Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Polynomial-in-time dependent symmetries are analysed for polynomial-in-time dependent evolution equations. Graded Lie algebras, especially Virasoro algebras, are used to construct nonlinear variable-coefficient evolution equations, both in 1+1 dimensions and in 2+1 dimensions, which possess higher-degree polynomial-in-time dependent symmetries. The theory also provides a kind of new realisation of graded Lie algebras. Some illustrative examples are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge

Semiflexible Filamentous Composites

Inspired by the ubiquity of composite filamentous networks in nature we investigate models of biopolymer networks that consist of interconnected floppy and stiff filaments. Numerical simulations carried out in three dimensions allow us to explore the microscopic partitioning of stresses and strains between the stiff and floppy fractions c_s and c_f, and reveal a non-trivial relationship between the mechanical behavior and the relative fraction of stiff polymer: when there are few stiff polymers, non-percolated stiff ``inclusions`` are protected from large deformations by an encompassing floppy matrix, while at higher fractions of stiff material the stiff network is independently percolated and dominates the mechanical response.Comment: Phys. Rev. Lett, to appear (4 pages, 2 figures

Josephson junctions with negative second harmonic in the current-phase relation: properties of novel varphi-junctions

Several recent experiments revealed a change of the sign of the first harmonic in the current-phase relation of Josephson junctions (JJ) based on novel superconductors, e.g., d-wave based or JJ with ferromagnetic barrier. In this situation the role of the second harmonic becomes dominant and it determines the scenario of a 0-pi transition. We discuss different mechanisms of the second harmonic generation and its sign. If the second harmonic is negative the 0-pi transition becomes continuous and the realization of the so-called varphi junction is possible. We study the unusual properties of such a novel JJ and analyze the possible experimental techniques for their observation.Comment: submitted to PR

Metallic wear in failed titanium-alloy total hip replacements. A histological and quantitative analysis

We conducted extensive histological examination of the tissues that were adjacent to the prosthesis in nine hips that had a failed total arthroplasty. The prostheses were composed of titanium alloy (Ti-6Al-4V) and ultra-high molecular weight polyethylene. The average time that the prosthesis had been in place in the tissue was 33.5 months (range, eleven to fifty-seven months). Seven arthroplasties were revised because of aseptic loosening and two, for infection. In eight hips cement had been used and in one (that had a porous-coated implant for fifty-two months) no cement had been utilized. Intense histiocytic and plasma-cell reaction was noted in the pseudocapsular tissue. There was copious metallic staining of the lining cells. Polyethylene debris and particles of cement with concomitant giant-cell reaction were present in five hips. Atomic absorption spectrophotometry revealed values for titanium of fifty-sic to 3700 micrograms per gram of dry tissue (average, 1047 micrograms per gram; normal, zero microgram per gram), for aluminum of 2.1 to 396 micrograms per gram (average, 115 micrograms per gram; normal, zero micrograms per gram), and for vanadium of 2.9 to 220 micrograms per gram (average, sixty-seven micrograms per gram; normal, 1.2 micrograms per gram). The highest values were found in the hip in which surgical revision was performed at fifty-seven months. The concentrations of the three elements in the soft tissues were similar to those in the metal of the prostheses. The factors to which failure was attributed were: vertical orientation of the acetabular component (five hips), poor cementing technique on the femoral side (three hips), infection (two hips), and separation of a sintered pad made of pure titanium (one hip). A femoral component that is made of titanium alloy can undergo severe wear of the surface and on the stem, where it is loose, with liberation of potentially toxic local concentrations of metal debris into the surrounding tissues. It may contribute to infection and loosening

Cavity-induced coherence effects in spontaneous emission from pre-Selection of polarization

Spontaneous emission can create coherences in a multilevel atom having close lying levels, subject to the condition that the atomic dipole matrix elements are non-orthogonal. This condition is rarely met in atomic systems. We report the possibility of bypassing this condition and thereby creating coherences by letting the atom with orthogonal dipoles to interact with the vacuum of a pre-selected polarized cavity mode rather than the free space vacuum. We derive a master equation for the reduced density operator of a model four level atomic system, and obtain its analytical solution to describe the interference effects. We report the quantum beat structure in the populations.Comment: 6 pages in REVTEX multicolumn format, 5 figures, new references added, journal reference adde

