Journal articles: 'Linear and non-linear geometries'

1

Cross, M. C. "Non-linear traveling wave states in finite geometries." Physica D: Nonlinear Phenomena 37, no. 1-3 (July 1989): 315–18. http://dx.doi.org/10.1016/0167-2789(89)90139-5.

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Pralle, Harm, and Johannes Ueberberg. "Linear geometries of Baer subspaces." Bulletin of the Belgian Mathematical Society - Simon Stevin 6, no. 4 (1999): 559–69. http://dx.doi.org/10.36045/bbms/1103055582.

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3

De Winter, S. "Linear representations of semipartial geometries." Bulletin of the Belgian Mathematical Society - Simon Stevin 12, no. 5 (January 2006): 767–80. http://dx.doi.org/10.36045/bbms/1136902614.

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4

Madore, J., T. Masson, and J. Mourad. "Linear connections on matrix geometries." Classical and Quantum Gravity 12, no. 6 (June 1, 1995): 1429–40. http://dx.doi.org/10.1088/0264-9381/12/6/009.

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5

Knapp, Wolfgang. "Linear closures of finite geometries." Journal of Geometry 107, no. 2 (March 4, 2016): 467–81. http://dx.doi.org/10.1007/s00022-016-0322-6.

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6

Wang, Xiao-Jun. "Non-linear corrections to aberration sensitivity of unstable-cavity geometries." Optics Express 16, no. 26 (December 9, 2008): 21223. http://dx.doi.org/10.1364/oe.16.021223.

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7

Komatsu, K. "Non-linear sloshing analysis of liquid in tanks with arbitrary geometries." International Journal of Non-Linear Mechanics 22, no. 3 (January 1987): 193–207. http://dx.doi.org/10.1016/0020-7462(87)90002-3.

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Tamilmani, Rajesh, and Emmanuel Stefanakis. "Enriched geometric simplification of linear features." GEOMATICA 71, no. 1 (March 2017): 3–19. http://dx.doi.org/10.5623/cig2017-101.

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Polyline geometries are used to represent linear features, such as roads, rivers and pipelines on maps. The generalization process results in a polyline that represents the feature either at a different resolution or different scale from the original geometries. In addition, the simplification process may result in losing the geometric properties associated with the intermediate points on the original geometries. These intermediate points can contain attributes or characteristics depending on the application domain. For example, points on the road network can contain information about accumulated length of the road, positional velocity, speed limit or accumulated gas consumption. This paper involves implementing the SELF (Semantically Enriched Line simpliFication) data structure to preserve the length attributes associated with individual points on actual linear features [Stefanakis 2015]. The number of points to be stored in the SELF structure is optimized by applying alternative compression techniques. The data structure has been implemented in PostgreSQL 9.4 [2014] with PostGIS [2016] extension using PL/pgSQL to support static and non-functional polylines. Extended experimental work has been carried out to better understand the impact of simplification on both synthetic and real (natural and artificial) linear features such as rivers and pipelines. The efficiency of SELF structure with regard to geo metric property preservation has been tested at various levels of simplification.

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Rodrigues, Vitor, Maria Costa, Etelvina Gomes, Dmitry Isakov, and Michael Belsley. "L-alaninium perrhenate: crystal structure and non-linear optical properties." Open Chemistry 12, no. 10 (October 1, 2014): 1016–22. http://dx.doi.org/10.2478/s11532-014-0548-9.

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AbstractThe crystal structure and non-linear optical properties of L-alaninium perrhenate, C3H8NO2+ ReO4 −, are reported. The protonated amino acid and the perrhenate anion have their usual geometries. The three-dimensional hydrogen-bonded network can be seen as a stacking of layers parallel to the (100) planes. Each layer is formed by chains of alternating positive and negative ions along the b and c axes. Hydrogen bonding of adjacent layers forms alternating chains along the a axis. A high damage threshold and a second-harmonic generation efficiency three times that of KDP make this new material potentially useful in non-linear optics.

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Usatenko, Zoryana, Piotr Kuterba, Hassan Chamati, and Dirk Romeis. "Linear and ring polymers in confined geometries." European Physical Journal Special Topics 226, no. 4 (April 2017): 651–65. http://dx.doi.org/10.1140/epjst/e2016-60335-0.

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11

De Clerck, F., and H. Van Maldeghem. "On Linear Representations of (α, β)-Geometries." European Journal of Combinatorics 15, no. 1 (January 1994): 3–11. http://dx.doi.org/10.1006/eujc.1994.1002.

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Gu, Zewen, Xiaonan Hou, and Jianqiao Ye. "Advanced static and dynamic analysis method for helical springs of non-linear geometries." Journal of Sound and Vibration 513 (November 2021): 116414. http://dx.doi.org/10.1016/j.jsv.2021.116414.

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ATKIN, R. J., and I. W. STEWART. "Non-linear solutions for smectic C liquid crystals in wedge and cylinder geometries." Liquid Crystals 22, no. 5 (May 1997): 585–94. http://dx.doi.org/10.1080/026782997208992.

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Lasso Andino, Oscar, and Christian L. Vásconez. "The quantum non-linear σ-model RG flow and integrability in wormhole geometries." Nuclear Physics B 990 (May 2023): 116178. http://dx.doi.org/10.1016/j.nuclphysb.2023.116178.

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Aulitto, Alessia, Avraham Hirschberg, Ines Lopez Arteaga, and Esmée L. R. H. Buijssen. "Effect of slit length on linear and non-linear acoustic transfer impedance of a micro-slit plate." Acta Acustica 6 (2022): 6. http://dx.doi.org/10.1051/aacus/2021059.

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The effect of the slit length on the acoustic transfer impedance of micro-slit plates (MSPs) is investigated in the linear and non-linear regime for a specific slit geometry. This geometry is inspired by slits obtained by cutting and bending the plate. MSPs are plates with arrays of slit-shaped perforations, with the width of the order of the acoustic viscous boundary layer thickness. Impedance tube measurements on two accurately manufactured plates are compared to numerical solution of the Linearized Navier-Stokes equations and to analytical limits. The impedance of the plate is obtained by the impedance of a single slit divided by the plate porosity. The resistance of a slit is independent on the slit length and on the plate porosity. In the linear regime the resistance is accurately predicted by a two-dimensional numerical model. In the non-linear regime, the resistance is strongly dependent on the amplitude of the acoustic waves. The inertance of the slit is weakly dependent on the slit length and on the plate porosity, for low and moderate amplitudes. For high amplitudes, a complicated amplitude dependency of the inertia of short slits is found. One expects that most of the conclusions obtained can be generalised to other slit geometries.

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16

Vandendriessche, Peter. "LDPC codes associated with linear representations of geometries." Advances in Mathematics of Communications 4, no. 3 (2010): 405–17. http://dx.doi.org/10.3934/amc.2010.4.405.

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17

Lee, G. S. "Analysis of linear resonances in modern Josephson geometries." IEEE Transactions on Appiled Superconductivity 1, no. 3 (1991): 121–25. http://dx.doi.org/10.1109/77.84625.

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18

Suen, Chung-yi. "Construction of -run linear graphs by finite geometries." Journal of Statistical Planning and Inference 133, no. 2 (August 2005): 523–36. http://dx.doi.org/10.1016/j.jspi.2004.01.008.

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19

Del Fra, A., A. Pasini, and S. Shpectorov. "Geometries with bi-affine and bi-linear diagrams." European Journal of Combinatorics 16, no. 5 (September 1995): 439–59. http://dx.doi.org/10.1016/0195-6698(95)90001-2.

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20

Miyamoto, Ayaho, Michael E. King, and Manabu Fujii. "Non-linear dynamic analysis and design concepts for RC beams under impulsive loads." Bulletin of the New Zealand Society for Earthquake Engineering 22, no. 2 (June 30, 1989): 98–111. http://dx.doi.org/10.5459/bnzsee.22.2.98-111.

