Matrix Nonlinear Schr\"odinger Equations and Moment Maps into Loop Algebras†{}^\dag

It is shown how Darboux coordinates on a reduced symplectic vector space may be used to parametrize the phase space on which the finite gap solutions of matrix nonlinear Schr\"odinger equations are realized as isospectral Hamiltonian flows. The parametrization follows from a moment map embedding of the symplectic vector space, reduced by suitable group actions, into the dual \tilde\grg^{+*} of the algebra \tilde\grg^+ of positive frequency loops in a Lie algebra \grg. The resulting phase space is identified with a Poisson subspace of \tilde\grg^{+*} consisting of elements that are rational in the loop parameter. Reduced coordinates associated to the various Hermitian symmetric Lie algebras (\grg,\grk) corresponding to the classical Lie algebras are obtained.Comment: 17 pgs, plus 4 Tables Preprint CRM-183

Isospectral flow in Loop Algebras and Quasiperiodic Solutions of the Sine-Gordon Equation

The sine-Gordon equation is considered in the hamiltonian framework provided by the Adler-Kostant-Symes theorem. The phase space, a finite dimensional coadjoint orbit in the dual space \grg^* of a loop algebra \grg, is parametrized by a finite dimensional symplectic vector space $W$ embedded into \grg^* by a moment map. Real quasiperiodic solutions are computed in terms of theta functions using a Liouville generating function which generates a canonical transformation to linear coordinates on the Jacobi variety of a suitable hyperelliptic curve.Comment: 12 pg

Trapped at Work: The Barriers Model of Abusive Supervision.

While research on abusive supervision is thriving, we still know very little about the sustained nature of the phenomenon. Additionally, most papers focusing on the prolonged character of the detrimental relational dynamic take a within-dyad perspective, largely ignoring within-person, group or other external influences. Addressing these gaps in the literature, we introduce the Barriers Model of Abusive Supervision. This model posits a hierarchically organized set of obstacles that make it difficult for followers to escape the abusive supervisor, explaining why abuse can continue over long periods of time. Specifically, we present an onion-shaped model in which the follower has a central position with each subsequent layer representing a more external cluster of barriers to leaving the abusive supervisor. Ranging from external to internal, these layers are: Barriers in the larger societal context (Layer 1; e.g., ambiguous laws), barriers in the organizational context (Layer 2; e.g., unclear policies), barriers due to the abusive supervisor (Layer 3; e.g., isolating followers), and barriers within the abused follower (Layer 4; e.g., implicit leadership theories). We hope that our model inspires future research on the sustained nature of abusive supervision and provides practitioners with the necessary background information to help abused followers escape their supervisors

Prediction of stable walking for a toy that cannot stand

Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and which has no statically stable near-standing configurations can walk stably. We show here that a simple rigid-body statically-unstable mathematical model based loosely on the physical toy can predict stable limit-cycle walking motions. These calculations add to the repertoire of rigid-body mechanism behaviors as well as further implicating passive-dynamics as a possible contributor to stability of animal motions.Comment: Note: only corrections so far have been fixing typo's in these comments. 3 pages, 2 eps figures, uses epsf.tex, revtex.sty, amsfonts.sty, aps.sty, aps10.sty, prabib.sty; Accepted for publication in Phys. Rev. E. 4/9/2001 ; information about Andy Ruina's lab (including Coleman's, Garcia's and Ruina's other publications and associated video clips) can be found at: http://www.tam.cornell.edu/~ruina/hplab/index.html and more about Georg Bock's Simulation Group with whom Katja Mombaur is affiliated can be found at http://www.iwr.uni-heidelberg.de/~agboc

Lymphoid Microenvironments in the Thymus and Lymph Node

The three-dimensional architecture of the thymus and mesenteric lymph node reveals several different stromal cell types important in the development and function of T cells. In the thymic cortex, T cells proliferate and differentiate in a meshwork of epithelial-reticular cells. They then migrate towards the medulla where they may interact with interdigitating cells. T cells migrate from the thymus through perivascular spaces, surrounding large vessels at the cortico-medullary boundary. In this area also large thymic cystic cavities are found, their function remains at present unclear. Mature selected T cells leave the thymus most probably by the venous bloodstream, to enter peripheral lymph nodes. Upon entering the lymph node they cross the wall of high endothelial venules. On the other hand, lymph enters the node by afferent lymphatics draining into various types of sinuses. Here, macrophages are strategically located to phagocytose and process antigen. These cells then expose antigen to T cells and B cells within the lymph node parenchyma, thus creating a microenvironment for the onset of an immune response. The various microenvironments important in T cell development and T cell function are shown in this paper using scanning electron microscopy as a dissecting tool. We discuss our morphological findings in the light of recent data on the physiology of T cell differentiation and function

How Crouch Gait Can Dynamically Induce Stiff-Knee Gait

Children with cerebral palsy frequently experience foot dragging and tripping during walking due to a lack of adequate knee flexion in swing (stiff-knee gait). Stiff-knee gait is often accompanied by an overly flexed knee during stance (crouch gait). Studies on stiff-knee gait have mostly focused on excessive knee muscle activity during (pre)swing, but the passive dynamics of the limbs may also have an important effect. To examine the effects of a crouched posture on swing knee flexion, we developed a forward-dynamic model of human walking with a passive swing knee, capable of stable cyclic walking for a range of stance knee crouch angles. As crouch angle during stance was increased, the knee naturally flexed much less during swing, resulting in a 'stiff-knee' gait pattern and reduced foot clearance. Reduced swing knee flexion was primarily due to altered gravitational moments around the joints during initial swing. We also considered the effects of increased push-off strength and swing hip flexion torque, which both increased swing knee flexion, but the effect of crouch angle was dominant. These findings demonstrate that decreased knee flexion during swing can occur purely as the dynamical result of crouch, rather than from altered muscle function or pathoneurological control alone. © 2010 The Author(s)