On the Kert\'esz line: Some rigorous bounds

We study the Kert\'esz line of the $q$--state Potts model at (inverse) temperature $\beta$, in presence of an external magnetic field $h$. This line separates two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin-Kasteleyn representation of the model. It is known that the Kert\'esz line $h_K (\beta)$ coincides with the line of first order phase transition for small fields when $q$ is large enough. Here we prove that the first order phase transition implies a jump in the density of the infinite cluster, hence the Kert\'esz line remains below the line of first order phase transition. We also analyze the region of large fields and prove, using techniques of stochastic comparisons, that $h_K (\beta)$ equals $\log (q - 1) - \log (\beta - \beta_p)$ to the leading order, as $\beta$ goes to $\beta_p = - \log (1 - p_c)$ where $p_c$ is the threshold for bond percolation.Comment: 11 pages, 1 figur

Depth map compression via 3D region-based representation

In 3D video, view synthesis is used to create new virtual views between encoded camera views. Errors in the coding of the depth maps introduce geometry inconsistencies in synthesized views. In this paper, a new 3D plane representation of the scene is presented which improves the performance of current standard video codecs in the view synthesis domain. Two image segmentation algorithms are proposed for generating a color and depth segmentation. Using both partitions, depth maps are segmented into regions without sharp discontinuities without having to explicitly signal all depth edges. The resulting regions are represented using a planar model in the 3D world scene. This 3D representation allows an efficient encoding while preserving the 3D characteristics of the scene. The 3D planes open up the possibility to code multiview images with a unique representation.Postprint (author's final draft

Automatic waterline registration of a ship model in waves

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ACTIVE HIP ACTUATION FOR WALKING BIPED WITH PASSIVE OPTION

Biped robots are desired as the ideal solution over wheel vehicles when traversing over rough terrain due to the simplicity and efficiency when mimicking the natural and dynamic motion of a human gait. The Intelligent Systems and Automation Laboratory (ISAL) at the University of Kansas designed and built a three legged 2D biped walking robot to establish a testbed for future testing. This paper focuses on the development and testing of a novel hip joint that allows actuation with the ability to remain passive. This study was completed concurrently with the development of a full robot as part of other projects. The biped robot, known as the Jaywalker, is comprised of two main actuation systems: the Hybrid Parallel Ankle Actuator (HPAA) and the Hip Ratchet System (HRS). This study focused on the design and testing of the HRS which achieves hip actuation through the use of a locking mechanism integrated into each hip joint that couples the legs to a shared drive system. The ability to lock and unlock the hip joint through the HRS enables the Jaywalker to function in passive or actuated states at the hips. Testing of the HRS was conducted in both passive and actuated states on the Jaywalker testbed. Testing of the hip provided proof in the concept of using a single drive in combination with a ratchet mechanism to actuate the hip while providing a passive option. The HRS also provided the capability to vary step lengths future testing that requires turning, rough terrain, and stair climbing

Wave effects on the turning ability of an ultra large container ship in shallow water

The influence of waves on ship behaviour can lead to hazardous scenarios which put at risk the ship, the crew and the surroundings. For this reason, investigating the effect of waves on manoeuvring is of relevant interest. Waves may impair the overall manoeuvring performance of ships hence increasing risks such as collisions, which are of critical importance when considering dense traffic around harbour entrances and in unsheltered access channels. These are conditions met by Ultra Large Container Ships (ULCS) when approaching a port, e.g. in the North Sea access channels to the main sea ports of Belgium. Note that due to the large draft of ULCS and the limited water depth, shallow water effects will also influenced the ship. Thus, in such scenarios the combined effects of shallow water and waves on the ship's manoeuvring need to be studied. The present work investigates the effect of waves on the turning ability of an ULCS in shallow water. Simulations are carried out using the two time scale approach. The restricted water depth corresponds to 50% Under Keel Clearance (UKC). To gain a better insight on the forces acting on the ship, the propulsion, and the rudder behaviour in waves experimental studies were conducted. These tests were carried out in the Towing Tank for Manoeuvres in Confined Water at Flanders Hydraulics Research (in co-operation with Ghent University) with a scale model of an ULCS. Different wave lengths, wave amplitudes, ships speeds, propeller rates, and rudder angles were tested. The turning ability characteristics obtained from simulations in waves and calm water are presented, and discussed

On the discovery of non-Euclidean geometry

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carlos Dorce[en] The main goal of this work is to investigate the historical transition from Euclidean to non-Euclidean geometry, to understand what the motivation of such a transition was and to understand to the best of my abilities how it was achieved. This will be done by reviewing the relevant authors’ original work and the correspondence between some of them