A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

A new method for the in vivo identification of mechanical properties in arteries from cine MRI images: Theoretical framework and validation

Quantifying the stiffness properties of soft tissues is essential for the diagnosis of many cardiovascular diseases such as atherosclerosis. In these pathologies it is widely agreed that the arterial wall stiffness is an indicator of vulnerability. The present paper focuses on the carotid artery and proposes a new inversion methodology for deriving the stiffness properties of the wall from cine-MRI (magnetic resonance imaging) data. We address this problem by setting-up a cost function defined as the distance between the modeled pixel signals and the measured ones. Minimizing this cost function yields the unknown stiffness properties of both the arterial wall and the surrounding tissues. The sensitivity of the identified properties to various sources of uncertainty is studied. Validation of the method is performed on a rubber phantom. The elastic modulus identified using the developed methodology lies within a mean error of 9.6%. It is then applied to two young healthy subjects as a proof of practical feasibility, with identified values of 625 kPa and 587 kPa for one of the carotid of each subject.

Absorption of intense electromagnetic beams in a magnetoplasma

The multiphoton inverse bremsstrahlung absorption of two intense electromagnetic beams passing through a magnetized plasma is studied. The rate of absorption of electromagnetic energy by the electrons is calculated by deriving a kinetic equation for the electrons. It is found that the absorption enhances when the frequency of one electromagnetic beam is more, and that of the other electromagnetic beam is less, than the electron-cyclotron frequency. A possible application to extragalactic radio sources is discussed.

Fasteners in Composite Plates - Effects of Interfacial Friction

The effects of tangential friction at pin—hole interfaces are appropriately modelled for the analysis of fasteners in large composite (orthotropic) plate loaded along its edges. The pin—hole contact could be of interference, clearance or neat fit. When the plate load is monotonically increased, interference fits give rise to receding contact, whereas clearance fits result in advancing contact. In either case, the changing contact situations lead to non-linear moving boundary value problems. The neat fit comes out as a special case in which the contact and separation regions are invariant with the applied load level and so the problem remains linear. The description of boundary conditions in the presence of tangential friction, will depend on whether the problem is one of advancing or receding contact, advancing contact presenting a special problem. A model is developed for the limiting case of a rigid pin and an ideally rough interface (infinitely large friction coefficient). The non-linearity resulting from the continuously varying proportions of contact and separation at the interface, is handled by an “Inverse Formulation” which was successfully applied earlier by the authors for smooth (zero friction) interfacial conditions. The additional difficulty introduced by advancing contact is handled by adopting a “Marching Solution”. The modelling and the procedure are illustrated in respect of symmetric plate load cases. Numerical results are presented bringing out the effects of interfacial friction and plate orthotropy on load-contact relations and plate stresses.

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.

Flow through a plateau border of cellular foam

Experimentally measured average velocities through plateau borders of stationary cellular foam, when compared with those calculated with the assumption of rigid Plateau Border walls, show that the assumption of rigid walls severely underestimates the velocities. An analysis of the situation wherein plateau border walls have velocities, as decided by the surface viscosity of the system, is presented here. The plateau border is idealized as a pipe of equilateral triangular cross-section with vertices of the triangle having zero velocity. The pertinent form of Navier-Stoke's equations with inhomogeneous boundary conditions and its solution through a procedure of successive approximations is presented in dimensionless form. The solution reduces to the known solution of slow steady flow through a triangular pipe, when surface viscosity is infinite. Results indicate that the assumption of rigid plateau border walls is valid only when value of the inverse of dimensionless surface viscosity is less than 0.044. Beyond that the assumption severely underestimates the flow and the effect of nonrigidity of the wall must be considered.

Factors potentiating the risk of sudden infant death syndrome associated with the prone position

Background. In several studies the sudden infant death syndrome (SIDS) has been significantly associated with sleeping in the prone position. It is not known how the prone position increases the risk of SIDS. Methods. We analyzed data from a case-control study (58 infants with SIDS and 120 control infants) and a prospective cohort study (22 infants with SIDS and 213 control infants) in Tasmania. Interactions were examined in matched analyses with a multiplicative model of interaction. Results. In the case-control study, SIDS was significantly associated with sleeping in the prone position, as compared with other positions (unadjusted odds ratio, 4.5; 95 percent confidence interval, 2.1 to 9.6). The strength of this association was increased among infants who slept on natural-fiber mattresses (P = 0.05), infants who were swaddled (P = 0.09), infants who slept in heated rooms (P = 0.006), and infants who had had a recent illness (P = 0.02). These variables had no significant effect on infants who did not sleep in the prone position. A history of recent illness was significantly associated with SIDS among infants who slept prone (odds ratio, 5.7; 95 percent confidence interval, 1.8 to 19) but not among infants who slept in other positions (odds ratio, 0.83). In the cohort study, the risk of SIDS was greater among infants who slept prone on natural-fiber mattresses (odds ratio, 6.6; 95 percent confidence interval, 1.3 to 33) than among infants who slept prone on other types of mattresses (odds ratio, 1.8). Conclusions. When infants sleep prone, the elevated risk of SIDS is increased by each of four factors: the use of natural-fiber mattresses, swaddling, recent illness, and the use of heating in bedrooms.

Elastic analysis of pin joints in plates under some combined pin and plate loads

Joints are primary sources of weakness in structures. Pin joints are very common and are used where periodic disassembly of components is needed. A circular pin in a circular hole in an infinitely large plate is an abstraction of such a pin joint. A two-dimensional plane-stress analysis of such a configuration is carried out, here, subjected to pin-bearing and/or biaxial-plate loading. The pin is assumed to be rigid compared to the plate material. For pin load the reactive stresses at the edges of the infinite plate tend to zero though their integral over the external boundary equals to the pin load. The pin-hole interface is unbonded and so beyond some load levels the plate separates from the pin and the extent of separation is a non-linear function of load level. The problem is solved by inverse technique where the extent of contact is specified and the causative loads are evaluated directly. In the situations where combined load is acting the separation-contact zone specification generally needs two parameters (angles) to be specified. The present report deals with analysing such a situation in metallic (or isotropic) plates. Numerical results are provided for parametric representation and the methodology is demonstrated.

Fast Iterative Division of p-adic Numbers

A fast iterative scheme based on the Newton method is described for finding the reciprocal of a finite segment p-adic numbers (Hensel code). The rate of generation of the reciprocal digits per step can be made quadratic or higher order by a proper choice of the starting value and the iterating function. The extension of this method to find the inverse transform of the Hensel code of a rational polynomial over a finite field is also indicated.

Pin-Loaded Holes in Large Orthotropic Plates

Pin-loaded holes commonly occur in engineering structures. However, accurate analysis of such holes presents formidable difficulties because of the load-dependent contact of the pin with the plate. Significant progress has recently been achieved in the analysis of holes in isotropic plates. This paper develops a simple and accurate method for the partial contact analysis of pin-loaded holes in composites. The method is based on an inverse formulation that seeks to determine loads in a given contact-separation configuration. A unified approach for all types of fit was used. Continuum solutions were obtained for infinitely large plates of various typical orthotropic properties with holes loaded by smooth rigid pins. These solutions were then compared with those for isotropic plates. The effects of orthotropy and the type of fit were studied through load-contact relationships, distribution of stresses and displacements, and their variation with load. The results are of direct relevance to the analysis and design of pin joints in composite plates.

A large orthotropic plate with misfit pin under arbitrarily oriented biaxial loading

The problem of misfit (interference or clearance) pin in a large orthotropic plate was solved earlier by the authors for biaxial loading in the principal directions of orthotropy. Here, a more general case of arbitrarily oriented loading is considered. The most important aspect of the problem studied is the partial contact at the pin-hole interface. The solution is obtained by extending the use of ‘inverse technique’ which was successfully applied earlier by the authors to problems of pins in isotropic and orthotropic domains. The loss of symmetry because of the arbitrary orientation of loading makes the problem more complex. Additional parameters are then involved in the inversion of the problem for the solution. Numerical results are presented primarily for a smooth interference fit pin in a typical orthotropic plate.

Development of special fastener elements

A special finite element (FASNEL) is developed for the analysis of a neat or misfit fastener in a two-dimensional metallic/composite (orthotropic) plate subjected to biaxial loading. The misfit fasteners could be of interference or clearance type. These fasteners, which are common in engineering structures, cause stress concentrations and are potential sources of failure. Such cases of stress concentration present considerable numerical problems for analysis with conventional finite elements. In FASNEL the shape functions for displacements are derived from series stress function solutions satisfying the governing difffferential equation of the plate and some of the boundary conditions on the hole boundary. The region of the plate outside FASNEL is filled with CST or quadrilateral elements. When a plate with a fastener is gradually loaded the fastener-plate interface exhibits a state of partial contact/separation above a certain load level. In misfit fastener, the extent of contact/separation changes with applied load, leading to a nonlinear moving boundary problem and this is handled by FASNEL using an inverse formulation. The analysis is developed at present for a filled hole in a finite elastic plate providing two axes of symmetry. Numerical studies are conducted on a smooth rigid fastener in a finite elastic plate subjected to uniaxial loading to demonstrate the capability of FASNEL.

CIMMYT-selected derived synthetic bread wheats for rainfed environments: Yield evaluation in Mexico and Australia.

Synthetic backcrossed-derived bread wheats (SBWs) from CIMMYT were grown in the Northwest of Mexico at Centro de Investigaciones Agrícolas del Noroeste (CIANO) and sites across Australia during three seasons. During three consecutive years Australia received “shipments” of different SBWs from CIMMYT for evaluation. A different set of lines was evaluated each season, as new materials became available from the CIMMYT crop enhancement program. These consisted of approximately 100 advanced lines (F7) per year. SBWs had been top and backcrossed to CIMMYT cultivars in the first two shipments and to Australian wheat cultivars in the third one. At CIANO, the SBWs were trialled under receding soil moisture conditions. We evaluated both the performance of each line across all environments and the genotype-by-environment interaction using an analysis that fits a multiplicative mixed model, adjusted for spatial field trends. Data were organised in three groups of multienvironment trials (MET) containing germplasm from shipment 1 (METShip1), 2 (METShip2), and 3 (METShip3), respectively. Large components of variance for the genotype × environment interaction were found for each MET analysis, due to the diversity of environments included and the limited replication over years (only in METShip2, lines were tested over 2 years). The average percentage of genetic variance explained by the factor analytic models with two factors was 50.3% for METShip1, 46.7% for METShip2, and 48.7% for METShip3. Yield comparison focused only on lines that were present in all locations within a METShip, or “core” SBWs. A number of core SBWs, crossed to both Australian and CIMMYT backgrounds, outperformed the local benchmark checks at sites from the northern end of the Australian wheat belt, with reduced success at more southern locations. In general, lines that succeeded in the north were different from those in the south. The moderate positive genetic correlation between CIANO and locations in the northern wheat growing region likely reflects similarities in average temperature during flowering, high evaporative demand, and a short flowering interval. We are currently studying attributes of this germplasm that may contribute to adaptation, with the aim of improving the selection process in both Mexico and Australia.

Leaf chlorophyll concentration relates to transpiration efficiency in peanut

Two pot experiments were conducted in two different seasons at the University of Agricultural Science, Bangalore, India, to study (a) the relationship between chlorophyll concentration (by measuring the leaf light-transmittance characteristics using a SPAD metre) and transpiration efficiency (TE) and (b) the effect of leaf N on chlorophyll and TE relationship in peanut. In Experiment (Expt) I, six peanut genotypes with wide genetic variation for the specific leaf area (SLA) were used. In Expt II, three non-nodulating isogenic lines were used to study the effect of N levels on leaf chlorophyll concentration–TE relationship without potential confounding effects in biological nitrogen fixation. Leaf N was manipulated by applying N fertiliser in Expt II. Chlorophyll concentration, TE (g dry matter kg−1 of H2O transpired, measured using gravimetric method), specific leaf nitrogen (g N m−2, SLN), SLA (cm2 g−1), carbon isotope composition (Δ13C) were determined in the leaves sampled during the treatment period (35–55 days after sowing) in the two experiments. Results showed that the leaf chlorophyll concentration expressed as soil plant analytical development (SPAD) chlorophyll metre reading (SCMR) varied significantly among genotypes in Expt I and as a result of N application in Expt II. Changes in leaf N levels were strongly associated with changes in SCMR, TE and Δ13C. In both the experiments, a significant positive relationship between SCMR and TE with similar slopes but differing intercepts was noticed. However, correction of TE for seasonal differences in vapour pressure deficit (VPD) between the two experiments resulted in a single and stronger relationship between SCMR and TE. There was a significant inverse relationship between SCMR and Δ13C, suggesting a close linkage between chlorophyll concentration and Δ13C in peanut. This study provides the first evidence for a significant positive relationship between TE and leaf chlorophyll concentration in peanut. The study also describes the effect of growing environment on the relationships among SLA, SLN and SCMR.

Quantitative assessment of total phenol contents of European oak (Quercus petraea and Quercus robur) by diffuse reflectance NIR spectroscopy on solid wood surfaces

Near infrared spectroscopy (NIRS) combined with multivariate analysis techniques was applied to assess phenol content of European oak. NIRS data were firstly collected directly from solid heartwood surfaces: in doing so, the spectra were recorded separately from the longitudinal radial and the transverse section surfaces by diffuse reflectance. The spectral data were then pretreated by several pre-processing procedures, such as multiplicative scatter correction, first derivative, second derivative and standard normal variate. The tannin contents of sawmill collected from the longitudinal radial and transverse section surfaces were determined by quantitative extraction with water/methanol (1:4, by vol). Then, total phenol contents in tannin extracts were measured by the Folin-Ciocalteu method. The NIR data were correlated against the Folin-Ciocalteu results. Calibration models built with partial least squares regression displayed strong correlation - as expressed by high determination correlation coefficient (r2) and high ratio of performance to deviation (RPD) - between measured and predicted total phenols content, and weak calibration and prediction errors (RMSEC, RMSEP). The best calibration was provided with second derivative spectra (r2 value of 0.93 for the longitudinal radial plane and of 0.91 for the transverse section plane). This study illustrates that the NIRS technique when used in conjunction with multivariate analysis could provide reliable, quick and non-destructive assessment of European oak heartwood extractives.