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The behaviour of reinforced concrete (RC) beams under impulsive loading was studied in both the elastic and elasto-plastic regions by use of the finite element analysis. The calculations were then compared with experimental results for verification. Various impact force-time characteristics, beam geometries, material strengths and steel fibre contents were altered to study the effects on items such as behaviour in the critical region, energy absorption at failure and local deformation. These factors were then used to draft out a guideline on design concepts necessary for RC beams under impulsive loads.

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Moroni, Giovanni, Wahyudin P. Syam, and Stefano Petrò. "Comparison of chaos optimization functions for performance improvement of fitting of non-linear geometries." Measurement 86 (May 2016): 79–92. http://dx.doi.org/10.1016/j.measurement.2016.02.045.

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22

Mammoli, Andrea A. "Solution of non-linear boundary integral equations in complex geometries with auxiliary integral subtraction." International Journal for Numerical Methods in Engineering 55, no. 9 (2002): 1115–28. http://dx.doi.org/10.1002/nme.539.

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23

Clauß, Benjamin, Stephan Schaller, and Andreas Schubert. "Unrunddrehen mit luftgelagertem Linearantrieb/Non-circular turning with air-guided linear drive." wt Werkstattstechnik online 110, no. 11-12 (2020): 748–51. http://dx.doi.org/10.37544/1436-4980-2020-11-12-12.

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Unrunde Bauteile sind für Anwendungen in der Antriebs- und der Fügetechnik hochrelevant. Die zum Erzeugen erforderlichen Sondermaschinen weisen durch die geringe Fertigungsflexibilität häufig ein hohes Investitionsrisiko auf. Daher wurde ein prototypischer Antrieb entwickelt, der eine Unrundbearbeitung mittels Drehen auch auf bestehenden Werkzeugmaschinen erlaubt. Funktionsnachweise erfolgten durch die Erzeugung verschiedener Unrundgeometrien an Proben aus vergütetem und gehärtetem Stahl. Non-circular parts are of high relevance for powertrain and joining applications. The required special-purpose machine tools typically exhibit a high investment risk due to a low manufacturing flexibility. Accordingly, a prototypical drive was developed to enable non-circular machining by turning with existing machine tools. Proofs of functionality are based on machining different non-circular geometries using quenched and tempered as well as hardened steel.

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Streckbein, P., R. G. Streckbein, J. F. Wilbrand, C. Y. Malik, H. Schaaf, H. P. Howaldt, and M. Flach. "Non-linear 3D Evaluation of Different Oral Implant-Abutment Connections." Journal of Dental Research 91, no. 12 (October 8, 2012): 1184–89. http://dx.doi.org/10.1177/0022034512463396.

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Micro-gaps and osseous overload in the implant-abutment connection are the most common causes of peri-implant bone resorption and implant failure. These undesirable events can be visualized on standardized three-dimensional finite element models and by radiographic methods. The present study investigated the influence of 7 available implant systems (Ankylos, Astra, Bego, Brånemark, Camlog, Straumann, and Xive) with different implant-abutment connections on bone overload and the appearance of micro-gaps in vitro. The individual geometries of the implants were transferred to three-dimensional finite element models. In a non-linear analysis considering the pre-loading of the occlusion screw, friction between the implant and abutment, the influence of the cone angle on bone strain, and the appearance of micro-gaps were determined. Increased bone strains were correlated with small (< 15°) cone angles. Conical implant-abutment connections efficiently avoided micro-gaps but had a negative effect on peri-implant bone strain. Bone strain was reduced in implants with greater wall thickness (Ankylos) or a smaller cone angle (Bego). The results of our in silico study provide a solid basis for the reduction of peri-implant bone strain and micro-gaps in the implant-abutment connection to improve long-term stability.

