Action minimizing fronts in general FPU-type chains

We study atomic chains with nonlinear nearest neighbour interactions and prove the existence of fronts (heteroclinic travelling waves with constant asymptotic states). Generalizing recent results of Herrmann and Rademacher we allow for non-convex interaction potentials and find fronts with non-monotone profile. These fronts minimize an action integral and can only exists if the asymptotic states fulfil the macroscopic constraints and if the interaction potential satisfies a geometric graph condition. Finally, we illustrate our findings by numerical simulations.Comment: 19 pages, several figure

Nonlinear weakly curved rod by Γ-Convergence

We present a nonlinear model of weakly curved rod, namely the type of curved rod where the curvature is of the order of the diameter of the cross-section. We use an approach analogous to the one for rods and curved rods and start from the strain energy functional of three dimensional nonlinear elasticity. We do not impose any constitutional behavior of the material and work in a general framework. To derive the model, by means of Γ-convergence, we need to set the order of strain energy (i.e., its relation to the thickness of the body h). We analyze the situation when the strain energy (divided by the order of volume) is of the order h 4. This is the same approach as the one used in Föppl-von Kármán model for plates and the analogous model for rods. The obtained model is analogous to Marguerre-von Kármán for shallow shells and its linearization is the linear shallow arch model which can be found in the literature

A Study Of A New Class Of Discrete Nonlinear Schroedinger Equations

A new class of 1D discrete nonlinear Schr${\ddot{\rm{o}}}$dinger Hamiltonians with tunable nonlinerities is introduced, which includes the integrable Ablowitz-Ladik system as a limit. A new subset of equations, which are derived from these Hamiltonians using a generalized definition of Poisson brackets, and collectively refered to as the N-AL equation, is studied. The symmetry properties of the equation are discussed. These equations are shown to possess propagating localized solutions, having the continuous translational symmetry of the one-soliton solution of the Ablowitz-Ladik nonlinear Schr${\ddot{\rm{o}}}$dinger equation. The N-AL systems are shown to be suitable to study the combined effect of the dynamical imbalance of nonlinearity and dispersion and the Peierls-Nabarro potential, arising from the lattice discreteness, on the propagating solitary wave like profiles. A perturbative analysis shows that the N-AL systems can have discrete breather solutions, due to the presence of saddle center bifurcations in phase portraits. The unstaggered localized states are shown to have positive effective mass. On the other hand, large width but small amplitude staggered localized states have negative effective mass. The collison dynamics of two colliding solitary wave profiles are studied numerically. Notwithstanding colliding solitary wave profiles are seen to exhibit nontrivial nonsolitonic interactions, certain universal features are observed in the collison dynamics. Future scopes of this work and possible applications of the N-AL systems are discussed.Comment: 17 pages, 15 figures, revtex4, xmgr, gn

DEVELOPMENT OF QGIS PLUGIN FOR URBAN ENERGY SIMULATION USING 3D CITY MODEL AT THE CITY DISTRICT LEVEL

In the context of climate change, the increasing demand for energy-efficient buildings and sustainable urban development has become a pressing issue due to the significant proportion of global energy consumption and carbon dioxide (CO2) emissions attributable to the building sector. This requires a concerted effort to reduce its environmental impact, and Geographic Information System (GIS) applications are vital tools for achieving this by optimizing heat supply, calculating costs, analyzing profitability, and balancing CO2 emissions. This study aims to address the challenge of achieving energy efficiency and reducing CO2 emissions in the building sector, specifically at the district level. To this end, the research objective is to develop a QGIS plugin that can simulate urban energy demand at the district level by integrating 2D data with CityGML files and connecting QGIS to SimStadt software via API to visualize the simulated urban energy results in 3D on the Web Globe. The proposed plugin leverages the open-source QGIS tool QField to capture building conditions and connect 2D and 3D data on urban energy simulation. Supplementary to this, this plugin provides up-to-date information on energy demand, consumption, CO2 emissions, building component conditions via updating related tables in the database. Decision-makers can use this comprehensive and user-friendly tool to understand and act on the results, ultimately leading to a CO2-neutral district by 2045. The development of the QGIS plugin represents a significant step towards sustainable urban development and climate change mitigation by utilizing GIS applications for optimizing energy demand and reducing CO2 emissions in the built environment

On the commutability of homogenization and linearization in finite elasticity

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density

Modernizing geospatial services: an investigation into modern OGC API implementation and comparative analysis with traditional standards in a web application

The study explores the transition from traditional geospatial service standards to modern Open Geospatial Consortium (OGC) API standards in web applications, focusing on urban development management. The main goal is to compare the performance and practical implications of integrating modern and traditional geospatial technologies. Two prototype system architectures were formulated based on the underlying principle of three-tier architectures. Database operations were facilitated by PostgreSQL (PostGIS), while server-side functionalities employed GeoServer and pygeoapi for data publication and OpenLayers served as the frontend for data visualization. The primary data source for this study is ALKIS (Authoritative Real Estate Cadastre Information System of Germany). The investigation encompasses two principal facets: a theoretical evaluation of two distinct server implementations utilizing conventional standards (GeoServer) and contemporary standards (pygeoapi), alongside a practical testing phase. Theoretical comparisons underscore GeoServer’s robustness, well-established user base, and comprehensive feature set, along with its highly efficient folder structure and detailed, user-friendly documentation. In contrast, pygeoapi is characterized by its emphasis on simplicity and utilization of modern technologies such as OpenAPI for implementing a RESTful API. During hands-on testing, it was observed that pygeoapi consistently exhibited longer rendering times than GeoServer. Moreover, as the feature count increased, both platforms showed a linear escalation in rendering times. To address prolonged rendering times in pygeoapi, incorporating vector tiles led to a significant reduction in rendering times. Regarding the affect of different data format, PostgreSQL (PostGIS) consistently outperforms other data formats used in pygeoapi, while Shapefile and PostgreSQL (PostGIS) perform well in GeoServer. This research aims to effectively integrate geospatial technologies, bridging the gap between established standards and emerging APIs in web applications

Shape programming for narrow ribbons of nematic elastomers

Using the theory of Γ-convergence, we derive from three-dimensional elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e., ribbons exhibiting spontaneous curvature and twist. We apply the models to shape-selection problems for thin films of nematic elastomers with twist and splay-bend texture of the nematic director. For the former, we discuss the possibility of helicoid-like shapes as an alternative to spiral ribbons