一类非线性发展方程的渐近吸引子

无穷维动力系统的基本理念是将一个无穷维系统约化为一个有限维系统,但是,要进一步研究约化后的有限维系统的动力学行为是非常困难的,因为它们的结构是未知的。为了克服这个困难,诸如近似惯性流形等概念已被引入,对于Navier-Stokes方程,其近似惯性流形的存在性问题已被讨论,它是通过挤压性质找到一个Lipschitz函数,说明其整体吸引子位于该函数图的某个小领域,而文中是通过构造一个有限维解序列,说明长时间后其趋于方程的整体吸引子,理论上给出了一类发展方程的渐近吸引子的构造方法.

2D Navier-Stokes方程的渐近吸引子(英文)

考虑了2D周期边界条件下Navier-Stokes方程渐近吸引子,即构造了一个有限维解序列,首先证明了该序列不会远离方程的整体吸引子,然后证明了它在长时间后无限趋于方程的整体吸引子,并给出了渐近吸引子的维数估计.

全空间中一类部分耗散反应扩散方程的整体吸引子

有界区域上的反应扩散方程组解的长时间行为已被很多人研究过,一般来说,整体吸引子的存在性依赖于某种紧性,对于有界区域,紧性由先验估计和Sobolev嵌入紧性而获得。由于在无界区域嵌入不再有紧性,为了克服此困难,目前大概有2个途径:一是采取在加权Sobolev空间上考虑;二是在有着适当光滑性的有界连续函数空间中讨论。笔者主要考虑了无界区域上反应扩散方程的解的渐近行为,证明其整体吸引子存在,其中反应项系数与空间变量有关,使得该问题更符合实际意义,推广了Wang B.和Marion M.已有的结果。

Partial Frequencies and Chladni’s Law in Church Bells

The rim partials of a church bell (those with an antinode at the soundbow) generate the strike pitch or perceived note of the bell. The spacing in frequency of the higher rim partials has an important effect on the tonal quality of the bell. Investigations into the partial frequencies of 2752 bells, both bronze and steel, of a wide variety of dates, founders and sizes, show a simple and unexpected relationship between the frequencies of the rim partials. This relationship explains why attempts to tune the higher rim partials independently have failed. A modified version of Chladni’s law provides insight into the musical relationship of the partials, and predicts the partials of individual bells well, but fails to give a simple model of the spacing between the partials seen in bells with different profiles.

Refined Agent Model Using Shape-Based Grained Structure: Application to Membrane Molecules

Multi-agent model is well-known to suit design of complex systems. This paradigm allows describing autonomous entities to interact together directly or through their environment. It is specially adapted to design 3D simulations taking into account spatial constraints on agents. In this work, we have designed a multi-agent model which adds a feature to the classical representation of agent: a body, encapsulating a physical model of the agent. We have applied this model to lipids and proteins belonging to the inner mitochondrial membrane, a biological membrane. Information provided by atomic structures is available through international databases and has been used to design a shape-based grain model for the agent body. We selected a model with three grains per molecule in which each grain is characterized by a type determining how they interact together and consequently the agent behaviors. Lipids and two kinds of protein structures have been described within this model allowing us to simulate their organization in membranes.

A Malvaceae mystery: A mallow maelstrom of genome multiplications and maybe misleading methods?

Previous research suggests that Gossypium has undergone a 5-to 6-fold multiplication following its divergence from Theobroma. However, the number of events, or where they occurred in the Malvaceae phylogeny remains unknown. We analyzed transcriptomic and genomic data from representatives of eight of the nine Malvaceae subfamilies. Phylogenetic analysis of nuclear data placed Dombeya(Dombeyoideae) as sister to the rest of Malvadendrina clade, but the plastid DNA tree strongly supported Durio(Helicteroideae) in this position. Intraspecific Ks plots indicated that all sampled taxa, except Theobroma(Byttnerioideae), Corchorus(Grewioideae), and Dombeya(Dombeyoideae), have experienced whole genome multiplications(WGMs). Quartet analysis suggested WGMs were shared by Malvoideae-Bombacoideae and Sterculioideae-Tilioideae, but did not resolve whether these are shared with each other or Helicteroideae(Durio).Gene tree reconciliation and Bayesian concordance analysis suggested a complex history. Alternative hypotheses are suggested, each involving two independent autotetraploid and one allopolyploid event. They differ in that one entails an allopolyploid origin for the Durio lineage,whereas the other invokes an allopolyploid origin for Malvoideae-Bombacoideae. We highlight the need for more genomic information in the Malvaceae and improved methods to resolve complex evolutionary histories that may include allopolyploidy, incomplete lineage sorting, and variable rates of gene and genome evolution.

UNIFORM QUADRATIC CONVERGENCE OF A MONOTONE WEIGHTED AVERAGE METHOD FOR SEMILINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS＊

This paper deals with a monotone weighted average iterative method for solving semilinear singularly perturbed parabolic problems. Monotone sequences, based on the ac- celerated monotone iterative method, are constructed for a nonlinear difference scheme which approximates the semilinear parabolic problem. This monotone convergence leads to the existence-uniqueness theorem. An analysis of uniform convergence of the monotone weighted average iterative method to the solutions of the nonlinear difference scheme and continuous problem is given. Numerical experiments are presented.

