An accurate method to include lubrication forces in numerical simulations of dense Stokesian suspensions

2015 ◽  
Vol 769 ◽  
pp. 369-386 ◽  
Author(s):  
A. Lefebvre-Lepot ◽  
B. Merlet ◽  
T. N. Nguyen
Keyword(s):  
Short Range ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Parameter Tuning ◽  
Accurate Method ◽  
Spherical Particles ◽  
Particle Model ◽  
Stokesian Dynamics ◽  
New Feature ◽  
The Many

We address the problem of computing the hydrodynamic forces and torques among $N$ solid spherical particles moving with given rotational and translational velocities in Stokes flow. We consider the original fluid–particle model without introducing new hypotheses or models. Our method includes the singular lubrication interactions which may occur when some particles come close to one another. The main new feature is that short-range interactions are propagated to the whole flow, including accurately the many-body lubrication interactions. The method builds on a pre-existing fluid solver and is flexible with respect to the choice of this solver. The error is the error generated by the fluid solver when computing non-singular flows (i.e. with negligible short-range interactions). Therefore, only a small number of degrees of freedom are required and we obtain very accurate simulations within a reasonable computational cost. Our method is closely related to a method proposed by Sangani & Mo (Phys. Fluids, vol. 6, 1994, pp. 1653–1662) but, in contrast with the latter, it does not require parameter tuning. We compare our method with the Stokesian dynamics of Durlofsky et al. (J. Fluid Mech., vol. 180, 1987, pp. 21–49) and show the higher accuracy of the former (both by analysis and by numerical experiments).

A 3D Complexity-Adaptive Approach to Exploit Sparsity in Elastic Wave Propagation

Geophysics ◽  
2021 ◽  
pp. 1-64
Author(s):  
Claudia Haindl ◽  
Kuangdai Leng ◽  
Tarje Nissen-Meyer
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Parameter Tuning ◽  
Performance Limits ◽  
Absorbing Boundary ◽  
Adaptive Approach ◽  
Order Of Magnitude ◽  
Speed Up ◽  
Complex Settings ◽  
Close Fit

We present an adaptive approach to seismic modeling by which the computational cost of a 3D simulation can be reduced while retaining resolution and accuracy. This Azimuthal Complexity Adaptation (ACA) approach relies upon the inherent smoothness of wavefields around the azimuth of a source-centered cylindrical coordinate system. Azimuthal oversampling is thereby detected and eliminated. The ACA method has recently been introduced as part of AxiSEM3D, an open-source solver for global seismology. We employ a generalization of this solver which can handle local-scale Cartesian models, and which features a combination of an absorbing boundary condition and a sponge boundary with automated parameter tuning. The ACA method is benchmarked against an established 3D method using a model featuring bathymetry and a salt body. We obtain a close fit where the models are implemented equally in both solvers and an expectedly poor fit otherwise, with the ACA method running an order of magnitude faster than the classic 3D method. Further, we present maps of maximum azimuthal wavenumbers that are created to facilitate azimuthal complexity adaptation. We show how these maps can be interpreted in terms of the 3D complexity of the wavefield and in terms of seismic resolution. The expected performance limits of the ACA method for complex 3D structures are tested on the SEG/EAGE salt model. In this case, ACA still reduces the overall degrees of freedom by 92% compared to a complexity-blind AxiSEM3D simulation. In comparison with the reference 3D method, we again find a close fit and a speed-up of a factor 7. We explore how the performance of ACA is affected by model smoothness by subjecting the SEG/EAGE salt model to Gaussian smoothing. This results in a doubling of the speed-up. ACA thus represents a convergent, versatile and efficient method for a variety of complex settings and scales.

scholarly journals Accelerated Stokesian Dynamics simulations

2001 ◽  
Vol 448 ◽  
pp. 115-146 ◽  
Author(s):  
ASIMINA SIEROU ◽  
JOHN F. BRADY
Keyword(s):  
Reynolds Number ◽  
Freezing Point ◽  
Computational Cost ◽  
Spherical Shape ◽  
Stokesian Dynamics ◽  
Reynolds Number Flow ◽  
Wave Space ◽  
Number Flow ◽  
The Many ◽  
Dynamics Simulations

