arXiv subjects

Chun Liu

Publications and source records attributed to Chun Liu.

At least 91 records · Page 5Linked to original sources

arXiv2021

Modeling and simulation of nuclear architecture reorganization process using a phase field approach

We develop a special phase field/diffusive interface method to model the nuclear architecture reorganization process. In particular, we use a Lagrange multiplier approach in the phase field model to preserve the specific physical and geometrical constraints for the biological events. We develop several efficient and robust linear and weakly nonlinear schemes for this new model. To validate the model and numerical methods, we present ample numerical simulations which in particular reproduce several processes of nuclear architecture reorganization from the experiment literature.

math.NA↗

arXiv2021

A phase field model for mass transport with semi-permeable interfaces

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface depends on its conductance and the difference of the concentration on each side. The diffusive interface phase-field framework used here has several advantages over the sharp interface method. First of all, explicit tracking of the interface is no longer necessary. Secondly, the interfacial condition can be incorporated with a variable diffusion coefficient. A detailed asymptotic analysis confirms the diffusive interface model converges to the existing sharp interface model as the interface thickness goes to zero. A decoupled energy stable numerical scheme is developed to solve this system efficiently. Numerical simulations first illustrate the consistency of theoretical results on the sharp interface limit. Then a convergence study and energy decay test are conducted to ensure the efficiency and stability of the numerical scheme. To illustrate the effectiveness of our phase-field approach, several examples are provided, including a study of a two-phase mass transfer problem where drops with deformable interfaces are suspended in a moving fluid.

math.NA↗

arXiv2021

The Brinkman-Fourier System with Ideal Gas Equilibrium

In this work, we will introduce a general framework to derive the thermodynamics of a fluid mechanical system, which guarantees the consistence between the energetic variational approaches with the laws of thermodynamics. In particular, we will focus on the coupling between the thermal and mechanical forces. We follow the framework for a classical gas with ideal gas equilibrium and present the existences of weak solutions to this thermodynamic system coupled with the Brinkman-type equation to govern the velocity field.

math.AP↗

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↗

arXiv2021

Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space

We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical reaction with general mass kinetics. From this we recover a linearized model for a system close to equilibrium and we analyze the global-in-time well-posedness of the system for small initial data for a critical Besov space.

math.AP↗

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

b-baryon semi-tauonic decays in the Standard Model

Within the framework of HQET, $Λ_{b}\rightarrowΛ_{c}τ\barν_τ$ and $Ω_{b}\rightarrowΩ_{c}^{(*)}τ\barν_τ$ weak decays are studied to the order of $1/m_c$ and $1/m_b$. Helicity amplitudes are written down. Relevant Isgur-Wise functions given by QCD sum rule and large $N_c$ methods are applied in the numerical analysis. The baryonic R-ratios $R(Λ_c)$ and $R(Ω_c^{(*)})$ are obtained.

hep-ph↗

arXiv2020

Positivity of temperature for some non-isothermal fluid models

We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by using a clear algebraic approach, we show a maximum/minimum principle for some quantities composed by the absolute temperature $θ$ and density $ρ$ under some special conditions, which in turn gives the positivity of the temperature. This important fact implies the thermodynamic consistency for our models.

math.AP↗

arXiv2020

CPM R-CNN: Calibrating Point-guided Misalignment in Object Detection

In object detection, offset-guided and point-guided regression dominate anchor-based and anchor-free method separately. Recently, point-guided approach is introduced to anchor-based method. However, we observe points predicted by this way are misaligned with matched region of proposals and score of localization, causing a notable gap in performance. In this paper, we propose CPM R-CNN which contains three efficient modules to optimize anchor-based point-guided method. According to sufficient evaluations on the COCO dataset, CPM R-CNN is demonstrated efficient to improve the localization accuracy by calibrating mentioned misalignment. Compared with Faster R-CNN and Grid R-CNN based on ResNet-101 with FPN, our approach can substantially improve detection mAP by 3.3% and 1.5% respectively without whistles and bells. Moreover, our best model achieves improvement by a large margin to 49.9% on COCO test-dev. Code and models will be publicly available.

cs.CV↗

arXiv2020

Renovating Parsing R-CNN for Accurate Multiple Human Parsing

Multiple human parsing aims to segment various human parts and associate each part with the corresponding instance simultaneously. This is a very challenging task due to the diverse human appearance, semantic ambiguity of different body parts, and complex background. Through analysis of multiple human parsing task, we observe that human-centric global perception and accurate instance-level parsing scoring are crucial for obtaining high-quality results. But the most state-of-the-art methods have not paid enough attention to these issues. To reverse this phenomenon, we present Renovating Parsing R-CNN (RP R-CNN), which introduces a global semantic enhanced feature pyramid network and a parsing re-scoring network into the existing high-performance pipeline. The proposed RP R-CNN adopts global semantic representation to enhance multi-scale features for generating human parsing maps, and regresses a confidence score to represent its quality. Extensive experiments show that RP R-CNN performs favorably against state-of-the-art methods on CIHP and MHP-v2 datasets. Code and models are available at https://github.com/soeaver/RP-R-CNN.

cs.CV↗

arXiv2020

A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system

In this paper we propose and analyze a finite difference numerical scheme for the Poisson-Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP model, we make use of the Energetic Variational Approach (EnVarA), so that the PNP system could be reformulated as a non-constant mobility $H^{-1}$ gradient flow, with singular logarithmic energy potentials involved. To ensure the unique solvability and energy stability, the mobility function is explicitly treated, while both the logarithmic and the electric potential diffusion terms are treated implicitly, due to the convex nature of these two energy functional parts. The positivity-preserving property for both concentrations, $n$ and $p$, is established at a theoretical level. This is based on the subtle fact that the singular nature of the logarithmic term around the value of $0$ prevents the numerical solution reaching the singular value, so that the numerical scheme is always well-defined. In addition, an optimal rate convergence analysis is provided in this work, in which many highly non-standard estimates have to be involved, due to the nonlinear parabolic coefficients. The higher order asymptotic expansion (up to third order temporal accuracy and fourth order spatial accuracy), the rough error estimate (to establish the $\ell^\infty$ bound for $n$ and $p$), and the refined error estimate have to be carried out to accomplish such a convergence result. In our knowledge, this work will be the first to combine the following three theoretical properties for a numerical scheme for the PNP system: (i) unique solvability and positivity, (ii) energy stability, and (iii) optimal rate convergence. A few numerical results are also presented in this article, which demonstrates the robustness of the proposed numerical scheme.

math.NA↗

arXiv2020

Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag

Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play an essential role in defining the materials properties across multiple scales. In this work, we study the large time asymptotic behavior of the model for the motion of grain boundaries with the dynamic lattice misorientations and the triple junctions drag.

math.AP↗

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

Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag

Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in defining the main characteristics of materials across a wide range of scales. In this work, we propose a model for the evolution of the grain boundary network with dynamic boundary conditions at the triple junctions, triple junctions drag, and with dynamic lattice misorientations. Using the energetic variational approach, we derive system of geometric differential equations to describe motion of such grain boundaries. Next, we relax curvature effect of the grain boundaries to isolate the effect of the dynamics of lattice misorientations and triple junctions drag, and we establish local well-posedness result for the considered model.

math.AP↗

arXiv2020

Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach

In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with external potentials, optimal transport problems, and aggregation-diffusion models. Based on the Energetic Variational Approach, a trajectory equation is first derived by using the balance between the maximal dissipation principle and least action principle. By a convex-splitting technique, we propose energy dissipating numerical schemes for the trajectory equation. Rigorous numerical analysis reveals that the nonlinear numerical schemes are uniquely solvable, naturally respect mass conservation and positivity at fully discrete level, and preserve steady states. Under certain smoothness assumptions, the numerical schemes are shown to be second order accurate in space and first order accurate in time. Extensive numerical simulations are performed to demonstrate several valuable features of the proposed schemes. In addition to the preservation of physical structures, such as positivity, mass conservation, discrete energy dissipation, blue and steady states, numerical simulations further reveal that our numerical schemes are capable of solving \emph{degenerate} cases of the Fokker--Planck equations effectively and robustly. It is shown that the developed numerical schemes have convergence order even in degenerate cases with the presence of solutions having compact support, can accurately and robustly compute the waiting time of free boundaries without any oscillation, and can approximate blow-up singularity up to machine precision.

math.NA↗

arXiv2020

A second order accurate numerical scheme for the porous medium equation by an energetic variational approach

The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate numerical schemes have been developed and analyzed. In this paper, we construct and analyze a second order accurate numerical scheme in both time and space. The unique solvability, energy stability are established, based on the convexity analysis. In addition, we provide a detailed convergence analysis for the proposed numerical scheme. A careful higher order asymptotic expansion is performed and two step error estimates are undertaken. In more details, a rough estimate is needed to control the highly nonlinear term in a discrete $W^{1,\infty}$ norm, and a refined estimate is applied to derive the optimal error order. Some numerical examples are presented as well.

math.NA↗

arXiv2020

Prospects of light sterile neutrino searches in long-baseline neutrino oscillations

The neutrino oscillation probabilities in vacuum and matter are discussed, considering the framework of three active and one light sterile neutrinos. We study in detail the rephasing invariants and CP asymmetry observables, and investigate the four-neutrino oscillations in long-baseline neutrino experiments, such as DUNE, NO$ν$A and T2HK. Our results show that the matter effect enhances quite a significantly the oscillation probabilities of electron neutrino and electron antineutrino appearance channels within a certain energy range, while no considerable change arises in the CP asymmetry analysis due to the matter effect. Moreover, separation between the results with and without the sterile neutrino is not so significant and that is also affected by CP-violating phases. Comparing the results for these three experiments, all of them have similar features, nevertheless, sizes and separations of the oscillation probabilities in DUNE are bit larger.

hep-ph↗

arXiv2020

Numerical analysis of neutrino physics within a high scale supersymmetry model via machine learning

A machine learning method is applied to analyze lepton mass matrices numerically. The matrices were obtained within a framework of high scale SUSY and a flavor symmetry, which are too complicated to be solved analytically. In this numerical calculation, the heuristic method in machine learning is adopted. Neutrino masses, mixings, and CP violation are obtained. It is found that neutrinos are normally ordered and the favorable effective Majorana mass is about $7\times 10^{-3}$ eV.

hep-ph↗