Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

An electroanalytical application of 2-aminothiazole-modified silica gel after adsorption and separation of Hg(II) from heavy metals in aqueous solution

2-Aminothiazole covalently attached to a silica gel surface was prepared in order to obtain an adsorbent for Hg(II) ions having the following characteristics: good sorption capacity, chemical stability under conditions of use, and, especially, high selectivity. The accumulation voltammetry of mercury(II) was investigated at a carbon paste electrode chemically modified with silica gel functionalized with 2-aminothiazole (SIAMT-CPE). The repetitive cyclic voltammogram of mercury(II) solution in the potential range -0.2 to + 0.6 V versus Ag/AgCl (0.02 mol L-1 KNO3; V = 20 mV s(-1)) show two peaks one at about 0.1 V and other at 0.205 V. The anodic wave peak at 0.205 V is well defined and does not change during the cycles and it was therefore further investigated for analytical purposes using differential pulse anodic stripping voltammetry in differents supporting electrolytes. The mercury response was evaluated with respect to pH, electrode composition, preconcentration time, mercury concentration, cleaning solution, possible interferences and other variables. The precision for six determinations (n = 6) of 0.02 and 0.20 mg L-1 Hg(II) was 4.1 and 3.5% (relative standard deviation), respectively. The detection limit was estimated as 0.10 mu g L-1 mercury(II) by means of 3:1 current-to-noise ratio in connection with the optimization of the various parameters involved and using the highest-possible analyser sensitivity. (c) 2006 Elsevier Ltd. All rights reserved.

The separation of secondary oil-water dispersions in particulate beds

The literature relating to haze formation, methods of separation, coalescence mechanisms, and models by which droplets <100 μm are collected, coalesced and transferred, have been reviewed with particular reference to particulate bed coalescers. The separation of secondary oil-water dispersions was studied experimentally using packed beds of monosized glass ballotini particles. The variables investigated were superficial velocity, bed depth, particle size, and the phase ratio and drop size distribution of inlet secondary dispersion. A modified pump loop was used to generate secondary dispersions of toluene or Clairsol 350 in water with phase ratios between 0.5-6.0 v/v%.Inlet drop size distributions were determined using a Malvern Particle Size Analyser;effluent, coalesced droplets were sized by photography. Single phase flow pressure drop data were correlated by means of a Carman-Kozeny type equation. Correlations were obtained relating single and two phase pressure drops, as (ΔP2/μc)/ΔP1/μd) = kp Ua Lb dcc dpd Cine A flow equation was derived to correlate the two phase pressure drop data as, ΔP2/(ρcU2) = 8.64*107 [dc/D]-0.27 [L/D]0.71 [dp/D]-0.17 [NRe]1.5 [e1]-0.14 [Cin]0.26  In a comparison between functions to characterise the inlet drop size distributions a modification of the Weibull function provided the best fit of experimental data. The general mean drop diameter was correlated by: q_p q_p p_q /β      Γ ((q-3/β) +1) d qp = d fr  .α        Γ ((P-3/β +1 The measured and predicted mean inlet drop diameters agreed within ±15%. Secondary dispersion separation depends largely upon drop capture within a bed. A theoretical analysis of drop capture mechanisms in this work indicated that indirect interception and London-van der Waal's mechanisms predominate. Mathematical models of dispersed phase concentration m the bed were developed by considering drop motion to be analogous to molecular diffusion.The number of possible channels in a bed was predicted from a model in which the pores comprised randomly-interconnected passage-ways between adjacent packing elements and axial flow occured in cylinders on an equilateral triangular pitch. An expression was derived for length of service channels in a queuing system leading to the prediction of filter coefficients. The insight provided into the mechanisms of drop collection and travel, and the correlations of operating parameters, should assist design of industrial particulate bed coalescers.

An electroanalytical application of 2-aminothiazole-modified silica gel after adsorption and separation of Hg(II) from heavy metals in aqueous solution

2-Aminothiazole covalently attached to a silica gel surface was prepared in order to obtain an adsorbent for Hg(II) ions having the following characteristics: good sorption capacity, chemical stability under conditions of use, and, especially, high selectivity. The accumulation voltammetry of mercury(II) was investigated at a carbon paste electrode chemically modified with silica gel functionalized with 2-aminothiazole (SIAMT-CPE). The repetitive cyclic voltammogram of mercury(II) solution in the potential range -0.2 to + 0.6 V versus Ag/AgCl (0.02 mol L-1 KNO3; V = 20 mV s(-1)) show two peaks one at about 0.1 V and other at 0.205 V. The anodic wave peak at 0.205 V is well defined and does not change during the cycles and it was therefore further investigated for analytical purposes using differential pulse anodic stripping voltammetry in differents supporting electrolytes. The mercury response was evaluated with respect to pH, electrode composition, preconcentration time, mercury concentration, cleaning solution, possible interferences and other variables. The precision for six determinations (n = 6) of 0.02 and 0.20 mg L-1 Hg(II) was 4.1 and 3.5% (relative standard deviation), respectively. The detection limit was estimated as 0.10 mu g L-1 mercury(II) by means of 3:1 current-to-noise ratio in connection with the optimization of the various parameters involved and using the highest-possible analyser sensitivity. (c) 2006 Elsevier Ltd. All rights reserved.