A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called accelerated Stokesian Dynamics (ASD), is presented. The equations governing the motion of N particles suspended in a viscous fluid at low particle Reynolds number are solved accurately and efficiently, including all hydrodynamic interactions, but with a significantly lower computational cost of O(N ln N). The main differences from the conventional SD method lie in the calculation of the many-body long-range interactions, where the Ewald-summed wave-space contribution is calculated as a Fourier transform sum and in the iterative inversion of the now sparse resistance matrix. The new method is applied to problems in the rheology of both structured and random suspensions, and accurate results are obtained with much larger numbers of particles. With access to larger N, the high-frequency dynamic viscosities and short-time self-diffusivities of random suspensions for volume fractions above the freezing point are now studied. The ASD method opens up an entire new class of suspension problems that can be investigated, including particles of non-spherical shape and a distribution of sizes, and the method can readily be extended to other low-Reynolds-number-flow problems.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

Driving Torsion Scans with Wavefront Propagation

2020 ◽  
Author(s):  
Yudong Qiu ◽  
Daniel Smith ◽  
Chaya Stern ◽  
mudong feng ◽  
Lee-Ping Wang
Keyword(s):  
Potential Energy ◽  
Force Field ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Initial Guess ◽  
Field Development ◽  
Force Field Development ◽  
Wavefront Propagation ◽  
Open Source Software Package

<div>The parameterization of torsional / dihedral angle potential energy terms is a crucial part of developing molecular mechanics force fields.</div><div>Quantum mechanical (QM) methods are often used to provide samples of the potential energy surface (PES) for fitting the empirical parameters in these force field terms.</div><div>To ensure that the sampled molecular configurations are thermodynamically feasible, constrained QM geometry optimizations are typically carried out, which relax the orthogonal degrees of freedom while fixing the target torsion angle(s) on a grid of values.</div><div>However, the quality of results and computational cost are affected by various factors on a non-trivial PES, such as dependence on the chosen scan direction and the lack of efficient approaches to integrate results started from multiple initial guesses.</div><div>In this paper we propose a systematic and versatile workflow called \textit{TorsionDrive} to generate energy-minimized structures on a grid of torsion constraints by means of a recursive wavefront propagation algorithm, which resolves the deficiencies of conventional scanning approaches and generates higher quality QM data for force field development.</div><div>The capabilities of our method are presented for multi-dimensional scans and multiple initial guess structures, and an integration with the MolSSI QCArchive distributed computing ecosystem is described.</div><div>The method is implemented in an open-source software package that is compatible with many QM software packages and energy minimization codes.</div>

scholarly journals Probing the interplay between lattice dynamics and short-range magnetic correlations in CuGeO3 with femtosecond RIXS

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
E. Paris ◽  
C. W. Nicholson ◽  
S. Johnston ◽  
Y. Tseng ◽  
M. Rumo ◽  
...  
Keyword(s):  
Short Range ◽  
Degrees Of Freedom ◽  
Time Resolved ◽  
Model Calculations ◽  
Spin Correlations ◽  
Singlet Exciton ◽  
Magnetic Correlations ◽  
Local Lattice ◽  
Frustrated Systems ◽  
A Charge

AbstractInvestigations of magnetically ordered phases on the femtosecond timescale have provided significant insights into the influence of charge and lattice degrees of freedom on the magnetic sub-system. However, short-range magnetic correlations occurring in the absence of long-range order, for example in spin-frustrated systems, are inaccessible to many ultrafast techniques. Here, we show how time-resolved resonant inelastic X-ray scattering (trRIXS) is capable of probing such short-ranged magnetic dynamics in a charge-transfer insulator through the detection of a Zhang–Rice singlet exciton. Utilizing trRIXS measurements at the O K-edge, and in combination with model calculations, we probe the short-range spin correlations in the frustrated spin chain material CuGeO3 following photo-excitation, revealing a strong coupling between the local lattice and spin sub-systems.

scholarly journals THE DYNAMIC RESPONSE OF OFFSHORE STRUCTURES TO TIME-DEPENDENT FORCES

1964 ◽  
Vol 1 (9) ◽  
pp. 29
Author(s):  
William S. Gaither ◽  
David P. Billington
Keyword(s):  
Degrees Of Freedom ◽  
Wind Waves ◽  
Offshore Structures ◽  
Time Dependent ◽  
Wave Forces ◽  
Ocean Bottom ◽  
Single Wave ◽  
Single Degree Of Freedom ◽  
The Many ◽  
Floating Objects

This paper is addressed to the problem of structural behavior in an offshore environment, and the application of a more rigorous analysis for time-dependent forces than is currently used. Design of pile supported structures subjected to wave forces has, in the past, been treated in two parts; (1) a static analysis based on the loading of a single wave, and (2) a dynamic analysis which sought to determine the resonant frequency by assuming that the structure could be approximated as a single-degree-of-freedom system. (Ref. 4 and 6) The behavior of these structures would be better understood if the dynamic nature of the loading and the many degrees of freedom of the system were included. A structure which is built in the open ocean is subjected to periodic forces due to wind, waves, floating objects, and due occasionally to machinery mounted on the structure. To resist motion, the structure relies on the stiffness of the elements from which it is built and the restraints of the ocean bottom into which the supporting legs are driven.

DEONTOLOGY, THRESHOLDS, AND EFFICIENCY

Legal Theory ◽  
2011 ◽  
Vol 17 (4) ◽  
pp. 301-317 ◽  
Author(s):  
Christopher T. Wonnell
Keyword(s):  
Decision Making ◽  
Degrees Of Freedom ◽  
Moral Judgments ◽  
Rule Following ◽  
Threshold Functions ◽  
Ex Post ◽  
Ex Ante ◽  
The Many ◽  
The Relationship ◽  
Public Decision

This article explores four topics raised by Eyal Zamir and Barak Medina's treatment of constrained deontology. First, it examines whether mathematical threshold functions are the proper way to think about limits on deontology, given the discontinuities of our moral judgments and the desired phenomenology of rule-following. Second, it asks whether constrained deontology is appropriate for public as well as private decision-making, taking issue with the book's conclusion that deontological options are inapplicable to public decision-making, whereas deontological constraints are applicable. Third, it examines the issue of the relationship between deontology and efficiency, asking whether deontological constraints should yield in situations where everyone would expect to benefit from their suspension, either ex ante or ex post. Finally, the article concludes that constrained deontology is susceptible to political abuse because of the many degrees of freedom involved in identifying constrained actions and the point at which those constraints yield to consequentialist benefits.

Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach

2018 ◽  
Vol 26 (01) ◽  
pp. 1750030 ◽  
Author(s):  
V. Hernández ◽  
J. Estrada ◽  
E. Moreno ◽  
S. Rodríguez ◽  
A. Mansur
Keyword(s):  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Computational Cost ◽  
Dispersion Curves ◽  
Wave Number ◽  
Spline Functions ◽  
Shape Functions ◽  
B Spline ◽  
Generalized Eigenvalue ◽  
Generalized Eigenvalue Problems

Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

A Weighted Rearranged Spectral Equation Method for Structural Model Updating

1995 ◽  
Author(s):  
José Roberto F. Arruda ◽  
Carlson Antonio M. Verçosa
Keyword(s):  
Degrees Of Freedom ◽  
Structural Model ◽  
Model Updating ◽  
Structural Connectivity ◽  
Computational Cost ◽  
Force Balance ◽  
Dynamic Force ◽  
Stiffness Coefficients ◽  
Spring System ◽  
Spectral Equation

Abstract A new structural model updating method based on the dynamic force balance is presented. The method consists of rearranging the spectral equation so that measured modes and natural frequencies can be used to compute directly updated stiffness coefficients. The proposed method preserves both the structural connectivity and reciprocity, which translate into sparsity and symmetry of the stiffness matrix, respectively. Large changes in small-valued stiffness coefficients are avoided using parameter weighting in the rearranged spectral equation solution. It is shown that the proposed method produces results which are similar to the results obtained using Alvar Kabe’s method, with the advantages of simpler formulation and smaller computational cost. A simple example of an 8 degrees-of-freedom mass-spring system, originally used by Kabe to present his method, is used here to evaluate the proposed method.

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