Cylindrical Lattice Research Articles

Microtubule Nucleation and Stabilization by Doublecortin

Doublecortin (DCX) is a microtubule (MT)-associated protein indispensable for migrating neurons during brain development. DCX nucleates and stabilises MTs via homologous DC domains. The C-terminal DC domain (C-DC) is separated from the N-terminal counterpart (N-DC) by a 42-residue linker. Intellectual disability (smooth brain) and epilepsy-causing mutations cluster around both DC domains. Thus, both domains are thought to interact with MTs, but their exact roles remain obscure. For MT nucleation, the naturally bent tubulin dimers associating longitudinally and laterally need to straighten up to form cylindrical lattice. Stabilization of such lattice relies on counteracting the natural tendency of tubulin to curl outward. The DCX binding site on the MT lattice is at the vertex of four tubulin dimers, so DCX binding stabilizes both longitudinal and lateral lattice contacts. But it is neither clear which of the two DC domains mediates this MT-stabilizing interaction nor which is involved in MT nucleation. We found that the construct in which C-DC was replaced with another N-DC showed much lower MT-nucleating activity and – in contrast to wild-type DCX – it produced not only the physiological 13-protofilament (PF) MT architecture, but also 14-PF MTs. Near-atomic resolution cryo-EM reconstructions enabled visualisation of the structural differences between the DC domains suggesting that N-DC has higher affinity for the mature MT lattice while the newly-formed lattice is predominantly decorated with C-DC. Molecular modelling suggests that C-DC can bind between moderately curved PFs, whereas N-DC cannot. The predicted C-DC binding mode largely overlaps with patient mutations. Taken together, the data suggest that C-DC facilitates nucleation of physiological 13-PF MTs, while N-DC gradually replaces C-DC along the lattice, ensuring robust stabilisation of the straight polymer.

CoCr porous scaffolds manufactured via selective laser melting in orthopedics: Topographical, mechanical, and biological characterization

Over the last decade, advances in additive manufacturing have allowed to obtain complex 3D porous lattice in materials suitable for orthopedic applications. Whereas 3D-melted titanium alloys have been extensively investigated, little is the current knowledge on the feasibility of bone-replicating CoCr porous scaffolds manufactured via selective laser melting (SLM). Moreover, the effect of topography on bone cells viability and proliferation has not been fully explored yet. Small cylindrical porous lattices were modeled from micro-CT images of human trabecular bone, and from the repetition of spherical-hollow and body-centered cubic unit cells, and manufactured via SLM from CoCr powder. Macro- and microcharacterization of the porous samples were assessed using optical microscope, micro-CT, and SEM. The scaffolds mechanical properties, measured via ISO testing, compared well with those of the human bone. Osteoblast-like cells proliferation and viability were assessed in vitro, and compared to those cultured on a standard nonporous implant-to-bone interface, showing steady increase on all geometries over time. SEM analysis confirmed the quality of cells morphology, spread, and organization on all lattices. The SLM process appeared not to alter the biocompatibility of CoCr; however, 15-100 μm irregularities and macroalterations were observed in the porous scaffolds with respect to the 3D nominal models. © 2019 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater 107B: 2343-2353, 2019.

Numerical and Experimental Investigation of the Mechanical Behavior of Cable‐Supported Barrel Vault Structures with Varying Temperature

The cable‐supported barrel vault (CSBV) structure system is a new type of hybrid spatial steel structure based on a beam string structure (or truss string structure), suspendomes, and cylindrical lattice shells. Steel cables (e.g., steel wire rope cables, steel strand cables, semiparallel steel tendons, and steel rods) are key components of CSBV structures. However, they have different elastic moduli and thermal expansion coefficients. In this study, the roof of a textile workshop (the first CSBV structure in China) was analyzed with four types of cables under the effect of varying temperature. Under half‐span loading and full‐span loading, the structural internal force and displacement at varying temperatures were obtained from finite element models employing four different types of steel cables. The internal force, displacement, and horizontal arch thrust changed linearly with increasing temperature. Moreover, the dynamic characteristics of CSBV with varying temperature were analyzed. The frequency of the CSBV changed linearly with increasing temperature. Based on the dynamic characteristics of CSBV with varying temperature, a seismic response time‐history analysis was performed. The variation in the maximum responses of the internal force, displacement, and horizontal arch thrust was obtained. In each case, the mechanical behavior of the CSBV with semiparallel steel tendon cables was strongly affected by the temperature. Therefore, semiparallel steel tendons are not recommended as components of CSBV in cases where large temperature changes can be expected. Thereafter, a scale model of a CSBV was designed and used for experiments and corresponding finite element analyses under varying temperature. Experimental results show that the finite element method is effective for analyzing the mechanical behavior of CSBV under varying temperature.

