1,619 research outputs found
The Symplectic Penrose Kite
The purpose of this article is to view the Penrose kite from the perspective
of symplectic geometry.Comment: 24 pages, 7 figures, minor changes in last version, to appear in
Comm. Math. Phys
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
Adjoint bi-continuous semigroups and semigroups on the space of measures
For a given bi-continuous semigroup T on a Banach space X we define its
adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some
abstract conditions this adjoint semigroup is again bi-continuous with respect
to the weak topology (X^o,X). An application is the following: For K a Polish
space we consider operator semigroups on the space C(K) of bounded, continuous
functions (endowed with the compact-open topology) and on the space M(K) of
bounded Baire measures (endowed with the weak*-topology). We show that
bi-continuous semigroups on M(K) are precisely those that are adjoints of a
bi-continuous semigroups on C(K). We also prove that the class of bi-continuous
semigroups on C(K) with respect to the compact-open topology coincides with the
class of equicontinuous semigroups with respect to the strict topology. In
general, if K is not Polish space this is not the case
Molecular gyroscopes and biological effects of weak ELF magnetic fields
Extremely-low-frequency magnetic fields are known to affect biological
systems. In many cases, biological effects display `windows' in biologically
effective parameters of the magnetic fields: most dramatic is the fact that
relatively intense magnetic fields sometimes do not cause appreciable effect,
while smaller fields of the order of 10--100 T do. Linear resonant
physical processes do not explain frequency windows in this case. Amplitude
window phenomena suggest a nonlinear physical mechanism. Such a nonlinear
mechanism has been proposed recently to explain those `windows'. It considers
quantum-interference effects on protein-bound substrate ions. Magnetic fields
cause an interference of ion quantum states and change the probability of
ion-protein dissociation. This ion-interference mechanism predicts specific
magnetic-field frequency and amplitude windows within which biological effects
occur. It agrees with a lot of experiments. However, according to the
mechanism, the lifetime of ion quantum states within a protein
cavity should be of unrealistic value, more than 0.01 s for frequency band
10--100 Hz. In this paper, a biophysical mechanism has been proposed that (i)
retains the attractive features of the ion interference mechanism and (ii) uses
the principles of gyroscopic motion and removes the necessity to postulate
large lifetimes. The mechanism considers dynamics of the density matrix of the
molecular groups, which are attached to the walls of protein cavities by two
covalent bonds, i.e., molecular gyroscopes. Numerical computations have shown
almost free rotations of the molecular gyros. The relaxation time due to van
der Waals forces was about 0.01 s for the cavity size of 28 angstr\"{o}ms.Comment: 10 pages, 7 figure
Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow
We establish moment estimates for the invariant measure of a stochastic
partial differential equation describing motion by mean curvature flow in (1+1)
dimension, leading to polynomial stability of the associated Markov semigroup.
We also prove maximal dissipativity for the related Kolmogorov operator
Dynamical Masses of Low Mass Stars in the Taurus and Ophiuchus Star Forming Regions
We report new dynamical masses for 5 pre-main sequence (PMS) stars in the
L1495 region of the Taurus star-forming region (SFR) and 6 in the L1688 region
of the Ophiuchus SFR. Since these regions have VLBA parallaxes these are
absolute measurements of the stars' masses and are independent of their
effective temperatures and luminosities. Seven of the stars have masses
solar masses, thus providing data in a mass range with little data, and of
these, 6 are measured to precision . We find 8 stars with masses in the
range 0.09 to 1.1 solar mass that agree well with the current generation of PMS
evolutionary models. The ages of the stars we measured in the Taurus SFR are in
the range 1-3 MY, and MY for those in L1688. We also measured the
dynamical masses of 14 stars in the ALMA archival data for Akeson~\&~Jensen's
Cycle 0 project on binaries in the Taurus SFR. We find that the masses of 7 of
the targets are so large that they cannot be reconciled with reported values of
their luminosity and effective temperature. We suggest that these targets are
themselves binaries or triples.Comment: 20 page
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
Smooth stable and unstable manifolds for stochastic partial differential equations
Invariant manifolds are fundamental tools for describing and understanding
nonlinear dynamics. In this paper, we present a theory of stable and unstable
manifolds for infinite dimensional random dynamical systems generated by a
class of stochastic partial differential equations. We first show the existence
of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's
method. Then, we prove the smoothness of these invariant manifolds
Wolf-like or dog-like? A comparison of gazing behaviour across three dog breeds tested in their familiar environments
Human-directed gazing, a keystone in dog\u2013human communication, has been suggested to derive from both domestication and breed selection. The influence of genetic similarity to wolves and selective pressures on human-directed gazing is still under debate. Here, we used the \u2018unsolvable task\u2019 to compare Czechoslovakian Wolfdogs (CWDs, a close-to-wolf breed), German Shepherd Dogs (GSDs) and Labrador Retrievers (LRs). In the \u2018solvable task\u2019, all dogs learned to obtain the reward; however, differently from GSDs and LRs, CWDs rarely gazed at humans. In the \u2018unsolvable task\u2019, CWDs gazed significantly less towards humans compared to LRs but not to GSDs. Although all dogs were similarly motivated to explore the apparatus, CWDs and GSDs spent a larger amount of time in manipulating it compared to LRs. A clear difference emerged in gazing at the experimenter versus owner. CWDs gazed preferentially towards the experimenter (the unfamiliar subject manipulating the food), GSDs towards their owners and LRs gazed at humans independently from their level of familiarity. In conclusion, it emerges that the artificial selection operated on CWDs produced a breed more similar to ancient breeds (more wolf-like due to a less-intense artificial selection) and not very human-oriented. The next step is to clarify GSDs\u2019 behaviour and better understand the genetic role of this breed in shaping CWDs\u2019 heterospecific behaviour
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