329,308 research outputs found
When is a Stokes line not a Stokes line?
No full textDuring the course of a Stokes phenomenon, an asymptotic expansion can change its form as a further series, prefactored by an exponentially small term and a Stokes multiplier, appears in the representation. The initially exponentially small contribution may nevertheless grow to dominate the behaviour for other values of the asymptotic or associated parameters.We introduce the concept of a higher order Stokes phenomenon, at which a Stokes multiplier itself can change value. We show that the higher order Stokes phenomenon can be used to explain the apparent sudden birth of Stokes lines at regular points, why some Stokes lines are irrelevant to a given problem and why it is indispensible to the proper derivation of expansions that involve three or more possible asymptotic contributions. We provide an example of how the higher order Stokes phenomenon can have important effects on the large time behaviour of linear partial differential equations.Subsequently we apply these techniques to Burgers equation, a non-linear partial differential equation developed to model turbulent fluid flow. We find that the higher order Stokes phenomenon plays a major, yet very subtle role in the smoothed shock wave formation of this equation
NAVIER–STOKES EQUATIONS ON THE β-PLANE
No full textMathematical analysis has been undertaken for the vorticity formulation of the two dimensional Navier–Stokes equation on the β-plane with periodic boundary conditions. This equation describes the flow of fluid near the equator of the Earth. The long time behaviour of the solution of this equation is investigated and we show that, given a sufficiently regular forcing, the solution of the equation is nearly zonal. We use this result to show that, for sufficiently large β, the global attractor of this system reduces to a point. Another result can be obtained if we assume that the forcing is time-independent and sufficiently smooth. If the forcing lies in some Gevrey space, the slow manifold of the Navier–Stokes equation on the β-plane can be approximated with O(εn/2) accuracy for arbitrary n = 0, 1, · · · , as well as with exponential accuracy
Stokes diagnostics of simulated solar magneto-convection
No full textWe present results of synthetic spectro-polarimetric diagnostics of radiative MHD simulations of solar surface convection with magnetic fields. Stokes profiles of Zeeman-sensitive lines of neutral iron in the visible and infrared spectral ranges emerging from the simulated atmosphere have been calculated in order to study their relation to the relevant physical quantities and compare with observational results. We have analyzed the dependence of the Stokes-I line strength and width as well as of the Stokes-V signal and asymmetries on the magnetic field strength. Furthermore, we have evaluated the correspondence between the actual velocities in the simulation with values determined from the Stokes-I (Doppler shift of the centre of gravity) and Stokes-V profiles (zero-crossing shift). We confirm that the line weakening in strong magnetic fields results from a higher temperature (at equal optical depth) in the magnetic flux concentrations. We also confirm that considerable Stokes-V asymmetries originate in the peripheral parts of strong magnetic flux concentrations, where the line of sight cuts through the magnetopause of the expanding flux concentration into the surrounding convective donwflow
Integral representation of a solution to the Stokes-Darcy problem
No full textWith methods of potential theory we develop a representation of a solution of the coupled Stokes-Darcy model in a Lipschitz domain for boundary data in H-1/2
Brain-computer interfacing in rehabilitation
No full textBrain–computer interfacing (BCI) systems involve controlling a computer using brain signals detected by electroencephalography (EEG). Signal processing software uses the EEG signal to control a cursor or application, such as word processing (Birbaumer et al., 1999 and Pfurtscheller et al., 1993). The field of BCI research is at a relatively early stage of producing reliable, robust systems that are widely accessible for everyday use. Several BCI research groups are developing systems to enable communication and environmental control for people with severe disabilities. A more recent area of exploration with BCI is for investigating mechanisms of normal function, dysfunction and recovery, as well as aiding diagnosis and re-training of function. The generation and control of EEG signals for driving a BCI system require training of the user. Methods include imagery tasks, evoked potentials and operant conditioning (for reviews see (Curran and Stokes, 2003 E. Curran and M. Stokes, Brain Cog 51 (2003), pp. 326–335.Curran and Stokes, 2003 and Kübler et al., 2001)). Signal processing techniques continue to be refined (James and Hesse, 2005) and are improving the accuracy and reliability of BCI technology but translation into routine clinical use is limited by several factors influencing accessibility and compliance. Surface or implanted recording devices can be used and for transient use in most areas of rehabilitation, surface electrodes are appropriate. An important aim of BCI research is to bridge the gap between major technological advances and the relatively limited success in practical applications. More clinical disciplines are encouraged to become involved in BCI research to achieve this aim.<br/
Dispelling the Myths Behind First-author Citation Counts
