Laboratory studies, analysis, and interpretation of the spectra of hydrocarbons present in planetary atmospheres including cyanoacetylene, acetylene, propane, and ethane

Combining broadband Fourier transform spectrometers (FTS) from the McMath facility at NSO and from NRC in Ottawa and narrow band TDL data from the laboratories with computational physics techniques has produced a broad range of results for the study of planetary atmospheres. Motivation for the effort flows from the Voyager/IRIS observations and the needs of Voyager analysis for laboratory results. In addition, anticipation of the Cassini mission adds incentive to pursue studies of observed and potentially observable constituents of planetary atmospheres. Current studies include cyanoacetylene, acetylene, propane, and ethane. Particular attention is devoted to cyanoacetylen (H3CN) which is observed in the atmosphere of Titan. The results of a high resolution infrared laboratory study of the line positions of the 663, 449, and 22.5/cm fundamental bands are presented. Line position, reproducible to better than 5 MHz for the first two bands, are available for infrared astrophysical searches. Intensity and broadening studies are in progress. Acetylene is a nearly ubiquitous atmospheric constituent of the outer planets and Titan due to the nature of methane photochemistry. Results of ambient temperature absolute intensity measurements are presented for the fundamental and two two-quantum hotband in the 730/cm region. Low temperature hotband intensity and linewidth measurements are planned

From nonlinear to linearized elasticity via Γ-convergence: the case of multiwell energies satisfying weak coercivity conditions

Linearized elasticity models are derived, via Γ-convergence, from suitably rescaled non- linear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the typical quadratic bound from below is replaced by a weaker p bound, 1 < p < 2, away from the wells. This study is motivated by, and our results are applied to, energies arising in the modeling of nematic elastomers

On entanglement evolution across defects in critical chains

We consider a local quench where two free-fermion half-chains are coupled via a defect. We show that the logarithmic increase of the entanglement entropy is governed by the same effective central charge which appears in the ground-state properties and which is known exactly. For unequal initial filling of the half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p

Cardinal characteristics at in a small u (κ) model

We provide a model where u(κ)<2κu(κ)<2κ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties

Towards an Axiomatization of Simple Analog Algorithms

International audienceWe propose a formalization of analog algorithms, extending the framework of abstract state machines to continuous-time models of computation

Hypernatural Numbers as Ultrafilters

In this paper we present a use of nonstandard methods in the theory of ultrafilters and in related applications to combinatorics of numbers

Recent Advances in Σ-definability over Continuous Data Types

The purpose of this paper is to survey our recent research in computability and definability over continuous data types such as the real numbers, real-valued functions and functionals. We investigate the expressive power and algorithmic properties of the language of Sigma-formulas intended to represent computability over the real numbers. In order to adequately represent computability we extend the reals by the structure of hereditarily finite sets. In this setting it is crucial to consider the real numbers without equality since the equality test is undecidable over the reals. We prove Engeler's Lemma for Sigma-definability over the reals without the equality test which relates Sigma-definability with definability in the constructive infinitary language L_{omega_1 omega}. Thus, a relation over the real numbers is Sigma-definable if and only if it is definable by a disjunction of a recursively enumerable set of quantifier free formulas. This result reveals computational aspects of Sigma-definability and also gives topological characterisation of Sigma-definable relations over the reals without the equality test. We also illustrate how computability over the real numbers can be expressed in the language of Sigma-formulas