Fully Coupled Thermo-Hydrodynamic Simulation Model for Journal Bearings

The isothermal form of Reynolds fluid film equation is used to predict the pressure generation in hydrodynamic journal bearings if temperature effects are neglected. Often, however, temperature effects may be important and cannot be neglected, because oil viscosity significantly varies with temperature. Also, thermal expansion of journal shaft and bearing housing must be taken into account since the bearing clearance changes with increasing temperature. Hence, the Reynolds pressure field equation, the energy equation for the fluid film and the heat transfer equations for journal and bearing housing have to be solved simultaneously. The coupled thermo-hydrodynamic fluid flow problem is mathematically defined by a system of nonlinear integro-differential equations. The governing equations are discretized and solved by a finite element approach. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A covariant representation of the Ball–Chiu vertex

In nonabelian gauge theory the three-gluon vertex function contains important structural information, in particular on infrared divergences, and is also an essential ingredient in the Schwinger–Dyson equations. Much effort has gone into analyzing its general structure, and at the one-loop level also a number of explicit computations have been done, using various approaches. Here we use the string-inspired formalism to unify the calculations of the scalar, spinor and gluon loop contributions to the one-loop vertex, leading to an extremely compact representation in all cases. The vertex is computed fully off-shell and in dimensionally continued form, so that it can be used as a building block for higher-loop calculations. We find that the Bern–Kosower loop replacement rules, originally derived for the on-shell case, hold off-shell as well. We explain the relation of the structure of this representation to the low-energy effective action, and establish the precise connection with the standard Ball–Chiu decomposition of the vertex. This allows us also to predict that the vanishing of the completely antisymmetric coefficient function S   of this decomposition is not a one-loop accident, but persists at higher-loop orders. The sum rule found by Binger and Brodsky, which leads to the vanishing of the one-loop vertex in N=4$N=4$ SYM theory, in the present approach relates to worldline supersymmetry.     

Specifications of dust-ion-acoustic shock waves affected by dust charge variation in four-component dissipative quantum plasma

ABSTRACT

Nonlinear propagation of dust-ion-acoustic shock waves in an unmagnetized, collisionless four-component quantum plasma containing electrons, positrons, ions and negatively charged dust grains affected by dust charge variations and viscosity of ions is studied using quantum hydrodynamic model. Considering dust charge variation give rise to calculating of charging currents of the plasma particles. These currents have been calculated with orbit limited motion theory and using Fermi-distribution functions or Boltzmann–Maxwell distribution depending on quantum or classical particles, respectively. The basic characteristics of quantum dust-ion-acoustic shock waves are investigated by deriving Korteweg–de Vries–Burgers equation under the reductive perturbation method. Depending on the relative values of the dispersive and dissipative coefficients, oscillatory and monotonic shock waves can propagate in the plasma model. The effect of chemical potential and density of dust particles on the shock wave’s height and thickness is investigated. In addition, the critical value of H (H_c) is calculated and it is shown that for R?>?0 compressive shock waves and for R?<?0 rarefactive ones can exist. The present study is applicable to researchers on quantum nonlinear structures in dense astrophysical objects and ultra-small micro- and nano-electronic devices.     

Cohen–Macaulay Modules in Dimension >s and Results on Local Cohomology

Let (R,𝔪) be a local ring and s ≥ ?1. Using the notion of M-sequence in dimension > s, we introduce Cohen–Macaulay modules in dimension > s. Among other things concerning Cohen–Macaulay modules in dimension > s, some finiteness results of the support and the associated primes of local cohomology modules are investigated.     

A study on the early-stage decomposition in the Al–Mg–Si–Cu alloy AA6111 by electrical resistivity and three-dimensional atom probe

Electrical resistivity measurements and three-dimensional atom probe (3DAP) analysis were employed to investigate early-stage decomposition of the Al alloy AA6111 in the temperature range 60–180°C where electrical resistivity initially increased with ageing time. 3DAP measurements provided information on the shape, number density and solute content of the precipitates, as well as the solute concentration of the matrix, for the ageing conditions corresponding to the resistivity maxima. Using the 3DAP results, the precipitate size distributions for these ageing conditions were determined in terms of the measured number of solute atoms per precipitate. The number density and the Cu content of the precipitates decreased with increasing temperature, whereas the Mg/Si ratio increased. The size distribution of precipitates at the higher ageing temperatures showed the addition of larger size precipitates to the precipitate population. A modification to Matthiessen's law was employed to describe the anomalous resistivity increase by considering the effect of solutes and precipitates on the resistivity evolution. Using the 3DAP results in analysing the resistivity anomaly, it was found that the decrease in the resistivity maxima with increasing temperature was associated with the decrease in the number density of precipitates and not the scattering power of precipitates. The 3DAP results were further used to provide information on the mechanisms of early-stage decomposition and the temperature dependence of the nucleation rate. From this, the nucleation rate appeared to be controlled by the migration of solute atoms, which was assisted by quenched-in vacancies.     

Numerical solution of fractional differential equations via a Volterra integral equation approach

The main focus of this paper is to present a numerical method for the solution of fractional differential equations. In this method, the properties of the Caputo derivative are used to reduce the given fractional differential equation into a Volterra integral equation. The entire domain is divided into several small domains, and by collocating the integral equation at two adjacent points a system of two algebraic equations in two unknowns is obtained. The method is applied to solve linear and nonlinear fractional differential equations. Also the error analysis is presented. Some examples are given and the numerical simulations are also provided to illustrate the effectiveness of the new method.     

Weighted Composition Operators Between Zygmund Type Spaces and Their Essential Norms

Let ${u \in \mathcal{H}(\mathbb{D})}$ and φ be an analytic self-map of ${\mathbb{D}}$ . We estimate the essential norms of weighted composition operators uC _φ acting on Zygmund type spaces in terms of u, φ, their derivatives and the n-th power φ ⁿ of φ. Moreover, we give similar characterizations for boundedness of uC _φ between Zygmund type spaces.     

Turbulent combined forced and natural convection of nanofluid in a 3D rectangular channel using two-phase model approach

Journal of Thermal Analysis and Calorimetry - The nanofluid is a mixture of base fluid and solid nanoparticles in nanosize. The heat transfer generated by the nanofluid is more than the base fluid...     

Preparation of an efficient catalyst through injection of CuI on modified poly (styrene-co-maleic anhydride) and theoretical investigation of the structural and electronic properties of catalyst

A novel polymer supported [poly (styrene-co-maleic imide) (SMI)]Cu(I) nano-particles was prepared via in situ reaction of 4-amino-5-methyl-4H-1,2,4-triazole-3-thione with [poly (styrene-co-maleic anhydride)] (SMA) along with immobilization of CuI. These nano-particles were fully characterized by using scanning electron microscopy (SEM), energy dispersive spectroscopy analysis, Xray (EDAX), inductively coupled plasma (ICP) analysis, ¹H NMR and FT-IR techniques. Moreover, the structural and electronic features of metal–ligand interactions in the complex model of polymer-supported copper nanocatalyst were assessed using density functional theory calculations. The catalytic activity of these supported Cu(I) nonoparticles was examined in one of the classiest name reaction so–called “click reaction” which is coined K. B Sharpless for the regioselective synthesis of 1,2,3-triazole derivatives using a multicomponent reaction (MCR) involving benzyl halides, sodium azide and terminal alkynes in water as a green solvent. This heterogeneous catalyst showed excellent catalytic activity and was separated by simple filtration and was used at least in five consecutive runs without a significant decrease in its activity.