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Partitioning space into cells with certain extreme geometrical properties is a central problem in many fields of science and technology. Here we investigate the Quantizer problem, defined as the optimisation of the moment of inertia of Voronoi cells, i.e., similarly-sized ‘sphere-like’ polyhedra that tile space are preferred. We employ Lloyd’s centroidal Voronoi diagram algorithm to solve this problem and find that it converges to disordered states associated with deep local minima. These states are universal in the sense that their structure factors are characterised by a complete independence of a wide class of initial conditions they evolved from. They moreover exhibit an anomalous suppression of long-wavelength density fluctuations and quickly become effectively hyperuniform. Our findings warrant the search for novel amorphous hyperuniform phases and cellular materials with unique physical properties., Disordered hyperuniformity implies a hidden order on length scales that can be found in various amorphous materials. Klatt et al. analyse the evolution of random point patterns using Llyod’s algorithm and show that they converge to an effectively hyperuniform state regardless of the initial conditions.

We develop a density functional for hard particles with a smooth uniaxial shape (including non-inversion-symmetric particles) within the framework of fundamental measure theory. By applying it to a system of tapered, aspherical liquid-crystal formers, reminiscent of pears, we analyse their behaviour near a hard substrate. The theory predicts a complex orientational ordering close to the substrate, which can be directly related to the particle shape, in good agreement with our simulation results. Furthermore, the lack of particle inversion-symmetry implies the possibility of alternating orientations in subsequent layers as found in a smectic/lamellar phase of such particles. Both theory and Monte Carlo simulations confirm that such ordering occurs in our system. Our results are relevant for adsorption processes of asymmetric colloidal particles and molecules at hard interfaces and show once again that tapering strongly affects the properties of orientationally ordered phases.

Granular heaps of particles created by deposition of mono-disperse particles raining from an extended source of finite size are characterized by a non-homogeneous field of density. It was speculated that this inhomogeneity is due to the transient shape of the sediment during the process of construction of the heap, thus reflecting the history of the creation of the heap. By comparison of structural characteristics of the heap with sediments created on top of inclined planes exploiting the method of Minkowski tensors, we provide further evidence to support this hypothesis. Moreover, for the case of sediments generated by homogeneous rain on surfaces, we provide relationships between the inclination of the surface and the Minkowski measures characterizing the isotropy of local particle environments.

The wing scales of the Green Hairstreak butterfly Callophrys rubi consist of crystalline domains with sizes of a few micrometers, which exhibit a congenitally handed porous chitin microstructure identified as the chiral triply periodic single-gyroid structure. Here, the chirality and crystallographic texture of these domains are investigated by means of electron tomography. The tomograms unambiguously reveal the coexistence of the two enantiomeric forms of opposite handedness: the left- and right-handed gyroids. These two enantiomers appear with nonequal probabilities, implying that molecularly chiral constituents of the biological formation process presumably invoke a chiral symmetry break, resulting in a preferred enantiomeric form of the gyroid structure. Assuming validity of the formation model proposed by Ghiradella H (1989) J Morphol 202(1):69-88 and Saranathan V, et al. (2010) Proc Natl Acad Sci USA 107(26):11676-11681, where the two enantiomeric labyrinthine domains of the gyroid are connected to the extracellular and intra-SER spaces, our findings imply that the structural chirality of the single gyroid is, however, not caused by the molecular chirality of chitin. Furthermore, the wing scales are found to be highly textured, with a substantial fraction of domains exhibiting the001directions of the gyroid crystal aligned parallel to the scale surface normal. Both findings are needed to completely understand the photonic purpose of the single gyroid in gyroid-forming butterflies. More importantly, they show the level of control that morphogenesis exerts over secondary features of biological nanostructures, such as chirality or crystallographic texture, providing inspiration for biomimetic replication strategies for synthetic self-assembly mechanisms.

Circular dichroism is a useful property for filtering or separating beams containing opposite spin angular momentum. Of the many geometries exhibiting circular dichroism, the gyroid has proven to be an excellent template for exploring circular dichroism in three dimensions. However, the bandwidth of the circular dichroism from dielectric gyroids is limited by its narrow circularly polarized stop band. Here we investigate conductive silver gyroid micro-structures using direct laser writing of polymeric templates followed by the electroless deposition of a uniform silver coating. We show that the transformation from dielectric to silver gyroid micro-structure can increase the circular dichroism bandwidth by close to a factor of 3.

