Cylindrical Lattice Research Articles

Structural Form and Mechanical Properties of the Suspended Cylindrical Lattice Shells

Suspended-dome is a typical space structure composed of cables, struts and beam elements. By introducing pre-stressing technology, the stiffness and load carrying capacity of the single-layer shell is significantly improved. However, the structural planes of suspended-dome are mostly circular, which affects the promotion application of the suspended-dome. This paper presents a new form of suspended cylindrical lattice shell, which is a combination of an upper single-layer cylindrical shell and a lower suspended system. According to the grid type of single-layer cylindrical shell and the form of the suspended system, four types of suspended cylindrical lattice shells are defined including n-loop suspended orthogonal grid with one bracing type, n-loop suspended two way orthogonal grid type, n-loop suspended lamella grid type, and n-loop suspended three-way grid type. The mechanical properties of n-loop suspended orthogonal grid with one brace type of suspended cylindrical shell are investigated. The eigenvalue buckling and non-linear instability are also analyzed. A model experiment based on a practical engineering application is finally introduced. The comparison between the theoretic values and the experimental values shows the present analysis method is correct and reliable.

Cylindrical periodic surface lattice as a metadielectric: Concept of a surface-field Cherenkov source of coherent radiation

A two-dimensional (2D), cylindrical, periodic surface lattice (PSL) forming a surface field cavity is considered. The lattice is created by introducing 2D periodic perturbations on the inner surface of a cylindrical waveguide. The PSL facilitates a resonant coupling of the surface and near cutoff volume fields, leading to the formation of a high-$Q$ cavity eigenmode. The cavity eigenmode is described and investigated using a modal approach, considering the model of a cylindrical waveguide partially loaded with a metadielectric. By using a PSL-based cavity, the concept of a high-power, 0.2-THz Cherenkov source is developed. It is shown that if the PSL satisfies certain defined conditions, single-mode operation is observed.

Real-Time Resolution of Self-Intersection in Dynamic Cylindrical Free-Form Deformation

This paper presents a method of self-intersection detection and resolution for dynamic cylindrical-lattice-based free-form deformation (FFD). The lattice-based approach allows efficient computation of deformation of complex geometries. But excessive deformation can cause visual anomalies such as surface infiltration and distortion. This paper derives a geometrically intuitive sufficient condition to guarantee that the FFD function is a homeomorphism and there is no self-intersection. The FFD function is defined by linear and quadratic B-Spline functions with the control points of the cylindrical lattice cell. The sufficient condition is satisfied if each trilinear function of the nine prism-shaped pentahedrons derived from the cell has a positive Jacobian determinant. The positivity is satisfied if the 12 tetrahedrons derived from the pentahedron have positive volumes. Based on the sufficient condition, the proposed method converts the self-intersection problem into a point-face collision detection and response problem suitable for dynamic simulation. The efficiency and accuracy of the self-intersection detection algorithm is analyzed and compared with a previous method. The results show that the proposed technique allows simulation of excessive deformation of tubular objects in an efficient and realistic manner.

Optimization of geometric parameters of latticed structures using genetic algorithm

