Relevant bibliographies by topics / Structured lattices

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Structured lattices'

Author: Grafiati
Published: 11 January 2025

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Journal articles on the topic "Structured lattices"

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Frascella, A., and C. Guido. "Structured lattices and ground categories ofL-sets." International Journal of Mathematics and Mathematical Sciences 2005, no. 17 (2005): 2783–803. http://dx.doi.org/10.1155/ijmms.2005.2783.

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Complete lattices are considered with suitable families of lattice morphisms that provide a structure(L,Φ), useful to characterize ground categories ofL-sets by means of powerset operators associated to morphisms of these categories. The construction of ground categories and powerset operators presented here extends and unifies most approaches previously considered, allowing the use of noncrisp objects and, with some restriction, the change of base. A sufficiently large category ofL-sets that includes all possible ground categories on a structured lattice(L,Φ)is provided and studied, and its usefulness is justified. Many explanatory examples have been given and connection with the categories considered by J. A. Goguen and by S. E. Rodabaugh are stated.
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Bathla, Pranjal, and John Kennedy. "3D Printed Structured Porous Treatments for Flow Control around a Circular Cylinder." Fluids 5, no. 3 (August 14, 2020): 136. http://dx.doi.org/10.3390/fluids5030136.

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The use of porous coatings is one of the passive flow control methods used to reduce turbulence, noise and vibrations generated due to fluid flow. Porous coatings for flow stabilization have potential for a light-weight, cost-effective, and customizable solution. The design and performance of a structured porous coating depend on multiple control parameters like lattice size, strut thickness, lattice structure/geometry, etc. This study investigated the suitability of MSLA 3D printers to manufacture porous coatings based on unit cell designs to optimize porous lattices for flow control behind a cylinder. The Reynolds number used was 6.1×104–1.5×105 and the flow measurements were taken using a hotwire probe. Different experiment sets were conducted for single cylinder with varying control parameters to achieve best performing lattice designs. It was found that lattice structures with higher porosity produced lower turbulence intensity in the wake of the cylinder. However, for constant porosity lattice structures, there was negligible difference in turbulence and mean wake velocity levels. Coating thickness did not have a linear relationship with turbulence reduction, suggesting an optimal thickness value. For constant porosity coatings, cell count in coating thickness did not influence the turbulence or mean wake velocity. Partial coating designs like helical and spaced coatings had comparable performance to that of a full coating. MSLA printers were found capable of manufacturing thin and complex porous lattices.
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HORE, VICTORIA R. A., JOHN B. TROY, and STEPHEN J. EGLEN. "Parasol cell mosaics are unlikely to drive the formation of structured orientation maps in primary visual cortex." Visual Neuroscience 29, no. 6 (October 30, 2012): 283–99. http://dx.doi.org/10.1017/s0952523812000338.

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AbstractThe receptive fields of on- and off-center parasol cell mosaics independently tile the retina to ensure efficient sampling of visual space. A recent theoretical model represented the on- and off-center mosaics by noisy hexagonal lattices of slightly different density. When the two lattices are overlaid, long-range Moiré interference patterns are generated. These Moiré interference patterns have been suggested to drive the formation of highly structured orientation maps in visual cortex. Here, we show that noisy hexagonal lattices do not capture the spatial statistics of parasol cell mosaics. An alternative model based upon local exclusion zones, termed as the pairwise interaction point process (PIPP) model, generates patterns that are statistically indistinguishable from parasol cell mosaics. A key difference between the PIPP model and the hexagonal lattice model is that the PIPP model does not generate Moiré interference patterns, and hence stimulated orientation maps do not show any hexagonal structure. Finally, we estimate the spatial extent of spatial correlations in parasol cell mosaics to be only 200–350 μm, far less than that required to generate Moiré interference. We conclude that parasol cell mosaics are too disordered to drive the formation of highly structured orientation maps in visual cortex.
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Budinski, Ljubomir, Julius Fabian, and Matija Stipić. "Lattice Boltzmann method for groundwater flow in non-orthogonal structured lattices." Computers & Mathematics with Applications 70, no. 10 (November 2015): 2601–15. http://dx.doi.org/10.1016/j.camwa.2015.09.027.

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Kumar, K. Raj, and Giuseppe Caire. "Space–Time Codes From Structured Lattices." IEEE Transactions on Information Theory 55, no. 2 (February 2009): 547–56. http://dx.doi.org/10.1109/tit.2008.2009595.

