Mathematical Analysis of a PDE System for Biological Network Formation

Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai [13 Hu , D. (2013). Optimization, Adaptation, and Initialization of Biological Transport Networks. Workshop on multiscale problems from physics, biology and material sciences. May 28–31st, 2014, Shanghai. Available at: http://math.sjtu.edu.cn/conference/multiscale2014/ (accessed 6 January 2015). [Google Scholar], 15 Hu , D. , Cai , D. ( 2013 ). Adaptation and optimization of biological transport networks . Phys. Rev. Lett. 111 : 138701 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. The model describes the pressure field thanks to Darcy's type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate D ≥ 0 representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behavior. It turns out that, by energy dissipation, steady states play a central role to understand the network formation capacity of the system. We show that for a large diffusion coefficient D, the zero steady state is stable, while network formation occurs for small values of D due to the instability of the zero steady state, and the borderline case D = 0 exhibits a large class of dynamically stable (in the linearized sense) steady states.     

Well/Ill Posedness for the Euler-Korteweg-Poisson System and Related Problems

We consider a general Euler-Korteweg-Poisson system in R ³, supplemented with the space periodic boundary conditions, where the quantum hydrodynamics equations and the classical fluid dynamics equations with capillarity are recovered as particular examples. We show that the system admits infinitely many global-in-time weak solutions for any sufficiently smooth initial data including the case of a vanishing initial density - the vacuum zones. Moreover, there is a vast family of initial data, for which the Cauchy problem possesses infinitely many dissipative weak solutions, i.e. the weak solutions satisfying the energy inequality. Finally, we establish the weak-strong uniqueness property in a class of solutions without vacuum. In this paper we show that, even in presence of a dispersive tensor, we have the same phenomena found by De Lellis and Székelyhidi.     

Synthesis,spectroscopic and crystal structure analysis of 2-(4-fluorobenzyl)-6-(4-methoxyphenyl)imidazo[2,1-b][1,3,4]thiadiazole and its morpholinomethyl derivative

The preparation of 2-(4-fluorobenzyl)-6-(4-methoxyphenyl)-5-morpholin-1-ylmethyl imidazo[2,1-b][1,3,4]thiadiazole via the intermediate 2-(4-fluorobenzyl)-6-(4-methoxyphenyl)Imidazo[2,1-b][1,3,4] thiadiazole is described. Elemental analysis, IR spectrum, ¹H NMR and X-ray crystal structure analyses were carried out to determine the compositions and molecular structures of the two compounds. The crystal packing exhibits intermolecular C–H?O, C–H?N, C–H?F and π–π stacking interactions leading to the formation of the supramolecular network.     

Evolution of coercivity and its angular dependence in CoFe nanostructures subjected to field cooling

Evolution of coercivity and its angular dependence in CoFe nanostructures subjected to field cooling has been investigated in this work. Spherical CoFe grains with an average diameter of 30 nm were grown on a silicon substrate using electron beam evaporation. Further, the as‐deposited sample was subjected to field cooling. The morphology and topography of the sample before and after field cooling were characterized by atomic force microscopy and SEM. Magnetic force microscopy indicated that there is a good uniformity of magnetization throughout the sample after field cooling. Vibrating sample magnetometer measurements indicate that the coercivity in CoFe nanostructures is dependent on shape of the nanostructures. Copyright © 2013 John Wiley & Sons, Ltd.     

Reprint of : Spin polarization induced by an electric field in the presence of weak localization effects

We evaluate the spin polarization (Edelstein or inverse spin galvanic effect) and the spin Hall current induced by an applied electric field by including the weak localization corrections for a two-dimensional electron gas. We show that the weak localization effects yield logarithmic corrections to both the spin polarization conductivity relating the spin polarization and the electric field and to the spin Hall angle relating the spin and charge currents. The renormalization of both the spin polarization conductivity and the spin Hall angle combine to produce a zero correction to the total spin Hall conductivity as required by an exact identity. Suggestions for the experimental observation of the effect are given.     

扩散过程中弱相干光场的退相干

研究了扩散过程中弱相干光场量子特性的演化.利用正规乘积、反正规乘积和Weyl编序算符内的积分技术,采用热纠缠态表象求解密度矩阵主方程,利用Kraus算符给出扩散过程中密度算符解的表达式,导出初态为弱相干态的量子态密度算符演化规律.讨论了扩散对光场压缩效应和反聚束效应的影响.结果表明:随着扩散过程的进行,弱相干场压缩深度和压缩范围均在减小;扩散初期光场呈反聚束效应,扩散时间大于一定值后反聚束效应消失.     

Weak Euler Approximation for Itô Diffusion and Jump Processes

This article studies the rate of convergence of the weak Euler approximation for Itô diffusion and jump processes with Hölder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in Hölder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.     

脉动热管的毛细管结构和尺度效应实验研究

脉动热管的毛细管结构变化如何影响其性能是研究者关注的问题.本文对毛细管截面为正方形和正三角形,水力直径范围为1 mm左右的回路型脉动热管的传热性能进行了实验研究.结果表明,角管脉动热管的倾角变化时,底加热明显优于顶加热;三角形截面脉动热管的热阻比正方形截面脉动热管的热阻更低.脉动热管在水力直径为1.5 mm时比1mm时的性能要好.实验研究为理论分析打下了基础.     

Discrimination of Excited States of Acetylacetone through Theoretical Molecular-Frame Photoelectron Angular Distributions

Photoelectron angular distribution (PAD) in the laboratory frame for randomly oriented molecules is typically described by a single anisotropy parameter, the so-called asymmetry parameter. However, especially from a theoretical perspective, it is more natural to consider molecular photoionization by using a molecular frame. The molecular frame PADs (MFPADs) may be used to extract information about the electronic structure of the system studied. In the last decade, significant experimental efforts have been directed to MFPAD measurements. MFPADs are highly characterizing signatures of the final ionic states. In particular, they are very sensitive to the nature of the final state, which is embodied in the corresponding Dyson orbital. In our previous work on acetylacetone, a prototype system for studying intra-molecular hydrogen bond interactions, we followed the dynamics of the excited states involved in the photoexcitation–deexcitation process of this molecule. It remains to be explored the possibility of discriminating between different excited states through the MFPAD profiles. The calculation of MFPADs to differentiate excited states can pave the way to the possibility of a clear discrimination for all the cases where the recognition of excited states is otherwise intricate.