Figura del mes

Figure of the month

Black holes traveling at supersonic on a sea of gas produce a shock cone, like the wake behind a ship on the sea. That shock cone is interesting because it vibrates and may explain some of the high energy observations related to Quasi Periodic Oscillations (QPOs). It was recently shown that when the black hole rotates, the cone oscillates and gets destroyed. Our numerical relativity group recently discovered through numerical simulations, that when using advanced numerical methods that allow the gas to truly enter the rotating black hole (not as previously reported by other groups), the shock cone is stable. In the figure the density of the shock cone and its motion is shown for a wind moving at Mach 5. The results were recently published in the Monthly Notices of the Royal Astronomical Society, 426 (2012) 732-738, by our students Alejandro Cruz Osorio and Fabio D. Lora Clavijo, and Dr. Francisco Siddhartha Guzman, members of the Numerical Relativity Group at the IFM.

Figure of the month

KASCADE-Grande is an air-shower observatory devoted to the detection of cosmic rays with energies in the range of $10^{16}$ and $10^{18}$ eV. This energy region is of particular interest for the cosmic ray astrophysics, since it is the place where several models predict the existence of a galactic- extragalactic transition in the cosmic ray spectrum and the presence of a break in the flux of its heavy component. The detection of these features requires detailed and simultaneous measurements of the energy and composition of cosmic rays with sufficient statistics. This kind of studies are possible for the first time in KASCADE-Grande due to the accurate measurements of several air-shower observables, i.e., the number of charged particle, electrons and muons in the shower, using the different detector systems of the observatory.
By classifying the detected air showers into electron-poor and electron- rich events on the basis of the charged over muon number ratio, the corresponding energy spectra of the light (electron-rich) and heavy (electron-poor) components of cosmic rays in the interval $10^{16}- 10^{18}$ eV were obtained (see figure). It was discovered that the energy spectrum of the heavy component shows a knee-like structure around 90 PeV. This feature is responsible for a steepening recently observed by the KASCADE-Grande experiment in the all-particle energy spectrum.
Dr. J.C. Arteaga-Velazquez, researcher of the IFM, worked on the development of one of these techniques to reconstruct the light and heavy spectra of cosmic rays. Results were published in PRL 107, 171104 (2011) . arXiv:1107.5885v2 [astro-ph].

One of the outstanding problems in theoretical particle physics is the qualitative and quantitative understanding of the phenomenon of confinement: the fact that quarks or any other colored combination of elementary particles can never be observed as isolated physical states. One of the main directions of research followed over the last decade is the application of the variational principle to Yang-Mills theories in Coulomb gauge (with static color charges) which, upon using a Gaussian ansatz for the vacuum functional of the theory, yields a set of equations of Dyson-Schwinger type. However, including the potential between static color charges (approximated by the so-called color Coulomb potential) leads to inconsistencies. Very recently, we have adapted a functional renormalization group of Wilsonian type to this Hamiltonian formulation. The corresponding flow equations can be solved consistently, in particular, the so-called Coulomb form factor shows a power behavior in the infrared presented in the double-logarithmic plot (for momenta above the infrared cutoff k_{min} introduced for technical reasons). Together with the numerical result for the ghost correlator, one obtains a potential that varies in momentum space like p^{-3.85} in the limit of small momenta, quite close to the expected p^{-4} which corresponds to a potential that rises linearly with the distance between the color charges, see M. Leder, H. Reinhardt, A. Weber, and J.M. Pawlowski, preprint arXiv:1105.0800 [hep-th].

This figure shows this equal-mass head-on collision of two virialized balls of self-gravitating Bose Condensate (BEC) described by the Gross-Pitaevskii equation (mean field description of a BEC at T=0). BECs are considered to be a dark matter candidate. This figure in fact represents the collision of two BEC dark matter halos (either galactic or cluster size). Notice the pattern of interference that soon will be shown to provide predictions that support or rule out the BEC as dark matter. (Left) the gravitational potential along the head-on axis, (middle) the density of probability along the head-on axis and (right) 2d flavor of the density of probability. Notice the solitonic-like behavior of the two blobs. This result was published in Phys.Rev.D83:103513,2011 , and is avalable also at arXiv:1105.2066v1 [astro-ph.CO].

In the period 1960-1963 and in a series of works published in the most prestigious mathematics international journal, called Annals of Mathematics, Prof. Kunihiko Kodaira gave a classification of smooth projective surfaces over the field of complex numbers. Later on, in the period 1969-1977, David Mumford and Enrico Bombieri extended this classification to smooth projective surfaces over any algebraically closed field of any arbitrary characteristic. Special interest has been given to understand the geometry of the case of smooth projective rational surfaces over a fixed algebraically closed field (such interest owes its origin to the italian school of Algebraic Geometry of the nineteen and the begining of the twentieth centuries such as Castelnuovo, Chisini, Del Pezzo, Enriques and Severi to cite a few). Significant results have been obtained by Prof. Brian Harbourne from the University of Nebraska-Lincoln (USA) between 1985 and 2009, also in the period 2002-2009 by the members of the research group, calles Singacom, of the University of Valladolid (Spain) and whose coordinator is Prof. Antonio Campillo. Recently, between 2007 and 2010, the members of the group, called Algebraic Geometry Team, of the University of Michoacan and whose coordinator is Prof. Mustapha Lahyane have obtained significant results about the Geometry of new classes of smooth projective rational surfaces over an algebraically closed field of any characteristic. The results are based on two new concepts: the first is numerical and the second is a generalization of the so called Enriques diagrams (Enriques diagrams have been used intensively by the members of the Singacom group, by the Barcelona group whose coordinator is Prof. Eduardo Casas-Alvero and by Prof. Gerard Gonzalez-Sprinberg from the University of Grenoble (France)) . The picture shows a new family of smooth projective rational surfaces whose all geometries, except the two irreducible and reduced curves (the two green ones in the picture), are encoded in a well-defined divisor associated to the surface. This amazing result constitutes a particular case of many results obtained by Prof. Mustapha Lahyane (IFM-UMSNH) and which are published in the volume 214 (issue 7, July 2010, pages 1217-1248) of the Jorunal of Pure and Applied Algebra.

Life time of wormholes can be extended if electric charge is added. In previous studies [Class. Quantum Grav. 26 (2009) 015010, Class. Quantum Grav. 26 (2009) 015011], González, Guzmán and Sarbach, members of the IFM showed that standard Wormholes supported by a ghost scalar field are unstable, both, based on the analysis of perturbations and in the non-linear regime using numerical relativity. They established that the time scale associated to the collapse into a black hole is of the order of the throat's areal radius divided by the speed of light, which is of the order of a few microseconds for a throat with areal radius of one kilometer. In their more recent paper [Phys. Rev. D 80, 024023 (2009)], our three members show that Wormhole solutions with electrictromagnetic charge are also unstable in the regime allowed for the study (a mixture of perturbation analysis and numerical methods), however the time scale for the collapse can be increased by a factor of 100 (!).

Resultado, Marzo 2009
The book Beyond partial differential equations. On linear and quasi-linear abstract hyperbolic evolution equations by Professor Horst Beyer (IFM), published in the Lecture Notes on Mathematics #1898, has been included in the sixteen HIGHLIGHTS selected by the editors of Zentralblatt MATH for 2008. (see more).

Resultado, Diciembre 2008

Figura del Mes: Propagador del Electrón en la teoría de Maxwell-Chern-Simons QED3. En la figura se muestran las proyecciones vectoriales y escalares en la base quiral del propagador del electrón en la teoría de Maxwell-Chern-Simons QED3 en diferentes normas covariantes. Se muestra una comparación entre el cálculo al orden dominante en la teoría de perturbaciones y el resultado no perturbativo obtenido a través de la transformación de Landau-Khalatnikov-Fradkin del propagador desnudo. La teoría de Maxwell-Chern-Simons QED3 describe las interacciones entre electrones restringidos a moverse en un plano y fotones que poseen una masa topológica. Estos resultados han sido publicados recientemente en revista Journal of Physics A: Mathematical and Theoretical por Adnan Bashir, Alfredo Raya y Saúl Sánchez Madrigal (ver J. Phys. A41, 505401, 2008). El artículo ha sido seleccionado por el comité editorial del IOP Publishing para incluirse en el IOP Select, http://Select.iop.org, una colección especial de artículos publicados en revistas de esta editorial.

