Topological Interlocking Research Articles

Topological interlocking of protective tiles for the space shuttle

We propose a new concept of design of heat- and impact-resistant tile covering for space shuttles based upon topological interlocking of tiles. The key features of this type of tiling are as follows: firstly, the tiles are kept in place by virtue of the geometry of their contacting surfaces alone, so that no binding agent needs to be used; secondly, failure of an individual element does not compromise the structural integrity of the tile assembly and, moreover, a failed tile will be kept in place by its neighbours, thus maintaining its thermal protection function; thirdly, topological interlocking removes the need for connectors or other stress concentrators deleterious in extreme conditions of space flight and re-entry. Topological interlocking is scale and material independent, which permits combining tiles made from different materials in any proportion.

Fracture Resistant Structures Based on Topological Interlocking with Non‐planar Contacts

Topological interlocking of elements based on matching of curved contact surfaces (see Figure) offers flexible structures highly tolerant to local failures. Unlike structures based on interlocking polyhedra, they form continuous layers to be used, e.g., for surface protection. The structures are especially promising with brittle materials, since in contrast to solid structures, failure of individual blocks does not lead to global failure.

Topological interlocking of platonic solids: A way to new materials and structures

The structural integrity of natural and engineered materials relies on chemical or mechanical bonding between the building blocks of which they consist. Materials whose building blocks are not joined, but rather interlocked topologically, possess remarkable mechanical and functional properties. We show that identical elements, in the shape of the five platonic solids, can be arranged into layer-like structures in which they are interlocked topologically. It is shown that truncated icosahedra (buckyballs) can also be arranged in a layer with topological interlocking. The geometrical possibility of such assemblies opens up interesting avenues in the design of structures and materials.

Toughening by Fragmentation—How Topology Helps

In this brief overview, we present recent work on the novel concept of topological interlocking as a means of designing new materials and structures. Starting from a special self-supporting arrangement of tetrahedron-shaped elements that was discovered first, we proceed with the introduction of other shapes exhibiting topological interlocking. Unusual mechanical properties of assemblies of tetrahedrons that were studied both experimentally and theoretically are discussed. Possible applications can range from large scale mortar free construction in civil engineering to novel advanced materials based on microscale interlocking elements.

116 Topological interlocking within microprocessor-based control systems for substations

116 Topological interlocking within microprocessor-based control systems for substations

Topological Interlocking within Microprocessor-Based Control Systems for Substations

The paper deals with a new topological interlocking method which has been implemented in a microprocessor-based real-time control system for substations. This method eliminates the disadvantages of conventional interlocking methods based on Boolean equations and leads to increased switching security and enlarged operating possibilities. The first part of the paper describes the computer-internal representation of the switchgear topology and the computer-aided configuring of the data base. Next, the article turns to the decision-making process of the topological interlocking and the implementation as substation interlocking in a decentralized control system. Finally the paper outlines the essentials of intelligent switching sequences as an example of automation functions based on topological interlocking.

The structure of sister minichromosome DNA before anaphase in Saccharomyces cerevisiae.

The role of DNA topology in holding sister chromatids together before anaphase was investigated by analyzing the structure of a small circular minichromosome in cell cycle (cdc) mutants of the yeast Saccharomyces cerevisiae. In the majority of cells arrested after S phase but before anaphase, sister minichromosome molecules are not topologically interlocked with each other. The analysis of the ploidy of minichromosomes in cells that are released from arrest demonstrates that the sister molecules are properly segregated when the cell cycle block is removed. Therefore, sister minichromosome molecules need not remain topologically interlocked until anaphase in order to be properly segregated, and topological interlocking of sister DNA molecules apparently is not the primary force holding sister chromatids together.

