Medium carbon steel deep drawing: A study on the evolution of mechanical properties, texture and simulations, from cold rolling to the end product

Medium carbon steels are mostly used for simple applications; nevertheless new applications have been developed for which good sheet formability is required. This class of steels has an inherent low formability. A medium carbon hot rolled SAE 1050 steel has been selected for this study. It has been cold rolled with reductions in the 7-80% range. Samples have been used to assess the cold work hardening curve. For samples with a 50 and 80% thickness reduction, an annealing heat treatment has been performed to obtain recrystallization. The material has been characterized in the ""as received"", cold rolled and annealed conditions, using several methods: optical microscopy, X-ray diffraction (texture), Vickers hardness and tensile testing. The 50% cold rolled and recrystallized material has been further studied in terms of sheet metal formability and texture evolution during the actual stamping of a steel toecap that has been used to validate the finite element simulations. (C) 2008 Elsevier B.V. All rights reserved.

Theoretical approach including friction for determining strain limits in punch stretching of anisotropic sheet metals

A new analytical theory including friction was developed to assess strain limits in punch stretching of anisotropic sheet metals. This new approach takes into consideration the anisotropic behaviour of sheet materials and could explain the mechanical behaviour of a variety of anisotropic sheet materials. The theory explains the sheet metal failure so for the drawing as the stretching region of the forming limit curve, particularly for materials that present the strain-ratio dependence of limit strain ε 1, where dε 1/dρ is not always greater than zero. dε 1/ dρ or dε 1/dε 2 could be equal to or smaller than zero for a range of materials. Therefore, this new theory can explains such experimental observations, besides to assuming that membrane element relations near the pole, for the case of punch stretching are dependent of sheet metal properties as the process history and also suggests that the onset of local necking is controlled by shear. Thus, theoretical results obtained through this new approach are compared with experimental results available in the literature. It is demonstrated the effect of friction on a FLC curve for both regions, drawing and stretching. © 2010 American Institute of Physics.

Thermodynamic and topological instability approaches for forecasting glass-forming ability in the ternary Al-Ni-Y system

A thermodynamic approach to predict bulk glass-forming compositions in binary metallic systems was recently proposed. In this approach. the parameter gamma* = Delta H-amor/(Delta H-inter - Delta H-amor) indicates the glass-forming ability (GFA) from the standpoint of the driving force to form different competing phases, and Delta H-amor and Delta H-inter are the enthalpies for-lass and intermetallic formation, respectively. Good glass-forming compositions should have a large negative enthalpy for glass formation and a very small difference for intermetallic formation, thus making the glassy phase easily reachable even under low cooling rates. The gamma* parameter showed a good correlation with GFA experimental data in the Ni-Nb binary system. In this work, a simple extension of the gamma* parameter is applied in the ternary Al-Ni-Y system. The calculated gamma* isocontours in the ternary diagram are compared with experimental results of glass formation in that system. Despite sonic misfitting, the best glass formers are found quite close to the highest gamma* values, leading to the conclusion that this thermodynamic approach can lie extended to ternary systems, serving as a useful tool for the development of new glass-forming compositions. Finally the thermodynamic approach is compared with the topological instability criteria used to predict the thermal behavior of glassy Al alloys. (C) 2007 Elsevier B. V. All rights reserved.

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Lujasta rakenneteräksestä tehdyn rakenteen vikasietoisuuden määritys

Tässä työssä tutkittiin Ruukin valmistamista lujista Optim 700 MC Plus sekä Optim 700 QL teräksistä tehtyjen hitsattujen palkkirakenteiden vikasietoisuutta sekä murtumiskäyttäytymistä laboratoriossa suoritettujen täyden mittakaavan kokeiden avulla. Koerakenteet suunniteltiin siten, että rakenteen kylmämuovauksen sekä hitsauksen vaikutukset yhdessä rakenteen geometrian vaikutuksen kanssa heikentävät rakenteen murtumissitkeyttä rakenteeseen tehdyn teräväkärkisen alkusärön tasossa. Suunnitellussa koesarjassa varioidaan testauslämpötilan lisäksi hitsauksen lämmöntuontia sekä koerakenteeseen tehtävän alkusärön kokoa. Tässä työssä tavoitteena oli yleisesti esittää menettely hitsatun säröllisen teräsrakenteen kestävyyden arviointia varten. Optim 700 MC Plus teräksestä tehdyn koerakenteen käyttäytymistä tutkittiin laskennallisesti murtumismekaniikan avulla. Laadittujen FEM - mallien avulla laskettiin rakenteen murtumisparametrien arvot kummallekin tutkittavalle teräkselle. Optim 700 MC Plus materiaalista valmistetuille koerakenteen säröalueen rakennedetaljia vastaavalle koekappaleille suoritettiin murtumissitkeyskokeita. Murtumissitkeyskokeista saatujen tulosten avulla pystyttiin kuvaamaan täyden mittakaavan koerakenteessa olevan särön murtumiskäyttäytymistä mitoitusmenetelmissä. Koerakenteelle laskettiin tässä työssä kriittisen särökoon ja sitä vastaavan kuorman arvot perustuen rakenteen oletettuun hauraaseen, epästabiiliin sitkeään sekä plastiseen murtumiskäyttäytymiseen. Tässä työssä testattiin molemmista tutkittavista materiaaleista valmistetut täyden mittakaavan koerakenteet -40 °C lämpötilassa. Molemmat testatut rakenteet käyttäytyvät mitattujen siirtymätulosten perusteella melko hauraasti. Optim 700 MC Plus materiaalille saatujen laskentatulosten voidaan todeta testatun koekappaleen perusteella soveltuvan hauraasti käyttäytyvän rakenteen mitoitukseen.

Investigations into the determinations of hydride-forming elements

Analytical methods for the determination of trace amounts of germanium, tin and arsenic were established using hydride generation coupled with direct current plasma atomic emission spectrometry. A continuous gas flowing batch system for the hydride generation was investigated and was applied to the determination of germanium(Ge), tin(Sn), antimony(Sb) and lead(Pb) (Preliminary results suggest that it is also applicable to arsenic)As) ). With this system, the reproducibility of signals was improved and the determination was speeded up, compared with the conventional batch type hydride generation system. Each determination was complete within one minute. Interferences from a number of transition metal ions, especially from Pd(II), Pt(IV), Ni(II), Cu(II), Co(II), and Fe(II, III), have proven to be very serious under normal conditions, in the determination of germanium, tin, and arsenic. These interference effects were eliminated or significantly reduced in the presence of L-cystine or L-cysteine. Thus, a 10-1000 fold excess of Ni(II), Cu(II), Co(II), Fe(II), Pt(IV), Pd(II), etc. can be tolerated without interference, In the presence of L-cystine or L-cysteine, compared with absence of interference reducing agent. The methods for the determination of Ge, Sn, and As were examined by the analyses of standard reference materials. Interference effects from the sample matrix, for example, in transition metal-rich samples, copper, iron and steel, were eliminated by L-cystine (for As and Sn) and by LI cysteine (for Ge). The analysis of a number of standard reference materials gave excellent results of As and Sn contents in agreement with the certified values, showing there was no systematic interference. The detection limits for both germanium and tin were 20 pg ml- I . Preliminary studies were carried out for the determination of antimony and lead. Antimony was found to react with NaBH4, remaInIng from the previous determinations, giving an analytical signal. A reversed injection manner, i.e., injection of the NaBH4 solution prior to the analyte solution was used to avoid uncertainty caused by residual NaBH4 present and to ensure that an excess of NaB H4 was available. A solution of 0.4% L-cysteine was found to reduce the interference from selected transition metal ions, Co(II), Cu(II), Ni(II) and Pt(IV). Hydrochloric acid - hydrogen peroxide, nitric acid - ammonium persulphate, and potassium dichromate malic acid reaction systems for lead hydride generation were compared. The potassium dichromate - malic acid reaction medium proved to be the best with respect to reproducibility and minimal interference. Cu(II), Ni(II), and Fe(II) caused strong interference In lead determinations, which was not reduced by L-cysteine or Lcystine. Sodium citrate, ascorbic acid, dithizone, thiosemicarbazide and penicillamine reduced interferences to some extent. Further interference reduction studies were carried out uSIng a number of amino acids, glycine, alanine, valine, leucine and histidine, as possible interference reducing agents in the determination of germanium. From glycine, alanine, valine to leucine, the interference reduction effect in germanium determinations decreased. Histidine II was found to be very promising In the reduction of interference. In fact, histidine proved more efficient than L-cystine and L-cysteine In the reduction of interference from Ni(II) in the determination of germanium. Signal enhancement by easily ionized elements (EIEs), usually regarded as an interference effect in analysis by DCP-AES, was studied and successfully applied to advantage in improving the sensitivity and detection limit in the determination of As, Ge, Sn, Sb, and Pb. The effect of alkali and alkaline-earth elements on the determination of the above five hydride forming elements was studied. With the appropriate EIE, a signal enhancement of 40-115% was achieved. Linear calibration and good reproducibility were also obtained in the presence of EIEs. III

Monte Carlo phase diagram for diblock copolymer melts

A partial phase diagram is constructed for diblock copolymer melts using lattice-based Monte Carlo simulations. This is done by locating the order-disorder transition (ODT) with the aid of a recently proposed order parameter and identifying the ordered phase over a wide range of copolymer compositions (0.2 <= f <= 0.8). Consistent with experiments, the disordered phase is found to exhibit direct first-order transitions to each of the ordered morphologies. This includes the spontaneous formation of a perforated-lamellar phase, which presumably forms in place of the gyroid morphology due to finite-size and/or nonequilibrium effects. Also included in our study is a detailed examination of disordered cylinder-forming (f=0.3) diblock copolymers, revealing a substantial degree of pretransitional chain stretching and short-range order that set in well before the ODT, as observed previously in analogous studies on lamellar-forming (f=0.5) molecules. (c) 2006 American Institute of Physics.

