Transient analysis of a viscoelastic torsion pendulum: Error analysis

The error analysis for the transient torsion pendulum test is developed based on a linearized approximation. Tables are given for the efficient utilization of the equations in evaluating the accuracy range of the test data.     

Transient analysis of a viscoelastic torsion pendulum

The transient torsion pendulum of arbitrary cross section is analyzed as a device for obtaining physical properties of a viscoelastic material. The damped sinusoidal motion yields a damping factor and frequency from which the complex modulus is computed. The particular cases of circular and rectangular cross section are considered with tables and approximations simplifying the practical application of the method.     

Transient analysis of electroosmotic flow in a slit microchannel

The transient aspects of electroosmotic flow in a slit microchannel are studied. Exact solutions for the electrical potential profile and the transient electroosmotic flow field are obtained by solving the complete Poisson-Boltzmann equation and the Navier-Stokes equation under an analytical approximation for the hyperbolic sine function. The characteristics of the transient electroosmotic flow are discussed under influences of the electric double layer and the geometric size of the microchannel.     

Transient analysis of a batch reactor with temperature fluctuations

Temperature fluctuations for two consecutive reactions in a batch reactor have been modeled as Gaussian white noise. Analytical solutions of the Fokker-Plank equations show that noise significantly changes the concentration profiles, lowers the yield and destroys the error distribution.

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Error propagation in normalization of stable isotope data: a Monte Carlo analysis

A higher analytical precision of a stable isotope ratio mass spectrometer does not automatically guarantee accurate determination of the true isotope composition (δ‐value) of samples, since estimates of true δ‐values are obtained from the normalization of raw isotope data. We performed both Monte Carlo simulations and laboratory experiments to investigate aspects of error propagation during the normalization of carbon stable isotope data. We found that increasing both the number of different reference standards and the number of repetitions of each of these standards reduces the normalization error. A 50% reduction in the normalization error can be achieved over the two‐point normalization by either analyzing two standards four times each, or four standards two times each. If the true δ‐value of a sample is approximately known a priori, the normalization error may then be reduced through a targeted choice of locally optimal standards. However, the difference in improvement is minimal and, therefore, a more practical strategy is to use two or more standards covering the whole stable isotope scale. The selection of different sets of standards by different laboratories or for different batches of samples in the same laboratory may lead to significant differences in the normalized δ‐values of the same samples, leading to inconsistent results. Hence, the same set of standards should always be used for a particular element and a particular stable isotope analytical technique. Copyright © 2010 John Wiley & Sons, Ltd.     

On-line fermentation gas analysis: Error analysis and application of mass spectrometry

On-line fermentation gas analysis is of general interest because it permits the determination of metabolic rates in almost any biological process using living organisms. The consumption and production of gases (O₂, CO₂, CH₄, etc.) and volatile compounds may be determined without causing any risk of infection. Elemental balancing permits the determination of other metabolic rates if the stoichiometry is known. This was studied with the production of poly-β-hydroxybutyrate (PHB) by Alcaligenes latus. Estimations were based on the measurement of gas partial pressure and flow-rates, pH and alkali consumption rate. Experiments with a small quadrupole mass spectrometer showed unacceptable error propagation. Therefore, dynamic error propagation for all rates was studied using simulation. It was found that, for example, a 1% relative offset-calibration error for oxygen can result in an error in PHB estimation of > 50%. It is suggested that this culture is used in combination with elemental balancing for thorough tests of the accuracy of on-line gas analysis equipment. An on-line process gas analyser based on a quadrupole mass spectrometer (Balzers PGM 407) gave the following precision values (abs. vol.?%) during cultivation of Bacillus subtilis: nitrogen (m/z 14), 0.024; oxygen (m/z 32), 0.020; argon (m/z 40), 0.0011; and carbon dioxide (m/z 44), 0.0034. These values, combined with automatic recalibration, would be sufficient for reasonable estimation of PHB, biomass and substrates.     

Transient natural convection: scale analysis of dry cooling towers

Journal of Thermal Analysis and Calorimetry - Transient free convection from a heated surface immersed in a cold ambient is investigated using scale analysis. The heated plate is our model for the...     

Power dissipation in a vibrating disc column

The power dissipation in a vibrating disc column of 17.2 cm inside diameter has been measured in a liquid single-phase system and in a gas—liquid two-phase system. For frequencies less than 5 Hz, the power dissipation in the column is mainly controlled by the maximum drag force exerted on the vibrating disc at the maximum velocity of disc vibration and is nearly proportional to (2π Af)³, where A is the amplitude and f is the frequency of disc vibration. An empirical correlation for estimating the instantaneous power dissipation in the vibrating disc column has been obtained. The effect of aeration on the power dissipation in the column is considerably smaller than that on the power dissipation in common stirred tanks with a rotary agitator such as a propeller or turbine impeller.     

Power dissipation in a vibrating disc column

The power dissipation in a vibrating disc column of 17.2 cm inside diameter has been measured in a liquid single-phase system and in a gas—liquid two-phase system. For frequencies less than 5 Hz, the power dissipation in the column is mainly controlled by the maximum drag force exerted on the vibrating disc at the maximum velocity of disc vibration and is nearly proportional to (27π Af)³, where A is the amplitude and f is the frequency of disc vibration. An empirical correlation for estimating the instantaneous power dissipation in the vibrating disc column has been obtained. The effect of aeration on the power dissipation in the column is considerably smaller than that on the power dissipation in common stirred tanks with a rotary agitator such as a propeller or turbine impeller.     

Transient analysis of electrolytically initiated polymerization

Electrochemically initiated polymerization at a planar electrode is treated theoretically and an approximate solution to the full time-dependent problem is found assuming the electrode process to be reversible (so that the Nernst relation holds). The homogeneous kinetics lead to a second-order coupled non-linear initial-boundary value problem, and the method developed for its solution is general and applicable to other problems. The approximate solution is converted to an equation for the transient current-versus-time curve, for electrode initiated polymerization, which can be used for the experimental determination of the polymerization and termination rate constants. An analysis procedure for such determination is outlined.     

Error analysis of idealized nanopore sequencing

This numerical study provides an error analysis of an idealized nanopore sequencing method in which ionic current measurements are used to sequence intact single‐stranded DNA in the pore, while an enzyme controls DNA motion. Examples of systematic channel errors when more than one nucleotide affects the current amplitude are detailed, which if present will persist regardless of coverage. Absent such errors, random errors associated with tracking through homopolymer regions are shown to necessitate reading known sequences (Escherichia coli K‐12) at least 140 times to achieve 99.99% accuracy (Q40). By exploiting the ability to reread each strand at each pore in an array, arbitrary positioning on an error rate versus throughput tradeoff curve is possible if systematic errors are absent, with throughput governed by the number of pores in the array and the enzyme turnover rate.     

Site-directed electronic tunneling through a vibrating molecular network

The effect of electronic-nuclear coupling on electronic transport through a complex molecular network is studied. Electronic tunneling dynamics in a network of N donor/acceptor sites, connected by molecular bridges, is shown to be controlled by electronic-nuclear coupling at the bridges. Particularly, electronic coupling to an accepting nuclear mode at the contact site between the donor and the rest of the network is shown to affect the tunneling path selection to specific acceptors. In the "deep" tunneling regime, the network is mapped onto an N-level system using a recursive perturbation expansion, enabling analytical treatment of the electronic dynamics. The analytic formulation is applied for two model systems, demonstrating site-directed tunneling by electronic-nuclear coupling. Numerical simulations suggest that this phenomenon is not limited to the deep tunneling regime.     

Error analysis in Barker's method: extension to ternary systems

An extension of Barker's method to ternary systems is briefly outlined. Expressions for the standard deviations of the excess molar Gibbs free energy and the equilibrium pressure as functions of composition are obtained. These expressions are applied to accurate experimental data for the cryogenic (liquid) mixture CH₃F+N₂O+Xe recently measured in our laboratory.     

Error analysis and improvements of coupled-cluster theory

Summary The error in the energy of the traditional coupled-cluster (TCC) approach and of several variants is analyzed in terms of the error of the cluster operatorS. A key feature of this analysis is that TCC can be based on an energy functional (asymmetric inS andS ) that is made stationary with respect to variation ofS . The error of TCC scales with the particle numbern, but it is not quadratic in . An improved coupled-cluster method (ICC) is presented that is the next step in a hierarchy from TCC to an exact variational theory. An alternative hierarchy is possible that leads to the extended coupled-cluster (ECC) method of Arponen. Variational (VCC) and unitary (UCC) coupled cluster theories and their stationary conditions and errors are analyzed along similar lines and practicable VCC or UCC approaches are presented. An infinite summation of certain terms in the VCC expectation value is shown to lead to a coupled-pair functional of the type proposed by Ahlrichs. The various CC schemes discussed here are compared on the CC-D, CC-SD and CC-SDT levels and beyond this. Special aspects referring to properties are also discussed.     

Thermodynamic analysis of sorption isotherms of chromium(VI) anionic species on reed biomass

A new sorbent material for removing Cr(VI) anionic species from aqueous solutions has been investigated. Adsorption equilibrium and thermodynamics of Cr(VI) anionic species onto reed biomass were studied at different initial concentrations, sorbent concentrations, pH levels, temperatures, and ionic strength. Equilibrium isotherm was analyzed by Langmuir model. The experimental sorption data fit the model very well. The maximum sorption capacity of Cr(VI) onto reed biomass was found to be 33 mg · g^?1. It was noted that the Cr(VI) adsorption by reed biomass decreased with increase in pH. An increase in temperature resulted in a higher Cr(VI) loading per unit weight of the adsorbent. Removal of Cr(VI) by reed biomass seems to be mainly by chemisorption. The change in entropy (ΔS^°) and heat of adsorption (ΔH^°) for Cr(VI) adsorption on reed biomass were estimated as 2205 kJ · kg^?1 · K^?1 and 822 kJ · kg^?1, respectively. The values of isosteric heat of adsorption varied with the surface loading of Cr(VI).     