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25

Ahmed, Hoda A., Mohamed Hagar, Omaima A. Alhaddad, and Ayman A. Zaki. "Optical and Geometrical Characterizations of Non-Linear Supramolecular Liquid Crystal Complexes." Crystals 10, no. 8 (August 14, 2020): 701. http://dx.doi.org/10.3390/cryst10080701.

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Nonlinear architecture liquid crystalline materials of supramolecular 1:1 H-bonded complexes (I/II and I/III) were prepared through a self-assembly intermolecular interaction between azopyridine (I) and 4-n-alkoxybenzoic acid (II) as well as 4-n-alkoxyphenylazo benzoic acid (III). The H-bond formation of the prepared supramolecular hydrogen bonded (SMHB) complexes was confirmed by Fourier-transform infrared spectroscopy (FT-IR) and differential scanning calorimetry (DSC). Optical and mesomorphic behaviors of the prepared complexes were studied by polarized optical microscopy (POM) as well as DSC. Theoretical calculations were performed by the density functional theory (DFT) and used to predict the molecular geometries of the synthesized complexes, and the results were used to explain the experimental mesomorphic and optical properties in terms of their estimated thermal parameters. Ordinary and extraordinary refractive indices as well as birefringence at different temperatures were investigated for each sample using an Abbe refractometer and modified spectrophotometer techniques. Microscopic and macroscopic order parameters were calculated for individual compounds and their supramolecular complexes.

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Li, Shi Rong, and Ya Dong Hu. "Solution for Geometrically Non-Linear Elastic Deformation of Simple Frames by a Shooting Method." Key Engineering Materials 462-463 (January 2011): 668–73. http://dx.doi.org/10.4028/www.scientific.net/kem.462-463.668.

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Based on an exact geometric nonlinear theory for plane curved beams, geometrically nonlinear equilibrium equations and boundary conditions governing the nonlinear bending of a simple plane frame structure subjected distributed loads were derived. By using the shooting method to numerically solve the boundary value problem of nonlinear ordinary differential equations, large deformation equilibrium configurations of a simple frame with both straight and the curved beam elements subjected uniformly distributed load were obtained. The theory and methodology presented can be used to analyze large deformation of plane simple frames with a variety of geometries and loadings.

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Asmolov, Evgeny S., Tatiana V. Nizkaya, and Olga I. Vinogradova. "Accurate Solutions to Non-Linear PDEs Underlying a Propulsion of Catalytic Microswimmers." Mathematics 10, no. 9 (May 1, 2022): 1503. http://dx.doi.org/10.3390/math10091503.

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Catalytic swimmers self-propel in electrolyte solutions thanks to an inhomogeneous ion release from their surface. Here, we consider the experimentally relevant limit of thin electrostatic diffuse layers, where the method of matched asymptotic expansions can be employed. While the analytical solution for ion concentration and electric potential in the inner region is known, the electrostatic problem in the outer region was previously solved but only for a linear case. Additionally, only main geometries such as a sphere or cylinder have been favoured. Here, we derive a non-linear outer solution for the electric field and concentrations for swimmers of any shape with given ion surface fluxes that then allow us to find the velocity of particle self-propulsion. The power of our formalism is to include the complicated effects of the anisotropy and inhomogeneity of surface ion fluxes under relevant boundary conditions. This is demonstrated by exact solutions for electric potential profiles in some particular cases with the consequent calculations of self-propulsion velocities.

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Landjev, Ivan N. "Linear codes over finite fields and finite projective geometries." Discrete Mathematics 213, no. 1-3 (February 2000): 211–44. http://dx.doi.org/10.1016/s0012-365x(99)00183-1.

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V R, Rajesh, and Biju T. Kuzhiveli. "Comparative analysis of linear motor geometries for Stirling coolers." IOP Conference Series: Materials Science and Engineering 278 (December 2017): 012042. http://dx.doi.org/10.1088/1757-899x/278/1/012042.

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Sin, Peter, Julien Sorci, and Qing Xiang. "Linear representations of finite geometries and associated LDPC codes." Journal of Combinatorial Theory, Series A 173 (July 2020): 105238. http://dx.doi.org/10.1016/j.jcta.2020.105238.