PurposeThe purpose of this paper is to analyze a squared lattice cylindrical shell under compressive axial load and to optimize the geometric parameters to achieve the maximum buckling load. Also a comparison between buckling loads of a squared lattice cylinder and a solid hollow cylinder with equal weight, length and outer diameter is performed to reveal the superior performance of the squared lattice cylindrical shells.Design/methodology/approachA cylindrical lattice shell includes circumferential and longitudinal rods with geometric parameters such as cross‐section areas of the rods, distances and angles between them. In this study, the governing differential equation for buckling load which can be presumed as a criterion for designing lattice structures with a specific weight is derived and is used as an objective function in genetic algorithm (GA) method to calculate the optimum geometric parameters of the shell. The optimum parameters were modelled in finite element method (FEM) in order to verify the buckling loads obtained from GA. In another effort, the FEM was applied to analyze the solid hollow cylinders.FindingsThe results demonstrate relatively close agreement between the buckling loads obtained from GA and FEM for such shells. It was also shown that latticed cylinders have better performance to carry compressive axial loads than the equivalent solid hollow cylinders with equal weights, lengths and outer diameters.Research limitations/implicationsThe studies reported in this paper have been carried out for a single squared lattice shell without using two‐side skins. However, using skins can give better performance in carrying compressive axial loads.Practical implicationsThe results in this paper show that this type of effective, economical lightweight and functional structures could be applied as inter‐stages, inter‐tanks, aircraft fuselage, rocket motor cases, pressure vessels and other elements of civil engineering structures in order to have greater strength and lower weight.Originality/valueSquared lattice cylindrical shell with optimum geometric design could provide the chance for eliminating the stiffeners of shells in aerospace structures in order to decrease the weight and increase the load‐bearing capacity.

Deducing Kinetochore Protein Distributions along and Around a Microtubule Plus-End from FRET Measurements

The eukaryotic kinetochore is a sophisticated motor that moves and segregates chromosomes during cell division. As a microtubule-based motor, the kinetochore is distinct from all other motor proteins and microtubule-associated proteins: it attaches end-on to ∼ 40 nm zone behind the plus-end of one or more microtubules, and it acts as a force coupler rather than an active force generator. These characteristics ensure that chromosome movement is tightly coupled with polymer growth and shortening at the plus-end. They also strongly suggest that kinetochore protein architecture, the distributions of the microtubule-binding kinetochore proteins along and around the microtubule plus-end and their dynamics, dictate the molecular mechanisms that generate movement. We have developed a FRET-based approach to determine the nanometer-scale distributions of multiple copies of the three principle microtubule-binding kinetochore complexes: Dam1, Ndc80, and Spc105. Sensitized emission measurements are carried out in metaphase and anaphase budding yeast (Saccharomyces cerevisiae) cells expressing kinetochore proteins labeled with Cerulean (donor) and Venus (acceptor) at desired locations. Preliminary measurements probing the distribution of the Ndc80 complex molecules show that the microtubule-binding head domains of adjacent Ndc80 molecules are ∼ five nm apart, but this distance increases significantly at the other end of the molecule. The Dam1 complex is located more than 10 nm away from these head domains of Ndc80. We are developing Monte Carlo approaches to simulate the energy transfer processes among a known number of donor and acceptor molecules using known protein structures of some of the kinetochore proteins and the cylindrical microtubule lattice. These simulations will identify molecular distributions consistent with the FRET data, and illuminate the structural basis for microtubule end-coupled movement of the kinetochore.

RESPONSE EVALUATION OF HIGH-RISE CYLINDRICAL LATTICE SHELL ROOFS WITH SUPPORTING SUBSTRUCTURES

Seismic response of cylindrical lattice shell roofs are known to be affected by its rise and supporting substructures. The authors have proposed simple method for estimating response of such shell roofs using amplification factors, however, that does not cover high-rise shell roofs.In this paper, simple response evaluation method for lattice shell roofs with high-rise proportions supported by various stiffness of substructures is proposed using continuous approach as the previous studies including those for high-rise domes, and their validities are discussed against response spectrum analyses based on CQC method.

Excitation of surface field cavity and coherence of electromagnetic field scattering on two-dimensional cylindrical lattice

The excitation of a surface field cavity based on a large area two-dimensional cylindrical lattice and surface field scattering within the cavity are investigated. It is shown that the interaction between surface and volume fields via distributed scatterers becomes coherent and the cavity excitation takes place only when it is irradiated with a near cut-off transverse-magnetic polarized field. The coherence of the radiation observed from the surface field scattering is investigated.

