An energy-stable parametric finite element method for the planar Willmore flow

We propose an energy-stable parametric finite element method (PFEM) for the planar Willmore flow and establish its unconditional energy stability of the full discretization scheme. The key lies in the introduction of two novel geometric identities to describe the planar Willmore flow: the first one involves the coupling of the outward unit normal vector $\boldsymbol{n}$ and the normal velocity $V$, and the second one concerns the time derivative of the mean curvature $\kappa$. Based on them, we derive a set of new geometric partial differential equations for the planar Willmore flow, leading to our new fully-discretized and unconditionally energy-stable PFEM. Our stability analysis is also based on the two new geometric identities. Extensive numerical experiments are provided to illustrate its efficiency and validate its unconditional energy stability

A unified structure-preserving parametric finite element method for anisotropic surface diffusion

We propose and analyze a unified structure-preserving parametric finite element method (SP-PFEM) for the anisotropic surface diffusion of curves in two dimensions $(d=2)$ and surfaces in three dimensions $(d=3)$ with an arbitrary anisotropic surface energy density $\gamma(\boldsymbol{n})$, where $\boldsymbol{n}\in \mathbb{S}^{d-1}$ represents the outward unit vector. By introducing a novel unified surface energy matrix $\boldsymbol{G}_k(\boldsymbol{n})$ depending on $\gamma(\boldsymbol{n})$, the Cahn--Hoffman $\boldsymbol{\xi}$-vector and a stabilizing function $k(\boldsymbol{n}):\ \mathbb{S}^{d-1}\to {\mathbb R}$, we obtain a unified and conservative variational formulation for the anisotropic surface diffusion via different surface differential operators including the surface gradient operator, the surface divergence operator and the surface Laplace--Beltrami operator. A SP-PFEM discretization is presented for the variational problem. In order to establish the unconditional energy stability of the proposed SP-PFEM under a very mild condition on $\gamma(\boldsymbol{n})$, we propose a new framework via {\sl local energy estimate} for proving energy stability/structure-preserving properties of the parametric finite element method for the anisotropic surface diffusion. This framework sheds light on how to prove unconditional energy stability of other numerical methods for geometric partial differential equations. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as structure-preserving properties of the proposed SP-PFEM for the anisotropic surface diffusion with arbitrary anisotropic surface energy density $\gamma(\boldsymbol{n})$ arising from different applications

STF: Spatial Temporal Fusion for Trajectory Prediction

Trajectory prediction is a challenging task that aims to predict the future trajectory of vehicles or pedestrians over a short time horizon based on their historical positions. The main reason is that the trajectory is a kind of complex data, including spatial and temporal information, which is crucial for accurate prediction. Intuitively, the more information the model can capture, the more precise the future trajectory can be predicted. However, previous works based on deep learning methods processed spatial and temporal information separately, leading to inadequate spatial information capture, which means they failed to capture the complete spatial information. Therefore, it is of significance to capture information more fully and effectively on vehicle interactions. In this study, we introduced an integrated 3D graph that incorporates both spatial and temporal edges. Based on this, we proposed the integrated 3D graph, which considers the cross-time interaction information. In specific, we design a Spatial-Temporal Fusion (STF) model including Multi-layer perceptions (MLP) and Graph Attention (GAT) to capture the spatial and temporal information historical trajectories simultaneously on the 3D graph. Our experiment on the ApolloScape Trajectory Datasets shows that the proposed STF outperforms several baseline methods, especially on the long-time-horizon trajectory prediction.Comment: 6 pages, 6 figure

Four lignans from Portulaca oleracea L. and its antioxidant activities

International audienceA new lignan, named oleralignan (1) and three known compounds (+)-syringaresinol (2), (+)-lirioresinol A (3) and monomethyl 3,30,4,40-tetrahydroxy-δ-truxinate (4) were isolated from the P. oleracea for the first time. The compound (1) were identified by 1D, 2D NMR spectroscopic methods and high resolution electrospray ionization time-of-flight mass spectrometry. In addition, it was found that the four lignans presented the scavenging activities in 1,1-diphenyl-2-picryl-hydrazyl (DPPH) radical quenching assay more than that of hydroxyl anisole (BHA)

Effect of corrosion on the bond behavior of steel-reinforced, alkali-activated slag concrete

Alkali-activated slag concrete (ASC) is regarded as one of the most promising sustainable construction materials for replacing ordinary Portland cement concrete (OPC) due to its comparable strength and outstanding durability in challenging environments. In this study, the corrosion of steel bars embedded in ASC and OPC was studied by means of an electrically accelerated corrosion test of steel bars in concrete. Meanwhile, the bond performance of the corroded steel bars embedded in ASC was tested and compared with corresponding OPC groups. The results showed that ASC and OPC behaved differently in terms of bond deterioration. The high chemical resistance of ASC decreased the corrosion of steel bars and, thus, increased the residue bond strength and the bond stiffness. © 2023 by the authors

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. We use the convex $\ell_1$ and the nonconvex $\ell_1-\ell_2$ functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods

Biotransformation of doxycycline by \u3ci\u3eBrevundimonas naejangsanensis\u3c/i\u3e and \u3ci\u3eSphingobacterium mizutaii\u3c/i\u3e strains

The fate of doxycycline (DC), a second generation tetracycline antibiotic, in the environment has drawn increasing attention in recent years due to its wide usage. Little is known about the biodegradability of DC in the environment. The objective of this study was to characterize the biotransformation of DC by pure bacterial strains with respect to reaction kinetics under different environmental conditions and biotransformation products. Two bacterial strains, Brevundimonas naejangsanensis DD1 and Sphingobacterium mizutaii DD2, were isolated from chicken litter and characterized for their biotransformation capability of DC. Results show both strains rely on cometabolism to biotransform DC with tryptone as primary growth substrate. DD2 had higher biotransformation kinetics than DD1. The two strains prefer similar pHs (7 and 8) and temperature (30 °C), however, they exhibited opposite responses to increasing background tryptone concentration. While hydrolysis converted DC to its isomer or epimer, the two bacterial strains converted DC to various biotransformation products through a series of demethylation, dehydration, decarbonylation and deamination. Findings from the study can be used to better predict the fate of DC in the environment

BioScape: A Modeling and Simulation Language for Bacteria-Materials Interactions

We design BioScape, a concurrent language for the stochastic simulation of biological and bio-materials processes in a reactive environment in 3D space. BioScape is based on the Stochastic Pi-Calculus, and it is motivated by the need for individual-based, continuous motion, and continuous space simulation in modeling complex bacteria-materials interactions. Our driving example is a bio-triggered drug delivery system for infection-resistant medical implants. Our models in BioScape will help in identifying biological targets and materials strategies to treat biomaterials associated bacterial infections. The novel aspects of BioScape include syntactic primitives to declare the scope in space where species can move, diffusion rate, shape, and reaction distance, and an operational semantics that deals with the specifics of 3D locations, verifying reaction distance, and featuring random movement. We define a translation from BioScape to 3π and prove its soundness with respect to the operational semantics.Fil: Compagnoni, Adriana. Stevens Institute of Technology; Estados UnidosFil: Sharma, Vishaka. Stevens Institute of Technology; Estados UnidosFil: Bao, Yifei. Stevens Institute of Technology; Estados UnidosFil: Libera, Matthew. Stevens Institute of Technology; Estados UnidosFil: Sukhishvili, Svetlana. Stevens Institute of Technology; Estados UnidosFil: Bidinger, Philippe. VERIMAG; FranciaFil: Boglio, Livio. Universita Di Torino; ItaliaFil: Bonelli, Eduardo Augusto. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnologia; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin