Partial Rotations Research Articles

Selective Optical Control of Electron Spin Coherence in Singly ChargedGaAs−Al0.3Ga0.7AsQuantum Dots

Coherent transient excitation of the spin ground states in singly charged quantum dots creates optically coupled and decoupled states of the electron spin. We demonstrate selective excitation from the spin ground states to the trion state through phase sensitive control of the spin coherence via these three states, leading to partial rotations of the spin vector. This progress lays the ground work for achieving complete ultrafast spin rotations.

Play fighting in androgen-insensitivetfm rats: Evidence that androgen receptors are necessary for the development of adult playful attack and defense

The frequency of playful attack and the style of playful defense, are modifiable by gonadal steroids and change after puberty in male and female rats. The present study examined the play behavior exhibited by testicular feminized mutation (tfm)-affected males, who are insensitive to androgens but can bind estrogens aromatized from androgens, to determine the relative contributions of androgens and estrogens to the age-related changes in play behavior. tfm males did not exhibit a decrease in playful attack with age and were more likely to maintain the use of complete rotations, a juvenile form of playful defense, into adulthood. tfm males did however, show age related changes in the use of partial rotations and upright postures, two other forms of playful defense, that were similar to normal males. These data suggest that the development of play fighting and defense in males is dependent on both androgen- and estrogen-receptor-mediated effects.

X-ray volumetric imaging in image-guided radiotherapy: The new standard in on-treatment imaging

X-ray volumetric imaging (XVI) for the first time allows for the on-treatment acquisition of three-dimensional (3D) kV cone beam computed tomography (CT) images. Clinical imaging using the Synergy System (Elekta, Crawley, UK) commenced in July 2003. This study evaluated image quality and dose delivered and assessed clinical utility for treatment verification at a range of anatomic sites. Single XVIs were acquired from 30 patients undergoing radiotherapy for tumors at 10 different anatomic sites. Patients were imaged in their setup position. Radiation doses received were measured using TLDs on the skin surface. The utility of XVI in verifying target volume coverage was qualitatively assessed by experienced clinicians. X-ray volumetric imaging acquisition was completed in the treatment position at all anatomic sites. At sites where a full gantry rotation was not possible, XVIs were reconstructed from projection images acquired from partial rotations. Soft-tissue definition of organ boundaries allowed direct assessment of 3D target volume coverage at all sites. Individual image quality depended on both imaging parameters and patient characteristics. Radiation dose ranged from 0.003 Gy in the head to 0.03 Gy in the pelvis. On-treatment XVI provided 3D verification images with soft-tissue definition at all anatomic sites at acceptably low radiation doses. This technology sets a new standard in treatment verification and will facilitate novel adaptive radiotherapy techniques.

Surface anisotropy in nanomagnets: transverse or Néel?

Through the hysteresis loop and magnetization spatial distribution we study and compare two models for surface anisotropy in nanomagnets: a model with transverse anisotropy axes and Néel's model. While surface anisotropy in the transverse model induces several jumps in the hysteresis loop because of the cluster-wise switching of spins, in the Néel model the jumps correspond to successive coherent partial rotations of the whole bunch of spins. These calculations together with some hints from available experimental results, suggest that Néel's model for surface anisotropy is more appropriate.

Generalised transform factorisation for massive parallelism

A formalism and an algorithm for configuring and sequencing parallel to massively parallel processors for the application of generalised spectral analysis transforms are presented. Successive partial rotations of a base-p hypercube, where p is an arbitrary integer, are shown to produce dynamic contention-free memory allocation, in a generalised parallelism processor architecture. The approach is illustrated by factorisations involving the processing of matrices of transforms which are functions of four variables. Parallel operations are implemented as matrix multiplications. Each matrix, of dimension N /spl times/ N, where N = p/sup n/, n integer, has a structure that depends on a variable parameter k. The level of parallelism, in the form of M = p/sup m/ processors, can be chosen arbitrarily by varying m between zero and its maximum value of n - 1. The result is an equation describing the generalised parallelism factorisation as a function of the four variables n, p, k and m. Applications of the approach are shown in relation to complex matrix structures of image processing generalised spectral analysis transforms. The same approach can be applied to a much larger class of parallel and multiprocessing systems for digital signal processing applications.

