Experiments on Multidimensional Solitons

This article presents an overview of experimental efforts in recent years related to multidimensional solitons in Bose-Einstein condensates. We discuss the techniques used to generate and observe multidimensional nonlinear waves in Bose-Einstein condensates with repulsive interactions. We further summarize observations of planar soliton fronts undergoing the snake instability, the formation of vortex rings, and the emergence of hybrid structures.Comment: review paper, to appear as Chapter 5b in "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer-Verlag

Kothe dual of Banach lattices generated by vector measures

We study the Kothe dual spaces of Banach function lattices generated by abstract methods having roots in the theory of interpolation spaces. We apply these results to Banach spaces of integrable functions with respect to Banach space valued countably additive vector measures. As an application we derive a description of the Banach dual of a large class of these spaces, including Orlicz spaces of integrable functions with respect to vector measuresThe first author was supported by the Foundation for Polish Science (FNP). The second author was supported by the Ministerio de Economia y Competitividad (Spain) under Grant #MTM2012-36740-C02-02.Mastylo, M.; Sánchez Pérez, EA. (2014). Kothe dual of Banach lattices generated by vector measures. Monatshefte fur Mathematik. 173(4):541-557. https://doi.org/10.1007/s00605-013-0560-8S5415571734Aronszajn, N., Gagliardo, E.: Interpolation spaces and interpolation methods. Ann. Mat. Pura. Appl. 68, 51–118 (1965)Bartle, R.G., Dunford, N., Schwartz, J.: Weak compactness and vector measures. Canad. J. Math. 7, 289–305 (1955)Brudnyi, Yu.A., Krugljak, N.Ya.: Interpolation functors and interpolation spaces $$I$$ I . North-Holland, Amsterdam (1991)Curbera, G.P.: Operators into $$L^1$$ L 1 of a vector measure and applications to Banach lattices. Math. Ann. 293, 317–330 (1992)Curbera, G.P., Ricker, W.J.: The Fatou property in $$p$$ p -convex Banach lattices. J. Math. Anal. Appl. 328, 287–294 (2007)Delgado, O.: Banach function subspaces of $$L^1$$ L 1 of a vector measure and related Orlicz spaces. Indag. Math. 15(4), 485–495 (2004)Diestel, J., Jr., Uhl, J.J.: Vector measures, Amer. Math. Soc. Surveys 15, Providence, R.I. (1977)Fernández, A., Mayoral, F., Naranjo, F., Sánchez-Pérez, E.A.: Spaces of $$p$$ p -integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)Ferrando, I., Rodríguez, J.: The weak topology on $$L_p$$ L p of a vector measure. Topol. Appl. 155, 1439–1444 (2008)Ferrando, I., Sánchez Pérez, E.A.: Tensor product representation of the (pre)dual of the $$L_p$$ L p -space of a vector measure. J. Aust. Math. Soc. 87, 211–225 (2009)Galaz-Fontes, F.: The dual space of $$L^p$$ L p of a vector measure. Positivity 14(4), 715–729 (2010)Kamińska, A.: Indices, convexity and concavity in Musielak-Orlicz spaces, dedicated to Julian Musielak. Funct. Approx. Comment. Math. 26, 67–84 (1998)Kantorovich, L.V., Akilov, G.P.: Functional analysis, 2nd edn. Pergamon Press, New York (1982)Krein, S.G., Petunin, Yu.I., Semenov, E.M.: Interpolation of linear operators. In: Translations of mathematical monographs, 54. American Mathematical Society, Providence, R.I., (1982)Lewis, D.R.: Integration with respect to vector measures. Pacific. J. Math. 33, 157–165 (1970)Lewis, D.R.: On integrability and summability in vector spaces. Ill. J. Math. 16, 583–599 (1973)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Lozanovskii, G.Ya.: On some Banach lattices, (Russian). Sibirsk. Mat. Z. 10, 419–430 (1969)Musielak, J.: Orlicz spaces and modular spaces. In: Lecture Notes in Math. 1034, Springer-Verlag, Berlin (1983)Okada, S.: The dual space of $$L^1(\mu )$$ L 1 ( μ ) of a vector measure $$\mu$$ μ . J. Math. Anal. Appl. 177, 583–599 (1993)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces, operator theory. Adv. Appl., vol. 180, Birkhäuser, Basel (2008)Rao, M.M., Zen, Z.D.: Applications of Orlicz spaces. Marcel Dekker, Inc., New York (2002)Rivera, M.J.: Orlicz spaces of integrable functions with respect to vector-valued measures. Rocky Mt. J. Math. 38(2), 619–637 (2008)Sánchez Pérez, E.A.: Compactness arguments for spaces of $$p$$ p -integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces. Ill. J. Math. 45(3), 907–923 (2001)Sánchez Pérez, E.A.: Vector measure duality and tensor product representation of $$L_p$$ L p spaces of vector measures. Proc. Amer. Math. Soc. 132, 3319–3326 (2004)Zaanen, A.C.: Integration. North Holland, Amsterdam (1967

