1,720,977 research outputs found
Data for Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid
No full textThe dataset contains the solution of the mathematical problem presented in "Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid".
We determine the globally minimum time T needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is assumed to be large so that the drag on the plate arises from skin friction in a thin viscous boundary layer. The minimum is determined computationally using a steepest descent, where an adjoint formulation is used to compute the gradients. Because the equations governing fluid mechanics for this problem are nonlinear, multiple local minima could exist. Exploiting the quadratic nature of the objective function and the constraining differential equations, we derive and apply a ‘spectral condition’ to show the converged local optimum to be a global one. The condition states that the optimum is global if the Hessian of the Lagrangian in the state variables constructed using the converged adjoint field is positive semi-definite at every instance. The globally optimum kinematics of the plate starts from rest with speed ∝t1/4 and comes to rest with speed ∝(T−t)1/4 as a function of time t. For distances much longer than the plate, the work-minimizing kinematics consists of an optimum startup, a constant-speed cruising, and an optimum stopping
Work-minimizing kinematics for small displacement of an infinitely long cylinder
Get PDFWe consider the time-dependent speed of an infinitely long cylinder that minimizes the net work done on the surrounding fluid to travel a given distance perpendicular to its axis in a fixed amount of time. The flow that develops is two-dimensional. An analytical solution is possible using calculus of variations for the case that the distance travelled and the viscous boundary layer thickness that develops are much smaller than the circle radius. If t represents the time since the commencement of motion and T the final time, then the optimum speed profile is Ct^{1/4}(T-t)^{1/4} , where C is determined by the distance travelled. The result also holds for rigid-body translations and rotation of cylinders formed by extrusion of smooth but otherwise arbitrary curves
Two studies in hydrodynamic stability : interfacial instabilities and applications of bounding theory
No full textInterfacial phenomena, viz. roll waves and elastic tremor, are considered in the first
part, whereas in the second bounding theory is applied to double-diffusive convection
and shear flows.
Roll waves are investigated using shallow-water equations with bottom drag and diffusivity.
We explore the effect of bottom topography on linear stability of turbulent flow,
followed by an investigation of the nonlinear dynamics. Low-amplitude topography and
hydraulic jumps are found to destabilize turbulent roll waves, while higher amplitude
topography stabilizes them. The nonlinear dynamics of these waves is explored with
numerical and asymptotic solutions of the shallow-water equations. We find that trains
of roll waves undergo coarsening dynamics, however coarsening does not continue indefinitely
but becomes interrupted at intermediate scales, creating patterns with preferred
wavelengths. We quantify the coarsening dynamics in terms of linear stability of steady
roll-wave trains.
For elastic tremor, e.g. observed in musical reed instruments and vocal cords, a
first principles explanation is given for the onset of these oscillations using linear stability
theory. An analytical solution is built on the assumptions of thin-film flow and
stiff elastic material and the criterion for the destabilization of natural elastic oscillations
is derived. Acoustic excitation (e.g. organ pipes) is treated as an analogue, with
compressibility playing the role of elasticity, with similar mechanism possibly at work.
In double diffusive convection, the flux of the unstably stratified species is bounded
using the background method in the presence of opposite stratification of the other
species. In order to incorporate a dependence of the bound on the stably stratified
component, Joseph's (Stability of fluid motion, 1976, Springer-Verlag) energy stability
112
analysis is extended. At large Rayleigh number, the bound is found to behave like R[sub T][sup ½]
for fixed ratio R[sub S]/R[sub T], where R[sub T] and R[sub S] are the Rayleigh numbers of the unstably and
stably stratified components, respectively.
The energy stability of plane Couette flow is improved for two dimensional perturbations.
The energy is chosen from a family of norms so as to maximize the critical
Reynolds number. An explicit relation for the critical Reynolds number is found in
terms of the perturbation direction.Science, Faculty ofMathematics, Department ofGraduat
Brachistochronous motion of a flat plate parallel to its surface immersed in a fluid
Get PDFWe determine the globally minimum time T needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is assumed to be large so that the drag on the plate arises from skin friction in a thin viscous boundary layer. The minimum is determined computationally using a steepest descent, where an adjoint formulation is used to compute the gradients. Because the equations governing fluid mechanics for this problem are nonlinear, multiple local minima could exist. Exploiting the quadratic nature of the objective function and the constraining differential equations, we derive and apply a ‘spectral condition’ to show the converged local optimum to be a global one. The condition states that the optimum is global if the Hessian of the Lagrangian in the state variables constructed using the converged adjoint field is positive semi-definite at every instance. The globally optimum kinematics of the plate starts from rest with speed ∝t1/4 and comes to rest with speed ∝(T−t)1/4 as a function of time t. For distances much longer than the plate, the work-minimizing kinematics consists of an optimum startup, a constant-speed cruising, and an optimum stopping
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe 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
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