Determination of silica aerogels nanostructure characteristics by using small angle neutron scattering technique

Small angle neutron scattering (SANS) technique has been widely employed in probing the microstructure of amorphous materials in the nanometer range (1 to 100 nm). In this study, small angle neutron scattering was used to study the structure of the silica aerogels and titanium containing silica aerogels by using SANS facility at MINT, Malaysia and BATAN, Indonesia. Besides scattering method, imaging technique such as transmission and scanning electron microscopy (TEM and SEM) can be used to provide real-space structure. However, microscopy image may include artifacts and may not be truly representative of the sample. While SANS does not provide real space structure directly, the technique does probe the sample in its entirety. In this work, the aerogels physical properties such as particle size and fractal dimension as a function of pH were studied. In a typical scattering experiment, an incident neutron beam is bombarded to the sample and is elastically scattered. The scattered intensity is measured as a function of the scattering angle which occurs at small angle of less than 100. Reactor was used as our neutron source. The monochromated neutron beam has a wavelength of 0.5 Ã…. The sample which is in powder form is filled into a quartz cell with a 2 mm pathlength. A complete data set consists of three measurements; scattering measured from the sample, scattering from the empty sample holder and scattering from the dark counts due to complete absorber in sample position. The scattered neutrons were detected by a 128 X 128 array area sensitive, gas-filled proportional counter, which is known as Position Sensitive Detector (PSD). A personal computer which is linked to the PSD neutron counting system is used for data collection. SANS neutron counting system programs include the display of scattered neutron data in two and three dimensional isometric view. The resulting 2D scattering pattern is reduced to 1D profile for further analysis. Plots of I(Q) vs Q were derived. Results show that as pH decreases fractal dimension decreases from 3.60 to 2.44. On the other hand, particle size increases from 9.87 nm to 11.26 nm with decreasing pH of the aerogels. Titanium containing silica aerogels has bigger fractal dimension and smaller particle size compared to silica aerogels

On the first Hochschild cohomology of admissible algebras

Our aim in this paper is to investigate the first Hochschild cohomology of {\em admissible algebras} which can be seen as a generalization of basic algebras. For this purpose, we study differential operators on an admissible algebra. Firstly, differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the $k$-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field $k$ of characteristic $0$.Comment: 16 page

Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young's seminormal basis

Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic $p>0$, $\Delta(\lambda)$ denote the Weyl module of $G$ of highest weight $\lambda$ and $\iota_{\lambda,\mu}:\Delta(\lambda+\mu)\to \Delta(\lambda)\otimes\Delta(\mu)$ be the canonical $G$-morphism. We study the split condition for $\iota_{\lambda,\mu}$ over $\mathbb{Z}_{(p)}$, and apply this as an approach to compare the Jantzen filtrations of the Weyl modules $\Delta(\lambda)$ and $\Delta(\lambda+\mu)$. In the case when $G$ is of type $A$, we show that the split condition is closely related to the product of certain Young symmetrizers and, under some mild conditions, is further characterized by the denominator of a certain Young's seminormal basis vector. We obtain explicit formulas for the split condition in some cases

Register automata with linear arithmetic

We propose a novel automata model over the alphabet of rational numbers, which we call register automata over the rationals (RA-Q). It reads a sequence of rational numbers and outputs another rational number. RA-Q is an extension of the well-known register automata (RA) over infinite alphabets, which are finite automata equipped with a finite number of registers/variables for storing values. Like in the standard RA, the RA-Q model allows both equality and ordering tests between values. It, moreover, allows to perform linear arithmetic between certain variables. The model is quite expressive: in addition to the standard RA, it also generalizes other well-known models such as affine programs and arithmetic circuits. The main feature of RA-Q is that despite the use of linear arithmetic, the so-called invariant problem---a generalization of the standard non-emptiness problem---is decidable. We also investigate other natural decision problems, namely, commutativity, equivalence, and reachability. For deterministic RA-Q, commutativity and equivalence are polynomial-time inter-reducible with the invariant problem

Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters

By transforming an exact stability condition, a new Nyquist-like plot is proposed to predict occurrences of three typical instabilities in DC-DC converters. The three instabilities are saddle-node bifurcation (coexistence of multiple solutions), period-doubling bifurcation (subharmonic oscillation), and Neimark bifurcation (quasi-periodic oscillation). In a single plot, it accurately predicts whether an instability occurs and what type the instability is. The plot is equivalent to the Nyquist plot, and it is a useful design tool to avoid these instabilities. Nine examples are used to illustrate the accuracy of this new plot to predict instabilities in the buck or boost converter with fixed or variable switching frequency.Comment: Submitted to an IEEE journal in 201

Experimental investigation on thermal comfort model between local thermal sensation and overall thermal sensation

To study the human local and overall thermal sensations, a series of experiments under various conditions were carried out in a climate control chamber. The adopted analysis method considered the effect of the weight coefficient of local average skin temperature and density of the cold receptors’ distribution in different local body areas. The results demonstrated that the thermal sensation of head, chest, back and hands is warmer than overall thermal sensation. The mean thermal sensation votes of those local areas were more densely distributed. In addition, the thermal sensation of arms, tight and calf was colder than the overall thermal sensation, which pronounced that thermal sensation votes were more dispersed. The thermal sensation of chest and back had a strong linear correlation with overall thermal sensation. Considering the actual scope of air-conditioning regulation, the human body was classified into three local parts: a) head, b) upper part of body and c) lower part of body. The prediction model of both the three-part thermal sensation and overall thermal sensation was developed. Weight coefficients were 0.21, 0.60 and 0.19 respectively. The model provides scientist basis for guiding the sage installation place of the personal ventilation system to achieve efficient energy use