In this work, we carry out an analytical and numerical investigation of travelling waves representing arced vegetation patterns on sloped terrains. These patterns are reported to appear also in ecosystems which are not water deprived; therefore, we study the hypothesis that their appearance is due to plant–soil negative feedback, namely due to biomass-(auto)toxicity interactions.

To this aim, we introduce a reaction-diffusion-advection model describing the dynamics of vegetation biomass and toxicity which includes the effect of sloped terrains on the spatial distribution of these variables. Our analytical investigation shows the absence of Turing patterns, whereas travelling waves (moving uphill in the slope direction) emerge. Investigating the corresponding dispersion relation, we provide an analytic expression for the asymptotic speed of the wave. Numerical simulations not only just confirm this analytical quantity but also reveal the impact of toxicity on the structure of the emerging travelling pattern.

Our analysis represents a further step in understanding the mechanisms behind relevant plants‘ spatial distributions observed in real life. In particular, since vegetation patterns (both stationary and transient) are known to play a crucial role in determining the underlying ecosystems’ resilience, the framework presented here allows us to better understand the emergence of such structures to a larger variety of ecological scenarios and hence improve the relative strategies to ensure the ecosystems’ resilience.

We consider a generalization of the well-known nonlinear Nicholson blowflies model with stochastic perturbations. Stability in probability of the positive equilibrium of the considered equation is studied. Two types of stability conditions: delay-dependent and delay-independent conditions are obtained, using the method of Lyapunov functionals and the method of linear matrix inequalities. The obtained results are illustrated by numerical simulations by means of some examples. The results are new, and complement the existing ones.

The rapid formation of supermassive black holes (SMBHs) at high redshifts is still a puzzle. One hypothesis is that intermediate-mass black holes (IMBHs) serve as seeds for their formation, which could arise from hierarchical mergers in dense star clusters. There are two possible pathways for IMBH formation: 1) very massive stars may form in young star clusters, such as Pop3 clusters, and evolve into IMBHs within a few million years; 2) multiple stellar-mass black holes can merge into IMBHs in dense nuclear star clusters. Detailed insights into these scenarios can be obtained through high-resolution star-by-star simulations of dense star clusters. Furthermore, upcoming observations of faint quasars, nuclear star clusters, and Pop3 stars with the James Webb Space Telescope (JWST) will offer valuable data to constrain theoretical models and deepen our understanding of the rapid formation of SMBHs.

The gravitational lensing signal produced by a galaxy or a galaxy cluster is determined by its total matter distribution, providing us with a way to directly constrain their dark matter content. State-of-the-art numerical simulations successfully reproduce many observed properties of galaxies and can be used as a source of mock observations and predictions. Many gravitational lensing studies aim at constraining the nature of dark matter, discriminating between cold dark matter and alternative models. However, many past results are based on the comparison to simulations that did not include baryonic physics. Here we show that the presence of baryons can significantly alter the predictions: we look at the structural properties (profiles and shapes) of elliptical galaxies and at the inner density slope of subhaloes. Our results demonstrate that future simulations must model the interplay between baryons and alternative dark matter, to generate realistic predictions that could significantly modify the current constraints.

We introduce an approach and a software tool for solving coupled energy networks composed of gas and electric power networks. Those networks are coupled to stochastic fluctuations to address possibly fluctuating demand due to fluctuating demands and supplies. Through computational results, the presented approach is tested on networks of realistic size.

We study the effect of minor mergers on star formation using simulations. We use GADGET4 code which has both collisionless and hydrodynamical particles. Our goal is to establish a relation between gas percentage present in the galaxies and the star formation in the merged galaxy. We use 1:10 minor mergers and we run the isolated simulations with varying gas percentages in the primary galaxy. We observe that the gas particles convert into stars due to the impact of the minor merger. As the gas percentage increases in the primary disk of the galaxy, more number of stars are formed. We also observed that newly formed star particles settle down in the disk of the primary galaxy and increase the thickness of the disk. We also observe that the thickness of the stellar disk containing the old stars also increases due to the impact of the merger.

