Solitons in combined linear and nonlinear lattice potentials

We study ordinary solitons and gap solitons (GSs) in the effectively one-dimensional Gross-Pitaevskii equation, with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of the (in)commensurability between the lattices, the development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices, the family of ordinary solitons is similar to its counterpart in the free space. The situation is different in the case of the subharmonic commensurability, with L_{lin}=(1/2)L_{nonlin}, or incommensurability. In those cases, there is an existence threshold for the solitons, and the scaling relation between their amplitude and width is different from that in the free space. GS families demonstrate a bistability, unless the direct commensurability takes place. Specific scaling relations are found for them too. Ordinary solitons can be readily set in motion by kicking. GSs are mobile too, featuring inelastic collisions. The analytical approximations are shown to be quite accurate, predicting correct scaling relations for the soliton families in different cases. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, while the stability of GS families follows an inverted ("anti-VK") criterion, which is explained by means of the averaging approximation.Comment: 9 pages, 6 figure

A Prototype for the PASS Permanent All Sky Survey

A prototype system for the Permanent All Sky Survey (PASS) project is presented. PASS is a continuous photometric survey of the entire celestial sphere with a high temporal resolution. Its major objectives are the detection of all giant-planet transits (with periods up to some weeks) across stars up to mag 10.5, and to deliver continuously photometry that is useful for the study of any variable stars. The prototype is based on CCD cameras with short focal length optics on a fixed mount. A small dome to house it at Teide Observatory, Tenerife, is currently being constructed. A placement at the antarctic Dome C is also being considered. The prototype will be used for a feasibility study of PASS, to define the best observing strategies, and to perform a detailed characterization of the capabilities and scope of the survey. Afterwards, a first partial sky surveying will be started with it. That first survey may be able to detect transiting planets during its first few hundred hours of operation. It will also deliver a data set around which software modules dealing with the various scientific objectives of PASS will be developed. The PASS project is still in its early phase and teams interested in specific scientific objectives, in providing technical expertise, or in participating with own observations are invited to collaborate.Comment: Accepted for Astronomische Nachrichten (special issue for 3rd Potsdam Thinkshop 'Robotic Astronomy' in July 2004). 4 pages, 4 fig

Modelling biological invasions: individual to population scales at interfaces

Extracting the population level behaviour of biological systems from that of the individual is critical in understanding dynamics across multiple scales and thus has been the subject of numerous investigations. Here, the influence of spatial heterogeneity in such contexts is explored for interfaces with a separation of the length scales characterising the individual and the interface, a situation that can arise in applications involving cellular modelling. As an illustrative example, we consider cell movement between white and grey matter in the brain which may be relevant in considering the invasive dynamics of glioma. We show that while one can safely neglect intrinsic noise, at least when considering glioma cell invasion, profound differences in population behaviours emerge in the presence of interfaces with only subtle alterations in the dynamics at the individual level. Transport driven by local cell sensing generates predictions of cell accumulations along interfaces where cell motility changes. This behaviour is not predicted with the commonly used Fickian diffusion transport model, but can be extracted from preliminary observations of specific cell lines in recent, novel, cryo-imaging. Consequently, these findings suggest a need to consider the impact of individual behaviour, spatial heterogeneity and especially interfaces in experimental and modelling frameworks of cellular dynamics, for instance in the characterisation of glioma cell motility

Experimental study of Taylor's hypothesis in a turbulent soap film

An experimental study of Taylor's hypothesis in a quasi-two-dimensional turbulent soap film is presented. A two probe laser Doppler velocimeter enables a non-intrusive simultaneous measurement of the velocity at spatially separated points. The breakdown of Taylor's hypothesis is quantified using the cross correlation between two points displaced in both space and time; correlation is better than 90% for scales less than the integral scale. A quantitative study of the decorrelation beyond the integral scale is presented, including an analysis of the failure of Taylor's hypothesis using techniques from predictability studies of turbulent flows. Our results are compared with similar studies of 3D turbulence.Comment: 27 pages, + 19 figure

Light and Shadows over Petra: astronomy and landscape in Nabataean lands

The Nabateans built several monuments in Petra and elsewhere displaying a decoration with a preference for astronomical motifs, possibly as a reflection of their religion. However, due to the lack of direct written accounts and the scarcity of inscriptions we do not have a clear knowledge on the precise nature of such believes and how these reflected on the calendar or the religious time-keeping system of this ancient society. A statistical analysis of the orientation of their sacred monuments demonstrates that astronomical orientations were often part of an elaborated plan and possibly a trace of the astral nature of Nabataean religion. Petra and other monuments in the ancient Nabataean kingdom have proven to be marvellous laboratories of the interaction between landscape features and astronomical events showing impressive hierophanies on particular monuments related to cultic times and worships. Among other findings, the famous Ad Deir has shown a fascinating ensemble of light and shadow effects, perhaps connected with the bulk of Nabataean mythology, while from the impressive Urn tomb, a series of suggestive solstitial and equinoctial alignments emanate which might have lately helped its selection as the cathedral of the city. This paper demonstrates that the sky was a substantial element on Nabataean religion and reveals new evidence for cultic worship centred on the celestial sphere.Comment: 13 pages, 8 figures, Accepted for publication in Nexus Network Journal (2013

Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves

Tissue distribution of mercury and its relationship with selenium in atlantic bluefin tuna (Thunnus thynnus l.)

Mercury (Hg) is an important heavy metal to consider in marine predators, while selenium (Se) has a natural antagonistic effect on this metal in fish. The Atlantic bluefin tuna (ABFT, Thunnus thynnus) is a pelagic top-level predator of the trophic web and their Hg muscular content is an object of concern in food safety. Nevertheless, little is known about levels of this metal in remaining tissues, which may be important as by-product source, and its relationship with Se. Thus, concentration of both elements in liver, kidney, brain, gill and bone, in addition to muscle, of ABFT were determined. The kidney was the tissue with the highest concentration of Hg (Total-Hg, THg) and Se, and the Se/THg concentration ratio was similar in all tissues, except bone and muscle. The Selenium Health Benefit Value (HBVSe ) was positive in each specimen and tissue, indicating that the Se plays an important role against Hg not only in the muscle. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.Preprin

Oscillations of a solid sphere falling through a wormlike micellar fluid

We present an experimental study of the motion of a solid sphere falling through a wormlike micellar fluid. While smaller or lighter spheres quickly reach a terminal velocity, larger or heavier spheres are found to oscillate in the direction of their falling motion. The onset of this instability correlates with a critical value of the velocity gradient scale $\Gamma_{c}\sim 1$ s$^{-1}$. We relate this condition to the known complex rheology of wormlike micellar fluids, and suggest that the unsteady motion of the sphere is caused by the formation and breaking of flow-induced structures.Comment: 4 pages, 4 figure