Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

Stiffness and damping coefficients of 3-axial groove water lubricated bearing using perturbation technique

A Computational fluid dynamics (CFD) approach is used to model fluid flow in a journal bearing with three equi-spaced axial grooves and supplied with water from one end. Water is subjected to both velocity (Couette) & pressure induced (Poiseuille) flow. The working fluid passing through the bearing clearance generates driving force components that may increase the unstable vibration of the rotor. It is important to know the accurate rotor dynamic force component for predicting the instability of rotor bearing systems. In this paper a study has been made to obtain the stiffness and damping coefficients of 3 axial groove bearing using Perturbation technique.

The influence of Monte Carlo source parameters on detector design and dose perturbation in small field dosimetry

To obtain accurate Monte Carlo simulations of small radiation fields, it is important model the initial source parameters (electron energy and spot size) accurately. However recent studies have shown that small field dosimetry correction factors are insensitive to these parameters. The aim of this work is to extend this concept to test if these parameters affect dose perturbations in general, which is important for detector design and calculating perturbation correction factors. The EGSnrc C++ user code cavity was used for all simulations. Varying amounts of air between 0 and 2 mm were deliberately introduced upstream to a diode and the dose perturbation caused by the air was quantified. These simulations were then repeated using a range of initial electron energies (5.5 to 7.0 MeV) and electron spot sizes (0.7 to 2.2 FWHM). The resultant dose perturbations were large. For example 2 mm of air caused a dose reduction of up to 31% when simulated with a 6 mm field size. However these values did not vary by more than 2 % when simulated across the full range of source parameters tested. If a detector is modified by the introduction of air, one can be confident that the response of the detector will be the same across all similar linear accelerators and the Monte Carlo modelling of each machine is not required.

The renormalization group: A perturbation method for the graduate curriculum

In this paper the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. Lett., 73 (1994), pp.1311-1315; Phys. Rev. E, 54 (1996), pp.376-394] is presented in a pedagogical way to increase its visibility in applied mathematics and to argue favorably for its incorporation into the corresponding graduate curriculum.The method is illustrated by some linear and nonlinear singular perturbation problems. Key word. © 2012 Society for Industrial and Applied Mathematics.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Tropomyosin Tm5NM1 spatially restricts src kinase activity through perturbation of rab11 vesicle trafficking

In order for cells to stop moving, they must synchronously stabilize actin filaments and their associated focal adhesions. How these two structures are coordinated in time and space is not known. We show here that the actin association protein Tm5NM1, which induces stable actin filaments, concurrently suppresses the trafficking of focal-adhesion-regulatory molecules. Using combinations of fluorescent biosensors and fluorescence recovery after photobleaching (FRAP), we demonstrate that Tm5NM1 reduces the level of delivery of Src kinase to focal adhesions, resulting in reduced phosphorylation of adhesion-resident Src substrates. Live imaging of Rab11-positive recycling endosomes that carry Src to focal adhesions reveals disruption of this pathway. We propose that tropomyosin synchronizes adhesion dynamics with the cytoskeleton by regulating actin-dependent trafficking of essential focal-adhesion molecules.

Efficient probabilistic contingency analysis through a stability measure considering wind perturbation

The integration of stochastic wind power has accentuated a challenge for power system stability assessment. Since the power system is a time-variant system under wind generation fluctuations, pure time-domain simulations are difficult to provide real-time stability assessment. As a result, the worst-case scenario is simulated to give a very conservative assessment of system transient stability. In this study, a probabilistic contingency analysis through a stability measure method is proposed to provide a less conservative contingency analysis which covers 5-min wind fluctuations and a successive fault. This probabilistic approach would estimate the transfer limit of a critical line for a given fault with stochastic wind generation and active control devices in a multi-machine system. This approach achieves a lower computation cost and improved accuracy using a new stability measure and polynomial interpolation, and is feasible for online contingency analysis.

