OPTIMIZATION OF TREE STRUCTURES WITH RHOMBIC GRIDS

Представлено конструктивно-компоновочное решение стержней Y-образных и Ψ-образных очертаний в фермах с ромбической решеткой или фермах с ромбической решеткой и полустойками (полуподвесками), техническая новизна которого подтверждена результатами патентной экспертизы. Универсальность этого решения для ферменных конструкций обеспечивает ту эффективность, с какой оно применимо к грузовым верхним поясам, грузовым нижним поясам или грузовым верхним и нижним поясам одной и той же решетки. Повышена степень унификации фермы из прямоугольных гнутосварных профилей (профильных труб) за счет использования в верхнем поясе форм и наружных габаритов поперечных сечений, принятых для нижнего пояса. При этом ресурсы несущей способности разнятся между ними в пределах однопроцентного порога, что обеспечивает необходимую и достаточную равнопрочность обоих поясов для их более рациональной унификации. Узловые соединения стержней разных очертаний с верхними поясами позволяют оптимизировать опорные условия настилов и прогонов с уменьшением размеров их грузовых площадей. Возрастание общего количества прогонов приводит к снижению их суммарной массы и массы кровельного ограждения, что весьма актуально для вариантного и оптимального проектирования строительных конструкций с учетом риска лавинообразного обрушения. Выявлена перспективность применения нового технического решения в составе несущих и связевых систем различных зданий и сооружений. The structural and layout solution of rods of Y-shaped and Ψ-shaped outlines in trusses with a rhombic lattice or trusses with a rhombic lattice and half-posts (half-suspensions) is presented, the technical novelty of which is confirmed by the results of patent examination. The versatility of this truss solution is as effective as it is for load tops, load bottoms, or load tops and bottoms of the same grid. The degree of unification of the truss of rectangular bent-welded profiles (shaped pipes) has been increased due to the use in the upper chord of the forms and outer dimensions of the cross-sections adopted for the lower chord. At the same time, the resources of the bearing capacity differ between them within a one- percent threshold, which ensures the necessary and sufficient equal strength of both belts for their more rational unification. Nodal connections of rods of different shapes with the upper chords allow to optimize the support conditions of decks and purlins with a decrease in the size of their cargo areas. An increase in the total number of runs leads to a decrease in their total mass and the mass of the roofing, which is very important for the variant and optimal design of building structures, taking into account the risk of an avalanche collapse. The prospect of using a new technical solution in the composition of bearing and communication systems of various buildings and structures has been revealed.

Controlling of longwave oscillatory Marangoni patterns on a rhombic lattice

We apply nonlinear feedback control to govern the stability of long-wave oscillatory Marangoni patterns. We focus on the patterns caused by instability in thin liquid film heated from below with a deformable free surface. This instability emerges in the case of substrate of low thermal conductivity, when two monotonic long-wave instabilities, Pearson's and deformational ones, are coupled. We provide weakly nonlinear analysis within the amplitude equations, which govern the evolution of the layer thickness and the temperature deviation. The action of the nonlinear feedback control on the nonlinear interaction of two standing waves is investigated. It is shown that quadratic feedback control can produce additional stable structures (standing rolls, standing squares and standing rectangles), which are subject to instability leading to traveling wave in the uncontrolled case.

Complex multicomponent patterns rendered on a 3D DNA-barrel pegboard

DNA origami, in which a long scaffold strand is assembled with a many short staple strands into parallel arrays of double helices, has proven a powerful method for custom nanofabrication. However, currently the design and optimization of custom 3D DNA-origami shapes is a barrier to rapid application to new areas. Here we introduce a modular barrel architecture, and demonstrate hierarchical assembly of a 100 megadalton DNA-origami barrel of ~90 nm diameter and ~250 nm height, that provides a rhombic-lattice canvas of a thousand pixels each, with pitch of ~8 nm, on its inner and outer surfaces. Complex patterns rendered on these surfaces were resolved using up to twelve rounds of Exchange-PAINT super-resolution microscopy. We envision these structures as versatile nanoscale pegboards for applications requiring complex 3D arrangements of matter, which will serve to promote rapid uptake of this technology in diverse fields beyond specialist groups working in DNA nanotechnology.

Topological Corner Modes in Graphene-Coated Nanowire Waveguide

We study the plasmonic second-order topological modes in nanowire waveguides which are covered by monolayer graphene. The waveguide arrays are arranged in the kagome lattice. In a triangle-shaped lattice, the topological modes are localized at the corner of the triangle by tuning the spatial spacing between the different waveguides. The corner modes also depend on the corner shape, which only exist at one corner in a rhombic lattice. In addition to the corner modes, both structures also support the topological edge mode. We show that the corner modes experience a smaller modal wavelength, longer propagation distance, and smaller mode volume than the edge modes. The study may be utilized to explore the topological bound modes at the nanoscale.

Fundamental Domains for Rhombic Lattices with Dihedral Symmetry of Order 8

We show by construction that every rhombic lattice $\Gamma$ in $\mathbb{R}^{2}$ has a fundamental domain whose symmetry group contains the point group of $\Gamma$ as a subgroup of index $2$. This solves the last open case of a question raised in a preprint by the authors on fundamental domains for planar lattices whose symmetry groups properly contain the point groups of the lattices.

Single-side and double-side swing behaviours of a flexible porous coordination polymer with a rhombic-lattice structure

A rhombic porous coordination polymer can show special reversible–irreversible structural transformations with single-side and double-side swing, as well as sophisticated bond reconstitution behaviours.