Rotationally invariant and rotationally robust codes for the AWGN and the noncoherent channel

The paper investigates the design and robustness of rotationally invariant (RI) codes. First, RI codes are extended to the case of serially concatenated (SC) trellis-coded modulation (TCM) and several high-rate powerful RI-SCTCM codes are designed over 8-phase-shift keying and 16-quadrature amplitude modulation alphabets. The investigation continues by considering more realistic channels that introduce cycle slips during phase estimation, and thus rotate only part of the transmitted codeword. It is proven that RI codes with small state space are robust in these channels, even when traditional coherent decoders are utilized. Furthermore, it is demonstrated through simulations that the addition of a simple stopping criterion to the coherent iterative decoding algorithm is sufficient for robustness of the more powerful RI-SCTCM codes when partial codeword rotations are considered. Finally, it is investigated whether RI codes are useful for transmission in the noncoherent channel. It is proved that RI codes are as good as any other good codes for this channel when the phase dynamics are low, and optimal decoding is performed. However, it is shown that for a certain class of receivers, RI codes are also robust to partial phase rotations in this channel.

Inverted spin valves with IrMn biasing layer

Inverted IrMn-based spin valves (ISV) were fabricated with the aim of low thickness/high output dual spin valve applications. Optimized structures exhibit the following characteristics: H/sub exch/=750 Oe, R/sub sq./=18.5 /spl Omega//sq., /spl Delta/R/R=7.5% and T/sub b/=250/spl deg/C with IrMn thickness as low as 75 A. The blocking temperature distribution, however, exhibits nonzero components from 150/spl deg/C onwards. Accordingly, accelerated sheet films lifetime experiments and current heating on full read/write heads show that partial rotations of the pinned layer occur well below T/sub b/. These structures therefore appear to be insufficiently stable for disk-drive applications.

Local Chain Motions and Relaxations of Polycarbonates with Differenct Side Groups.

The dynamic mechanical properties of bisphenol A polycarbonate (BPA-PC: poly (oxycarbonyloxy-1, 4-phenyleneisopropylidene-1, 4-phenylene)) and bisphenol AP polycarbonate (BPAP-PC: poly (oxycarbonyloxy-1, 4-phenylene-1-phenyl-1, 1-ethylidene-1, 4-phenylene)) were measured, and the differences in their dynamic mechanical relaxation were analyzed based on the conformational changes and subunit rotations estimated by MM2. The results indicated that the partial rotations of the carbonate and oxycarbonyl groups have low energy barrier and are reasonably ascribed to the major modes of the γ relaxation of both BPA-PC and BPAP-PC. In BPA-PC these rotations should be conjugated with the rotation of the phenylene groups to allow the low temperature relaxation which follows the γ relaxation. The correlated double rotations and flip-flop rotations of the phenylene groups as well as the full rotations of the carbonate may be responsible for the β relaxations of both polycarbonates which may lead to the α relaxations at higher temperature. The excellent toughness of BPA-PC is ascribed to these various modes of partial rotations of the carbonate and the phenylene groups by which the occurring inner stress can be diffused.

Comment concerning ‘The rotation group in plate tectonics and the representation of uncertainties of plate reconstructions’ by T. Chang, J. Stock and P. Molnar

