arXiv subjects

Kai Jiang

Publications and source records attributed to Kai Jiang.

142 records · Page 8Linked to original sources

arXiv2019

Error analysis of SAV finite element method to phase field crystal model

In this paper, we construct and analyze an energy stable scheme by combining the latest developed scalar auxiliary variable (SAV) approach and linear finite element method (FEM) for phase field crystal (PFC) model, and show rigorously that the scheme is first-order in time and second-order in space for the L 2 and H -1 gradient flow equations. To reduce efficiently computational cost and capture accurately the phase interface, we give a simple adaptive strategy, equipped with a posteriori gradient estimator, i.e. L 2 norm of the recovered gradient. Extensive numerical experiments are presented to verify our theoretical results and to demonstrate the effectiveness and accuracy of our proposed method.

math.NA↗

arXiv2019

Local normal forms of dynamical systems with a singular underlying geometric structure

In this paper we prove the existence of a simultaneous local normalization for couples $(X,\mathcal{G})$, where $X$ is a vector field which vanishes at a point and $\mathcal{G}$ is a singular underlying geometric structure which is invariant with respect to $X$, in many different cases: singular volume forms, singular symplectic and Poisson structures, and singular contact structures. Similarly to Birkhoff normalization for Hamiltonian vector fields, our normalization is also only formal, in general. However, when $\mathcal{G}$ and $X$ are (real or complex) analytic and $X$ is analytically integrable or Darboux-integrable then our simultaneous normalization is also analytic. Our proofs are based on the toric approach to normalization of dynamical systems, the toric conservation law, and the equivariant path method. We also consider the case when $\mathcal{G}$ is singular but $X$ does not vanish at the origin.

math.DS↗

arXiv2019

Stability of three-dimensional icosahedral quasicrystals in multi-component systems

The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, which provides a unified numerical framework to study periodic crystals and quasicrystals, is used to compute free energies to high accuracy. Compared with traditional approaches, the advantage of the projection method has been also discussed detailedly. A rigorous and systematical computation demonstrates that three-dimensional icosahedral quasicrystal, two-dimensional decagonal quasicrystal are stable phases in such a simple multi-component coupled-mode Swift-Hohenberg model. The result extends the multiple length-scales interaction mechanism which can stabilize quasicrystals from single-component to multi-component systems.

cond-mat.soft↗

arXiv2019

An efficient method for computing stationary states of phase field crystal models

Computing stationary states is an important topic for phase field crystal (PFC) models. Great efforts have been made for energy dissipation of the numerical schemes when using gradient flows. However, it is always time-consuming due to the requirement of small effective time steps. In this paper, we propose an adaptive accelerated proximal gradient method for finding the stationary states of PFC models. The energy dissipation is guaranteed and the convergence property is established for the discretized energy functional. Moreover, the connections between generalized proximal operator with classical (semi-)implicit and explicit schemes for gradient flow are given. Extensive numerical experiments, including two three dimensional periodic crystals in Landau-Brazovskii (LB) model and a two dimensional quasicrystal in Lifshitz-Petrich (LP) model, demonstrate that our approach has adaptive time steps which lead to significant acceleration over semi-implicit methods for computing complex structures. Furthermore, our result reveals a deep physical mechanism of the simple LB model via which the sigma phase is first discovered.

math.NA↗

arXiv2019

Normalization of singular contact forms and primitive 1-forms

A differential 1-form $α$ on a manifold of odd dimension $2n+1$, which satisfies the contact condition $α\wedge (dα)^n \neq 0$ almost everywhere, but which vanishes at a point $O$, i.e. $α(O) = 0$, is called a \textit{singular contact form} at $O$. The aim of this paper is to study local normal forms (formal, analytic and smooth) of such singular contact forms. Our study leads naturally to the study of normal forms of singular primitive 1-forms of a symplectic form $ω$ in dimension $2n$, i.e. differential 1-forms $γ$ which vanish at a point and such that $dγ= ω$, and their corresponding conformal vector fields. Our results are an extension and improvement of previous results obtained by other authors, in particular Lychagin \cite{Lychagin-1stOrder1975}, Webster \cite{Webster-1stOrder1987} and Zhitomirskii \cite{Zhito-1Form1986,Zhito-1Form1992}. We make use of both the classical normalization techniques and the toric approach to the normalization problem for dynamical systems \cite{Zung_Birkhoff2005, Zung_Integrable2016, Zung_AA2018}.

math.DG↗

arXiv2018

A finite element method of the self-consistent field theory on general curved surfaces

Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory (SCFT) has been proven to be a powerful tool for studying the equilibrium ordered structures. Many numerical methods have been developed to solve the SCFT model. However, most of these focus on the bulk systems, and little work on the confined systems, especially on general curved surfaces. In this work, we developed a linear surface finite element method, which has a rigorous mathematical theory to guarantee numerical precsion, to study the self-assembled phases of block copolymers on general curved surfaces based on the SCFT. Furthermore, to capture the consistent surface for a given self-assembled pattern, an adaptive approach to optimize the size of the general curved surface has been proposed. To demonstrate the power of this approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces, including five closed surfaces and an unclosed surface. Numerical results illustrate the efficiency of the proposed method. The obtained ordered structures are consistent with the previous results on standard surfaces, such as sphere and torus. Certainly, the proposed numerical framework has the capability of studying the phase behaviors on general surfaces precisely.

cond-mat.soft↗

arXiv2018

Origin of Improved Photoelectrochemical Water Splitting in Mixed Perovskite Oxides

Owing to the versatility in their chemical and physical properties, transition metal perovskite oxides have emerged as a new category of highly efficient photocatalysts for photoelectrochemical water splitting. Here, to understand the underlying mechanism for the enhanced photoelectrochemical water splitting in mixed perovskites, we explore ideal epitaxial thin films of the BiFeO3-SrTiO3 system. The electronic struture and carrier dynamics are determined from both experiment and density-functional theory calculations. The intrinsic phenomena are measured in this ideal sytem, contrasting to commonly studied polycrstalline solid solutions where extrinsic structural features obscure the intrinsic phenomena. We determined that when SrTiO3 is added to BiFeO3 the conduction band minimum position is raised and an exponential tail of trap states from hybridized Ti 3d and Fe 3d orbitals emerges near the conduction band edge. The presence of these trap states strongly suppresses the fast electron-hole recombination and improves the photocurrent density in the visible-light region, up to 16 times at 0 VRHE compared to the pure end member compositions. Our work provides a new design approach for optimising the photoelectrochemical performance in mixed perovksite oxides.

cond-mat.mtrl-sci↗

arXiv2017

A Circulating Biomarker-based Framework for Diagnosis of Hepatocellular Carcinoma in a Clinically Relevant Model of Non-alcoholic Steatohepatitis; An OAD to NASH

Although cirrhosis is a key risk factor for the development of hepatocellular carcinoma (HCC), mounting evidence indicates that in a subset of patients presenting with non-alcoholic steatohepatitis (NASH), HCC manifests in the absence of cirrhosis. Given the sheer size of the non-alcoholic fatty liver disease (NAFLD) epidemic, and the dismal prognosis associated with late-stage primary liver cancer, there is an urgent need for HCC surveillance in the NASH patient. In the present study, adult male mice randomized to control diet or a fast food diet (FFD) were followed for up to 14 mo and serum level of a panel of HCC-relevant biomarkers was compared with liver biopsies at 3 and 14 mo. Both NAFLD Activity Score (NAS) and hepatic hydroxyproline content were elevated at 3 and 14 mo on FFD. Picrosirius red staining of liver sections revealed a filigree pattern of fibrillar collagen deposition with no cirrhosis at 14 mo on FFD. Nevertheless, 46% of animals bore one or more tumors on their livers confirmed as HCC in hematoxylin-eosin-stained liver sections. Receiver operating characteristic (ROC) curves analysis for serum levels of the HCC biomarkers osteopontin (OPN), alpha-fetoprotein (AFP) and Dickkopf-1 (DKK1) returned concordance-statistic/area under ROC curve of > 0.89. These data suggest that serum levels of OPN (threshold, 218 ng/mL; sensitivity, 82%; specificity, 86%), AFP (136 ng/mL; 91%; 97%) and DKK1 (2.4 ng/mL; 82%; 81%) are diagnostic for HCC in a clinically relevant model of NASH

q-bio.TO↗

arXiv2017

Compaction and condensation of DNA mediated by the C-terminal domain of Hfq

Hfq is a bacterial protein that is involved in several aspects of nucleic acids metabolism. It has been described as one of the nucleoid associated proteins shaping the bacterial chromosome, although it is better known to influence translation and turnover of cellular RNAs. Here, we explore the role of Escherichia coli Hfq C-terminal domain in the compaction of double stranded DNA. Various experimental methodologies, including fluorescence microscopy imaging of single DNA molecules confined inside nanofluidic channels, atomic force microscopy, isothermal titration microcalorimetry, and electrophoretic mobility assays have been used to follow the assembly of the C-terminal and N-terminal regions of Hfq on DNA. Results highlight the role of Hfq C-terminal arms in DNA binding, change in mechanical properties of the double helix and compaction of DNA into a condensed form. The propensity for bridging and compaction of DNA by the C-terminal domain might be related to aggregation of bound protein and may have implications for protein binding related gene regulation.

physics.bio-ph↗

arXiv2016

Strain effect engineered in α-Al2O3/monolayer MoS2 interface by first principle calculations

With the advances in low dimensional transition metal dichalcolgenides (TMDCs) based metal oxide semiconductor field effect transistor (MOSFET), the interface between semiconductors and dielectrics has received considerable attention due to its dramatic effects on the morphology and charge transport of semiconductors. In this study, first principle calculations were utilized to investigate the strain effect induced by the interface between Al2O3 (0001) and monolayer MoS2. The results indicate that Al2O3 in 1.3nm thickness can apply the strain of 0.3% on MoS2 monolayer. The strain effect monotonically increases with the larger thickness of the dielectric layer. Also, the study on temperature effect indicates the monotonic lattice expansion induced by the higher temperature. Our study proposes that the dielectric engineering can be an effective tool for strain effect in the nanotechnology.

physics.comp-ph↗

arXiv2016

Dirac Fermions induced in strained zigzag phosphorus nanotubes and the applications in field effect transistors

In this work, Dirac fermions have been obtained and engineered in one-dimensional (1D) zigzag phosphorus nanotubes (ZPNTs). We have performed a comprehensive first-principle computational study of the electronic properties of ZPNTs with various diameters. The results indicate that as the lattice parameter (Lc) along axial direction increases, ZPNTs undergo transitions from metal to semimetal and semimetal to semiconductor, whereas Dirac fermions appear at Lc ranging from 3.90Å to 4.10Å. In particular, a field effect transistor (FET) based on a 12-ZPNT (with 12 unit cells in transverse direction) exhibits semiconductor behaviors with efficient gate-effect modulation at Lc= 4.60Å. However, only weak gate modulation is demonstrated when the nanotube becomes semimetal at Lc= 4.10Å. This study indicates that ZPNTs are profoundly appealing in applications in the strain sensors. Our findings pave the way for development of high-performance strain-engineered electronics based on Dirac Fermions in 1D materials.

cond-mat.mes-hall↗

arXiv2015

Stability of Soft Quasicrystals in a Coupled-Mode Swift-Hohenberg Model for Three-Component Systems

In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms. Classic two-mode approximation method and direct numerical minimization are applied to the model. In the latter approach, we apply the projection method to deal with the potentially quasiperiodic ground states. A variable cell method of optimizing the shape and size of higher-dimensional periodic cell is developed to minimize the free energy with respect to the order parameters. Based on the developed numerical methods, we rediscover decagonal and dodecagonal quasicrystalline phases, and find diverse periodic phases and complex modulated phases. Furthermore, phase diagrams are obtained in various phase spaces by comparing the free energies of different candidate structures. It does show not only the important roles of system parameters, but also the effect of optimizing computational domain. In particular, the optimization of computational cell allows us to capture the ground states and phase behavior with higher fidelity. We also make some discussions on our results and show the potential of applying our numerical methods to a larger class of mean-field free energy functionals.

