Numerical Analysis--Mathematics of Scientific Computing.

Kincaid, David R.; Cheney, Ward

doi:10.2307/2152998

Cited by 213 publications

(37 citation statements)

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“…( 10)-( 14) via Euler discretization with an isotropic Laplacian on an N 2 lattice (N = 128). We impose periodic boundary conditions in both directions [52], so as to remove the edge effects and mimic the bulk system. The discretization mesh sizes are chosen to be ∆t = 0.01 and ∆x = 1.0.…”

Section: Resultsmentioning

confidence: 99%

Symbiotic Dynamics in Living Liquid Crystals

Vats¹,

Yadav²,

Banerjee³

et al. 2023

Preprint

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An amalgamate of nematic liquid crystals and active matter, referred to as living liquid crystals, is a promising self-healing material with futuristic applications for targeted delivery of information and micro-cargo. We provide a phenomenological model to study the symbiotic pattern dynamics in this contemporary system using the Toner-Tu model for active matter (AM), the Landau-de Gennes free energy for liquid crystals (LCs), and an experimentally motivated coupling term that favours co-alignment of the active and nematic components. Our extensive theoretical studies unfold two novel steady states, chimeras and solitons, with sharp regions of distinct orientational order that sweep through the coupled system in synchrony. The induced dynamics in the passive nematic is unprecedented. We show that the symbiotic dynamics of the AM and LC components can be exploited to induce and manipulate order in an otherwise disordered system.

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Section: Resultsmentioning

confidence: 99%

Symbiotic Dynamics in Living Liquid Crystals

Vats¹,

Yadav²,

Banerjee³

et al. 2023

Preprint

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“…, Zu,t+1 , Zχ,t+1 , Z∇χ,t+1 , γu,t+1 , γ χ,t+1 , γ∇χ,t+1 ← performNonlinearSolve else end 54 Kelley [1995] and Kelley [2003] but we utilize an initialization procedure called Homotopy or the continuation method detailed in section 3.6 of Kincaid and Cheney [2009] where we break each increment into pseudo-time steps such that…”

Section: Model Algorithmmentioning

confidence: 99%

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Miller

2022

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It has very quickly become apparent to me that a Ph.D. is not the result of the efforts of a single person but rather the net product of the investments of many in the author. In particular, Dr. Richard Regueiro has been a constant source of knowledge and advice as he has guided me through this effort as my thesis adviser. His insight and direction have been crucial in developing my understanding of the material and the extensions I have made to it. I have often heard it said that the choice of adviser is likely the most crucial decision a person will make in their doctoral work and I have been extraordinarily fortunate in this regard. The hours spent collaborating with him have been a joy and I look forward to many more future endeavors.I owe my interest in computational mechanics to Miles Buechler and Devin Shunk who invited me to take Dr. Mark Carrara's continuum mechanics course. To say that course, and the subsequent work with them on material modeling were influential on my present trajectory would be an understatement. Philip Schembri has also been, as much as he would deny it, deeply insightful in his technical advice. For funding I would like to thank

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“…Initial attempts at solving the problem employed the classic approximation method using the least-squares method [19]. Since the proposed approximation function cannot be reduced by substitution to a linear or polynomial function with their ready-made equations, the definition was considered.…”

Section: Principles Of Calculating Approximation Coefficientsmentioning

confidence: 99%

“…Since the proposed approximation function cannot be reduced by substitution to a linear or polynomial function with their ready-made equations, the definition was considered. This approximation problem can be approached as a non-linear least-squares method [19].…”

Section: Principles Of Calculating Approximation Coefficientsmentioning

confidence: 99%

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Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

et al. 2020

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Genetic algorithms are used to parameter identification of the model of oscillatory processes in complicated motion transmission of electric drives containing long elastic shafts as systems of distributed mechanical parameters. Shaft equations are generated on the basis of a modified Hamilton–Ostrogradski principle, which serves as the foundation to analyse the lumped parameter system and distributed parameter system. They serve to compute basic functions of analytical mechanics of velocity continuum and rotational angles of shaft elements. It is demonstrated that the application of the distributed parameter method to multi-mass rotational systems, that contain long elastic elements and complicated control systems, is not always possible. The genetic algorithm is applied to determine the coefficients of approximation the system of Rotational Transmission with Elastic Shaft by equivalent differential equations. The fitness function is determined as least-square error. The obtained results confirm that application of the genetic algorithms allow one to replace the use of a complicated distributed parameter model of mechanical system by a considerably simpler model, and to eliminate sophisticated calculation procedures and identification of boundary conditions for wave motion equations of long elastic elements.

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Numerical Analysis--Mathematics of Scientific Computing.

Cited by 213 publications

References 0 publications

Symbiotic Dynamics in Living Liquid Crystals

Symbiotic Dynamics in Living Liquid Crystals

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

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