Stability, mobility and power currents in a two-dimensional model for waveguide arrays with nonlinear coupling

A two-dimensional nonlinear Schrodinger lattice with nonlinear coupling, modelling a square array of weakly coupled linear optical waveguides embedded in a nonlinear Kerr material, is studied. We find that despite a vanishing energy difference (Peierls-Nabarro barrier) of fundamental stationary modes the mobility of localized excitations is very poor. This is attributed to a large separation in parameter space of the bifurcation points of the involved stationary modes. At these points the stability of the fundamental modes is changed and an asymmetric intermediate solution appears that connects the points. The control of the power flow across the array when excited with plane waves is also addressed and shown to exhibit great flexibility that may lead to applications for power-coupling devices. In certain parameter regimes, the direction of a stable propagating plane-wave current is shown to be continuously tunable by amplitude variation (with fixed phase gradient). More exotic effects of the nonlinear coupling terms like compact discrete breathers and vortices, and stationary complex modes with non-trivial phase relations are also briefly discussed. Regimes of dynamical linear stability are found for all these types of solutions.Comment: 31 pages, 12 figures, submitted to Physica D (21 September 2006, revised 23 April 2008

Tradition as asset or burden for transitions from forests as cropping systems to multifunctional forest landscapes: Sweden as a case study

Expectations of what forests and woodlands should provide vary among locations, stakeholder groups, and over time. Developing multifunctional forests requires understanding of the dynamic roles of traditions and cultural legacies in social-ecological systems at multiple levels and scales. Implementing policies about multifunctional forests requires a landscape and social-ecological perspective, and recognition of both spatial and temporal features at multiple scales. This study explores the dissemination of even-aged silviculture in central, eastern and northern Europe, and the consequences of choosing different vantage points in social-ecological systems for mapping of barriers, and to identify levers, towards multifunctional forest landscapes. Using a narrative approach, we first summarise the development of even-aged silviculture in four European regions. Next, we focus on Sweden as a keen adopter of even-aged silviculture, and identify levers at three groups of vantage points. They were (1) biosphere with biodiversity as short-hand for composition, structure and function of ecosystems, which support human well-being at multiple scales; (2) society in terms of different levels of stakeholder interactions from local to global, and (3) economy represented by value chain hierarchies and currencies. The emergence of even-aged silviculture >200 years ago formed an expanding frontier from central to northern Europe. Sustained yield wood production and biodiversity conservation encompass different portfolios of ecosystem aspects and spatio-temporal scales. Ignorance and lack of knowledge about these differences enforce their mutual rivalry. An exploratory review of six groups of stakeholders at multiple levels in the traditional industrial forest value chain highlights inequalities in terms of distribution of income and power across different levels of governance. This effectively marginalises other than powerful industrial actors. The distribution of financial results along the value chain is dynamic in space and time, and not all benefits of forest ecosystems can be measured using monetary valuation. There are also other currencies and incentives. A discussion of cultural trajectories in central and eastern European, Russian and Swedish forest management illustrates that forest history patterns repeat themselves. Longitudinal case studies of countries and regions can help foster holistic multi-dimensional and multilevel systems thinking. Application of deep levers of change is likely to require external drivers. A key challenge is to handle the manufacturing of doubt and decay of truth, i.e., the appearance of alternative facts, and the diminishing role of evidence and systems analyses in political and civic discourses. This transition is fuelled by new and rapidly evolving digital arenas

Communication breakdown : dissecting the COM interfaces between the subunits of nonribosomal peptide synthetases

Nonribosomal peptides are a structurally diverse and bioactive class of natural products constructed by multidomain enzymatic assembly lines known as nonribosomal peptide synthetases (NRPSs). While the core catalytic domains and even entire protein subunits of NRPSs have been structurally elucidated, little biophysical work has been reported on the docking domains that promote interactions—and thus transfer of biosynthetic intermediates—between subunits. In the present study, we closely examine the COM domains that mediate COMmunication between donor epimerization (E) and acceptor condensation (C) domains found at the termini of NRPS subunits. Through a combination of X-ray crystallography, circular dichroism spectroscopy, solution- and solid-state NMR spectroscopy, and molecular dynamics (MD) simulations, we provide direct evidence for an intrinsically disordered donor COM region that folds into a dynamic helical motif upon binding to a suitable acceptor. Furthermore, our NMR titration and carbene footprinting experiments illuminate the residues involved at the COM interaction interface, and our MD simulations demonstrate folding consistent with experimental data. Although our results lend credence to the previously proposed helix-hand mode of interaction, they also underscore the importance of viewing COM interfaces as dynamic ensembles rather than single rigid structures and suggest that engineering experiments should account for the interactions which transiently guide folding in addition to those which stabilize the final complex. Through activity assays and affinity measurements, we further substantiate the role of the donor COM region in binding the acceptor C domain and implicate this short motif as readily transposable for noncognate domain crosstalk. Finally, our bioinformatics analyses show that COM domains are widespread in natural product pathways and function at interfaces beyond the canonical type described above, setting a high priority for thorough characterization of these docking domains. Our findings lay the groundwork for future attempts to rationally engineer NRPS domain–domain interactions with the ultimate goal of generating bioactive molecules