Porous materials have many applications for laser–matter interaction experiments related to inertial confinement fusion. Obtaining new knowledge about the properties of the laser-produced plasma of porous media is a challenging task. In this work, we report, for the first time to the best of our knowledge, the time-dependent measurement of the reflected light of a terawatt laser pulse from the laser-produced plasma of low-Z foam material of overcritical density. The experiments have been performed with the ABC laser, with targets constituted by foam of overcritical density and by solid media of the same chemical composition. We implemented in the MULTI-FM code a model for the light reflection to reproduce and interpret the experimental results. Using the simulations together with the experimental results, we indicate a criterion for estimating the homogenization time of the laser-produced plasma, whose measurement is challenging with direct diagnostic techniques and still not achieved.

The 1717 Christmas flood is one of the most catastrophic storm surges the Frisian coast (Netherlands and Germany) has ever experienced. With more than 13,700 casualties it is the last severe storm surge with a death toll of this order. At the same time, little is known about the hydrodynamic conditions and the morphological effects associated with this storm surge.

In this study, 41 potential dyke failures in the Province of Groningen (Netherlands) associated with the 1717 Christmas flood were systematically reconstructed and mapped by using historical maps and literature and by analysing the recent topography in search of typical pothole structures and sediment fans. The dimensions of the sediment fans as derived from the topography show a good accordance with the dimensions documented by vibracore profiles, direct push tests and electrical resistivity tomography data taken at three fieldwork sites. Moreover, the fan dimensions closely agree with the dimensions as simulated using a process-based morphodynamic numerical model for one of the three sites, the village of Wierhuizen. Consequently, the recent topography is still indicative for the locations and dimensions of dyke failures and sediment fans associated with the 1717 Christmas flood. Considering the large number of detected dyke failures (41) and the large dimensions of the potholes and particularly of the sediment fans up to a few hundred metres wide and up to 0.7 m thick, this study proves significant morphological effects of the 1717 Christmas flood on the mainland of the Province of Groningen.

Based on the numerical simulation approach and the comparison with field data and field observations, a maximum seaward water level of 5 m NAP for the dyke failure at Wierhuizen during the Christmas flood can be derived. A similar maximum water level is indicated for the two other fieldwork sites Vierhuizen and Kohol, which is in good agreement with the maximum storm surge level of 4.62 m NAP historically documented for the city of Emden located almost 50 km to the east of Wierhuizen.

The results of the current study demonstrate that the reconstruction of historical dyke failures based on (i) historical sources, (ii) recent lidar/high-resolution topographical data, (iii) multi-proxy sedimentary field data and (iv) hydro- and morphodynamic numerical simulations is a highly promising approach to derive hydrodynamic conditions and the morphological onshore response of the 1717 Christmas flood in the Province of Groningen. This knowledge is essential to improve our understanding of extreme storm surge dynamics, their influence on the coastal landscape and the associated hazards for the coastal population.

In São Paulo, Brazil, the first case of coronavirus disease 2019 (CoViD-19) was confirmed on 26 February, the first death due to CoViD-19 was registered on 16 March, and on 24 March, São Paulo implemented the isolation of persons in non-essential activities. A mathematical model was formulated based on non-linear ordinary differential equations considering young (60 years old or less) and elder (60 years old or more) subpopulations, aiming to describe the introduction and dissemination of the new coronavirus in São Paulo. This deterministic model used the data collected from São Paulo to estimate the model parameters, obtaining R0 = 6.8 for the basic reproduction number. The model also allowed to estimate that 50% of the population of São Paulo was in isolation, which permitted to describe the current epidemiological status. The goal of isolation implemented in São Paulo to control the rapid increase of the new coronavirus epidemic was partially succeeded, concluding that if isolation of at least 80% of the population had been implemented, the collapse in the health care system could be avoided. Nevertheless, the isolated persons must be released one day. Based on this model, we studied the potential epidemiological scenarios of release by varying the proportions of the release of young and elder persons. We also evaluated three different strategies of release: All isolated persons are released simultaneously, two and three releases divided in equal proportions. The better scenarios occurred when young persons are released, but maintaining elder persons isolated for a while. When compared with the epidemic without isolation, all strategies of release did not attain the goal of reducing substantially the number of hospitalisations due to severe CoViD-19. Hence, we concluded that the best decision must be postponing the beginning of the release.