Micelles forming biaxial lyotropic nematic phases

The paper by Yu and Saupe on the first biaxial nematic phase created excitement for a number of reasons. Some theories of biaxial phases already existed, but experimental observation was still lacking. The phase was discovered in a lyotropic system with three components, which in theory is difficult. Lyotropic liquid crystals are composed of supramolecular assemblies of amphiphilic molecules, which may change shape and size as a function of concentration and temperature. The experimental phase diagram of the lyotropic biaxial phase was rather complex, with the biaxial region inserted between nematic cylindrical and nematic discotic phases via second-order transitions. In addition, re-entrant behaviour was evident. Saupe investigated further systems experimentally, observing that the biaxial phase might be absent in cases where a direct transition between the cylindrical and discotic phases occurred. He provided a range of theoretical and experimental contributions on the properties of these lyotropics, but was very cautious regarding the detailed amphiphilic assemblies involved. The present paper reviews this area, focusing on proposals for the structure of the micellar assemblies. Emphasis is placed on recent papers which indicate a transformation of the two uniaxial shapes, in mixing conditions, both from the theoretical and the experimental point of view, and to questions still requiring further study.

Structure, mobility and clustering of interstitial O in La2CuO4+delta in the limit of small delta

Anelastic spectra (elastic energy absorption as a function of temperature) are reported which provide evidence that excess O in La2CuO4+delta starts forming two different types of defects already at very low concentrations, where no phase separation or changes in the type of O intercalation are believed to occur. The absorption peak with the lowest activation enthalpy, H/k(B) = 5600 K, is visible at lowest values of delta and is attributed to the hopping of single interstitial O2- ions. The second process, with a slightly slower dynamics, appears at higher values of delta and soon becomes preponderant over the former process. The latter process is proposed to be due to stable pairs of O atoms and is put in connection with the formation of partially covalent bonds between interstitial and apical oxygen; such bonds would reduce the doping efficiency of excess O at increasing delta. The geometry of the interstitial O defect is discussed. O 1998 Published by Elsevier B.V. B.V. All rights reserved.

Análises de falhas em eixo de laminadora

Pós-graduação em Engenharia Mecânica - FEG

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.

Surface modification by metal ion implantation forming metallic nanoparticles in insulating matrix.

There is special interest in the incorporation of metallic nanoparticles in a surrounding dielectric matrix for obtaining composites with desirable characteristics such as for surface plasmon resonance, which can be used in photonics and sensing, and controlled surface electrical conductivity. We investigated nanocomposites produced through metallic ion implantation in insulating substrate, where the implanted metal self-assembles into nanoparticles. During the implantation, the excess of metal atom concentration above the solubility limit leads to nucleation and growth of metal nanoparticles, driven by the temperature and temperature gradients within the implanted sample including the beam-induced thermal characteristics. The nanoparticles nucleate near the maximum of the implantation depth profile (projected range), that can be estimated by computer simulation using the TRIDYN. This is a Monte Carlo simulation program based on the TRIM (Transport and Range of Ions in Matter) code that takes into account compositional changes in the substrate due to two factors: previously implanted dopant atoms, and sputtering of the substrate surface. Our study suggests that the nanoparticles form a bidimentional array buried few nanometers below the substrate surface. More specifically we have studied Au/PMMA (polymethylmethacrylate), Pt/PMMA, Ti/alumina and Au/alumina systems. Transmission electron microscopy of the implanted samples showed the metallic nanoparticles formed in the insulating matrix. The nanocomposites were characterized by measuring the resistivity of the composite layer as function of the dose implanted. These experimental results were compared with a model based on percolation theory, in which electron transport through the composite is explained by conduction through a random resistor network formed by the metallic nanoparticles. Excellent agreement was found between the experimental results and the predictions of the theory. It was possible to conclude, in all cases, that the conductivity process is due only to percolation (when the conducting elements are in geometric contact) and that the contribution from tunneling conduction is negligible.

Thermodynamics of Forming Water Clusters at Various Temperatures and Pressures by Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO Model Chemistries; Implications for Atmospheric Chemistry

The Gaussian-2, Gaussian-3, complete basis set- (CBS-) QB3, and CBS-APNO methods have been used to calculate ΔH° and ΔG° values for neutral clusters of water, (H2O)n, where n = 2−6. The structures are similar to those determined from experiment and from previous high-level calculations. The thermodynamic calculations by the G2, G3, and CBS-APNO methods compare well against the estimated MP2(CBS) limit. The cyclic pentamer and hexamer structures release the most heat per hydrogen bond formed of any of the clusters. While the cage and prism forms of the hexamer are the lowest energy structures at very low temperatures, as temperature is increased the cyclic structure is favored. The free energies of cluster formation at different temperatures reveal interesting insights, the most striking being that the cyclic trimer, cyclic tetramer, and cyclic pentamer, like the dimer, should be detectable in the lower troposphere. We predict water dimer concentrations of 9 × 1014 molecules/cm3, water trimer concentrations of 2.6 × 1012 molecules/cm3, tetramer concentrations of approximately 5.8 × 1011 molecules/cm3, and pentamer concentrations of approximately 3.5 × 1010 molecules/cm3 in saturated air at 298 K. These results have important implications for understanding the gas-phase chemistry of the lower troposphere.

A Simple Visual Demonstration of Phase Diagram Concepts for an Introductory Materials Science Course Using Colored Solvents

A simple and effective demonstration to help students comprehend phase diagrams and understand phase equilibria and transformations is created using common chemical solvents available in the laboratory. Common misconceptions surrounding phase diagram operations, such as components versus phases, reversibility of phase transformations, and the lever rule are addressed. Three different binary liquid mixtures of varying compatibility create contrastive phase equilibrium cases, where colorful dyes selectively dissolved in each of corresponding phases allow for quick and unambiguous perceptions of solubility limit and phase transformations. Direct feedback and test scores from a group of students show evidence of the effectiveness of the visual and active teaching tool.

Resonancias de los paradigmas científicos en las arquitecturas de la Escuela de Madrid

Los años cincuenta y sesenta son los años de la incorporación definitiva de la arquitectura española al panorama internacional. Entre los arquitectos que protagonizan ese salto sin retorno, se encuentra el grupo de aquellos que unos años más tarde serán denominados por Juan Daniel Fullaondo como Escuela de Madrid. Carlos Flores, en su libro Arquitectura Española Contemporánea 1880-1950, se refiere a esos arquitectos como aquellos que se aplicaban a la difícil tarea de restablecer en España un tipo de arquitectura que conectaba con las teorías, soluciones y lenguajes establecidos por Europa durante las primeras décadas del siglo XX. Sigfried Giedion plantea en Espacio, Tiempo y Arquitectura el origen de una nueva tradición, surgida a partir de la revolución óptica de principios de siglo. Con tradición se refiere a una nueva cultura, que abarca la interrelación de las diferentes actividades del hombre: la similitud de los métodos que se usan en la arquitectura, la construcción, la pintura, el urbanismo o la ciencia. Esa novedad, fundamentada en su independencia y desvinculación con el periodo anterior, se inscribe dentro del esquema evolutivo que Thomas Kuhn plantea en su texto La Estructura de la Revoluciones Científicas, conforme a periodos no acumulativos. Kuhn habla del surgimiento de anomalías en cada periodo, origen de las crisis de pensamiento cuya explicación precisará un necesario cambio paradigmático. En la ciencia, en el campo de la óptica Thomas Young demuestra a principios del siglo XIX la naturaleza ondulatoria de la luz con su experimento de doble rendija; en el electromagnetismo se produce el salto conceptual que supone la postulación de la existencia del campo eléctrico por parte de Michael Faraday, y en termodinámica la consideración apuntada por Planck de que la radiación de la energía de produce de forma discreta, a través de cuantos. En las artes plásticas, paralelamente, Gleizes y Metzinger, en su recopilación de logros cubistas recogida en Sobre el Cubismo, hablan de la evolución sufrida durante el siglo XIX por la pintura: desde el idealismo de principios de siglo, para pasando por el realismo y la representación impresionista de la realidad, concluir prescindiendo de la perspectiva clásica. También la matemática, una vez desarrolladas por Gauss o Lobachevsky y Bolyai geometrías coherentes que incumplen el quinto postulado de Euclides, terminará dando validez a través de Riemann a los espacios ambiente en los que habitan dichas geometrías, desvinculando la relación directa entre espacio geométrico –el espacio ambiente al que da lugar un tipo de geometría- y el espacio físico. Capi Corrales refleja en su libro Contando el Espacio, cómo hasta la teoría de la relatividad y el cubismo, las geometrías no euclídeas no se hicieron notorias también fuera del campo de las matemáticas. El origen de la nueva tradición con la que Giedion se refiere a la nueva cultura de la modernidad coincide con los saltos paradigmáticos que suponen la teoría de la relatividad en las ciencias y el cubismo en las artes plásticas. Ambas se prolongan durante las primeras décadas hasta la teoría cuántica y la abstracción absoluta, barreras que los dos principales precursores de la relatividad y el cubismo, Einstein y Picasso, nunca llegan a franquear. En ese sentido Giedion habla también, además del origen, de su desarrollo, e incorpora las aportaciones periféricas en la arquitectura de Brasil, Japón o Finlandia, incluyendo por tanto la revisión orgánica propugnada por Zevi como parte de esa nueva tradición, quedando abierta a la incorporación tardía de nuevas aportaciones al desarrollo de esa cultura de la modernidad. Eliminado el concepto de la estética trascendental de Kant del tiempo como una referencia absoluta, y asumido el valor constante de la velocidad de la luz, para la teoría de la relatividad no existe una simultaneidad auténtica. Queda así fijada la velocidad de la luz como uno de los límites del universo, y la equivalencia entre masa y energía. En el cubismo la simultaneidad espacial viene motivada por la eliminación del punto de vista preferente, cuyo resultado es la multiplicidad descriptiva de la realidad, que se visualiza en la descomposición en planos, tanto del objeto como del espacio, y la consecuente continuidad entre fondo y figura que en arquitectura se refleja en la continuidad entre edificio y territorio. Sin la consideración de un punto de vista absoluto, no existe una forma auténtica. El cubismo, y su posterior desarrollo por las vanguardias plásticas, hacen uso de la geometría como mecanismo de recomposición de la figura y el espacio, adoptando mecanismos de penetración, superposición y transparencia. Gyorgy Kepes indica en El Lenguaje de la Visión que la