Background: Pain control after breast reconstruction with Deep Inferior Epigastric Perforator (DIEP) often requires intravenous narcotic analgesia and inpatient hospitalization. Intrathecal morphine (ITM) administration analgesia is increasing in popularity because it decreases the use of intravenous analgesic medications and offer comparable pain relief with less systemic side effects. Questions/purposes: The aim of this retrospective study was to evaluate the effect of intrathecal morphine on postoperative morbidity of breast reconstruction by Deep Inferior Epigastric Perforator flap and compare it with intravenous narcotic analgesia. Methods: 269 patients underwent immediate or delayed DIEP reconstruction after mastectomy, by the same surgeon, at Jules Bordet Institute. Patients receiving ITM analgesia (300 μ) were matched 1:3 with patients undergoing intravenous narcotic analgesia for pain control in the same years by the same surgeon. Differences in peri- and postoperative complications across the two groups were assessed. Results: The two groups were comparable in terms of demographic characteristics and factors of morbidity. Intraoperative variables were not statistically different between the groups except for intraoperative blood loss (P = 0.0001), transfusion (P = 0.0001) and Intraoperative liquid requirement (p = 0.0001). Intra and postoperative blood pressure were lower in ITM group (p < 0.05). Patients in ITM group showed lower postoperative analgesia requirement (P < 0,0001), less respiratory complications and less acute respiratory failure (P = 0,003 and P = 0,004, respectively). No statistically significant differences in the length of hospital stay (LOS) were noted Conclusion: We found that intrathecal morphine analgesia was associated with less blood loss and fluid administration, better postoperative pain control, and less respiratory complications with an acceptable security profile than intravenous narcotic analgesia. Clinical relevance: This study suggests that using intrathecal morphine may result in less blood loss and blood transfusion, better postoperative pain control, and less respiratory complications.

Objective The antiphospholipid syndrome (APS) is a systemic auto-immune disease with an unclear pathophysiology. The aim of our study was to understand the development of APS on a cellular level. Therefore, we analyzed the influence of human serum of APS patients on endothelial expression of specific genes and proteins in comparison to a control group. Methods In this study, we analyzed the expression of ICAM-1, VCAM-1, E-selectin and annexin V in primary cultures of human umbilical vein endothelial cells (HUVEC) in response to 10% (v/v) serum of control patients (n = 6), patients with systemic lupus erythematosus (SLE) and no APS (n = 4) or APS patients (n = 9) for 24 h. Total RNA was prepared from confluent endothelial cell layers and mRNA expression of ICAM-1, VCAM-1 and E-selectin was analyzed by reverse transcription polymerase-chain reaction (RT-PCR). The protein expression was determined by Western blot. Serum protein concentrations of soluble forms of adhesion molecules sICAM-1 and sVCAM-1 were quantified by ELISA. Gene expression data were correlated with clinical parameters. Results The mRNA expression of ICAM-1 was increased in cells incubated with serum from APS patients (166 ± 22% of control; P = 0.023). Serum of patients with (SLE)/no APS caused a 1.4-fold higher ICAM-1 mRNA level. Western blot analysis showed an increase in protein expression of adhesion molecules ICAM-1 (260 ± 49%; P = 0.011) and VCAM-1 (357 ± 97%; P = 0.023) in cells that were incubated with serum from APS patients. Plasma analysis showed elevated levels of sVCAM-1 in APS patients (189 ± 34%; P = 0.045) compared to the levels measured in the control group. The sVCAM-1 plasma level was correlating with the frequency of abortions. Conclusion An augmented expression of endothelial adhesion molecules is involved in the pathophysiology of patients with antiphospholipid syndrome.

Background The national history of mild/moderate aortic stenosis (AS) has been previously reported in 3 studies. Aim We sought to assess the impact of the severity of AS in a group of patients initially managed medically. Methods A consecutive group of 399 patients with AS as assessed in our echolab (6.2.2002‐22.7.2003). Patients with a previous aortic prosthesis or operated within 3 months after diagnosis of AS were excluded. Patients were classified according to AS severity: * mild AS (AV area > 1.5‐2 cm2) * moderate AS (AV area 1‐1.5 cm2) * severe AS (AV area 0.8‐0.99 cm2) * very severe AS (AV area 0.8 cm2 had no impact on survival. The relative impact of the AS severity in addition to the clinical parameters (log Euroscore, age, NYHA, LVEJF) was assessed by the ROC model. The predictive performance was only slightly improved (by 2 ‐ 3%) by including the AS severity. Conclusion Survival in patients with very severe AS is reduced in comparison to patients with less severe AS. Survival in patients with less severe AS (AV area > 0.8 cm2) depends mainly on clinical characteristics, but not on degree of AS severity. There seems to be a place for randomized trials on the management of patients with less severe AS (AV area: 0.8‐1 cm2).