Advanced cooling techniques involving internal enhanced heat transfer and external film cooling and thermal barrier coatings (TBCs) are employed for gas turbine hot components to reduce metal temperatures and to extend their lifetime. A deeper understanding of the interaction mechanism of these thermal protection methods and the conjugate thermal behaviours of the turbine parts provides valuable guideline for the design stage. In this study, a conjugate heat transfer model of a turbine vane endwall with internal impingement and external film cooling is constructed to document the effects of TBCs on the overall cooling effectiveness using numerical simulations. Experiments on the same model with no TBCs are performed to validate the computational methods. Round and crater holes due to the inclusion of TBCs are investigated as well to address how film-cooling configurations affect the aero-thermal performance of the endwall. Results show that the TBCs have a profound effect in reducing the endwall metal temperatures for both cases. The TBC thermal protection for the endwall is shown to be more significant than the effect of increasing coolant mass flow rate. Although the crater holes have better film cooling performance than the traditional round holes, a slight decrement of overall cooling effectiveness is found for the crater configuration due to more endwall metal surfaces directly exposed to external mainstream flows. Energy loss coefficients at the vane passage exit show a relevant negative impact of adding TBCs on the cascade aerodynamic performance, particularly for the round hole case.

The work presents the analysis of the free boundary value problem related to the one-dimensional invasion model of new species in biofilm reactors. In the framework of continuum approach to mathematical modelling of biofilm growth, the problem consists of a system of non-linear hyperbolic partial differential equations governing the microbial species growth and a system of semi-linear elliptic partial differential equations describing the substrate trends. The model is completed with a system of elliptic partial differential equations governing the diffusion and reaction of planktonic cells, which are able to switch their mode of growth from planktonic to sessile when specific environmental conditions are found. Two systems of non-linear differential equations for the substrate and planktonic cells mass balance within the bulk liquid are also considered. The free boundary evolution is governed by a differential equation that accounts for detachment. The qualitative analysis is performed and a uniqueness and existence result is presented. Furthermore, two special models of biological and engineering interest are discussed numerically. The invasion of Anammox bacteria in a constituted biofilm inhabiting the deammonification units of the wastewater treatment plants is simulated. Numerical simulations are run to evaluate the influence of the colonization process on biofilm structure and activity.

The generalized theory of terawatt laser pulse interaction with a low-dense porous substance of light chemical elements including laser light absorption and energy transfer in a wide region of parameter variation is developed on the base of the model of laser-supported hydrothermal wave in a partially homogenized plasma. Laser light absorption, hydrodynamic motion, and electron thermal conductivity are implemented in the hydrodynamic code, according to the degree of laser-driven homogenization of the laser-produced plasma. The results of numerical simulations obtained by using the hydrodynamic code are presented. The features of laser-supported hydrothermal wave in both possible cases of a porous substance with a density smaller and larger than critical plasma density are discussed along with the comparison with the experiments. The results are addressed to the development of design of laser thermonuclear target as well as and powerful neutron and X-ray sources.

In this work, we examine the mathematical analysis and numerical simulation of pattern formation in a subdiffusive multicomponents fractional-reaction-diffusion system that models the spatial interrelationship between two preys and predator species. The major result is centered on the analysis of the system for linear stability. Analysis of the main model reflects that the dynamical system is locally and globally asymptotically stable. We propose some useful theorems based on the existence and permanence of the species to validate our theoretical findings. Reliable and efficient methods in space and time are formulated to handle any space fractional reaction-diffusion system. We numerically present the complexity of the dynamics that are theoretically discussed. The simulation results in one, two and three dimensions show some amazing scenarios.