Transfer-matrix renormalization group method for general Markov random fields

We seek the numerical calculation of partition functions of general Markov random fields (MRFs) on an infinitely long twisted cylindrical lattice by using the transfer-matrix renormalization group (TMRG) method. The TMRG is a variant of the density-matrix renormalization group (DMRG) which automatically truncates the Hilbert space so that the properties of large systems can be precisely calculated while the dimension of the renormalized Hilbert space remains constant. We apply the TMRG to the decimation of the fundamental transfer matrix that we have proposed previously for general MRFs. Instead of the standard S••E scheme for TMRG, we propose a new E•S•E scheme and propose an alternative method for selecting the renormalized basis. Specifically, the new E•S•E scheme keeps those singular-value decomposition (SVD) components of the fundamental transfer matrix that are relevant for the Perron state and truncates the other irrelevant ones. Results for the Ising model show that our method exhibits very impressive accuracy under a rather restricted computational resource. Simulations for another four general MRFs demonstrate that our TMRG method is superior to the classical Monte Carlo method in accuracy, computational speed, and in the possibility of treating a much larger system.

"MEMORY BYTES" — MOLECULAR MATCH FORCaMKIIPHOSPHORYLATION ENCODING OF MICROTUBULE LATTICES

Learning, memory and long-term potentiation (LTP) are supported by factors including post-synaptic calcium ion flux activating and transforming the hexagonal calcium-calmodulin kinase II (CaMKII) holoenzyme. Upon calcium-induced activation, up to six kinase domains extend upward, and up to six kinase domains extend downward from the CaMKII association domain, the fully activated holoenzyme resembling a robotic insect 20 nanometers in length. Each extended kinase domain can be phosphorylated, and able to phosphorylate other proteins, thus potentially further encoding synaptic information at intraneuronal molecular sites for memory storage, processing and distribution. Candidate sites for phosphorylation-encoded molecular memory include microtubules, cylindrical lattice polymers of the protein tubulin. Using molecular modeling, we find spatial dimensions and geometry of the six extended CaMKII kinase domains can precisely match those of microtubule hexagonal lattice neighborhoods (both A- and B-lattices), and show two feasible phosphorylation mechanisms. In one, phosphorylation sites (e.g., valine 208) on a CaMKII extended kinase domain interact with serine 444 on a C-terminal "tail" of tubulin. In the second, the CaMKII kinase domain unfurls, enabling phosphorylation sites to contact threonine and serine sites on the tubulin surface. We suggest sets of six CaMKII kinase domains phosphorylate hexagonal microtubule lattice neighborhoods collectively, e.g., conveying synaptic information as ordered arrays of six "bits", and thus a "byte", with (minimally) 2⁶ (64) possible bit states per CaMKII-microtubule interaction. We model two levels of interaction between CaMKII and microtubules, suggesting a testable framework for molecular memory encoding.

Vibration Analysis for Elastic Vascular Stent

A mathematical modeling for breathing vibration problem of vascular stent is presented. The vascular stent is considered in structure as an elastic cylindrical lattice shell, in which the cell element is treated as a spatial frame structure. Based on the force equilibrium and the deformation geometry analysis for the cell element, calculative formulae for effective elastic parameters of the lattice shell are obtained by using homogenization method. Hence, the vascular stent is modeled as an orthogonally anisotropic thin shell. The equation of vibration for vascular stent is derived from Flügge shell theory. The computation of natural frequency of vibration is performed. The analytic results from the presented formulae are close to that from finite element method by the means of ANSYS, which validates the applicability of the presented modeling of vascular stent structures. The vibration analysis could be a useful reference for practical engineering designs of vascular stent.

Surface-field cavity based on a two-dimensional cylindrical lattice

The results of theoretical and experimental studies of a high-Q cavity based on a cylindrical, periodic lattice are presented. The coupling of localized surface and volume electromagnetic fields results in cavity mode selection over radial, azimuthal, and longitudinal indices and formation of a high-Q cavity eigenmode. Numerical analyses of the field evolution inside the cavity were carried out. Application of these two-dimensional periodic structures in the development of high-power terahertz masers is proposed.