We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia d structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E 68 , 021708. ( doi:10.1103/PhysRevE.68.021708 )) and Ellison et al. (2006 Phys. Rev. Lett. 97 , 237801. ( doi:10.1103/PhysRevLett.97.237801 )). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression–decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.

Background Coronary artery disease (CAD) is the leading cause of OHCA. However, diagnosis of ACI remains challenging, particularly in patients without ST-segment elevation on the post-resuscitation ECG. In this regard, a consensus statement recommends the implementation of a work-up strategy in the emergency room (ER) to exclude non-coronary causes of collapse within 2 hours. Purpose We present data on coronary angiograms for patients who underwent cardiac catheterization after resuscitation. Afterwards, we sought to identify parameters associated with ACI. Methods Retrospective single-centre study performed on 64 consecutive patients with resuscitated OHCA who underwent a diagnostic coronary angiography (CA). Data collection was performed from the patient records at the ER and the catheterization laboratory. ST-segment elevation was noted in 29 patients (45%). ST-segment depression or T-wave abnormalities were noted in 35 patients (55%). Results Invasive coronary strategy allowed to identify an acute culprit lesion in 46 cases (72%). 29 patients with ST-segment elevation underwent an immediate angioplasty for an acute coronary occlusion. 17 patients without ST-segment elevation underwent an ad hoc percutaneous coronary intervention for a critical lesion. Stable CAD was found in 9 cases (14%) and a normal angiogram was found in only 9 cases (14%) ( Fig. 1 ). The independent predictors of ACI were convertible rhythm (OR 16.02; 95% CI 4.48–57.29), personal history of CAD (OR 15.12; 95% CI 4.19–54.53) and presence of at least 2 cardiovascular risk factors (OR 10.68; 95% CI 2.55–44.74) ( Table 1 ). Conclusion ACI was the leading precipitant of collapse. ST-segment elevation was highly predictive of coronary occlusion. A culprit coronary lesion was identified in nearly 50% of patients undergoing CA despite the lack of ST-segment elevation. Our findings also suggest that the identification of risk criteria may help to improve the recognition of ACI after OHCA.

Self-assembly remains the most efficient route to the formation of ordered nanostructures, including the double gyroid network phase in diblock copolymers based on two intergrown network domains. Here we use self-consistent field theory to show that a tricontinuous structure with monoclinic symmetry, called 3ths(5), based on the intergrowth of three distorted ths nets, is an equilibrium phase of triblock star-copolymer melts when an extended molecular core is introduced. The introduction of the core enhances the role of chain stretching by enforcing larger structural length scales, thus destabilizing the hexagonal columnar phase in favor of morphologies with less packing frustration. This study further demonstrates that the introduction of molecular cores is a general concept for tuning the relative importance of entropic and enthalpic free energy contributions, hence providing a tool to stabilize an extended repertoire of self-assembled nanostructured materials.

The wings of butterflies and moths generate some of the most spectacular visual displays observed in nature [1-3]. Particularly striking effects are seen when light interferes with nanostructure materials in the wing scales, generating bright, directional colors that often serve as dynamic visual signals [4]. Structural coloration is not known in night-flying Lepidoptera, yet here we show a highly unusual form of wing coloration in a nocturnal, sexually dimorphic moth, Eudocima materna (Noctuidae). Males feature three dark wing patches on the dorsal forewings, and the apparent size of these patches strongly varies depending on the angle of the wing to the viewer. These optical special effects are generated using specialized wing scales that are tilted on the wing and behave like mirrors. At near-normal incidence of light, these "mirror scales" act as thin-film reflectors to produce a sparkly effect, but when light is incident at ∼20°-30° from normal, the reflectance spectrum is dominated by the diffuse scattering of the underlying, black melanin-containing scales, causing a shape-shifting effect. The strong sexual dimorphism in the arrangement and architecture of the scale nanostructures suggests that these patterns might function for sexual signaling. Flickering of the male's wings would yield a flashing, supernormal visual stimulus [5] to a viewer located 20°-30° away from the vertical, while being invisible to a viewer directly above the animal. Our findings reveal a novel use of structural coloration in nature that yields a dynamic, time-dependent achromatic optical signal that may be optimized for visual signaling in dim light.

Amphiphilic lipids aggregate in aqueous solution into a variety of structural arrangements. Among the plethora of ordered structures that have been reported, many have also been observed in nature. In addition, due to their unique morphologies, the hydrophilic and hydrophobic domains, very high internal interfacial surface area, and the multitude of possible order-order transitions depending on environmental changes, very promising applications have been developed for these systems in recent years. These include crystallization in inverse bicontinuous cubic phases for membrane protein structure determination, generation of advanced materials, sustained release of bioactive molecules, and control of chemical reactions. The outstanding diverse functionalities of lyotropic liquid crystalline phases found in nature and industry are closely related to the topology, including how their nanoscopic domains are organized. This leads to notable examples of correlation between structure and macroscopic properties, which is itself central to the performance of materials in general. The physical origin of the formation of the known classes of lipidic lyotropic liquid crystalline phases, their structure, and their occurrence in nature are described, and their application in materials science and engineering, biology, medical, and pharmaceutical products, and food science and technology are exemplified.

The single Gyroid, a triply-periodic ordered chiral network of cubic symmetry, appears as a nanostructure in the green-colored wing scales of various butterflies. In lossless and perfectly ordered single Gyroid materials, the structural chirality leads to circularly polarized reflections from crystals oriented in the [100] direction. Here we report a circular polarisation study of the macroscopic reflections of the wing scales of Callophrys rubi and Teinopalpus imperialis that reveals no circular dichroism, that is, we find no significant difference in the reflectance values for left- and right-circularly polarized light. The reasons for the absence of circularly polarized reflections is likely to be a compound effect of various factors, including crystallite orientation, presence of both left- and right-handed single Gyroid enantiomers, and structural disorder. Each of these factors weakens, but does not fully extinguish, the circular polarisation signal. We further find a substantial amount of blue-absorbing pigment in those wing scales of C. rubi that are structured according to the single Gyroid. Numerical simulations demonstrate that absorption, while evidently reducing overall reflectance, does generally not reduce the circular dichroism strength. The experimental findings of this paper, however, clearly demonstrate that circular dichroism is absent from the reflections of the butterfly wing scale. Henceforth, the chiro-optical response of the idealised structure does not fulfil a biological photonic function.

Several approaches to quantitative local structure characterization for particulate assemblies, such as structural glasses or jammed packings, use the partition of space provided by the Voronoi diagram. The conventional construction for spherical mono-disperse particles, by which the Voronoi cell of a particle is that of its centre point, cannot be applied to configurations of aspherical or polydisperse particles. Here, we discuss the construction of a Set Voronoi diagram for configurations of aspherical particles in three-dimensional space. The Set Voronoi cell of a given particle is composed of all points in space that are closer to the surface (as opposed to the centre) of the given particle than to the surface of any other; this definition reduces to the conventional Voronoi diagram for the case of mono-disperse spheres. An algorithm for the computation of the Set Voronoi diagram for convex particles is described, as a special case of a Voronoi-based medial axis algorithm, based on a triangula...

The linearly polarizing beamsplitter1, 2 is a widely used optical component in photonics. It is typically built from a linearly birefringent crystal such as calcite, which has different critical reflection angles for s- and p-polarized light3, leading to the transmission of one linear polarization and angled reflection of the other. However, the analogue for splitting circularly polarized light has yet to be demonstrated due to a lack of natural materials with sufficient circular birefringence. Here, we present a nano-engineered photonic-crystal chiral beamsplitter that fulfils this task. It consists of a prism featuring a nanoscale chiral gyroid network4, 5, 6, 7, 8, 9, 10 and can separate left- and right-handed circularly polarized light in the wavelength region around 1.615 µm. The structure is fabricated using a galvo-dithered direct laser writing method and could become a useful component for developing integrated photonic circuits that provide a new form of polarization control.

Der vorliegende Artikel zeigt die Entwicklung der Anlagenwirtschaft und der damit verbundenen Forschungsarbeit am Department Wirtschafts- und Betriebswissenschaften (WBW) der Montanuniversitat Leoben. So hat die am Institut geleistete Forschung den Begriff der Anlagenwirtschaft masgeblich mitgepragt, war man doch stets Vorreiter in der Bearbeitung von Fragestellungen rund um die Themengebiete des industriellen Anlagenmanagements. Ausgehend von den anfangs funktional orientierten Ansatzen betrieblicher Instandhaltungssysteme gibt der Artikel einen kurzen Einblick in die Evolution dieser, hin zu hochentwickelten Managementsystemen fur ein ganzheitliches Anlagenmanagement und zeigt den weitern Forschungsbedarf in diesem Gebiet auf.

In diesem Artikel wird auf die Entwicklung des leistungswirtschaftlichen Risikomanagements und der damit verbundenen Forschungsarbeit am Department Wirtschafts- und Betriebswissenschaften (WBW) der Montanuniversitat Leoben eingegangen. Ausgehend vom Bedarf der Industrie nach Standards, welche die Ablaufe und Strukturen zur Risikohandhabung in Organisationen und Systemen regeln, entwickelten sich im Laufe des letzten Jahrzehnts vermehrt Regelwerke, auch im leistungswirtschaftlichen Bereich, die sich vor allem dem Umgang mit Risiken in den Bereichen Sicherheit sowie Gesundheits- und Umweltschutz widmen. Diese Regulative verlangen wiederum nach praktikablen Ansatzen zur systematischen Risikohandhabung. Bezugnehmend auf Gestaltungsgrundsatze fur Industriebetriebe zeigt der Artikel Ansatze einer ganzheitlichen Risikomanagementbetrachtung auf und gibt Ausblick auf den weiteren Forschungsbedarf in diesem Gebiet.

