Analysis of regular and irregular acoustic streaming patterns in a rectangular enclosure

This study reports an experimental investigation of the non-linear phenomena of regular (classical) and irregular streaming patterns generated in an air-filled rigid-walled square channel subjected to the acoustic standing waves of different frequencies and intensities. The interaction of acoustic waves and thermoviscous fluids is responsible for these phenomena. The resonator’s walls are maintained at isothermal condition. Synchronized particle image velocimetry (PIV) technique has been used to measure the streaming velocity fields. The experimental results show that at a given excitation frequency, regular streaming flow patterns are observed up to a certain value of the excitation amplitude. As the amplitude increases beyond this limit, the regular streaming is distorted to an irregular flow structure. The regular and irregular streaming are classified in terms of streaming Reynolds number . It is found that for Re_s2<50, classical streaming flow patterns are established and then deform to irregular and complex shapes as Re_s2 exceeds 50.     

Charged Pion Form Factor Determination in the Range of Q2 = 0.6 ～ 1.6 (GeV/c)2

Using the most recent differential cross section data for ep quasi-elastic scattering, the charged pion formation and its form factor Fπ is calculated in the energy range of 2.4 ～ 4 GeV at Q2 = 0.6 ～ 1.6 (GeV/c)2. The functional dependence of the charged pion form factor to the separated cross section σL is investigated and compared to the previously determined result.     

Uniform silver nanoparticles on tunable porous N‐doped carbon nanospheres for aerobic oxidative synthesis of aryl nitriles from benzylic alcohols

Tunable N‐doped carbon nanospheres from sucrose as carbon source and Tris(2‐aminoethyl)amine (TAEA) as nitrogen source by a simple and easily reproducible method were prepared. It was demonstrated that the tunable N‐doping of carbon spheres could be realized by altering the ratio of TAEA in the raw materials. The content of doped nitrogen, surface area, pore volume and pore size of carbon nanospheres were increased with the increasing of TAEA amount in the hydrothermal process. Prepared N‐doped carbon nanospheres act as solid ligand for anchoring of Ag NPs which generated via chemical reduction of Ag ions. Benzylic alcohols and aldehydes were converted into the aryl nitriles by using Ag/N‐CS‐1 nanospheres as the catalyst and O₂ as the oxidant, efficiently. This catalyst was stable and could use for 6 successful runs.     

Studies of a mathematical model for temperature-modulated bioluminescence tomography

We introduce and study a mathematical model for temperature-modulated bioluminescence tomography (TBT). The model is capable of self-adjusting values of experimental parameters that are used in the formulation. Major theoretical results of this article include: Solution existence of the model, convergence of numerical solutions, an iterative scheme based on linearization, studies of the solution limiting behaviours when normalized total energy function and/or some or all the energy percentages in individual spectral bands are known exactly. Several numerical examples are included to illustrate the improvement of the accuracy of the reconstructed bioluminescent source distribution due to the employment of measurements from multiple temperature distributions.     

Thallium(I) supramolecular compounds: Structural and properties consideration

During the last two decades, supramolecular compounds and especially coordination polymers have received great attention and the number of their synthesized compounds is still growing, which is mainly due to their potential application in various fields such as microelectronics, nonlinear optics, ion exchange, catalysis, gas storage, separation and luminescence. Formation of polymers with main group metal ions such as thallium(I) is disproportionately sparse when compared with those of other metals. Because of the interest structures, properties and applications of thallium polymers, it is necessary to understand thallium's ability to bind donors and form supramolecular compounds. This review tries to give an overview of all supramolecular compounds which were reported from thallium(I) after 1990 and to investigate their properties and applications. Thallium(I) usually forms neutral species and exhibits greater tendency to forming one-dimensional supramolecular compounds. Thallium(I) also favors secondary interactions on its coordination sphere (especially with unsaturated carbon atoms forms organometallic polymers) with stereochemically active lone pair and hemidirected coordination sphere around it.     

The finiteness dimension of local cohomology modules and its dual notion

Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. We explore the behavior of the two notions f_a(M), the finiteness dimension of M with respect to a, and, its dual notion q_a(M), the Artinianness dimension of M with respect to a. When (R,m) is local and r?f_a(M) is less than , the m-finiteness dimension of M relative to a, we prove that is not Artinian, and so the filter depth of a on M does not exceed f_a(M). Also, we show that if M has finite dimension and is Artinian for all i>t, where t is a given positive integer, then is Artinian. This immediately implies that if q?q_a(M)>0, then is not finitely generated, and so f_a(M)≤q_a(M).     

Anderson Polymer in a Fractional Brownian Environment: Asymptotic Behavior of the Partition Function

We consider the Anderson polymer partition function

$$\begin{aligned} u(t):=\mathbb {E}^X\left[ e^{\int _0^t \mathrm {d}B^{X(s)}_s}\right] \,, \end{aligned}$$

where \(\{B^{x}_t\,;\, t\ge 0\}_{x\in \mathbb {Z}^d}\) is a family of independent fractional Brownian motions all with Hurst parameter \(H\in (0,1)\), and \(\{X(t)\}_{t\in \mathbb {R}^{\ge 0}}\) is a continuous-time simple symmetric random walk on \(\mathbb {Z}^d\) with jump rate \(\kappa \) and started from the origin. \(\mathbb {E}^X\) is the expectation with respect to this random walk. We prove that when \(H\le 1/2\), the function u(t) almost surely grows asymptotically like \(e^{\lambda t}\), where \(\lambda >0\) is a deterministic number. More precisely, we show that as t approaches \(+\infty \), the expression \(\{\frac{1}{t}\log u(t)\}_{t\in \mathbb {R}^{>0}}\) converges both almost surely and in the \(\hbox {L}^1\) sense to some positive deterministic number \(\lambda \). For \(H>1/2\), we first show that \(\lim _{t\rightarrow \infty } \frac{1}{t}\log u(t)\) exists both almost surely and in the \(\hbox {L}^1\) sense and equals a strictly positive deterministic number (possibly \(+\infty \)); hence, almost surely u(t) grows asymptotically at least like \(e^{\alpha t}\) for some deterministic constant \(\alpha >0\). On the other hand, we also show that almost surely and in the \(\hbox {L}^1\) sense, \(\limsup _{t\rightarrow \infty } \frac{1}{t\sqrt{\log t}}\log u(t)\) is a deterministic finite real number (possibly zero), hence proving that almost surely u(t) grows asymptotically at most like \(e^{\beta t\sqrt{\log t}}\) for some deterministic positive constant \(\beta \). Finally, for \(H>1/2\) when \(\mathbb {Z}^d\) is replaced by a circle endowed with a Hölder continuous covariance function, we show that \(\limsup _{t\rightarrow \infty } \frac{1}{t}\log u(t)\) is a deterministic finite positive real number, hence proving that almost surely u(t) grows asymptotically at most like \(e^{c t}\) for some deterministic positive constant c.