arXiv subjects

Yiwei Wang

Publications and source records attributed to Yiwei Wang.

214 records · Page 12Linked to original sources

arXiv2021

A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance

In this paper, we propose and analyze a positivity-preserving, energy stable numerical scheme for certain type reaction-diffusion systems involving the Law of Mass Action with the detailed balance condition. The numerical scheme is constructed based on a recently developed energetic variational formulation, in which the reaction part is reformulated in terms of reaction trajectories. The fact that both the reaction and the diffusion parts dissipate the same free energy opens a path of an energy stable, operator splitting scheme for these systems. At the reaction stage, we solve equations of reaction trajectories by treating all the logarithmic terms in the reformulated form implicitly due to their convex nature. The positivity-preserving property and unique solvability can be theoretically proved, based on the singular behavior of the logarithmic function around the limiting value. Moreover, the energy stability of this scheme at the reaction stage can be proved by a careful convexity analysis. Similar techniques are used to establish the positivity-preserving property and energy stability for the standard semi-implicit solver at the diffusion stage. As a result, a combination of these two stages leads to a positivity-preserving and energy-stable numerical scheme for the original reaction-diffusion system. To our best knowledge, it is the first time to report an energy-dissipation-law-based operator splitting scheme to a nonlinear PDE with variational structures. Several numerical examples are presented to demonstrate the robustness of the proposed operator splitting scheme.

math.NA↗

arXiv2020

Field Theory of Reaction-Diffusion: Mass Action with an Energetic Variational Approach

We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by the choice of the free energy and the dynamics of the chemical reaction is determined by the choice of the dissipation. This approach enables us to couple chemical reactions with other effects, such as diffusion and drift in an electric field. As an illustration, we apply our approach to a non-equilibrium reaction-diffusion system in a specific but canonical set-up. We show by numerical simulation that the input-output relation of such a system depends on the choice of the dissipation.

physics.chem-ph↗

arXiv2020

GraphCrop: Subgraph Cropping for Graph Classification

We present a new method to regularize graph neural networks (GNNs) for better generalization in graph classification. Observing that the omission of sub-structures does not necessarily change the class label of the whole graph, we develop the \textbf{GraphCrop} (Subgraph Cropping) data augmentation method to simulate the real-world noise of sub-structure omission. In principle, GraphCrop utilizes a node-centric strategy to crop a contiguous subgraph from the original graph while maintaining its connectivity. By preserving the valid structure contexts for graph classification, we encourage GNNs to understand the content of graph structures in a global sense, rather than rely on a few key nodes or edges, which may not always be present. GraphCrop is parameter learning free and easy to implement within existing GNN-based graph classifiers. Qualitatively, GraphCrop expands the existing training set by generating novel and informative augmented graphs, which retain the original graph labels in most cases. Quantitatively, GraphCrop yields significant and consistent gains on multiple standard datasets, and thus enhances the popular GNNs to outperform the baseline methods.

cs.SI↗

arXiv2020

A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach

In this paper, we propose a variational Lagrangian scheme for a modified phase-field model, which can compute the equilibrium states for the original Allen-Cahn type model. Our discretization is based on a prescribed energy-dissipation law in terms of the flow map. By employing a discrete energetic variational approach, this scheme preserves the variational structure of the original energy-dissipation law and is energy stable. Plentiful numerical tests show that, by choosing the initial value properly, our methods can produce the desired equilibrium and capture the thin diffuse interface with a small number of mesh points.

math.NA↗

arXiv2020

Revisiting Convolutional Neural Networks for Citywide Crowd Flow Analytics

Citywide crowd flow analytics is of great importance to smart city efforts. It aims to model the crowd flow (e.g., inflow and outflow) of each region in a city based on historical observations. Nowadays, Convolutional Neural Networks (CNNs) have been widely adopted in raster-based crowd flow analytics by virtue of their capability in capturing spatial dependencies. After revisiting CNN-based methods for different analytics tasks, we expose two common critical drawbacks in the existing uses: 1) inefficiency in learning global spatial dependencies, and 2) overlooking latent region functions. To tackle these challenges, in this paper we present a novel framework entitled DeepLGR that can be easily generalized to address various citywide crowd flow analytics problems. This framework consists of three parts: 1) a local feature extraction module to learn representations for each region; 2) a global context module to extract global contextual priors and upsample them to generate the global features; and 3) a region-specific predictor based on tensor decomposition to provide customized predictions for each region, which is very parameter-efficient compared to previous methods. Extensive experiments on two typical crowd flow analytics tasks demonstrate the effectiveness, stability, and generality of our framework.

cs.CV↗

arXiv2020

Dynamic tuning of the director field in liquid crystal shells using block copolymers