Invariant solutions of the supersymmetric sine-Gordon equation

A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the super-sine-Gordon equation expressed in terms of a bosonic superfield involving anticommuting independent variables. In each case, a Lie (super)algebra of symmetries is determined and a classification of all subgroups having generic orbits of codimension 1 in the space of independent variables is performed. The method of symmetry reduction is systematically applied in order to derive invariant solutions of the supersymmetric model. Several types of algebraic, hyperbolic and doubly periodic solutions are obtained in explicit form.Comment: 27 pages, major revision, the published versio

A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations

A new class of 1D discrete nonlinear Schr${\ddot{\rm{o}}}$dinger Hamiltonians with tunable nonlinerities is introduced, which includes the integrable Ablowitz-Ladik system as a limit. A new subset of equations, which are derived from these Hamiltonians using a generalized definition of Poisson brackets, and collectively refered to as the N-AL equation, is studied. The symmetry properties of the equation are discussed. These equations are shown to possess propagating localized solutions, having the continuous translational symmetry of the one-soliton solution of the Ablowitz-Ladik nonlinear Schr${\ddot{\rm{o}}}$dinger equation. The N-AL systems are shown to be suitable to study the combined effect of the dynamical imbalance of nonlinearity and dispersion and the Peierls-Nabarro potential, arising from the lattice discreteness, on the propagating solitary wave like profiles. A perturbative analysis shows that the N-AL systems can have discrete breather solutions, due to the presence of saddle center bifurcations in phase portraits. The unstaggered localized states are shown to have positive effective mass. On the other hand, large width but small amplitude staggered localized states have negative effective mass. The collison dynamics of two colliding solitary wave profiles are studied numerically. Notwithstanding colliding solitary wave profiles are seen to exhibit nontrivial nonsolitonic interactions, certain universal features are observed in the collison dynamics. Future scopes of this work and possible applications of the N-AL systems are discussed.Comment: 17 pages, 15 figures, revtex4, xmgr, gn

A New Nonlinear Liquid Drop Model. Clusters as Solitons on The Nuclear Surface

By introducing in the hydrodynamic model, i.e. in the hydrodynamic equations and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equation (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by the ratio of the square amplitudes in the two minima.Comment: 27 pages, LateX, 8 figures, Submitted J. Phys. G: Nucl. Part. Phys., PACS: 23.60.+e, 21.60.Gx, 24.30.-v, 25.70.e

New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.Comment: 23 page

Improving obstetric care in low-resource settings: implementation of facility-based maternal death reviews in five pilot hospitals in Senegal

<p>Abstract</p> <p>Background</p> <p>In sub-Saharan Africa, maternal and perinatal mortality and morbidity are major problems. Service availability and quality of care in health facilities are heterogeneous and most often inadequate. In resource-poor settings, the facility-based maternal death review or audit is one of the most promising strategies to improve health service performance. We aim to explore and describe health workers' perceptions of facility-based maternal death reviews and to identify barriers to and facilitators of the implementation of this approach in pilot health facilities of Senegal.</p> <p>Methods</p> <p>This study was conducted in five reference hospitals in Senegal with different characteristics. Data were collected from focus group discussions, participant observations of audit meetings, audit documents and interviews with the staff of the maternity unit. Data were analysed by means of both quantitative and qualitative approaches.</p> <p>Results</p> <p>Health professionals and service administrators were receptive and adhered relatively well to the process and the results of the audits, although some considered the situation destabilizing or even threatening. The main barriers to the implementation of maternal deaths reviews were: (1) bad quality of information in medical files; (2) non-participation of the head of department in the audit meetings; (3) lack of feedback to the staff who did not attend the audit meetings. The main facilitators were: (1) high level of professional qualifications or experience of the data collector; (2) involvement of the head of the maternity unit, acting as a moderator during the audit meetings; (3) participation of managers in the audit session to plan appropriate and realistic actions to prevent other maternal deaths.</p> <p>Conclusion</p> <p>The identification of the barriers to and the facilitators of the implementation of maternal death reviews is an essential step for the future adaptation of this method in countries with few resources. We recommend for future implementation of this method a prior enhancement of the perinatal information system and initial training of the members of the audit committee – particularly the data collector and the head of the maternity unit. Local leadership is essential to promote, initiate and monitor the audit process in the health facilities.</p