Luttinger-Liquid Behavior in the Alternating Spin-Chain System Copper Nitrate

We determine the phase diagram of copper nitrate Cu(NO$_3$)$_2\cdot$2.5D$_2$O in the context of quantum phase transitions and novel states of matter. We establish this compound as an ideal candidate to study quasi-1D Luttinger liquids, 3D Bose-Einstein-Condensation of triplons, and the crossover between 1D and 3D physics. Magnetocaloric effect, magnetization, and neutron scattering data provide clear evidence for transitions into a Luttinger liquid regime and a 3D long-range ordered phase as function of field and temperature. Theoretical simulations of this model material allow us to fully establish the phase diagram and to discuss it in the context of dimerized spin systems.Comment: 5 pages, 4 figure

Dealloying of Platinum-Aluminum Thin Films Part II. Electrode Performance

Highly porous Pt/Al thin film electrodes on yttria stabilized zirconia electrolytes were prepared by dealloying of co-sputtered Pt/Al films. The oxygen reduction capability of the resulting electrodes was analyzed in a solid oxide fuel cell setup at elevated temperatures. During initial heating to 523 K exceptionally high performances compared to conventional Pt thin film electrodes were measured. This results from the high internal surface area and large three phase boundary length obtained by the dealloying process. Exposure to elevated temperatures of 673 K or 873 K gave rise to degradation of the electrode performance, which was primarily attributed to the oxidation of remaining Al in the thin films.Comment: 5 pages, 4 figure

Modeling and control of UAV bearing formations with bilateral high-level steering

In this paper we address the problem of controlling the motion of a group of unmanned aerial vehicles (UAVs) bound to keep a formation defined in terms of only relative angles (i.e. a bearing formation). This problem can naturally arise within the context of several multi-robot applications such as, e.g. exploration, coverage, and surveillance. First, we introduce and thoroughly analyze the concept and properties of bearing formations, and provide a class of minimally linear sets of bearings sufficient to uniquely define such formations. We then propose a bearing-only formation controller requiring only bearing measurements, converging almost globally, and maintaining bounded inter-agent distances despite the lack of direct metric information.The controller still leaves the possibility of imposing group motions tangent to the current bearing formation. These can be either autonomously chosen by the robots because of any additional task (e.g. exploration), or exploited by an assisting human co-operator. For this latter 'human-in-the-loop' case, we propose a multi-master/multi-slave bilateral shared control system providing the co-operator with some suitable force cues informative of the UAV performance. The proposed theoretical framework is extensively validated by means of simulations and experiments with quadrotor UAVs equipped with onboard cameras. Practical limitations, e.g. limited field-of-view, are also considered. © The Author(s) 2012

6D physical interaction with a fully actuated aerial robot

This paper presents the design, control, and experimental validation of a novel fully-actuated aerial robot for physically interactive tasks, named Tilt-Hex. We show how the Tilt-Hex, a tilted-propeller hexarotor is able to control the full pose (position and orientation independently) using a geometric control, and to exert a full-wrench (force and torque independently) with a rigidly attached end-effector using an admittance control paradigm. An outer loop control governs the desired admittance behavior and an inner loop based on geometric control ensures pose tracking. The interaction forces are estimated by a momentum based observer. Control and observation are made possible by a precise control and measurement of the speed of each propeller. An extensive experimental campaign shows that the Tilt-Hex is able to outperform the classical underactuated multi-rotors in terms of stability, accuracy and dexterity and represent one of the best choice at date for tasks requiring aerial physical interaction

Physical realization of a quantum spin liquid based on a novel frustration mechanism

Unlike conventional magnets where the magnetic moments are partially or completely static in the ground state, in a quantum spin liquid they remain in collective motion down to the lowest temperatures. The importance of this state is that it is coherent and highly entangled without breaking local symmetries. Such phenomena is usually sought in simple lattices where antiferromagnetic interactions and/or anisotropies that favor specific alignments of the magnetic moments are "frustrated" by lattice geometries incompatible with such order e.g. triangular structures. Despite an extensive search among such compounds, experimental realizations remain very few. Here we describe the investigation of a novel, unexplored magnetic system consisting of strong ferromagnetic and weaker antiferromagnetic isotropic interactions as realized by the compound Ca$_{10}$Cr$_7$O$_{28}$. Despite its exotic structure we show both experimentally and theoretically that it displays all the features expected of a quantum spin liquid including coherent spin dynamics in the ground state and the complete absence of static magnetism.Comment: Modified version accepted in Nature Physic

