On the dynamics of generic non-Abelian free actions

We investigate some global generic properties of the dynamics associated to non-Abelian free actions in certain special cases. The main properties considered in this paper are related to the existence of dense orbits, to ergodicity and to topological rigidity. We first deal with them in the case of conservative homeomorphisms of a manifold and C ¹-diffeomorphisms of a surface. Groups of analytic diffeomorphisms of a manifold which, in addition, contain a Morse-Smale element and possess a generating set close to the identity are considered as well. From our discussion we also derive the existence of a rigidity phenomenon for groups of skew-products which is opposed to the phenomenon present in Furstenbergs celebrated example of a minimal diffeomorphism that is not ergodic (cf. [Ma]).     

A property on reinforcing edge-disjoint spanning hypertrees in uniform hypergraphs

Suppose that $H$ is a simple uniform hypergraph satisfying $\left|E\left(H\right)\right|=k(\left|V\left(H\right)\right|?1)$. A $k$-partition $\pi =(X_1,X_2,\dots ,X_k)$ of $E\left(H\right)$ such that $\left|X_i\right|=\left|V\left(H\right)\right|?1$ for $1\le i\le k$ is a uniform $k$-partition. Let $P_k\left(H\right)$ be the collection of all uniform $k$-partitions of $E\left(H\right)$ and define $\epsilon \left(\pi \right)={\sum }_{i=1}^{k}c\left(H\left(X_i\right)\right)?k$, where $c\left(H\right)$ denotes the number of maximal partition-connected sub-hypergraphs of $H$. Let $\epsilon \left(H\right)={min}_{\pi \in P_k\left(H\right)}\epsilon \left(\pi \right)$. Then $\epsilon \left(H\right)\ge 0$ with equality holds if and only if $H$ is a union of $k$ edge-disjoint spanning hypertrees. The parameter $\epsilon \left(H\right)$ is used to measure how close $H$ is being from a union of $k$ edge-disjoint spanning hypertrees.We prove that if $H$ is a simple uniform hypergraph with $\left|E\left(H\right)\right|=k(\left|V\left(H\right)\right|?1)$ and $\epsilon \left(H\right)>0$, then there exist $e\in E\left(H\right)$ and $e^{\prime }\in E\left(H^c\right)$ such that $\epsilon (H?e+e^{\prime })<\epsilon \left(H\right)$. This generalizes a former result, which settles a conjecture of Payan. The result iteratively defines a finite $\epsilon$-decreasing sequence of uniform hypergraphs $H_0,H_1,H_2,\dots ,H_m$ such that $H_0=H$, $H_m$ is the union of $k$ edge-disjoint spanning hypertrees, and such that two consecutive hypergraphs in the sequence differ by exactly one hyperedge.     

Transport of Neutrally Buoyant and Dense Variably Sized Colloids in a Two-Dimensional Fracture with Anisotropic Aperture

The transport of monodisperse as well as polydisperse colloid suspensions in a two-dimensional, water saturated fracture with spatially variable and anisotropic aperture is investigated with a particle tracking model. Both neutrally buoyant and dense colloid suspensions are considered. Although flow and transport in fractured subsurface formations have been studied extensively by numerous investigators, the transport of dense, polydisperse colloid suspensions in a fracture with spatially variable and anisotropic aperture has not been previously explored. Simulated snapshots and breakthrough curves of ensemble averages of several realizations of a log-normally distributed aperture field show that polydisperse colloids exhibit greater spreading than monodisperse colloids, and dense colloids show greater retardation than neutrally buoyant colloids. Moreover, it is demonstrated that aperture anisotropy oriented along the flow direction substantially increases colloid spreading; whereas, aperture anisotropy oriented transverse to the flow direction retards colloid movement.     

Nonmetal-to-metal transition in dense fluid helium

The nonmetal-to-metal transition in dense fluid helium is discussed, which has been, in analogy to metallization of hydrogen, predicted as first-order plasma phase transition using chemical models for the equation of state and plasma composition. However, recent ab initio simulations performed for dense fluid helium indicate that this transition is continuous in the considered regime, without a density jump and latent heat as characteristic of a first-order phase transition. Implications for some astrophysical plasmas are discussed.     