We wish to make a few comments on Chang et al.’s paper. The use of covariance matrices or their geometric counterpart error ellipses to describe rotation errors is not a new idea. For present-day plate motion models Chase (1978) and Minster & Jordan (1978) used this description with angular variables, but these are easily converted to lengths. We believe that we (Jurdy & Stefanick 1987, referred to as J&S) were the first to treat the full three-dimensional problem of representing and combining rotation errors as tensors including optimal estimates. Chang et al.’s paper does not discuss any of these contributions. Moreover, the authors factor rotations into a mean rotation followed by a set of perturbing rotations and the latter are treated statistically. This separation is artificial and obscures the geometric content of a description of errors and does not allow a comparison of alternative estimates or the formation of an optimal estimate if they are independent. We wish to go into detail on these points. We defined our fit of rotations so that there would be an exact fit for one rotation (Stock & Molnar 1983) and then found those rotations which would correspond to an rms misfit of 10 km at the endpoints of the common boundary or at a sequence of points along the common boundary. (The results would be slightly different in the two cases.) This was done so that we could compare our method for combining errors with Stock & Molnar’s method of partial uncertainty rotations which, for combining errors, was combinatorial and required 74 rotation combinations. The agreement was very good. That was our purpose. We made no attempt to make real picks of magnetic anomalies and to estimate the individual errors and make a x 2 fit. If this were done there would be no exact fit and we would have found the rotation which gave the best fit as well as the set of rotations which gave acceptable values for x2. A rotation or a set of rotations is most intuitively represented by an axial vector or set of axial vectors ending in some error ellipsoid. If we have several estimates of a rotation due to alternative chains or different authors then we can imagine several ellipsoids (hopefully intersecting) and if the estimates are independent we can combine the results and obtain an optimal estimate and corresponding error ellipsoid which will roughly coincide with the intersection of the original ellipsoids. Geometrically this is straightforward. Representing the reconstruction of Stock & Molnar (1983) and Molnar & Stock (1985) in our description (J&S), we illustrated the combination of errors for two different chains of reconstructions for the Pacific plate relative to the North American for chron 6, 20 Ma:

A Conceptual Model of Changes in Root Cohesion in Response to Vegetation Management

AbstractCohesion contributed by plant root systems is an important factor in determining the stability of steep, vegetated slopes subject to shallow landslides. The effects of vegetation removal on root cohesion can be simulated by two functional relationships: (i) root deterioration as described by an exponential decay function and (ii) regrowth of newly planted or invading vegetation as described by a sigmoid relationship. The rates of these simultaneous functions determine the temporal changes in net rooting strength. The general root strength model developed in this paper is adapted to specific silvicultural systems such as clearcutting, partial cutting, shelterwood cutting, and thinning. The models simulate the long‐term effects of vegetation management on root cohesion by overlaying the impacts of a prior vegetation removal on a more recent removal. Examples presented for specific silvicultural systems indicate that vegetation and site conditions that promote rapid root strength deterioration and slow regrowth may depress net rooting strength over several management rotations. Progressively shorter clearcut or partial cut rotations can cause a steady temporal decline in root strength. Longer intervals between initial and final shelterwood cuttings promote greater rooting strength than short intervals.

Steepened magnetosonic waves at comet Giacobini‐Zinner

We examine intense hydromagnetic waves at comet Giacobini‐Zinner to investigate the mode and direction of wave propagation and thereby provide important constraints on potential mechanisms for wave origin in the vicinity of the comet. The character of the wave polarization changes from basically elliptical far from the comet to almost linear followed by either a rapid partial rotation (less than 360°) or multiple rotations (high‐frequency wave packets) in the vicinity of the bow wave. Simultaneous high‐resolution measurements of electron density fluctuations demonstrate that the long‐period (∼100 s) waves are propagating in the magnetosonic (fast MHD) mode. Principal axis analyses of the long‐period waves and accompanying partial rotations show that the sum of the wave phase rotations is 360°. This indicates that both are parts of the same wave. The change in polarization characteristics near the comet is simply a consequence of wave steepening. From the time sequence of the steepened waveforms observed by ICE, we demonstrate that the waves must propagate in the general direction along the magnetic field toward the Sun with phase velocities less than the solar wind speed. They are consequently blown back across the spacecraft and observed with a left‐hand sense of rotation. All available observations are therefore consistent with wave generation by the right‐hand resonant ion ring instability which predicts waves propagating in the ion beam (solar) direction. Based on the Wu‐Davidson linear growth rate expression, the total convective gain is shown to exhibit a weak (logarithmic) dependence on distance from the comet reaching a maximum of 30 e‐folding in the vicinity of the bow wave. Conditions necessary for the origin of multiple rotations currently are not well understood. Arguments for their being standing whistler waves consisting of a partial rotation plus multiples of 360° rotations are presented. Models of such emissions should be able to explain them as integral parts of the steepened magnetosonic waves. The large amplitudes, ΔB/|B| ∼ O(1), and small‐scale sizes (rotational discontinuities) of the cometary waves suggest that rapid pitch angle scattering and energy transfer with energetic ions should occur. Since the waves are highly compressive, Δ|B|/|B| ≃ O(0.5), one can also anticipate possible first‐order Fermi and gradient B drift acceleration.