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Dziobiak, Wieslaw, Jaroslav Ježek, and Ralph McKenzie. "Avoidable structures, II: Finite distributive lattices and nicely structured ordered sets." Algebra universalis 60, no. 3 (March 16, 2009): 259–91. http://dx.doi.org/10.1007/s00012-009-2098-0.

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Boley, J. William, Wim M. van Rees, Charles Lissandrello, Mark N. Horenstein, Ryan L. Truby, Arda Kotikian, Jennifer A. Lewis, and L. Mahadevan. "Shape-shifting structured lattices via multimaterial 4D printing." Proceedings of the National Academy of Sciences 116, no. 42 (October 2, 2019): 20856–62. http://dx.doi.org/10.1073/pnas.1908806116.

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Shape-morphing structured materials have the ability to transform a range of applications. However, their design and fabrication remain challenging due to the difficulty of controlling the underlying metric tensor in space and time. Here, we exploit a combination of multiple materials, geometry, and 4-dimensional (4D) printing to create structured heterogeneous lattices that overcome this problem. Our printable inks are composed of elastomeric matrices with tunable cross-link density and anisotropic filler that enable precise control of their elastic modulus (E) and coefficient of thermal expansion (α). The inks are printed in the form of lattices with curved bilayer ribs whose geometry is individually programmed to achieve local control over the metric tensor. For independent control of extrinsic curvature, we created multiplexed bilayer ribs composed of 4 materials, which enables us to encode a wide range of 3-dimensional (3D) shape changes in response to temperature. As exemplars, we designed and printed planar lattices that morph into frequency-shifting antennae and a human face, demonstrating functionality and geometric complexity, respectively. Our inverse geometric design and multimaterial 4D printing method can be readily extended to other stimuli-responsive materials and different 2-dimensional (2D) and 3D cell designs to create scalable, reversible, shape-shifting structures with unprecedented complexity.
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Anoop, V. S., and S. Asharaf. "Extracting Conceptual Relationships and Inducing Concept Lattices from Unstructured Text." Journal of Intelligent Systems 28, no. 4 (September 25, 2019): 669–81. http://dx.doi.org/10.1515/jisys-2017-0225.

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Abstract Concept and relationship extraction from unstructured text data plays a key role in meaning aware computing paradigms, which make computers intelligent by helping them learn, interpret, and synthesis information. These concepts and relationships leverage knowledge in the form of ontological structures, which is the backbone of semantic web. This paper proposes a framework that extracts concepts and relationships from unstructured text data and then learns lattices that connect concepts and relationships. The proposed framework uses an off-the-shelf tool for identifying common concepts from a plain text corpus and then implements machine learning algorithms for classifying common relations that connect those concepts. Formal concept analysis is then used for generating concept lattices, which is a proven and principled method of creating formal ontologies that aid machines to learn things. A rigorous and structured experimental evaluation of the proposed method on real-world datasets has been conducted. The results show that the newly proposed framework outperforms state-of-the-art approaches in concept extraction and lattice generation.
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Khoromskaia, Venera, and Boris N. Khoromskij. "Block Circulant and Toeplitz Structures in the Linearized Hartree–Fock Equation on Finite Lattices: Tensor Approach." Computational Methods in Applied Mathematics 17, no. 3 (July 1, 2017): 431–55. http://dx.doi.org/10.1515/cmam-2017-0004.

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AbstractThis paper introduces and analyzes the new grid-based tensor approach to approximate solutions of the elliptic eigenvalue problem for the 3D lattice-structured systems. We consider the linearized Hartree–Fock equation over a spatial{L_{1}\times L_{2}\times L_{3}}lattice for both periodic and non-periodic problem setting, discretized in the localized Gaussian-type orbitals basis. In the periodic case, the Galerkin system matrix obeys a three-level block-circulant structure that allows the FFT-based diagonalization, while for the finite extended systems in a box (Dirichlet boundary conditions) we arrive at the perturbed block-Toeplitz representation providing fast matrix-vector multiplication and low storage size. The proposed grid-based tensor techniques manifest the twofold benefits: (a) the entries of the Fock matrix are computed by 1D operations using low-rank tensors represented on a 3D grid, (b) in the periodic case the low-rank tensor structure in the diagonal blocks of the Fock matrix in the Fourier space reduces the conventional 3D FFT to the product of 1D FFTs. Lattice type systems in a box with Dirichlet boundary conditions are treated numerically by our previous tensor solver for single molecules, which makes possible calculations on rather large{L_{1}\times L_{2}\times L_{3}}lattices due to reduced numerical cost for 3D problems. The numerical simulations for both box-type and periodic{L\times 1\times 1}lattice chain in a 3D rectangular “tube” withLup to several hundred confirm the theoretical complexity bounds for the block-structured eigenvalue solvers in the limit of largeL.
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STRACCIA, UMBERTO. "DESCRIPTION LOGICS OVER LATTICES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14, no. 01 (February 2006): 1–16. http://dx.doi.org/10.1142/s0218488506003807.