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Anemüller, Jörn. "Machine listening in spatial acoustic scenes with deep networks in different microphone geometries." Proceedings of the Northern Lights Deep Learning Workshop 1 (February 6, 2020): 6. http://dx.doi.org/10.7557/18.5151.

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Multi-channel acoustic source localization evaluates direction-dependentinter-microphone differences in order to estimate the position of an acousticsource embedded in an interfering sound field. We here investigate a deep neuralnetwork (DNN) approach to source localization that improves on previous workwith learned, linear support-vector-machine localizers. DNNs with depthsbetween 4 and 15 layers were trained to predict azimuth direction of targetspeech in 72 directional bins of width 5 degree, embedded in an isotropic,multi-speech-source noise field. Several system parameters were varied, inparticular number of microphones in the bilateral hearing aid scenario wasset to 2, 4, and 6, respectively. Results show that DNNs provide a clear improvement inlocalization performance over a linear classifier reference system.Increasing the number of microphones from 2 to 4 results in a larger increase ofperformance for the DNNs than for the linear system. However, 6 microphonesprovide only a small additional gain. The DNN architectures perform betterwith 4 microphones than the linear approach does with 6 microphones, thusindicating that location-specific information in source-interference scenariosis encoded non-linearly in the sound field.

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Bailey, Breanna, and Sidiq A. Osomo. "Prediction of Nominal Compressive Strength in Steel Piles Subject to Corrosion Losses: A Finite Element Approach." Journal of Civil Engineering and Construction 9, no. 1 (February 15, 2020): 24–30. http://dx.doi.org/10.32732/jcec.2020.9.1.24.

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This paper presents a method for predicting the nominal compressive strength of steel I-shaped piles subject to cross-sectional losses caused by corrosion. The method requires a finite element linear buckling analysis of the corroded cross-section. Results from the finite element buckling analysis may be integrated into design capacity equations contained in the 15th edition of the American Institute of Steel Construction Steel Construction Manual. Non-linear post-buckling analyses were used to verify the accuracy of the proposed method. Three cross-sectional geometries (W14x82, W14x90, and W14x120) were analyzed at varying degrees of cross-sectional loss. Results show close agreement between the non-linear finite element analyses and the proposed method of calculating nominal compressive strength.

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Keir, Joe. "Wave Propagation on Microstate Geometries." Annales Henri Poincaré 21, no. 3 (December 14, 2019): 705–60. http://dx.doi.org/10.1007/s00023-019-00874-4.

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AbstractSupersymmetric microstate geometries were recently conjectured (Eperon et al. in JHEP 10:031, 2016. 10.1007/JHEP10(2016)031) to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, we give a thorough mathematical treatment of the linear wave equation on both two- and three-charge supersymmetric microstate geometries, finding a number of surprising results. In both cases, we prove that solutions to the wave equation have uniformly bounded local energy, despite the fact that three-charge microstates possess an ergoregion; these geometries therefore avoid Friedman’s “ergosphere instability” (Friedman in Commun Math Phys 63(3):243–255, 1978). In fact, in the three-charge case we are able to construct solutions to the wave equation with local energy that neither grows nor decays, although these data must have non-trivial dependence on the Kaluza–Klein coordinate. In the two-charge case, we construct quasimodes and use these to bound the uniform decay rate, showing that the only possible uniform decay statements on these backgrounds have very slow decay rates. We find that these decay rates are sublogarithmic, verifying the numerical results of Eperon et al. (2016). The same construction can be made in the three-charge case, and in both cases the data for the quasimodes can be chosen to have trivial dependence on the Kaluza–Klein coordinates.

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Serrano, Erik, and Bertil Enquist. "Contact-free measurement and non-linear finite element analyses of strain distribution along wood adhesive bonds." Holzforschung 59, no. 6 (November 1, 2005): 641–46. http://dx.doi.org/10.1515/hf.2005.103.