descomposición cubista del objeto implica la sucesiva autonomía de los planos, hasta convertirse en elementos constituyentes. Algo que refleja las axonometrías arquitectónicas de Van Doesburg y que culmina con los espacios propuestos por Mies van der Rohe en sus primeros proyectos europeos. Estos mecanismos, encuentran eco en los primeros planteamientos de Javier Carvajal: en la ampliación del Panteón de españoles del cementerio de Campo Verano, un recinto virtual reconstruido mentalmente a partir del uso de tres únicos planos; o en el Pabellón de Nueva York, que organiza su planta baja desde el recorrido, introduciendo el parámetro temporal como una dimensión más. Al uso diferenciado del plano como elemento constituyente, Carvajal incorpora su plegado y su disposición conformando envolventes como mecanismo de cualificación espacial y formal, potenciando la prolongación entre arquitectura y territorio. Una continuidad que quedará culminada en las dos viviendas unifamiliares construidas en Somosaguas. La descomposición volumétrica conduce a unos niveles de abstracción que hace precisa la incorporación de elementos de la memoria -fuentes, patios, celosías…- a modo de red de señales, como las que Picasso y Braque introducen en sus cuadros para permitir su interpretación. Braque insiste en el interés por el espacio que rodea a los objetos. Una búsqueda de la tactilidad del espacio contraria a la perspectiva que aleja el objeto del observador, y que en los jardines de las viviendas de Somosaguas parece emanar de su propia materialidad. Un espacio táctil alejado del espacio geométrico y que Braque identifica con el espacio representativo en el que Poincaré, en La Ciencia y la Hipótesis, ubica nuestras sensaciones. Desdibujar los límites del objeto prolonga el espacio indefinidamente. Con el paso en el arte griego del mito al logos, se abre paso a la matemática como herramienta de comprensión de la naturaleza hasta el siglo XIX. Leon Lederman, en Simetría y la Belleza del Universo, apunta a que una de las mayores contribuciones de la teoría de Einstein es hacer cambiar el modo de pensar la naturaleza, orientándolo hacia la búsqueda de los principios de simetría que subyacen bajo las leyes físicas. Considerando que la simetría es la invariancia de un objeto o un sistema frente a una transformación y que las leyes físicas son las mismas en cualquier punto del espacio, el espacio de nuestro universo posee una simetría traslacional continua. En la ocupación del espacio de las primeras propuestas de Corrales y Molezún aparecen estructuras subyacentes que responden a enlosetados: paralelogramos sometidos a transformaciones continuas, que la naturaleza identifica tridimensionalmente con los grupos cristalográficos. Las plantas del museo de Arte Contemporáneo de la Castellana, la residencia de Miraflores, el pabellón de Bruselas o la torre Peugeot pertenecen a este grupo. La arquitectura como proceso de ocupación continua del territorio y de su trasposición al plano de cubierta, se materializa en líneas estructurales coincidentes con la estructura matemática de sus simetrías de traslación cuya posibilidad de prolongación infinita queda potenciada por el uso de la envolvente transparente. Junto a esta transparencia literal, inherente al material, Colin Rowe y Robert Slutzky nos alertan sobre otra transparencia inherente a la estructura: la transparencia fenomenal, ilustrada por los cuadros de Juan Gris, y cuya intuición aparece reflejada en la casa Huarte en Puerta de Hierro de Madrid. Corrales y Molezún insisten en una lectura de su volumetría alejada de la frontalidad, en la que los contornos de sus cubiertas inclinadas y las visuales tangenciales sugeridas por la organización de sus recorridos introducen una estructura diagonal que se superpone al entendimiento ortogonal de su planta, dibujando una intrincada red de líneas quebradas que permiten al espacio fluctuar entre las secuencia volumétrica propuesta. Los datos relativos al contenido energético de la luz y el concepto de átomo parten de la consideración de la emisión de energía en cuantos realizada por Planck, y concluyen con una circunstancia paradójica: la doble naturaleza de la luz -demostrada por la explicación de Einstein del efecto fotoeléctrico- y la doble naturaleza de la materia -asumida por Bohr y demostrada por el efecto Compton-. Schrödinger y Heisenberg formularán finalmente la ecuación universal del movimiento que rige en las ondas de materia, y cuya representación matemática es lo que se conoce como función de onda. El objeto es así identificado con su función de onda. Su ondulatoriedad expresará la probabilidad de encontrarse en un lugar determinado. Gyorgy Kepes subraya la necesidad de simplificar el lenguaje para pasar de la objetividad que aún permanece en la pintura cubista a la abstracción total del espacio. Y es así como los artistas plásticos reducen los objetos a simples formas geométricas, haciendo aflorar a la vez, las fuerzas plásticas que los tensionan o equilibran, en un proceso que acaba por eliminar cualquier atisbo de materia. Robert Rosenblum en La Pintura Moderna y la Tradición del Romanticismo Nórdico habla de cómo ese rechazo de la materia en favor de un vacío casi impalpable, campos luminosos de color denso que difunden un sereno resplandor y parecen engendrar las energías elementales de la luz natural, está directamente vinculado a la relación con la naturaleza que establece el romanticismo nórdico. La expresión de la energía de la naturaleza concentrada en un vacío que ya había sido motivo de reflexión para Michael Faraday en su postulación del concepto de campo eléctrico. Sáenz de Oíza incide en la expresión de la condición material de la energía en su propuesta junto a