The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335

Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

On the probability of occurrence of rogue waves

A number of extreme and rogue wave studies have been conducted theoretically, numerically, experimentally and based on field data in the last years, which have significantly advanced our knowledge of ocean waves. So far, however, consensus on the probability of occurrence of rogue waves has not been achieved. The present investigation is addressing this topic from the perspective of design needs. Probability of occurrence of extreme and rogue wave crests in deep water is here discussed based on higher order time simulations, experiments and hindcast data. Focus is given to occurrence of rogue waves in high sea states

Modulational instability and wave amplification in finite water depth

The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths <i>kh</i> &leq; 1.36 (where <i>k</i> is the wavenumber of the plane wave and <i>h</i> is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for <i>kh</i> &leq; 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for <i>kh</i> < 0.8

A simple trapped-ion architecture for high-fidelity Toffoli gates

We discuss a simple architecture for a quantum Toffoli gate implemented using three trapped ions. The gate, which in principle can be implemented with a single laser-induced operation, is effective under rather general conditions and is strikingly robust (within any experimentally realistic range of values) against dephasing, heating and random fluctuations of the Hamiltonian parameters. We provide a full characterization of the unitary and noise-affected gate using three-qubit quantum process tomography

Evading quantum mechanics

Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.Comment: v2: changed the title, added a figure, and made some minor update

A Two-Player Game of Life

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.Comment: 7 pages, 3 figure

From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

The North Sea Andrea storm and numerical simulations

A coupling of a spectral wave model with a nonlinear phase-resolving model is used to reconstruct the evolution of wave statistics during a storm crossing the North Sea on 8–9 November 2007. During this storm a rogue wave (named the Andrea wave) was recorded at the Ekofisk field. The wave has characteristics comparable to the well-known New Year wave measured by Statoil at the Draupner platform 1 January 1995. Hindcast data of the storm at the nearest grid point to the Ekofisk field are here applied as input to calculate the evolution of random realizations of the sea surface and its statistical properties. Numerical simulations are carried out using the Euler equations with a higher-order spectral method (HOSM). Results are compared with some characteristics of the Andrea wave record measured by the down-looking lasers at Ekofisk

Well-being of suckling calves under two different rearing systems: case study in the central milk basin of Argentina

En el presente trabajo se llevo a cabo un estudio de caso con enfoque cuantitativo. El objetivo de este estudio fue evaluar el bienestar en teneros lechales durante la época invernal bajo dos diferentes sistemas de crianza, que se utilizan en la zona. Los terneros, se alojaron en dos sistemas: en estaca los machos y en jaula las hembras. Los animales recibieron dos tomas diarias de leche (4 l/día), balanceado iniciador y agua ad libitum. Se registraron pesos iníciales y finales. La ganancia de peso se analizó mediante técnicas estadísticas descriptivas. Se tomaron muestra de saliva para determinar cortisol (CS) en cuatro momentos del día. Los datos fueron analizados para detectar variaciones horarias. El CS no mostró fluctuaciones diarias. Durante quince días y día por medio, se registraron las conductas: parado, echado, comiendo y otras. La metodología de observación y registro utilizada fue el muestreo de barrido a intervalos regulares. Los datos de analizaron con la prueba del c2. El efecto tratamiento fue significativo sobre el comportamiento (p<0,01). Los animales de los dos sistemas gastaron el 50% del tiempo en la conducta de reposo.Well-being of suckling calves under two different rearing systems. Case study in the central milk basin of Argentina. In this paper we conducted a case study with quantitative approach. The aim of this study was to assess welfare in suckling calves during the winter season under two different rearing systems, which are used in the area. Calves were housed in two systems: a stake in males and females cage. All animals received 4 L milk per day, in two servings. Water and a commercial starter were offered ad libitum. Initial and final weights were recorded, weight gain was analyzed using descriptive statistical techniques. Saliva samples were taken at four times over the day, to analyze saliva cortisol (SC). Data were analyzed for time variations. Neither daily fluctuations in SC concentrations nor system effects were detected in SC concentrations. Different behaviors: standing, lying, eating and "others" were observed every other day over a fortnight. Scan sampling at regular intervals was utilized. Data were analyzed by a c2 test. Systems effects were observed on behavioral conducts (p<0.01). Animals in both systems spent 50% of their time lying.Fil: Leva, Paula Edit. Universidad Nacional del Litoral. Facultad de Ciencias Agrarias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: García, M. S.. Universidad Nacional del Litoral. Facultad de Ciencias Agrarias; ArgentinaFil: Toffoli Arnaudo, Guillermo Daniel. Universidad Nacional del Litoral. Facultad de Ciencias Agrarias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rodríguez, A. G.. Universidad Nacional del Litoral. Facultad de Ciencias Agrarias; ArgentinaFil: Rey, Florencia. Universidad Nacional del Litoral. Facultad de Ciencias Veterinarias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin