scholarly journals Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

2017 ◽  
Vol 114 (17) ◽  
pp. E3376-E3384 ◽  
Author(s):  
Thomas Gibaud ◽  
C. Nadir Kaplan ◽  
Prerna Sharma ◽  
Mark J. Zakhary ◽  
Andrew Ward ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Gaussian Curvature ◽  
Deformation Energy ◽  
Excluded Volume ◽  
Membrane Elasticity ◽  
Colloidal Monolayer ◽  
Colloidal Membranes ◽  
Open Structures ◽  
3D Shapes ◽  
Insight Into

In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length–thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.

scholarly journals Additive lattice kirigami

2016 ◽  
Vol 2 (9) ◽  
pp. e1601258 ◽  
Author(s):  
Toen Castle ◽  
Daniel M. Sussman ◽  
Michael Tanis ◽  
Randall D. Kamien
Keyword(s):  
Gaussian Curvature ◽  
Three Dimensional ◽  
Complex Structures ◽  
3D Structures ◽  
Flat Sheet ◽  
Simple Rules ◽  
New Material ◽  
3D Shapes ◽  
Huge Variety

Kirigami uses bending, folding, cutting, and pasting to create complex three-dimensional (3D) structures from a flat sheet. In the case of lattice kirigami, this cutting and rejoining introduces defects into an underlying 2D lattice in the form of points of nonzero Gaussian curvature. A set of simple rules was previously used to generate a wide variety of stepped structures; we now pare back these rules to their minimum. This allows us to describe a set of techniques that unify a wide variety of cut-and-paste actions under the rubric of lattice kirigami, including adding new material and rejoining material across arbitrary cuts in the sheet. We also explore the use of more complex lattices and the different structures that consequently arise. Regardless of the choice of lattice, creating complex structures may require multiple overlapping kirigami cuts, where subsequent cuts are not performed on a locally flat lattice. Our additive kirigami method describes such cuts, providing a simple methodology and a set of techniques to build a huge variety of complex 3D shapes.

GROUP-THEORETIC BIFURCATION MECHANISM OF PATTERN FORMATION IN THREE-DIMENSIONAL UNIFORM MATERIALS

2002 ◽  
Vol 12 (12) ◽  
pp. 2767-2797 ◽  
Author(s):  
REIKO TANAKA ◽  
ISAO SAIKI ◽  
KIYOHIRO IKEDA
Keyword(s):  
Fourier Series ◽  
Pattern Formation ◽  
Symmetry Breaking ◽  
Three Dimensional ◽  
Standard Group ◽  
Theoretic Approach ◽  
Qualitative Information ◽  
Geometric Patterns ◽  
Secondary Bifurcations ◽  
Insight Into

An underlying mathematical mechanism for formation of periodic geometric patterns in uniform materials is investigated. Symmetry of a rectangular parallelepiped domain with periodic boundaries is modeled as an equivariance to a group O (2) × O (2) × O (2). The standard group-theoretic approach is used to investigate possible patterns of this domain that emerge through direct and some secondary bifurcations. This investigation clarifies the mechanism of successive symmetry-breaking bifurcation, which entails a variety of geometrical patterns in three-dimensional uniform materials. In particular, a few characteristic geometric patterns, such as oblique layer, column and diamond patterns, are identified and classified. Pattern simulations are conducted on geometrical patterns of joints in a calcite and folds in a stratum to reinforce pertinence of the pattern formation mechanism. Images of three-dimensional patterns of joints and folds are expanded into the triple Fourier series, and transient processes of bifurcation are reconstructed to arrive at possible courses of successive bifurcation. Qualitative information from this approach can offer insight into transient courses of deformation, which have been overlooked up to now.

scholarly journals Extended Divisibility Relations for Constraint Polynomials of the Asymmetric Quantum Rabi Model

2020 ◽  
pp. 149-168
Author(s):  
Cid Reyes-Bustos
Keyword(s):  
Symmetry Breaking ◽  
Quantum Optics ◽  
Bargmann Space ◽  
Asymmetric Quantum ◽  
Rabi Model ◽  
Symmetry Breaking Term ◽  
Divisibility Properties ◽  
Breaking Term ◽  
Insight Into