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It is generally accepted that knowledge based systems would be smarter if they could manage uncertainty and/or imprecision. In this paper we extend Description Logics, well-known logics for managing structured knowledge, allowing to express that a sentence is not just true or false, but true to some degree, which is taken from a certainty lattice.
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Dissertations / Theses on the topic "Structured lattices"

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Felderhoff, Joël. "Difficultés de Problèmes de Réseaux Structurés pour la Cryptographie Post-Quantique." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0059.

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La sécurité des protocoles cryptographiques repose sur la difficulté présumée de problèmes algorithmiques. Parmi ceux qui ont été identifiés jusque-là, les meilleurs problèmes pouvant servir de fondation à une cryptographie résistante aux ordinateurs quantiques sont issus des réseaux euclidiens. Les réseaux euclidiens sont une structure mathématique définie comme un ensemble de vecteurs de l’espace générés par les combinaisons entières d’un nombre fini de vecteurs réels linéairement indépendants (sa base). Un exemple typique de problème de sécurité relié est le Shortest Vector Problem (SVP). Étant donné une base d’un réseau euclidien en dimension n, trouver un vecteur court non nul. Pour des raisons d’efficacité, ces problèmes sont restreints à des réseaux issus de la théorie des nombres, dit structurés. Les hypothèses de sécurité relatives à ces réseaux particuliers étant différentes de celles des réseaux non structurés, il est nécessaire de les étudier spécifiquement, c’est l’objet de cette thèse. Nous avons étudié le cas des modules NTRU et uSVP en rang 2, prouvant que le problème SVP est équivalent sur ces deux familles de réseaux. Nous montrons également une réduction pire-cas vers cas-moyens pour les réseaux uSVP en rang 2. Ensuite nous avons démontré que résoudre SVP sur un idéal premier de petite norme n’était pas plus facile que de résoudre SVP sur n’importe quel idéal
The security of cryptographic protocols is based on the presumed difficulty of algorithmic problems. Among those identified so far, some of the best problems to serve as a foundation for quantum-proof cryptography come from lattices. Lattices are a mathematical structure defined as a set of space vectors generated by integer combinations of a finite number of linearly independent real vectors (its basis). A typical example of a related security problem is the Shortest Vector Problem (SVP). Given a base of an n-dimensional lattice, find a non-zero short vector. For efficiency reasons, these problems are restricted to lattices arising from number theory, known as structured lattices. As the security assumptions for these particular lattices are different from those for unstructured lattices, it is necessary to study them specifically, which is the aim of this thesis.We have studied the case of NTRU and uSVP modules in rank 2, proving that the SVP problem is equivalent on these two families of lattices. We also show a worst-case to average-case reduction for rank-2 uSVP lattices. Then we show that solving SVP on a prime ideal of small norm is no easier than solving SVP on any ideal
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ASHOK, RAMYA. "A DATABASE SYSTEM TO STORE AND RETRIEVE A CONCEPT LATTICE STRUCTURE." University of Cincinnati / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1130552767.

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Jenkins, Sarah Nield Morrish. "Mechanical properties and structural evaluation of diamond structure Ti6Al4V lattices made by Electron Beam Melting." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/20954/.

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Banihashemi, Amir H. "Decoding complexity and trellis structure of lattices." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22189.pdf.

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Burns, D. "Factorisability, group lattices, and Galois module structure." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.335599.

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O'Connor, Joseph. "Fluid-structure interactions of wall-mounted flexible slender structures." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/fluidstructure-interactions-of-wallmounted-flexible-slender-structures(1dab2986-b78f-4ff9-9b2e-5d2181cfa009).html.

