Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

Time and Amplitude of Afterpulse Measured with a Large Size Photomultiplier Tube

We have studied the afterpulse of a hemispherical photomultiplier tube for an upcoming reactor neutrino experiment. The timing, the amplitude, and the rate of the afterpulse for a 10 inch photomultiplier tube were measured with a 400 MHz FADC up to 16 \ms time window after the initial signal generated by an LED light pulse. The time and amplitude correlation of the afterpulse shows several distinctive groups. We describe the dependencies of the afterpulse on the applied high voltage and the amplitude of the main light pulse. The present data could shed light upon the general mechanism of the afterpulse.Comment: 11 figure

The influence of gene expression time delays on Gierer-Meinhardt pattern formation systems

There are numerous examples of morphogen gradients controlling long range signalling in developmental and cellular systems. The prospect of two such interacting morphogens instigating long range self-organisation in biological systems via a Turing bifurcation has been explored, postulated, or implicated in the context of numerous developmental processes. However, modelling investigations of cellular systems typically neglect the influence of gene expression on such dynamics, even though transcription and translation are observed to be important in morphogenetic systems. In particular, the influence of gene expression on a large class of Turing bifurcation models, namely those with pure kinetics such as the Gierer–Meinhardt system, is unexplored. Our investigations demonstrate that the behaviour of the Gierer–Meinhardt model profoundly changes on the inclusion of gene expression dynamics and is sensitive to the sub-cellular details of gene expression. Features such as concentration blow up, morphogen oscillations and radical sensitivities to the duration of gene expression are observed and, at best, severely restrict the possible parameter spaces for feasible biological behaviour. These results also indicate that the behaviour of Turing pattern formation systems on the inclusion of gene expression time delays may provide a means of distinguishing between possible forms of interaction kinetics. Finally, this study also emphasises that sub-cellular and gene expression dynamics should not be simply neglected in models of long range biological pattern formation via morphogens

Crossing borders: new teachers co-constructing professional identity in performative times

This paper draws on a range of theoretical perspectives on the construction of new teachers’ professional identity. It focuses particularly on the impact of the development in many national education systems of a performative culture of the management and regulation of teachers’ work. Whilst the role of interactions with professional colleagues and school managers in the performative school has been extensively researched, less attention has been paid to new teachers’ interactions with students. This paper highlights the need for further research focusing on the process of identity co-construction with students. A key theoretical concept employed is that of liminality, the space within which identities are in transition as teachers adjust to the culture of a new professional workplace, and the nature of the engagement of new teachers, or teachers who change schools, with students. The authors argue that an investigation into the processes of this co-construction of identity offers scope for new insights into the extent to which teachers might construct either a teacher identity at odds with their personal and professional values, or a more ‘authentic’ identity that counters performative discourses. These insights will in turn add to our understanding of the complex range of factors impacting on teacher resilience and motivation

Magnetic trapping of ultracold neutrons

Three-dimensional magnetic confinement of neutrons is reported. Neutrons are loaded into an Ioffe-type superconducting magnetic trap through inelastic scattering of cold neutrons with 4He. Scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay. The electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light. This light is frequency downconverted to the visible and detected. Results are presented in which 500 +/- 155 neutrons are magnetically trapped in each loading cycle, consistent with theoretical predictions. The lifetime of the observed signal, 660 s +290/-170 s, is consistent with the neutron beta-decay lifetime.Comment: 17 pages, 18 figures, accepted for publication in Physical Review

The parent?infant dyad and the construction of the subjective self

Developmental psychology and psychopathology has in the past been more concerned with the quality of self-representation than with the development of the subjective agency which underpins our experience of feeling, thought and action, a key function of mentalisation. This review begins by contrasting a Cartesian view of pre-wired introspective subjectivity with a constructionist model based on the assumption of an innate contingency detector which orients the infant towards aspects of the social world that react congruently and in a specifically cued informative manner that expresses and facilitates the assimilation of cultural knowledge. Research on the neural mechanisms associated with mentalisation and social influences on its development are reviewed. It is suggested that the infant focuses on the attachment figure as a source of reliable information about the world. The construction of the sense of a subjective self is then an aspect of acquiring knowledge about the world through the caregiver's pedagogical communicative displays which in this context focuses on the child's thoughts and feelings. We argue that a number of possible mechanisms, including complementary activation of attachment and mentalisation, the disruptive effect of maltreatment on parent-child communication, the biobehavioural overlap of cues for learning and cues for attachment, may have a role in ensuring that the quality of relationship with the caregiver influences the development of the child's experience of thoughts and feelings

Measurement of the correlation between flow harmonics of different order in lead-lead collisions at √sNN = 2.76 TeV with the ATLAS detector

Correlations between the elliptic or triangular flow coefficients vm (m=2 or 3) and other flow harmonics vn (n=2 to 5) are measured using √sNN=2.76 TeV Pb+Pb collision data collected in 2010 by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of 7 μb−1. The vm−vn correlations are measured in midrapidity as a function of centrality, and, for events within the same centrality interval, as a function of event ellipticity or triangularity defined in a forward rapidity region. For events within the same centrality interval, v3 is found to be anticorrelated with v2 and this anticorrelation is consistent with similar anticorrelations between the corresponding eccentricities, ε2 and ε3. However, it is observed that v4 increases strongly with v2, and v5 increases strongly with both v2 and v3. The trend and strength of the vm−vn correlations for n=4 and 5 are found to disagree with εm−εn correlations predicted by initial-geometry models. Instead, these correlations are found to be consistent with the combined effects of a linear contribution to vn and a nonlinear term that is a function of v22 or of v2v3, as predicted by hydrodynamic models. A simple two-component fit is used to separate these two contributions. The extracted linear and nonlinear contributions to v4 and v5 are found to be consistent with previously measured event-plane correlations

Search for vectorlike B quarks in events with one isolated lepton, missing transverse momentum, and jets at √s = 8 TeV with the ATLAS detector

A search has been performed for pair production of heavy vectorlike down-type (B) quarks. The analysis explores the lepton-plus-jets final state, characterized by events with one isolated charged lepton (electron or muon), significant missing transverse momentum, and multiple jets. One or more jets are required to be tagged as arising from b quarks, and at least one pair of jets must be tagged as arising from the hadronic decay of an electroweak boson. The analysis uses the full data sample of pp collisions recorded in 2012 by the ATLAS detector at the LHC, operating at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 20.3 fb −1 . No significant excess of events is observed above the expected background. Limits are set on vectorlike B production, as a function of the B branching ratios, assuming the allowable decay modes are B → Wt/Zb/Hb. In the chiral limit with a branching ratio of 100% for the decay B → Wt, the observed (expected) 95% C.L. lower limit on the vectorlike B mass is 810 GeV (760 GeV). In the case where the vectorlike B quark has branching ratio values corresponding to those of an SU(2) singlet state, the observed (expected) 95% C.L. lower limit on the vectorlike B mass is 640 GeV (505 GeV). The same analysis, when used to investigate pair production of a colored, charge 5/3 exotic fermion T 5/3 , with subsequent decay T 5/3 → Wt, sets an observed (expected) 95% C.L. lower limit on the T 5/3 mass of 840 GeV (780 GeV)