Louvered cavities are extensively employed in engineering applications. In the configurations of flow past these cavities, self-sustained oscillations will be excited. This can give rise to structure vibrations or noise. Numerical models are established to analyze excitation condition for of these oscillations. Computational results reveal that the excitation condition can be quantitatively described by the ratio of gap width G to the boundary layer thickness δ at the separation edge. When G/δ exceeds a certain critical value G/δc, self-sustained oscillations are excited. Otherwise, disturbances will dissipate and the flow configuration along the louver will be like a parallel plate flow. The critical value G/δc decreases with the ratio of G to the thickness of the louver plate H. This suggests that the excitation condition is more easily satisfied for a louver with sparse fins. The bottom boundary of the cavity restricts the feedback flow and then suppresses the excitation of self-sustained oscillations. With an increasing cavity height Hc, which reflects the distance between the louver and the bottom boundary, the critical value G/δc decreases and the decreasing rate reduces gradually. In contrast, because G/δc is relatively insensitive to the cavity length Lc, the side boundaries have no obvious influence on the excitation condition.

We here discuss the various dynamo models which have been designed to explain the generation and evolution of large-scale magnetic fields in stars. We focus on the models that have been applied to the Sun and can be tested for other solar-type stars now that modern observational techniques provide us with detailed stellar magnetic field observations. Mean-field flux-transport dynamo models have been developed for decades to explain the solar cycle and applications to more rapidly-rotating stars are discussed. Tremendous recent progress has been made on 3D global convective dynamo models. They do not however for now produce regular flux emergence that could be responsible for surface active regions and questions about the role of these active regions in the dynamo mechanism are still difficult to address with such models. We finally discuss 3D kinematic dynamo models which could constitute a promising combined approach, in which data assimilation could be applied.

An optimal control problem is considered to find a stable surface traction, which minimizes the discrepancy between a given displacement field and its estimation. Firstly, the inverse elastic problem is constructed by variational inequalities, and a stable approximation of surface traction is obtained with Tikhonov regularization. Then a finite element discretization of the inverse elastic problem is analyzed. Moreover, the error estimation of the numerical solutions is deduced. Finally, a numerical algorithm is detailed and three examples in two-dimensional case illustrate the efficiency of the algorithm.

We present the first model that couples high-resolution simulations of the formation of local group galaxies with calculations of the galactic habitable zone (GHZ), a region of space which has sufficient metallicity to form terrestrial planets without being subject to hazardous radiation. These simulations allow us to make substantial progress in mapping out the asymmetric three-dimensional GHZ and its time evolution for the Milky Way (MW) and Triangulum (M33) galaxies, as opposed to works that generally assume an azimuthally symmetric GHZ. Applying typical habitability metrics to MW and M33, we find that while a large number of habitable planets exist as close as a few kiloparsecs from the galactic centre, the probability of individual planetary systems being habitable rises as one approaches the edge of the stellar disc. Tidal streams and satellite galaxies also appear to be fertile grounds for habitable planet formation. In short, we find that both galaxies arrive at similar GHZs by different evolutionary paths, as measured by the first and third quartiles of surviving biospheres. For the MW, this interquartile range begins as a narrow band at large radii, expanding to encompass much of the Galaxy at intermediate times before settling at a range of 2–13 kpc. In the case of M33, the opposite behaviour occurs – the initial and final interquartile ranges are quite similar, showing gradual evolution. This suggests that Galaxy assembly history strongly influences the time evolution of the GHZ, which will affect the relative time lag between biospheres in different galactic locations. We end by noting the caveats involved in such studies and demonstrate that high-resolution cosmological simulations will play a vital role in understanding habitability on galactic scales, provided that these simulations accurately resolve chemical evolution.

In high-power laser systems (HPLSs), understanding debris-removal trajectories is important in eliminating debris from the surfaces of transport mirrors online and keeping other optical components free from contamination. NS equations, the RNG $k{-}{\it\varepsilon}$ model and the discrete phase model of the Euler–Lagrange method are used to conduct numerical simulations on the trajectories of contaminant particles of different sizes and types on the mirror surface using Fluent commercial software. A useful device is fabricated based on the simulation results. This device can capture and collect debris from the mirror surface online. Consequently, the effect of debris contamination on other optical components is avoided, cleaning time is shortened, and ultimately, the cleanliness of the mirrors in HPLSs is ensured.