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The fluid-structure interactions of wall-mounted slender structures, such as cilia, filaments, flaps, and flags, play an important role in a broad range of physical processes: from the coherent waving motion of vegetation, to the passive flow control capability of hair-like surface coatings. While these systems are ubiquitous, their coupled nonlinear response exhibits a wide variety of behaviours that is yet to be fully understood, especially when multiple structures are considered. The purpose of this work is to investigate, via numerical simulation, the fluid-structure interactions of arrays of slender structures over a range of input conditions. A direct modelling approach, whereby the individual structures and their dynamics are fully resolved, is realised via a lattice Boltzmann-immersed boundary model, which is coupled to two different structural solvers: an Euler-Bernoulli beam model, and a finite element model. Results are presented for three selected test cases - which build in scale from a single flap in a periodic array, to a small finite array of flaps, and finally to a large finite array - and the key behaviour modes are characterised and quantified. Results show a broad range of behaviours, which depend on the flow conditions and structural properties. In particular, the emergence of coherent waving motions are shown to be closely related to the natural frequency of the array. Furthermore, this behaviour is associated with a lock-in between the natural frequency of the array and the predicted frequency of the fluid instabilities. The original contributions of this work are: the development and application of a numerical tool for direct modelling of large arrays of slender structures; the characterisation of the behaviour of slender structures over a range of input conditions; and the exposition of key behaviour modes of slender structures and their relation to input conditions.
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Goel, Archak. "Design of Functionally Graded BCC Type Lattice Structures Using B-spline Surfaces for Additive Manufacturing." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1552398559313737.

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Hou, An. "Strength of composite lattice structures." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/12475.

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Obiedat, Mohammad. "Incrementally Sorted Lattice Data Structures." Thesis, The George Washington University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3732474.

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Data structures are vital entities that strongly impact the efficiency of several software applications. Compactness, predictable memory access patterns, and good temporal and spacial locality of the structure's operations are increasingly becoming essential factors in the selection of a data structure for a specific application. In general, the less data we store and move the better for efficiency and power consumption, especially in infrastructure software and applications for hand-held devices like smartphones. In this dissertation, we extensively study a data structure named lattice data structure (LDS) that is as compact and suitable for memory hierarchies as the array, yet with a rich structure that enables devising procedures with better time bounds.

To achieve performance similar to the performance of the optimal O(log(N)) time complexity of the searching operations of other structures, we provide a hybrid searching algorithm that can be implemented by searching the lattice using the basic searching algorithm when the degree of the sortedness of the lattice is less than or equal to 0.9h, and the jump searching algorithm when the degree of the sortedness of the lattice is greater than 0.9h. A sorting procedure that can be used, during the system idle time, to incrementally increase the degree of sortedness of the lattice is given. We also provide randomized and parallel searching algorithms that can be used instead of the usual jump-and-walk searching algorithms.

A lattice can be represented by a one-dimensional array, where each cell is represented by one array element. The worst case time complexity of the basic LDS operations and the average time complexity of some of the order-statistic operations are better than the corresponding time complexities of most of other data structures operations. This makes the LDS a good choice for memory-constrained systems, for systems where power consumption is a critical issue, and for real-time systems. A potential application of the LDS is to use it as an index structure for in-memory databases.

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Kouach, Mona. "Methods for modelling lattice structures." Thesis, KTH, Hållfasthetslära (Avd.), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-260498.

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The application of lattice structures have become increasingly popular as additive manufacturing (AM) opens up the possibility to manufacture complex configurations. However, modelling such structures can be computationally expensive. The following thesis has been conducted in order for the department of Structural Analysis, at SAAB in Järfälla, to converge with the future use of AM and lattice structures. An approach to model lattice structures using homogenization is presented where three similar methods involving representative volume element (RVE) have been developed and evaluated. The stiffness matrices, of the RVEs, for different sizes of lattice structures, comprising of BCC strut-based units, have been obtained. The stiffness matrices were compared and analysed on a larger solid structure in order to see the deformational predictability of a lattice-based structure of the same size. The results showed that all methods were good approximations with slight differences in terms of boundary conditions (BCs) at the outer edge. The comparative analyses showed that two of the three methods matches the deformational predictability. The BCs in all methods have different influences which makes it pivotal to establish the BCs of the structure before using the approach presented in this thesis.
Ökad implementering av gitterstrukturer i komponenter är ett resultat av utvecklingen inom additiv tillverkning. Metoden öppnar upp för tillverkning av komplexa strukturer med färre delmoment. Dock så uppkommer det svårigheter vid simulering av dessa komplexa strukturer då beräkningar snabbt tyngs ner med ökad komplexitet. Följande examensarbete har utförts hos avdelningen Strukturanalys, på SAAB i Järfälla, för att de ska kunna möta upp det framtida behovet av beräkningar på additivt tillverkade gitterstrukturer. I det här arbetet presenteras ett tillvägagångsätt för modellering av gitterstrukturer med hjälp av represantiva volymselement. Styvhetsmatriser har räknats fram, för en vald gitterkonfiguration, som sedan viktats mot tre snarlika representativa volymselement. En jämförelseanalys mellan de olika styvhetsmatriserna har sedan gjorts på en större och solid modell för att se hur väl metoderna förutsett deformationen av en gitterstruktur i samma storlek. Resultaten har visat att samtliga metoder är bra approximationer med tämligen små skillnader från randeffekterna. Vid jämförelseanalysen simulerades gitterstrukturen bäst med två av de tre metoder. En av slutsatserna är att det är viktigt att förstå inverkan av randvillkoren hos gitterstrukturer innan implementering görs med det tillvägagångssätt som presenterats i det här examensarbetet.
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Books on the topic "Structured lattices"