Ceramic membranes for separation of proteins and DNA by in situ growth of alumina nanofibres with a nanomesh of metal oxide nanofibres

Ceramic membranes were fabricated by in situ synthesis of alumina nanofibres in the pores of an alumina support as a separation layer, and exhibited a high permeation selectivity for bovine serum albumin relative to bovine hemoglobin (over 60 times) and can effectively retain DNA molecules at high fluxes.

Separation of acoustic emission signals from small size multi-cylinder diesel engine

This paper presents techniques which can lead to diagnosis of faults in a small size multi-cylinder diesel engine. Preliminary analysis of the acoustic emission (AE) signals is outline, including time-frequency analysis and selection of optimum frequency band.The results of applying mean field independent component analysis (MFICA) to separate the AE root mean square (RMS) signals and the effects of changing parameter values are also outlined. The results on separation of RMS signals show thsi technique has the potential of increasing the probability to successfully identify the AE events associated with the various mechanical events within the combustion process of multi-cylinder diesel engines.

To separate or not to separate? Parental decision-making regarding the separation of twins in the early years of schooling

In recent times concerns about possible adverse effects of early separation and advocacy for individual rights have resulted in a movement away from organizational level policies about the separation of twin children as they enter school. Instead, individualized approaches that focus on the twin children’s characteristics and family perspectives have been proposed. This study, conducted in Australia where all but a few families had choice about the class placement of their twin children, questioned parents (N = 156) about their placement decisions. Results indicated that most parents opted for placement together in the early years of schooling. The choice to separate twins at school entry was associated with parent identification of risk in the twin relationship, while being kept together was associated with parent identification of absence of such risk. The findings are discussed in light of the current evidence against separation, and suggest that parent choices regarding the separation of twin children in the early years are informative to educational policy and practice.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.

On separation of concurrency and conflicts in acyclic process models

Recently, a new approach for structuring acyclic process models has been introduced. The algorithm is based on a transformation between the Refined Process Structure Tree (RPST) of a control flow graph and the Modular Decomposition Tree (MDT) of ordering relations. In this paper, an extension of the algorithm is presented that allows to partially structure process models in the case when a process model cannot be structured completely. We distinguish four different types of unstructuredness of process models and show that only two are possible in practice. For one of these two types of unstructuredness an algorithm is proposed that returns the maximally structured representation of a process model.

Single-step synthesis and magnetic separation of graphene and carbon nanotubes in arc discharge plasmas

The unique properties of graphene and carbon nanotubes made them the most promising nanomaterials attracting enormous attention, due to the prospects for applications in various nanodevices, from nanoelectronics to sensors and energy conversion devices. Here we report on a novel deterministic, single-step approach to simultaneous production and magnetic separation of graphene flakes and carbon nanotubes in an arc discharge by splitting the high-temperature growth and low-temperature separation zones using a non-uniform magnetic field and tailor-designed catalyst alloy, and depositing nanotubes and graphene in different areas. Our results are very relevant to the development of commercially-viable, single-step production of bulk amounts of high-quality graphene.

Charged-controlled separation of nitrogen from natural gas using boron nitride fullerene

Natural gas (the main component is methane) has been widely used as a fuel and raw material in industry. Removal of nitrogen (N2) from methane (CH4) can reduce the cost of natural gas transport and improve its efficiency. However, their extremely similar size increases the difficulty of separating N2 from CH4. In this study, we have performed a comprehensive investigation of N2 and CH4 adsorption on different charge states of boron nitride (BN) nanocage fullerene, B36N36, by using a density functional theory approach. The calculational results indicate that B36N36 in the negatively charged state has high selectivity in separating N2 from CH4. Moreover, once the extra electron is removed from the BN nanocage, the N2 will be released from the material. This study demonstrates that the B36N36 fullerene can be used as a highly selective and reusable material for the separation of N2 from CH4. The study also provides a clue to experimental design and application of BN nanomaterials for natural gas purification.