresponding to the jet tip velocities.The methods are demonstrated and explained, using the results of three firings with one type of shaped charge as an example. The shots were made at 6, 12, and 24 calibers standoff distance, and the cratering history was also determined in these trials.

Precision in determination of astronomical refraction from aerological data

AbstractVarious errors in determination of the local pure astronomical refraction are evaluated versus the apparent zenith distance z0. Numerical integration with the step imposed by heights of an aerological sounding brings the error smaller than 0″01 until z0 = 70°. For larger zenith distances integration with a more dense step is possible after fitting the data to a five‐parameter functional dependence of the refractive index on height. The fitting is simultaneously a good equalization of aerological data reducing considerably their experimental error as well as short‐term local fluctuations of the atmosphere. After equalization, the error in the refraction originating from the error in the aerological data is found to approach 0″01 at z0 = 72°, 0″1 at z0 = 82°, 1″ at z0 = 87°, and 10″ at the horizon. This has to be taken into account when considering systematic deviations of the local pure refraction from that determined in a standard way. The purely stochastic error in the refraction originating in the error of the refractive index at the observation site is discussed within the context of local fluctuations of the atmosphere. It is evaluated that until z0 = 85° the precision in determining the astronomical refraction in a single observation is limited by refraction anomalies (image motion) and only above 85° the error in aerological data becomes more important.

Van der Waals induced dipoles

Expressions are derived for calculating the induced dipole moment of an arbitrary molecule A interacting with an arbitrary system B through first- and second-order Coulomb interaction. The theory is formulated in terms of linear and quadratic charge-density susceptibilities and takes account of charge penetration but not exchange between the systems. The theory is specialized to the interaction of two nonoverlapping molecules and to a molecule interacting with a nonferroelectric solid, metallic, or crystalline. In the case of two interacting molecules, the induced moment is developed in inverse powers of R, the distance between the centers of the molecules, up to and including R−7; the coefficients of the series are given in terms of the total charges, permanent moments, polarizabilities, and hyperpolarizabilities. In the case of the solid, the results are given in terms of the molecule–solid distance z0, the dielectric function of the solid, and the permanent moments, polarizabilities, and hyperpolarizabilities of the molecule. The expressions for the dispersion and induction dipoles derived here in terms of the charge-density (hyper) susceptibilities are the most general to date in that ionic contributions are included, and the expansion in terms of the (hyper)polarizabilities is the most explicit for nonoverlapping systems. Our results are compared with the work in the literature.

Ultrasonic power measurements utilizing a microsphere scatterer and the integrated optical effect: Theory

Microsphere scatterers have been used with reasonably good success to study the acoustical pressure fields produced by ultrasound transducers [P. L. Edwards, B. D. Cook, and H. D. Dardy, J. Acoust. Soc. Am. 68, 1528–1530 (1980); and P. L. Edwards and J. Jarzyuski, J. Acoust. Soc. Am. 68, 356–359 (1980)]. The theoretical integrated optical effect has been calculated for simple transducers vibrating as pistons. [F. Ingenito and B. D. Cook, J. Acoust. Soc. Am. 45, 572–577 (1969)]. In this investigation, the theoretical integrated optical effect was calculated for spherical waves produced by a small sphere placed in the field of a monochromatic source. The line integral of the acoustic pressure was numerically evaluated for values of the ratio of the light‐to‐sphere distance (z0) to ultrasonic wavelength (Λ) from unity to 40. The temporal peak value of the pressure integral was found to occur with a phase shift of approximately (+45°) relative to the spherically scattered pressure wave. The value of the pressure integral varied from approximately 0.5 to 0.08 over this range. From these results, it should be possible to experimentally determine the power scattered by the sphere and thus the intensity incident upon the sphere using a recently described optical technique [W. A. Riley, L. A. Love, and D. W. Griffith, J. Acoust. Soc. Am. Suppl. 1 69, S91 (1981)]. This method should be applicable to broadband systems and offers the potential of calibration of high intensity ultrasonic fields. [Work supported by NIGMS 27755].

Light emission by magnetic and electric dipoles close to a plane dielectric interface III Radiation patterns of dipoles with arbitrary orientation

We have derived analytic expressions for the angular distribution of light emitted by an atomic system, e.g., a fluorescent molecule, located in a dielectric medium 1 at distance z0 from the interface to a different dielectric medium 2. The theory is rigorously valid for electric and magnetic dipole transitions with arbitrary orientation of the dipole transition moment. (In Paper II [ J. Opt. Soc. Am.57, 1615– 1619 ( 1977)], only the special case of dipoles oriented perpendicular to the interface had been treated.) The radiation patterns of dipoles located on the interface (z0 = 0) and oriented parallel to it, and ensembles of such dipoles radiating incoherently with randomly oriented dipole moments were examined in particular. They differ greatly from the corresponding well-known dipole radiation patterns in an unbounded medium 1, due to the wide-angle interferences of emitted plane waves, and radiation from evanescent waves in the dipole’s near field into medium 2, if this is denser than medium 1.