Cos Theta Research Articles

Phase-field approach for faceted solidification.

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma plot with rounded cusps that can approach arbitrarily closely the true gamma plot with sharp cusps that correspond to faceted orientations. The phase-field equations are solved in the thin-interface limit with local equilibrium at the solid-liquid interface [A. Karma and W.-J. Rappel, Phys. Rev. E 53, R3017 (1996)]. The convergence of our approach is first demonstrated for equilibrium shapes. The growth of faceted needle crystals in an undercooled melt is then studied as a function of undercooling and the cusp amplitude delta for a gamma plot of the form gamma=gamma0[1+delta(/sin theta/+/cos theta/)]. The phase-field results are consistent with the scaling law Lambda approximately V(-1/2) observed experimentally, where Lambda is the facet length and V is the growth rate. In addition, the variation of V and Lambda with delta is found to be reasonably well predicted by an approximate sharp-interface analytical theory that includes capillary effects and assumes circular and parabolic forms for the front and trailing rough parts of the needle crystal, respectively.

Oblique incidence hypervelocity impacts on rock

The behaviour of granite rock under normal incidence hypervelocity impact in the laboratory has been studied using impacts of 2-mm diameter stainless-steel spheres at between 1 and 6 km s(-1). It was found that, at normal incidence, there is a strong dependence of crater size with impact speed (v). Crater mass was found to depend on v((2.3+/-0.4)), i.e. compatible with scaling with impact energy. However, crater depth and diameter have different and dissimilar dependences on impact speed, such that the crater shape (depth/diameter) is not a constant, but decreases as impact speed increases, being 0.26 at 1 km s(-1) and falling linearly to 0.16 at 6 km s(-1). In addition, a second data set with the same projectile and target combination was taken at a mean impact speed of 5.4 +/- 0.2 km s(-1), with the angle of incidence of impact ranging from 0degrees (normal incidence) to 85degrees (glancing incidence). The oblique incidence data show that crater depth and excavated mass start to decrease immediately when non-normal incidence occurs. Crater length and width initially decrease at a slower rate, with little decrease apparent until the angle of impact exceeds 50degrees from the normal. At the highest angles of incidence (85degrees, glancing incidence), there is a sudden change in crater shape, with crater length no longer decreasing as impact angle increases. It was found that for oblique impacts, excavated crater mass scales linearly with cos theta and not with the square of costheta as indicated in earlier work. This is similar to the scaling observed in other brittle and ductile materials. Finally, when used to predict populations of non-circular craters on large Solar system bodies, the results yield estimates (3 per cent) close to the observed rate (5 per cent) on Venus, Mars and the Moon.

Monte Carlo simulation of a planar lattice model withP4interactions

Monte Carlo study of a two-dimensional lattice with three-dimensional spins (d=2,n=3) interacting with nearest neighbors via a -P4(cos theta) potential, where P4 is the fourth Legendre polynomial and theta is the angle between two spins, has been reported for lattice sizes ranging from 10 x 10 to 160 x 160. A cluster algorithm for spin updating with a histogram reweighting technique has been used and finite size scaling has been performed. The model exhibits a strong first order phase transition at a dimensionless temperature 0.376+/-0.015. The phase transition appears to be driven by condensation of topological defects and the defect density D increases sharply at the transition temperature. The temperature derivative dD/dT* is found to obey a linear scaling relation with the lattice size L. The behavior of the model seems to be remarkably different from the two-dimensional P2 model, that has been investigated by other authors, although both models possess the same symmetry and topological defects play an important role in the phase transition.

Structural dependencies of interresidue scalar coupling (h3)J(NC') and donor (1)H chemical shifts in the hydrogen bonding regions of proteins.

