Model predictions and experimental results for the rotordynamic characteristics of leakage flows in centrifugal pumps

The role played by fluid forces in determining the rotordynamic stability and characteristics of a centrifugal pump is gaining increasing attention. The present research investigates the contributions to the rotordynamic forces from the discharge-to-suction leakage flows between the front shroud of the rotating impeller and the stationary pump casing. An experiment was designed to measure the rotordynamic shroud forces due to simulated leakage flows for different parameters such as flowrate, shroud clearance, face seal clearance, and eccentricity. The functional dependence on the ratio of whirl frequency to rotating frequency (termed the whirl ratio) is very similar to that measured in experiments and similar to that predicted by the theoretical work of Childs [1]. Childs' bulk flow model yielded some unusual results including peaks in the rotordynamic forces at particular positive whirl ratios, a phenomenon which Childs tentatively described as a "resonance" of the leakage flow. This unexpected phenomenon developed at small positive whirl ratios when the inlet swirl velocity ratio exceeds about 0.5. Childs points out that a typical swirl velocity ratio at inlet (pump discharge) would be about 0.5 and may not, therefore, be large enough for the resonance to be manifest. To explore whether this effect occurs, an inlet guide vane was constructed which introduced a known amount of swirl into the flow upstream of the leakage flow inlet. A detailed comparison of model predictions with the present experimental program is presented. The experimental results showed no evidence of the "resonances," even at much larger swirl inlet velocities than explored by Childs

The Relativistic Rindler Hydrodynamics

We consider a (d+2)-dimensional class of Lorentzian geometries holographically dual to a relativistic fluid flow in (d+1) dimensions. The fluid is defined on a (d+1)-dimensional time-like surface which is embedded in the (d+2)-dimensional bulk space-time and equipped with a flat intrinsic metric. We find two types of geometries that are solutions to the vacuum Einstein equations: the Rindler metric and the Taub plane symmetric vacuum. These correspond to dual perfect fluids with vanishing and negative energy densities respectively. While the Rindler geometry is characterized by a causal horizon, the Taub geometry has a timelike naked singularity, indicating pathological behavior. We construct the Rindler hydrodynamics up to the second order in derivatives of the fluid variables and show the positivity of its entropy current divergence.Comment: 25 pages, 2 appendices; v3: improved presentation, corrected typo

Parity Breaking Transport in Lifshitz Hydrodynamics

We derive the constitutive relations of first order charged hydrodynamics for theories with Lifshitz scaling and broken parity in $2+1$ and $3+1$ spacetime dimensions. In addition to the anomalous (in $3+1$) or Hall (in $2+1$) transport of relativistic hydrodynamics, there is an additional non-dissipative transport allowed by the absence of boost invariance. We analyze the non-relativistic limit and use a phenomenological model of a strange metal to argue that these effects can be measured in principle by using electromagnetic fields with non-zero gradients.Comment: Corrected Appendix A1. Revised the end of subsection 2.1, added the case z \neq

On Non-Relativistic Supersymmetry and its Spontaneous Breaking

We study non-relativistic supersymmetric field theories in diverse dimensions. The theories consist of scalars and fermions and possess two, four or eight real supercharges. We analyze their spontaneous supersymmetry breaking structure and calculate the gapless spectrum. We calculate the perturbative quantum corrections at the supersymmetric vacua and show that while supersymmetry is preserved, scale invariance is broken and the theories are IR free

New Frameworks for Offline and Streaming Coreset Constructions

A coreset for a set of points is a small subset of weighted points that approximately preserves important properties of the original set. Specifically, if $P$ is a set of points, $Q$ is a set of queries, and $f:P\times Q\to\mathbb{R}$ is a cost function, then a set $S\subseteq P$ with weights $w:P\to[0,\infty)$ is an $\epsilon$-coreset for some parameter $\epsilon>0$ if $\sum_{s\in S}w(s)f(s,q)$ is a $(1+\epsilon)$ multiplicative approximation to $\sum_{p\in P}f(p,q)$ for all $q\in Q$. Coresets are used to solve fundamental problems in machine learning under various big data models of computation. Many of the suggested coresets in the recent decade used, or could have used a general framework for constructing coresets whose size depends quadratically on what is known as total sensitivity $t$. In this paper we improve this bound from $O(t^2)$ to $O(t\log t)$. Thus our results imply more space efficient solutions to a number of problems, including projective clustering, $k$-line clustering, and subspace approximation. Moreover, we generalize the notion of sensitivity sampling for sup-sampling that supports non-multiplicative approximations, negative cost functions and more. The main technical result is a generic reduction to the sample complexity of learning a class of functions with bounded VC dimension. We show that obtaining an $(\nu,\alpha)$-sample for this class of functions with appropriate parameters $\nu$ and $\alpha$ suffices to achieve space efficient $\epsilon$-coresets. Our result implies more efficient coreset constructions for a number of interesting problems in machine learning; we show applications to $k$-median/$k$-means, $k$-line clustering, $j$-subspace approximation, and the integer $(j,k)$-projective clustering problem

Relationship Maintenance Persahabatan Jarak Jauh Beda Etnis

Relationship Maintenance Persahabatan Jarak Jauh Beda Etnis merupakan topik yang peneliti angkat sebagai judul skripsi. Persahabatan jarak jauh ini melibatkan sepasang wanita dari dua etnis berbeda yakni dari Papua dan Tionghoa. Dalam penelitian ini juga memaparkan proses bagaimana sepasang wanita ini menjadi sahabat sampai bagaimana mereka mempertahankan persahabatan mereka yang terpisah oleh jarak, dimana JB tinggal di Papua dan ER tinggal di Salatiga. Teknik analisis yang digunakan dalam penelitian ini adalah teknik analisis narasi kualitatif yang menggambarkan relationship maintenance dari persahabatan jarak jauh sepasang wanita yang berbeda etnis tersebut. Hasil temuan dari penelitian ini adalah untuk mempertahankan hubungan persahabatan jarak jauh diperlukan komitmen, cara-cara dalam berkomunikasi dan penggunaan media komunikasi yang dapat mendukung kegiatan komunikasi tersebut guna mempertahankan hubungan persahabatan beda etnis ini