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H, Sowa, ed. Cubic structure types described in their space groups with the aid of frameworks. Karlsruhe, [West Germany]: Fachinformationszentrum Energie, Physik, Mathematik, 1985.

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Müller-Hoissen, Folkert, Jean Marcel Pallo, and Jim Stasheff, eds. Associahedra, Tamari Lattices and Related Structures. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0405-9.

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Fuentes, Benjamin J. Optical lattices: Structures, atoms, and solitons. Hauppauge, N.Y: Nova Science Publishers, 2012.

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Leung, Henry Hon Hung. Trellis structure and decoding of lattices. Ottawa: National Library of Canada, 1994.

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American Society of Civil Engineers., ed. Design of latticed steel transmission structures. Reston, Va: American Society of Civil Engineers, 2000.

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American Society of Civil Engineers. Design of latticed steel transmission structures. Reston, Virginia: American Society of Civil Engineers, 2015.

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Zhu, K. Nonlinear dynamic analysis of lattice structures. Brisbane: Department of Civil Engineering, University of Queensland, 1992.

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Zhu, K. Nonlinear dynamic analysis of lattice structures. Brisbane: Universityof Queensland, Dept. of Civil Engineering, 1990.

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Akademii͡a nauk SSSR. I͡Akutskiĭ nauchnyĭ t͡sentr. Otdel prikladnoĭ matematiki i vychislitelʹnoĭ tekhniki, ed. Matematicheskie metody sinteza mnogosloĭnykh struktur pri vozdeĭstvii voln. I͡Akutsk: I͡Akutskiĭ nauchnyĭ t͡sentr SO AN SSSR, 1990.

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Galvin, Brian Russell. Numerical studies of localized vibrating structures in nonlinear lattices. Monterey, Calif: Naval Postgraduate School, 1991.

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Book chapters on the topic "Structured lattices"

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Michelitsch, Thomas M., Alejandro P. Riascos, Bernard A. Collet, Andrzej F. Nowakowski, and Franck C. G. A. Nicolleau. "Generalized Space–Time Fractional Dynamics in Networks and Lattices." In Advanced Structured Materials, 221–49. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38708-2_14.

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Porubov, Alexey V., Alena E. Osokina, and Ilya D. Antonov. "Nonlinear Dynamics of Two-Dimensional Lattices with Complex Structure." In Advanced Structured Materials, 309–34. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38708-2_18.

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Michelitsch, Thomas, Bernard Collet, Alejandro Perez Riascos, Andrzej Nowakowski, and Franck Nicolleau. "On Recurrence and Transience of Fractional RandomWalks in Lattices." In Advanced Structured Materials, 555–80. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72440-9_29.

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Dos Reis, Francisco, and Jean-François Ganghoffer. "Construction of Micropolar Continua from the Homogenization of Repetitive Planar Lattices." In Advanced Structured Materials, 193–217. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19219-7_9.

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Turco, Emilio, Maciej Golaszewski, Ivan Giorgio, and Luca Placidi. "Can a Hencky-Type Model Predict the Mechanical Behaviour of Pantographic Lattices?" In Advanced Structured Materials, 285–311. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-3764-1_18.

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Turco, Emilio. "How the Properties of Pantographic Elementary Lattices Determine the Properties of Pantographic Metamaterials." In Advanced Structured Materials, 489–506. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13307-8_33.

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Goda, Ibrahim, Francisco Dos Reis, and Jean-François Ganghoffer. "Limit Analysis of Lattices Based on the Asymptotic Homogenization Method and Prediction of Size Effects in Bone Plastic Collapse." In Advanced Structured Materials, 179–211. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-31721-2_9.

