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Microchannel cooling is often the preferred choice for compact heat sinks. However, widely adopted topology optimisation (TO) techniques such as density-based and level-set methods often struggle to generate very thin channel strips unless maximum length scale constraints are imposed and very fine meshes are employed. To address this limitation, multi-scale design methodologies have emerged. This paper builds upon recent advances in de-homogenisation techniques to contribute to the multi-scale design of microchannels for cooling applications. We start by selecting a single-class microstructure and employ numerical homogenisation to build an offline library. This library is then fed in online macro-scale topology optimisation, where both microstructure parameters and local orientation fields are optimised. By using a sawtooth-function-based mapping, the de-homogenised results capture fine details across different length scales through a unique homogenised design. Our findings show that the generated microchannels outperform conventional pillar arrays, offering valuable insights for heat sink designers. Additionally, imperfections observed in the de-homogenised results serve as benchmarks for future improvements, addressing concerns related to modelling accuracy, manufacturability, and overall performance enhancements.

EasyPBC is an ABAQUS CAE plugin developed to estimate the homogenised effective elastic properties of user created periodic representative volume element (RVE), all within ABAQUS without the need to use third-party software. The plugin automatically applies the concepts of the periodic RVE homogenisation method in the software’s user interface by categorising, creating, and linking sets necessary for achieving deformable periodic boundary surfaces, which can distort and no longer remain plane. Additionally, it allows the user to benefit from finite element analysis data within ABAQUS CAE interface after calculating homogenised properties. In this article, the algorithm of the plugin based on periodic RVE homogenisation method is explained, which could be developed for other commercial FE software packages. Furthermore, examples of its implementation and verification are illustrated.

Aim: The process of urbanization can lead to specialist species being replaced by generalist species in space and time, increasing similarity among bird communities. This phenomenon is termed biotic homogenization and is directly related to taxonomic and functional diversity. However, the effects of urbanization on phylogenetic diversity remain unclear. Our study addresses the effects of the process of urbanization on the evolutionary distinctiveness (a quantitative measure of the genetic or evolutionary uniqueness of species) of bird communities. Location: Europe. Methods: Mixed models were used to compare the effects of urbanization on the evolutionary distinctiveness of bird communities in rural and urban environments in six different European cities from different ecoregions. Results: Our study presents unique large-scale evidence of a negative impact of urban environments on the evolutionary uniqueness of birds. Compared with bird communities in rural environments, bird communities in urban environments have lower average evolutionary distinctiveness in all countries, independent of ecoregion, and these values are unrelated to the taxonomic diversity present in each country. Main conclusions: Our findings provide important information on the spectrum of effects on global biodiversity of changes in land use related to the process of urbanization. Therefore, urban environments are a factor of concern for maintaining diversity across the tree of life of birds, and we suggest that urbanization planning could help buffer against extreme loss of phylogenetic diversity caused by this process.

In this monograph, we review the theory and establish new and general results regarding spreading properties for heterogeneous reaction-diffusion equations: The characterizations of these sets involve two new notions of generalized principal eigenvalues for linear parabolic operators in unbounded domains. In particular, it allows us to show that

Homogenisation is a widely used technique in manufacturing powdered milk with a direct impact on product solubility, and the homogenisation pressure is a central attribute of this process. We aimed to understand the effect of increasing homogenisation pressures (0/0, 15/5, and 75/5 MPa, 1st/2nd stages) on particle-size distribution during homogenised whole milk powder manufacture and rehydration of the final product. The fluid milk was thermally treated, homogenised, concentrated by rotary evaporation, and then dried using a spray dryer. Particle size (Dv90) was monitored at all stages of the manufacturing process. The final product (milk powder) was analysed using particle-size distribution, electronic scanning microscopy, water activity, and isotherms. The results demonstrated that increasing the homogenisation pressure leads to milk powder with smaller particle size when rehydrated (Dv90 values: 6.08, 1.48 and 0.64 μm for 0, 20 and 80 MPa, respectively). Furthermore, the volume (%) of the particles in the ‘sub-micro’ region (smaller than 1.0 μm) presented an inversely proportional profile to the homogenisation pressure (homogenised fluid milk: 86.1, 29.3 and 2.4%; concentrated milk: 86.1, 26.5 and 5.7%, and reconstituted milk powder: 84.2, 31.8 and 10.9%). Surprisingly, this pattern was not observed in the SPAN value (which corresponds to the width or range of the size distribution based on the volume). Additionally, the increase in the homogenisation pressure did not affect the sorption isotherm pattern. These results demonstrate that increasing the homogenisation pressure decreases the particle size of the reconstituted powdered milk, indicating the potential for future studies on how this phenomenon affects its physicochemical and final product properties.

