Phases of holographic interfaces

We compute the phase diagram of the simplest holographic bottom-up model of conformal interfaces. The model consists of a thin domain wall between three-dimensional Anti-de Sitter (AdS) vacua, anchored on a boundary circle. We distinguish five phases depending on the existence of a black hole, the intersection of its horizon with the wall, and the fate of inertial observers. We show that, like the Hawking-Page phase transition, the capture of the wall by the horizon is also a first order transition and comment on its field-theory interpretation. The static solutions of the domain-wall equations include gravitational avatars of the Faraday cage, black holes with negative specific heat, and an intriguing phenomenon of suspended vacuum bubbles corresponding to an exotic interface/anti-interface fusion. Part of our analysis overlaps with recent work by Simidzija and Van Raamsdonk but the interpretation is different.

Field oriented predictive control strategy for induction machine drives

Purpose This study aims to drive the induction machine system with a low switching frequency. Design/methodology/approach An unconventional inverter control strategy – field-oriented predictive control (FOPC) – is presented. The strategy limits current distortion by setting a boundary circle. The voltage vector, which could keep current trajectories in boundary, is selected to obtain a low switching frequency. Findings A dual simulation step technique is developed to investigate the influence of sampling frequency on current distortion control and switching frequency. Current control distortion can be improved, i.e. reduced, by increasing the sampling frequency; however, the switching frequency will also increase. Such a law is discovered by the dual simulation step technique and finally verified by experiments. Originality/value A new predictive control method, FOPC, is derived from the rotor filed coordinate machine model and presented in this paper. FOPC circumvents derivative calculations, and thus avoids high-frequency noise amplification.

Evaluation of the quality for sheet deep drawing using a magnetorheological fluid (MRF)

Sealing problems, subsequent cleaning processes and poor force transmission effect etc. series of problems which strongly restrict the development and application of traditional medium pressure-based sheet forming technology. To overcome these problems, the magnetorheological fluid (MRF) can be used as the alternative force transmission medium. In this study, the deep drawing process of a 304 stainless steel sheet using MRF was investigated. The die cavity was filled with MRF and electric current was used to quantitatively adjust the magnetic fields distribution, which then controls the deformation behavior of the forming sheet. As compared to the conventional deep drawing process, experimental results clearly show that significant improvement in the produced sample quality was obtained when using the MRF with the electric current of 2 A. These improvements include: the height of the boundary circle reduces by 20%, the wall thickness distribution is more uniform, the rebound ratio correspondingly reduces from 9.6% to 0.67%, and the degree of sticking mode and the size precision are significantly increased. The results of this study provide scientific guidance to solve the bottleneck in the traditional deep drawing forming technology. The potential applications of the MRF-based new deep drawing technology to improve the product quality were explored.

Genus Ranges of Chord Diagrams

A chord diagram consists of a circle, called the backbone, with line segments, called chords, whose endpoints are attached to distinct points on the circle. The genus of a chord diagram is the genus of the orientable surface obtained by thickening the backbone to an annulus and attaching bands to the inner boundary circle at the ends of each chord. Variations of this construction are considered here, where bands are possibly attached to the outer boundary circle of the annulus. The genus range of a chord diagram is the genus values over all such variations of surfaces thus obtained from a given chord diagram. Genus ranges of chord diagrams for a fixed number of chords are studied. Integer intervals that can be, and those that cannot be, realized as genus ranges are investigated. Computer calculations are presented, and play a key role in discovering and proving the properties of genus ranges.

A Method of Detecting Circle by Improved Hough Transform

A new algorithms for parameters of an image irregular boundary circle parameters is presented, which is based on “Curve-Approximate Method” .For a set of an image circle boundary points by image pre-processing, firstly this paper introduces a substitute variant curve approximate reputably while picking out the irregular boundary points in all points, until to fit the terminate condition. Finally, it succeeds to get the optimal estimation of parameters of a circle. Example show that the algorithms runs more quickly and automatically than traditional generalized hough transform, and a good result is obtained if the irregular boundary points is small proportion in all points of a circle.

CONTINUOUS EXTENSIONS ARE NOT HÖLDER

Let Q denote a quadratic polynomial and A∞ the super-attracting basin of Q at the point ∞ on the Riemann sphere [Formula: see text]. There exists a unique Riemann mapping Φ from the open disk [Formula: see text] onto A∞ such that Φ(∞)=∞, Φ'(∞)=1 and Φ-1 conjugates Q:A∞→A∞ to the squaring map S:D→D:z↦z2. In this paper, we show if Q is real and infinitely renormalizable of bounded type then the continuous extension of Φ to the closed disk cannot have any Hölder continuity on the boundary circle [Formula: see text].

Green's function of the clamped punctured disk

If a thin elastic circular plate B: ∣z∣ < 1 is clamped (simply supported, respectively) along its edge ∣z∣ = 1, its deflection at z ∈ B under a point load at ζ ∈ B, measured positively in the direction of the gravitational pull, is the biharmonic Green's function β(z, ζ) of the clamped plate (γ(z, ζ) of the simply supported plate, respectively). We ask: how do β(z, ζ) and γ(z, ζ) compare with the corresponding deflections β0(z, ζ) and γ0(z, ζ) of the punctured circular plate B0: 0 < ∣ z ∣ < 1 that is “clamped” or “simply supported”, respectively, also at the origin? We shall show that γ(z, ζ) is not affected by the puncturing, that is, γ(·, ζ) = γ0(·, ζ), whereas β(·, ζ) is:on B0 × B0. Moreover, while β((·, ζ) is of constant sign, β0(·, ζ) is not. This gives a simple counterexmple to the conjecture of Hadamard [6] that the deflection of a clampled thin elastic plate be always of constant sign:The biharmonic Gree's function of a clampled concentric circular annulus is not of constant sign if the radius of the inner boundary circle is sufficiently small.Earlier counterexamples to Hadamard's conjecture were given by Duffin [2], Garabedian [4], Loewner [7], and Szegö [9]. Interest in the problem was recently revived by the invited address of Duffin [3] before the Annual Meeting of the American Mathematical Society in 1974. The drawback of the counterexample we will present is that, whereas the classical examples are all simply connected, ours is not. In the simplicity of the proof, however, there is no comparison.