Notas sobre la concepción de Maxwell acerca de la fisica experimental

El Laboratorio Cavendish fue inaugurado en 1874 y James Clerk Maxwell fue su primer director. En ese momento Maxwell ocupaba el cargo de Profesor de Física Experimental en la cátedra Cavendish de la Universidad de Cambridge. La creación de este laboratorio tuvo la intención de fortalecer la física experimental en el Reino Unido. Se asocia su creación con la "necesidad de entrenamiento práctico de científicos e ingenieros" tras el éxito de la Gran Exhibición Industrial de 1851, que dejó claramente expuestos los requerimientos de una sociedad industrial. Hasta ese momento, la física en Inglaterra significaba física teórica y se la pensaba en el ámbito de las matemáticas. Hubo mucha especulación sobre la elección del Profesor de Física Experimental. Tanto William Thomson (de Glasgow) como John Rayleigh (de Essex) fueron candidatos con grandes posibilidades, pero ambos rechazaron la oferta Cuando se anunció la designación de Maxwell, hubo cierto asombro (y malestar) en la comunidad científica londinense. El nuevo profesor Maxwell era, por aquel entonces, relativamente desconocido. Su nombramiento como profesor fue anunciado el 8 de marzo de 1871, y más allá de las críticas iniciales, su clase inaugural fue seguida por una gran cantidad de estudiantes e investigadores de Cambridge. Sus libros más influyentes, Teoría Cinética ( 1871) y el Tratado de Electricidad y Magnetismo ( 1873), -no habían sido todavía publicados. En esta clase, Maxwell dejó claramente expuesta la impronta que él darla unos años después al Laboratorio Cavendish, cuando fuera su Director. Una de sus primeras acciones al asumir como Director del laboratorio, fue la construcción de un conjunto de equipos de física experimental, muchos de los cuales eran producto de sus propios desarrollos y concepciones. Entre ellos se destaca un modelo mecánico que tenía por objetivo representar la interacción de dos circuitos eléctricos. El estudio de este modelo es el propósito primordial del presente trabajo. Para una mejor comprensión de los objetivos perseguidos por Maxwell con este tipo de desarrollos, haremos, por un lado una breve descripción de las ideas que Maxwell tenía sobre la física experimental y por el otro, un análisis del modelo desde la concepción mecanicista que él tenía del electromagnetismo

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.Comment: 14 pages, corrected equation 1

Data-adaptive harmonic spectra and multilayer Stuart-Landau models

Harmonic decompositions of multivariate time series are considered for which we adopt an integral operator approach with periodic semigroup kernels. Spectral decomposition theorems are derived that cover the important cases of two-time statistics drawn from a mixing invariant measure. The corresponding eigenvalues can be grouped per Fourier frequency, and are actually given, at each frequency, as the singular values of a cross-spectral matrix depending on the data. These eigenvalues obey furthermore a variational principle that allows us to define naturally a multidimensional power spectrum. The eigenmodes, as far as they are concerned, exhibit a data-adaptive character manifested in their phase which allows us in turn to define a multidimensional phase spectrum. The resulting data-adaptive harmonic (DAH) modes allow for reducing the data-driven modeling effort to elemental models stacked per frequency, only coupled at different frequencies by the same noise realization. In particular, the DAH decomposition extracts time-dependent coefficients stacked by Fourier frequency which can be efficiently modeled---provided the decay of temporal correlations is sufficiently well-resolved---within a class of multilayer stochastic models (MSMs) tailored here on stochastic Stuart-Landau oscillators. Applications to the Lorenz 96 model and to a stochastic heat equation driven by a space-time white noise, are considered. In both cases, the DAH decomposition allows for an extraction of spatio-temporal modes revealing key features of the dynamics in the embedded phase space. The multilayer Stuart-Landau models (MSLMs) are shown to successfully model the typical patterns of the corresponding time-evolving fields, as well as their statistics of occurrence.Comment: 26 pages, double columns; 15 figure