The present thesis addresses a broad range of weak convergence problems arising in Nonlinear Analysis. The thesis is divided into three related but essentially independent parts. In the first part we study the general theory of Compensated Compactness. We begin by giving a new characterization of partial differential operators with constant rank, a mild non-degeneracy assumption which plays an important role in the theory. We then characterize completely the class of nonlinearities which are weakly continuous with respect to constant rank PDEs; in particular, we prove that it agrees with the class of nonlinear operators with Hardy space integrability, answering positively a question by Coifman-Lions-Meyer-Semmes. As an application of this theory we study homogenization problems, both with and without constant rank assumptions. In the constant rank setting we revisit the classical G-closure problem and discuss its connection with quasiconvexity. In the non-constant rank setting we study a homogenization problem for the Einstein vacuum equations in General Relativity: under some symmetry and gauge assumptions, we prove a conjecture by Burnett from 1989 which describes the effective behaviour of a sequence of vacuum space-times. This part of the thesis contains joint work with Jan Kristensen (University of Oxford), Bogdan Raită (MPI Leipzig), Matthew Schrecker (UCL) and Rita Teixeira da Costa (University of Cambridge). The second part of this thesis is concerned with quasiconvexity in the classical, curl-free, Calculus of Variations. We contribute to the understanding of the geometry of the class of quasiconvex functions, in particular through its extremal points. We prove a Choquet-type theorem for quasiconvex functions and we provide several examples of extremal quasiconvex functions, proving in particular a conjecture made by Šverák. We then further investigate, through numerical experiments, the relationship between rank-one convexity and quasiconvexity, particularly in low dimensions. We also give a concise proof of Ornstein's L1 non-inequality in low dimensions. This part of the thesis contains joint work with Daniel Faraco (Universidad Autónoma de Madrid) and Rita Teixeira da Costa (University of Cambridge). The third part of this thesis deals with low regularity problems for nonlinear underdetermined PDEs. We mostly focus on the prescribed Jacobian equation, although applications to energy-dissipative solutions of the incompressible Euler equations are also discussed. Concerning the prescribed Jacobian equation, we prove an ill-posedness result for the Dirichlet problem. We also study the uniqueness and symmetry properties of energy minimisers with prescribed Jacobian, concluding that in general they are non-unique and non-symmetric. These results answer several questions posed by Hélein, Hogan- Li-McIntosh-Zhang and Ye in the 1990s and provide some of the first results concerning low regularity solutions of the Jacobian equation. We also prove a nonlinear version of the classical Open Mapping Theorem from Functional Analysis. Our result applies to a wide range of PDEs and, in particular, it applies to the weakly continuous nonlinearities characterized in the first part of this thesis, of which the Jacobian determinant is a particular example. As consequences of this nonlinear Open Mapping Theo- rem, we prove: i) a partial selection criterion for solutions of the Jacobian equation in the critical Sobolev space, and ii) generic non-existence of weak solutions to the incompressible Euler equations over Rⁿ with fastly decaying kinetic energy. This part of the thesis contains joint work with Lukas Koch (University of Oxford) and Sauli Lindberg (Aalto University).