Micropolar flow in a porous channel with high mass transfer

Two dimensional flow of a micropolar fluid in a porous channel is investigated. The flow is driven by suction or injection at the channel walls, and the micropolar model due to Eringen is used to describe the working fluid. An extension of Berman's similarity transform is used to reduce the governing equations to a set of non-linear coupled ordinary differential equations. The latter are solved for large mass transfer via a perturbation analysis where the inverse of the cross-flow Reynolds number is used as the perturbing parameter. Complementary numerical solutions for strong injection are also obtained using a quasilinearisation scheme, and good agreement is observed between the solutions obtained from the perturbation analysis and the computations.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Flow of a micropolar fluid bounded by a stretching sheet

We consider boundary layer flow of a micropolar fluid driven by a porous stretching sheet. A similarity solution is defined, and numerical solutions using Runge-Kutta and quasilinearisation schemes are obtained. A perturbation analysis is also used to derive analytic solutions to first order in the perturbing parameter. The resulting closed form solutions involve relatively complex expressions, and the analysis is made more tractable by a combination of offline and online work using a computational algebra system (CAS). For this combined numerical and analytic approach, the perturbation analysis yields a number of benefits with regard to the numerical work. The existence of a closed form solution helps to discriminate between acceptable and spurious numerical solutions. Also, the expressions obtained from the perturbation work can provide an accurate description of the solution for ranges of parameters where the numerical approaches considered here prove computationally more difficult.

The mechanism of breath aerosol formation

Background: Aerosol production during normal breathing is often attributed to turbulence in the respiratory tract. That mechanism is not consistent with a high degree of asymmetry between aerosol production during inhalation and exhalation. The objective was to investigate production symmetry during breathing. Methods: The aerosol size distribution in exhaled breath was examined for different breathing patterns including normal breathing, varied breath holding periods and contrasting inhalation and exhalation rates. The aerosol droplet size distribution measured in the exhaled breath was examined in real time using an aerodynamic particle sizer. Results and Conclusions: The dependence of the particle concentration decay rate on diameter during breath holding was consistent with gravitational settling in the alveolar spaces. Also, deep exhalation resulted in a 4 to 6 fold increase in concentration and rapid inhalation produced a further 2 to 3 fold increase in concentration. In contrast rapid exhalation had little effect on the measured concentration. A positive correlation of the breath aerosol concentration with subject age was observed. The results were consistent with the breath aerosol being produced through fluid film rupture in the respiratory bronchioles in the early stages of inhalation and the resulting aerosol being drawn into the alveoli and held before exhalation. The observed asymmetry of production in the breathing cycle with very little aerosol being produced during exhalation, is inconsistent with the widely assumed turbulence induced aerosolization mechanism.

Distribution of respiratory droplets in enclosed environments under different air distribution methods

Dispersion characteristics of respiratory droplets in indoor environments are of special interest in controlling transmission of airborne diseases. This study adopts an Eulerian method to investigate the spatial concentration distribution and temporal evolution of exhaled and sneezed/coughed droplets within the range of 1.0~10.0μm in an office room with three air distribution methods, i.e. mixing ventilation (MV), displacement ventilation (DV), and under-floor air distribution (UFAD). The diffusion, gravitational settling, and deposition mechanism of particulate matters are well accounted in the one-way coupling Eulerian approach. The simulation results find that exhaled droplets with diameters up to 10.0μm from normal respiration process are uniformly distributed in MV, while they are trapped in the breathing height by thermal stratifications in DV and UFAD, resulting in a high droplet concentration and a high exposure risk to other occupants. Sneezed/coughed droplets are diluted much slower in DV/UFAD than in MV. Low air speed in the breathing zone in DV/UFAD can lead to prolonged residence of droplets in the breathing zone.

Increasing stochastic perturbations enhances acquisition and learning of complex sport movements

Traditionally, the aquisition of skills and sport movement has been characterised by numerous repetitions of presumed model movement pattern to be acquired by learners. This approach has been questioned by research identifying the presence of individualised movement patterns and the low probability of occurrence of two identical movements within and between individuals. In contrast, the differential learning approach claims advantage for incurring variability in the learning process by adding stochastic perturbations during practice. These ideas are exemplified by data from a high jump experiment which compared the effectiveness of classical and a differential training approach with pre-post test design. Results showed clear advantages for the group with additional stochastic perturbation during the aquisition phase in comparison to classically trained athletes. Analogies to similar phenomenological effects in the neurobiological literature are discussed.