When a nematic liquid crystal (LC) is confined on a self-closing spherical shell, topological constraints arise with intriguing consequences that depend critically on how the LC is aligned in the shell. We demonstrate reversible dynamic tuning of the alignment, and thereby the topology, of nematic LC shells stabilized by the nonionic amphiphilic block copolymer Pluronic F127. Deep in the nematic phase, the director is tangential to the interface, but upon approaching the temperature TNI of the nematic-isotropic transition, the director realigns to normal. We link this to a delicate interplay between an interfacial tension that is nearly independent of director orientation, and the configuration-dependent elastic deformation energy of an LC confined in a shell. The process is primarily triggered by the heating-induced reduction of the nematic order parameter, hence realignment temperatures differ by several tens of degrees between LCs with high and low TNI, respectively. The temperature of realignment is always lower on the positive-curved shell outside than at the negative-curved inside, yielding a complex topological reconfiguration on heating. Complementing experimental investigations with mathematical modeling and computer simulations, we identify and investigate three different trajectories, distinguished by their configurations of topological defects in the initial tangential-aligned shell. Our results uncover a new aspect of the complex response of LCs to curved confinement, demonstrating that the order of the LC itself can influence the alignment and thereby the topology of the system. They also reveal the potential of amphiphilic block copolymer stabilizers for enabling continuous tunability of LC shell configuration, opening doors for in-depth studies of topological dynamics as well as novel applications in, e.g., sensing and programmed soft actuators.

cond-mat.soft↗

arXiv2020

On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach

In this paper, we present a systematic framework to derive a Lagrangian scheme for porous medium type generalized diffusion equations by employing a discrete energetic variational approach. Such discrete energetic variational approaches are analogous to energetic variational approaches in a semidiscrete level, which provide a basis of deriving the "semi-discrete equations" and can be applied to a large class of partial differential equations with energy-dissipation laws and kinematic relations. The numerical schemes derived by this framework can inherit various properties from the continuous energy-dissipation law, such as conservation of mass and the dissipation of the discrete energy. As an illustration, we develop two numerical schemes for the multidimensional porous medium equations (PME), based on two different energy-dissipation laws. We focus on the numerical scheme based on the energy-dissipation law with $\frac{1}{2} \int_Ω |\mathbf{u}|^2 \mathrm{d} \mathbf{x}$ as the dissipation. Several numerical experiments demonstrate the accuracy of this scheme as well as its ability in capturing the free boundary and estimating the waiting time for the PME in both 1D and 2D.

math.NA↗

arXiv2019

Tailored Morphologies in 2D Ferronematic Wells

We focus on a dilute uniform suspension of magnetic nanoparticles in a nematic-filled micron-sized shallow well with tangent boundary conditions, as a paradigm system with two coupled order parameters. This system exhibits spontaneous magnetization without magnetic fields. We numerically obtain the stable nematic and associated magnetization morphologies, induced purely by the geometry, boundary conditions and the coupling between the magnetic nanoparticles and the host nematic medium. Our most striking observations pertain to domain walls in the magnetization profile whose location can be manipulated by the coupling and material properties, and stable interior and boundary nematic defects, whose location and multiplicity can be tailored by the coupling too. These novel morphologies are not accessible in uncoupled systems and can be used for new multistable systems with singularities and stable interfaces.

cond-mat.soft↗

arXiv2019

The Well Order Reconstruction Solution for Three-Dimensional Wells, in the Landau-de Gennes theory

We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by $λ$, and the well height denoted by $ε$. The WORS are distinctive equilibria reported in [10] for square domains, without taking the third dimension into account, which have two mutually perpendicular defect lines running along the square diagonals, intersecting at the square centre. We prove the existence of WORS on three-dimensional wells for arbitrary well heights, with (i) natural boundary conditions and (ii) realistic surface energies on the top and bottom well surfaces, along with Dirichlet conditions on the lateral surfaces. Moreover, the WORS is globally stable for $λ$ small enough in both cases and unstable as $λ$ increases. We numerically compute novel mixed 3D solutions for large $λ$ and $ε$ followed by a numerical investigation of the effects of surface anchoring on the WORS, exemplifying the relevance of the WORS solution in a 3D context.

math.AP↗

arXiv2019

How Shall I Drive? Interaction Modeling and Motion Planning towards Empathetic and Socially-Graceful Driving

While intelligence of autonomous vehicles (AVs) has significantly advanced in recent years, accidents involving AVs suggest that these autonomous systems lack gracefulness in driving when interacting with human drivers. In the setting of a two-player game, we propose model predictive control based on social gracefulness, which is measured by the discrepancy between the actions taken by the AV and those that could have been taken in favor of the human driver. We define social awareness as the ability of an agent to infer such favorable actions based on knowledge about the other agent's intent, and further show that empathy, i.e., the ability to understand others' intent by simultaneously inferring others' understanding of the agent's self intent, is critical to successful intent inference. Lastly, through an intersection case, we show that the proposed gracefulness objective allows an AV to learn more sophisticated behavior, such as passive-aggressive motions that gently force the other agent to yield.

cs.RO↗

arXiv2018

Theoretical Remarks on Cybotactic Clusters of Bent-Core Nematic Liquid Crystals in 1D Settings