Star Spot Induced Radial Velocity Variability in LkCa 19

We describe a new radial velocity survey of T Tauri stars and present the first results. Our search is motivated by an interest in detecting massive young planets, as well as investigating the origin of the brown dwarf desert. As part of this survey, we discovered large-amplitude, periodic, radial velocity variations in the spectrum of the weak line T Tauri star LkCa 19. Using line bisector analysis and a new simulation of the effect of star spots on the photometric and radial velocity variability of T Tauri stars, we show that our measured radial velocities for LkCa19 are fully consistent with variations caused by the presence of large star spots on this rapidly rotating young star. These results illustrate the level of activity-induced radial velocity noise associated with at least some very young stars. This activity-induced noise will set lower limits on the mass of a companion detectable around LkCa 19, and similarly active young stars.Comment: ApJ accepted, 27 pages, 12 figures, aaste

Approximating the coefficients in semilinear stochastic partial differential equations

We investigate, in the setting of UMD Banach spaces E, the continuous dependence on the data A, F, G and X_0 of mild solutions of semilinear stochastic evolution equations with multiplicative noise of the form dX(t) = [AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical Brownian motion on a Hilbert space H. We prove continuous dependence of the compensated solutions X(t)-e^{tA}X_0 in the norms L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n are uniformly sectorial and converge to A in the strong resolvent sense, and that the approximating nonlinearities F_n and G_n are uniformly Lipschitz continuous in suitable norms and converge to F and G pointwise. Our results are applied to a class of semilinear parabolic SPDEs with finite-dimensional multiplicative noise.Comment: Referee's comments have been incorporate

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

The Smallest Mass Ratio Young Star Spectroscopic Binaries

Using high resolution near-infrared spectroscopy with the Keck telescope, we have detected the radial velocity signatures of the cool secondary components in four optically identified pre-main-sequence, single-lined spectroscopic binaries. All are weak-lined T Tauri stars with well-defined center of mass velocities. The mass ratio for one young binary, NTTS 160905-1859, is M2/M1 = 0.18+/-0.01, the smallest yet measured dynamically for a pre-main-sequence spectroscopic binary. These new results demonstrate the power of infrared spectroscopy for the dynamical identification of cool secondaries. Visible light spectroscopy, to date, has not revealed any pre-main-sequence secondary stars with masses <0.5 M_sun, while two of the young systems reported here are in that range. We compare our targets with a compilation of the published young double-lined spectroscopic binaries and discuss our unique contribution to this sample.Comment: Accepted for publication in the April, 2002, ApJ; 6 figure

A Dynamical Mass Constraint for Pre-Main-Sequence Evolutionary Tracks: The Binary NTT 045251+3016

We present an astrometric/spectroscopic orbital solution for the pre-main-sequence binary NTT 045251+3016. Our measurements for the primary and secondary masses are 1.45 +/- 0.19 M_sun and 0.81 +/- 0.09 M_sun, respectively, and 145 +/- 8 pc for the distance of the system, consistent with prior estimates for the Taurus-Auriga star-forming region. The evolutionary tracks of D'Antona & Mazzitelli (1997), Baraffe et al. (1998), and Palla & Stahler (1999) are tested against these dynamical mass measurements. Due to the intrinsic color/T_eff variation within the K5 spectral class, each pre-main-sequence model provides a mass range for the primary. The theoretical mass range derived from the Baraffe et al. (1998) tracks that use a mixing length parameter alpha=1.0 is closest to our measured primary mass, deviating between 1.3 and 1.6 sigma. The set of Baraffe et al. (1998) tracks that use alpha=1.9 deviate between 1.6 and 2.1 sigma from our measured primary mass. The mass range given by the Palla & Stahler (1999) tracks for the primary star deviate between 1.6 and 2.9 sigma. The D'Antona & Mazzitelli (1997) tracks give a mass range that deviates by at least 3.0 sigma from our derived primary mass, strongly suggesting that these tracks are inconsistent with our observation. Observations of the secondary are less constraining than those of the primary, but the deviations between the dynamical mass of the secondary and the mass inferred for the secondary from the various pre-main-sequence tracks mirror the deviations of the primary star. All of the pre-main-sequence tracks are consistent with coevality of the components of NTT 045251+3016.Comment: 27 pages, 6 figures, 5 tables -- accepted by A