Dealloying of Platinum-Aluminum Thin Films Part I. Dynamics of Pattern Formation

Applying focused ion beam (FIB) nanotomography and Rutherford backscattering spectroscopy (RBS) to dealloyed platinum-aluminum thin films an in-depth analysis of the dominating physical mechanisms of porosity formation during the dealloying process is performed. The dynamical porosity formation due to the dissolution of the less noble aluminum in the alloy is treated as result of a reaction-diffusion system. The RBS analysis yields that the porosity formation is mainly caused by a linearly propagating diffusion front, i.e. the liquid/solid interface, with a uniform speed of 42(3) nm/s when using a 4M aqueous NaOH solution at room temperature. The experimentally observed front evolution is captured by the normal diffusive Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) equation and can be interpreted as a branching random walk phenomenon. The etching front produces a gradual porosity with an enhanced porosity in the surface-near regions of the thin film due to prolonged exposure of the alloy to the alkaline solution.Comment: 4 pages, 5 figure

Second order and stability analysis for optimal sparse control of the FitzHugh-Nagumo equation

Optimal sparse control problems are considered for the FitzHugh–Nagumo system including the so-called Schlögl model. The nondifferentiable objective functional of tracking type includes a quadratic Tikhonov regularization term and the L1-norm of the control that accounts for the sparsity. Though the objective functional is not differentiable, a theory of second order sufficient optimality conditions is established for Tikhonov regularization parameter ν > 0 and also for the case ν = 0. In this context, also local minima are discussed that are strong in the sense of the calculus of variations. The second order conditions are used as the main assumption for proving the stability of locally optimal solutions with respect to ν → 0 and with respect to perturbations of the desired state functions. The theory is confirmed by numerical examples that are resolved with high precision to confirm that the optimal solution obeys the system of necessary optimality conditions.This author’s research was partially supported by the Spanish Ministerio de Econom´ıa y Competitividad under project MTM2011-22711

Formula for the nnth kk-Generalized Fibonacci-like Number

In this paper we provided a formula for the $n$th term of the $k$-generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having $k$ arbitrary initial terms, where the succeeding terms are obtained by adding its previous $k$ terms. The formula for the $n$th term of the $k$-generalized Fibonacci-like sequence was obtained by observing patterns in the derived formula for the nth term of the Fibonacci-like, Tribonacci-like, and Tetrabonacci-like sequence. The formula for the $k$-generalized Fibonacci sequence was also derived and was used in the process of proving the main result of this paper

Hillock formation of Pt thin films on Yttria stabilized Zirconia single crystals

The stability of a metal thin films on a dielectric substrate is conditioned by the magnitude of the interactive forces at the interface. In the case of a non-reactive interface and weak adhesion, the minimization of free surface energy gives rise to an instability of the thin film. In order to study these effects, Pt thin films with a thickness of 50 nm were deposited via ion-beam sputtering on yttria stabilized zirconia single crystals. All Pt films were subjected to heat treatments up to 973 K for 2 h. The morphological evolution of Pt thin films has been investigated by means of scanning electron microscopy (SEM), atomic force microscopy (AFM) and standard image analysis techniques. Three main observations have been made: i) the deposition method has a direct impact on the morphological evolution of the film during annealing. Instead of hole formation, that is typically observed as response to a thermal treatment, anisotropic pyramidal shaped hillocks are formed on top of the film. ii) It is shown by comparing the hillocks' aspect ratio with finite element method (FEM) simulations that the hillock formation can be assigned to a stress relaxation process inside the thin film. iii) By measuring the equilibrium shapes and the shape fluctuations of the formed Pt hillocks the anisotropy of the step free energy and its stiffness have been derived in addition to the anisotropic kink energy of the hillock's edges.Comment: 8 pages, 7 figure

Weighted ergodic theorems for Banach-Kantorovich lattice Lp(∇^,μ^)L_{p}(\hat{\nabla},\hat{\mu})

In the present paper we prove weighted ergodic theorems and multiparameter weighted ergodic theorems for positive contractions acting on $L_p(\hat{\nabla},\hat{\mu})$. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.Comment: 11 page