A comparative study of the nonuniqueness problem of the potential equation

The nonuniqueness problem occurring at transonic speeds with the conservative potential equation is investigated numerically. The study indicates that the problem is not an inviscid phenomenon, but results from approximate treatment of shock waves inherent in the conservative potential model. A new bound on the limit of validity of the conservative potential model is proposed

Is law an immoral profession? An appetizer for the cultivators of ethics and juridical deontology

Muchas de las recomendaciones de la deontología jurídica conducentes a elaborar, en términos bien abstractos, algún perfil del buen jurista son básicamente ingenuas, pero sobre todo inútiles. Ellas suelen partir de un doble prejuicio, muy arraigado en la actualidad: a) por un lado, de que es posible enseñar moral a cualquier profesional —en este caso, al jurista ya formado— para lo cual se suelen implementar simplemente unos códigos de ética e impartir unos cursos deontológicos (¡de fin de semana!) al respecto; y, b) por otro lado, de que la profesión legal se puede ejercer de conformidad con parámetros estrictamente morales. En este artículo se desarman teoréticamente ambas creencias y se muestra cómo el ejercicio práctico del Derecho requiere —por la misma dinámica implícita en la profesión— una cierta dosis de deshonestidad y con ello de inmoralidad. Cuánta sea esa dosis dependerá de las circunstancias personales de cada profesional considerado in concreto. Finalmente, el trabajo analiza (no a título de un recetario, sino de algunas pistas heurísticas) cómo combatir, hasta donde se puede, esta inmoralidad intrínseca de la actividad jurídica.Many of the advices of legal ethics and deontology leading to elaborate, in a very abstract manner, the profile of a good lawyer are basically naive, but above all useless. These advices are born of a double prejudice which is very common nowadays: a) first, that it is possible to teach morality to any professional person —in this case to the lawyer who has already graduated— for which purpose some codes of ethics meticulously written and some moral courses (taught at weekend time!) will suffice. b) Second, that it is possible to practice the legal profession according to strict moral criteria. In this essay, both beliefs are theoretically demystified to show that the daily practice of law requires, in view of its internal logic and dynamic, a certain magnitude of dishonesty and therefore of immorality. The amount of this will depend on the particular person considered. Finally, the article studies (not as a mere recipe, but as a heuristic suggestion) how to fight, so far as possible, this intrinsic immorality of the legal profession

Supercritical super-Brownian motion with a general branching mechanism and travelling waves

We consider the classical problem of existence, uniqueness and asymptotics of monotone solutions to the travelling wave equation associated to the parabolic semi-group equation of a super-Brownian motion with a general branching mechanism. Whilst we are strongly guided by the probabilistic reasoning of Kyprianou (2004) for branching Brownian motion, the current paper offers a number of new insights. Our analysis incorporates the role of Seneta-Heyde norming which, in the current setting, draws on classical work of Grey (1974). We give a pathwise explanation of Evans' immortal particle picture (the spine decomposition) which uses the Dynkin-Kuznetsov N-measure as a key ingredient. Moreover, in the spirit of Neveu's stopping lines we make repeated use of Dynkin's exit measures. Additional complications arise from the general nature of the branching mechanism. As a consequence of the analysis we also offer an exact X(log X)^2 moment dichotomy for the almost sure convergence of the so-called derivative martingale at its critical parameter to a non-trivial limit. This differs to the case of branching Brownian motion and branching random walk where a moment `gap' appears in the necessary and sufficient conditions.Comment: 34 page

Shock-fitted Euler solutions to shock-vortex interactions

The interaction of a shock wave with a hot spot, a single vortex and a vortex street is studied within the framework of the two dimensional compressible Euler equations. The numerical results obtained by the pseudospectral method and the finite difference MacCormack method are compared. In both the methods the shock wave is fitted as a boundary of the computational domain

Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus

We analyze the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L^{-3} to the energy and the corrections of order L^{-2} and L^{-3} to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: only integer powers of L^{-1} occur, unmodified by logarithms (except of course for the leading $\log L$ term in the specific heat); and the energy expansion contains only odd powers of L^{-1}. In the specific-heat expansion any power of L^{-1} can appear, but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion.Comment: 26 pages (LaTeX). Self-unpacking file containing the tex file and three macros (indent.sty, eqsection.sty, subeqnarray.sty). Added discussions on the results and new references. Version to be published in J. Phys.

A hypercyclic finite rank perturbation of a unitary operator

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space \H are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.Comment: published in Mathematische Annale

REAM intensity modulator-enabled 10Gb/s colorless upstream transmission of real-time optical OFDM signals in a single-fiber-based bidirectional PON architecture

Reflective electro-absorption modulation-intensity modulators (REAM-IMs) are utilized, for the first time, to experimentally demonstrate colorless ONUs in single-fiber-based, bidirectional, intensity-modulation and direct-detection (IMDD), optical OFDM PONs (OOFDM-PONs) incorporating 25km SSMFs and OLT-side-seeded CW optical signals. The colorlessness of the REAM-IMs is characterized, based on which optimum REAM-IM operating conditions are identified. In the aforementioned PON architecture, 10Gb/s colorless upstream transmissions of end-to-end realtime OOFDM signals are successfully achieved for various wavelengths within the entire C-band. Over such a wavelength window, corresponding minimum received optical powers at the FEC limit vary in a range as small as <0.5dB. In addition, experimental measurements also indicate that Rayleigh backscattering imposes a 2.8dB optical power penalty on the 10Gb/s over 25km upstream OOFDM signal transmission. Furthermore, making use of on-line adaptive bit and power loading, a linear trade-off between aggregated signal line rate and optical power budget is observed, which shows that, for the present PON system, a 10% reduction in signal line rate can improve the optical power budget by 2.6dB. © 2012 Optical Society of America