Measurement of dense plasma temperature of the shock-compressed silicon

Measurements of the brightness temperature and compressibility of a dense silicon plasma formed by powerful shock waves (SWs) passing through a single-crystal sample have been carried out. Plane SWs were created using an explosive technique: the traditional plane acceleration of a steel driver plate made it possible to obtain pressures in silicon up to 133 GPa, and the use of “Mach” cumulative generators realized the pressures up to 510 GPa. The shock Hugoniot of silicon was determined by the impedance matching with α-quartz as the reference. The intensity of emitted thermal radiation was measured in the infrared range λ ∼ 1.5 μm, where silicon is optically transparent, and in the visible range of the spectrum. A significant (up to five times) understatement of the measured values of the brightness temperature in comparison with the values calculated by the equation of state was found. Taking into account the reflective properties of the SW in silicon does not lead to an agreement with the experiment. The estimates of relaxation processes behind the shock front suggest the presence of a zone of the establishment of ionization equilibrium with a width of ∼10 μm.     

On the reactivity of naphthalene and biphenyl dianions: tying up loose ends concerning an SN2‐ET dichotomy in alkylation reactions

Naphthalene and biphenyl dianions are interesting compounds that can be obtained by double reduction of the corresponding arenes in solution with certain alkali metals. These dianions are highly reactive and rather elusive species with very high laying and highly delocalized electrons. They share many aspects of the reactivity of the alkali metal they originated from and consequently behave primarily as strong electron transfer (ET) reagents. We report here kinetic evidence for a different type of reactivity in their alkylation reactions with alkyl fluorides. By using cyclopropylmethyl fluoride (c‐C₃H₅CH₂F) as a very fast radical probe, we were able to settle that this alkylation does not involve the classical electron transfer reaction followed by radical coupling between diffusing radicals, but supports the alternative S_N2 concerted mechanism, discerning thus this mechanistic S_N2‐ET dichotomy. Copyright © 2015 John Wiley & Sons, Ltd.     

快速床动力学统一模型Ⅱ:上部稀相与下部浓相固含率的预报

在前文建立的分相共存快速床动力学模型的基础上,对分相模型中存在颗粒团聚物时的上升稀相进行了受力分析。以有限直径提升管中颗粒终端速度的修正,导出了上升稀相受力关于等效管径与浓稀相滑移速度的修正表达式。将本模型预报的上部稀相固含率与已有的实验数据经验关联式进行了对比,并根据所得结果初步优化了模型参数(k=8,n=6)。进而,根据所得模型参数计算了下部浓相固含率随曳力函数f(ε)的变化规律;与李佑楚经验关联式相比,同样具有合理的一致性。本文工作进一步验证了快速床动力学统一模型的整体合理性。     

Phase structures of neutral dense quark matter and applicationto strange stars

In the contact interaction model,the quark propagator has only one solution,namely,the chiral symmetry breaking solution,at vanishing temperature and density in the case of physical quark mass.We generalize the condensate feedback onto the coupling strength from the 2 flavor case to the 2+1 flavor case,and find the Wigner solution appears in some regions,which enables us to tackle chiral phase transition as two-phase coexistences.At finite chemical potential,we analyze the chiral phase transition in the conditions of electric charge neutrality andβequilibrium.The four chemical potentials,μ_u,μ_d,μ_s and He,are constrained by three conditions,so that one inde-pendent variable remains:we choose the average quark chemical potential as the free variable.All quark masses and number densities suffer discontinuities at the phase transition point.The strange quarks appear after the phase trans-ition since the system needg more energy to produce a d.-quark than an s-quark.Taking the EOS as an input,the TOV equations are solved numerically,and we show that the mass--radius relation is sensitive to the EOS.The max-imum mass of strange quark stars is not susceptible to the parameter Aq we introduced.     

Automatic Search Dense Connection Module for Super-Resolution

The development of display technology has continuously increased the requirements for image resolution. However, the imaging systems of many cameras are limited by their physical conditions, and the image resolution is often restrictive. Recently, several models based on deep convolutional neural network (CNN) have gained significant performance for image super-resolution (SR), while extensive memory consumption and computation overhead hinder practical applications. For this purpose, we present a lightweight network that automatically searches dense connection (ASDCN) for image super-resolution (SR), which effectively reduces redundancy in dense connection and focuses on more valuable features. We employ neural architecture search (NAS) to model the searching of dense connections. Qualitative and quantitative experiments on five public datasets show that our derived model achieves superior performance over the state-of-the-art models.