Angular Alignment Research Articles

An integro-differential equation model for alignment and orientational aggregation

We study an integro-differential equation modeling angular alignment of interacting bundles of cells or filaments. A bifurcation analysis of the related stationary problem was done by Geigant and Stoll in [E. Geigant, M. Stoll, Bifurcation analysis of an orientational aggregation model, J. Math. Biol. 46 (6) (2003) 537–563]. Here we analyze the time-dependent problem and prove that the type of alignment (one- or multi-directional) depends on the initial distribution, the interaction potential, and the preferred optimal orientation of the bundles of cells or filaments. Our main technical tool is the analysis of the evolution of suitable functionals for the cell density, which allows to also specify the direction(s) where the final alignment takes place.

Adolescent patellofemoral pain: Implicating the medial patellofemoral ligament as the main pain generator

The purpose of this study is to define the clinical presentation of adolescent patellofemoral pain. A review was completed of all patients with patellofemoral pain at a children's hospital sports clinic over a 3-year period. One hundred and one patients (91 female) with 136 symptomatic knees were identified. Mean age was 14.4 years. Knee pain was localized to the anteromedial or anterior region of the knee in 96% of patients and was typically produced with running (94%), jumping (92%) and stair use (69%). On physical examination there was usually a non antalgic gait (99%), no patellofemoral crepitation (98%), normal lower extremity angular (84%) and rotational alignment (94%), with no foot malalignment (>97%). The medial patellofemoral ligament (MPFL) was the most palpably tender area of the knee in 98% of patients. During "lateral apprehension" testing, 89% had pain at the MPFL, but not true apprehension. A "J-sign" was present at terminal knee extension in 65%. Mean Q-angle was 18.7 degrees . Means of all radiographic measures were within normal ranges. The prototypical patient had anterior/anteromedial knee pain of insidious onset during running and jumping. The most consistent physical findings were focal tenderness at the MPFL, positive terminal J-sign, and an elevated Q-angle. Most patients required only nonsurgical treatments, but 18% underwent surgical interventions for persistent pain.

Quasiclassical calculation of the chemical reaction Ba+CH3I

This paper reports the quasiclassical trajectory (QCT) calculations on extended London–Eyring–Polanyi–Sato (LEPS) potential energy surface (PES) for the reaction of Ba atom with CH3I. In the calculations, the Sato parameters needed in construction of the reaction PES are obtained from simulation of experimental results of BaI product vibrational distributions. The parameters obtained are further tested by comparison of the calculated BaI vibrational distributions with another research group's experimental results at different collision energy. In addition, the reaction cross-section versus collision energy, product BaI angular distribution and alignment are obtained by QCT calculations on the PES. The possible reaction configurations are also discussed upon the calculations.

Subtraction of test mass angular noise in the LISA technology package interferometer

When the position of a test mass in one dimension is measured with picometer accuracy, angular alignment jitter inevitably couples noise into the measurement. We present recent sensitivity measurements of the LISA technology package interferometer with articulated mirrors as test masses, actuated by piezo-electric transducers. The required longitudinal displacement resolution of 9 pm\(/\sqrt{\text{Hz}}\) above 3 mHz has been demonstrated with an angular noise that corresponds to the expected for on-orbit operation. The excess noise contribution of this test mass jitter onto the sensitive displacement readout was completely subtracted by fitting the angular interferometric data streams to the longitudinal displacement measurement. Thus, this cross-coupling constitutes no limitation to the required performance of the LISA technology package interferometry.

Rotational angular momentum polarization: The influence of stray magnetic fields

We show that weak residual magnetic fields can significantly affect the preparation and measurement of molecular rotational angular momentum alignment in a typical gas-phase stereodynamics apparatus. Specifically, polarization spectroscopy, a third-order nonlinear spectroscopic technique, is used to prepare and probe the collisional and noncollisional losses of rotational angular momentum alignment of OH X (2)Pi. Residual magnetic fields of the order of the geomagnetic field are shown to have a significant effect on the prepared polarization on a submicrosecond timescale. This can be expected to be a significant effect for many gas-phase free radicals, such as those of interest in combustion, atmospheric chemistry, and the burgeoning field of cold molecules. We demonstrate a simple experimental remedy for this problem.