Abstract The quantum Rabi model (QRM) is widely regarded as one of the fundamental models of quantum optics. One of its generalizations is the asymmetric quantum Rabi model (AQRM), obtained by introducing a symmetry-breaking term depending on a parameter $$\varepsilon \in \mathbb {R}$$ to the Hamiltonian of the QRM. The AQRM was shown to possess degeneracies in the spectrum for values $$\epsilon \in 1/2\mathbb {Z}$$ via the study of the divisibility of the so-called constraint polynomials. In this article, we aim to provide further insight into the structure of Juddian solutions of the AQRM by extending the divisibility properties and the relations between the constraint polynomials with the solution of the AQRM in the Bargmann space. In particular we discuss a conjecture proposed by Masato Wakayama.

scholarly journals Carbon-Origami: Controlling 3D Shapes and Microstructure

2021 ◽  
Vol 4 (1) ◽  
pp. 47
Author(s):  
Marc Madou
Keyword(s):  
Multiwall Carbon Nanotubes ◽  
Polymer Precursor ◽  
Precise Control ◽  
Polymer Precursors ◽  
Sensing Applications ◽  
One Step ◽  
3D Shapes ◽  
Multiwall Carbon ◽  
Insight Into ◽  
Pan Fibers

Over the last two decades, we have gained more and more insight into how to convert patterned polymer precursors into predicable 3D carbon shapes using pyrolysis/carbonization (carbon origami are a more recent example). Over the last four years, we have started gaining control over the internal carbon microstructure and its functionality. The key to the latter is a precise control of the polymer precursor chains and the exact polymer atomic composition of the polymer before and during pyrolysis. Contradicting Rosalind Franklin, we have found that it is possible to graphitize even non-graphitizing carbons, simply by applying mechanical stresses to align the polymer precursor chains and stabilizing them in position before pyrolysis. Perhaps the most surprising outcome of this work is the demonstration of the conversion of PAN fibers through pyrolysis into turbostratic graphene-suspended wires with diameters as small as 2 nanometers. The suspended graphene bridges have a conductivity similar to that of multiwall carbon nanotubes (MWCNTs), a Young’s modulus of >400 GPa, and electrochemically the material behaves similarly to graphene doped with nitrogen. The latter material represents a very electroactive electrode ideally suited for energy and sensing applications. The current fabrication process for graphene doped with nitrogen is lengthy and complicated; ours is a one-step, simple process that is easily scalable.

scholarly journals The structure of CYP101D2 unveils a potential path for substrate entry into the active site

2010 ◽  
Vol 433 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Wen Yang ◽  
Stephen G. Bell ◽  
Hui Wang ◽  
Weihong Zhou ◽  
Mark Bartlam ◽  
...  
Keyword(s):  
Active Site ◽  
Binding Sites ◽  
Bound Water ◽  
Selection Mechanism ◽  
Conformational Selection ◽  
Access Channel ◽  
Open Structures ◽  
Haem Iron ◽  
Insight Into ◽  
Positively Charged

The cytochrome P450 CYP101D2 from Novosphingobium aromaticivorans DSM12444 is closely related to CYP101D1 from the same bacterium and to P450cam (CYP101A1) from Pseudomonas putida. All three are capable of oxidizing camphor stereoselectively to 5-exo-hydroxycamphor. The crystal structure of CYP101D2 revealed that the likely ferredoxin-binding site on the proximal face is largely positively charged, similar to that of CYP101D1. However, both the native and camphor-soaked forms of CYP101D2 had open conformations with an access channel. In the active site of the camphor-soaked form, the camphor carbonyl interacted with the haem-iron-bound water. Two other potential camphor-binding sites were also identified from electron densities in the camphor-soaked structure: one located in the access channel, flanked by the B/C and F/G loops and the I helix, and the other in a cavity on the surface of the enzyme near the F helix side of the F/G loop. The observed open structures may be conformers of the CYP101D2 enzyme that enable the substrate to enter the buried active site via a conformational selection mechanism. The second and third binding sites may be intermediate locations of substrate entry and translocation into the active site, and provide insight into a multi-step substrate-binding mechanism.

Calibration problems in hydrogen luminosities

1966 ◽  
Vol 24 ◽  
pp. 322-330
Author(s):  
A. Beer
Keyword(s):  
Galactic Structure ◽  
B Stars ◽  
Insight Into

The investigations which I should like to summarize in this paper concern recent photo-electric luminosity determinations of O and B stars. Their final aim has been the derivation of new stellar distances, and some insight into certain patterns of galactic structure.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

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