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Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals

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Physical Review E 2018年第5期97卷 052701-052701页

作者： Hayley R. O. Sohn Paul J. Ackerman Timothy J. Boyle Ghadah H. Sheetah Bengt Fornberg Ivan I. Smalyukh Soft Materials Research Center and Materials Science and Engineering Program University of Colorado Boulder Colorado 80309 USA Department of Physics and Department of Electrical Computer and Energy Engineering University of Colorado Boulder Colorado 80309 USA Department of Applied Mathematics University of Colorado Boulder Colorado 80309 USA Renewable and Sustainable Energy Institute National Renewable Energy Laboratory and University of Colorado Boulder Colorado 80309 USA

Active colloids and liquid crystals are capable of locally converting the macroscopically supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here we uncover how topological solitons in liquid crystals can locally transform electric energy to translational motion and allow for the transport of cargo along directions dependent on frequency of the applied electric field. By combining polarized optical video microscopy and numerical modeling that reproduces both the equilibrium structures of solitons and their temporal evolution in applied fields, we uncover the physical underpinnings behind this reconfigurable motion and study how it depends on the structure and topology of solitons. We show that, unexpectedly, the directional motion of solitons with and without the cargo arises mainly from the asymmetry in rotational dynamics of molecular ordering in liquid crystal rather than from the asymmetry of fluid flows, as in conventional active soft matter systems.

关键词： Chirality Topological defects Active nematics Cholesteric liquid crystals Nanoparticles Nematic liquid crystals Soft colloids Solitons

Nonlinear Waves in Rods and Beams of Power-Law Materials

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Journal of applied mathematics 2017年第none期2017卷 1-6页

作者： Wei, Dongming Skrzypacz, Piotr Yu, Xijun Department of Mathematics School of Science and Technology Nazarbayev University Astana010000 Kazakhstan Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing100088 China

Some novel traveling waves and special solutions to the 1D nonlinear dynamic equations of rod and beam of power-law materials are found in closed forms. The traveling solutions represent waves of high elevation that propagates without change of forms in time. These waves resemble the usual kink waves except that they do not possess bounded elevations. The special solutions satisfying certain boundary and initial conditions are presented to demonstrate the nonlinear behavior of the materials. This note demonstrates the apparent distinctions between linear elastic and nonlinear plastic waves. © 2017 Dongming Wei et al.

关键词： Nonlinear equations

Author Correction: Genetic drivers and cellular selection of female mosaic X chromosome loss

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Nature 2024年第8043期636卷 E7页

作者： Aoxing Liu Giulio Genovese Yajie Zhao Matti Pirinen Seyedeh M Zekavat Katherine A Kentistou Zhiyu Yang Kai Yu Caitlyn Vlasschaert Xiaoxi Liu Derek W Brown Georgi Hudjashov Bryan R Gorman Joe Dennis Weiyin Zhou Yukihide Momozawa Saiju Pyarajan Valdislav Tuzov Fanny-Dhelia Pajuste Mervi Aavikko Timo P Sipilä Awaisa Ghazal Wen-Yi Huang Neal D Freedman Lei Song Eugene J Gardner Vijay G Sankaran Aarno Palotie Hanna M Ollila Taru Tukiainen Stephen J Chanock Reedik Mägi Pradeep Natarajan Mark J Daly Alexander Bick Steven A McCarroll Chikashi Terao Po-Ru Loh Andrea Ganna John R B Perry Mitchell J Machiela Institute for Molecular Medicine Finland (FIMM) HiLIFE University of Helsinki Helsinki Finland. liuaoxin@***. Analytic and Translational Genetics Unit Massachusetts General Hospital Boston MA USA. liuaoxin@***. Center for Genomic Medicine Massachusetts General Hospital Boston MA USA. liuaoxin@***. Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA USA. liuaoxin@***. Stanley Center for Psychiatric Research Broad Institute of MIT and Harvard Cambridge MA USA. liuaoxin@***. Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA USA. giulio@***. Stanley Center for Psychiatric Research Broad Institute of MIT and Harvard Cambridge MA USA. giulio@***. Department of Genetics Harvard Medical School Boston MA USA. giulio@***. MRC Epidemiology Unit Institute of Metabolic Science University of Cambridge Cambridge UK. Institute for Molecular Medicine Finland (FIMM) HiLIFE University of Helsinki Helsinki Finland. Department of Public Health University of Helsinki Helsinki Finland. Department of Mathematics and Statistics University of Helsinki Helsinki Finland. Program in Medical and Population Genetics Broad Institute of MIT and Harvard Cambridge MA USA. Cardiovascular Research Center Massachusetts General Hospital Boston MA USA. Department of Ophthalmology Massachusetts Eye and Ear Harvard Medical School Boston MA USA. Division of Cancer Epidemiology and Genetics National Cancer Institute Rockville MD USA. Department of Medicine Queen's University Kingston Ontario Canada. Laboratory for Statistical and Translational Genetics RIKEN Center for Integrative Medical Sciences Yokohama Japan. Cancer Prevention Fellowship Program Division of Cancer Prevention National Cancer Institute Rockville MD USA. Estonian Genome Centre Institute of Genomics University of Tartu Tartu Estonia. Center for Data and Computational Sciences (C-DACS) VA Cooperative Studies Program VA Boston Health

