Entanglement negativity in the harmonic chain out of equilibrium

We study the entanglement in a chain of harmonic oscillators driven out of equilibrium by preparing the two sides of the system at different temperatures, and subsequently joining them together. The steady state is constructed explicitly and the logarithmic negativity is calculated between two adjacent segments of the chain. We find that, for low temperatures, the steady-state entanglement is a sum of contributions pertaining to left-and right-moving excitations emitted from the two reservoirs. In turn, the steady-state entanglement is a simple average of the Gibbs-state values and thus its scaling can be obtained from conformal field theory. A similar averaging behaviour is observed during the entire time evolution. As a particular case, we also discuss a local quench where both sides of the chain are initialized in their respective ground states.

Complexity and Uniqueness of the Aromatic Profile of Smoked and Unsmoked Herreno Cheese

In this work, the volatile fraction of unsmoked and smoked Herreno cheese, a type of soft cheese from the Canary Islands, has been characterized for the first time. In order to evaluate if the position in the smokehouse could influence the volatile profile of the smoked variety, cheeses smoked at two different heights were studied. The volatile components were extracted by Solid Phase Microextraction using a divinylbenzene/carboxen/polydimethylsiloxane fiber, followed by Gas Chromatography/Mass Spectrometry. In total, 228 components were detected. The most numerous groups of components in the unsmoked Herreno cheese were hydrocarbons, followed by terpenes and sesquiterpenes, whereas acids and ketones were the most abundant. It is worth noticing the high number of aldehydes and ketones, and the low number of alcohols and esters in this cheese in relation to others, as well as the presence of some specific unsaturated hydrocarbons, terpenes, sesquiterpenes and nitrogenated derivatives. The smoking process enriches the volatile profile of Herreno cheese with ketones and diketones, methyl esters, aliphatic and aromatic aldehydes, hydrocarbons, terpenes, nitrogenated compounds, and especially with ethers and phenolic derivatives. Among these, methylindanones or certain terpenes like a-terpinolene, have not been detected previously in other types of smoked cheese. Lastly, the results obtained suggest a slightly higher smoking degree in the cheeses smoked at a greater height.

Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

On The Uniqueness of Correspondence Under Orthographic and Perspective Projections

The task of shape recovery from a motion sequence requires the establishment of correspondence between image points. The two processes, the matching process and the shape recovery one, are traditionally viewed as independent. Yet, information obtained during the process of shape recovery can be used to guide the matching process. This paper discusses the mutual relationship between the two processes. The paper is divided into two parts. In the first part we review the constraints imposed on the correspondence by rigid transformations and extend them to objects that undergo general affine (non rigid) transformation (including stretch and shear), as well as to rigid objects with smooth surfaces. In all these cases corresponding points lie along epipolar lines, and these lines can be recovered from a small set of corresponding points. In the second part of the paper we discuss the potential use of epipolar lines in the matching process. We present an algorithm that recovers the correspondence from three contour images. The algorithm was implemented and used to construct object models for recognition. In addition we discuss how epipolar lines can be used to solve the aperture problem.

Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

Adsorption of methylene blue onto activated carbon produced from steam activated bituminous coal: A study of equilibrium adsorption isotherm.

Chemical Engineering Journal, 124 (2006) 103.

Comment on "On the Uniqueness of Stable Marriage Matchings" [Economic Letters 69(1):1-8, 2000]

We prove with the help of a counterexample that Lemma 6 and Corollary 7 from Eeckhout [1] are incorrect.

Out-of-equilibrium thermodynamics of quantum optomechanical systems

We address the out-of-equilibrium thermodynamics of an isolated quantum system consisting of a cavity optomechanical device. We explore the dynamical response of the system when driven out of equilibrium by a sudden quench of the coupling parameter and compute analytically the full distribution of the work generated by the process. We consider linear and quadratic optomechanical coupling, where the cavity field is parametrically coupled to either the position or the square of the position of a mechanical oscillator, respectively. In the former case we find that the average work generated by the quench is zero, whilst the latter leads to a non-zero average value. Through fluctuations theorems we access the most relevant thermodynamical figures of merit, such as the free energy difference and the amount of irreversible work generated. We thus provide a full charac- terization of the out-of-equilibrium thermodynamics in the quantum regime for nonlinearly coupled bosonic modes. Our study is the first due step towards the construction and full quantum analysis of an optomechanical machine working fully out of equilibrium.