Resultado, Julio 2008

Figura del Mes: En esta figura se presenta el potencial mecánico-cuántico y los estados ligados de la función de onda de las fluctuaciones de una métrica pentadimensional. Si consideramos que nuestro universo tiene cinco dimensiones en lugar de cuatro y suponemos que la métrica del espacio tiempo está deformada por cierta función que sólo dependa de la quinta dimensión (por el factor de deformación), podemos hallar una solución exacta denominada métrica de fondo. Al perturbar esta métrica y realizar un estudio de la dinámica de los modos transversos de traza nula de dichas fluctuaciones, podemos ver que éstas obedecen una ecuación de Schroedinger con un potencial tipo Poeschl-Teller (línea en negro), como en la Mecánica Cuántica, que tiende asintóticamente a un valor positivo, hecho que garantiza la existencia de un salto en el espectro de masas (mass gap) y elimina el problema de la posible detección experimental de los modos masivos ultraligeros. En realidad se tienen dos estados ligados: uno sin masa (en rojo) y una excitación masiva (en azul); el estado no masivo es interpretado como el gravitón tetradimensional. También existe todo un espectro de modos masivos que asintóticamente se comportan como ondas planas y son los responsables de pequeñas correcciones a la segunda ley de Newton, mismas que pueden ser calculadas explícitamente. Este análisis refleja que a pesar de que hasta el momento sólo hemos observado cuatro dimensiones, la existencia de las dimensiones extra no entra en contradicción con los experimentos gravitatorios realizados hasta la fecha: lo que se requiere es la realización de experimentos más precisos que puedan arrojar evidencias o refutar la existencia de las dimensiones adicionales de nuestro espacio tiempo, como los que se van a realizar en el Large Hadron Collider (LHC) durante el otoño próximo. Estos resultados han sido publicados recientemente en la revista Physical Review D por Nandinii Barbosa Cendejas, Alfredo Herrera Aguilar, Marco Antonio Reyes Santos y Christian Schubert. Ver Phys. Rev. D 77, 126013 (2008).

Resultado, Junio 2008

Figura del Mes: Construimos una asintótica para tiempos grandes para todas las soluciones del sistema de Lamb no lineal, que tienen energía finita, y por primera vez se establece tal asint\'otica en la norma energética global para dichas soluciones. Es decir, cada solución a el sistema acoplado decae a una suma de dos componentes cuando $t\to+\infty$: un estado estacionario y una onda que se dispersó. Las ondas que se dispersan corresponden a estados asitóticos incidentes y reflejados. Finalmente se construyen los operadores de dispersión y se obtienen condiciones necesarias para los estados asintóticos. Estos resultados están reportados en el artículo {\sf ``Scattering in the Zero-mass Lamb System" } aceptado para su publicación en PHYSICS LETTERS A y cuyos autores son: Dr. Anatoli Merzon y M.C. Marco Antonio Taneco-Hernández.Para saber máa presiona aquí. (Para ver la figura con mejor calidad: hacer click en la figura).

Resultado, Abril 2008

Figura del Mes: Estas fuguras muestran haces de geodesicas nulas durante el colapso de un hoyo de gusano en un hoyo negro [un hoyo de gusano es una variedad con dos regiones asintóticas planas, conectadas a través de una garganta]. Estos resultados se calcularon usando métodos numéricos para resolver las ecuaciones de Einstein. (Izquierda) Se muestra el Horizonte Aparente (verde) y un haz de rayos nulos (rojo) que divergen de una superficie identificada con un Horizonte de Eventos. Para x>0 (x<0) el Horizonte Aparente queda fuera (dentro) del Horizonte de Eventos, lo que podría indicar que el primero fuera una superficie tipo-espacio. La línea gruesa negra muestra una posible trayectoria de una geodésica nula que va de un universo al otro y se puede reflejar de regreso sin quedar atrapada por el agujero negro. (Derecha) Se muestran los conos de luz sobre el Horizonte Aparente para x>0; las flechas azules y negras indican las direcciones salientes y entrantes de los conos de luz. Este resultado indica que el Horizonte Aparente es en realidad una superficie tipo-tiempo. Estos resultados han sido registrados por J. A. González, F. S. Guzmán, O. Sarbach, investigadores del IFM y pronto serán publicados. El trabajo que contiene estos resultados titulado "How to throw a boomerang through a wormhole", obtuvo el primer lugar en el Primer Concurso Nacional de Ciencias Físicas de Segundo Congreso Nacional Universitario de Física, UDLA 2008. [Aquí el poster ganador]. (Para ver la figura con mejor calidad: hacer click en la figura).

Resultado, Noviembre-Diciembre 2007