A spectral-infinite-element solution of Poisson’s equation: An application to self gravity

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arXiv 2017年

作者： Gharti, Hom Nath Tromp, Jeroen Department of Geosciences Princeton University PrincetonNJ08544 United States Program in Applied & Computational Mathematics Princeton University PrincetonNJ United States

We solve Poisson’s equation by combining a spectral-element method with a mapped infinite-element method. We focus on problems in geostatics and geodynamics, where Earth’s gravitational field is determined by Poisson’s equation inside the Earth and Laplace’s equation in the rest of space. Spectral elements are used to capture the internal field, and infinite elements are used to represent the external field. To solve the weak form of Poisson/Laplace equation, we use Gauss-Legendre-Lobatto quadrature in spectral elements inside the domain of interest. Outside the domain, we use Gauss-Radau quadrature in the infinite direction, and Gauss-Legendre-Lobatto quadrature in the other directions. We illustrate the efficiency and accuracy of the method by comparing the gravitational fields of a homogeneous sphere and the Preliminary Reference Earth Model (PREM) with (semi-)analytical solutions. Copyright © 2017, The Authors. All rights reserved.

关键词： Earth (planet)

Built to Last: Functional and structural mechanisms in the moth olfactory network mitigate effects of neural injury

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arXiv 2018年

作者： Delahunt, Charles Maia, Pedro D. Nathan Kutz, J. Computational Neuroscience Center University of Washington SeattleWA United States Weill Cornell Medicine Department of Radiology New YorkNY United States Weill Cornell Medicine Brain and Mind Research Institute New YorkNY United States Department of Applied Mathematics University of Washington SeattleWA United States

Most organisms are exposed to neural damage throughout their lives, which can reduce their ability to carry out core behavioral tasks. Their neural circuits need to maintain functionality despite injury, which often requires that key readout signals from the system be preserved. In this work, we explore whether and how certain structural and functional network motifs act as injury mitigation mechanisms by protecting these readouts. Specifically, we examine how (i) Hebbian learning, (ii) high levels of noise, and (iii) presence of parallel inhibitory and excitatory connections contribute to robustness of the olfactory system in the Manduca sexta moth. We simulate injuries on a detailed computational model of the moth olfactory network in which structures-under-test are parametrically varied. Neuronal impairments are modeled as focal axonal swellings, an axonal pathology observed across all severities of traumatic brain injuries and present in other leading brain disorders. Axonal swellings effectively compromise spike train propagation along the axon and consequently reduce the effective neural firing rate delivered to downstream neurons. All three of the network motifs examined significantly mitigate the effects of injury on readout neurons, either by reducing injury's impact on readout neuron responses or by restoring these responses to pre-injury levels through reinforcement learning. These motifs may thus be partially explained by their value as adaptive mechanisms to minimize the functional effects of neural injury. More generally, these experiments suggest that robustness to injury is a vital design principle to consider when analyzing biological neural systems. Indeed, it is possible that some neural structures and mechanisms, including the ability to learn, are best understood as evolutionary solutions to the challenge of maintaining system function despite injury. Copyright © 2018, The Authors. All rights reserved.

关键词： Neurons

Sampling real algebraic varieties for topological data analysis

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arXiv 2018年

作者： Dufresne, Emilie Edwards, Parker B. Harrington, Heather A. Hauenstein, Jonathan D. School of Mathematical Sciences University of Nottingham University Park NottinghamNG7 2RD United Kingdom Department of Mathematics University of Florida PO Box 118105 GainesvilleFL32611 United States Mathematical Institute Radcliffe Observatory Quarter Woodstock Road OxfordOX2 6GG United Kingdom Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points. We present a new adaptive algorithm for finding provably dense samples of points on real algebraic varieties given a set of defining polynomials. The algorithm utilizes methods from numerical algebraic geometry to give formal guarantees about the density of the sampling and it also employs geometric heuristics to reduce the size of the sample. As TDA methods consume significant computational resources that scale poorly in the number of sample points, our sampling minimization makes applying TDA methods more feasible. We provide a software package that implements the algorithm and also demonstrate the implementation with several examples. Copyright © 2018, The Authors. All rights reserved.

