Interaction of matter-wave gap solitons in optical lattices

We study mobility and interaction of gap solitons in a Bose-Einstein condensate (BEC) confined by an optical lattice potential. Such localized wavepackets can exist only in the gaps of the matter-wave band-gap spectrum and their interaction properties are shown to serve as a measure of discreteness imposed onto a BEC by the lattice potential. We show that inelastic collisions of two weakly localized near-the-band-edge gap solitons provide simple and effective means for generating strongly localized in-gap solitons through soliton fusion.Comment: 12 pages, 7 figure

Discrete Nonlinear Schrodinger Equations Free of the Peierls-Nabarro Potential

We derive a class of discrete nonlinear Schr{\"o}dinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is demonstrated that the derived class of discretizations contains subclasses conserving classical norm or a modified norm and classical momentum. These equations are interesting from the physical standpoint since they support stationary discrete solitons free of the Peierls-Nabarro potential. As a consequence, even in highly-discrete regimes, solitons are not trapped by the lattice and they can be accelerated by even weak external fields. Focusing on the cubic nonlinearity we then consider a small perturbation around stationary soliton solutions and, solving corresponding eigenvalue problem, we (i) demonstrate that solitons are stable; (ii) show that they have two additional zero-frequency modes responsible for their effective translational invariance; (iii) derive semi-analytical solutions for discrete solitons moving at slow speed. To highlight the unusual properties of solitons in the new discrete models we compare them with that of the classical DNLS equation giving several numerical examples.Comment: Misprints noticed in the journal publication are corrected [in Eq. (1) and Eq. (34)

Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps

We study the dynamics of one-dimensional solitons in the attractive and repulsive Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is \emph{negative}. This gives rise to a prediction for the experiment: such a soliton cannot be not held by the usual parabolic trap, but it can be captured (performing harmonic oscillations) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton a in long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to the interaction with the OL. At a late stage, the damped motion becomes chaotic. We also investigate the evolution of a two-soliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or anti-trap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negative-mass soliton in the anti-trap implies that a bright optical soliton in a self-defocusing medium with a periodic structure of the refractive index may be stable in an anti-waveguide.Comment: 22pages, 9 figures, submitted to Journal of Physics

A review of modelling methodologies for flood source area (FSA) identification

Flooding is an important global hazard that causes an average annual loss of over 40 billion USD and affects a population of over 250 million globally. The complex process of flooding depends on spatial and temporal factors such as weather patterns, topography, and geomorphology. In urban environments where the landscape is ever-changing, spatial factors such as ground cover, green spaces, and drainage systems have a significant impact. Understanding source areas that have a major impact on flooding is, therefore, crucial for strategic flood risk management (FRM). Although flood source area (FSA) identification is not a new concept, its application is only recently being applied in flood modelling research. Continuous improvements in the technology and methodology related to flood models have enabled this research to move beyond traditional methods, such that, in recent years, modelling projects have looked beyond affected areas and recognised the need to address flooding at its source, to study its influence on overall flood risk. These modelling approaches are emerging in the field of FRM and propose innovative methodologies for flood risk mitigation and design implementation; however, they are relatively under-examined. In this paper, we present a review of the modelling approaches currently used to identify FSAs, i.e. unit flood response (UFR) and adaptation-driven approaches (ADA). We highlight their potential for use in adaptive decision making and outline the key challenges for the adoption of such approaches in FRM practises

The IAHS Science for Solutions decade, with Hydrology Engaging Local People IN one Global world (HELPING)

The new scientific decade (2023-2032) of the International Association of Hydrological Sciences (IAHS) aims at searching for sustainable solutions to undesired water conditions – whether it be too little, too much or too polluted. Many of the current issues originate from global change, while solutions to problems must embrace local understanding and context. The decade will explore the current water crises by searching for actionable knowledge within three themes: global and local interactions, sustainable solutions and innovative cross-cutting methods. We capitalise on previous IAHS Scientific Decades shaping a trilogy; from Hydrological Predictions (PUB) to Change and Interdisciplinarity (Panta Rhei) to Solutions (HELPING). The vision is to solve fundamental water-related environmental and societal problems by engaging with other disciplines and local stakeholders. The decade endorses mutual learning and co-creation to progress towards UN sustainable development goals. Hence, HELPING is a vehicle for putting science in action, driven by scientists working on local hydrology in coordination with local, regional, and global processes