Annealing a magnetic cactus into phyllotaxis

The appearance of mathematical regularities in the disposition of leaves on a stem, scales on a pine-cone, and spines on a cactus has puzzled scholars for millennia; similar so-called phyllotactic patterns are seen in self-organized growth, polypeptides, convection, magnetic flux lattices and ion beams. Levitov showed that a cylindrical lattice of repulsive particles can reproduce phyllotaxis under the (unproved) assumption that minimum of energy would be achieved by two-dimensional Bravais lattices. Here we provide experimental and numerical evidence that the Phyllotactic lattice is actually a ground state. When mechanically annealed, our experimental "magnetic cactus" precisely reproduces botanical phyllotaxis, along with domain boundaries (called transitions in Botany) between different phyllotactic patterns. We employ a structural genetic algorithm to explore the more general axially unconstrained case, which reveals multijugate (multiple spirals) as well as monojugate (single-spiral) phyllotaxis.

Nucleation dynamics in two-dimensional cylindrical Ising models and chemotaxis

The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e., the process which allows cells to identify and follow a gradient of chemical attractant). As a first step in this direction we study the nucleation dynamics of the two-dimensional Ising model defined on a cylindrical lattice whose radius changes as a function of time. Geometry variation is obtained by changing the relative value of the couplings between spins in the compactified (vertical) direction with respect to the horizontal one. This allows us to keep the lattice size unchanged and study in a single simulation the values of the compactification radius which change in time. We show both with theoretical arguments and numerical simulations that squeezing the geometry allows the system to speed up nucleation times even in presence of a very small energy gap between the stable and the metastable states. We then address the implications of our analysis for directional chemotaxis. The initial steps of chemotaxis can be modeled as a nucleation process occurring on the cell membrane as a consequence of the external chemical gradient (which plays the role of energy gap between the stable and metastable phases). In nature most of the cells modify their geometry by extending quasi-one-dimensional protrusions (filopodia) so as to enhance their sensitivity to chemoattractant. Our results show that this geometry variation has indeed the effect of greatly decreasing the time scale of the nucleation process even in presence of very small amounts of chemoattractants.

RELATION BETWEEN LOAD-CARRYING CAPACITY AND SEISMIC MOTION LEVEL OF DYNAMIC COLLAPSE FOR LATTICE ARCH AND CYLINDRICAL ROOF

Lattice structures consisting of various mesh patterns show different static buckling and post-buckling behaviors even if the compression members have the same slenderness ratios. There are not sufficient studies in the literature to finding document to know the effect of these static characteristics on the seismic resistant capacity. In this paper as for plane lattice arches and double-layer cylindrical lattice roofs, the relation between dynamic collapse behavior and static collapse behavior, under excessive vertical loads, is numerically investigated to present a prediction method for the load level of dynamic collapse. The prediction method can be done with the information of load-deformation curves, natural periods and velocity response spectrum of seismic motions. The value predicted may be modified with the information of the elastic and plastic strain energies at a limit state of structures.

Asymptotics of the partition function of a general Markov random field on an infinite rectangular lattice

We investigate theoretically and numerically the asymptotics of the partition function of a general Markov random field (MRF) on an infinite rectangular lattice. We first propose the general local energy function (LEF)-parameterized MRF. Then we prove that the thermodynamic limit of the free energy of the MRF can be exactly characterized by the Perron root of the fundamental transfer matrix of a particular Markov additive process (MAP). This matrix possesses a special structure and many interesting properties that enable parallel computation of the Perron root and may be beneficial for deriving an analytical form of the free energy. We also develop another transfer matrix for numerical computation of the desired Perron root. Specifically, the former is a site-to-site transfer matrix on a twisted cylindrical lattice, while the latter is the one associated with a row-to-row transition on a vertical strip. Numerical results show that our methods exhibit consistent finite-size scaling behavior even for small values of the lattice width. This study reveals that the fundamental transfer matrix is an alternative direction of research on the analysis of the partition function of general MRFs within the scope of matrix algebra.

