Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at ...intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. Here this method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ~1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.
The flagellar beat is extracted from human sperm digital imaging microscopy and used to determine the flow around the cell and its trajectory, via boundary element simulation. Comparison of the ...predicted cell trajectory with observation demonstrates that simulation can predict fine-scale sperm dynamics at the qualitative level. The flow field is also observed to reduce to a time-dependent summation of regularized Stokes flow singularities, approximated at leading order by a blinking force triplet. Such regularized singularity decompositions may be used to upscale cell level detail into population models of human sperm motility.
We develop a continuous adjoint formulation and implementation for controlling the deformation of clean, neutrally buoyant droplets in Stokes flow through farfield velocity boundary conditions. The ...focus is on dynamics where surface tension plays an important role through the Young-Laplace law. To perform the optimization, we require access to first-order gradient information, which we obtain from the linearized sensitivity equations and their corresponding adjoint by applying shape calculus to the space-time tube formed by the interface evolution. We show that the adjoint evolution equation can be efficiently expressed through a scalar adjoint transverse field. The optimal control problem is discretized by high-order boundary integral methods using Quadrature by Expansion coupled with a spherical harmonic representation of the droplet surface geometry. We show the accuracy and stability of the scheme on several tracking-type control problems.
•Optimal control of two-phase Stokes flows with surface tension.•Extensions to multiple droplets in three-dimensional setting.•Algorithmic and theoretical improvements in adjoint formulation.•High-order boundary integral methods for state and adjoint discretization.
Optimal conduit shape for Stokes flow Ceretani, Andrea N.; Hu, Weiwei; Rautenberg, Carlos N.
Systems & control letters,
March 2023, 2023-03-00, Letnik:
173
Journal Article
Recenzirano
Odprti dostop
We consider the problem of the optimal shape of a two dimensional duct which contains a fluid governed by the Stokes equations with mixed boundary conditions. The conduit domain is assumed to be ...non-smooth and perturbations are allowed only on the walls, while the objective functional aims at minimizing the head loss and to enforce a uniform velocity profile at the outlet. We show existence of solutions to the shape optimization problem and determine the existence of the shape derivative.
•We present the initial results of a novel method of using neural networks for soil XCT image segmentation.•Depending on the sample, the accuracy in terms of permeability hit 5% error.•To segment ...soil images, we used hybrid U-net + ResNet-101 architecture.•It was shown that the low representativity of XCT images could explain low accuracy cases.•Larger image libraries, better ground-truth data and network architecture were proposed as ways forward.
Direct imaging methods, among which X-ray computed tomography (XCT) continues to dominate, enable the study of soil structure at different scales. However, to compute different morphological parameters or assess soil physical properties using pore-scale modelling we need to perform image segmentation to divide the XCT greyscale image representing local absorption of X-ray radiation into major constituents or phases. Here we focused on the simplest type of segmentation procedure – binarization into pores and solid phases. We present the initial results for soil XCT image segmentation using convolutional neural networks (CNN). We assumed that current state-of-the-art local segmentation approaches could provide ground truth data to perform neural network training. We used hybrid U-net + ResNet-101 architecture and segmented seven soil XCT images. The training was performed by excluding the segmented image from training and validation datasets. The segmentations’ accuracy was assessed using standard computer vision metrics (precision, recall, intersection over union or IoU) and pore-scale simulations to compute the permeability of resulting 3D binary soil images. Depending on the soil sample, the error of segmentations in terms of computed hydraulic properties varied from 5% to 130%. The IoU metric was found to be the most sensitive to false positive and false negative porosity predictions by the neural network. To explain observed variations, we performed ground-truth and original XCT greyscale images analysis with the help of correlation and covariance functions. In addition to a comparison between images, we also trained another segmentation neural network that used all samples as a training/verification dataset that helped to explain the inaccuracies caused by insufficient representativeness of some soil sample structures in the training dataset. We discussed possible ways to improve the segmentation results in the future, including the usage of larger soil image libraries, physically modelled ground-truth data, and advanced neural network architectures.
The problem studied was the non-reciprocal cyclic swimming motion of three spheres linked with axially aligned retractable arms in Stokes flow. The arms are assumed to be able to retract at a steady ...speed to half their length, and then at a later time in the motion extend at the same steady speed back to their original length. It is important in the field of medical biology, because this motion could enable a micro-robotic device to swim within the arterial and cellular fluid to perform medical biological procedures such as surgery or drug delivery. The method used was the development of a theoretical mathematical model in low Reynolds number Stokes flow, that takes the mathematical expression for steady motion of a sphere, and from this obtains the motion for three spheres by assuming leading order interactions between the spheres. This gives an interaction matrix from which the important results of the study are obtained which are exact mathematical expressions for the mean distance travelled, mean drift velocity and energy efficiency of the motion. These are that the mean distance travelled is 3a0ln(9/8), the mean drift velocity is (3a0/2A)ln(9/8), and the energy efficiency of the motion is 9a02/(4A2)ln(9/8)2, where a0 is the sphere radius and A is the arm length. The conclusions to be drawn from the results are that the most efficient design has the largest ratio for sphere radius in relation to arm length. The novelty of the work is that it gives exact mathematical expressions for distance travelled, velocity and energy efficiency not given previously in the literature.
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•Determining an explicit formula for the forward motion of a simple linked sphere microscopic robot swimmer.•Determining an explicit formula for the energy efficiency of the motion going as the square of the ratio of the sphere radius to arm length.•Principal result: Sphere radius to arm length ratio needs to be as large as possible for most energy efficient motion.
This paper makes investigations on the time-decay rates for the 3-dimensional Navier-Stokes flow in exterior domains. Boundedness of the convolution operator with the Gaussian kernel from the ...intersection L01(Ω)∩L1(Ω,|x|αdx) for some 0<α≤1 to the space Lr(Ω) for all 1≤r<∞ is firstly established, from which, an innovated estimate ‖u(t)‖r≤Ct−α2−32(1−1r) (t≥T0, 1<r≤∞) is derived. Decay rates of the higher-order spatial and temporal derivatives of the flow are mainly studied then. In order to derive the estimates ‖∇∂tku(t)‖r≤Ct−k+12−α2−32(1−1r) adequately, translation transformation v˜kv(t)=∂tku(t+Tk) has been made.
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