cond-mat.soft↗

arXiv2015

Self-Assembly of Asymmetrically Interacting ABC Star Triblock Copolymer Melts

The phase behavior of asymmetrically interacting ABC star triblock copolymer melts is investigated by the self-consistent field theory (SCFT). Motivated by the experimental systems, in this study, we focus on the systems in which the Flory-Huggins interaction parameters satisfy $χ_{AC}>χ_{BC}\approx χ_{AB}$. Using various initialization strategies, a large number of periodic structures have been obtained in our calculations. A fourth-order pseudospectral algorithm combined with Anderson mixing method is used to compute the free energy of candidate structures carefully. The stability has been detailedly analyzed by splitting the free energy into internal and entropic parts. A complete and complex triangular phase diagram is presented for a model with $χ_{AC}>χ_{BC}= χ_{AB}$ in which fifteen ordered phases, including two-, and three-dimensional structures, have been predicted to be stable from the SCFT calculations. Generally speaking, with the asymmetrical interactions, the hierarchical structures tend to be formed near the B-rich corner of the triangular phase diagram. This work broadens the previous theoretical results from equal interaction systems to unequal interaction systems. The predicted phase behavior is in good agreement with experimental observations and previous theoretical results.

cond-mat.soft↗

arXiv2015

Stability of Two-Dimensional Soft Quasicrystals

The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.

cond-mat.soft↗

arXiv2013

Numerical Methods for Quasicrystals

Quasicrystals are one kind of space-filling structures. The traditional crystalline approximant method utilizes periodic structures to approximate quasicrystals. The errors of this approach come from two parts: the numerical discretization, and the approximate error of Simultaneous Diophantine Approximation which also determines the size of the domain necessary for accurate solution. As the approximate error decreases, the computational complexity grows rapidly, and moreover, the approximate error always exits unless the computational region is the full space. In this work we focus on the development of numerical method to compute quasicrystals with high accuracy. With the help of higher-dimensional reciprocal space, a new projection method is developed to compute quasicrystals. The approach enables us to calculate quasicrystals rather than crystalline approximants. Compared with the crystalline approximant method, the projection method overcomes the restrictions of the Simultaneous Diophantine Approximation, and can also use periodic boundary conditions conveniently. Meanwhile, the proposed method efficiently reduces the computational complexity through implementing in a unit cell and using pseudospectral method. For illustrative purpose we work with the Lifshitz-Petrich model, though our present algorithm will apply to more general systems including quasicrystals. We find that the projection method can maintain the rotational symmetry accurately. More significantly, the algorithm can calculate the free energy density to high precision.

physics.comp-ph↗

arXiv2013

Analytic Structure of the SCFT Energy Functional of Multicomponent Block Copolymers

This paper concerns the analytic structure of the self-consistent field theory (SCFT) energy functional of multicomponent block copolymer systems which contain more than two chemically distinct blocks. The SCFT has enjoyed considered success and wide usage in investigation of the complex phase behavior of block copolymers. It is well-known that the physical solutions of the SCFT equations are saddle points, however, the analytic structure of the SCFT energy functional has received little attention over the years. A recent work by Fredrickson and collaborators [see the monograph by Fredrickson, The Equilibrium Theory of Inhomogeneous Polymers, (2006), pp. 203-209] has analysed the mathematical structure of the field energy functional for polymeric systems, and clarified the index-1 saddle point nature of the problem produced by the incompressibility constraint. In this paper, our goals are to draw further attention to multicomponent block copolymers utilizing the Hubbard-Stratonovich transformation used by Fredrickson and co-workers. We first show that the saddle point character of the SCFT energy functional of multicomponent block copolymer systems may be high index, not only produced by the incompressibility constraint, but also by the Flory-Huggins interaction parameters. Our analysis will be beneficial to many theoretical studies, such as the nucleation theory of ordered phases, the mesoscopic dynamics. As an application, we then utilize the discovery to develop the gradient-based iterative schemes to solve the SCFT equations, and illustrate its performance through several numerical experiments taking ABC star triblock copolymers as an example.

physics.comp-ph↗