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Abstract The strain distribution along wood adhesive bonds was studied using a contact-free measurement system based on a white-light digital image correlation (DIC) technique. Two different specimen geometries and three different adhesives were investigated. The specimen geometries were according to the standards EN302-1 and ASTM D905. The adhesives tested were a phenolic resorcinol (PRF), a one-component polyurethane (PUR) and an epoxy (EPX). In addition to the experimental investigation, a finite element study using a non-linear fracture mechanics model for the adhesive bond line was carried out, aimed at investigating whether deformation measurements could predict differences in the mechanical behaviour of the adhesives. The measurement technique was found to be capable of distinguishing, in terms of their strain distributions at a given load, adhesives that differed markedly from one another. For example, the brittle PRF adhesive showed more localised strains than the more ductile EPX and PUR adhesives did at the same load level. Another conclusion from this study is that the measurement technique used is applicable to situations in which large strains occur. Thus, the technique used here is of great interest for use in the calibration of finite element models and constitutive theories and for the design of test set-ups.

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Odehnal, Boris. "Generalized Conchoids." KoG, no. 21 (2017): 35–46. http://dx.doi.org/10.31896/k.21.3.

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We adapt the classical definition of conchoids as known from the Euclidean plane to geometries that can be modeled within quadrics. Based on a construction by means of cross ratios, a generalized conchoid transformation is obtained. Basic properties of the generalized conchoid transformation are worked out. At hand of some prominent examples - line geometry and sphere geometry - the actions of these conchoid transformations are studied. Linear and also non-linear transformations are presented and relations to well-known transformations are disclosed.

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Burton, D. A., R. W. Tucker, and C. Wang. "Spin driven motion in intense spacetime wave geometries." Theoretical and Applied Mechanics, no. 28-29 (2002): 77–92. http://dx.doi.org/10.2298/tam0229077b.

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The motion of a massive particle with intrinsic spin in a gravitational Einstein vacuum plane wave background is explored using the pole-dipole approximation to the Dixon multipole expansion for matter with compact support. Motivated by application to astrophysical processes the dynamical behavior of the spin and particle motion is described by numerically solving a system of non-linear first order ordinary differential equations. Some results are displayed in a reference frame adapted to the transverse nature of a monochromatic polarised gravitational wave of arbitrary intensity. .

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Kiermaier, Michael, and Johannes Zwanzger. "New ring-linear codes from dualization in projective Hjelmslev geometries." Designs, Codes and Cryptography 66, no. 1-3 (April 5, 2012): 39–55. http://dx.doi.org/10.1007/s10623-012-9650-1.

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Ustimenko, V. A. "A linear interpretation of the flag geometries of Chevalley groups." Ukrainian Mathematical Journal 42, no. 3 (March 1990): 341–44. http://dx.doi.org/10.1007/bf01057020.

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Syms, Richard R. A., and Steven Wright. "Paper-based evaporation concentrators: Comparison of linear and radial geometries." Biomicrofluidics 17, no. 1 (January 2023): 014102. http://dx.doi.org/10.1063/5.0129510.

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Paper-based evaporation concentrators with linear and radial geometries are compared. A new method of finding approximate analytic solutions of the advection–dispersion equation is proposed, based on the behavior of concentrators with infinite sources. Analytic approximations are compared with numerical solutions, and the advantage of radial concentration is highlighted: linear concentration rates scale with the square root of the Péclet number Pe while radial rates scale with Pe itself, leading to faster radial concentration beyond a critical value. Experiments are performed with Brilliant Blue FCF dye, using optical transmission and the Beer–Lambert law for quantitation. Dye concentrations are chosen for operation in the linear absorbance regime. Radial concentration is demonstrated under ambient conditions on filter paper disks with 60 mm diameter evaporation areas fed from a perimeter source, in a reverse of the well-known “coffee stain” experiment. Airflow enhanced concentration in strips and wedges is compared directly, using laser-patterned chromatography paper. The advantage of radial concentration is confirmed (and enhanced by diversion of concentrate to the corners of strips) and concentration factors greater than [Formula: see text] (the dynamic range of measurement) are obtained in ∼2 h using 30 mm long columns.