No full textWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Intermittency and regularity issues in 3D Navier-Stokes turbulence
No full textTwo related open problems in the theory of 3 D Navier-Stokes turbulence are discussed in this paper. The first is the phenomenon of intermittency in the dissipation field. Dissipation-range intermittency was first discovered experimentally by Batchelor and Townsend over fifty years ago. It is characterized by spatio-temporal binary behaviour in which long, quiescent periods in the velocity signal are interrupted by short, active ‘events’ during which there are violent fluctuations away from the average. The second and related problem is whether solutions of the 3 D Navier-Stokes equations develop finite time singularities during these events. This paper shows that Leray’s weak solutions of the three-dimensional incompressible Navier-Stokes equations can have a binary character in time. The time-axis is split into ‘good’ and ‘bad’ intervals: on the ‘good’ intervals solutions are bounded and regular, whereas singularities are still possible within the ‘bad’ intervals. An estimate for the width of the latter is very small and decreases with increasing Reynolds number. It also decreases relative to the lengths of the good intervals as the Reynolds number increases. Within these ‘bad’ intervals, lower bounds on the local energy dissipation rate and other quantities, such as || u (·, t )|| ∞ and ||∇ u (·, t )|| ∞ , are very large, resulting in strong dynamics at sub-Kolmogorov scales. Intersections of bad intervals for n ≧1 are related to the potentially singular set in time. It is also proved that the Navier-Stokes equations are conditionally regular provided, in a given ‘bad’ interval, the energy has a lower bound that is decaying exponentially in time.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46170/1/205_2005_Article_382.pd
The numerical solution of the Navier-Stokes equations for laminar incompressible flow past a paraboloid of revolution
No full textA numerical method is presented for the solution of the Navier-Stokes equations for flow past a paraboloid of revolution. The flow field has been computed for a large range of Reynolds numbers. Results are presented for the skinfriction and the pressure together with their respective drag coefficients. The total drag has been checked by means of an application of the momentum theorem.
Análise do acoplamento pressão-velocidade nas equações de Navier-Stokes utilizando o método dos volumes finitos baseado em elementos e solução acoplada
No full textDissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-graduação em Engenharia Mecânica.Este trabalho tem como objetivo estudar os métodos FIELDS e Rhie-Chow para tratamento do acoplamento pressão-velocidade na solução das equações de Navier-Stokes e realizar sua implementação computacional. Estes métodos apresentam diferentes maneiras de introduzir a pressão na equação de conservação da massa para a solução acoplada da pressão e velocidade. Ambos se utilizam de técnicas baseadas em funções de interpolação, que são decorrentes das próprias equações de conservação da quantidade de movimento, de forma a estabelecer um forte acoplamento entre as variáveis das equações. A aplicação em malhas não-estruturadas é realizada através do método dos volumes finitos baseado em elementos. Com o simulador desenvolvido, os métodos FIELDS e Rhie-Chow são avaliados através da solução de problemas conhecidos na literatura. Primeiro, são realizadas avaliações individuais dos métodos quanto à sua estabilidade e consistência. Em seguida são traçados comparativos entre as soluções obtidas. São analisadas características como: qualidade das soluções, convergência, influência do passo de tempo, tempos de solução dos sistemas lineares e montagem da matriz de coeficientes. The main goal of this work is the study of the FIELDS and Rhie-Chow methods for treatment of the pressure-velocity coupling in the solution of the Navier-Stokes equations and develop their computational codes. These methods have different ways of introducing the pressure in the mass conservation equation when a coupled solution is sought. Both use techniques based on interpolation functions, which come from the momentum conservation equations, in a way that a strong coupling between the equations is established. The use on unstructured meshes is performed by the element based finite volume method. The FIELDS and Rhie-Chow methods are evaluated by solving well-known testing problems from the literature. First, they are individually evaluated based on their stability and robustness. Then, the solutions are compared and analyzed according to the following criteria: solution quality, convergence, time step influence, CPU time spent to solve linear systems and assembling the global coefficient matrix
Numerical stabilization of the Stokes problem in vorticity–velocity–pressure formulation
No full textWe work on a vorticity, velocity and pressure formulation of the bidimensional Stokes problem for incompressible fluids. In previous papers, the authors have developed a natural implementation of this scheme. We have then observed that, in case of unstructured meshes with Dirichlet boundary conditions on the velocity, the convergence is not optimal. In this paper, we propose to add ‘‘bubble’’ velocity functions with compact support along the boundary to improve convergence. We then prove a convergence theorem and illustrate by numerical results better behaviour of the scheme in general cases
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