Catalytic pyrolysis of Phragmites (reed): Investigation of its potential as a biomass feedstock

In this paper, thermogravimetry, TG, and pyrolysis are used for the thermochemical evaluation of the common reed (Pragmites australis) as a candidate biomass feedstock. The TG analysis indicated that the material loses 4% of its weight below 150 °C through dehydration. The main decomposition reaction occurs between 200 and 390 °C. The rate of weight loss, represented by the derivative thermogravimetric, DTG, signal indicated a multi-step reaction. Kinetic analysis helped in the resolution of the temperature ranges of the overlapping steps. The first step corresponds to the degradation of the hemi-cellulosic fraction and the second to the cellulosic fraction degradation. The TG and DTG signals of reed samples treated with increasing concentration of potassium carbonate (0.6–10 wt%) indicated a catalytic effect of the salt on reed decomposition. The temperature of maximum weight loss rate, DTGmax, exponentially decreased with increasing catalyst content, whilst the initial temperature of the decomposition decreased linearly. The pyrolysis studies were carried out in a Pyrex vertical reactor with sintered glass disc to hold the sample and to aid the fluidization with the nitrogen stream flowing upwards. The reactor was connected to a cyclone and condenser and a gas sampling device. Tar and char are collected and weighed. The gas chromatographic analysis of the evolved gases demonstrated the effect of pyrolysis temperature (400, 450, and 500 °C) on their composition. The temperature increase favors the yields of hydrocarbons, carbon monoxide and hydrogen at the expense of methanol and carbon dioxide. Similarly, reed samples treated with K2CO3 at 10 wt% were pyrolyzed and analyzed. Comparisons for the various parameters (yields, gas composition and carbon–hydrogen recovery) between the untreated and catalyzed reed conversion were also made.     

Error analysis of molecular dynamics and fractal time approximants from a combinatorial perspective

Trotter's theorem forms the theoretical basis of most modern molecular dynamics. In essence this theorem states that a time displacement operator (a Lie operator) constructed by exponentiating a sum of noncommuting operators can be approximated by a product of single operators provided the time interval is "very small." In theory "very small" implies infinitesimally small (at which point the approximate product becomes exact), while in practical analysis a finite time interval is divided into several small subintervals or steps. It follows, therefore, that the larger the number of steps the better the approximation to the exact time displacement operator. The question therefore arises: How many steps are sufficient? For bounded operators, standard theorems are available to provide the answer. In this paper we show that a very simple combinatorial formula can be derived which allows the computation of the global differences (as a function of the number of steps) between the Taylor coefficients of the exact time displacement operator and an approximate one constructed by using a finite number of steps. The formula holds for both bounded and nonbounded operators and shows, quantitatively, what is qualitatively expected-that the error decreases with increasing number of steps. Furthermore, the formula applies irrespective of the complexity of the system, boundary conditions, or the thermodynamic ensemble employed for averaging the initial conditions. The analysis yields explicit expressions for the Taylor coefficients which are then used to compute the errors. In the case of the algorithmically based practical numerical simulations in which fixed, albeit small, steps are repeatedly applied, the rise in the number of steps does not reduce the size of the steps but increases the total time of interest. The combinatorial formula shows that, here, the errors diverge. Furthermore, this work can be used to supplement other efforts such as the use of shadow Hamiltonians where the truncation of the series expansion of the latter will produce errors in the higher order propagator moments.     

Drying of granules in vibrating suspended bed: Engineering simulation

Engineering algorithm for simulation and designing of a continuous convective drying apparatus serving for drying heat-stable and heat-labile granules in a vibratory fluidized bed (vibrating, suspended bed) was suggested. The algorithm was based on a joint use of mass and heat balance equations, empirical dependences, and comparison of technological parameters with parameters got by the mathematical simulation of dynamics in the vibratory fluidized bed of variable weight. For example, we suggested a calculation algorithm of technological parameters of drying the heat-stable zeolite granules in the vibrating suspended bed. The results for a unit cost of heat and moisture evaporation standards in 3-stage drying were compared with the same for pneumatic drying apparatus, with devices of the fluidized and vibratory fluidized beds, and with sublimation dryers known in industry.     

The average hamiltonian view of low-energy scattering by a vibrating molecule

The average hamiltonian theory is used to examine the effect of molecular vibration on low-energy scattering. When the relative motion of the colliding molecules is slow on the timescale of molecular vibration, it is appropriate to transform the problem into an oscillating reference frame and to describe the collision in that frame by the average hamiltonian over one period of oscillation. The first-order result is identical to the distorted-wave Born approximation. High-order corrections introduce phase shifts for elastic scattering due to molecular vibration and provide transition amplitudes for inelastic scattering. The extent to which the higher-order corrections modify the distorted waves establishes criteria for the validity of the DWA. These criteria are used to examine recent distorted-wave calculations of V-V energy transfer rate constants.