A study is presented of the structural dependencies for scalar J-coupling and the amide donor (1)H chemical shifts in the hydrogen bonding regions of proteins. An analysis of the interactions between the donor hydrogen and acceptor oxygen orbitals in an N-H...O=C moiety suggests that there are three major structural factors for (15)N-(13)C coupling across hydrogen bonds: (1) the H...O' internuclear separation r(HO)('), (2) the H...O'=C' angle theta(2), and (3) indirect contributions involving the oxygen loan pair electrons should lead to a dependence on the H...O'=C'-N' dihedral angle rho. Density functional theory (DFT) and finite perturbation theory (FPT) were used to obtain the Fermi contact (FC) contributions to interresidue coupling in formamide dimers with systematic variation of these structural parameters. The computed (h3)J(NC)(') exhibit good correlations with cos(2) theta;(2) combined with an exponential dependence on r(HO)('). The correlation is further improved by including a dependence on the dihedral angle rho. For each of the 34 H-bonds having observable interresidue coupling in the immunoglobulin binding domain of streptococcal protein G, a formamide dimer was generated from the crystallographic structure with energy-optimized donor H-atom positions. The computed coupling constants are in reasonable agreement with the experimental, and there are excellent correlations with the simple equations involving theta;(2) and r(HO) if alpha-helix and beta-sheet regions are treated separately. This dichotomy is removed by introducing the dependence on the dihedral angle rho. Justification for the use of formamide dimers is provided by almost identical interresidue coupling constants for larger sequences extracted from the X-ray structure. The amide donor (1)H chemical shifts, which were based on DFT and GIAO (gauge including atomic orbital) methods, are in poorer agreement with the experimental data but exhibit excellent correlation with r(HO)('), theta(2), and rho.

Thermal force effects on satellites

Thermal force effects due to the Earth infrared radiation acting on artificial satellites can explain most of the residual orbit decay observed on high altitude satellites. In this work, we propose an improved thermal model that presents the total thermal effect as a sum of the summer-winter and the "generalized" day-night effects. We show that a unified model may take into account the sin theta' term (where theta' is the co-latitude of the thermal energy source) for the day-night force component and the cos theta' term for the summer-winter force component. These terms are associated with temperature variations on the satellite's surface due to its movement around the thermal energy source and allow the simultaneous application of these two forces resulting in a unified total thermal force that has two components: the Summer-Winter force, in the satellite spin axis direction (z), and the generalized Day-Night force, in the satellite equatorial plane (xy). We calculate the along-track accelerations for a test-satellite (parameters based on the LAGEOS satellite data) and obtain the average along-track acceleration <S> = -3.46 x 10-13 ms-2, for the day-night effect, and <S> = -2.85 x 10-12 ms-2, for the summer-winter effect, that leads to a residual orbit decay of nearly 1.08 mmd-1. Finally, we analyze the behavior of the average radial and along-track accelerations, and the thermal lag angle, as a function of the satellite's altitude, and show that there is a "selective law" that associates the maximum thermal effect to the radius and altitude of the satellite, and control the satellite orbit decay.

The Determination of Ethylene-Propylene Copolymer-Grafted-Glycidyl Methacrylate by the Contact Angle Method

The contact angles theta of some liquids on ethylene-propylene copolymer-grafted-glycidyl methacrylate (EPM-g-GMA) were measured. The critical surface tensions r(c) of EPM-g-GMA were evaluated by the Zisman Plot (cos theta versus r(L)), Young-Dupre-Good-Girifalco plot (1 + cos theta versus 1/r(L)(0.5)) and log (1 + cos theta) versus log(r(L)) plot. The following results were obtained: the r(c) values varied significantly with the estimation methods. The critical surface tension r(c) decreased with the increase of the degree of grafting of EPM-g-GMA.

Forward modelling of geophysical survey data using cylindrical elemental volumes

A simple model is presented for the gravitational field due to a finite cylinder, and this is elaborated so that (in principle) the gravitational field from a body of any shape may be found in terms of the field of such primitive cylinders. The primitive field is described as a moment-expansion in terms of odd-order Legendre polynomials P-2p+1 (cos theta), p=0, 1, 2,..., where theta is the angle between the field point and the cylinder's axis, and in terms of the radial distance R of the field point from the centre of mass of the cylinder, such that the parameters describing the shape of the cylinder, and the field point parameters, are separated. This allows gravitational field modelling calculations to be carried out extremely quickly in the space domain for gravitational sources of any shape. Moreover, the form of the solutions-due to the separation mentioned above-allows a clear insight into the underlying physical mechanisms involved in the synthesis of such fields, making such elements suitable in the solution of inverse gravitational problems in the space domain, as well.

