On rational boundary conditions for higher-order long-wave models

Higher-order corrections to classical long-wave theories enable simple and efficient modelling of the onset of wave dispersion and size effects produced by underlying micro-structure. Since such models feature higher spatial derivatives, one needs to formulate additional boundary conditions when confined to bounded domains. There is a certain controversy associated with these boundary conditions, because it does not seem possible to justify their choice by purely physical considerations. In this paper an asymptotic model for onedimensional chain of particles is chosen as an exemplary higher-order theory. We demonstrate how the presence of higher-order derivative terms results in the existence of non-physical “extraneous” boundary layer-type solutions and argue that the additional boundary conditions should generally be formulated to eliminate the contribution of these boundary layers into the averaged solution. Several new methods of deriving additional boundary conditions are presented for essential boundary. The results are illustrated by numerical examples featuring comparisons with an exact solution for the finite chain

Nonlinear Supersymmetry as a Hidden Symmetry

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QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe

Metamorphic testing and its applications

The phases in magnetic materials can be studied ultrasonically. Magnetic phase transition points can be determined from discontinuities in ultrasonic velocity as a function of temperature. Conventionally this is done using piezoelectric transducers (normally quartz) pulsed with a tone burst generator. Very accurate velocity measurements are required as the change in velocity is typically 1 part in 104 [1]. A common problem experienced with contacting transducers is the fracturing of the acoustic couplant bond at low temperatures. Non-contacting acoustic techniques have no problems with bond failure, electromagnetic acoustic transducers (EMATs) can be used for measurements on rare earth magnetic materials

Lanthanide contraction and magnetism in the heavy rare earth elements

The heavy rare earth elements crystallize into hexagonally close packed ( h. c. p.) structures and share a common outer electronic configuration, differing only in the number of 4f electrons they have(1). These chemically inert 4f electrons set up localized magnetic moments, which are coupled via an indirect exchange interaction involving the conduction electrons. This leads to the formation of a wide variety of magnetic structures, the periodicities of which are often incommensurate with the underlying crystal lattice(2). Such incommensurate ordering is associated with a 'webbed' topology(3,4) of the momentum space surface separating the occupied and unoccupied electron states ( the Fermi surface). The shape of this surface - and hence the magnetic structure - for the heavy rare earth elements is known to depend on the ratio of the interplanar spacing c and the interatomic, intraplanar spacing a of the h. c. p. lattice(5). A theoretical understanding of this problem is, however, far from complete. Here, using gadolinium as a prototype for all the heavy rare earth elements, we generate a unified magnetic phase diagram, which unequivocally links the magnetic structures of the heavy rare earths to their lattice parameters. In addition to verifying the importance of the c/a ratio, we find that the atomic unit cell volume plays a separate, distinct role in determining the magnetic properties: we show that the trend from ferromagnetism to incommensurate ordering as atomic number increases is connected to the concomitant decrease in unit cell volume. This volume decrease occurs because of the so-called lanthanide contraction(6), where the addition of electrons to the poorly shielding 4f orbitals leads to an increase in effective nuclear charge and, correspondingly, a decrease in ionic radii