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Spin-based magnetic random-access memory for high-performance computing

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National Science Review 2024年第3期11卷 20-23页

作者： Kaiming Cai Tianli Jin Wen Siang Lew School of Physics Huazhong University of Science and Technology Interuniversity Microelectronics Centre(IMEC) School of Physical and mathematical sciences Nanyang Technological University

Memory serves as a critical component in today's electronic systems for data storage and processing. In traditional computer architectures, the logic and memory units are physically separated, due to the performance gap in operational speed and capacity among memories, resulting in the fundamental limitation of the von Neumann computers.

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Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

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Communications on Applied Mathematics and Computation 2024年第1期6卷 190-217页

作者： Fangyao Zhu Juntao Huang Yang Yang department of mathematical sciences Michigan Technological UniversityHoughtonMI49931USA department of Mathematics and Statistics Texas Tech UniversityLubbockTX79409USA

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive *** are several difficulties in constructing suitable numerical *** of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and ***,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step *** obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG *** traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass *** solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is *** the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and *** time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the *** methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be ***,it is not straightforward to combine the bound-preserving DG methods and the Patankar time *** positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target *** match the degree of freedom,we use polynomials on rectangular meshes for problems in two space *** evolve in time,we first read the polynomials at the Gaussian ***,suitable slope l

关键词： Compressible Euler equations Chemical reacting flows Bound-preserving Discontinuous Galerkin(DG)method Modified Patankar method

GLOBAL SOLUTIONS IN THE CRITICAL SOBOLEV SPACE FOR THE LANDAU EQUATION

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Acta Mathematica Scientia 2024年第4期44卷 1347-1372页

作者： Hao WANG department of mathematical sciences Tsinghua UniversityBeijing 100084China

The Landau equation is studied for hard potential with-2≤γ≤*** a perturbation setting,a unique global solution of the Cauchy problem to the Landau equation is established in a critical Sobolev space H_(x)^(d)L_(v)^(2)(d>3/2),which extends the results of[11]in the torus domain to the whole space R_(x)^(3).Here we utilize the pseudo-differential calculus to derive our desired result.

关键词： Landau equation nonlinear energy method global existence pseudo-differential calculus

Existence and asymptotics of normalized solutions for the logarithmic Schrödinger system

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Science China Mathematics 2024年第9期67卷 2019-2048页

作者： Qian Zhang Wenming Zou department of mathematical sciences Tsinghua UniversityBeijing 100084China

This paper is concerned with the following logarithmic Schrodinger system:{-Δu_(1)+ω_(1)u_(1)=u_(1)u_(1)logu_(1)^(2)+2p/p+q|u_(2)|^(q)|u_(1)|^(p-2)u_(1),-Δu_(2)+ω_(2)u_(2)=u_(2)u_(2)log u_(2)^(2)+2q/p+q|u_(1)|^(p)|u_(2)|^(q-2)u_(2),∫_(Ω)|u_(i)|^(2)dx=ρ_(i),i=1,2,(u_(1),u_(2))∈H_(0)^(1)(Ω;R^(2)),where Ω=R^(N)or Ω■R^(N)(N≥3)is a bounded smooth domain,andω_(i)R,μ_(i),ρ_(i)>0 for i=1,***,p,q≥1,and 2≤p+q≤2^(*),where 2^(*):=2N/*** using a Gagliardo-Nirenberg inequality and a careful estimation of u log u^(2),firstly,we provide a unified proof of the existence of the normalized ground state solution for all 2≤p+q≤2^(*).Secondly,we consider the stability of normalized ground state ***,we analyze the behavior of solutions for the Sobolev-subcritical case and pass to the limit as the exponent p+q approaches 2^(*).Notably,the uncertainty of the sign of u log u^(2)in(0,+∞)is one of the difficulties of this paper,and also one of the motivations we are interested *** particular,we can establish the existence of positive normalized ground state solutions for the Brézis-Nirenberg type problem with logarithmic perturbations(i.e.,p+q=2^(*)).In addition,our study includes proving the existence of solutions to the logarithmic type Bréis-Nirenberg problem with and without the L^(2)-*** ∫_(Ω)|u_(i)|^(2)dx=ρ_(i)(i=1,2)by two different methods,*** results seem to be the first result of the normalized solution of the coupled nonlinear Schrodinger system with logarithmic perturbations.