On the statistical properties of estimated rotations

This paper discusses theorems from the mathematical statistics literature on confidence regions for an estimated rotation. The theorems can be used to analyze pairs of homologous intersections of fracture zones with magnetic anomaly lineations on opposing plates. Two classes of probability models on the data are considered: The “fixed u” and the “random u” models, corresponding to, in the geophysical context, whether error is attributed to the measurements on one or on both plates. For each model, large sample and concentrated error approximate confidence regions are given. It is found that the geometric features of the confidence regions are in rough agreement with the analysis of partial uncertainty rotations by Stock and Molnar. The paper concludes with some rudimentary small sample, diffuse error distribution theory. For illustrative purposes, a data set from the Gulf of Aden is repeatedly analyzed using a variety of probabilistic models.

Conformations and internal rotation of tri-isopropylmethane. Dynamic NMR and molecular mechanics studies

The isopropyl group hydrogens of tri-isopropylmethane, 2,4-dimethyl-3-(1-methylethyl)-pentane spend about 75% of time gauche to the unique methine hydrogen and about 25% anti, as shown by the NMR coupling constant. The temperature dependence of the NMR spectrum shows that interconversion of stable conformations or sets of conformations requires overcoming a barrier of 6.6 kcal mol . Molecular mechanics calculations suggest that conformations with all three isopropyl hydrogens gauche, in the same sense or those with two gauche in the same sense and one anti are the most stable, although dihedral angles in these conformations are quite different from 60°. The calculations predict a barrier rather lower than that observed, but give a description of the complicated series of partial rotations that allow interconversion of enantiomeric stable conformations.

Magneto-optical rotation studies of electrolyte solutions. Part 5.—Measurements on aqueous solutions of hydrophobic solutes

The magneto-optical rotations of aqueous solutions of a number of hydrophobic electrolytes have been measured and compared with solutions of normal electrolytes, and the partial molal magnetic rotations of solute and solvent have been evaluated by a method previously described. The changes in the solvent partial molal rotation with concentration of solute have been interpreted in terms of the structure-forming and structure-breaking properties of the solutes on the solvent. The results parallel the n.m.r. findings of other workers and it is necessary to assume a different type of solvation for hydrophobic electrolytes than for normal electrolytes to explain the results.

Magneto optical rotatory dispersion studies of simple electrolyte solutions. Part 4.—The calculation of partial molal magnetic rotations and the solvent structure-breaking entropy effects of electrolytes.

A method is given for the calculation of partial molal contributions of solute and solvent towards the measured magnetic rotation of concentrated electrolyte solutions. The changes in partial molal magnetic rotation of the solvent in solutions of group I and group II metal halides, simple nitrates and perchlorates, and the corresponding acids, have been correlated with the structure-breaking effects of the hydrated solutes upon the bulk solvent, as indicated by the structure-breaking entropies calculated from a recent compilation of entropy of transfer of ions. The values of partial molal magnetic rotation of solute indicate the major contribution of the anion towards the measured magnetic rotation.

The Rotatory Dispersion and Stereochemistry of Organic Compounds. VI. Some Observations on the Sign of Partial Rotations in the Derivatives of Xylofuranose and Mannopyranose

The Rotatory Dispersion and Stereochemistry of Organic Compounds. VI. Some Observations on the Sign of Partial Rotations in the Derivatives of Xylofuranose and Mannopyranose

Optical activity in ketones. The rotatory dispersion and circular dichroism of m-methyl cyclohexanone and of pulegone in their ketonic absorption bands

Recent investigations of the rotatory dispersions of aldehydes and ketones led to the conclusion that the optical activity of these compounds is due almost entirely to the electrons of the carbonyl group and not directly to the asymmetric carbon atoms. A particularly striking example of this was found in the aldehydic sugar derivative, μ-arabinose pentaacetate, by Hudson, Wolfrom and Lowry (1933), who showed that when the calculated partial rotation contributed by the absorption band between 3000 and 2600 A was subtracted from the observed rotations for the whole molecule, a negligible residual rotation was left at every wave-length at which measurements were made between 6700 and 2300 A. In general, however, absorption frequencies lying in the Schumann region appear to make a small contribution; but the analysis has always been complicated in the cases so far examined by the fact that the molecules contain either two asymmetric carbon atoms, e. g. in camphor (Kuhn and Gore 1931), menthone and carvomenthone (Lowry and Lishmund 1935a), or as many as four in the open-chain sugar derivatives (Hudson and others 1933; Baldwin, Wolfrom and Lowry 1935). The absence of any large direct contribution from the asymmetric atoms might therefore be explained in two ways, namely, either that their partial rotations are actually very small, or, as may well be the case in the sugars (cf. Lowry 1935, p. 274), that, though large, they are of opposing signs and tend to annul one another at wavelengths remote from the region of absorption. It was thus desirable to examine an optically active ketone whose molecule contains only a single asymmetric carbon atom, with no other disturbing factor, and m-methyl cyclohexanone (I) was selected for this purpose.

Rotatory Dispersion of Configurationally Related Alkyl Azides

From the viewpoint of chemical behavior, the —N3 group may be regarded as a pseudohalogen. Like iodides, azides possess an absorption band in the near ultraviolet region. For both practical and theoretical reasons it was important to obtain information on the rotatory properties of the azides as compared with those of the corresponding halides. The correlation of the configurations of primary and secondary azides is discussed in this communication. From the analysis of the rotatory dispersion of the primary azides and halides it became evident that the partial rotations of the azido group and of the halogen atom may be of opposite sign in configurationally related substances. An unexpected observation was made with regard to the members of a homologous series of secondary azides, namely, the rotation in the visible region as well as the partial rotation of the azido group, changes sign on passing from the second member of the series to the third. A tentative explanation of the phenomenon is given. It was found that in all alkyl azides the absorption band at λ2880 is not anisotropic or at best, insignificantly so.

Relations between optical rotatory power and constitution in the steroids

The group of biologically important compounds containing the reduced cyclo pentenophenanthrene ring system (the “steroids”) provides a field for the exploration of relations between optical rotatory power and constitution which has hitherto received little attention. In the present paper a preliminary survey has been made of the scattered data in the literature with the object of finding in the first place whether constant partial rotations can be assigned to certain carbon atoms and groups. Even with compounds of established constitution the results are not by any means so concordant as those obtained by Hudson with many of the series of carbohydrates, but there is indubitable evidence of regularity, in spite of the fact that many of the determinations recorded are of a low order of accuracy, have been made with impure specimens of materials notoriously difficult to purify, or are discordant among themselves. For numerous substances determinations of optical activity under conditions which allow comparison with related compounds are lacking, and it is to be hoped that such evidence of regularity as is brought forward in this communication will lead to the filling of some of these gaps. The steroid skeleton, with an indication of the system of numeration adopted, is shown in fig. 1. A number of pairs of compounds are known in which there are opposite configurations of carbon atoms 3, 4, 5, and 17, and we have investigated whether it is possible to apply to these a rule analogous to Hudson’s “first rule of isorotation”, i. e ., whether the partial rotations of carbon atoms 3, 4, 5, and 17, as measured by the effect of reversing the configuration, are affected by changes in the structure of the remainder of the molecule. In Tables I-IV are summarized the data collected, with three exceptions, from the literature for the specific rotations of these diastereoisomeric pairs of compounds, determined for the D line and, as far as possible, the same solvents. Where more than one determination exists, the values of [α] D are, in general, the means of the recorded figures for presumably pure compounds, and no attempt has been made to select them critically. The last two columns show the differences of [α] D and the differences of [M] D ([M] D being defined as [α] D x (mol. wt.)/100); ∆[M] D corresponding to twice the partial rotation of the carbon atom concerned.

Analysis of Rotatory Dispersion Curves. II Configurationally Related Substituted Fatty Acids

The rotatory dispersion curves of substituted fatty acids of the types COOH |H–C–SH | R and COOH |H–C–SO3H | Rhave been measured in the visible and ultraviolet regions. The results are in harmony with the rule previously reported that in members of homologous series, the total rotation of consecutive members may differ in sign, but the signs of the partial rotations remain constant.