José Luis Romany para la capilla en el Camino de Santiago. La evocación de diferentes fuerzas electromagnéticas, las únicas junto a las gravitatorias susceptibles de ser experimentadas por el hombre, aparecerán visualizadas también en el carácter emergente de algunas de sus obras: el Santuario de Aránzazu o Torres Blancas; pero también en la naturaleza fluyente de sus contornos, la dispersión perimetral de los espacios -el umbral como centro del universoo la configuración del límite como respuesta a las tensiones germinales de la naturaleza. Miguel Fisac, a la vuelta de su viaje a los países nórdicos, aborda una simplificación lingüística orientada hacia la adecuación funcional de los espacios. En el Instituto de Daimiel, el Instituto de formación del profesorado o los complejos para los Padres Dominicos en Valladolid o Alcobendas, organiza progresivamente la arquitectura en diferentes volúmenes funcionales, incidiendo de un modo paralelo en la manifestación de los vínculos que se establecen entre dichos volúmenes como una visualización de las fuerzas que los tensionan y equilibran. En ellos la prolongación de la realidad física más allá de los límites de la envolvente ya es algo más que una simple intuición. Un proceso en el que el tratamiento de la luz como un material de construcción más, tendrá un especial protagonismo. En la iglesia de la Coronación, la iluminación del muro curvo escenifica la condición ondulatoria de la luz, manifestándose como si de un patrón de interferencia se tratara. Frente a la disolución de lo material, el espacio se manifiesta aquí como un medio denso, alejado de la tradicional noción de vacío. Una doble naturaleza, onda y partícula, que será intuido también por Fisac en la materia a través de su uso comprometido del hormigón como único material de construcción. Richard Feynmann nos alerta de la ocupación del espacio por multitud de fuerzas electromagnéticas que, al igual que la luz, precisan de receptores específicos para captar su presencia. Sus célebres diagramas suponen además la visualización definitiva de los procesos subatómicos. Al igual que la abstracción absoluta en las artes plásticas, esas representaciones diagramáticas no son asimilables a imágenes obtenidas de nuestra experiencia. Una intuición plasmada en el uso del diagrama, que irán adquiriendo progresivamente los dibujos de Alejandro de la Sota. La sección del gimnasio Maravillas recoge los trazos de sus principales elementos constructivos: estructura, cerramientos, compartimentaciones…, pero también, y con la misma intensidad, los de las fuerzas que generan su espacio, considerando así su condición de elementos constituyentes. El vacío, nos deja claro Sota, es el lugar donde habitan dichas tensiones. La posterior simplificación de las formas acompañadas de la obsesión por su aligeramiento, la casi desaparición de la envolvente, incide en aquella idea con la que Paul Klee define la actividad del artista en su Teoría del Arte Moderno, y en la que se transmite el distanciamiento hacia lo aparente: No se trata de reproducir lo visible, se trata de volver visible. Así, en Bankunión y Aviaco, como en tantos otros proyectos, frente al objetivo de la forma, Sota plantea el límite como la acotación de un ámbito de actuación. Su propia representación aséptica y diagramática transmite la renuncia a una especificidad espacial. Gilles Deleuze expresa ese posicionamiento en Pintura, el Concepto de Diagrama: el diagrama como la posibilidad de cuadros infinitos, o la posibilidad infinita de cuadros. Aparece así una concepción probabilística del espacio en la que frente a la renuncia por la forma, la tendencia al aligeramiento, y lo difuso de su definición – ideas claras, definición borrosa, en palabras de Llinás referidas al modo de operar de Sota-, la insistente atención a algunos elementos como escaleras, protecciones o miradores parece trasmitir la idea de que la arquitectura queda condensada en aquellos acontecimientos que delatan su condición dinámica, transitoria. Primando la relación frente al objeto, el vínculo frente a lo tangible. English summary. The fifties and sixties were the years of the final incorporation of Spanish architecture to the international scene. Among the architects who star that no return leap, is the group of those who a few years later will be named by Juan Daniel Fullaondo as Escuela de Madrid. Carlos Flores, in his book Arquitectura Española Contemporánea 1880-1950, refers to those architects as those that applied to the difficult task of restoring in Spain an architecture that connected with theories, solutions and established languages in Europe during the first decades of the twentieth century. Sigfried Giedion proposes in Space, Time and Architecture, the origin of a new tradition, arising from the optical revolution at the beginning of the century. With tradition he refers to a new culture, covering the interplay of different human activities: the similarity of the methods used in architecture, building, painting, urban planning or science. This new feature, based on its independence and detachment from the previous period, is part of the evolutionary scheme that Thomas Kuhn proposes in his text The Structure of Scientific Revolutions, according to non-accumulative periods. Kuhn talks about the emergence of anomalies in each period, origin of thought crisis whose explanation will require a paradigm shift needed. In science, in the field of optical Thomas Young demonstrates at the early nineteenth century the wave nature of light with its double-slit experiment , in electromagnetism the postulation of the existence of the electric field by Michael Faraday involves a conceptual leap, and in thermodynamic, the consideration pointed by Planck about quantum energy radiation. In the arts, in a parallel process, Gleizes and Metzinger , in his collection of cubism achievements on their book Du Cubisme, speak of evolution occurring during the nineteenth century by the painting: from the idealism of beginning of the century, going for realism and impressionist representation of reality, and finishing regardless of the classical perspective . Mathematics also, once developed by Gauss and Lobachevsky and Bolyai consistent geometries that violate Euclid's fifth postulate , will end validating Riemann’s ambient spaces in which these geometries inhabit, decoupling the direct relationship between geometric space -the space environment that results in a type of geometry- , and physical space. Capi Corrales reflectes in his book Contando el Espacio, that non-Euclidean geometries were not noticeable outside the field of mathematics until the theory of relativity and cubism. The origin of the new tradition that Giedion relates to the new culture of modernity coincides with paradigmatic leaps pointed by the theory of relativity in science and Cubism in the visual arts. Both are extended during the first decades until quantum theory and absolute abstraction, barriers that the two main precursors of relativity and cubism, Einstein and Picasso never overcome. In that sense Giedion speaks about the origin, but also the development, and incorporates peripheral inputs from Brazil, Japan and Finland architecture, thus including organic revision advocated by Zevi as part of this new tradition, being open to the late addition of new contributions to the development of that culture of modernity. Removed the concept of Kant's transcendental aesthetics, of time as an absolute reference, and assumed the constant value of the speed of light, theory of relativity says there is no authentic concurrency. It is thus fixed the speed of light as one of the limits of the universe, and the equivalence of mass and energy. In cubism, spatial simultaneity results from the elimination of preferential points of view, resulting in the multiplicity descriptive of reality, which is displayed in decomposition levels, both the object and the space, and the resulting continuity between figure and background that architecture is reflected in the continuity between building and land. Without the consideration of an absolute point of view, there isn’t an authentic shape. Cubism, and its subsequent development by the vanguard arts, make use of geometry as a means of rebuilding the figure and space, taking penetration mechanisms, overlapping and transparency. Gyorgy Kepes suggest in Languaje of Vision, that cubist decomposition of the object involves successive planes autonomy, to become constituent elements. Something that reflects the Van Doesburg’s architectural axonometrics and culminates with the spaces proposed by Mies van der Rohe in his first European projects. These mechanisms are reflected in the first approaches by Javier Carvajal: the extension of Spanish Pantheon in Campo Verano Cemetery, virtual enclosure mentally reconstructed from 24 the use of only three planes, or in the Spanish Pavilion of New York, which organizes its ground floor from the tour, introducing the time parameter as an additional dimension. Carvajal adds to the differential use of the plane as a constituent, Carvajal incorporates its folding and forming enclosures available as a mechanism for spatial and formal qualification, promoting the extension between architecture and territory. A continuity that will be completed in the two houses built in Somosaguas. Volumetric decomposition, as the fragmentation achieved in the last cubist experiences, needs the incorporation of elements of memory - fountains, patios, shutters...- as a network of signals, such as those introduced by Picasso and Braque in their paintings to allow their interpretation. Braque insists in his interest in the space surrounding the objects. A search of the tactility of space contrary to the perspective, which moves the observer away from the object, and that in the gardens of Somosaguas seems to emanate from its own materiality. A tactile space away from the geometric space and Braque identified with the representative space in which Poincaré in La Science et l´hypothèse, located our feelings. To blur those boundaries of the object extends the space indefinitely. With the passage in Greek art from myth to logos, it opens up to mathematics as a tool for understanding the nature until the nineteenth century. Leon Lederman, in Symmetry and beautiful Universe, suggests that one of the greatest contributions of Einstein's theory is to change the mindset of nature, namely the search for symmetry principles that underlie physical laws. Considering that symmetry is the invariance of an object or system from a transformation and that physical laws are the same at any point in space, the space of our universe has a continuous translational symmetry. In the space occupation of the first proposals by Corrales and Molezún underlying structures appear that match enlosetados: parallelograms under continuous transformations, which nature identifies tridimensionally with the crystallographic groups. Plants in the Contemporary Art Museum in La Castellana, the residence in Miraflores, the Brussels pavilion or the Peugeot tower belong to this group. The architecture as a process of continuous occupation of the territory and of its transposition to the deck, embodied in structural lines coincide with the mathematical structure of the translational symmetry and infinite extension whose possibility is enhanced by the use of the transparent cover. Alongside this literal transparency inherent to the material, Colin Rowe and Robert Slutzky alert us another transparency inherent in the structure: phenomenal transparency, illustrated by the Juan Gris’ works, and whose intuition is reflected in the Huarte’s house in Puerta de Hierro in Madrid. Corrales and Molezún insist on a reading of its volume away from the frontal, in which the outline of their inclined roofs and tangential visual suggested by the organization of his circulations introduce a diagonal structure which overlaps the orthogonal understanding of its plant, drawing an intricate web of broken lines that allow the space fluctuate between the volumetric sequence proposal. Information concerning to the energy mean of light and the concept of atom start from the consideration by Plank about the energy emission, and conclude with a paradoxical situation: the dual nature of light - demonstrated by the explanation of Einstein's photoelectric effect-, and the dual nature of matter -assumed by Bohr and demonstrated by the Compton effect-. Finally, Schrödinger and Heisenberg will formulate the universal movement equation governing in undulatory matter, whose mathematical representation is what is known as a wave function. The object is thus identified with its wave function. Its undulatory expression speaks about the probability of being found in a certain place. Gyorgy Kepes emphasizess the need to simplify the language to move from the objectivity that still remains in the cubist painting to the total abstraction of the space. And this is how artists reduced the objects to simple geometric shapes, making emerge at a time, the plastic forces that tense or balance them, in a process that eventually eliminate any trace of matter. Robert Rosenblum in Modern Painting and the Northern Romantic Tradition. Friedrich to Rothko talks about how this rejection of matter in an almost impalpable vacuum: dense color light fields that broadcast a serene glow and seem to generate the elemental energies of natural light is directly linked to the relationship with nature that sets the northern romanticism. An expression of the power of nature concentrated in a vacuum which had been reason for thought by Michael Faraday in his application of the concept of electric field. Saenz de Oíza touches upon the material expression of the energy in its proposal with Jose Luis Romany to the chapel on the Camino de Santiago. The presence of electromagnetic forces, the only ones with the gravitational one capable of being experienced by the man will also visualize in the emerging nature of some of his works: the sanctuary of Aránzazu or Torres Blancas, but also in the flowing nature of its contours, and the inclusion of interest in the realization of space fluctuating boundary: the threshold as the center of the universe. Miguel Fisac, back from his trip to the Northern Countries, starts on a linguistic simplification oriented to the functional adequacy of spaces. In the Daimiel Institute, in the Institute to Teacher Formation or in the complex to the Dominican Fathers in Valladolid or Alcobendas, progressively organized into different functional volumes architecture, focusing in a parallel way in the manifestation of the links established between these volumes as a visualization of the forces that tense and balance them. The prolongation of the physical reality beyond the limits of the envelope is already something more than a simple intuition. A process in which the treatment of light as a construction material, have a special role. In the Coronation church, curved wall lighting dramatizes the undulatory condition of the light, manifesting as if an interference pattern is involved. Versus the dissolution of the material, the space is expressed here as a dense atmosphere, away from the traditional notion of the vacuum. A dual nature, wave and particle, which is also sensed by Fisac in his committed use of concrete as a unique construction material. Richard Feynman alerts us to the occupation of space by many electromagnetic forces, which like the light, require specific receptors to capture their presence. His famous diagrams also involve the final visualization of atomic processes. As absolute abstraction in the visual arts, these representations are not assimilated to images obtained from our experience. A diagrammatic nature, abstracted from figuration, which will obtein the pictures of Alejandro de la Sota. The section of Maravillas gym collects traces of its main building blocks: structure, enclosures... but also, and with the same intensity, of the forces that generate their space as constituent elements. Sota makes it clear: the vacuum is where inhabit these tensions. The subsequent simplification of forms, accompanied by the obsession with his lightening, the near disappearance of the envelope, touches upon that idea which Paul Klee defines the activity of the artist in his Modern Art Theory, the spacing out to the apparent: it is not to reproduce the visible, it is to turn visible. Thus, in Bankunión and Aviaco, as in many other projects, against the shape, raises the limit as the dimension of a scope. His own aseptic and diagrammatic representation transmits waiver to a spatial specificity that Gilles Deleuze clearly expressed in Painting. The Concept Diagram: The diagram as the possibility of infinite pictures, or infinite possibility of the picture. Thus appears the probabilistic concept of space in which, opposite to the diffuse of its definition -clear ideas, diffuse definition, as Llinas said- the insistent attention to some elements like stairs, guards or lookouts seems to concentrate the architecture in its dynamic condition, transitional. The relationship opposite the object, the link opposite the tangible.