Effect of oscillation amplitude on force coefficients of a cylinder oscillated in transverse or in-line directions

A finite difference solution is presented for 2D low Reynolds number flow (Re=140 and 160) past a circular cylinder placed in a uniform flow. The cylinder is oscillated mechanically either in-line or transversely under lock-in conditions. Abrupt jumps between two state curves were found for a cylinder oscillated in in-line direction in the time-mean (TM) values of lift and torque coefficients when plotted against amplitude of oscillation. Pre- and post-jump analysis carried out included the investigation of phase angle differences, limit cycles and flow patterns confirming the existence of switches in the vortex structure at certain oscillation amplitude values. The TM of drag and base pressure coefficient and the rms values of all force coefficients were continuous functions of oscillation amplitude. When the cylinder was oscillated transversely to the main stream, however, no jumps were found in the corresponding curves. Here the TM of lift and torque were found to be zero (true also for a stationary cylinder) at all amplitude values. Even though the transverse oscillation breaks the symmetry of the flow, there appears to be symmetry over a period

Reducible means and reducible inequalities

It is well-known that if a real valued function acting on a convex set satisfies the $n$-variable Jensen inequality, for some natural number $n\geq 2$, then, for all $k\in\{1,\dots, n\}$, it fulfills the $k$-variable Jensen inequality as well. In other words, the arithmetic mean and the Jensen inequality (as a convexity property) are both reducible. Motivated by this phenomenon, we investigate this property concerning more general means and convexity notions. We introduce a wide class of means which generalize the well-known means for arbitrary linear spaces and enjoy a so-called reducibility property. Finally, we give a sufficient condition for the reducibility of the $(M,N)$-convexity property of functions and also for H\"older--Minkowski type inequalities

Első- és másodrendű időbeli diszkretizáció körhenger körüli áramlás esetén

This paper deals with the two-dimensional numerical simulation of low-Reynolds number flow past a stationary circular cylinder using the finite difference method. We investigate the effect of temporal discretization (1st order Euler and 2nd order Runge-Kutta) on force coefficients and Strouhal number. Additionally, solvers for two types of hardware: CPU and GPGPU (General-Purpose computing on Graphics Processing Units) are used for validation of the code. Computations were carried out for Reynolds numbers 100 and 150, for different dimensionless time steps (0.0001; 0.0002; 0.0004; 0.0005) and at different mesh sizes (512x450; 360x260). Computational results obtained for the 1st and 2nd order methods agree well using both CPU and GPGPU, though the latter is much faster. Results also compare well with values in the literature. The 2nd order method is generally considered better, but its advantage of high accuracy at larger time steps cannot be utilized here, since the code demands relatively small time steps (it diverges at larger time steps due to using successive over-relaxation). Results obtained with 1st order Euler discretization proved to be equally accurate in this case

On small bases for which 1 has countably many expansions

Let $q\in(1,2)$. A $q$-expansion of a number $x$ in $[0,\frac{1}{q-1}]$ is a sequence $(\delta_i)_{i=1}^\infty\in\{0,1\}^{\mathbb{N}}$ satisfying $$x=\sum_{i=1}^\infty\frac{\delta_i}{q^i}.$$ Let $\mathcal{B}_{\aleph_0}$ denote the set of $q$ for which there exists $x$ with a countable number of $q$-expansions, and let $\mathcal{B}_{1, \aleph_0}$ denote the set of $q$ for which $1$ has a countable number of $q$-expansions. In \cite{Sidorov6} it was shown that $\min\mathcal{B}_{\aleph_0}=\min\mathcal{B}_{1,\aleph_0}=\frac{1+\sqrt{5}}{2},$ and in \cite{Baker} it was shown that $\mathcal{B}_{\aleph_0}\cap(\frac{1+\sqrt{5}}{2}, q_1]=\{ q_1\}$, where $q_1(\approx1.64541)$ is the positive root of $x^6-x^4-x^3-2x^2-x-1=0$. In this paper we show that the second smallest point of $\mathcal{B}_{1,\aleph_0}$ is $q_3(\approx1.68042)$, the positive root of $x^5-x^4-x^3-x+1=0$. Enroute to proving this result we show that $\mathcal{B}_{\aleph_0}\cap(q_1, q_3]=\{ q_2, q_3\}$, where $q_2(\approx1.65462)$ is the positive root of $x^6-2x^4-x^3-1=0$.Comment: 14 pages, 2 figure

Content-based trust and bias classification via biclustering

In this paper we improve trust, bias and factuality classification over Web data on the domain level. Unlike the majority of literature in this area that aims at extracting opinion and handling short text on the micro level, we aim to aid a researcher or an archivist in obtaining a large collection that, on the high level, originates from unbiased and trustworthy sources. Our method generates features as Jensen-Shannon distances from centers in a host-term biclustering. On top of the distance features, we apply kernel methods and also combine with baseline text classifiers. We test our method on the ECML/PKDD Discovery Challenge data set DC2010. Our method improves over the best achieved text classification NDCG results by over 3--10% for neutrality, bias and trustworthiness. The fact that the ECML/PKDD Discovery Challenge 2010 participants reached an AUC only slightly above 0.5 indicates the hardness of the task