A continuous family of partition statistics equidistributed with length

This article investigates a remarkable generalization of the generating function that enumerates partitions by area and number of parts. This generating function is given by the infinite product ∏ i ⩾ 1 1 / ( 1 − t q i ) . We give uncountably many new combinatorial interpretations of this infinite product involving partition statistics that arose originally in the context of Hilbert schemes. We construct explicit bijections proving that all of these statistics are equidistributed with the length statistic on partitions of n. Our bijections employ various combinatorial constructions involving cylindrical lattice paths, Eulerian tours on directed multigraphs, and oriented trees.

Algebraic Reduction of the Ising Model

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superintegrable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.

VIBRATION TESTS OF CYLINDRICAL LATTICE SHELL ROOFS SUBJECTED TO EARTHQUAKE MOTIONS WITH ARBITRARY DIRECTION

Seismic response of cylindrical lattice shell roofs with supporting substructures is known to be amplified in vertical direction even under horizontal input, and their amplitude changes along the direction of earthquake motion. However, the seismic response behavior under the inputs in arbitrary direction has not been sufficiently investigated. In this paper, seismic vibration tests are carried out using small scale models with supporting substructure in order to make clear the effects of difference of input direction and relationship between mechanical properties of roofs and substructures on response behavior of shell roofs. It is confirmed that the simple response evaluation methods proposed in previous papers apply to the responses subjected to earthquake motions with arbitrary direction.

Microdomain Ordering in Laterally Confined Block Copolymer Thin Films

We examine the effects of small-scale, hexagonal, lateral confinement on microdomain ordering in diblock copolymer thin films using self-consistent field theory simulations. Specifically, we examine a hexagonal confinement well with side length L approximately equal to five cylindrical microdomain lattice spacings. The commensurability constraints of the small-scale, lateral confinement, coupled with surface-induced effects allow the confining well to have a significant effect on the perfection of microdomain order. We identify commensurability windows in L that depend on the segment−wall interaction and the “temperature” annealing rate (modeled as a Flory χ ∼ 1/T annealing rate). The effect of added majority-block homopolymer is also explored.

Hierarchical assembly of the siliceous skeletal lattice of the hexactinellid sponge Euplectella aspergillum

Despite its inherent mechanical fragility, silica is widely used as a skeletal material in a great diversity of organisms ranging from diatoms and radiolaria to sponges and higher plants. In addition to their micro- and nanoscale structural regularity, many of these hard tissues form complex hierarchically ordered composites. One such example is found in the siliceous skeletal system of the Western Pacific hexactinellid sponge, Euplectella aspergillum. In this species, the skeleton comprises an elaborate cylindrical lattice-like structure with at least six hierarchical levels spanning the length scale from nanometers to centimeters. The basic building blocks are laminated skeletal elements (spicules) that consist of a central proteinaceous axial filament surrounded by alternating concentric domains of consolidated silica nanoparticles and organic interlayers. Two intersecting grids of non-planar cruciform spicules define a locally quadrate, globally cylindrical skeletal lattice that provides the framework onto which other skeletal constituents are deposited. The grids are supported by bundles of spicules that form vertical, horizontal and diagonally ordered struts. The overall cylindrical lattice is capped at its upper end by a terminal sieve plate and rooted into the sea floor at its base by a flexible cluster of barbed fibrillar anchor spicules. External diagonally oriented spiral ridges that extend perpendicular to the surface further strengthen the lattice. A secondarily deposited laminated silica matrix that cements the structure together additionally reinforces the resulting skeletal mass. The mechanical consequences of each of these various levels of structural complexity are discussed.