On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie

A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particulary important function, related to the $\tau$-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for an convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Benney gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized

String equations in Whitham hierarchies: tau-functions and Virasoro constraints

A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The tau-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characterized. Illustrative examples of exact solutions of Whitham hierarchies are derived and applications to conformal maps dynamics are indicated.Comment: 26 pages, 2 figure

S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies

We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these $S$-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the $S$-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic type systems. In particular, for the 1-component and 2-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel package

Additional symmetries and solutions of the dispersionless KP hierarchy

The dispersionless KP hierarchy is considered from the point of view of the twistor formalism. A set of explicit additional symmetries is characterized and its action on the solutions of the twistor equations is studied. A method for dealing with the twistor equations by taking advantage of hodograph type equations is proposed. This method is applied for determining the orbits of solutions satisfying reduction constraints of Gelfand--Dikii type under the action of additional symmetries.Comment: 21 page

Commercial scale membrane distillation for solar desalination

Abstract Membrane distillation is an attractive technology for solar-powered decentralized desalination that has not yet reached commercial breakthrough on a large scale. The main barriers are energy consumption and cost. Since the latter are mostly related to the former, thermal energy efficiency is key to assessing the potential of the different available membrane distillation systems at a commercial scale. As discussed here, existing membrane distillation technologies use mostly flat sheet membranes in plate and frame and spiral-wound modules. Modules based on hollow fibre membranes are also considered, as well as the concept of multi-effect vacuum membrane distillation for improved heat recovery. The heat efficiency of each system is analysed based on available experimental results. Better internal heat recovery and capacity for upscaling are found to be important elements of distinction which make multi-channelled spiral-wound modules working in air-gap configuration stand out currently, with the lowest heat consumption of all large scale modules. Potential for improvement of this and other technologies is also discussed, and an estimation based on the associated costs for solar energy is used for establishing boundary conditions towards the implementation of membrane distillation for solar desalination

Struggles and pacification in the history of american kinesiology

En este artículo estudiamos la disputa epistemológica y pedagógica sobre la kinesiología/educación física que ha tenido lugar en las universidades de Estados Unidos desde 1990 hasta la actualidad. Hemos recogido el pensamiento de una muestra amplia de autores involucrados, con el propósito de obtener una visión de conjunto de un proceso que, de acuerdo con Morrow (2006), trata de esclarecer ¿de dónde venimos?, ¿qué somos?, ¿a dónde vamos? Tras el cotejo y análisis de la documentación más relevante concluimos que el periodo 1990-2013, caracterizado por una enconada pugna de paradigmas –en la que han estado implicados humanistas, positivistas, crosdisciplinaristas y subdisciplinaristas–, ha dado como resultado el dominio del paradigma integrador de Kretchmar (2007, 2008)In this article we review the epistemological and pedagogical debate on Kinesiology and Physical Education that has been going on in the universities of the US from 1990 to the present. We have compiled the opinions of a wide sample of authors, with the intention of getting the most complete picture of a process that, according to Morrow (2006), seeks to answer the questions "where we come from, who we are, and where we are going". After comparing and analysing the most relevant documents, we conclude that the period 1990-2013, characterized by a bitter struggle between paradigms fought by humanists, positivists, cross-disciplinarists, and sub-disciplinarists, has revealed the eventual predominance of the integrative paradigm of Kretchmar (2007, 2008

Culture of paso de la amada, creator of ‘mesoamerican ballgame’

Se realiza una revisión sobre el origen del juego de pelota mesoamericano en el preclásico temprano (ca.1.700-1.000 a.C.). Por la antigüedad propuesta para sus vestigios sobre el juego de pelota, son candidatos a ser los ‘creadores del juego’ las culturas de Paso de la Amada, los pre-olmecas de San Lorenzo y El Opeño. Los vestigios referidos son fundamentalmente, la cancha de Paso de la Amada, las pelotas de hule de Manatí y las figurillas de El Opeño. Se concluye que la gran cancha de Paso de la Amada, la mayor construcción de Mesoamérica de su tiempo, aparece como el vestigio más antiguo del juego, y se le relaciona con la aparición de la primera sociedad no igualitaria en Mesoamérica. Se sugiere que los pobladores de Paso de la Amada, hacia 1650 a.C., fueron los creadores del juego y no los olmecas como generalmente se ha defendidoWe study here the origin of the Mesoamerican ballgame during the early formative period (ca. 1700 B.C.). We select as candidates for the creators of the Mesoamerican ballgame the cultures of Paso de la Amada, pre-Olmec at San Lorenzo, and El Opeño, as they have the oldest vestiges of the ballgame. These vestiges are, to be exact, a ball court at Paso de la Amada, some rubber balls at Manati, and ceramic figurines at El Opeño. We conclude that the great ball court at Paso de la Amada, the biggest building of Mesoamerica at that time, appears as the oldest vestige of the game and it is in relation with the emergence of ranked societies in Mesoamerica. We suggest that the people of Paso de la Amada, around 1650 BC, were the creators of the game, and not the Olmecs, as generally defende