BATSE Observations of the Large-Scale Isotropy of Gamma-Ray Bursts

We use dipole and quadrupole statistics to test the large-scale isotropy of the first 1005 gamma-ray bursts observed by the Burst and Transient Source Experiment (BATSE). In addition to the entire sample of 1005 gamma-ray bursts, many subsets are examined. We use a variety of dipole and quadrupole statistics to search for Galactic and other predicted anisotropies and for anisotropies in a coordinate-system independent manner. We find the gamma-ray burst locations to be consistent with isotropy, e.g., for the total sample the observed Galactic dipole moment (cos theta) differs from the value predicted for isotropy by 0.9 sigma and the observed Galactic quadrupole moment (sin(exp 2) b - 1/3) by 0.3 sigma. We estimate for various models the anisotropies that could have been detected. If one-half of the locations were within 86 deg of the Galactic center, or within 28 deg of the Galactic plane, the ensuing dipole or quadrupole moment would have typically been detected at the 99% confidence level. We compare the observations with the dipole and quadrupole moments of various Galactic models. Several Galactic gamma-ray bursts models have moments within 2 sigma of the observations; most of the Galactic models proposed to date are no longer in acceptable agreement with the data. Although a spherical dark matter halo distribution could be consistent with the data, the required core radius is larger than the core radius of the dark matter halo used to explain the Galaxy's rotation curve. Gamma-ray bursts are much more isotropic than any observed Galactic population, strongly favoring but not requiring an origin at cosmological distances.

Three-photon induced fluorescence of the calcium probe Indo-1

We report the calcium-dependent emission spectral properties of the calcium probe Indo-1 for three-photon excitation. We found that Indo-1 could be readily excited with the femtosecond pulses from a mode-locked Ti:sapphire laser at 885 nm. This wavelength is too long for two-photon excitation, which is expected to occur for wavelengths no longer than twice the longest single-photon absorption wavelength of 400 nm. For excitation at 885 nm the emission intensity was found to depend on the cube of the laser power, as expected for simultaneous interaction with three photons. At wavelengths below 840 nm the emission intensity depends on the square of the laser power, indicating two-photon excitation at shorter wavelengths. The intensity decays of Indo-1 were found to be dependent on Ca2+ and essentially identical for one- and three-photon excitation. The emission anisotropy of Indo-1 was found to be considerably higher for three-photon excitation than for one-photon excitation, consistent with cos6 theta photoselection, as compared with cos2 theta photoselection for one-photon excitation. The high values of the anisotropy are in agreement with those expected for a three-photon process. Calcium-dependent emission spectra were observed for Indo-1 with three-photon excitation, demonstrating that three-photon excitation of Indo-1 can be used for calcium imaging by emission intensity ratio measurements. The calcium-dependent emission spectra indicate a higher three-photon cross-section for the calcium-free form of Indo-1 than for the calcium-bound form. The possible advantages of three-photon excitation include the availability of the appropriate wavelengths with solid-state lasers, enhanced spatial resolution due to a reduced size of the excited volume, absence of light quenching, and possibly high selectivity of the three-photon excitation process.

Highly doubly excited S states of the helium atom

We calculate and analyse S-wave resonances of helium up to an energy of -0.02 au applying the complex rotation technique. Rydberg series converging to the hydrogenic thresholds of the He+ ion are analysed by quantum defect theory. For moderately excited inner electrons the series converging to different thresholds begin to overlap resulting in perturbed Rydberg series. We find that approximate quantum numbers as well as propensity rules governing the decay of the resonances and the perturbation scheme of the Rydberg series prevail. With increasing excitation of the inner electron however, only series whose states tend to extreme interelectronic angles (cos theta )=+or-1 remain regular.

Quantitative calculations of fluorescence polarization and absorption anisotropy kinetics of double- and triple-chromophore complexes with energy transfer

A new method is presented for calculation of the fluorescence depolarization and kinetics of absorption anisotropy for molecular complexes with a limited number of chromophores. The method considers absorption and emission of light by both chromophores, and also energy transfer between them, with regard to their mutual orientations. The chromophores in each individual complex are rigidly positioned. The complexes are randomly distributed and oriented in space, and there is no energy transfer between them. The new "practical" formula for absorption anisotropy and fluorescence depolarization kinetics, P(t) = [3B(t) - 1 + 2A(t)]/[3 + B(t) + 4A(t)], is derived both for double- and triple-chromophore complexes with delta-pulse excitation. The parameter B(t) is given by (a) B(t) = cos2(theta) for double-chromophore complexes, and (b) B(t) = q12(t)cos2(theta 12) + q13(t)-cos2(theta 13) + q23(t)cos2(theta 23) for triple-chromophore complexes, where q12(t) + q13(t) + q23(t) = 1. Here theta ij are the angles between the chromophore transition dipole moments in the individual molecular complex. The parameters qij(t) and A(t) are dependent on chromophore spectroscopic features and on the rates of energy transfer.