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Loeb, Arthur L. "Lattices and Lattice Complexes." In Space Structures, 123–25. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0437-4_15.

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Bain, Michael. "Structured Features from Concept Lattices for Unsupervised Learning and Classification." In Lecture Notes in Computer Science, 557–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-36187-1_49.

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Lyubashevsky, Vadim, and Thomas Prest. "Quadratic Time, Linear Space Algorithms for Gram-Schmidt Orthogonalization and Gaussian Sampling in Structured Lattices." In Advances in Cryptology -- EUROCRYPT 2015, 789–815. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46800-5_30.

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Conference papers on the topic "Structured lattices"

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Chuman, Victor, Filip Milojković, Pol Van Dorpe, and Niels Verellen. "Three-Dimensional Sparse Lattices for High-Throughput Fluorescence Microscopy." In Imaging Systems and Applications, IM3G.2. Washington, D.C.: Optica Publishing Group, 2024. http://dx.doi.org/10.1364/isa.2024.im3g.2.

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We propose using sparse optical lattices to enable the design of structured illumination microscopy systems based on photonic integrated circuits (PIC). We show simulations of sample lattices and their application to digital confocal microscopy.
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Cameron, Andrew R., Sandra W. L. Cheng, Sacha Schwarz, Connor Kapahi, Dusan Sarenac, Michael Grabowecky, David G. Cory, Thomas Jennewein, Dmitry A. Pushin, and Kevin J. Resch. "Remotely prepared structured wave lattices." In Quantum 2.0. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/quantum.2022.qth4a.3.

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Spin-orbit entangled photon states with a 2D lattice structure are generated and implemented in a remote state preparation protocol. These novel structured waves provide a method for quantum sensing and manipulation of periodic structures.
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Rogers, Benedict A., Max D. A. Valentine, Elise C. Pegg, Alexander J. G. Lunt, and Vimal Dhokia. "Additive Manufacturing of Star Structured Auxetic Lattices With Overhanging Links." In 2022 International Additive Manufacturing Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/iam2022-93965.

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Abstract Additive manufacturing has been the driving force behind the growth of metamaterials as a field. Commonly taking the form of lattices, these structures can achieve a range of novel macroscale properties that stem from the cumulative effects of locally designed mechanisms. A wide array of mechanical metamaterials have already been designed using computational methods, but these rarely undergo physical testing, often as a result of manufacturing difficulties. This work approaches the problem of manufacturing complex metamaterial test samples though a case study of 3D petal-based auxetic star lattices. These lattice structures have linkage structures with overhanging elements, which is a common feature in metamaterial concepts but challenging to print. Trials of the test samples were manufactured using a thermoplastic polyurethane filament combined with polyvinyl acetate support at 20, 30 and 40 mm unit cell sizes. It was found that the main geometric challenges for successful printing were the link thickness and the reliability of the prints. To address unreliability, the geometry was cut into layers of cells with adhesive-connected feet and printed in parts for post-process assembly. The layered approach was tested successfully and was estimated to reduce the number of cells needed to be attempted to print the full lattice by over 80%. The use of dissolvable support material proved viable for printing overhanging links, but requires use of fused deposition modelling so a relatively low part resolution. The trial led to a five point design guide methodology for metamaterial test samples. Combined with cell mathematical definitions that strictly bound link thickness to take minimum print resolution into account, this methodology can be applied to other metamaterials and help bridge the gap between theoretical lattices and physical testing.
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Lee, Sang Hyun, Ankit Ghiya, Sriram Vishwanath, Sung Soo Hwang, and Sunghwan Kim. "Structured dirty-paper coding using low-density lattices." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5496012.

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Mejdoub, Mahmoud, Leonardo Fonteles, Chokri BenAmar, and Marc Antonini. "Fast indexing method for image retrieval using tree-structured lattices." In 2008 International Workshop on Content-Based Multimedia Indexing. IEEE, 2008. http://dx.doi.org/10.1109/cbmi.2008.4564970.

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Yamane, Keisaku, Kohei Iwasa, Kohei Kakizawa, Kazuhiko Oka, Yasunori Toda, and Ryuji Morita. "Generation of intense ultrafast-rotating ring-shaped optical lattices with programmable control of rotational symmetry." In SPIE Technologies and Applications of Structured Light, edited by Takashige Omatsu. SPIE, 2017. http://dx.doi.org/10.1117/12.2275015.

