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

Electron Beam Nano-Etching in Oxides, Fluorides, Metals and Semiconductors

Etching, lithography, hole formation, surface restructuring and external machining can all be performed on a nanometre scale using an intense electron beam. Results are presented for a range of different materials which demonstrate the variety of mechanisms by which electron beam nano-etching can occur. For example, in crystalline 13-alumina hole formation occurs by surface indentations growing inwards to join up and form a nanometre diameter hole. In amorphous alumina, on the other hand, hole formation is from the inside-out: oxygen gas bubbles form under the electron beam, coalesce, and burst to leave a well defined nanometre diameter hole. In MgO and Si, holes develop from the electron exit surface: whereas in Al voids form along the irradiated volume, leading eventually to the development of a hole at the electron entrance surface. The potential of electron beam nano-etching to lithography and information storage is demonstrated by showing that the entire contents of the Encyclopaedia Britannica can be written on a pinhead

Molecular tiling on the surface of a bacterial spore- the exosporium of the Bacillus anthracis/cereus/thuringiensis group.

Bacteria of the genera Bacillus and Clostridium form highly resistant spores, which in the case of some pathogens act as the infectious agents. An exosporium forms the outermost layer of some spores; it plays roles in protection, adhesion, dissemination, host targeting in pathogens, and germination control. The exosporium of the Bacillus cereus group, including the anthrax pathogen, contains a 2D-crystalline basal layer, overlaid by a hairy nap. BclA and related proteins form the hairy nap, and require ExsFA (BxpB) for their localisation on the basal layer. Until now, the identity of the main structural protein components of the basal layer were unknown. We demonstrate here that ExsY forms one of the essential components. Through heterologous expression in E. coli, we also demonstrate that ExsY can self-assemble into ordered 2D arrays that mimic the structure of the exosporium basal layer. Self-assembly is likely to play an important role in the construction of the exosporium. The ExsY array is stable to heat and chemical denaturants, forming a robust layer that would contribute to overall spore resistance. Our structural analysis also provides novel insight into the location of other molecular components anchored onto the exosporium, such as BclA and ExsFA. This article is protected by copyright. All rights reserved

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

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

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

Acetabular fractures following rugby tackles: a case series

<p>Abstract</p> <p>Introduction</p> <p>Rugby is the third most popular team contact sport in the world and is increasing in popularity. In 1995, rugby in Europe turned professional, and with this has come an increased rate of injury.</p> <p>Case presentation</p> <p>In a six-month period from July to December, two open reduction and internal fixations of acetabular fractures were performed in young Caucasian men (16 and 24 years old) who sustained their injuries after rugby tackles. Both of these cases are described as well as the biomechanical factors contributing to the fracture and the recovery. Acetabular fractures of the hip during sport are rare occurrences.</p> <p>Conclusion</p> <p>Our recent experience of two cases over a six-month period creates concern that these high-energy injuries may become more frequent as rugby continues to adopt advanced training regimens. Protective equipment is unlikely to reduce the forces imparted across the hip joint; however, limiting 'the tackle' to only two players may well reduce the likelihood of this life-altering injury.</p