Galactic dual population models of gamma-ray bursts

We investigate in more detail the properties of two-population models for gamma-ray bursts in the galactic disk and halo. We calculate the gamma-ray burst statistical properties, mean value of (V/V(sub max)), mean value of cos Theta, and mean value of (sin(exp 2) b), as functions of the detection flux threshold for bursts coming from both Galactic disk and massive halo populations. We consider halo models inferred from the observational constraints on the large-scale Galactic structure and we compare the expected values of mean value of (V/V(sub max)), mean value of cos Theta, and mean value of (sin(exp 2) b), with those measured by Burst and Transient Source Experiment (BATSE) and other detectors. We find that the measured values are consistent with solely Galactic populations having a range of halo distributions, mixed with local disk distributions, which can account for as much as approximately 25% of the observed BATSE bursts. M31 does not contribute to these modeled bursts. We also demonstrate, contrary to recent arguments, that the size-frequency distributions of dual population models are quite consistent with the BATSE observations.

Galactic arm models of gamma-ray burst sources

Using the BATSE observations, evidence was presented recently that at least some of the gamma-ray burst sources could be in our Galactic spiral arms. Other analyses have disagreed with this conclusion, leading to an active debate as to whether this can be true. Taking a different approach, a large range of possible spiral arm spatial distributions for the gamma-ray burst sources is investigated here, and it is shown that none of these are able to simultaneously fit the current BATSE (V/V<SUB>max</SUB>), (cos theta), and (sin<SUP>2</SUP> b) observations if all the sources are in the spiral arms. If claims continue to be made that the burst sources are in the Galactic spiral arms, it will be necessary to produce an acceptable spatial distribution for the sources.

Dynamics of an integral membrane peptide: a deuterium NMR relaxation study of gramicidin

Solid state deuterium (2H) NMR inversion-recovery and Jeener-Broekaert relaxation experiments were performed on oriented multilamellar dispersions consisting of 1,2-dilauroyl-sn-glycero-3-phosphatidylcholine and 2H exchange-labeled gramicidin D, at a lipid to protein molar ratio (L/P) of 15:1, in order to study the dynamics of the channel conformation of the peptide in a liquid crystalline phase. Our dynamic model for the whole body motions of the peptide includes diffusion of the peptide around its helix axis and a wobbling diffusion around a second axis perpendicular to the local bilayer normal in a simple Maier-Saupe mean field potential. This anisotropic diffusion is characterized by the correlation times, tau R parallel and tau R perpendicular. Aligning the bilayer normal perpendicular to the magnetic field and graphing the relaxation rate, 1/T1Z, as a function of (1-S2N-2H), where S2N-2H represents the orientational order parameter, wer were able to estimate the correlation time, tau R parallel, for rotational diffusion. Although in the quadrupolar splitting, which varies as (3 cos2 theta D-1), has in general two possible solutions to theta D in the range 0 < or = theta D < or = 90 degrees, the 1/T1Z vs. (1-S2N-2H) curve can be used to determine a single value of theta D in this range. Thus, the 1/T1Z vs. (1-S2N-2H) profile can be used both to define the axial diffusion rate and to remove potential structural ambiguities in the splittings. The T1Z anisotropy permits us to solve for the two correlation times (tau R parallel = 6.8 x 10(-9) s and tau R perpendicular = 6 x 10(-6) s). The simulated parameters were corroborated by a Jeener-Broekaert experiment where the bilayer normal was parallel to the principal magnetic field. At this orientation the ratio, J2(2 omega 0)/J1(omega 0) was obtained in order to estimate the strength of the restoring potential in a model-independent fashion. This measurement yields the rms angle, <theta 2>1/2 (= 16 +/- 2 degrees at 34 degrees C), formed by the peptide helix axis and the average bilayer normal.

A simple numerical method for a modified Abel inversion in which the density can be approximated by elliptical symmetry

In electron beam or plasma diagnostics, the standard Abel inversion to obtain the corresponding densities cannot be used if the density does not have circular symmetry, that is, if it is not a symmetric radial function, F(r), of the radius in the beam cross section. We introduce a type of asymmetry not previously treated in the literature in which the density is constant on an ellipse in the beam cross section with eccentricity epsilon . From the equation for an ellipse in polar coordinates, we introduce a variable eta identical to r(1+cos2 theta epsilon 2/(1- epsilon 2)1/2 such that eta =a0 is the equation for an ellipse with semi-major axis a0. The corresponding density is represented by G( eta , epsilon ). This density can be found from the probe current I(x) by multiplying the standard Abel inversion of I(x) by the constant (1+ epsilon 2/(1- epsilon 2))1/2. To determine whether a density can be approximated by elliptical symmetry, it is necessary to use two probe measurements separated by an aperture. The aperture acts as an analyser, both to test for circular symmetry and, if not present, to analyse for elliptical symmetry as described in this paper. This technique is applied to the output of a Van de Graaff generator whose electron flux density is found to be approximated by elliptical symmetry.