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Chen, Jiangce, Martha Baldwin, Sneha Narra, and Christopher McComb. "Multi-Lattice Topology Optimization With Lattice Representation Learned by Generative Models." In ASME 2024 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/detc2024-145592.

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Abstract Additive manufacturing (AM) technologies are often capable of fabricating geometries that are more complex than traditional manufacturing methods. A notable innovation enabled by AM is the fabrication of multi-lattice structures, an advanced design concept featuring an array of heterogeneous lattices in the mesoscale that are arranged to achieve a diverse distribution of material properties at the macroscale. Compared to uniform lattice structures, multi-lattice structures permit greater design freedom and a larger design space, which makes it possible to achieve superior structure performance. However, the expanded design space introduces a substantial increase in the complexity of multi-lattice structure design. There is still lack of an optimization framework that can maximize the physical properties of the macro-structures through fully exploiting lattice diversity while ensuring lattice connectivity. To solve these challenges, this paper introduces a multi-scale topology optimization (TO) framework for multi-lattice structures which simultaneously optimizes the structure topology at macroscale and the lattice heterogeneity at mesoscale. The distribution of the pseudo-densities and lattice parameters are represented by neural networks (NNs) whose weights and biases are the design variables. The spatial gradients of NN over the physical domain reflect the dissimilarity of adjacent lattices. So, the connection between the lattices can be implicitly constrained by restricting the spatial gradients of NNs. The diversity of the lattices is guaranteed through a generative lattice model which is trained over a large lattice dataset and is embedded into the optimization framework. The performances of various NN types are compared, and we found that Fourier Neural Operators (FNOs) have the best flexibility in balancing the lattice diversity and local connectivity. In the design problems of structural compliance minimization under complex loading conditions, our results show that the multi-lattice TO structures achieve a higher stiffness-to-weight ratio than normal TO structures.
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Tang, Tsz Ling Elaine, Yan Liu, Da Lu, Erhan Batuhan Arisoy, and Suraj Musuvathy. "Lattice Structure Design Advisor for Additive Manufacturing Using Gaussian Process." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67282.

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Additive manufacturing (AM) exemplifies the potential of lattice structures to revolutionize structural design. It enables light weight lattice structures to be produced while maintaining the desirable structural performance. Lattice design can vary in different shapes and dimensions. Obtaining the structural performance of a particular lattice structure design is not a straight-forward process. Significant effort is required to perform mechanical testing experiments or to perform finite element analysis (FEA) to characterize the lattice design. In view of that, a guidance system to determine lattice design parameters based on desired functional performance for a specific lattice type is developed, which can be used in interactive design processes and workflows. Homogenization using FEA experiments is applied to characterize the macroscopic lattice structural properties. Mechanical properties of orthotropic cubic lattice f2ccz are estimated. It follows with a design of experiment study to characterize the effective structural properties of 39 lattices with respect to lattice design parameters (unit cell length and strut diameter). A Gaussian process is applied to develop models relating the lattice design parameter to macroscopic structural properties (forward model), and vice versa (inverse model). Both the forward and inverse models are examined and shown to be capable of modeling the FEA experimental dataset of 39 lattices. To illustrate the potential application of the lattice design advisor framework, a structural design use case including lattice part is presented. In the use case, the lattice structure design advisor is proven to be able to estimate an accurate homogenized material property of arbitrary lattice design parameter. This lattice structure design advisor can simplify and streamline the design, modeling and simulation process of lattice-filled structural designs.
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Ardebili, Mahmoud K., Kerim Tuna Ikikardaslar, Colt Ehrnfeld, and Feridun Delale. "3D Printed Cellular Structure Materials Under Impact and Compressive Loading." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23871.

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Abstract Advances in field of lattice structure design has become possible mainly due to the emerging capabilities of additive manufacturing (AM) or 3D printing. Lattices have the potential to reduce solid volumes, giving advantages such as weight reduction, decreased part production cost and ability to absorb energy under compressive and impact loading. These materials are anisotropic due to structural geometry and the additive nature of 3D-printed layers, which stack mainly in Normal or Lateral direction to the applied load. In this study 3D printed materials were fabricated that are nearly isotropic and are also lighter than base material. The lattice structure was formed using strut-based cell topologies that are adjoined as tetrahedrons. Two different tetrahedron density specimens were produced with Acrylonitrile Butadiene Styrene (ABS) using a Fusion Deposition Modelling (FDM) printer. The fabricated specimens were then tested for impact and compression capabilities. For comparison purposes, solid specimens with the same overall dimensions and highest infill ratio were also produced and tested. After compression and impact testing, results indicated that solid specimens’ impact energy absorption is higher with lateral stacking order relative to load, and compression resistance is higher for normal stacking order. The tetrahedron-filled specimens exhibited minimal stacking directional dependency and the higher count tetrahedron specimens provided more impact energy absorption and more resistance to compression than the lower count one. The normalization of specimens with respect to their weight indicated high density tetrahedron specimens’ impact energy absorption is nearly equal to that of solid specimens’. These results are initial steps in creating lattice structured materials that are isotropic, lighter and stronger than the base material.
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Ayaz Uddin, Mohammed, Imad Barsoum, Shanmugam Kumar, and Andreas Schiffer. "Enhancing Energy Absorption Capacity of Pyramidal Lattice Structures via Geometrical Tailoring and 3D Printing." In ASME 2024 Aerospace Structures, Structural Dynamics, and Materials Conference. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/ssdm2024-121512.