The bent-core liquid crystals (LCs) are highly regarded as the next-generation materials for electro-optic devices. The nematic (N) phase of these LCs possesses highly ordered smectic-like cybotactic clusters which are promising in terms of ferroelectric-like behaviour in the N phase itself. We have studied a one-dimensional (1D) Landau-deGennes model of spatially inhomogeneous order parameters for the N phase of bent-core LCs. We investigate the effects of spatial confinement and coupling (between these clusters and the surrounding LC molecules) on the order parameters to model cluster formation in recently reported experiments. The coupling is found to increase the cluster order parameter significantly, suggesting an enhancement in the cluster formation and could also predict a possible transition to a phase with weak nematic-like ordering in the vicinity of nematic-isotropic transition upon appreciable increase of the coupling parameter γ.

cond-mat.soft↗

arXiv2018

Order Reconstruction for Nematics on Squares with Isotropic Inclusions: A Landau-de Gennes Study

We prove the existence of a well order reconstruction solution (WORS) type Landau-de Gennes critical point on a square domain with an isotropic concentric square inclusion, with tangent boundary conditions on the outer square edges. There are two geometrical parameters - the outer square edge length $λ$, and the aspect ratio $ρ$, which is the ratio of the inner and outer square edge lengths. The WORS exists for all geometrical parameters and for all temperatures; we prove that the WORS is globally stable for either $λ$ small enough or for $ρ$ sufficiently close to unity. We study three different types of critical points in this model setting: critical points with the minimal two degrees of freedom consistent with the imposed boundary conditions, critical points with three degrees of freedom and critical points with five degrees of freedom. In the two-dimensional case, we use $Γ$-convergence techniques to identify the energy-minimizing competitors. We decompose the second variation of the Landau-de Gennes energy into three separate components to study the effects of different types of perturbations on the WORS solution and find that it is most susceptible to in-plane perturbations. In the three-dimensional setting, we numerically find up to $28$ critical points for moderately large values of $ρ$ and we find two critical points with the full five degrees of freedom for very small values of $ρ$, with an escaped profile around the isotropic square inclusion.

math.AP↗

arXiv2017

Remarks on Uniaxial Solutions in the Landau-de Gennes Theory

We study uniaxial solutions of the Euler-Lagrange equations for a Landau-de Gennes free energy for nematic liquid crystals, with a fourth order bulk potential, with and without elastic anisotropy. In the elastic isotropic case, we show that (i) all uniaxial solutions of the Euler-Lagrange equations, with a director field of certain symmetry, necessarily have the radial-hedgehog structure modulo an orthogonal transformation, (ii) the "escape into third dimension" director cannot correspond to a purely uniaxial solution of the Landau-de Gennes Euler-Lagrange equations and we do not use artificial assumptions on the scalar order parameter and (iii) there are no non-trivial uniaxial solutions that have $\mathbf{e}_z$ as an eigenvector. In the elastic anisotropic case, we prove that all uniaxial solutions of the corresponding Euler-Lagrange equations, with a certain symmetry, are strictly of the radial-hedgehog type, i.e. the elastic anisotropic case enforces the radial-hedgehog structure (or the degree $+1$-vortex structure) more strongly than the elastic isotropic case and the associated partial differential equations are technically far more difficult than in the elastic isotropic case.

math.AP↗

arXiv2015

Study on CEPC performances with different collision energies and geometric layouts

Circular Electron-Positron Collider(CEPC) is one of the largest plans in high energy physics study at China, which would serve as Higgs Factory firstly and then upgrade to a hadron collider. In this paper we give the 50km and 100km design in both single ring and double ring schemes, including $Z$ boson and $W$ boson and Higgs boson by using the optimized method. Also, we give the potential of CEPC running at $Z$ and $W$ poles. And we analysis the relationship of luminosity with circumference and filling factor, which gives a way to evaluate the choice of geometry. What's more, we compare the nominal performance of CEPC-SPPC and LHC and FCC.

physics.acc-ph↗

arXiv2015

Method Study of Parameter Choice for a Circular Proton-Proton Collider

In this paper we showed a systematic method of appropriate parameter choice for a circular pp collider by using analytical expression of beam-beam tune shift limit started from given design goal and technical limitations. A parameter space has been explored. Based on parameters scan and considerations from RF systems, a set of appropriate parameter designed for a 50Km and a 100Km circular proton-proton collider was proposed.

physics.acc-ph↗

arXiv2014

Study of alternative ILC final focus optical configurations

The role of the ILC final focus system (FFS) is to demagnify the beam to the sizes at the IP required to meet the ILC luminosity goals. The current design of final focus performs perfect chromaticity correction in both horizontal and vertical planes. Based on this design a set of alternative optical configurations were studied in which the horizontal beam size at the IP is increased while at the same time the vertical one is decreased, with the goal of reducing beamsstrahlung emission. Luminosity reduction due to the hour glass effect must be considered because betay*/sigmaz* becomes much smaller in this case. The beam-beam interaction simulation by Guineapig++ was used for evaluation. Reduced bunch lengths are used to make sure that the obtained luminosities are not lower than those of the ILC original (nominal) configuration.

physics.acc-ph↗