Generalized linear isotherm regularity equation of state applied to metals

A three-parameter equation of state (EOS) without physically incorrect oscillations is proposed based on the generalized Lennard-Jones (GLJ) potential and the approach in developing linear isotherm regularity (LIR) EOS of Parsafar and Mason [J. Phys. Chem., 1994, 49, 3049]. The proposed (GLIR) EOS can include the LIR EOS therein as a special case. The three-parameter GLIR, Parsafar and Mason (PM) [Phys. Rev. B, 1994, 49, 3049], Shanker, Singh and Kushwah (SSK) [Physica B, 1997, 229, 419], Parsafar, Spohr and Patey (PSP) [J. Phys. Chem. B, 2009, 113, 11980], and reformulated PM and SSK EOSs are applied to 30 metallic solids within wide pressure ranges. It is shown that the PM, PMR and PSP EOSs for most solids, and the SSK and SSKR EOSs for several solids, have physically incorrect turning points, and pressure becomes negative at high enough pressure. The GLIR EOS is capable not only of overcoming the problem existing in other five EOSs where the pressure becomes negative at high pressure, but also gives results superior to other EOSs.Comment: 9 pages, 3 figure

The low-noise optimisation method for gearbox in consideration of operating conditions

This paper presents a comprehensive procedure to calculate the steady dynamic response and the noise radiation generated from a stepping-down gearbox. In this process, the dynamic model of the cylindrical gear transmission system is built with the consideration of the time-varying mesh stiffness, gear errors and bearing supporting, while the data of dynamic bearing force is obtained through solving the model. Furthermore, taking the data of bearing force as the excitation, the gearbox vibrations and noise radiation are calculated by numerical simulation, and then the time history of node dynamic response, noise spectrum and resonance frequency range of the gearbox are obtained. Finally, the gearbox panel acoustic contribution at the resonance frequency range is calculated. Based on the conclusions from the gearbox panel acoustic contribution analyses and the mode shapes, two gearbox stiffness improving plans have been studied. By contrastive analysis of gearbox noise radiation, the effectiveness of the improving plans is confirmed. This study has provided useful theoretical guideline to the gearbox design

Binomial coefficients, Catalan numbers and Lucas quotients

Let $p$ be an odd prime and let $a,m$ be integers with $a>0$ and $m \not\equiv0\pmod p$. In this paper we determine $\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k$ mod $p^2$ for $d=0,1$; for example, $$\sum_{k=0}^{p^a-1}\frac{\binom{2k}k}{m^k}\equiv\left(\frac{m^2-4m}{p^a}\right)+\left(\frac{m^2-4m}{p^{a-1}}\right)u_{p-(\frac{m^2-4m}{p})}\pmod{p^2},$$ where $(-)$ is the Jacobi symbol, and $\{u_n\}_{n\geqslant0}$ is the Lucas sequence given by $u_0=0$, $u_1=1$ and $u_{n+1}=(m-2)u_n-u_{n-1}$ for $n=1,2,3,\ldots$. As an application, we determine $\sum_{0<k<p^a,\, k\equiv r\pmod{p-1}}C_k$ modulo $p^2$ for any integer $r$, where $C_k$ denotes the Catalan number $\binom{2k}k/(k+1)$. We also pose some related conjectures.Comment: 24 pages. Correct few typo

Multi-Nozzle Biopolymer Deposition for Freeform Fabrication of Tissue Constructs

Advanced freeform fabrication techniques have been recently used for the construction of tissue scaffolds because of the process repeatability and capability of high accuracy in fabrication resolution at the macro and micro scales. Among many applicable tissue scaffolding materials, polymeric materials have unique properties in terms of the biocompatibility and degradation, and have thus been widely utilized in tissue engineering applications. Hydrogels, such as alginate, has been one of the most important polymer scaffolding materials because of its biocompatibility and internal structure similarity to that of the extracellular matrix of many tissues, and its relatively moderate processing. Three-dimensional deposition has been an entreating freeform fabrication method of biopolymer and particularly hydrogel scaffolds because of its readiness to deposit fluids at ambient temperatures. This paper presents a recent development of biopolymer deposition based freeform fabrication for 3-diemnsinal tissue scaffolds. The system configuration of multi-nozzles used in the deposition of sodium alginate solutions and Poly-?- Caprolactone (PCL) are described. Studies on polymer deposition feasibility and structural formability are conducted, and the preliminary results are presented.Mechanical Engineerin

Modelling and control of the flame temperature distribution using probability density function shaping

This paper presents three control algorithms for the output probability density function (PDF) control of the 2D and 3D flame distribution systems. For the 2D flame distribution systems, control methods for both static and dynamic flame systems are presented, where at first the temperature distribution of the gas jet flames along the cross-section is approximated. Then the flame energy distribution (FED) is obtained as the output to be controlled by using a B-spline expansion technique. The general static output PDF control algorithm is used in the 2D static flame system, where the dynamic system consists of a static temperature model of gas jet flames and a second-order actuator. This leads to a second-order closed-loop system, where a singular state space model is used to describe the dynamics with the weights of the B-spline functions as the state variables. Finally, a predictive control algorithm is designed for such an output PDF system. For the 3D flame distribution systems, all the temperature values of the flames are firstly mapped into one temperature plane, and the shape of the temperature distribution on this plane can then be controlled by the 3D flame control method proposed in this paper. Three cases are studied for the proposed control methods and desired simulation results have been obtained

Substrate effects on quasiparticles and excitons in graphene nanoflakes

The effects of substrate on electronic and optical properties of triangular and hexagonal graphene nanoflakes with armchair edges are investigated by using a configuration interaction approach beyond double excitation scheme. The quasiparticle correction to the energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interactions and exhibit similar dependence on the dielectric constant of the substrate, which leads to a cancellation of their contributions to the optical gap. As a result, the optical gaps are shown to be insensitive to the dielectric environment and unexpectedly close to the single-particle gaps.Comment: 4 pages, 4 figure

Kinetics and mechanism of formic acid decomposition on Ru(001)

The steady-state rate of decomposition of formic acid on Ru(001) has been measured as a function of surface temperature, parametric in the pressure of formic acid. The products of the decomposition reaction are C0_2, H_2, CO, and H_2)0, i.e., both dehydrogenation and dehydration occur on Ru (001). A similar product distribution has been observed on Ni(110), Ni(100), Ru(100), Fe(100), and Ni(111) surfaces; whereas only dehydrogenation to C0_2 and H_2 occurs on the Cu(100), Cu(110), and Pt(111) surfaces. Only reversible adsorption and desorption of formic acid is observed on the less reactive Ag(110) surface at low temperatures, whereas the more reactive Mo(100) surface is oxidized by formic acid at low temperatures with the products of this reaction being H_2, CO, and H_(2)O (Ref. 10). We report here the confirmation of earlier observations of the occurrence of both dehydrogenation and dehydration of formic acid on Ru(001), and more importantly, we provide a detailed mechanistic description of the steady-state decomposition reaction on this surface in terms of elementary steps