Theories of Technological Progress and the British Textile Industry from Kay to Cartwright

Editada en la Fundación Empresa PúblicaLa industria textil británica continúa en el centro del debate sobre la revolución industrial. Las innovaciones técnicas en el período produjeron una aceleración extraordinaria del crecimiento del output y una considerable reducción de los precios de los tejidos. En este trabajo presentamos un estudio de la comunidad de los inventores responsables de la transformación tecnológica, lo que nos permite alcanzar una serie de conclusiones nuevas sobre el ritmo y dirección de la actividad innovadora durante la revolución industrialThe cotton textile industry remains central to all accounts of the first industrial revolution. Innovations in this period precipitated an extraordinary acceleration in the growth of output and a steep decline in the cost of producing all varieties of cloth. In this paper we outline an explanation through an analysis of the community of inventors responsible for the technological transformation, which enables us to offer some generalizations of the pace and pattern of the inventive activity in this period.Publicad

Collision of High Frequency Plane Gravitational and Electromagnetic Waves

We study the head-on collision of linearly polarized, high frequency plane gravitational waves and their electromagnetic counterparts in the Einstein-Maxwell theory. The post-collision space-times are obtained by solving the vacuum Einstein-Maxwell field equations in the geometrical optics approximation. The head-on collisions of all possible pairs of these systems of waves is described and the results are then generalised to non-linearly polarized waves which exhibit the maximum two degrees of freedom of polarization.Comment: Latex file, 17 pages, accepted for publication in International Journal of Modern Physics

Revisiting boundary layer flows of viscoelastic fluids

In this article we reconsider high Reynolds number boundary layer flows of fluids with viscoelastic properties. We show that a number of previous studies that have attempted to address this problem are, in fact, incomplete. We correctly reformulate the problem and solve the governing equations using a Chebyshev collocation scheme. By analysing the decay of the solutions to the far-field we determine the correct stress boundary conditions required to solve problems of this form. Our results show that both the fluid velocity within the boundary layer and the stress at the solid boundary increase due to the effect of viscoelasticity. As a consequence of this, we predict a thinning of the boundary layer as the value of the dimensionless viscoelastic flow parameter is increased. These results contradict a number of prominent studies in the literature but are supported by results owing from an asymptotic analysis based on the assumption of the smallness of the non-dimensional viscoelastic flow parameter

GSH23.0-0.7+117, a neutral hydrogen shell in the inner Galaxy

GSH23.0-0.7+117 is a well-defined neutral hydrogen shell discovered in the VLA Galactic Plane Survey (VGPS). Only the blueshifted side of the shell was detected. The expansion velocity and systemic velocity were determined through the systematic behavior of the HI emission with velocity. The center of the shell is at (l,b,v)=(23.05,-0.77,+117 km/s). The angular radius of the shell is 6.8', or 15 pc at a distance of 7.8 kpc. The HI mass divided by the volume of the half-shell implies an average density n_H = 11 +/- 4 cm^{-3} for the medium in which the shell expanded. The estimated age of GSH23.0-0.7+117 is 1 Myr, with an upper limit of 2 Myr. The modest expansion energy of 2 * 10^{48} erg can be provided by the stellar wind of a single O4 to O8 star over the age of the shell. The 3 sigma upper limit to the 1.4 GHz continuum flux density (S_{1.4} < 248 mJy) is used to derive an upper limit to the Lyman continuum luminosity generated inside the shell. This upper limit implies a maximum of one O9 star (O8 to O9.5 taking into account the error in the distance) inside the HI shell, unless most of the incident ionizing flux leaks through the HI shell. To allow this, the shell should be fragmented on scales smaller than the beam (2.3 pc). If the stellar wind bubble is not adiabatic, or the bubble has burst (as suggested by the HI channel maps), agreement between the energy and ionization requirements is even less likely. The limit set by the non-detection in the continuum provides a significant challenge for the interpretation of GSH23.0-0.7+117 as a stellar wind bubble. A similar analysis may be applicable to other Galactic HI shells that have not been detected in the continuum.Comment: 18 pages, 6 figures. Figures 1 and 4 separately in GIF format. Accepted for publication in Astrophysical Journa

Impulsive spherical gravitational waves

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the 2-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary non-linear holomorphic transformation. Using 2-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a world-line with constant acceleration

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.Comment: 43 pages, 10 figure

Effective chiral-spin Hamiltonian for odd-numbered coupled Heisenberg chains

An $L \times \infty$ system of odd number of coupled Heisenberg spin chains is studied using a degenerate perturbation theory, where $L$ is the number of coupled chains. An effective chain Hamiltonian is derived explicitly in terms of two spin half degrees of freedom of a closed chain of $L$ sites, valid in the regime the inter-chain coupling is stronger than the intra-chain coupling. The spin gap has been calculated numerically using the effective Hamiltonian for $L=3,5,7,9$ for a finite chain up to ten sites. It is suggested that the ground state of the effective Hamiltonian is correlated, by examining variational states for the effective chiral-spin chain Hamiltonian.Comment: 9 Pages, Latex, report ICTP-94-28

Quantum chaos in open systems: a quantum state diffusion analysis

Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with the environment, and makes the quasiclassical limit of such systems both more realistic and simpler in many respects than the more familiar quasiclassical limit for closed systems. A linearized version of this theory leads to the correct classical dynamics in the macroscopic limit, even for nonlinear and chaotic systems. We apply the theory to the forced, damped Duffing oscillator, comparing the numerical results of the full and linearized equations, and argue that this can be used to make explicit calculations in the decoherent histories formalism of quantum mechanics.Comment: 18 pages standard LaTeX + 9 figures; extensively trimmed; to appear in J. Phys.