We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is required for aspherical or polydisperse systems. Pomelo is designed to be easy to use and as generic as possible. It directly supports common particle shapes and offers a generic mode, which allows to deal with any type of particles that can be described mathematically. Pomelo can create output in different standard formats, which allows direct visualization and further processing. Finally, we describe three applications of the Set Voronoi code in granular and soft matter physics, namely the problem of packings of ellipsoidal particles with varying degrees of particle-particle friction, mechanical stable packings of tetrahedra and a model for liquid crystal systems of particles with shapes reminiscent of pears, 4 pages, 9 figures, Submitted to Powders and Grains 2017

We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model, which is formed by overlapping grains. Here we introduce an orientation bias of the grains that controls the degree of anisotropy of the generated patterns. We analyze in the Euclidean plane the percolation thresholds above which percolating clusters in $x$- and in $y$-direction emerge. Only in finite systems, distinct differences between effective percolation thresholds for different directions appear. If extrapolated to infinite system sizes, these differences vanish independent of the details of the model. In the infinite system, the uniqueness of the percolating cluster guarantees a unique percolation threshold. While percolation is isotropic even for anisotropic processes, the value of the percolation threshold depends on the model parameters, which we explore by simulating a score of models with varying degree of anisotropy. To which precision can we predict the percolation threshold without simulations? We discuss analytic formulas for approximations (based on the excluded area or the Euler characteristic) and compare them to our simulation results. Empirical parameters from similar systems allow for accurate predictions of the percolation thresholds (with deviations of $, 29 pages, 14 figures

We explore an alternate way of looking at the rheological response of a yield stress fluid: using discrete geometry to probe the heterogeneous distribution of stress in soap froth. We present quasi-static, uniaxial, isochoric compression and extension of three-dimensional random monodisperse soap froth in periodic boundary conditions and examine the stress and geometry that result. The stress and shape anisotropy of individual cells is quantified by Q, a scalar measure derived from the interface tensor that gauges each cell's contribution to the global stress. Cumulatively, the spatial distribution of highly deformed cells allows us to examine how stress is internally distributed. The topology of highly deformed cells, how they arrange relative to one another in space, gives insight into the heterogeneous distribution of stress.

To which degree are shape indices of individual cells of a tessellation characteristic for the stochastic process that generates them? Within the context of stochastic geometry and the physics of disordered materials, this corresponds to the question of relationships between different stochastic processes and models. In the context of applied image analysis of structured synthetic and biological materials, this question is central to the problem of inferring information about the formation process from spatial measurements of the resulting random structure. This chapter addresses this question by a theory-based simulation study of cell shape indices derived from tensor-valued intrinsic volumes, or Minkowski tensors, for a variety of common tessellation models. We focus on the relationship between two indices: (1) the dimensionless ratio 〈V 〉2∕〈A〉3 of empirical average cell volumes to areas, and (2) the degree of cell elongation quantified by the eigenvalue ratio 〈β10,2〉 of the interface Minkowski tensors W10,2. Simulation data for these quantities, as well as for distributions thereof and for correlations of cell shape and cell volume, are presented for Voronoi mosaics of the Poisson point process, determinantal and permanental point processes, Gibbs hard-core processes of spheres, and random sequential absorption processes as well as for Laguerre tessellations of configurations of polydisperse spheres, STIT-tessellations, and Poisson hyperplane tessellations. These data are complemented by experimental 3D image data of mechanically stable ellipsoid configurations, area-minimising liquid foam models, and mechanically stable crystalline sphere configurations. We find that, not surprisingly, the indices 〈V 〉2∕〈A〉3 and 〈β10,2〉 are not sufficient to unambiguously identify the generating process even amongst this limited set of processes. However, we identify significant differences of these shape indices between many of the tessellation models listed above. Therefore, given a realization of a tessellation (e.g., an experimental image), these shape indices are able to narrow the choice of possible generating processes, providing a powerful tool which can be further strengthened by considering density-resolved volume-shape correlations.

Purpose Structure-property relations, which relate the shape of the microstructure to physical properties such as transport or mechanical properties, need sensitive measures of structure. What are suitable fabric tensors to quantify the shape of anisotropic heterogeneous materials? The mean intercept length is among the most commonly used characteristics of anisotropy in porous media, e.g., of trabecular bone in medical physics. Yet, in this series of two papers we demonstrate that it has conceptual shortcomings that limit the validity of its results. Methods We test the validity of general assumptions regarding the properties of the mean-intercept length tensor using analytical formulas for the mean-intercept lengths in anisotropic Boolean models (derived in part I of this series), augmented by numerical simulations. We discuss in detail the functional form of the mean intercept length as a function of the test line orientations. Results As the most prominent result, we find that, at least for the example of overlapping grains modeling porous media, the polar plot of the mean intercept length is in general not an ellipse and hence not represented by a second-rank tensor. This is in stark contrast to the common understanding that for a large collection of grains the mean intercept length figure averages to an ellipse. The standard mean intercept length tensor defined by a least-square fit of an ellipse is based on a model mismatch, which causes an intrinsic lack of accuracy. Conclusions Our analysis reveals several shortcomings of the mean intercept length tensor analysis that pose conceptual problems and limitations on the information content of this commonly used analysis method. We suggest the Minkowski tensors from integral geometry as alternative sensitive measures of anisotropy. The Minkowski tensors allow for a robust, comprehensive, and systematic approach to quantify various aspects of structural anisotropy. We show the Minkowski tensors to be more sensitive, in the sense, that they can quantify the remnant anisotropy of structures not captured by the mean intercept length analysis. If applied to porous tissue and microstructures, this improved structure characterization can yield new insights into the relationships between geometry and material properties.

A fundamental understanding of the formation and properties of a complex spatial structure relies on robust quantitative tools to characterize morphology. A systematic approach to the characterization of average properties of anisotropic complex interfacial geometries is provided by integral geometry which furnishes a family of morphological descriptors known as tensorial Minkowski functionals. These functionals are curvature-weighted integrals of tensor products of position vectors and surface normal vectors over the interfacial surface. We here demonstrate their use by application to non-cubic triply periodic minimal surface model geometries, whose Weierstrass parametrizations allow for accurate numerical computation of the Minkowski tensors.

Tuning mechanical properties of and fluid flow through open-cell solid structures is a challenge for material science, in particular for the design of porous structures used as artificial bone scaffolds in tissue engineering. We present a method to tune the effective elastic properties of custom-designed open-cell solid foams and bone scaffold geometries by almost an order of magnitude while approximately preserving the pore space geometry and hence fluid transport properties. This strong response is achieved by a change of topology and node coordination of a network-like geometry underlying the scaffold design. Each node of a four-coordinated network is disconnected with probability p into two two-coordinated nodes, yielding network geometries that change continuously from foam- or network-like cellular structures to entangled fiber bundles. We demonstrate that increasing p leads to a strong, approximately exponential decay of mechanical stiffness while leaving the pore space geometry largely unchanged. This result is obtained by both voxel-based finite element methods and compression experiments on laser sintered models. The physical effects of randomizing network topology suggest a new design paradigm for solid foams, with adjustable mechanical properties.

We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has minimal packing and stretching frustration similar to those of the commonly found cubic bicontinuous mesophases. This hexagonal surface, of symmetry P6(3)/mmc with a lattice ratio of c/a = 0.832, is therefore a likely candidate geometry for self-assembled lipid/surfactant or copolymer mesophases. Furthermore, both the peak position ratios in its powder diffraction pattern and the elastic moduli closely resemble those of the cubic bicontinuous phases. We therefore argue that a genuine possibility of experimental misidentification exists.

The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ϕ is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ϕ, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(ϕ) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process.

The structure of the porous three-dimensional reticulated pattern in the wing scales of the butterfly Callophrys rubi (the Green Hairstreak) is explored in detail, via scanning and transmission electron microscopy. A full 3D tomographic reconstruction of a section of this material reveals that the predominantly chitin material is assembled in the wing scale to form a structure whose geometry bears a remarkable correspondence to the srs net, well-known in solid state chemistry and soft materials science. The porous solid is bounded to an excellent approximation by a parallel surface to the Gyroid, a three-periodic minimal surface with cubic crystallographic symmetry I4₁32, as foreshadowed by Stavenga and Michielson. The scale of the structure is commensurate with the wavelength of visible light, with an edge of the conventional cubic unit cell of the parallel-Gyroid of approximately 310 nm. The genesis of this structure is discussed, and we suggest it affords a remarkable example of templating of a chiral material via soft matter, analogous to the formation of mesoporous silica via surfactant assemblies in solution. In the butterfly, the templating is achieved by the lipid-protein membranes within the smooth endoplasmic reticulum (while it remains in the chrysalis), that likely form cubic membranes, folded according to the form of the Gyroid. The subsequent formation of the chiral hard chitin framework is suggested to be driven by the gradual polymerisation of the chitin precursors, whose inherent chiral assembly in solution (during growth) promotes the formation of a single enantiomer.

It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio νss=-1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio νLE≈-0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios νSS of the skeletal structure and νLE of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.

We describe a grand-canonical Monte Carlo simulation of a hard sphere fluid confined to porous media with arbitrary pore shape. The pore geometry is given by a triangulated surface representation of the solid-void interface. This algorithm is developed to study the dependence of thermodynamic quantities, such as the average density and adsorption, on the shape of the pore. Particular pore shape geometries that are analysed are the labyrinthine domains bounded by so-called triply-periodic minimal surfaces.

Die Fauna-Flora-Habitat-Richtlinie (FFH-RL, 92/43/EWG) enthalt neben dem Aufbau des Netzes Natura 2000 mit Arten und Lebensraumtypen auch Regeln fur den Artenschutz. Dreiviertel aller gemeldeten FFH-Gebiete beinhalten neben naturnahen Biotoptypen wie Waldern und Gewassern auch landwirtschaftliche Flachen. Wobei 18 % der Gebiete landwirtschaftliche Nutzflachen mit einem Anteil zwischen 25 und 50 % enthalten und 24 % sogar einen Anteil von uber 50 %. 48 Arten und drei Lebensraumtypen der FFH-RL haben einen Schwerpunkt im Agrarbereich. Hinzu kommen elf Lebensraumtypen, die von einer naturschutzgerechten landwirtschaftlichen Nutzung abhangig sind. Ein groser Teil dieser Lebensraume und Arten befindet sich derzeit nicht in einem gunstigen Erhaltungszustand. Der folgende Beitrag analysiert zum einen das Betroffensein der Landwirtschaft durch die Lebensraumtypen und Arten der FFH-RL, zum anderen werden einige indirekte negative Wirkungen aufgezeigt, die erheblichen Einfluss auf die Entwicklung der Erhaltungszustande von Lebensraumen und Arten haben konnen.

We investigate the emergence of subdiffusive transport by obstruction in continuum models for molecular crowding. While the underlying percolation transition for the accessible space displays universal behavior, the dynamic properties depend in a subtle non-universal way on the transport through narrow channels. At the same time, the different universality classes are robust with respect to introducing correlations in the obstacle matrix as we demonstrate for quenched hard-sphere liquids as underlying structures. Our results confirm that the microscopic dynamics can dominate the relaxational behavior even at long times, in striking contrast to glassy dynamics., Comment: to appear in Phys. Rev. Lett

This article explores global geometric features of bicontinuous space-partitions and their relevance to self-assembly of block-copolymers. Using a robust definition of `local channel radius', based on the concept of a medial surface [Schroder et al., Eur. Phys. J. B 35, 551 (2003)], we relate radius variations of the space-partition to polymolecular chain stretching in bicontinuous diblock- and terblock copolymer assemblies. We associate local surface patches with corresponding cellular volume elements, to define local volume-to-surface ratios. The distribution of these v/a ratios and of the channel radii are used to quantify the degree of packing frustration of molecular chains as a function of the specific bicontinuous geometry, modelled by triply-periodic minimal surfaces and related parallel interfaces. The Gyroid geometry emerges as the most nearly homogeneous bicontinuous form, with the smallest heterogeneity of channel radii, compared to the cubic Primitive and Diamond surfaces. We clarify a geometric feature of the Gyroid geometry: the three-coordinated nodes of the graph are not the widest points of the labyrinths; the widest points are at the midpoints of the edges. We also explore a more complex cubic triply-periodic surface, the I-WP surface, containing two geometrically distinct channel subdomains. One of the two channel systems is nearly as homogeneous in local channel diameters as the Gyroid, the other is more heterogeneous than the Primitive surface. Its hybrid nature suggests the possibility of an “alternating I-WP” phase in polydisperse linear ABC-terpolymer blends, with monodisperse molecular weight distributions (MWD) in the A and B blocks and a more polydisperse C block.

The 'simplest' entanglements of the graph of edges of the cube are enumerated, forming two-cell {6, 3} (hexagonal mesh) complexes on the genus-one two-dimensional torus. Five chiral pairs of knotted graphs are found. The examples contain non-trivial knotted and/or linked subgraphs [(2, 2), (2, 4) torus links and (3, 2), (4, 3) torus knots].