Stability and Mobility of Localized and Extended Excitations in Nonlinear Schrödinger Models

This thesis is mainly concerned with the properties of some discrete nonlinear Schrödinger equations. These naturally arise in many different physical contexts as the limiting form of general dynamical lattice equations that incorporate nonlinearity and coupling. Interest is focused on theoretical models of coupled optical waveguides constructed from materials with a nonlinear index of refraction. In arrays of waveguides the overlap of the evanescent electric field of the modes in neighbouring waveguides provides a coupling and the nonlinearity of the material provides a mechanism to halt the discrete diffraction that otherwise would spread localized energy across the array. In particular, waveguide structures where also a nonlinear coupling is taken into account are studied. It is noted that the equation for the evolution of the complex amplitudes of the electric field along an array of waveguides also can be used to describe the dynamics of Bose-Einstein condensates trapped in a periodic optical potential. Possible excitations in arrays in both one and two dimensions are considered, with emphasis on the effects of the nonlinear coupling. Localized excitations are considered from the viewpoint of the theory of discrete breathers, or intrinsic localized modes, i.e., solutions of the dynamical equations that are periodic in time and have a spatial localization. The general theory of such solutions, that appear under very general circumstances in nonlinear lattice equations, is reviewed. In an array of waveguides this means that light can propagate along the array confined essentially to one or a few waveguides. In general a distinction is made between excitations that are centred on a waveguide, or site in the lattice, and excitations that are centred inbetween waveguides. Usually only the former give stable propagation. When the localized beam can be displaced to neighbouring waveguides the array can operate as an optical switch. With the inclusion of nonlinear coupling between the sites, as in the model derived in this thesis, the stability of the site-centred and bond-centred solutions can be exchanged. It is shown how this leads to the existence of highly localized mobile solutions that can propagate transversely in the one-dimensional array of waveguides. The inversion of stability of stationary solutions occurs also in the two-dimensional array, but in this setting it fails to give good mobility of localized excitations. The reason for this is also explained. In a two-dimensional lattice a discrete breather can have the form of a vortex. This means that the phase of the complex amplitude will vary on a contour around the excitation, such that the phase is increased by 2πS, where S is the topological charge, on the completion of one turn. Some ring-like vortex excitations are considered and in particular a stable vortex with S=2 is found. It is also noted that the effect of charge flipping, i.e., when the topological charge periodically changes between -S and S, is connected to the existence of quasiperiodic solutions. The nonlinear coupling of the waveguide model will also give rise to some more exotic and novel properties of localized solutions, e.g., discrete breathers with a nontrivial phase. When the linear coupling and the nonlinear coupling have opposite signs, there can be a decoupling in the lattice that allows for compact solutions. These localized excitations will have no decaying tail. Of interest is also the flexibility in controlling the transport of power across the array when it is excited with a nonlinear plane wave. It is shown how a change of the amplitude of a plane wave can affect the magnitude and direction of power flow in the array. Also the continuum limit of the one-dimensional discrete waveguide model is considered with an equation incorporating both nonlocal and nonlinear dispersion. In general continuum equations the balance between nonlinearity and dispersion can lead to the formation of localized travelling waves, or solitons. With nonlinear dispersion it is seen that these solitons can be nonanalytic and have discontinuous spatial derivatives. The emergence of short-wavelength instabilities due to the simultaneous presence of nonlocal and nonlinear dispersion is also explained

Architecture of the flexible tail tube of bacteriophage SPP1

Bacteriophage SPP1 is a double-stranded DNA virus of the Siphoviridae family that infects the bacterium Bacillus subtilis. This family of phages features a long, flexible, non-contractile tail that has been difficult to characterize structurally. Here, we present the atomic structure of the tail tube of phage SPP1. Our hybrid structure is based on the integration of structural restraints from solid-state nuclear magnetic resonance (NMR) and a density map from cryo-EM. We show that the tail tube protein gp17.1 organizes into hexameric rings that are stacked by flexible linker domains and, thus, form a hollow flexible tube with a negatively charged lumen suitable for the transport of DNA. Additionally, we assess the dynamics of the system by combining relaxation measurements with variances in density maps

Impact and development of an Open Web Index for open web search

Web search is a crucial technology for the digital economy. Dominated by a few gatekeepers focused on commercial success, however, web publishers have to optimize their content for these gatekeepers, resulting in a closed ecosystem of search engines as well as the risk of publishers sacrificing quality. To encourage an open search ecosystem and offer users genuine choice among alternative search engines, we propose the development of an Open Web Index (OWI). We outline six core principles for developing and maintaining an open index, based on open data principles, legal compliance, and collaborative technology development. The combination of an open index with what we call declarative search engines will facilitate the development of vertical search engines and innovative web data products (including, e.g., large language models), enabling a fair and open information space. This framework underpins the EU-funded project OpenWebSearch.EU, marking the first step towards realizing an Open Web Index