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Abstract Pyramidal lattice structures have frequently been employed as the core material in the design of sandwich panels due to their impressive weight-specific strength. However, the struts in pyramidal lattice structures bend when subjected to axial, shear, or bending loads, leading to non-uniform stress distributions, especially at low relative densities. The current work introduces a geometrical tailoring scheme that provides the designer with additional parameters that can be adjusted to tune the cross-sectional properties of the lattice struts with the goal of obtaining more uniform stress distributions across their thickness. Specifically, the conventional square and circular pyramidal lattice struts are reshaped into I-beam-like cross-sections, forming a tailored pyramidal lattice. These geometrically tailored pyramidal lattices are 3D printed via the Digital Light Processing (DLP) technique. The quasi-static compressive responses of the lattices are experimentally evaluated in terms of elastic modulus, collapse strength, and energy absorption capacity. Additionally, the collapse mechanisms of the geometrically tailored structures were assessed via a non-linear finite element analysis which was validated against the experimental evidence. The results substantiate the validity of the geometrical tailoring strategy as the reported energy absorption capacity of the tailored pyramidal lattice structure exhibits a significant enhancement up to 64% and 15% respectively. The latter enhancements were attributed to the lateral buckling of struts, prompting the tailored struts to bend sideways during the collapse phase.
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Reports on the topic "Structured lattices"

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Fry, A. T., L. E. Crocker, M. J. Lodeiro, M. Poole, P. Woolliams, A. Koko, N. Leung, D. England, and C. Breheny. Tensile property measurement of lattice structures. National Physical Laboratory, July 2023. http://dx.doi.org/10.47120/npl.mat119.

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Liu, Keh-Fei, and Terrence Draper. Lattice QCD Calculation of Nucleon Structure. Office of Scientific and Technical Information (OSTI), August 2016. http://dx.doi.org/10.2172/1323029.

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Williams, James H., and Jr. Wave Propagation and Dynamics of Lattice Structures. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada190037.

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Williams, James H., and Jr. Wave Propagation and Dynamics of Lattice Structures. Fort Belvoir, VA: Defense Technical Information Center, October 1987. http://dx.doi.org/10.21236/ada190611.

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Williams, James H., and Jr. Wave Propagation and Dynamics of Lattice Structures. Fort Belvoir, VA: Defense Technical Information Center, October 1985. http://dx.doi.org/10.21236/ada170316.

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Braun, D. W., G. W. Crabtree, H. G. Kaper, G. K. Leaf, D. M. Levine, V. M. Vinokur, and A. E. Koshelev. The structure of a moving vortex lattice. Office of Scientific and Technical Information (OSTI), November 1995. http://dx.doi.org/10.2172/179299.

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Parsa, Z., and S. Tepikian. Overview of the structure resonances in the AGS-Booster lattices. Office of Scientific and Technical Information (OSTI), June 1986. http://dx.doi.org/10.2172/1150423.

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Skowronski, Marek, and D. W. Greve. Growth of Lattice Matched Nitride Alloys and Structures. Fort Belvoir, VA: Defense Technical Information Center, September 1998. http://dx.doi.org/10.21236/ada354115.

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Williams, James H., Nagem Jr., and Raymond J. Computation of Natural Frequencies of Planar Lattice Structure. Fort Belvoir, VA: Defense Technical Information Center, March 1987. http://dx.doi.org/10.21236/ada185387.

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Hughes, Nathan. Computed Tomography (CT) Analysis of 3D Printed Lattice Structures. Office of Scientific and Technical Information (OSTI), May 2023. http://dx.doi.org/10.2172/1975633.

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