关键词： logarithmic Schrodinger system Brézis-Nirenberg problem normalized solution existence and stability behavior of solutions

A UNIFORM CONVERGENT PETROV-GALERKIN METHOD FOR A CLASS OF TURNING POINT PROBLEMS

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Journal of Computational Mathematics 2024年第5期42卷 1356-1379页

作者： Li Feng Zhongyi Huang department of mathematical sciences Tsinghua UniversityBeijing 100084China

In this paper,we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method(PGFEM).We first give a priori estimate for the turning point problem with a single boundary turning *** we use PGFEM to solve it,where test functions are the solutions to piecewise approximate dual *** prove that our method has a first-order convergence rate in both L∞h norm and a discrete energy norm when we select the exact solutions to dual problems as test *** results show that our scheme is efficient for turning point problems with different types of singularities,and the convergency coincides with our theoretical results.

关键词： Turning point problem Petrov-Galerkin finite element method Uniform convergency

Markovian Quadratic BSDEs with an Unbounded Sub-quadratic Growth

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Chinese Annals of Mathematics,Series B 2024年第3期45卷 441-462页

作者： Jingnan JU Shanjian TANG Shanghai Center for mathematical sciences Fudan UniversityShanghai 200433China department of Finance and Control sciences School of Mathematical SciencesFudan UniversityShanghai 200433China

This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal *** generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable *** existence and uniqueness results are given to these *** an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.

关键词： Markovian BSDE Quadratic growth Unbounded sub-quadratic term coeficients Coupled FBSDE

High-performance sodium storage for cobalt phosphide composite array electrodes

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Rare Metals 2024年第8期43卷 3724-3734页

作者： Man Zhang Xiao-Xu Liu Tian-Yi Ji Yang Li Da-Wei Sheng Shao-Dong Li Pei-Pei Ren Ze-Xiang Shen School of Material Science and Engineering Shaanxi University of Science and TechnologyXi'an 710021China School of Physical and mathematical sciences Nanyang Technological UniversitySingapore 637371Singapore

Transition metal phosphides hold great potential as sodium-ion batteries anode materials owing to their high theoretical capacity and modest ***,volume changes and low intrinsic conductivity seriously largely hinder the further development of metal phosphide *** design of phosphide anode materials with reasonable structure is conducive to solving the problems of volume expansion and slow reaction kinetics during the *** this work,a composite material integrating zeolite imidazolate backbone(ZIF) and carbon materials was synthesized by the original growth ***,by the oxidation-phosphating process,CoP nanoarray composites riveted to carbon fiber(CoP@CF) were *** the CoP@CF,CoP nanoparticles are uniformly distributed on ZIF-derived carbon,reducing agglomeration and volume change during *** also provides a highly conductive network for the active material,improving the electrode ***,when evaluated as an anode for sodium-ion batteries,CoP@CF electrode displays enhanced reversible capacity(262 mAh·g^(-1) at 0.1 A·g^(-1)after 100 cycles),which is much better than that of pure CF electrode(57 mAh·g^(-1) at 0.1 A·g^(-1) after 100 cycles)prepared without the addition of *** rate performance of CoP@CF electrode is also superior to that of pure CF electrode at various current densities from 0.05 to1 A·g^(-1).The sodium storage behavior of CoP@CF was revealed by ex-situ X-ray photoelectron spectroscopy,X-ray diffraction,and synchrotron radiation absorption *** method provides a reference for the design and synthesis of anode materials in sodium-ion batteries.

关键词： Cobalt phosphide Array structure Freestanding anodes Sodium-ion batteries

Pseudo-Differential Operators of Homogeneous Symbol Class Associated with the Weinstein Transform

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1533-1562页

作者： Santosh Kumar UPADHYAY Mohd SARTAJ department of mathematical sciences Indian Institute of Technology(BHU)VaranasiIndia

In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are *** boundedness of pseudo-differential operators and commutator between two pseudo-differential o... 详细信息

关键词： Pseudo-Differential Operators Homogeneous Symbol Class Weinstein Operator Sobolev space Weinstein transform

Jackson-type inequalities on high-dimensional spheres

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Science China Mathematics 2024年第11期67卷 2571-2586页

作者： Yeli Niu Feng Dai department of Mathematics Shanghai Normal University department of mathematical and Statistical sciences University of Alberta

We study Jackson's inequality on high-dimensional spheres with respect to the modulus of smoothness defined via the rotation *** obtain a version of Jackson's inequality with a dimensionfree constant,extending Newman and Shapiro's well-known results in 1964 from the case of r = 1 and p = ∞ to more general *** results partially overcome the curse of *** also establish similar results on the equivalence of the K-functional and modulus of smoothness.

关键词： modulus of smoothness $K$-functional Jackson's inequality high-dimensional approximation

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