Speed dependent rotational angular momentum polarization of the O2 (aΔg1) fragment following ozone photolysis in the wavelength range 248–265nm

The translational anisotropy and rotational angular momentum polarization of a selection of rotational states of the O2 (a 1Deltag; v=0) photofragment formed from ozone photolysis at 248, 260, and 265 nm have been determined using the technique of resonance enhanced multiphoton ionization in combination with time of flight mass spectrometry. At 248 nm, the dissociation is well described as impulsive in nature with all rotational states exhibiting similarly large, near-limiting values for the bipolar moments describing their angular momentum alignment and orientation. At 265 nm, however, the angular momentum polarization parameters determined for consecutive odd and even rotational states exhibit clear differences. Studies at the intermediate wavelength of 260 nm strongly suggest that such a difference in the angular momentum polarization is speed dependent and this proposal is consistent with the angular momentum polarization parameters extracted and reported previously for longer photolysis wavelengths [G. Hancock et al., Phys. Chem. Chem. Phys. 5, 5386 (2003); S. J. Horrocks et al., J. Chem. Phys. 126, 044308 (2007)]. The alternation of angular momentum polarization for successive odd and even J states may be a consequence of the different mechanisms leading to the formation of the two O2 (a 1Deltag) Lambda doublets. Specifically, the involvement of out of plane parent rotational motion is proposed as the origin for the observed depolarization for the Delta- relative to the Delta+ state.

Photodissociation dynamics of OCS at 248nm: The S(D21) atomic angular momentum polarization

The dissociation of OCS has been investigated subsequent to excitation at 248nm. Speed distributions, speed dependent translational anisotropy parameters, angular momentum alignment, and orientation are reported for the channel leading to S(D21). In agreement with previous experiments, two product speed regimes have been identified, correlating with differing degrees of rotational excitation in the CO coproducts. The velocity dependence of the translational anisotropy is also shown to be in agreement with previous work. However, contrary to previous interpretations, the speed dependence is shown to primarily reflect the effects of nonaxial recoil and to be consistent with predominant excitation to the 2A′1 electronic state. It is proposed that the associated electronic transition moment is polarized in the molecular plane, at an angle greater than ∼60° to the initial linear OCS axis. The atomic angular momentum polarization data are interpreted in terms of a simple long-range interaction model to help identify likely surfaces populated during dissociation. Although the model neglects coherence between surfaces, the polarization data are shown to be consistent with the proposed dissociation mechanisms for the two product speed regimes. Large values for the low and high rank in-plane orientation parameters are reported. These are believed to be the first example of a polyatomic system where these effects are found to be of the same order of magnitude as the angular momentum alignment.

The photodissociation dynamics of OCS at 248nm: The S(PJ3) atomic angular momentum polarization

The dissociation of OCS has been investigated subsequent to excitation at 248 nm using velocity map ion imaging. Speed distributions, speed dependent translational anisotropy parameters, and the atomic angular momentum orientation and alignment are reported for the channel leading to S((3)P(J)). The speed distributions and beta parameters are in broad agreement with previous work and show behavior that is highly sensitive to the S-atom spin-orbit state. The data are shown to be consistent with the operation of at least two triplet production mechanisms. Interpretation of the angular momentum polarization data in terms of an adiabatic picture has been used to help identify a likely dissociation pathway for the majority of the S((3)P(J)) products, which strongly favors production of J=2 fragment atoms, correlated, it is proposed, with rotationally hot and vibrationally cold CO cofragments. For these fragments, optical excitation to the 2 (1)A(') surface is thought to constitute the first step, as for the singlet dissociation channel. This is followed by crossing, via a conical intersection, to the ground 1 (1)A(') state, from where intersystem crossing occurs, populating the 1 (3)A(')1 (3)A(")((3)Pi) states. The proposed mechanism provides a qualitative rationale for the observed spin-orbit populations, as well as the S((3)P(J)) quantum yield and angular momentum polarization. At least one other production mechanism, leading to a more statistical S-atom spin-orbit state distribution and rotationally cold, vibrationally hot CO cofragments, is thought to involve direct excitation to either the (3)Sigma(-) or (3)Pi states.

Focusing high energy X‐rays with stacked Fresnel zone plates

AbstractStacking technique was developed in order to increase focusing efficiency of Fresnel zone plates at high energies. Two identical Si chips each of which containing Fresnel zone plates were used for stacking. Alignment of the chips was achieved by on‐line observation of the moiré pattern from the two zone plates. The formation of moiré patterns was studied theoretically and experimentally at different experimental conditions. To provide the desired stability Si‐chips with zone plates were bonded together with slow solidification speed epoxy glue. Technique of angular alignment in order to compensate a linear displacement in the process of gluing was proposed. Two sets of stacked FZPs were produced and experimentally tested to focus 15 and 50 keV X‐rays. Gain in the efficiency by factor 2.5 was demonstrated at 15 keV. Focal spot of 1.8 μm vertically and 14 μm horizontally with 35% efficiency was measured at 50 keV. Forecast for the stacking of nanofocusing Fresnel zone plates was discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Correlation between atomic orientation and product angular momentum alignment in the reaction of oriented Ar (P23) with CH3OH

Atomic orientation effect for the CH(3)O(*) formation has been studied for the dissociative energy transfer reaction of oriented Ar ((3)P(2)) with CH(3)OH. The degree of polarization of CH(3)O(*) chemiluminescence was determined as a function of each magnetic M(J) (') substate in the collision frame. A drastic change of the product angular momentum alignment due to atomic orientation was recognized.

Formaldehyde photodissociation: Dependence on total angular momentum and rotational alignment of the CO product

Quasiclassical trajectory calculations are reported to investigate the effects of rotational excitation of formaldehyde on the branching ratios of the fragmentation products, H2+CO and H+HCO. The results of tens of thousands of trajectories show that increased rotational excitation causes suppression of the radical channel and enhancement of the molecular channel. Decomposing the molecular channel into "direct" and "roaming" channels shows that increased rotation switches from suppressing to enhancing the roaming products across our chosen energy range. However, decomposition into these pathways is difficult because the difference between them does not appear to have a distinct boundary. A vector correlation investigation of the CO rotation shows different characteristics in the roaming versus direct channels and this difference is a potentially useful signature of the roaming mechanism, as first speculated by Kable and Houston in their experimental study of photodissociation of acetaldehyde [P. L. Houston and S. H. Kable, Proc. Nat. Acad. Sci. 103, 16079 (2006)].

Optical mosaic gratings made by consecutive, phase-interlocked, holographic exposures using diffraction from latent fringes

We propose and demonstrate a method for fabricating large optical mosaic gratings, i.e., gratings made by consecutive, phase-interlocked, holographic exposures on single substrates. It takes advantage of the latent fringes generated by the preceding exposure to align the substrate for the following exposure. Good angular alignment accuracy and period consistency between the fringes recorded by consecutive exposures can be achieved by using the large-area moiré pattern produced by the latent fringes and the alignment beams. Phase-interlocking accuracy of less than 4 degrees between consecutive exposures was experimentally achieved by using the heterodyne detection technique.

Collective bands in 80,82Kr

Deformed shell-model calculations are performed to study the structure of the collective bands in 80,82Kr. In our microscopic model, the single particle orbits 1p3/2, 0f5/2, 1p1/2, and 0g9/2 constitute the configuration space with 56Ni as the inert core. A modified Kuo interaction for this basis space is used in our calculation. The different levels are classified into collective bands on the basis of the B(E2) values among them. The calculated ground bands and quasi-gamma bands for both the nuclei agree reasonably well with experiment. The negative parity bands are also well-reproduced in our calculation. The calculated B(E2) values are compared with available experimental data. The nature of angular momentum alignment in the ground band is also discussed. PACS Nos.: 21.10.–k, 21.60.Jz, 27.50.+e

A general expression for the excitation cross-section of polarized atoms by polarized electrons

The general expression for the excitation cross-section of polarized atoms by polarized electrons is derived by using the methods of the theory of an atom adapted for polarization. The special cases of the general expression for the description of the angular distribution and alignment of excited atoms in the case of polarized and non-polarized atoms as well as the magnetic dichroism of the total excitation cross-section of polarized atoms are obtained. The cross-sections and alignment parameters for the excitation of the autoionizing states 2p53s22P3/2 for Na and 3p54s2 P3/2 for K are calculated in distorted wave (DW) with exchange approximation.

Differential scattering cross-sections for CNA2Π+Ar

We present the first results from a novel experimental approach to the measurement of state-to-state differential scattering cross-sections for inelastic scattering of electronically excited CN A(2)Pi with Ar. Photodissociation of ICN with linearly polarized 266 nm radiation generates CN X(2)Sigma(+) (upsilon(")=0,J(")) with a near mono-energetic speed distribution and large anisotropy. Saturated optical pumping of the nascent CN X(2)Sigma(+) transfers this speed distribution without distortion to selected rotational quantum states of the A(2)Pi (upsilon(')=4) level. The products of rotational energy transfer within the A(2)Pi (upsilon(')=4) level into the J(')=0.5, F(2), f, state are probed using frequency modulated stimulated emission spectroscopy on the A-X (4,2) band with a single frequency external cavity tunable diode laser. Doppler profiles of transitions from individual rotational, spin-orbit and lambda doublet specific levels are acquired for different geometrical arrangements of photolysis polarization and probe propagation directions. The resulting Doppler profiles, which for this J(')=0.5 state cannot display a rotational angular momentum alignment, are combined to yield composite Doppler profiles depending on speed and translational anisotropy, which are analyzed to determine fully state-to-state resolved differential scattering cross-sections.

