Triangle Configuration Research Articles

Statistical Properties of Fluctuation of Charged Fine Particles in an AC Trap

We have investigated the behavior of a small number of charged fine particles under Coulomb interactions in an AC trap. There is a transition from ballistic to diffusive motion in the mean square displacement of the angle, θ, for a single charged fine particle described by a nonlinear dissipative Mathieu equation. Stable forced oscillations with an angular frequency Ω exist for the displacement vector of two charged fine particles described by a coupled Mathieu-Coulomb equation. Displacement vector motion becomes chaotic, depending on the control parameters in a coupled Mathieu-Coulomb equation. Stable solutions with a triangular configuration, and which oscillate with an angular frequency Ω, exist for three particles. An irregular replacement of particles in the triangle configuration occurs, depending on the control parameters in a coupled Mathieu-Coulomb equation.

The effects of contact configurations on the rectification of dipyrimidinyl—diphenyl diblock molecular junctions

The transport properties of a conjugated dipyrimidinyl—diphenyl diblock oligomer sandwiched between two gold electrodes, as recently reported by [Díez-Pérez et al. Nature Chem. 1 635 (2009)], are theoretically investigated using the fully self-consistent nonequilibrium Green's function method combined with density functional theory. Two kinds of symmetrical anchoring geometries are considered. Calculated current—voltage curves show that the contact structure has a strong effect on the rectification behaviour of the molecular diode. For the equilateral triangle configuration, pronounced rectification behaviour comparable to the experimental measurement is revealed, and the theoretical analysis indicates that the observed rectification characteristic results from the asymmetric shift of the perturbed molecular energy levels under bias voltage. While for the tetrahedron configuration, both rectification and negative differential conductivity behaviours are observed. The calculated results further prove the close dependence of the transporting characteristics of molecular junctions on contact configuration.

Lens phacoemulsification in treatment primary angle closure glaucoma with block induced lens after laser peripheral iridotomy

AbstractPurpose To investigate the features of iridocilliary zone in patients with primary angle closure glaucoma (PACG) in cases of anterior chamber angle (ACA) block induced by lens after laser iridotomy and subsequent lens phacoemulsification with foldable IOL implantation.Methods 45 patients (54 eyes) with PACG have been selected for this investigation. Parameters of iridocilliary structures were measured using ultrasound biomicroscopy (UBM) model «Humphrey‐840».Results UBM allowed to determine the features of block induced by lens at PACG. In these cases there was the displacement of lens‐iris diaphragm forward independent of lens thickness with ACA block. The iris had a convex profile. The posterior chamber lost correct triangle configuration with decrease in section area by 1.3 times as compared to the norm. Most cases had a short‐term hypotensive effect after laser iridotomy with only segmental opening of ACA. The extreme anterior position of the lens‐iris diaphragm and small posterior chamber area persist at all cases. Configuration of the iris saved its convex. Subsequent phacoemulsiaicftion with foldable IOL implantation decreased the intraocular pressure (IOP) and eliminated block induced by lens with opening of the ACA. The restore of iris profile and posterior chamber configuration have been observed in all cases.Conclusion Laser iridotomy creates optimal conditions for lens phacoemulsiaicftion by removing angular block and decreasing IOP from preoperative level. Phacoemulsiaicftion is pathogenic operation in cases of PACG with ACA block induced by lens.

Fast Computation of Bispectrum Features with Generalized Slow Roll

We develop a fast technique based on the generalized slow roll (GSR) approach for computing the curvature bispectrum of inflationary models with features. We show that all triangle configurations can be expressed in terms of three simple integrals over the inflationary background with typical accuracy of better than ~20%. With a first order GSR approach the typical accuracy can be improved to better than the 5% level. We illustrate this technique with the step potential model that has been invoked to explain the WMAP temperature power spectrum glitches at ell ~ 20-40 and show that the maximum likelihood model falls short of observability by more than a factor of 100 in amplitude. We also explicitly demonstrate that the bispectrum consistency relation with the local slope of the power spectrum is satisfied for these models. In the GSR approach, the bispectrum arises from integrals of nearly the same function of the background slow-roll parameters as the power spectrum but with a stronger weight to the epoch before horizon crossing. Hence this technique enables reverse engineering of models with large bispectrum but small power spectrum features.

Recommendations for grounding systems in lightning protection systems

This paper presents some practical recommendations for designing grounding systems as part of an integral protection system against lightning strikes. These recommendations are made taking into account the results of academic software whose development was based on hybrid electromagnetic method and the method of moments. This paper presents the results of impedance and transient voltage for triangle, wye, counterpoises and mesh configurations. Some recommendation are made concerning the use and characteristics of earth electrodes, for example effective counterpoise length, where to locate grounding rods, where to connect down conductors in a mesh and the potential difference between points on the same grounding electrodes. These recommendations guide a systems' designer to ensure greater benefit from grounding setups without wasting money.

Lagrange solution for three wavelength solitary wave clusters in nematic liquid crystals

We investigate the interaction of three optical solitary waves propagating with angular momentum in bulk nematic liquid crystals. The resulting cluster of solitary waves, or nematicons, is shown to orbit about its common centre of “mass”. An elongated isosceles triangle configuration is derived, this solution being the equivalent of the Lagrange solution of Newtonian gravitation. This triangle solution is found to be stable owing to diffractive radiation. A modulation theory explains the existence of the triangle solution as due to the non-monotonicity of an effective potential for the interaction of the solitary waves. This modulation theory also gives good agreement with numerical solutions for the trajectories of the nematicons in the three colours. Finally, it is shown that a cut-off in the shed diffractive radiation prevents the break-up of the triangle due to radiative losses.

Fly-ear inspired micro-sensor for sound source localization in two dimensions

Inspired by the hearing organ of the fly Ormia ochracea, a miniature sound localization sensor is developed, which can be used to pinpoint a sound source in two dimensions described by the azimuth and elevation angles. The sensor device employs an equilateral triangle configuration consisting of three mechanically coupled circular membranes whose oscillations are detected by a fiber-optic system. The experimental results indicate that significant amplification of the directional cues and directional sensitivity can be achieved with the fly-ear inspired sensor design. This work can provide a basis for the development of miniature sound localization sensors in two dimensions.

LENGTH OF INFLATION AND NON-GAUSSIANITY

Certain inflation models are shown to have large non-Gaussianity in special cases. Namely, slow-roll inflation models with an effective higher derivative interaction, in which the length of inflation is finite and a scalar-matter-dominated period or power inflation is adopted as pre-inflation, are considered. Using Holman and Tolley's formula of the nonlinearity parameter in the flattened triangle configurations [Formula: see text], we calculate the value of [Formula: see text]. The value of [Formula: see text] is found to be largest [Formula: see text] when the inflation length is approximately 60 e-folds, and [Formula: see text] is found to depend strongly on the length of inflation and the cut-off scale.

A Biomechanical Comparison of Two Triple-Screw Methods for Femoral Neck Fracture Fixation in a Synthetic Bone Model

Fixation of femoral neck fractures is often accomplished by several screws inserted along the neck axis. Alignment and number of screws remain at the discretion of the surgeon. Two fracture repair methods were compared. Sixteen large, left, adult, synthetic femurs, known as Third Generation Composite Femurs (Pacific Research Laboratories, Vashon, WA), were osteotomized with a transverse cut perpendicular to the neck axis. Fractures were reduced and repaired using method 1 (n = 8) or method 2 (n = 8) cannulated cancellous screw methods. Method 1 screws were inserted parallel in an upside-down triangle configuration and abutted against the cortical walls inferiorly, anteriorly, and posteriorly. Method 2 screws were placed adjacent to one another as often done clinically. Femoral shafts were positioned in a nonclinical vertical orientation to obtain conservative "lower bound" measurements. Specimens were tested for torsional and axial stiffness using subclinical loads followed by axial failure tests. Method 1 showed statistically higher values compared with method 2 for torsional stiffness (9.9 vs. 7.9 Nm/deg, method 1/method 2 ratio = 1.25, p = 0.018), axial stiffness (1469.0 vs. 1278.1 N/mm, method 1/method 2 ratio = 1.15, p = 0.023), and axial failure load (3493.5 vs. 2863.5 N, method 1/method 2 ratio = 1.22, p = 0.000). However, there were no statistical differences in axial failure displacement (10.9 vs. 16.9 mm, method 1/method 2 ratio = 0.64, p = 0.101) or axial failure energy (29.9 vs. 35.9 J, method 1/method 2 ratio = 0.83, p = 0.453). For both methods, femoral heads move distally while screw shafts cut through the spongy cancellous matrix of the femoral neck in knife-like fashion. Method 1 was more mechanically stable than method 2 in femoral neck fracture fixation as detected by three of five biomechanical measurements and equivalent to method 2 for two of five biomechanical measurements.

Effect of integrity of the posterior cortex in displaced femoral neck fractures on outcome after surgical fixation in young adults

Aim To assess whether disruption of the posterior cortex of intracapsular femoral fractures leads to an increased incidence of complications following closed reduction and internal fixation by multiple cannulated screws in young adults. Methods A total of 146 consecutive adult patients with 146 femoral neck fractures were treated by closed reduction and internal fixation with parallel cannulated screw in inverted triangle or diamond configurations. All enrolled patients were divided into three groups: those with a non-displaced femoral neck fracture (Garden types I or II), those with a displaced femoral neck fracture (Garden types III or IV) but no posterior cortex disruption and those with a displaced femoral neck fracture (Garden types III or IV) and a disrupted posterior cortex. Results Based on an average follow-up of 4.76 years (range, 2–6 years), displaced femoral neck fractures with a disrupted posterior cortex demonstrated an increased risk for avascular necrosis of the femoral head, shortening, redisplacement and conversion of prosthetic replacement as compared with those fractures without posterior cortex disruption ( p = 0.002, 0.016, 0.001 and <0.0001, respectively). Conclusions As compared with a femoral neck fracture with an intact posterior cortex, a displaced femoral neck fracture with a disrupted posterior cortex increases the risk for avascular necrosis, redisplacement and shortening and raises the likelihood that prosthetic replacement will be needed. Orthopaedic surgeons should be aware of this prognostic factor.

Atomic and Electronic Structures of a Fullerene Molecule on a Ag/Si(111)\(\sqrt{3}{\times}\sqrt{3}\) Surface

We present first-principles total-energy calculations of a single fullerene (C 60 ) molecule on a Ag-terminated Si(111)\(\sqrt{3}{\times}\sqrt{3}\) surface (\(\sqrt{3}\)-Ag), which can provide a deep understanding to the interesting atomic and electronic structures of C 60 overlayers on \(\sqrt{3}\)-Ag. C 60 stably occupies the centers of the substrate triangles, and the on-top sites above Si and Ag atoms. In the most stable adsorption configuration with an adsorption energy of 0.87 eV, C 60 occupies a large Ag triangle site with a hexagon of C 60 facing the substrate. On a Si triangle site, unlike on the large Ag triangle site, a C–C bond that is shared by two adjacent hexagons takes the bottom position. Simulated scanning-tunneling microscopy (STM) images distinguish between the large Ag triangle and Si triangle configurations and are consistent with low-temperature STM observations [K. Tsuchie et al. : Phys. Rev. B 60 (1999) 11131]. Investigation of the energy band of the lowest-energy configuration re...

Reinforcement of inhibitory positional priming by spatial working memory contents

This study examined whether positional priming of pop-out is modulated by spatial working memory (WM). In Experiments 1A and 1B, observers were presented with a to-be-memorized item (Experiment 1A: triangle; Experiment 1B: circle) prior to performing a block of search trials, with triangular stimulus configurations (one target, two distractors) on an underlying elliptical frame. Each search block was followed by a memory test (i.e., memory conditions). In Experiment 1C, the presentation of the memory item (triangle) was immediately followed by the memory test, and the search block was performed after this test (i.e., no-memory condition). It was found that targets presented at a previous target were detected faster and targets presented at a previous distractor location slower, relative to a previous empty (‘neutral’) stimulus location, respectively. While facilitatory position priming was uninfluenced by the memory manipulation, inhibitory positional priming was larger in the memory than no-memory condition, but only when the memory stimulus (triangle) matched the (triangle) configuration formed by the three search items. This finding of larger inhibitory priming under memory conditions provides further evidence that positional priming, rather than being purely bottom-up determined, is open to top-down influences.

Explicit Dipole Trajectory Solution for Electromagnetically Controlled Spacecraft Clusters

Satellite formation flight is a much-anticipated technology for future space-science missions, such as high-resolution space-based telescopes. A potentially enabling technology under development allows clusters of spacecraft to maneuver without the use of propellant, instead using electromagnetic control of the relative degrees of freedom within the cluster. This electromagnetic formation-flight technology offers potentially limitless mission life, in exchange for a highly coupled, nonlinear control problem. Several methods have been explored to address this problem, and some have achieved considerable success at its optimal, or at least locally optimal, solution. This paper does not produce optimal trajectories for unconstrained maneuvers, but instead provides a method for determining all of the feasible control solutions that will produce a specified maneuver. An example is provided for the case of three spacecraft rotating in a planar, equilateral triangle configuration, while the plane of rotation is simultaneously changing direction, as might be encountered while retargeting a separated spacecraft interferometer. The approach may be used on its own to find feasible, albeit suboptimal, solutions, or in conjunction with an optimal-control solution, to probe its optimality, find alternative solutions, or plan for contingencies. The current research deals solely with free-space translational solutions, without consideration of torques that are developed or the resulting buildup or removal of angular momentum. Extension of the current approach to address these issues is the subject of a follow-on paper.

OPTIMAL CAPTURE OF NON-GAUSSIANITY IN WEAK-LENSING SURVEYS: POWER SPECTRUM, BISPECTRUM, AND HALO COUNTS

We compare the efficiency of weak lensing-selected galaxy clusters counts and of the weak lensing bispectrum at capturing non-Gaussian features in the dark matter distribution. We use the halo model to compute the weak lensing power spectrum, the bispectrum and the expected number of detected clusters, and derive constraints on cosmological parameters for a large, low systematic weak lensing survey, by focusing on the $\Omega_m$-$\sigma_8$ plane and on the dark energy equation of state. We separate the power spectrum into the resolved and the unresolved parts of the data, the resolved part being defined as detected clusters, and the unresolved part as the rest of the field. We consider four kinds of clusters counts, taking into account different amount of information : signal-to-noise ratio peak counts; counts as a function of clusters' mass; counts as a function of clusters' redshift; and counts as a function of clusters' mass and redshift. We show that when combined with the power spectrum, those four kinds of counts provide similar constraints, thus allowing one to perform the most direct counts, signal-to-noise peaks counts, and get percent level constraints on cosmological parameters. We show that the weak lensing bispectrum gives constraints comparable to those given by the power spectrum and captures non-Gaussian features as well as clusters counts, its combination with the power spectrum giving errors on cosmological parameters that are similar to, if not marginally smaller than, those obtained when combining the power spectrum with cluster counts. We finally note that in order to reach its potential, the weak lensing bispectrum must be computed using all triangle configurations, as equilateral triangles alone do not provide useful information.

Correction to “Three‐dimensional nonlinear evolution of equatorial ionospheric bubbles with gravity wave seeding and tidal wind effects”

[1] In the paper ‘‘Three-dimensional nonlinear evolution of equatorial ionospheric bubbles with gravity wave seeding and tidal wind effects’’ by M. J. Keskinen and Sharon L. Vadas (Geophysical Research Letters, 36, L12102, doi:10.1029/2009GL037892), Keskinen and Vadas [2009, hereafter KV09] presented the three-dimensional nonlinear evolution of equatorial ionospheric bubbles using a realistic lower atmospheric gravity wave (GW) source. There are a number of misrepresentations and errors by KV09 in regards to the presentation and discussion of the GW source function that was used in the plasma model. The figures and discussion of KV09 refer to a different GW specification, despite the fact that the correct GW specification was used in the plasma model, results of which are presented in Figure 4 of KV09. As a result, the model data shown in Figures 1, 2, and 3 of KV09 were not used to seed the 3D plasma model described by KV09. Correct Figures 1–3 are supplied in this erratum. Additionally, part of paragraph 8 and all of paragraphs 9, 10, and 11 of KV09 should be disregarded and replaced with the text below. [2] The dispersion relation discussed in the latter portion of paragraph 8 in KV09 was not the GW dispersion relation, but was rather the full complex dispersion relation derived from the compressible fluid equations by Vadas and Fritts [2005, hereafter VF2005]. Due to formula errors in KV09, readers interested in the compressible dispersion relation should refer directly to VF2005. The last half of paragraph 8 in VF09 should be replaced by the following: For anelastic GWs with horizontal phase speeds much less than the speed of sound, the GW dispersion relation is given by equation (26) from VF2005 or by equation (47) from Vadas and Fritts [2009, hereafter VF2009]. [3] Vadas and Liu [2009, Figure 1] shows a GOES-12 satellite image on 01 October, 2005, at 21:22 UT, in Brazil. For the KV09 study, we simulated the GWs excited by the energetic convective cluster at 59.0 W and 13.5 S. This cluster contained several tightly-clumped convective plumes, each having an approximate full-width horizontal diameter of 20 km and updraft velocities of 40 m/s. We defined a convective cluster to be composed of 3 convective plumes in an equilateral triangle configuration, with a separation of 50 km between the plume centers (VF2009). Figure 1 shows the GW spectrum excited by this cluster. Figure 1 replaces KV09’s Figure 1. This cluster excites GWs with horizontal wavelengths of lH > 100 km and vertical wavelengths of lz > 50 km, which are capable of penetrating well into the thermosphere prior to dissipating [Vadas, 2007; Fritts and Vadas, 2008]. [4] The ray trace model we used was described by VF2009. The hyperbolic tanh zonal wind and temperature models shown in Figure 2 of KV09 were not used in either the ray trace or plasma models. Instead, the wind and temperature models we used were determined mainly from the Thermosphere-Ionosphere-Mesosphere-Electrodynamics General Circulation Model. Vadas et al. [2009] describe the background wind and temperature models used. Because they include semidiurnal and diurnal tides, both zonal and meridional background wind components were present. [5] The GWs whose spectrum is plotted in Figure 1 were located at 59.0 Wand 13.5 S at an altitude of z = 13.6 km at 21:22 UT. Those GWs were then ray traced into the middle and upper atmosphere through the spatially and temporallyvarying background winds and temperatures. We then reconstructed the GW wind, temperature, and density perturbations as a function of (x, y, z, t) using the method described by VF2009. We extracted the vertical profiles (cuts) of this solution at 10 different locations and times. These profiles were inputted into the 3D plasma model

Bispectrum covariance in the flat-sky limit

<i>Aims. <i/>To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to rely upon an accurate theoretical background concerning the bispectrum and its noise properties. If only small portions of the sky are considered, it is often desirable to perform the analysis in the flat-sky limit. We aim at a formal, detailed derivation of the bispectrum covariance in the flat-sky approximation, focusing on a pure two-dimensional Fourier-plane approach.<i>Methods. <i/>We define an unbiased estimator of the bispectrum, which takes the average over the overlap of annuli in Fourier space, and compute its full covariance. The outcome of our formalism is compared to the flat-sky spherical harmonic approximation in terms of the covariance, the behavior under parity transformations, and the information content. We introduce a geometrical interpretation of the averaging process in the estimator, thus providing an intuitive understanding.<i>Results. <i/>Contrary to foregoing work, we find a difference by a factor of two between the covariances of the Fourier-plane and the spherical harmonic approach. We argue that this discrepancy can be explained by the differing behavior with respect to parity. However, in an exemplary analysis it is demonstrated that the Fisher information of both formalisms agrees to high accuracy. Via the geometrical interpretation we are able to link the normalization in the bispectrum estimator to the area enclosed by the triangle configuration at consideration as well as to the Wigner symbol, which leads to convenient approximation formulae for the covariances of both approaches.

CMB temperature bispectrum induced by cosmic strings

The cosmic microwave background (CMB) bispectrum of the temperature anisotropies induced by a network of cosmic strings is derived for small angular scales, under the assumption that the principal cause of temperature fluctuations is the Gott-Kaiser-Stebbins effect. We provide analytical expressions for all isosceles triangle configurations in Fourier space. Their overall amplitude is amplified as the inverse cube of the angle and diverges for flat triangles. The isosceles configurations generically lead to a negative bispectrum with a power-law decay ${\ensuremath{\ell}}^{\ensuremath{-}6}$ for large multipole $\ensuremath{\ell}$. However, collapsed triangles are found to be associated with a positive bispectrum whereas the squeezed triangles still exhibit negative values. We then compare our analytical estimates to a direct computation of the bispectrum from a set of 300 statistically independent temperature maps obtained from Nambu-Goto cosmic string simulations in a Friedmann-Lema\^{\i}tre-Robertson-Walker universe. We find good agreement for the overall amplitude, the power-law behavior, and the angle dependency of the various triangle configurations. At $\ensuremath{\ell}\ensuremath{\sim}500$ the cosmic string Gott-Kaiser-Stebbins effect contributes approximately the same equilateral CMB bispectrum amplitude as an inflationary model with $|{f}_{\mathrm{NL}}^{\mathrm{loc}}|\ensuremath{\simeq}{10}^{3}$, if the strings contribute about 10% of the temperature power spectrum at $\ensuremath{\ell}=10$. Current bounds on ${f}_{\mathrm{NL}}$ are not derived using cosmic string bispectrum templates, and so our ${f}_{\mathrm{NL}}$ estimate cannot be used to derive bounds on strings. However it does suggest that string bispectrum templates should be included in the search of CMB non-Gaussianities.

Classification of four-body central configurations with three equal masses

It is known that a central configuration of the planar four body problem consisting of three particles of equal mass possesses a symmetry if the configuration is convex or is concave with the unequal mass in the interior. We use analytic methods to show that besides the family of equilateral triangle configurations, there are exactly one family of concave and one family of convex central configurations, which completely classifies such central configurations.

Stability of relative equilibria of three vortices

Three point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably more involved. The only comprehensive analysis available in the literature, by Tavantzis and Ting [Phys. Fluids 31, 1392 (1988)], is not easy to follow nor is it very physically intuitive. The symmetry between the three vortices is lost in this analysis. A different analysis is given based on explicit formulas for the three eigenvalues determining the stability, including a new formula for the angular velocity of rotation of a collinear relative equilibrium. A graphical representation of the space of vortex circulations is introduced, and the resultants between various polynomials that enter the problem are used. This approach adds considerable transparency to the solution of the stability problem and provides more physical understanding. The main results are summarized in a diagram that gives both the stability and instability of the various collinear relative equilibria and their sense of rotation.

Full-configuration-interaction calculation of three-body nonadditive contribution to helium interaction potential

The three-body nonadditive interaction energy between helium atoms was calculated at 253 trimer configurations using the full-configuration-interaction (FCI) method. The analytic potential fitted to these energies is the best current representation of the three-body nonadditive interactions between helium atoms. At the equilateral triangle configuration with R=5.6 bohr, near the minimum of the total potential, the nonadditive three-body energy calculated at the FCI level amounts to -88.5 mK, compared to -98.5 mK at the coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] level. The uncertainty of the former result resulting from basis set incompleteness is estimated to be 1.5 mK. The relative uncertainty of our present complete three-body fit, including the uncertainties resulting from the fitting procedure, is estimated at 2%, a fivefold improvement over the previous best potential. Overall, the FCI contribution beyond CCSD(T) is rather important, being of the same order of magnitude as the uncertainty of the sum of two-body interactions. The inclusion of this contribution makes uncertainties of the total trimer interaction energies dominated by the uncertainties of the two-body component.