We carry out convergence and error analysis of the scalar auxiliary variable (SAV) methods for L² and H⁻¹ gradient flows with a typical form of free energy. We first derive H² bounds, under certain ...assumptions suitable for both the gradient flows and the SAV schemes, which allow us to establish the convergence of the SAV schemes under mild conditions. We then derive error estimates with further regularity assumptions. We also discuss several other gradient flows, which cannot be cast in the general framework used in this paper, but for which convergence and error analysis can still be established using a similar procedure.
We propose a new approach, which we term as scalar auxiliary variable (SAV) approach, to construct efficient and accurate time discretization schemes for a large class of gradient flows. The SAV ...approach is built upon the recently introduced IEQ approach. It enjoys all advantages of the IEQ approach but overcomes most of its shortcomings. In particular, the SAV approach leads to numerical schemes that are unconditionally energy stable and extremely efficient in the sense that only decoupled equations with constant coefficients need to be solved at each time step. The scheme is not restricted to specific forms of the nonlinear part of the free energy, so it applies to a large class of gradient flows. Numerical results are presented to show that the accuracy and effectiveness of the SAV approach over the existing methods.
Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed ...presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
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•The current practice is to use 100% skin absorption default value when experimental data is lacking.•An in silico skin absorption model tailored for fragrances, assigns absorption ...values of 10%, 40%, or 80% based on Jmax.•The model may be used confidently for non-fragrance material provided they meet certain specified criteria.•A hypothetical example on the application of this skin absorption model in the safety assessment is presented.
Fragrance materials are widely used in cosmetics and other consumer products. The Research Institute for Fragrance Materials (RIFM) evaluates the safety of these ingredients and skin absorption is an important parameter in refining systemic exposure. Currently, RIFM's safety assessment process assumes 100% skin absorption when experimental data are lacking. This 100% absorption default is not supportable and alternate default values were proposed. This study aims to develop and validate a practical skin absorption model (SAM) specific for fragrance material. It estimates skin absorption based on the methodology proposed by Kroes et al. SAM uses three default absorption values based on the maximum flux (Jmax) – namely, 10%, 40%, and 80%. Jmax may be calculated by using QSAR models that determine octanol/water partition coefficient (Kow), water solubility (S) and permeability coefficient (Kp). Each of these QSAR models was refined and a semi-quantitative mechanistic model workflow is presented. SAM was validated with a large fragrance-focused data set containing 131 materials. All resulted in predicted values fitting the three-tiered absorption scenario based on Jmax ranges. This conservative SAM may be applied when fragrance material lack skin absorption data.
As a new family of two-dimensional (2D) materials, MXene, with many attractive physicochemical properties, has attracted increasing attentions and been applied for various applications. Here, for the ...first time, ultrathin MXene membranes with thickness down to several tens of nanometers were developed for pervaporation desalination by stacking synthesized atomic-thin MXene nanosheets. Influences such as lateral size of MXene nanosheets and feed temperature on the resulting membrane performance were systematically investigated. Owing to unique 2D interlayer channels as well as high hydrophilicity, the ultrathin MXene membrane with ~60nm exhibited high water flux (85.4Lm−2h−1) and salt rejection (99.5%) with feed concentration of 3.5wt% NaCl at 65°C. In addition, the MXene membrane showed a good long-term stability and performance in synthetic seawater system. The high-performing ultrathin 2D MXene membrane developed here in this work offers great potential for pervaporation applications.
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•Ultrathin 2D Ti3C2Tx MXene membrane was designed and fabricated.•MXene membrane was first reported for pervaporation process.•Abundant oxygen-containing groups enabled MXene membranes to be hydrophilic.•High water flux (85.4Lm-2h-1) with high salt rejection (99.5%) was realized.
We propose a new Lagrange multiplier approach to design unconditional energy stable schemes for gradient flows. The new approach leads to unconditionally energy stable schemes that are as accurate ...and efficient as the recently proposed SAV approach (Shen, Xu, and Yang 2018), but enjoys two additional advantages: (i) schemes based on the new approach dissipate the original energy, as opposed to a modified energy in the recently proposed SAV approach (Shen, Xu, and Yang 2018);and (ii) they do not require the nonlinear part of the free energy to be bounded from below as is required in the SAV approach. The price we pay for these advantages is that a nonlinear algebraic equation has to be solved to determine the Lagrange multiplier. We present ample numerical results to validate the new approach, and, as a particular example of challenging applications, we consider a block copolymer (BCP)/coupled Cahn–Hilliard model, and carry out new and nontrivial simulations which are consistent with experiment results.
•We propose a new Lagrange Multiplier approach to design unconditional energy stable schemes for gradient flows.•The new approach leads to unconditionally energy stable schemes that are as accurate and efficient as the recently proposed SAV approach, but enjoys two additional advantages: (i) schemes based on the new approach dissipate the original energy, as opposed to a modified energy in the recently proposed SAV approach; and (ii) they do not require the nonlinear part of the free energy to be bounded from below as is required in the SAV approach.•The price we pay for these advantages is that a nonlinear algebraic equation has to be solved to determine the Lagrange multiplier.
New vector-like quarks are predicted in many new physics scenarios beyond the Standard Model (SM). Based on a model-independent framework, we investigate the prospect of discovering the
SU
(2) ...singlet vector-like bottom quark (VLQ-
B
) in
e
+
e
-
collisions at 3 TeV Compact Linear Collider. We study the single VLQ-
B
production process
e
-
e
+
→
B
b
¯
→
Z
b
b
¯
with two types of decay channel:
Z
→
ℓ
+
ℓ
-
, and
Z
→
ν
ν
¯
. By carrying out a full simulation for the signals and the relevant SM backgrounds, the
2
σ
exclusion limit and
5
σ
discovery prospects are, respectively, obtained on the
B
quark mass and the coupling strength
g
∗
with the integrated luminosity of 5
ab
-
1
. Our numerical results show that the possible signals of the singlet VLQ-
B
might be detected at the future high-energy
e
+
e
-
linear colliders.
Integrating the literature on international human resource management (IHRM) with corporate social responsibility, this paper introduces the concept of socially responsible IHRM (SRIHRM) and develops ...its construct in key IHRM functions. This paper also discusses the complexities in the implementation of and the factors that may determine multinational enterprises' decisions regarding SRIHRM practices. Avenues for further research and discussions on the practical implications are suggested.
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for ...gradient flows, and show rigorously that the scheme is second-order in both time and space in various discrete norms. When equipped with an adaptive time strategy, the SAV/CN-BCFD scheme is accurate and extremely efficient. Numerical experiments on typical Allen-Cahn and Cahn-Hilliard equations are presented to verify our theoretical results and to show the robustness and accuracy of the SAV/CN-BCFD scheme.
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