Kinematics nomenclature for physiological accelerations with special reference to vestibular applications

Kinematics nomenclature for physiological accelerations and special reference to vestibular apparatu

Elicitation of horizontal nystagmus by periodic linear acceleration

Horizontal nystagmus elicitation in man by periodic linear acceleratio

Effect of blade geometry on the aerodynamic loads produced by vertical-axis wind turbines

Accurate aerodynamic modelling of vertical-axis wind turbines poses a significant challenge. The rotation of the turbine induces large variations in the angle of attack of its blades that can manifest as dynamic stall. In addition, interactions between the blades of the turbine and the wake that they produce can result in impulsive changes to the aerodynamic loading. The Vorticity Transport Model has been used to simulate the aerodynamic performance and wake dynamics of three different vertical-axis wind turbine configurations. It is known that vertical-axis turbines with either straight or curved blades deliver torque to their shaft that fluctuates at the blade passage frequency of the rotor. In contrast, a turbine with helically twisted blades delivers a relatively steady torque to the shaft. In this article, the interactions between helically twisted blades and the vortices within their wake are shown to result in localized perturbations to the aerodynamic loading on the rotor that can disrupt the otherwise relatively smooth power output that is predicted by simplistic aerodynamic tools that do not model the wake to sufficient fidelity. Furthermore, vertical-axis wind turbines with curved blades are shown to be somewhat more susceptible to local dynamic stall than turbines with straight blades

On Local Equivalence, Surface Code States and Matroids

Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same. Despite the fact this settles the LU-LC conjecture, a sufficient condition for stabilizer states that violate the LU-LC conjecture is missing. In this paper, we investigate further the properties of stabilizer states with respect to local equivalence. Our first result shows that there exist infinitely many stabilizer states which violate the LU-LC conjecture. In particular, we show that for all numbers of qubits $n\geq 28$, there exist distance two stabilizer states which are counterexamples to the LU-LC conjecture. We prove that for all odd $n\geq 195$, there exist stabilizer states with distance greater than two which are LU equivalent but not LC equivalent. Two important classes of stabilizer states that are of great interest in quantum computation are the cluster states and stabilizer states of the surface codes. To date, the status of these states with respect to the LU-LC conjecture was not studied. We show that, under some minimal restrictions, both these classes of states preclude any counterexamples. In this context, we also show that the associated surface codes do not have any encoded non-Clifford transversal gates. We characterize the CSS surface code states in terms of a class of minor closed binary matroids. In addition to making connection with an important open problem in binary matroid theory, this characterization does in some cases provide an efficient test for CSS states that are not counterexamples.Comment: LaTeX, 13 pages; Revised introduction, minor changes and corrections mainly in section V

Otolith shear and the visual perception of force direction - Discrepancies and a proposed resolution

Otolith shear and visual perception of force direction with resolution of discrepancies by tangent equatio

Exactness of the Original Grover Search Algorithm

It is well-known that when searching one out of four, the original Grover's search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover's algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.Comment: 8 pages, 2 figure

Maximum-Entropy Weighting of Multi-Component Earth Climate Models

A maximum entropy-based framework is presented for the synthesis of projections from multiple Earth climate models. This identifies the most representative (most probable) model from a set of climate models -- as defined by specified constraints -- eliminating the need to calculate the entire set. Two approaches are developed, based on individual climate models or ensembles of models, subject to a single cost (energy) constraint or competing cost-benefit constraints. A finite-time limit on the minimum cost of modifying a model synthesis framework, at finite rates of change, is also reported.Comment: Inspired by discussions at the Mathematical and Statistical Approaches to Climate Modelling and Prediction workshop, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 11 Aug. to 22 Dec. 2010. Accepted for publication in Climate Dynamics, 8 August 201

Perfect Transfer of Arbitrary States in Quantum Spin Networks

We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to $N$-qubit spin networks of identical qubit couplings, we show that $2\log_3 N$ is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done in PRL 92, 187902.Comment: 12 pages, 3 figures with updated reference

Ground states for a class of deterministic spin models with glassy behaviour

We consider the deterministic model with glassy behaviour, recently introduced by Marinari, Parisi and Ritort, with \ha\ $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the discrete sine Fourier transform. The ground state found by these authors for $N$ odd and $2N+1$ prime is shown to become asymptotically dege\-ne\-ra\-te when $2N+1$ is a product of odd primes, and to disappear for $N$ even. This last result is based on the explicit construction of a set of eigenvectors for $J$, obtained through its formal identity with the imaginary part of the propagator of the quantized unit symplectic matrix over the $2$-torus.Comment: 15 pages, plain LaTe

An elementary algorithm to evaluate trigonometric functions to high precision

Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation