Handle Topology Changes Research Articles

Fast Simultaneous Feasibility Test for Security Constrained Unit Commitment

We present a novel fast security analysis method to perform a simultaneous feasibility test (SFT) for security constrained unit commitment (SCUC). Given an SCUC solution, SFT computes base and contingent line flows, overloads, and sensitivities for formulating the violated constraints in the SCUC solver. We use the Sherman-Morrison-Woodbury (SMW) formula to handle topology changes across hours and contingencies. We first developed this SMW-based SFT for contingencies relative to a static network as a generalization of line outage distribution factors (LODFs) achieving the speed of LODFs and modeling complex contingencies as in commercial SFTs. Speedup of the SMW method over commercial methods comes from moving computation from the solve phase to a startup phase. We now extend the SMW technique to network changes across hours and contingencies, permitting deployment on a single compute node due to speedup of the startup phase. The fast SMW-based SFT can be used in a callback, improving over the traditional SCUC-SFT iteration due to a stronger guarantee of satisfying security constraints and to overall speedup since the SCUC solver is invoked only once. The memory required by the SMW-based SFT is large but manageable, and we formulate a technique to decrease this by 80% when implemented.

Investigating mass transfer around spatially-decoupled electrolytic bubbles

Electrolytic bubbles have a profound impact on mass transport in the vicinity of electrodes and greatly influence the electrolyzer efficiency and cell overpotential. However, experimental measurements of concentration fields around electrolytic bubbles with high spatio-temporal resolution is challenging. In this study, a succession of spatially-decoupled electrolytic bubbles growing in an initially quiescent electrolyte is simulated. The bubbles grow and depart from a hydrophobic cavity at the center of a ring microelectrode. The gas-liquid interface is modeled using a moving mesh topology. A geometric cutting protocol is developed to handle topology changes during bubble departure. The simulated bubbles show good agreement with the bubble growth dynamics observed in experiments. The bubbles in this spatially-decoupled system outgrow the region of electrolyte that is saturated with dissolved hydrogen. This leaves the apex of the bubble interface exposed to an undersaturated region of the electrolyte which leads to an outward flux of hydrogen gas. This is shown to limit the gas evolution efficiency of bubbles even though that they grow at a constant volumetric rate. By analyzing the distribution of the flux of dissolved hydrogen along the bubble interface along with the development of dissolve hydrogen concentration profiles around the bubble, we show that the magnitude of the outward diffusive flux at the apex of the bubble decreases with increasing electrolysis current.

Droplet dynamics: A phase-field model of mobile charges, polarization, and its leaky dielectric approximation

This paper presents a Poisson–Nernst–Planck–Navier–Stokes–Cahn–Hillard (PNP–NS–CH) model for an electrically charged droplet suspended in a viscous fluid under an external electric field. Our model incorporates spatial variations in electric permittivity and diffusion constants, as well as interfacial capacitance. Based on a time scale analysis, we derive two approximations of the original model: a dynamic model for the net charge (assuming unchanged conductance) and a leaky-dielectric model (assuming unchanged conductance and net charge). For the leaky-dielectric model, we perform a detailed asymptotic analysis to demonstrate the convergence of the diffusive-interface leaky-dielectric model to the sharp interface model as the interface thickness approaches zero. Numerical computations are conducted to validate the asymptotic analysis and demonstrate the model's effectiveness in handling topology changes, such as electro-coalescence. Our numerical results from these two approximation models reveal that the polarization force, induced by the spatial variation in electric permittivity perpendicular to the external electric field, consistently dominates the Lorentz force arising from the net charge. The equilibrium shape of droplets is determined by the interplay between these two forces along the direction of the electric field. Moreover, in the presence of interfacial capacitance, a local variation in effective permittivity results in the accumulation of counter-ions near the interface, leading to a reduction in droplet deformation. Our numerical solutions also confirm that the leaky-dielectric model is a reasonable approximation of the original PNP–NS–CH model when the electric relaxation time is sufficiently short. Both the Lorentz force and droplet deformation decrease significantly when the diffusion of net charge increases.

Break and Splice: A Statistical Method for Non‐Rigid Point Cloud Registration

Abstract3D object matching and registration on point clouds are widely used in computer vision. However, most existing point cloud registration methods have limitations in handling non‐rigid point sets or topology changes (e.g. connections and separations). As a result, critical characteristics such as large inter‐frame motions of the point clouds may not be accurately captured. This paper proposes a statistical algorithm for non‐rigid point sets registration, addressing the challenge of handling topology changes without the need to estimate correspondence. The algorithm uses a novel Break and Splice framework to treat the non‐rigid registration challenges as a reproduction process and a Dirichlet Process Gaussian Mixture Model (DPGMM) to cluster a pair of point sets. Labels are assigned to the source point set with an iterative classification procedure, and the source is registered to the target with the same labels using the Bayesian Coherent Point Drift (BCPD) method. The results demonstrate that the proposed approach achieves lower registration errors and efficiently registers point sets undergoing topology changes and large inter‐frame motions. The proposed approach is evaluated on several data sets using various qualitative and quantitative metrics. The results demonstrate that the Break and Splice framework outperforms state‐of‐the‐art methods, achieving an average error reduction of about 60% and a registration time reduction of about 57.8%.

Unbiased inverse volume rendering with differential trackers

Volumetric representations are popular in inverse rendering because they have a simple parameterization, are smoothly varying, and transparently handle topology changes. However, incorporating the full volumetric transport of light is costly and challenging, often leading practitioners to implement simplified models, such as purely emissive and absorbing volumes with "baked" lighting. One such challenge is the efficient estimation of the gradients of the volume's appearance with respect to its scattering and absorption parameters. We show that the straightforward approach---differentiating a volumetric free-flight sampler---can lead to biased and high-variance gradients, hindering optimization. Instead, we propose using a new sampling strategy: differential ratio tracking , which is unbiased, yields low-variance gradients, and runs in linear time. Differential ratio tracking combines ratio tracking and reservoir sampling to estimate gradients by sampling distances proportional to the unweighted transmittance rather than the usual extinction-weighted transmittance. In addition, we observe local minima when optimizing scattering parameters to reproduce dense volumes or surfaces. We show that these local minima can be overcome by bootstrapping the optimization from nonphysical emissive volumes that are easily optimized.

Physics‐Based Inverse Rendering using Combined Implicit and Explicit Geometries

AbstractMathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology changes. Implicit representations like signed‐distance functions, on the other hand, offer better support of topology changes but are much more difficult to use for physics‐based differentiable rendering. We introduce a new physics‐based inverse rendering pipeline that uses both implicit and explicit representations. Our technique enjoys the benefit of both representations by supporting both topology changes and differentiable rendering of complex effects such as environmental illumination, soft shadows, and interreflection. We demonstrate the effectiveness of our technique using several synthetic and real examples.

Thin-film smoothed particle hydrodynamics fluid

We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton's interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

Thin-film smoothed particle hydrodynamics fluid

We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton's interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

Level set band method: A combination of density-based and level set methods for the topology optimization of continuums

The level set method (LSM), which is transplanted from the computer graphics field, has been successfully introduced into the structural topology optimization field for about two decades, but it still has not been widely applied to practical engineering problems as density-based methods do. One of the reasons is that it acts as a boundary evolution algorithm, which is not as flexible as density-based methods at controlling topology changes. In this study, a level set band method is proposed to overcome this drawback in handling topology changes in the level set framework. This scheme is proposed to improve the continuity of objective and constraint functions by incorporating one parameter, namely, level set band, to seamlessly combine LSM and density-based method to utilize their advantages. The proposed method demonstrates a flexible topology change by applying a certain size of the level set band and can converge to a clear boundary representation methodology. The method is easy to implement for improving existing LSMs and does not require the introduction of penalization or filtering factors that are prone to numerical issues. Several 2D and 3D numerical examples of compliance minimization problems are studied to illustrate the effects of the proposed method.

A parameterized level set method combined with polygonal finite elements in topology optimization

Level set-based topology optimization methods have received increased attention in the last decade due to the ease with which they can handle topology changes by splitting and merging boundaries. However, most implementations are limited to box-like design domains and cannot easily handle irregular domains that are common in practical engineering applications. In this paper, a modified level set model, which is parameterized and updated with radial basis functions (RBFs), is introduced to solve topology optimization problems in complex design domains. Because RBFs are not necessarily located in a structured manner, the parametrized level set method can be combined effortlessly with unstructured polygonal finite element meshes to easily handle complex design domains and also achieve the high accuracy characteristic of polygonal discretizations. Furthermore, the nucleation capability of the proposed approach along with an approximate reinitialization is shown to obtain more flexible topology changes of the optimal design, and smooth boundaries can be obtained without introducing smoothing scheme. Several numerical examples illustrate the effectiveness of the proposed model.

Spreading Aggregation: A distributed collision-free approach for data aggregation in large-scale wireless sensor networks

Recently, numerous works have shown that serial aggregation in large wireless sensor networks is scalable and very efficient, in terms of avoiding collisions and conserving energy and, more importantly, in terms of reducing response time. In this paper, a novel serial data aggregation approach, called Spreading Aggregation (SA), is proposed with the aim of shortening the traversal path and further reducing communications. First, given the fact that it is not based on a pre-established itinerary, SA is data structure maintenance-free and does not require any communications in this regard. Each time an aggregation process is launched, a new path is built, which decreases vulnerability to failure in links and nodes and allows the approach to handle topology changes. Second, SA is a localized approach that relies only on the one-hop neighbors table of each node to gradually construct the path, which makes it very scalable. A third interesting feature of SA is the merge of path construction and data processing. While the path is progressively constructed, data is simultaneously aggregated, saving a considerable amount of time and energy. In addition to all that, SA also saves energy and time due to its collision-free nature. In fact, in SA, only one packet is present in the entire network at any given time. In this paper, we formally prove the correctness of SA (i.e., free of looping and ensures the traversal of all connected nodes). Furthermore, the extensive OMNeT++ simulations, we performed, confirm that the proposed approach reduces communications, scales well in large networks, and conserves time and energy. The obtained results also show that SA outperforms state-of-the-art serial approaches.

Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes

In this paper, we introduce a novel parametric finite element method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford–Shah and the Chan–Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.

Modeling of Porous Metal Oxide Layer Growth in the Anodization Process

Most of the works on nanotubes growth are oriented on exploring suitable setups for optimal growth for the structures. Substantially less interest is devoted to first principles based mathematical modelling of the growth. We present a simple mathematical model of porous metal oxide layer growth in the anodization process. The mathematical model is essentially the model used by [Sample, Golovin: Formation of porous metal oxides in the anodization process, Phys. Rev. E 74, 2006]. The dynamics of the system is determined by the solution of the continuity equation for the electric current density, while the boundary conditions for the overpotential are given by the Butler-Volmer relation. The arising system of partial differential equations is solved using the finite element method. Unlike in the other works, the continuity equation for the electric current density is solved not only in the oxide layer, but also in the metal and the electrolyte. The positions of the interfaces are not known a priori and must be found in the process of the numerical solution of the problem. The core technical difficulty is the tracking of the metal/oxide and oxide/electrolyte interface. This issue is addresed via the application of the level-set method. The main benefit of using the level-set method is that it can easily handle topology changes and that the computation is done on a fixed mesh. Another important ingredient of the developed numerical scheme is that the problem is solved using the mixed formulation. The mixed formulation allows one to succesfully handle the boundary condition arising from the Butler-Volmer relation even in the level-set setting. It is shown that the chosen methodology correctly captures the discontinuities of the electric potential at the interfaces. The advocated numerical scheme has been implemented in FEniCS (software for the automated solution of differential equations by finite element methods). Results of the simulations with the physical parameters corresponding to the growth of aluminium oxide layer are presented. The computational methodology based on the level-set method and on the mixed formulation can be easily applied in two dimensional as well as in three dimensional setting. The successfully developed method for the interface tracking which is the core technical difficulty in the modelling of oxide layer growth allows one to think about further extensions of the model. In particular the flow in the electrolyte, the deformation inside the oxide layer as well as surface tension effects could be possibly numerically simulated in the future.

3D shape and texture morphing using 2D projection and reconstruction

We present an algorithm for morphing shape and view-dependent texture that utilizes an unstructured lumigraph representation to (1) gracefully handle topological changes, (2) create plausible appearance transformations, and (3) provide user control independent from the underlying mesh structure. It works by reducing the otherwise complex problem of a 3D shape and material morph into multiple simpler 2D morphs. The shape morph operates on 2D depth maps and then reconstructs a conventional mesh, making it insensitive to the input geometry quality. Our morphing algorithm robustly handles topology changes and outputs complete meshes and lumigraphs for later use. We show how 2D image morphs can be computed from 3D correspondences, while eliminating ambiguities that might result in the projected 2D morphs.

