Generic finite-size enhancement of pairing in mesoscopic Fermi systems

The finite-size-dependent enhancement of pairing in mesoscopic Fermi systems is studied under the assumption that the BCS approach is valid and that the two-body force is size independent. Different systems are investigated such as superconducting metallic grains and films as well as atomic nuclei. It is shown that the finite size enhancement of pairing in these systems is in part due to the presence of a surface which accounts quite well for the data of nuclei and explains a good fraction of the enhancement in Al grains.

Pairing with polarization effects in low-density neutron matter

We study the properties of the 1S0 pairing gap in low-density neutron matter. Different corrections to the lowest-order scattering length approximation are explored, resulting in a strong suppression with respect to the BCS result.

Nuclear pairing: surface or bulk?

We analyze how the spatial localization properties of pairing correlations are changing in a major neutron shell of heavy nuclei. It is shown that the radial distribution of the pairing density depends strongly on whether the chemical potential is close to a low or a high angular momentum level and has little sensitivity to whether the pairing force acts at the surface or in the bulk. The pairing density averaged over one major shell is, however, rather flat, exhibiting little dependence on the pairing force. Hartree-Fock-Bogoliubov calculations for the isotopic chain 100-132Sn are presented for demonstration purposes.

Density matrix functional theory that includes pairing correlations

The extension of density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the application of existing DFT plus pairing approaches to atoms, molecules, ultracooled and magnetically trapped atomic Fermi gases, and atomic nuclei where the number of particles is conserved exactly. The connection with Hartree-Fock-Bogoliubov (HFB) theory is discussed, and the method of quasilocal reduction of the nonlocal theory is also described. This quasilocal reduction allows equations of motion to be obtained which are much simpler for numerical solution than the equations corresponding to the nonlocal case. Our theory is applied to the study of some even Sn isotopes, and the results are compared with those obtained in the standard HFB theory and with the experimental ones.

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favorability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB)versus Thr(HB)-Asn(nHB). Significantly (p < or = 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi1 rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi1 conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi1 and chi2 conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favorability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http://www.rubic.rdg.ac.uk/betapairprefsparallel/).

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favourability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB) versus Thr(HB)-Asn(nHB). Significantly (p <= 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi(1) rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi(1) conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi(1) and chi(2) conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favourability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http:// www.rubic.rdg.ac.uk/betapairprefsparallel/). (c) 2005 Elsevier Ltd. All rights reserved.

I killed my father, I ate human flesh, I quiver with joy: an obsession with Pier Paolo Pasolini

Group show, curated by Invisible Exports Gallery. Featuring work by Michael Bilsborough, Lizzi Bougatsos, BREYER P-ORRIDGE, Asger Carlsen, Troels Carlsen, Walt Cassidy, Andy Coolquitt, Vaginal Davis, Carlton DeWoody, Joey Frank, Paul Gabrielli, Ludovica Gioscia, Luis Gispert, Terence Hannum, Karen Heagle, Timothy Hull, Doug Ischar, Brian Kenny, Jeremy Kost, Aaron Krach, Yeni Mao, Leigha Mason, Mark McCoy, Robert Melee, Lucas Michael, Jennifer Needleman, Brent Owens, Paul P., Paolo Di Paolo, Franklin Preston, John Russell, Xaviera Simmons, Duston Spear, Scott Treleaven, Ramon Vega, Jordan Wolfson, Dustin Yellin

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Oligomethylene-bridged dinuclear triorganotin triflates and diphenylphosphinates. Ion pairing in the solid state and electrolytic dissociation in solution of [Ph2Sn(CH2)nSnPh2X](O3SCF3) (X = OH, O2PPh2; n = 1-3)

The condensation of [Ph₂(OH)Sn(CH₂)_nSn(OH)Ph₂] (1-3; n = 1-3) with HO₃SCF₃ and HO₂PPh₂ provided [Ph₂Sn(CH₂)_nSnPh₂(OH)](O₃SCF₃) (4-6; n = 1-3) and [Ph₂(O₂PPh₂)Sn(CH₂)_nSn(O₂PPh₂)Ph₂] (10-12; n = 1-3), respectively. The reaction of [Ph₂Sn(CH₂)_nSnPh₂(OH)](O₃SCF₃) (4-6; n = 1-3) with HO₂PPh₂ and NaO₂PPh₂ gave rise to the formation of [Ph₂Sn(CH₂)_nSnPh₂(O₂PPh₂)](O₃SCF₃) (7-9; n = 1-3) and [Ph₂(OH)Sn(CH₂)_nSn(O₂PPh₂)Ph₂] (13-15; _n = 1-3), respectively. In the solid state, compounds 4-9 comprise ion pairs of cationic cyclo-[Ph₂SnCH₂SnPh₂(OH)]₂²⁺, cyclo-[Ph₂Sn(CH₂)_nSnPh₂(OH)]⁺ (n = 2, 3), and cyclo-[Ph₂Sn(CH₂)_nSnPh₂(O₂PPh₂)]⁺ (n = 1-3) and triflate anions. In MeCN, the eight-membered-ring system cyclo-[Ph₂SnCH₂SnPh₂(OH)]₂²⁺ appears to be in equilibrium with the four-membered-ring system cyclo-[Ph₂SnCH₂SnPh₂(OH)]⁺. In contrast, compounds 10-15 show no ionic character. Compounds 1-15 were characterized by multinuclear NMR spectroscopy in solution and in the solid state, IR spectroscopy, conductivity measurements, electrospray mass spectrometry, osmometric molecular weight determinations, and X-ray crystallography (4, 5, 7, and 12).

Ftir study of ion-pairing effects in plasticized polymer electrolytes

The effect of plasticizer on the ubiquitous ion-pairing observed in polymer electrolytes has been investigated using FTIR as a probe of the local environment of the triflate ion in sodium and lithium triflate based electrolytes. Plasticizers having a range of properties, such as, propylene carbonate, and dimethyl formamide (DMF), have been investigated in the pure state for comparison with the polymer (a random copolymer of ethylene oxide at propylene oxide (mol ratio 3: 1)). The different plasticizers exhibited strikingly different effects on the triflate ion bands normally observed in polyether salt systems. In particular, the cation associated triflate ion bands at 1288 and 1248 cm⁻¹ and the band at 1272 cm⁻¹ which has variously been assigned to the free ion and also to the strongly aggregated anion, are different. PC produces a rapid disappearance of the “free” ion band in favour of the monodentate ion pair. On the other hand, DMF strongly enhances the band near 1270 cm⁻¹ at salt concentrations higher than 0.7 mol kg⁻¹. These observations are discussed in terms of recent ab initio calculations of the triflate vibrational bands.