Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

IMPLICIT NONLINEAR NORMAL MODE INITIALIZATION FOR A BAROTROPIC PRIMITIVE EQUATION LIMITED AREA MODEL

A simple version of implicit nonlinear normal mode initialization is applied to a limited area one-level primitive equation model over a tropical domain. The model formulation is based on shallow water equations in spherical co-ordinate and potential enstrophy conserving finite difference scheme is employed. The model is used for predicting the movement of a typical monsoon depression formed over the Bay of Bengal. The above scheme is found to be very effective as it requires only three iterations for attaining balance between the mass and wind tields. However this model is not able to predict the movement of the depression very ac-curately due to the limitations of such a one-level model.

Impulsfluss an vertikalen Wänden – Messung und Parametrisierung

<p>Der globale Klimawandel hat einen großen Einfluss auf das städtische Klima, wobei sich durch die hohe Bebauungsdichte und Versiegelung viele Effekte wie Hitzewellen zusätzlich verstärken. Damit unsere Städte auch in Zukunft lebenswerte Orte bleiben, müssen diese an die veränderten klimatischen Bedingungen angepasst werden. Um diese Anforderungen umzusetzen, können dank der gestiegenen Rechenkapazitäten vermehrt wirbel- und gebäudeauflösende Large-Eddy-Simulations-(LES) Modelle wie das PALM-4U (Maronga et al., 2015) in der Praxis zur Stadtplanung eingesetzt werden. Die in diesen Modellen verwendeten Annahmen und Parametrisierungen zum Windprofil sowie Impulsfluss an vertikalen Wänden von Gebäuden basieren jedoch mangels geeigneter Daten zumeist auf Grenzschichtmessungen über nahezu homogenen Flächen (Businger, 1971). Daher stellt sich die Frage, wie gut diese Annahmen an vertikalen Wänden zutreffen. Wie sehen das Windprofil und der Impulsfluss an einer realen Fassade aus?</p> <p>Zur Untersuchung dieser Fragestellungen wurden im Rahmen des „Stadtklima im Wandel [UC]<sup>2</sup>“ Projektes zwei 6 m lange Ausleger in etwa 42 m (10. Stock) und 64 m (16. Stock) Höhe an der Fassade eines insgesamt 85 m hohen Gebäudes im Zentrum von Hamburg installiert. Um detaillierte Informationen zur Turbulenz zu erhalten, werden an beiden Auslegern in 2 m, 4 m und 6 m Entfernung zur Fassade die drei Windkomponenten mit 20 Hz erfasst. Die Messungen werden seit August 2021 durchgeführt, sodass unterschiedlichste Anströmungsrichtungen des Gebäudes als auch zahlreiche synoptische Situationen von schwachem bis stärkeren Wind gemessen wurden.</p> <p>Der einzigartige Messdatensatz an einer realen Hochhausfassade liefert detaillierte Einblicke in das Windprofil sowie den Impulsfluss an Gebäuden in Städten. Dies ermöglicht die Untersuchung der aktuell in vielen LES Modellen genutzten Annahmen wie zum Beispiel des logarithmischen Windprofils an Fassaden. Darüber hinaus wird die im PALM‑4U Modell verwendete Parametrisierung für den Impulsfluss mit den Messungen verglichen. Die Form des Windprofils an der Fassade ist unter anderem von der Anströmungsrichtung, der Geometrie sowie der Messposition am Gebäude abhängig. Die Turbulenzintensität nimmt unabhängig der Anströmung in allen drei Komponenten mit größerem Abstand zur Fassade hin ab. Die Ergebnisse werden in Hinblick auf verbesserte Parametrisierungen in Modellen diskutiert.</p> <p> </p> <p><strong>Literatur:</strong></p> <p>Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux-Profile Relationships in the Atmospheric Surface Layer’, <em>J. Atmos. Sci.</em> 28, 181–189.</p> <p>Maronga, B., Gryschka, M., Heinze, R., Hoffmann, F., Kanani-Sühring, F., Keck, M., Ketelsen, K., Letzel, M. O., Sühring, M., and Raasch, S. (2015): The Parallelized Large-Eddy Simulation Model (PALM) version 4.0 for atmospheric and oceanic flows: model formulation, recent developments, and future perspectives, Geosci. Model Dev., 8, 1539-1637, DOI:10.5194/gmd-8-2515-2015.</p>

The analysis of hepatitis B virus (HBV) transmission using an epidemic model

In this article, we propose an epidemic problem of hepatitis B with vaccination. So to do this, first we presents the model formulation and prove that the solutions are bounded and positive. We obtain the disease free equilibrium and calculate the basic reproduction number (R0). The reproductive number will be used to find the endemic state of the model. We discuss the qualitative analysis of the proposed problem and show that whenever, R0 < 1 then the disease free equilibrium is stable locally and globally. Moreover, whenever, R0 > 1, then the endemic state is asymptotically stable. We derive sufficient conditions for both the equilibria and its stabilities. Further more numerical simulation are carried out to illustrate the feasibility of the obtained results and verified that with actual data, we are in the position to put down the hepatitis B infection form the community. We also highlight the role of epidemic parameters in the disease propagation. Our numerical works verified the analytical results. Finally some important conclusion are given at the end of the article.

Maximizing gerrymandering through ising model optimization

By using the Ising model formulation for combinatorial optimization with 0–1 binary variables, we investigated the extent to which partisan gerrymandering is possible from a random but even distribution of supporters. Assuming that an electoral district consists of square subareas and that each subarea shares at least one edge with other subareas in the district, it was possible to find the most tilted assignment of seats in most cases. However, in cases where supporters' distribution included many enclaves, the maximum tilted assignment was usually found to fail. We also discussed the proposed algorithm is applicable to other fields such as the redistribution of delivery destinations.

Supplemental Material: Magmatic sill formation during dike opening

Detailed information on the model formulation and additional modeling results with alternative initial conditions.<br>

Design of Sustainable Renewable-Based Utility Plants in the Face of Uncertainty

This work presents the formulation of a two-stage stochastic mixed-integer linear programming (MILP) model to include uncertainty in the design of renewable-based utility plants. The model is based on a superstructure that integrates technologies to process biomass, waste, solar radiation, and wind and considers uncertainty in availability of the renewable resources and on the utility demands. The uncertain parameter space is calculated based on a monthly probability density function for each uncertain parameter and discretized into different levels. It is shown that as uncertainty is considered in the model formulation, design flexibility improves with respect to the deterministic-based designs, although the flexibility is achieved at the expense of higher underused facilities and therefore unused investment cost.