Topology optimization using an explicit interface representation

We introduce the Deformable Simplicial Complex method to topology optimization as a way to represent the interface explicitly yet being able to handle topology changes. Topology changes are handled by a series of mesh operations, which also ensures a well-formed mesh. The same mesh is therefore used for both finite element calculations and shape representation. In addition, the approach unifies shape and topology optimization in a complementary optimization strategy. The shape is optimized on the basis of the gradient-based optimization algorithm MMA whereas holes are introduced using topological derivatives. The presented method is tested on two standard minimum compliance problems which demonstrates that it is both simple to apply, robust and efficient.

Connectivity-free front tracking method for multiphase flows with free surfaces

In this study, a connectivity-free front tracking method is developed to simulate multiphase flows with free surfaces. This method is based on the point-set method which does not require any connectivities between interfacial points to represent the interface. The main advantage of the connectivity-free approach is the easiness in re-constructing the interface when large topology change occurs. It requires an indicator field to be constructed first based on the existing interface and the surface curvature and normal are then computed using the indicator field. Here, we adopt the reproducing kernel particle method (RKPM) interpolation function that provides the ability to deal with free-surface flows and the flexibility of using non-uniform meshes when local fine resolution is needed. A points regeneration scheme is developed to construct smooth interfaces and to automatically handle topology changes. The mass conservation is verified by performing a single vortex advection test. Several 2-D and 3-D numerical tests including an oscillating droplet, dam-breaking, two droplet impacting and multi-bubble merging are presented to show the accuracy and the robustness of the method.

Preserving Fluid Sheets with Adaptively Sampled Anisotropic Particles

This paper presents a particle-based model for preserving fluid sheets of animated liquids with an adaptively sampled Fluid-Implicit-Particle (FLIP) method. In our method, we preserve fluid sheets by filling the breaking sheets with particle splitting in the thin regions, and by collapsing them in the deep water. To identify the critically thin parts, we compute the anisotropy of the particle neighborhoods, and use this information as a resampling criterion to reconstruct thin liquid surfaces. Unlike previous approaches, our method does not suffer from diffusive surfaces or complex remeshing operations, and robustly handles topology changes with the use of a meshless representation. We extend the underlying FLIP model with an anisotropic position correction to improve the particle spacing, and adaptive sampling to efficiently perform simulations of larger volumes. Due to the Lagrangian nature of our method, it can be easily implemented and efficiently parallelized. The results show that our method can produce visually complex liquid animations with thin structures and vivid motions.

Efficient Rearrangement Algorithms for Shape Optimization on Elliptic Eigenvalue Problems

In this paper, several efficient rearrangement algorithms are proposed to find the optimal shape and topology for elliptic eigenvalue problems with inhomogeneous structures. The goal is to solve minimization and maximization of the k-th eigenvalue and maximization of spectrum ratios of the second order elliptic differential operator. Physically, these problems are motivated by the frequency control based on density distribution of vibrating membranes. The methods proposed are based on Rayleigh quotient formulation of eigenvalues and rearrangement algorithms which can handle topology changes automatically. Due to the efficient rearrangement strategy, the new proposed methods are more efficient than classical level set approaches based on shape and/or topological derivatives. Numerous numerical examples are provided to demonstrate the robustness and efficiency of new approach.

Robust Interactive Image Segmentation Using Convex Active Contours

The state-of-the-art interactive image segmentation algorithms are sensitive to the user inputs and often unable to produce an accurate boundary with a small amount of user interaction. They frequently rely on laborious user editing to refine the segmentation boundary. In this paper, we propose a robust and accurate interactive method based on the recently developed continuous-domain convex active contour model. The proposed method exhibits many desirable properties of an effective interactive image segmentation algorithm, including robustness to user inputs and different initializations, the ability to produce a smooth and accurate boundary contour, and the ability to handle topology changes. Experimental results on a benchmark data set show that the proposed tool is highly effective and outperforms the state-of-the-art interactive image segmentation algorithms.

Chapar: A Persistent Overlay Event System for MANETs

In this paper, we present Chapar, an event system designed for mobile ad hoc networks that supports the publish/subscribe model as well as point---to---point and point---to---multipoint message delivery. Chapar supports event persistency to resist transient disconnections and network partitioning. Following a cross-layer approach, Chapar is designed as an overlay network that uses Multipoint Relays (MPRs) defined in OLSR, as distributed brokers to disseminate the events in a mobile network. Chapar handles topology changes as it uses the underlaying OLSR routing protocol for message delivery. The implementation performance is promising in the sense that no extra signaling is generated for mobility support and the generated overlay traffic is considerably less than the underlying routing protocol traffic.