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Baiamonte, Giorgio. "Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments." Hydrology 7, no. 2 (April 10, 2020): 23. http://dx.doi.org/10.3390/hydrology7020023.

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In the field of hydrology, stage–discharge relationships are commonly used to estimate the discharge at the basin outlet or by experimental plots. Many experimental efforts have been made in order to derive stage–discharge relationships, according to the Buckingham theorem and dimensional analysis, for a multiplicity of gauge geometry. However, these relationships require experimental and physical meaningless numerical coefficients, thus they need extended calibration. The latter issue merits attention, since the empirical coefficients can be applied when the experimental conditions are strictly reproduced in the field. The aim of this paper is to derive a theoretically based stage–discharge relationship of a non-linear water reservoir that requires limited calibration, by using the continuity equation and the principle of conservation of energy. An analysis was performed using a rectangular water tank with a hole at the bottom. However, the suggested approach can be similarly used for tank geometries that differ from the example used in this study. Since the proposed approach is purely hydraulic, only limited calibration of the physical meaningful discharge coefficient characteristic of the hole is needed. A tank design procedure is suggested, and different theoretical and experimental applications of the proposed methodology are performed and discussed. For the considered cases, the mass water balance was also checked.

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Shrivastava, S., and J. Tang. "Large deformation finite element analysis of non-linear viscoelastic membranes with reference to thermoforming." Journal of Strain Analysis for Engineering Design 28, no. 1 (January 1, 1993): 31–51. http://dx.doi.org/10.1243/03093247v281031.

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This paper reports on the development of finite element formulations and computer programs for modelling free and constrained inflation of thin polymeric sheets in the context of thermoforming of plastic articles. In recognition of the generally time-dependent viscoelastic behaviour of polymers, and the large strains encountered in thermoforming applications, the material is modelled as non-linear visoelastic. For this purpose the constitutive relation proposed by Christensen (1)† is adopted, assuming the relaxation function to be exponential. Most of the published work on non-linear viscoelastic membranes deals with simple axisymmetric geometries, while the finite element formulations presented in this work are for both axisymmetric and non-axisymmetric membrane inflations, including contact against constraining surfaces. Both frictionless and slipless idealizations of contact conditions are studied. The finite element solutions of free and constrained inflations of circular membranes serve as illustrative examples for the axisymmetric case, while those for elliptical membranes demonstrate the non-axisymmetric cases. Comparison of the finite element results with the analytical solutions obtained (Appendix 1) for some simple free and constrained inflation problems shows good agreement.

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TABARRAEI, A., and N. SUKUMAR. "APPLICATION OF POLYGONAL FINITE ELEMENTS IN LINEAR ELASTICITY." International Journal of Computational Methods 03, no. 04 (December 2006): 503–20. http://dx.doi.org/10.1142/s021987620600117x.

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In this paper, a conforming polygonal finite element method is applied to problems in linear elasticity. Meshfree natural neighbor (Laplace) shape functions are used to construct conforming interpolating functions on any convex polygon. This provides greater flexibility to solve partial differential equations on complicated geometries. Closed-form expressions for Laplace shape functions on pentagonal, hexagonal, heptagonal, and octagonal reference elements are derived. Numerical examples are presented to demonstrate the accuracy of the method in two-dimensional elastostatics.

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Elhaddad, M., N. Zander, S. Kollmannsberger, A. Shadavakhsh, V. Nübel, and E. Rank. "Finite Cell Method: High-Order Structural Dynamics for Complex Geometries." International Journal of Structural Stability and Dynamics 15, no. 07 (August 31, 2015): 1540018. http://dx.doi.org/10.1142/s0219455415400180.

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In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A 1D benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate computational effort.