The structure of the upper layer of a comet is a product of its surface activity. The Rosetta Lander Imaging System (ROLIS) on board Philae acquired close-range images of the Agilkia site during its descent onto comet 67P/Churyumov-Gerasimenko. These images reveal a photometrically uniform surface covered by regolith composed of debris and blocks ranging in size from centimeters to 5 meters. At the highest resolution of 1 centimeter per pixel, the surface appears granular, with no apparent deposits of unresolved sand-sized particles. The thickness of the regolith varies across the imaged field from 0 to 1 to 2 meters. The presence of aeolian-like features resembling wind tails hints at regolith mobilization and erosion processes. Modeling suggests that abrasion driven by airfall-induced particle "splashing" is responsible for the observed formations.

Balanced infinite periodic minimal surface families that contain the cubic Gyroid (G), Diamond (D) and Primitive (P) surfaces are studied in terms of their global packing and local curvature properties. These properties are central to understanding the formation of mesophases in amphiphile and copolymer molecular systems. The surfaces investigated are the tetragonal, rhombohedral and hexagonal tD, tP, tG, rG, rPD and H surfaces. These non-cubic minimal surfaces furnish topology-preserving transformation pathways between the three cubic surfaces. We introduce `packing (or global) homogeneity', defined as the standard deviation Δd of the distribution of the channel diameter throughout the labyrinth, where the channel diameter d is determined from the medial surface skeleton centered within the labyrinthine domains. Curvature homogeneity is defined similarly as the standard deviation ΔK of the distribution of Gaussian curvature. All data are presented for distinct length normalisations: constant surface-to-volume ratio, constant average Gaussian curvature and constant average channel diameter. We provide first and second moments of the distribution of channel diameter for all members of these surfaces complementing curvature data from [A. Fogden, S. Hyde, Eur. Phys. J. B 7, 91 (1999)]. The cubic G and D surfaces are deep local minima of Δd along the surface families (with G more homogeneous than D), whereas the cubic P surface is an inflection point of Δd with adjacent, more homogeneous surface members. Both curvature and packing homogeneity favour the tetragonal route between G and D (via tG and tD surfaces) in preference to the rhombohedral route (via rG and rPD).

Dystroglycan is a component of the dystrophin glycoprotein complex that is cleaved into two polypeptides by an unidentified protease. To determine the role of post-translational processing on dystroglycan synthesis and trafficking we expressed the dystroglycan precursor and mutants thereof in a heterologous system. A point mutant in the processing site, S655A, prevented proteolytic cleavage but had no effect upon the surface localisation of dystroglycan. Mutation of two N-linked glycosylation sites that flank the cleavage site inhibited proteolytic processing of the precursor. Furthermore, chemical inhibition of N- and O-linked glycosylation interfered with the processing of the precursor and reduced the levels of dystroglycan at the cell surface. Dystroglycan processing was also inhibited by the proteasome inhibitor lactacystin. N-linked glycosylation is a prerequisite for efficient proteolytic processing and cleavage and glycosylation are dispensable for cell surface targeting of dystroglycan.

To assess the long-term outcome of patients with an enlarged ascending thoracic aorta (ATA), a retrospective study was performed. Methods Inclusion criteria: ATA diameter of 38 mm or more by ETT (813 consecutive cases). Inclusion period: 01.1.2003–31.12.2016. Results At baseline, the mean diameter of the ATA was 42 ± 3 mm, the mean Z-score was 2.7 ± 0.8. Six years later, the mean diameter was 41.9 ± 4.8 mm, the mean Z-score 2.4 ± 1.1. During the follow-up, 52 patients had an intervention on the ATA, 22 patients were operated within the first 3 months after the diagnostic echocardiogram. In the 791 remaining patients (without early intervention), the event rate (death, intervention on the ATA) was assessed by the competing risk model. In the group of patients with a baseline ATA diameter of less than 41 mm (Group A: n = 254), the cumulative incidence of death at 5 and 10 y was 34% and 61%; in the group of patients with an ATA diameter of 41–42 mm (Group B: n = 238) the incidence was 34% and 61% respectively, in the group of patients with an ATA diameter of 43-44 mm (Group C: n = 147), the incidence was 32% and 58%, in the group of patients with a diameter of 45 and more (Group D: n = 150), the incidence was 31.1% and 61% (NS). The cumulative incidence of intervention at 5 and 10 years was 0.4% and 1% in group A, 1.3 and 1.8% in group B, 0.7 and 1.4% in group C and 9.8 and 12.9% in group D (P 3, the incidence of intervention at 5 and 10 y was respectively 7.6% and 10.7% (P = 0.01). Conclusions The diameter of the enlarged ATA remained nearly unchanged over a period of 6 years. No impact of the enlarged ATA on survival was observed. Only patients with an ATA diameter of 45 mm and more (or a Z-score of 3 and more) needed an intervention at a rate of ±10% at 10 y after the initial echocardiographic diagnosis.