Circular bargraphs

In this paper, we introduce a new class of bargraphs – circular bargraphs, which are self-avoiding walks in a cylindrical lattice, and study the enumerations of them with respect to perimeter statistic. More precisely, we study the perimeter of a circular bargraph, a statistic defined naturally as the number of edges in the boundary of the bargraph. We also find an explicit formula for the total length of the perimeter over all bargraphs with n-cells.

Comparison of buckling loads of hyperboloidal and cylindrical lattice structures

Cylindrical lattice structures are types of lightweight structures and can utilize the orthotropy of fiber-reinforced composite materials. Maximization of the buckling loads is important because they dominate the strength of the structures. On the basis of the fact that a hyperboloidal shape deviation increases the buckling loads of cylindrical homogeneous shells, the changes in the buckling loads of cylindrical lattice structures with a hyperboloidal shape deviation are discussed. Further, the buckling loads of both conventional cylindrical lattice structures and shape-deviated hyperboloidal lattice structures with respect to the compressive, bending, and torsional loads are calculated using a finite element method. The results show that the shape deviation decreases the buckling loads, while the change in mass is negligible. The effects of the shape deviation on the buckling loads differ between homogeneous shell structures and lattice structures.

The similarity law and its verification of cylindrical lattice shell model under internal explosion

It is very important to ensure that the results of a scale model experiment of the large-span space steel structure under internal explosion could accurately show the characteristics of its original model. For this purpose, a one-way inclined bar type of single layer cylindrical lattice shell was taken as an example in this paper, and the similarity law between the scale models and the original model under the internal explosion was deduced by the dimension analysis principle. Then, the original model and the scale models under internal explosions were simulated by ANSYS/LS-DYNA, and the correctness and the feasibility of the similarity law were compared and confirmed. The research results showed that: if the scale models conform to the similarity law, the propagation law and the overpressure distribution of shock waves to the scale models subjected to internal explosions were consistent with the original model; the phenomena of critical destruction of the scale models were similar to the experimental results. But the accuracy of the loading effects of blast (such as the overpressure peak of shock waves, the positive pressure time and the impulse etc.) and the structural dynamic responses obtained by the scale models was affected by the geometric incomplete similarity of the scale models and the strain rate effect of steel respectively, which would reduce with the decrease of the scaling coefficient. Especially, the research results also indicated that if the scaling coefficient was not less than 0.1, the maximum deviations of the overpressure peak of shock waves, the positive pressure time after conversion and the specific impulse after conversion would be 10%, 4.78% and 29.8%, respectively, and if the scaling coefficient was less than 0.25, the stress responses and displacement responses of the scale model under internal explosion would not be reliable. Based on the research results, the reasonable scaling coefficients to the scale model experiment of cylindrical lattice shell under internal explosion are proposed.

Manufacture and prefabrication practice on a test model of a novel six-bar tetrahedral cylindrical lattice shell

A six-bar tetrahedral unit of a rhombic projection plane is a basic geometric invariable body with a simple configuration. A six-bar tetrahedral cylindrical lattice shell can be assembled by rhombic projection plane six-bar tetrahedral units with identical geometry sizes, which is conducive to standardized design, industrial production, and prefabricated construction. The popularization and application requirements of green architecture industry can also be met using such a shell. A model test of a six-bar tetrahedral cylindrical lattice shell was developed to simulate the practical application of the prefabricated structural system. A new type of joint for the prefabricated structure was proposed that is easy to assemble and is lightweight. A tridimensional fine-tuning bed jig was developed to ensure the manufacturing precision of the pre-made six-bar tetrahedral units. Stacking and transport of the units were practiced. The assembly process from units to the integral shell was conducted in an experimental hall; the result testified the advantages of easy stack, convenient transport, and highly efficient fabrication. The structural assembly errors of the shell were measured, and the measurement results verified the installation accuracy of the test model. This practical study lays the foundation for further engineering applications of six-bar tetrahedral cylindrical lattice shells.