Vector theory of diffraction by a single-mode fiber: application to mode-field diameter measurements

We derive a far-field diffraction integral by (vector) electromagnetic theory; the result differs from the (scalar) Rayleigh-Sommerfeld or Kirchhoff result in that it depends on polarization. For unpolarized light, we derive a factor (1 + cos(2) theta)((1/2))/ radical2 that replaces the usual obliquity factor. Omitting this factor can cause an error of the same order as the measurement uncertainty in determining the mode-field diameter of a single-mode fiber from far-field data.

Dipole and quadrupole tests of the isotropy of gamma-ray burst locations

view Abstract Citations (56) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dipole and Quadrupole Tests of the Isotropy of Gamma-Ray Burst Locations Briggs, Michael S. Abstract Dipole and quadrupole tests of the isotropy of locations on the sphere are discussed. The statistics (cos theta), the dipole moment to the Galactic center, and mean (sin-squared b - 1/3), the quadrupole moment about the Galactic plane, can be used to search for significant anisotropies in galactic coordinates. Such coordinate-system-based tests are the most powerful tests of dipole and quadrupole anisotropies in the particular coordinate system. Two statistics which have not been previously applied to gamma-ray burst data are described. The Rayleigh-Watson statistic measures the size of the dipole moment of the locations and the Bingham statistic measures the deviation of the eigenvalues of a quadrupole-like matrix from the values expected for isotropy. Tests based upon these two statistics search for dipole and quadrupole moments in spherical location data in a coordinate-system-independent, and thus model-independent, manner. They can detect an anisotropy in any direction and yield an analytic statistical significance to any detected anisotropy. The statistical tests are demonstrated herein using a variety of data sets. Publication: The Astrophysical Journal Pub Date: April 1993 DOI: 10.1086/172498 Bibcode: 1993ApJ...407..126B Keywords: Gamma Ray Astronomy; Gamma Ray Bursts; Statistical Analysis; Astronomical Models; Milky Way Galaxy; Spherical Coordinates; Space Radiation; GAMMA RAYS: BURSTS full text sources ADS |

Astigmatism, accommodation, the oblique effect and meridional amblyopia

The variation with accommodation in the dimensions of the geometrical blur ellipse that is formed on the retina of the astigmatic eye is explored in relation to orientation dependence of the corresponding line-spread function (LSF) and modulation transfer function (MTF). It is shown that if theta is the orientation of the line or grating with respect to the more powerful meridian of an eye having C dioptres of astigmatism, the optimal accommodation response varies as 0.5 C cos2 theta. The analysis is extended to include the effects of diffraction. Even at optimal focus, the diffraction-limited MTF at 45 degrees to the principal meridians of an eye with small amounts of astigmatism is substantially degraded. For example, with a 3 mm pupil and only 0.50 DC of astigmatism, the first zero in monochromatic modulation transfer at 555 nm occurs at approximately 32 c/deg in the oblique meridian as compared with 94 c/deg in the principal meridians. The results are used as the basis of a discussion of the possible role of infant and juvenile astigmatism in the development of the oblique effect and of meridional amblyopia.

Coherence properties of doughnut modes with and without a vortex

The degree of spatial coherence of a doughnut beam with a vortex along the axis is compared to that of a doughnut beam without a vortex. The first is fully coherent as expected, the second has degree of coherence mu =cos( theta 2- theta 1). These properties are verified by reconstructing a wavefront folder interferogram of the beams.

Doubly excited intershell states of two-electron atoms with large Z: exact wavefunctions and energies at N>>1

Lower 1.3S and 1.3P states of the (N,n) manifold of two-electron atoms are studied. Analytical wavefunctions of these states diagonalizing the r-112 operator at N>>1 are found. These As-N-functions provide the excellent approximations of exact wavefunctions even at small and moderate N (for lower states the overlap integral is greater than 0.999 at N=4 and n<or=10). Using As-N functions permits the specific features of the electron distribution over l to be elucidated. Variations of (cos theta ) along the series with fixed N are investigated and it is proved that the angle correlation becomes stronger as n increases. The analytical dependence of (r-112) on quantum numbers is obtained. It is shown that there exists two systems of states ( nu =1 and nu =-1), energies of each system corresponding to that of the harmonic oscillator with different zero-point energies and vibrational quanta.