Inelastic scattering of OH(X 2Π) with Ar and He: a combined polarization spectroscopy and quantum scattering study

One-colour polarization spectroscopy (PS) on the OH A (2)Sigma(+)- X (2)Pi(0,0) band has been used to measure the removal of bulk rotational angular momentum alignment of ground-state OH(X (2)Pi) in collisions with He and Ar. Pseudo-first-order PS signal decays at different collider partial pressures were used to determine second-order decay rate constants for the X (2)Pi(3/2), J = 1.5-6.5, e states. The PS signal decay rate constant, k(PS), is sensitive to all processes that remove population and destroy polarization. The contribution to k(PS) from pure (elastic) alignment depolarization within the initial level, k(DEP), can be extracted by subtracting the independently measured or predicted sum of the rate constants for total rotational energy transfer (RET), k(RET), and for Lambda-doublet changing, k(Lambda), collisions from k(PS). Literature values of k(RET) and k(Lambda) are available from experiments with He and Ar, and from quantum scattering calculations for Ar only. We therefore also present the results of new, exact, fully quantum mechanical calculations of k(RET) and k(Lambda) on the most recent ab initio OH(X)-He potential energy surface of Lee et al. [J. Chem. Phys. 2000, 113, 5736]. The results for k(DEP) from this subtraction for He are found to be modest, around 0.4 x 10(-10) cm(3) s(-1), whereas for Ar k(DEP) is found to range between 0.6 +/- 0.2 x 10(-10) cm(3) s(-1) and 1.7 +/- 0.3 x 10(-10) cm(3) s(-1), comparable to total population removal rate constants. The differences between k(DEP) for the two colliders are most likely explained by the presence of a substantially deeper attractive well for Ar than for He. The measurement of k(DEP) may provide a useful new tool that is more sensitive to the form of the long-range part of the intermolecular potential than rotational state-changing collisions.

Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides

We discuss, by a finite-difference time-domain method, a photonic crystal structure with two adjacent parallel line-defect waveguides to provoke highly-efficient directional emission of terahertz waves. The output field is analogous to a two-point-source interference pattern. Numerical simulations show that the maximum directional emission efficiency is up to 75%. Moreover, the efficiency is insensitive to transverse alignment error and angular alignment error. This structure is potentially important for high-efficiency coupling between freely propagated terahertz waves and Si waveguide systems.

Surface-mount sapphire interferometric temperature sensor

A fiber-optic high-temperature sensor is demonstrated by bonding a 45 degrees -polished single-crystal sapphire fiber on the surface of a sapphire wafer, whose optical thickness is temperature dependent and measured by white-light interferometry. A novel adhesive-free coupling between the silica and sapphire fibers is achieved by fusion splicing, and its performance is characterized. The sensor's interference signal is investigated for its dependence on angular alignment between the fiber and the wafer. A prototype sensor is tested to 1,170 degrees C with a resolution of 0.4 degrees C, demonstrating excellent potential for high-temperature measurement.

Impact of extension implant energy purity and angle on the electrical characteristics of a 65nm device technology

We show that a significant fraction of the overlap in advanced logic technologies originates in the as-implanted dopant profile. As a consequence, small changes in the as-implanted profile have a large impact on device characteristics. We have developed a virtual, high-performance, planar, bulk, 65nm technology that we use as a platform to investigate the impact of imperfections in the extension implant stemming from (1) contamination of the beam with higher energy ions and (2) angular alignment of the incident ion beam to the wafer. We find that a deceleration ratio of 7 and an energy contamination equal to 1% of the total dose double the off current. Small (of the order 1°) beam steering of the incident beam as seen by the wafer leads to large changes in on current (of the order of 20%) and speed. Steering that results in shadowing of the source has a far larger impact than drain-side shadowing. This can be alleviated significantly by a quad implant, provided the tilt angle is sufficiently large, on the order >5°. A quad implant twisted by 45° allows essentially complete recovery of the nominal device characteristics, even where beam steering leads to source-side shadowing.

Simple Model Calculations of Spin and Quantized Alignment for the <i≯A</i≯ ∼ 60–90 Superdeformed Mass Region

We have used a simple model based on the rotational energy formula E(I, K) to study the structure of the superdeformed (SD) mass region 60–90. The higher order inertial parameters A and B of such model were determined by using the Marquardt method of nonlinear least-squares routines to fit the proposed transition energies with their observed values. A good agreement between the calculated and corresponding experimental transition energies of the SD bands is obtained which supports our proposed model. In addition, the frequency dependence of the dynamic, θ(2), and static, θ(1), moments of inertia is used to determine the lowest spin (If) and the K-value of the considered SD bands; namely, 58Ni(b1), 58Cu, 59Cu(b1), 61Zn, 62Zn, 65Zn, 68Zn, 84Zr, 86Zr(b1), 88Mo(b1, b2, b3) and 89Tc. As a result of the identity exist among some of the considered SD bands, we have studied the incremental alignment and also the angular momentum alignment.