A comparison of two magnetic ultra-cold neutron trapping concepts using a Halbach-octupole array

This paper describes a new magnetic trap for ultra-cold neutrons (UCNs) made from a 1.2 m long Halbach-octupole array of permanent magnets with an inner bore radius of 47 mm combined with an assembly of superconducting end coils and bias field solenoid. The use of the trap in a vertical, magneto-gravitational and a horizontal setup are compared in terms of the effective volume and ability to control key systematic effects that need to be addressed in high precision neutron lifetime measurements

One parameter family of Compacton Solutions in a class of Generalized Korteweg-DeVries Equations

We study the generalized Korteweg-DeVries equations derivable from the Lagrangian: $L(l,p) = \int \left( \frac{1}{2} \varphi_{x} \varphi_{t} - { {(\varphi_{x})^{l}} \over {l(l-1)}} + \alpha(\varphi_{x})^{p} (\varphi_{xx})^{2} \right) dx,$ where the usual fields $u(x,t)$ of the generalized KdV equation are defined by $u(x,t) = \varphi_{x}(x,t)$. For $p$ an arbitrary continuous parameter $0< p \leq 2 ,l=p+2$ we find compacton solutions to these equations which have the feature that their width is independent of the amplitude. This generalizes previous results which considered $p=1,2$. For the exact compactons we find a relation between the energy, mass and velocity of the solitons. We show that this relationship can also be obtained using a variational method based on the principle of least action.Comment: Latex 4 pages and one figure available on reques

Solitary Waves and Compactons in a class of Generalized Korteweg-DeVries Equations

We study the class of generalized Korteweg-DeVries equations derivable from the Lagrangian: L(l,p) = \int \left( \frac{1}{2} \vp_{x} \vp_{t} - { {(\vp_{x})^{l}} \over {l(l-1)}} + \alpha(\vp_{x})^{p} (\vp_{xx})^{2} \right) dx, where the usual fields $u(x,t)$ of the generalized KdV equation are defined by u(x,t) = \vp_{x}(x,t). This class contains compactons, which are solitary waves with compact support, and when $l=p+2$, these solutions have the feature that their width is independent of the amplitude. We consider the Hamiltonian structure and integrability properties of this class of KdV equations. We show that many of the properties of the solitary waves and compactons are easily obtained using a variational method based on the principle of least action. Using a class of trial variational functions of the form $u(x,t) = A(t) \exp \left[-\beta (t) \left|x-q(t) \right|^{2n} \right]$ we find soliton-like solutions for all $n$, moving with fixed shape and constant velocity, $c$. We show that the velocity, mass, and energy of the variational travelling wave solutions are related by $c = 2 r E M^{-1}$, where $r = (p+l+2)/(p+6-l)$, independent of $n$.\newline \newline PACS numbers: 03.40.Kf, 47.20.Ky, Nb, 52.35.SbComment: 16 pages. LaTeX. Figures available upon request (Postscript or hard copy

Symmetries of a class of nonlinear fourth order partial differential equations

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations \be u_{tt} = \left(\kappa u + \gamma u^2\right)_{xx} + u u_{xxxx} +\mu u_{xxtt}+\alpha u_x u_{xxx} + \beta u_{xx}^2, \ee where $\alpha$, $\beta$, $\gamma$, $\kappa$ and $\mu$ are constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a ``Boussinesq-type'' equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both ``compacton'' and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are no} obtainable through the classical method

Multi-soliton energy transport in anharmonic lattices

We demonstrate the existence of dynamically stable multihump solitary waves in polaron-type models describing interaction of envelope and lattice excitations. In comparison with the earlier theory of multihump optical solitons [see Phys. Rev. Lett. {\bf 83}, 296 (1999)], our analysis reveals a novel physical mechanism for the formation of stable multihump solitary waves in nonintegrable multi-component nonlinear models.Comment: 4 pages, 4 figure

A Cerberus‐Inspired Anti‐Infective Multicomponent Gatekeeper Hydrogel against Infections with the Emerging “Superbug” Yeast Candida auris

The pathogenic yeast Candida auris has received increasing attention due to its ability to cause fatal infections, its resistance toward important fungicides, and its ability to persist on surfaces including medical devices in hospitals. To brace health care systems for this considerable risk, alternative therapeutic approaches such as antifungal peptides are urgently needed. In clinical wound care, a significant focus has been directed toward novel surgical (wound) dressings as first defense lines against C. auris. Inspired by Cerberus the Greek mythological “hound of Hades” that prevents the living from entering and the dead from leaving hell, the preparation of a gatekeeper hybrid hydrogel is reported featuring lectin-mediated high-affinity immobilization of C. auris cells from a collagen gel as a model substratum in combination with a release of an antifungal peptide drug to kill the trapped cells. The vision is an efficient and safe two-layer medical composite hydrogel for the treatment of severe wound infections that typically occur in hospitals. Providing this new armament to the repertoire of possibilities for wound care in critical (intensive care) units may open new routes to shield and defend patients from infections and clinical facilities from spreading and invasion of C. auris and probably other fungal pathogens

Ill-posedness of degenerate dispersive equations

In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation $u_t = (u^2)_{xxx} + (u^2)_{x}$ and the "degenerate Airy" equation $u_t = 2 u u_{xxx}$. For K(2,2) our results are computational in nature: we conduct a series of numerical simulations which demonstrate that data which is very small in $H^2$ can be of unit size at a fixed time which is independent of the data's size. For the degenerate Airy equation, our results are fully rigorous: we prove the existence of a compactly supported self-similar solution which, when combined with certain scaling invariances, implies ill-posedness (also in $H^2$)

Nonlinear Modes of Liquid Drops as Solitary Waves

The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such ``rotons'' were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to drop-like systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.Comment: 11 pages RevTex, 1 figure p