Electrically-driven phase transition in magnetite nanostructures

Magnetite (Fe$_{3}$O$_{4}$), an archetypal transition metal oxide, has been used for thousands of years, from lodestones in primitive compasses[1] to a candidate material for magnetoelectronic devices.[2] In 1939 Verwey[3] found that bulk magnetite undergoes a transition at T$_{V}$ $\approx$ 120 K from a high temperature "bad metal" conducting phase to a low-temperature insulating phase. He suggested[4] that high temperature conduction is via the fluctuating and correlated valences of the octahedral iron atoms, and that the transition is the onset of charge ordering upon cooling. The Verwey transition mechanism and the question of charge ordering remain highly controversial.[5-11] Here we show that magnetite nanocrystals and single-crystal thin films exhibit an electrically driven phase transition below the Verwey temperature. The signature of this transition is the onset of sharp conductance switching in high electric fields, hysteretic in voltage. We demonstrate that this transition is not due to local heating, but instead is due to the breakdown of the correlated insulating state when driven out of equilibrium by electrical bias. We anticipate that further studies of this newly observed transition and its low-temperature conducting phase will shed light on how charge ordering and vibrational degrees of freedom determine the ground state of this important compound.Comment: 17 pages, 4 figure

Impact of protein-polymer interactions in the antimicrobial activity of lysozyme/poly(3,4-ethylenedioxythiophene) biocapacitors

Biocapacitors constructed by combining lysozyme (LYZ) and poly(3,4-ethylenedioxythiophene) (PEDOT) retained the bactericidal activity of the protein when this was encapsulated within the polymeric matrix but lost the antimicrobial behaviour when the LYZ was adsorbed onto the polymer. In this work we use atomistic Molecular Dynamics simulations to examine the influence of protein···polymer interactions in the bactericidal activity of LYZ-containing biocapacitors. Results show that the anisotropic forces exerted by oxidized PEDOT chains on the adsorbed protein induce small structural changes that locally affect at the active centre, breaking the intra-residue interactions associated with the antibacterial mechanism. Conversely, isotropic polymer···protein interactions in biocapacitors with encapsulated LYZ do not affect the stability of the active centre. These observations suggest that the strong repulsive or attractive forces between p-doped polymer chains and the positively or negatively charged LYZ residues, respectively, are the only ones responsible for the protein activity.Peer ReviewedPostprint (author's final draft

An element through the looking glass: Exploring the Au-C, Au-H and Au-O energy landscape

Gold, the archetypal “noble metal”, used to be considered of little interest in catalysis. It is now clear that this was a misconception, and a multitude of gold-catalysed transformations has been reported. However, one consequence of the long-held view of gold as inert metal is that its organometallic chemistry contains many “unknowns”, and catalytic cycles devised to explain gold's reactivity draw largely on analogies with other transition metals. How realistic are such mechanistic assumptions? In the last few years a number of key compound classes have been discovered that can provide some answers. This Perspective attempts to summarise these developments, with particular emphasis on recently discovered gold(III) complexes with bonds to hydrogen, oxygen, alkenes and CO ligands

Experimental investigations of polymer hollow fibre heat exchangers for building heat recovery application

Due to low cost, light weight and corrosion resistant features, polymer heat exchangers have been extensively studied by researchers with the aim to replace metallic heat exchangers in a wide range of applications. Although the thermal conductivity of polymer material is generally lower than the metallic counterparts, the large specific surface area provided by the polymer hollow fibre heat exchanger (PHFHE) offers the same or even better heat transfer performance with smaller volume and lighter weight compared with the metallic shell-and-tube heat exchangers. This paper presents the construction and experimental investigations of polypropylene based polymer hollow fibre heat exchangers in the form of shell-and-tube. The measured overall heat transfer coefficients of such PHFHEs are in the range of 258–1675 W/m2K for water to water application. The effects of various parameters on the overall heat transfer coefficient including flow rates and numbers of fibres, the effectiveness of heat exchanger, the number of heat transfer unit (NTU), and the height of transfer unit (HTU) are also discussed in this paper. The results indicate that the PHFHEs could offer a conductance per unit volume of 4 × 106 W/m3K, which is 2–8 times higher than the conventional metal heat exchangers. This superior thermal performance together with its low cost, corrosive resistant and light weight features make PHFHEs potentially very good substitutes for metallic heat recovery system for building application

Data Descriptor: Ash leaf metabolomes reveal differences between trees tolerant and susceptible to ash dieback disease

CMS was funded by the ‘Nornex’ project jointly by UK BBSRC (BBS/E/J/000CA5323) and DEFRA and a BBSRC Tools and Resources grant (BB/N021452/1) awarded to M.G. and D.J.S