Our planet is facing significant changes of biodiversity across spatial scales. Although the negative effects of local biodiversity (α diversity) loss on ecosystem stability are well documented, the consequences of biodiversity changes at larger spatial scales, in particular biotic homogenization, that is, reduced species turnover across space (β diversity), remain poorly known. Using data from 39 grassland biodiversity experiments, we examine the effects of β diversity on the stability of simulated landscapes while controlling for potentially confounding biotic and abiotic factors. Our results show that higher β diversity generates more asynchronous dynamics among local communities and thereby contributes to the stability of ecosystem productivity at larger spatial scales. We further quantify the relative contributions of α and β diversity to ecosystem stability and find a relatively stronger effect of α diversity, possibly due to the limited spatial scale of our experiments. The stabilizing effects of both α and β diversity lead to a positive diversity–stability relationship at the landscape scale. Our findings demonstrate the destabilizing effect of biotic homogenization and suggest that biodiversity should be conserved at multiple spatial scales to maintain the stability of ecosystem functions and services.

Significance & Background: Although nurse-led clinics have developed rapidly in China recently, the functional positioning and construction levels vary greatly depending on the development of nursing specialization. In addition, due to the lack of a standardized survey instrument guided by theories based on advanced nursing practice, the content and focus of the survey varied greatly, and in particular, there was a lack of comprehensive information on the regional construction. Purpose: Based on Brown and Hamric's theory of advanced nursing practice, we investigated the construction level of nurse-led clinics in public hospitals from four dimensions, to understand the development quality and problems, and to promote the development towards the homogenization of international advanced nursing practice. Interventions: A cross-sectional survey study was conducted, taking nurses sitting in the nurse-led clinics of all public hospitals in Chengdu, Sichuan Province, as the research subjects, and using the Questionnaire on the Current Situation of the Construction of Nurse-led Clinics and the Registered Nurses' Professional Core Competency Scale as the survey tools. Descriptive statistics, entropy weight method and multiple linear regression were used to analyze the data. Results: The highest level of construction among the 171 nurseled clinics was 4.5949, the lowest was 0.0545, and the median (quartiles) was 0.3601 (0.2275, 0.6026) points. The top five rankings for both the mean construction score and the number of openings of the 26 nurse-led clinics were: psychological counseling clinic, PICC care clinic, and wound/ostomy clinic. The mean scores of the dimensions of the nurse-led clinics, from highest to lowest, were human resource construction (1.6884), service result (1.6338), organization construction (1.2073) and practice content (0.9362). The level of clinic construction is influenced by the opening time (t=-6.023, P<0.001) and the service type (t=3.753, P<0.001). There was a significant difference in the construction level of different types of nurse-led clinics (H=16.719, P=0.005). Discussion: Nurse-led clinics in Chengdu are developing rapidly, but there is an imbalance in development. Despite the better human resource construction and the variety of health service methods, the lack of management system, poor homogenization of service content and the prescription rights limit the scope of outpatient practice and development. It suggests that although the social demand for nurse-led clinics health services is high, the connotation of outpatient development still needs to be strengthened to enhance the homogenization level of clinic construction.

Computational homogenization is adopted to assess the homogenized two-dimensional response of periodic composite materials where the typical microstructural dimension is not negligible with respect to the structural sizes. A micropolar homogenization is, therefore, considered coupling a Cosserat medium at the macro-level with a Cauchy medium at the micro-level, where a repetitive Unit Cell (UC) is selected. A third order polynomial map is used to apply deformation modes on the repetitive UC consistent with the macro-level strain components. Hence, the perturbation displacement field arising in the heterogeneous medium is characterized. Thus, a newly defined micromechanical approach, based on the decomposition of the perturbation fields in terms of functions which depend on the macroscopic strain components, is adopted. Then, to estimate the effective micropolar constitutive response, the well known identification procedure based on the Hill-Mandel macro-homogeneity condition is exploited. Numerical examples for a specific composite with cubic symmetry are shown. The influence of the selection of the UC is analyzed and some critical issues are outlined.

We give a comprehensive presentation of the periodic unfolding method for perforated domains, both when the unit hole is a compact subset of the open unit cell and when this is impossible to achieve. In order to apply the method to boundary-value problems with nonhomogeneous Neumann conditions on the boundaries of the holes, the properties of the boundary unfolding operator are also extensively studied. The paper concludes with applications to such problems and examples of reiterated unfolding.