A NUMERICAL METHOD FOR SOLVING NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS OF FREDHOLM TYPE

The paper deals with a numerical method for solving nonlinear integro-parabolic prob- lems of Fredholm type. A monotone iterative method, based on the method of upper and lower solutions, is constructed. This iterative method yields two sequences which converge monotonically from above and below, respectively, to a solution of a nonlinear difference scheme. This monotone convergence leads to an existence-uniqueness theorem. An analy- sis of convergence rates of the monotone iterative method is given. Some basic techniques for construction of initial upper and lower solutions are given, and numerical experiments with two test problems are presented.

Determining the strange and antistrange quark distributions of the nucleon

The difference between the strange and antistrange quark distributions,δs（x） = s（x） ˉs（x）,and the combination of light quark sea and strange quark sea,Δ（x） =ˉ d（x） ＋ uˉ（x） s（x） ˉs（x）,are originated from non-perturbative processes and can be calculated using non-perturbative models of the nucleon.We report calculations of δs（x） and Δ（x） using the meson cloud model.Combining our calculations of Δ（x） with relatively well known light antiquark distributions obtained from global analysis of available experimental data,we estimate the total strange sea distributions of the nucleon.

Gold nanorods conjugated upconversion nanoparticles nanocomposites for simultaneous bioimaging,local temperature sensing and photothermal therapy of OML-1 oral cancer cells

The major challenge in photothermal therapy(PTT)is to develop nanocomposites that simultaneously exhibit bioimaging and PTT under a single near-infrared(NIR)irradiation with high therapeutic efficiency.Herein,we present a multifunctional nanocomposite synthesized by linking NaYF_(4):Yb^(3+),Er^(3+)upconversion nanoparticles(UCNPs)with gold nanorods(AuNR)to exhibit fluorescence label-ing,local temperature sensing and photothermal functions simul-taneously with a single NIR laser excitation.The AuNR-NaYF_(4):Yb^(3+),Er^(3+)nanocomposite particles displayed better photothermal prop-erties compared with pure AuNRs or a blend of AuNRs and NaYF_(4):Yb^(3+),Er^(3+)UCNPs.The temperature-dependent upconversion lumi-nescence(UCL)property was used to determine local temperature at the nanocomposite particles,which is useful for selecting appro-priate irradiation dosage for PTT.The therapeutic performance of the nanocomposites in PTT for OML-1 oral cancer cells was deter-mined.For cell labeling,we successfully labeled streptavidin-linked nanocomposite particles on the surface of OML-1 oral cancer using anti-human epidermal growth factor receptor 2(anti-Her2)anti-body.Finally,the nanocomposite particles caused exceptional destruction of cancer cells up to 70%dead cells under 976 nm laser irradiation for only one min at 0.3 W/cm^(2)which is below the maximal permissible exposure of human skin.

Minimising the spread of residence-time distribution for flat and heaped powders in a wedge-shaped planar hopper

A wedge-shaped planar mass-flow hopper system was modelled using stress-field theory as found in the literature, The authors present governing equations for stress and velocity fields under a radial- flow assumption in a converging hopper. The velocity in the silo above the hopper is modelled as plug flow, Two set-ups are modelled, one where powder layers in the hopper are assumed to be flat, and the second in which the layers are heaped at some characteristic angle, The ejection times and residence-time distributions are calculated and presented for a range of heap angles. For realistic heap angles, the spread of the residence-time distribution decreases with increasing heap angle; in one case, the spread is halved to a well-defined limit. At this limit （the critical heap angle） the geometry of the hopper can be optimised to minimise the spread of the residence-time distribution, and hence to minimise predicted mixing in the system. We present examples of curves for a variety of parameters that minimise the predicted mixing in the hopper-silo system.

A MONOTONE DOMAIN DECOMPOSITION ALGORITHM FOR SOLVING WEIGHTED AVERAGE APPROXIMATIONS TO NONLINEAR SINGULARLY PERTURBED PARABOLIC PROBLEMS

This paper presents and analyzes a monotone domain decomposition algorithm for solving nonlinear singularly perturbed reaction-diffusion problems of parabolic type. To solve the nonlinear weighted average finite difference scheme for the partial differential equation, we construct a monotone domain decomposition algorithm based on a Schwarz alternating method and a box-domain decomposition. This algorithm needs only to solve linear discrete systems at each iterative step and converges monotonically to the exact solution of the nonlinear discrete problem. domain decomposition algorithm is estimated The rate of convergence of the monotone Numerical experiments are presented.

A Remark on Partly Dissipative Reaction Diffusion Systems on IR^n

The long time behavior of the solutions of some partly dissipative reaction diffusion systems is studied. We prove the existence of a compact （L^2 × L^2 - H^1 × L^2） attractor for a partly dissipative reaction diffusion system in Rn. This improves a previous result obtained by A. Rodrigues-Bernal and B. Wang concerning the existence of a compact （L^2 × L^2 - L^2 × L^2） attractor for the same system.