Overview of the solid-solid interface: Mechanical stability

Photothermal and photovoltaic device structures require large-area thin film multilayers that must be uniformly processed and will withstand a hostile service environment for long periods without degradation. Our present experience with demanding thin film applications resides in microcircuits and optical applications. Thus little background for predictive capability exists for high cyclic temperature excursions, oxidation-corrosion ambients and abrasive winds to be expected for reflectors and collectors. Long-term mechanical stability will be governed by control of the stresses produced during growth followed by stabilization of the microstructure. Low temperature transport has long been known in films but data for many incorporated impurity species including H 2 and OH are not common. The stress relief that accompanies such recovery processes has been studied in detail in only one soft low melting film. Reliable creep data for films do not exist. At high temperatures, even diffusion into the bulk may be an important sink for material originally at interfaces. Surface morphology changes after annealing have been identified. At fast deposition rates, grain boundaries may become even wider and posses large quantities of impurities. Many dielectric films contain microscopic voids which give rise to reversible and irreversible behavior. Disorder is quenched in at low effective atom mobilities with the formation of amorphous or metastable phases. Even amorphous films have their own scale of structure, lower elastic constants and doubtful high temperature stabilization. There is a parallel with laser glazing and near-surface modification by ion beams that should be exploited. The mechanical strains that are produced in a film during growth are a result of the microstructure as well as of thermal expansion. Some control is possible but is often limited as a result of the (gaseous) impurities which may not be stable at high temperatures. Elastic stress distributions may be calculated but are useless without knowledge of plastic flow. Modifications of an interface by grading, stress compensation and topological interlocking are known to prevent failure. New techniques for the measurement of “adhesion” and the localized characterization of mechanical properties together with the application of fracture toughness concepts are necessary to understand interfacial strengths. Mechanical integrity requires the solution to many of these problems. Recent developments in high strength films, the prevention of grain growth by modulating the structure and the production of a specific microstructure for a desired optical property show that progress is possible. Opportunities for surface science will be to comprehend atomic mobilities in the formation and stabilization of real microstructures in solar environments, to produce new materials and to develop new techniques, especially in situ and non-destructive, to give early detection and predictive capability of failure.

Evidence for a partial RNA transcript of the small circular component of kinetoplast DNA of Crithidia acanthocephali

The major component of kinetoplast DNA (kDNA) in the protozoan Crithidia acanthocephali is an association of approximately 27,000, 0.8 micrometers (1.58 x 10(6) dalton) circular molecules apparently held together in a particular structural configuration by topological interlocking. We have carried out hybridization experiments between kDNA samples containing one or the other of the two complementary (H and L) strands of purified 0.8 micrometers molecules derived from mechanically disrupted associations and RNA samples prepared either from whole C. acanthocephali cells or from a mitochondrion-enriched fraction. The results of experiments involving cesium sulfate buoyant density centrifugation indicate that whole cell RNA contains a component(s) complementary to all kDNA H strands, but none complementary to kDNA L strands. Similar results were obtained using mitochondrion-associated RNA. Digestion of RNA/DNA hybrids and suitable controls with the single-strand-specific nuclease S1 indicated that 10% of the kDNA H strand is involved in hybrid formation. Visualization of RNA/DNA hybrids stained with bacteriophage T4 gene 32 protein revealed that hybridation involves a single region of each kDNA H strand, equal to approximately 10% of the molecule length. These data suggest that at least 10% of the small circular component of kDNA of Crithidia acanthocephali is transcribed.

Heterogeneity in sensitivity to cleavage by the restriction endonucleases ECORI and HindIII of circular kinetoplast DNA molecules of Crithidia acanthocephali.

Kinetoplast DNA (kDNA) of the protozoan Crithidia acanthocephali consists mainly of an association of approximately 27,000 covalently closed, 0.8-micron (1.58 X 10(6) daltons) circular molecules apparently held together in a particular structural configuration by topological interlocking. The sensitivities of circular kDNA molecules to the restriction endonucleases EcoRI and HindIII have been studied using agarose gel electrophoresis and electron microscopy. Digestion with EcoRI or HindIII of collections of single circular molecules obtained from sonicated kDNA associations resulted in a single cleavage of 9.3 and 12% of the molecules, respectively. Digestion of intact kDNA associations with EcoRI or HindIII resulted in cleavage of 9.2 and 10.4%, respectively, of the component circular molecules, but not in detectable disruption of the characteristic structure of the associations. Analysis of the products of sequential digestion of kDNA with the two enzymes indicated that approximately 8% of the circular molecules each contain a single site sensitive to EcoRI and a single site sensitive to HindIII; 1.5-3% contain only an EcoRI-sensitive site; 3-4% contain only a HindIII-sensitive site; and the remainder (approximately 86%) are insensitive to either enzyme. Further, data obtained from sequential digestion experiments and from studies of the partial denaturation products of the circular molecules digested with EcoRI or HindIII indicated that when they occur the EcoRI site and the HindIII site are each at a unique position in all molecules, 10-13% of the circular contour length apart. Similar digestion products were found for kDNAs from different cloned organisms, suggesting that the four different kinds of circular molecules, in regard to EcoRI and HindIII sensitivity, are found in similar proportions in the kDNA association of different organisms.

Replication of kinetoplast DNA of Crithidia acanthocephali. I. Density shift experiments using deuterium oxide.

The protozoan Crithidia acanthocephali contains, within a modified region of a mitochondrion, a mass of DNA known as kinetoplast DNA (kDNA). This DNA consists mainly of an association of approximately 27,000 covalently closed 0.8-mum circular molecules which are apparently held together in a definite ordered manner by topological interlocking. After culturing of C. acanthocephali cells for 25 generations in medium containing 75% deuterium oxide, both nuclear DNA (rhonative, nondeuterated=1.717 g/cm3) and kDNA (rhonative, nondeuterated=1.702 g/cm3) increased in buoyant density by 0.012 g/cm3. The replication of the two DNAs was studied by cesium chloride buoyant density analysis of DNAs from exponentially growing cells taken at 1.0, 1.4, 2.0, 3.0, and 4.0 cell doublings after transfer of cells from D2O-containing medium into medium containing only normal water. The results obtained from analysis of both native and denatured nuclear DNAs indicate that this DNA replicates semiconservatively. From an analysis of intact associations of kDNA, it appears that this DNA doubles once per generation and that the newly synthesized DNA does not segregate from parental DNA. Fractions of covalently closed single circular molecules and of open circular and unit length linear molecules were obtained from associations of kDNA by sonication, sucrose sedimentation, and cesium chloride-ethidium bromide equilibrium gradient centrifugation. Buoyant density profiles obtained from these fractions indicate that: (a) doubling of the kDNA results from the replication of each circular molecule rather than from repeated replication of a small fraction of the circular molecules; (b) replication of kDNA is semiconservative rather than conservative, but there is recombination between the circles at an undefined time during the cell cycle.

Kinetoplast DNA of Crithidia.

SYNOPSIS. The results of physiochemical and electron microscope studies on the structure of the kinetoplast DNA of Crithidia are discussed. The molecular weight of isolated kinetoplast DNA is approximately 41 × 109 daltons. The basic unit of organization of this DNA is a covalently closed circular molecule 0.8 μm in contour length (molecular weight 1.54 × 106 daltons). An average of 33 such circles are held together in a group by topological interlocking of each circle with a large number of other circles in the group. An average of 804 groups are held together into a structure termed an association. A group of circles is attached to several adjacent groups. This is accomplished by 1 or more circles each interlocking with many circles in 2 (but never more) of the groups. The groups of circles are arranged in such a way that the association, comprising about 27,000 circles, has a topologically 2‐dimensional form. A model is presented for the in situ arrangement of the kinetoplast DNA association. Data which we have obtained is consistent with the view that all of the circular molecules of kinetoplast DNA of one organism carry the same genetic information. The transcription product is a single RNA molecule of approximately the size of a single circular DNA molecule. From studies involving density shift experiments using deuterium oxide, buoyant density ultracentrifugation and electron microscopy we have determined the following concerning replication of kinetoplast DNA: (a) doubling of the kinetoplast DNA results from the replication of each circular molecule rather than from extensive replication of a small number of circular molecules; (b) replication of kinetoplast DNA is a semi‐conservative rather than a conservative process and there is recombination at an undefined time during the cell cycle; (c) a portion of a kinetoplast DNA association is in the form of long linear molecules during the replicative phase of that association.

The form and structure of kinetoplast DNA of Crithidia.

Cesium chloride centrifugation of each of the DNAs extracted from eight strains of Crithidia revealed a main band at rho = 1.717 g/cm(3) and a satellite band varying from rho = 1.701 to 1.705 g/cm(3) for the different strains By electron microscopy each DNA was shown to include circular molecules, 0.69-0.80 micro in mean contour length, and large, topologically two-dimensional masses of DNA in which the molecules appeared in the form of rosettes. DNA isolated from kinetoplast fractions of Crithidia acanthocephali was shown to consist of light satellite DNA and to be mainly in the form of large masses, 0.8 micro (mol wt = 1.54 x 10(6) daltons) circular molecules, and a few long, linear molecules. The results of experiments involving ultracentrifugation, heating, and quenching, sonication, and endodeoxyribonuclease digestion, combined with electron microscopy, are consistent with the following hypothesis. The large DNA masses are associations of 0.8 micro circles which are mainly covalently closed. The circles are held together in groups (the rosettes) of up to 46 by the topological interlocking of each circle with many other circles in the group. A group of circles is attached to an adjacent group by one or more circles, each interlocking with many circles of both groups. Each of the associations comprises, on the average, about 27,000 circles (total mol wt approximately 41 x 10(9) daltons). A model is proposed for the in situ arrangement of the associations which takes into consideration their form and structure, and appearance in thin sections