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Škrbić, Tatjana, Achille Giacometti, Trinh X. Hoang, Amos Maritan, and Jayanth R. Banavar. "A Tale of Two Chains: Geometries of a Chain Model and Protein Native State Structures." Polymers 16, no. 4 (February 12, 2024): 502. http://dx.doi.org/10.3390/polym16040502.

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Linear chain molecules play a central role in polymer physics with innumerable industrial applications. They are also ubiquitous constituents of living cells. Here, we highlight the similarities and differences between two distinct ways of viewing a linear chain. We do this, on the one hand, through the lens of simulations for a standard polymer chain of tethered spheres at low and high temperatures and, on the other hand, through published experimental data on an important class of biopolymers, proteins. We present detailed analyses of their local and non-local structures as well as the maps of their closest contacts. We seek to reconcile the startlingly different behaviors of the two types of chains based on symmetry considerations.

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Dieci, L., Fabio V. Difonzo, and N. Sukumar. "Nonnegative moment coordinates on finite element geometries." Mathematics in Engineering 6, no. 1 (2024): 81–99. http://dx.doi.org/10.3934/mine.2024004.

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<abstract><p>In this paper, we introduce new generalized barycentric coordinates (coined as <italic>moment coordinates</italic>) on convex and nonconvex quadrilaterals and convex hexahedra with planar faces. This work draws on recent advances in constructing interpolants to describe the motion of the Filippov sliding vector field in nonsmooth dynamical systems, in which nonnegative solutions of signed matrices based on (partial) distances are studied. For a finite element with $ n $ vertices (nodes) in $ \mathbb{R}^2 $, the constant and linear reproducing conditions are supplemented with additional linear moment equations to set up a linear system of equations of full rank $ n $, whose solution results in the nonnegative shape functions. On a simple (convex or nonconvex) quadrilateral, moment coordinates using signed distances are identical to mean value coordinates. For signed weights that are based on the product of distances to edges that are incident to a vertex and their edge lengths, we recover Wachspress coordinates on a convex quadrilateral. Moment coordinates are also constructed on a convex hexahedra with planar faces. We present proofs in support of the construction and plots of the shape functions that affirm its properties.</p></abstract>

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Alavi, Seyed Hassan, John Bamberg, and Cheryl E. Praeger. "Triple factorisations of the general linear group and their associated geometries." Linear Algebra and its Applications 469 (March 2015): 169–203. http://dx.doi.org/10.1016/j.laa.2014.11.018.

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Varadarajan, V., and J. L. Krolik. "Joint space-time interpolation for distorted linear and bistatic array geometries." IEEE Transactions on Signal Processing 54, no. 3 (March 2006): 848–60. http://dx.doi.org/10.1109/tsp.2005.862941.

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Löwen, Rainer, and Burkard Polster. "Linear geometries on the Moebius strip: A theorem of Skornyakov type." Bulletin of the Australian Mathematical Society 72, no. 1 (August 2005): 17–30. http://dx.doi.org/10.1017/s0004972700034833.

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We show that the continuity properties of a stable plane are automatically satisfied if we have a linear space with point set a Moebius strip, provided that the lines are closed subsets homeomorphic to the real line or to the circle. In other words, existence of a unique line joining two distinct points implies continuity of join and intersection. For linear spaces with an open disk as point set, the same result was proved by Skornyakov.

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Monari, Antonio, Gian Luigi Bendazzoli, and Stefano Evangelisti. "Theoretical Study of BeN Linear Chains: Optimized Geometries and Harmonic Frequencies." Journal of Chemical Theory and Computation 5, no. 5 (March 30, 2009): 1266–73. http://dx.doi.org/10.1021/ct9001027.

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Seibt, Joachim, and Volker Engel. "Absorption and emission spectroscopy of molecular trimers: Cyclic versus linear geometries." Chemical Physics 347, no. 1-3 (May 2008): 120–26. http://dx.doi.org/10.1016/j.chemphys.2007.10.014.

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Journal articles on the topic 'Linear and non-linear geometries'

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