关键词： Adaptive algorithms

An interior penalty discontinuous Galerkin approach for 3D incompressible Navier-Stokes equation for permeability estimation of porous media

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arXiv 2018年

作者： Liu, Chen Frank, Florian Alpak, Faruk O. Rivière, Béatrice Rice University Department of Computational and Applied Mathematics 6100 Main Street HoustonTX77005 United States Friedrich-Alexander-Universität Erlangen-Nürnberg Department Mathematik Cauerstraße 11 Erlangen91058 Germany Shell Technology Center 3333 Highway 6 South HoustonTX77082 United States

Permeability estimation of porous media from direct solving Navier-Stokes equation has a wide spectrum of applications in petroleum industry. In this paper, we utilize a pressure-correction projection algorithm in conjunction with the interior penalty discontinuous Galerkin scheme for space discretization to build an incompressible Navier-Stokes simulator and to use this simulator to calculate permeability of real rock sample. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems. Copyright © 2018, The Authors. All rights reserved.

关键词： Porous materials

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

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arXiv 2017年

作者： Wang, Han Zhang, Linfeng Han, Jiequn Weinan, E. Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model. Copyright © 2017, The Authors. All rights reserved.

关键词： Potential energy

Comparison of Polarized Radiative Transfer Codes used by the EHT Collaboration

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arXiv 2023年

作者： Prather, Ben S. Dexter, Jason Moscibrodzka, Monika Pu, Hung-Yi Bronzwaer, Thomas Davelaar, Jordy Younsi, Ziri Gammie, Charles F. Gold, Roman Wong, And George N. Akiyama, Kazunori Alberdi, Antxon Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Baczko, Anne-Kathrin Ball, David Baloković, Mislav Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blackburn, Lindy Blundell, Raymond Bouman, Katherine L. Bower, Geoffrey C. Boyce, Hope Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara Chael, Andrew Chan, Chi-Kwan Chang, Dominic O. Chatterjee, Koushik Chatterjee, Shami Chen, Ming-Tang Chen, Yongjun Cheng, Xiaopeng Cho, Ilje Christian, Pierre Conroy, Nicholas S. Conway, John E. Cordes, James M. Crawford, Thomas M. Crew, Geoffrey B. Cruz-Osorio, Alejandro Cui, Yuzhu De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dhruv, Vedant Doeleman, Sheperd S. Dougal, Sean Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Ed Alyson Ford, H. Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gómez-Ruiz, Arturo I. Gómez, José L. Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Haggard, Daryl Haworth, Kari Hecht, Michael H. Hesper, Ronald Heumann, Dirk Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Ikeda, Shiro Violette Impellizzeri, C.M. Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra Johnson, Michael D. Jorstad, Svetlana Joshi, Abhishek V. Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kino, Motoki Koay, Jun Yi Kocherlakota, Prashant K CCS-2 Los Alamos National Laboratory P.O. Box 1663 Los AlamosNM87545 United States JILA Department of Astrophysical and Planetary Sciences University of Colorado BoulderCO80309 United States Department of Astrophysics IMAPP Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Department of Physics National Taiwan Normal University No. 88 Sec.4 Tingzhou Rd. Taipei116 Taiwan Center of Astronomy and Gravitation National Taiwan Normal University No. 88 Sec. 4 Tingzhou Road Taipei116 Taiwan Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd Taipei10617 Taiwan Department of Astronomy Columbia Astrophysics Laboratory Columbia University 550 W 120th Street New YorkNY10027 United States Center for Computational Astrophysics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Mullard Space Science Laboratory University College London Holmbury St. Mary Dorking SurreyRH5 6NT United Kingdom Institut für Theoretische Physik Goethe-Universität Frankfurt Max-von-Laue-Straße 1 Frankfurt am MainD-60438 Germany Department of Physics University of Illinois 1110 West Green Street UrbanaIL61801 United States Department of Astronomy University of Illinois at Urbana-Champaign 1002 West Green Street UrbanaIL61801 United States NCSA University of Illinois 1205 W Clark St UrbanaIL61801 United States CP3-Origins University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Princeton Gravity Initiative Princeton University PrincetonNJ08544 United States Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Harvard University 20 Gar

Interpretation of resolved polarized images of black holes by the Event Horizon Telescope (EHT) requires predictions of the polarized emission observable by an Earth-based instrument for a particular model of the black hole accretion system. Such predictions are generated by general relativistic radiative transfer (GRRT) codes, which integrate the equations of polarized radiative transfer in curved spacetime. A selection of ray-tracing GRRT codes used within the EHT collaboration is evaluated for accuracy and consistency in producing a selection of test images, demonstrating that the various methods and implementations of radiative transfer calculations are highly consistent. When imaging an analytic accretion model, we find that all codes produce images similar within a pixel-wise normalized mean squared error (NMSE) of 0.012 in the worst case. When imaging a snapshot from a cell-based magnetohydrodynamic simulation, we find all test images to be similar within NMSEs of 0.02, 0.04, 0.04, and 0.12 in Stokes I, Q, U, and V respectively. We additionally find the values of several image metrics relevant to published EHT results to be in agreement to much better precision than measurement uncertainties. © 2023, CC BY.

关键词： Mean square error