Thermodynamic and transport properties of fluids and selected solids for cryogenic applications Summary report, 1 Dec. 1965 - 1 Nov. 1970

Summary data on thermodynamic and transport properties of fluids and solids for cryogenic application

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

Local adsorption structure and bonding of porphine on Cu(111) before and after self-metalation

We have experimentally determined the lateral registry and geometric structure of free-base porphine (2H-P) and copper-metalated porphine (Cu-P) adsorbed on Cu(111), by means of energy-scanned photoelectron diffraction (PhD), and compared the experimental results to density functional theory (DFT) calculations that included van der Waals corrections within the Tkatchenko-Scheffler approach. Both 2H-P and Cu-P adsorb with their center above a surface bridge site. Consistency is obtained between the experimental and DFT-predicted structural models, with a characteristic change in the corrugation of the four N atoms of the molecule's macrocycle following metalation. Interestingly, comparison with previously published data for cobalt porphine adsorbed on the same surface evidences a distinct increase in the average height of the N atoms above the surface through the series 2H-P, Cu-P, cobalt porphine. Such an increase strikingly anti-correlates the DFT-predicted adsorption strength, with 2H-P having the smallest adsorption height despite the weakest calculated adsorption energy. In addition, our findings suggest that for these macrocyclic compounds, substrate-to-molecule charge transfer and adsorption strength may not be univocally correlated

Dynamical Mordell-Lang conjecture for birational polynomial morphisms on A2\mathbb{A}^2

We prove the dynamical Mordell-Lang conjecture for birational polynomial morphisms on $\mathbb{A}^2$

Normal subgroups in the Cremona group (long version)

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and algebraic geometry to produce elements in the Cremona group that generate non trivial normal subgroups.Comment: With an appendix by Yves de Cornulier. Numerous but minors corrections were made, regarding proofs, references and terminology. This long version contains detailled proofs of several technical lemmas about hyperbolic space

Substantiating a political public sphere in the Scottish press : a comparative analysis

This article uses content analysis to characterize the performance of the media in a national public sphere, by setting apart those qualities that typify internal press coverage of a political event. The article looks at the coverage of the 1999 devolved Scottish election from the day before the election until the day after. It uses a word count to measure the election material in Scottish newspapers the Herald, the Press and Journal and the Scotsman, and United Kingdom newspapers the Guardian, the Independent and The Times, and categorizes that material according to discourse type, day and page selection. The article finds a number of qualities that typify the Scottish sample in particular, and might be broadly indicative of a political public sphere in action. Firstly, and not unexpectedly, it finds that the Scottish newspapers carry significantly more election coverage. Just as tellingly, though, the article finds that the Scottish papers offer a greater proportion of advice and background information, in the form of opinion columns and feature articles. It also finds that the Scottish papers place a greater concentration of both informative and evaluative material in the period before the vote, consistent with their making a contribution to informed political action. Lastly, the article finds that the Scottish sample situates coverage nearer the front of the paper and places a greater proportion on recto pages. The article therefore argues that the Scottish papers display features that distinguish them from the UK papers, and are broadly consistent with their forming part of a deliberative public sphere, and suggests that these qualities might be explored as a means of judging future media performance

A Force-Feedback Exoskeleton for Upper-Limb Rehabilitation in Virtual Reality

This paper presents the design and the clinical validation of an upper-limb force-feedback exoskeleton, the L-EXOS, for robotic-assisted rehabilitation in virtual reality (VR). The L-EXOS is a five degrees of freedom exoskeleton with a wearable structure and anthropomorphic workspace that can cover the full range of motion of human arm. A specific VR application focused on the reaching task was developed and evaluated on a group of eight post-stroke patients, to assess the efficacy of the system for the rehabilitation of upper limb. The evaluation showed a significant reduction of the performance error in the reaching task (paired t-test, p < 0.02

Revisiting the Tradespace Exploration Paradigm: Structuring the Exploration Process

A number of case applications of tradespace exploration have further extended the types of analyses and knowledge insights that can be gained about tradeoffs between design choices and perceived utility and cost of alternatives. These extensions include application beyond its heritage aerospace domain to the transportation domain, comparing distinct concepts on a common tradespace, considering the impact of changing needs and contexts over time, evaluation of alternatives in a “light effort” manner. In parallel with these case applications, a formalization of the tradespace exploration process has emerged, using a question-driven approach to ensure the knowledge generated is practical and useful to decision makers. These questions are introduced and applied to three example space systems in order to illustrate insights gained in answering the questions. The insights include identifying “good” designs, the strengths and weakness of selected alternatives across a tradespace, limiting constraints and requirements that could allow for less expensive solutions. Additionally, advanced insights include understanding the sensitivities of designs to changes in contexts and needs, and consideration of the differential impact of uncertainty across a set of alternatives with potential opportunities for risk mitigation.Massachusetts Institute of Technology. Engineering Systems Division (Systems Engineering Advancement Research Initiative (SEAri)

A birational mapping with a strange attractor: Post critical set and covariant curves

We consider some two-dimensional birational transformations. One of them is a birational deformation of the H\'enon map. For some of these birational mappings, the post critical set (i.e. the iterates of the critical set) is infinite and we show that this gives straightforwardly the algebraic covariant curves of the transformation when they exist. These covariant curves are used to build the preserved meromorphic two-form. One may have also an infinite post critical set yielding a covariant curve which is not algebraic (transcendent). For two of the birational mappings considered, the post critical set is not infinite and we claim that there is no algebraic covariant curve and no preserved meromorphic two-form. For these two mappings with non infinite post critical sets, attracting sets occur and we show that they pass the usual tests (Lyapunov exponents and the fractal dimension) for being strange attractors. The strange attractor of one of these two mappings is unbounded.Comment: 26 pages, 11 figure