Side Chain Dispersity Matters: Topologically Precise and Discrete Bottlebrush Polymers

The synthesis of bottlebrush polymers with topologically precise and fully discrete structures is reported. Key features of the synthesis include the combination of scalable synthesis and separation strategies to access discrete macromonomer libraries, followed by their polymerization and further separation into topologically uniform and discrete bottlebrushes. Discrete macromonomers prove crucial for regulating the structural heterogeneity of bottlebrushes and their macroscopic properties. When assembled as a monolayer at the air-water interface, bottlebrushes with discrete side chains display high packing density and distinct three-phase Langmuir-Blodgett isotherms. The impact of precisely regulating side chain dispersity and sequence on polymer properties was further demonstrated through tailoring the interbrush interactions and thermomechanical properties of well-defined block bottlebrushes.

Rigidity through a Projective Lens

In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar–joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body–hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas.

The Voyatzis Mansion in Aegina, Greece: A Historical and Architectural Approach and Physicochemical Documentation of the Wall Painting Decoration

This paper refers to the study of the Voyatzis mansion, in the port of Aegina, Greece. The building complex consists of two discrete structures, which were built at different times (before 1830, 1880 and 1890) and have housed either the Voyatzis family home or its business and work premises. The present research is focused on the documentation of the building, which was never published, and combines the architectural form and elements within its historical context as well as the physicochemical analysis of the painted decoration. The key hypothesis investigated is whether Konstantinos Voyatzis transferred the aesthetic approach and application techniques from Symi to Aegina, when he emigrated from his birthplace. The documentation of the ceiling decoration as well as the physicochemical study of the second floor’s internal wall painting decoration in the main rooms was carried out using in situ modern hyperspectral imaging in specific wavelengths of the visible and near-infrared region, as well as in false color infrared mode. Complementary SWIR imaging, using an InGaAs sensor at the range 900–1700 nm was also applied. The assumption was supported by the findings of the imaging techniques, which showed, apart from the secco method, the use of traditional pigments for the wall paintings, such as cobalt blue, brown, red and yellow earth pigments, chrome oxide green and black, sometimes in admixture with white. The use of guidelines and stencil in the case of the hallway was also recorded.

Exploring 3D printing techniques for the hybrid fabrication of discrete topology optimized structures

The application of topology optimization methods in architecture, while useful for conceptual design explorations, seems to be limited by the practical realization of continuum-type design outcomes. One way to overcome this limitation is setting up design and fabrication techniques, through which continuum domains become discrete structures. This study investigates to which extent discrete optimized systems can be built using a hybrid approach combining 3D printing and analogue fabrication techniques. The procedure is based on an algorithm in Grasshopper (Rhinoceros) that translates continuum topologies obtained in MATLAB into discrete systems, providing alternatives depending on the targeted volume fraction, the intended surface smoothness of the structural components and building material. The study focuses on fabrication aspects and structural performance of discrete structures using 3D printed nodes. Experimental tests evaluate the compressive strength of different types of filaments with varied infill percentages. Final prototypes are fabricated using a hybrid technique involving the use of 3D printed nodes to assemble bar-arrays comprising wooden members. Results provide a critical appraisal of the limitations and potentialities of 3D printing for hybrid fabrication of real scale structures.

Coloring Properties of Mixed Cycloids

In this paper, we investigate partitions of highly symmetrical discrete structures called cycloids. In general, a mixed hypergraph has two types of hyperedges. The vertices are colored in such a way that each C-edge has two vertices of the same color, and each D-edge has two vertices of distinct colors. In our case, a mixed cycloid is a mixed hypergraph whose vertices can be arranged in a cyclic order, and every consecutive p vertices form a C-edge, and every consecutive q vertices form a D-edge in the ordering. We completely determine the maximum number of colors that can be used for any p≥3 and any q≥2. We also develop an algorithm that generates a coloring with any number of colors between the minimum and maximum. Finally, we discuss the colorings of mixed cycloids when the maximum number of colors coincides with its upper bound, which is the largest cardinality of a set of vertices containing no C-edge.

AMPLITUDE DISTRIBUTION OF LINEAR ANTENNA SYSTEMS WITH CONTINUOUS APERTURES

Проведены исследования известных амплитудных распределений для линейных непрерывных раскрывов, а также получен ряд новых распределений с наилучшим соотношением коэффициента использования поверхности раскрыва для заданного уровня боковых лепестков. Среди рассмотренных известны амплитудные распределения типа “косинус m-й степени”. Отмечены амплитудные распределения из данного класса, диаграммы направленности которых обладают противофазными боковыми лепестками. Предложен новый класс амплитудных распределений для непрерывных раскрывов типа суперпозиции “косинус m-й степени” и “косинус m-2 степени” с разными весовыми коэффициентами, диаграммы направленности которых с противофазными боковыми лепестками дают результирующую с узким главным лепестком, меньшим значением уровня боковых лепестков и более высоким коэффициентом использования поверхности раскрыва в сравнении с классическим распределением “косинус m-й степени”. Приведен сравнительный анализ полученных непрерывных распределений с Дольф-Чебышевскими амплитудными распределениями для дискретных структур по критерию максимального коэффициента использования поверхности раскрыва для заданного уровня боковых лепестков. Показано, что коэффициент использования поверхности раскрыва сравниваемых амплитудных распределений при высоком уровне боковых лепестков отличается на 35%. Предложенный класс амплитудных распределений позволяет получать высокие значения коэффициента использования поверхности раскрыва для непрерывных структур и, следовательно, высокий коэффициент направленного действия We carried out investigations of the known amplitude distributions for linear continuous apertures and obtained a number of new distributions with the best ratio of the utilization factor of the aperture surface for a given level of side lobes. Among the considered, there are the well-known amplitude distributions of the “cosine of the m-th degree” type. We note amplitude distributions from this class, the directional patterns of which have antiphase side lobes. We propose a new class of amplitude distributions for continuous apertures of the superposition type “cosine of the m-th degree” and “cosine of the m-2 degree” with different weight coefficients, the radiation patterns of which with antiphase side lobes give the resultant with a narrow main lobe, a lower value of the level of side lobes and a higher utilization of the aperture surface in comparison with the classical distribution “cosine of the m-th degree”. We present a comparative analysis of the obtained continuous distributions with the Dolph-Chebyshev amplitude distributions for discrete structures according to the criterion of the maximum utilization of the aperture surface for a given level of side lobes. We show that the utilization factor of the aperture surface of the compared amplitude distributions at a high level of side lobes differs by 35%. The proposed class of amplitude distributions allows one to obtain high values of the coefficient of use of the aperture surface for continuous structures and, therefore, a high coefficient of directional action

Near quantitative synthesis of urea macrocycles enabled by bulky N-substituent

Macrocycles are unique molecular structures extensively used in the design of catalysts, therapeutics and supramolecular assemblies. Among all reactions reported to date, systems that can produce macrocycles in high yield under high reaction concentrations are rare. Here we report the use of dynamic hindered urea bond (HUB) for the construction of urea macrocycles with very high efficiency. Mixing of equal molar diisocyanate and hindered diamine leads to formation of macrocycles with discrete structures in nearly quantitative yields under high concentration of reactants. The bulky N-tert-butyl plays key roles to facilitate the formation of macrocycles, providing not only the kinetic control due to the formation of the cyclization-promoting cis C = O/tert-butyl conformation, but also possibly the thermodynamic stabilization of macrocycles with weak association interactions. The bulky N-tert-butyl can be readily removed by acid to eliminate the dynamicity of HUB and stabilize the macrocycle structures.