Dispersion laws in crystals having a rhombic lattice with centered bases

1969 ◽  
Vol 12 (11) ◽  
pp. 1445-1450
Author(s):  
N. V. Kudryavtseva ◽  
L. V. Tikhonova
Keyword(s):  
Rhombic Lattice

Band gap properties of two-dimensional photonic crystals with rhombic lattice

Optik ◽  
2012 ◽  
Vol 123 (6) ◽  
pp. 534-536 ◽  
Author(s):  
Zhenhai Wu ◽  
Kang Xie ◽  
Huajun Yang
Keyword(s):  
Photonic Crystals ◽  
Band Gap ◽  
Two Dimensional ◽  
Rhombic Lattice

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

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Shelley F. J. Wickham ◽  
Alexander Auer ◽  
Jianghong Min ◽  
Nandhini Ponnuswamy ◽  
Johannes B. Woehrstein ◽  
...  
Keyword(s):  
Dna Nanotechnology ◽  
Super Resolution ◽  
Dna Origami ◽  
Design And Optimization ◽  
Hierarchical Assembly ◽  
Double Helices ◽  
Specialist Groups ◽  
Parallel Arrays ◽  
Super Resolution Microscopy ◽  
Rhombic Lattice

AbstractDNA 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.

OPTIMIZATION OF TREE STRUCTURES WITH RHOMBIC GRIDS

2021 ◽  
pp. 54-68
Author(s):  
А.С. Марутян
Keyword(s):  
Cross Sections ◽  
Communication Systems ◽  
Technical Solution ◽  
Building Structures ◽  
Tree Structures ◽  
Different Shapes ◽  
Support Conditions ◽  
Necessary And Sufficient ◽  
Patent Examination ◽  
Rhombic Lattice

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.

scholarly journals Fundamental Domains for Rhombic Lattices with Dihedral Symmetry of Order 8

10.37236/7802 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Joseph Ray Clarence G. Damasco ◽  
Dirk Frettlöh ◽  
Manuel Joseph C. Loquias
Keyword(s):  
Symmetry Group ◽  
Fundamental Domain ◽  
Point Group ◽  
Symmetry Groups ◽  
Fundamental Domains ◽  
Open Case ◽  
Point Groups ◽  
Index 2 ◽  
Rhombic Lattice ◽  
Planar Lattices

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.  

Quantum transport in a one-dimensional flux rhombic lattice

2021 ◽  
Vol 51 (6) ◽  
pp. 502-505
Author(s):  
P S Muraev ◽  
A R Kolovsky
Keyword(s):  
Quantum Transport ◽  
One Dimensional ◽  
Rhombic Lattice

scholarly journals Nanopatterning Gold by Templated Solid State Dewetting on the Silica Warp and Weft of Diatoms

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Jon Hiltz ◽  
Ahmadreza Hajiaboli ◽  
Gursimranbir Singh ◽  
R. Bruce Lennox ◽  
Gregor F. Fussmann ◽  
...  
Keyword(s):  
Lattice Points ◽  
Particle Sizes ◽  
Temperature Dependent ◽  
Thermally Induced ◽  
Nitzschia Palea ◽  
Periodic Distribution ◽  
Multiple Particles ◽  
Faceted Particles ◽  
Rhombic Lattice ◽  
Selective Accumulation

The diatom,Nitzschia palea, exhibits complex silica shell (frustule) topography that resembles the warp and weft pattern of woven glass. The surface is perforated with a rhombic lattice of roughly oblong pores between periodically undulating transverse weft costae. Exfoliated frustules can be used to template gold nanoparticles by thermally induced dewetting of thin gold films. Acting as templates for the process, the frustules give rise to two coexisting hierarchies of particle sizes and patterned distributions of nanoparticles. By examining temperature dependent dewetting of 5, 10, and 15 nm Au films for various annealing times, we establish conditions for particle formation and patterning. The 5 nm film gives distributions of small particles randomly distributed over the surface and multiple particles at the rhombic lattice points in the pores. Thicker films yield larger faceted particles on the surface and particles that exhibit shapes that are roughly conformal with the shape of the pore container. The pores and costae are sources of curvature instabilities in the film that lead to mass transport of gold and selective accumulation in the weft valleys and pores. We suggest that, with respect to dewetting, the frustule comprises 2-dimensional sublattices of trapping sites. The pattern of dewetting is radically altered by interposing a self-assembled molecular adhesive of mercaptopropyltrimethoxysilane between the Au film overlayer and the frustule. By adjusting the interfacial energy in this manner, a fractal-like overlay of Au islands coexists with a periodic distribution of nanoparticles in the pores.

scholarly journals Controlling of longwave oscillatory Marangoni patterns on a rhombic lattice

2020 ◽  
Author(s):  
Anna Samoilova ◽  
Alexander Nepomnyashchy
Keyword(s):  
Feedback Control ◽  
Thin Liquid Film ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Amplitude Equations ◽  
Temperature Deviation ◽  
Weakly Nonlinear ◽  
Long Wave ◽  
The Stability ◽  
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.

Elliptic Functions with Disconnected Julia Sets

2016 ◽  
Vol 26 (06) ◽  
pp. 1650095 ◽  
Author(s):  
Lorelei Koss
Keyword(s):  
Fixed Point ◽  
Critical Points ◽  
Elliptic Function ◽  
Julia Set ◽  
Julia Sets ◽  
Elliptic Functions ◽  
Equivalence Classes ◽  
Weierstrass Elliptic Function ◽  
Typical Function ◽  
Rhombic Lattice

In this paper, we investigate elliptic functions of the form [Formula: see text], where [Formula: see text] is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin and five other equivalence classes of critical points. We investigate conditions on the lattice which guarantee that [Formula: see text] has a double toral band, and we show that this family contains the first known examples of elliptic functions for which the Julia set is disconnected but not Cantor.

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