육각 격자구조를 갖는 원통형 복합재 격자 구조물의 유한요소 모델링 기법 연구

In this paper, finite element modeling methods for cylindrical composite lattice structures were verified through natural frequency test. Finite element models for cylindrical composite lattice structure were developed using beam, shell and solid elements. Natural frequency test was measured using impact test method under free-boundary condition. The analysis result of the beam element model showed up to 23% errors because the beam element could not consider the degradation of mechanical properties of non-intersection parts of the composite lattice structures. On the other hand, the natural frequencies of finite element analysis for shell and solid element models showed good results with natural frequencies test. From the analysis of the experiment, finite element model for composite lattice structures should use shell or solid element which takes into consideration the intersection and non-intersection parts.

Composited holograms for the generation of cylindrical optical lattices and flower modes.

We present composited holograms to realize the azimuthal interference of cylindrical optical lattices (COLs) and the flower modes (FMs) of Fourier transform-truncated Bessel beams (FT-TBB). Three types of binarization operations are evaluated for the composited holograms generated by two FT-TBB with independent topological charges l1 and l2 and the same radial index p=1. Both the numerical solutions and experimental results demonstrate that the four types of COLs and FMs, namely, the conventional COL, interleaved COL, flower-core FM, and polygon-core FM, can be produced by the Fourier transformation of the composited holograms with the same radial index p=1 and topological combinations ||l1|-|l2||<2, ||l1|-|l2||=2, ||l1|-|l2||=3, and ||l1|-|l2||=4, respectively. Moreover, a modified hologram with a scalar factor is introduced for further tailoring of these multi-ring azimuthal distribution profiles. The evolutions of the intensity profiles for various values of the scale factor are presented. Our results indicate that the modified hologram is capable of an in-depth exploration of the desired intensity profile of COLs and FMs, providing a flexible platform for a light potential probe and microscopy.

Critical Phenomena in the Five-Stage Reaction of Catalytic Oxidation of Carbon Oxide on a Cylindrical Catalytic Surface

The dynamics of the kinetic model corresponding to the five-stage mechanism of the reaction of catalytic oxidation of carbon monoxide on a cylindrical lattice is studied. It is demonstrated that the curvature of the lattice can serve as an order parameter for the conditions for the loss of stability of stationary states uniform with respect to space and the possibility of the appearance of a multiplicity of the latter.

Anisotropy crossover in the frustrated Hubbard model on four-chain cylinders

Motivated by dimensional crossover in layered organic ${\kappa}$ salts, we determine the phase diagram of a system of four periodically coupled Hubbard chains with frustration at half filling as a function of the interchain hopping ${t_{\perp}/t}$ and interaction strength ${U/t}$ at a fixed ratio of frustration and interchain hopping ${t'/t_{\perp}=-0.5}$. We cover the range from the one-dimensional limit of uncoupled chains (${t_{\perp}/t=0.0}$) to the isotropic model (${t_{\perp}/t=1.0}$). For strong ${U/t}$, we find an antiferromagnetic insulator; in the weak-to-moderate-interaction regime, the phase diagram features quasi-one-dimensional antiferromagnetic behavior, an incommensurate spin-density wave, and a metallic phase as ${t_{\perp}/t}$ is increased. We characterize the phases through their magnetic ordering, dielectric response, and dominant static correlations. Our analysis is based primarily on a variant of the density-matrix renormalization-group algorithm based on an efficient hybrid-real-momentum-space formulation, in which we can treat relatively large lattices albeit of a limited width. This is complemented by a variational cluster approximation study with a cluster geometry corresponding to the cylindrical lattice allowing us to directly compare the two methods for this geometry. As an outlook, we make contact with work studying dimensional crossover in the full two-dimensional system.

Seismic isolation of buildings on two dimensional phononic crystal foundation

In order to realize the seismic isolation of buildings, we establish the two dimensional phononic crystal (PC) foundation which has the cell with the size close to the regular concrete test specimens, and is composed of the concrete base, rubber coating and lead cylindrical core. We study the in-plane band gap (BG) characteristics in it, through the analysis of the frequency dispersion relation and frequency response result. To lower the start BG frequency to the seismic frequency range, we also study the influences of material parameters (the elastic modulus of coating and density of cylindrical core) and geometry parameters (the thickness of coating, radius of cylindrical core and lattice constant) on BG ranges. The study could help to design the PC foundation for seismic isolation of building.

Buckling and vibration of composite lattice elliptical cylindrical shells

An approach to the finite element study of the buckling and dynamic behaviour of composite lattice cylindrical shells with elliptical cross sections is presented in this paper. The lattice shells are modelled as three-dimensional frame structures composed of curvilinear ribs using beam finite elements. A specialised algorithm is developed to generate the finite element model of the lattice shells based on multiple use of the repeating unit cell of the composite lattice structure. Using this model, the buckling behaviour of the shells subjected to axial loading and transverse bending are investigated. Fundamental frequencies of axial and transverse vibrations of the shells with a massive rigid disk attached to their ends are determined based on the modelling approach proposed in this work. The effects of parameters of the lattice structure on the values of critical buckling loads, buckling and vibration mode shapes, and the fundamental frequencies are examined using parametric analyses. Based on the computations, the angles of orientation of helical ribs delivering maximum critical loads and fundamental frequencies are identified. The results of this study can be applied to the design of the composite tubular bodies of spacecraft made in the form of cylindrical lattice shells with elliptical cross sections.

11.15: Seismic behaviour of single layer cylindrical lattice steel shells

ABSTRACTCylindrical lattice shell structures are commonly used in many applications such as in train stations, gymnasia, and sports halls. In comparison with their behaviour and design under gravity loading, their behaviour under seismic loading has received less attention, particularly in terms of the development of practical design procedures. Current European codes of practice lack specific guidance on the seismic design of these shells. In this paper, the salient considerations influencing the seismic response of single layer cylindrical lattice shells are examined. The effect of key geometric parameters such as the rise to span ratio, length to span ratio, inter‐element angles, as well as the structural mass, on the characteristic natural periods and corresponding vibration modes are investigated using the finite element program OpenSees for two typical situations of boundary conditions. The influence of these parameters on the axial forces and bending moments in the members when subjected to the horizontal and vertical components of an earthquake is also assessed. The response is evaluated in the linear and nonlinear ranges, including representative time history analyses, with due consideration of both material and geometric nonlinearities. The results provide an insight into the main factors that govern the seismic behaviour of single layer cylindrical lattice shells, with a view to supporting the development of practical design and assessment procedures for this structural form.

Manipulation and quantification of microtubule lattice integrity.

ABSTRACTMicrotubules are structural polymers that participate in a wide range of cellular functions. The addition and loss of tubulin subunits allows the microtubule to grow and shorten, as well as to develop and repair defects and gaps in its cylindrical lattice. These lattice defects act to modulate the interactions of microtubules with molecular motors and other microtubule-associated proteins. Therefore, tools to control and measure microtubule lattice structure will be invaluable for developing a quantitative understanding of how the structural state of the microtubule lattice may regulate its interactions with other proteins. In this work, we manipulated the lattice integrity of in vitro microtubules to create pools of microtubules with common nucleotide states, but with variations in structural states. We then developed a series of novel semi-automated analysis tools for both fluorescence and electron microscopy experiments to quantify the type and severity of alterations in microtubule lattice integrity. These techniques will enable new investigations that explore the role of microtubule lattice structure in interactions with microtubule-associated proteins.

An anisotropic and inhomogeneous hidden Markov model for the classification of water quality spatio‐temporal series on a national scale: The case of Scotland

This work presents a case study about the evaluation of the water quality dynamics in each of the 56 major catchments in Scotland, for a period of 10 years. Data are obtained by monthly sampling of water contaminants, in order to monitor discharges from the land to the sea. We are interested in the multivariate time series of ammonia, nitrate, and phosphorus. The time series may present issues that make their analysis complex: non‐linearity, non‐normality, weak dependency, seasonality, and missing values. The goals of this work are the classification of the observations into a small set of homogeneous groups representing ordered categories of pollution, the detection of change‐points, and the modeling of data heterogeneity. These aims are pursued by developing a novel spatio‐temporal hidden Markov model, whose hierarchical structure was motivated by the data set to study: the observations are displayed on a cylindrical lattice and driven by an anisotropic and inhomogeneous hidden Markov random field. As a result, four hidden states were selected, showing that catchments could be grouped spatially, with a strong relationship with the dominating land use. This method represents a useful tool for water managers to have a nationwide picture in combination of temporal dynamics.

Spin-orbit coupling, electron transport and pairing instabilities in two-dimensional square structures

Rashba spin-orbit effects and electron correlations in the two-dimensional cylindrical lattices of square geometries are assessed using mesoscopic two-, three- and four-leg ladder structures. Here the electron transport properties are systematically calculated by including the spin-orbit coupling in tight binding and Hubbard models threaded by a magnetic flux. These results highlight important aspects of possible symmetry breaking mechanisms in square ladder geometries driven by the combined effect of a magnetic gauge field spin-orbit interaction and temperature. The observed persistent current, spin and charge polarizations in the presence of spin-orbit coupling are driven by separation of electron and hole charges and opposite spins in real-space. The modeled spin-flip processes on the pairing mechanism induced by the spin-orbit coupling in assembled nanostructures (as arrays of clusters) engineered in various two-dimensional multi-leg structures provide an ideal playground for understanding spatial charge and spin density inhomogeneities leading to electron pairing and spontaneous phase separation instabilities in unconventional superconductors. Such studies also fall under the scope of current challenging problems in superconductivity and magnetism, topological insulators and spin dependent transport associated with numerous interfaces and heterostructures.

Quantum Hall physics with cold atoms in cylindrical optical lattices

We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by copropagating Laguerre-Gauss beams, i.e.~light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotating the lattice potential, we achieve a slowly varying flux through the hole of the cylinder, which allows us to probe the Hall response of the system as a realization of Laughlin's thought experiment. We study how in the presence of interactions fractional quantum Hall physics could be observed in this setup.

Tubulin Conformation and Anaesthetic Interaction - An Experimental Study

The current endeavour of neuroscience and philosophy is to discover the code of consciousness or rather how the material brain produces our in Material sense of awareness. Some scientists believe that consciousness is something distinct from the physical brain and body, as consciousness continues to exist even when the brain is not functioning. But from a scientific viewpoint, consciousness is a function of the brain. Since the brain is a material entity, consciousness is subject to the study of science. The human brain is a complex mass of tissue endowed with extraordinary capabilities. Microtubules turn out to be a common target of neurotransmitter action and play a significant role in learning and memory. Memory and consciousness are interrelated, thus, microtubules could be the link between these two phenomena. Microtubules are cylindrical hexagonal lattice polymers of the protein tubulin, comprising 15% of total brain protein. Microtubules regulate synapses and are suggested to process information via interactive bit-like states of tubulin. Microtubules are very dynamic polymers whose assembly and disassembly is determined by whether their heterodimer tubulin subunits are in a straight or curved conformation. Curvature is introduced by bending at the interfaces between monomers. This is because GTP hydrolysis promotes bends in protofilaments. However, while GDPbound protofilaments are still associated together as a microtubule or 2-D sheet, the contacts between neighbouring subunits constrain them to remain in a straight form. The resulting tension is proposed to store conformational energy that is released during depolymerisation. Also, the mechanism by which anaesthetics prevent consciousness remains largely unknown because the mechanism by which brain physiology produces consciousness is unexplained. Tubulins have other smaller non-polar regions that contain pi electron-rich indole rings separated by only about 2 nm. Penrose- Hameroff Orchestrated Objective Reduction (Orch-OR) Theory proposes that these electrons are close enough to become quantum entangled. They suppose that quantum-superposed states develop in tubulins, remain coherent and recruit more superposed tubulins until a mass-time-energy threshold, related to quantum gravity, is reached called as the 'bing' moment. This paper characterizes the conformation of tubulin in presence of anesthetics.

Optimal design concepts for flat isogrid and anisogrid lattice panels longitudinally compressed

The interest on composite anisogrid lattice structures as the baseline design concept for lightweight applications is increasingly growing. The potential weight efficiency of such concept is based on the proper design of the system of ribs, their orientation and cross-section. Although several analytical and numerical works are devoted to cylindrical and conical lattice shells axially compressed, no similar studies support the preliminary design phase of anisogrid flat panels without the skin. For this reason, the paper is focused on the formulation of the main design constraint equations valid for anisogrid lattice panels longitudinally compressed, in which local and global buckling failure modes are dominating, and on the consequent approach to minimum mass solutions through the analytical minimization of corresponding safety factors. Thus, approximate closed form solutions are developed to explore the general anisogrid case and the specific isogrid configuration due to its widespread use. Static stiffness properties of lattice panels are also included in this study in order to satisfy additional requirements other than strength. An application of this method is finally proposed showing a very good agreement with finite-element results.