Emergent <Emphasis Type=Italic>SO</Emphasis>(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.     

A Three-component Extension of the Camassa–Holm Hierarchy

We introduce a bi-Hamiltonian hierarchy on the loop-algebra of endowed with a suitable Poisson pair. It gives rise to the usual Camassa–Holm (CH) hierarchy by means of a bi-Hamiltonian reduction, and its first nontrivial flow provides a three-component extension of the CH equation.     

High energy radiation fluences in the ISS-USLab: Ion discrimination and particle abundances

The ALTEA (Anomalous Long Term Effects on Astronauts) detector was used to characterize the radiation environment inside the USLab of the International Space Station (ISS), where it measured the abundances of ions from Be to Fe. We compare the ALTEA results with Alteino results obtained in the PIRS module of the Russian segment of the ISS, and normalize to the high energy Si abundances given by Simpson. These are the first particle spectral measurements, which include ions up to Fe, performed in the USLab. The small differences observed between those made inside the USLab and the Simpson abundances can be attributed to the transport through the spacecraft hull. However, the low abundance of Fe cannot be attributed to only this process.     

Confinement of monopole field lines in a superconductor at T ≠ 0

We apply the Bogoliubov-de Gennes equations to the confinement of a monopole-antimonopole pair in a superconductor. This is related to the problem of a quark-antiquark pair bound by a confining string, consisting of a colour-electric flux tube, dual to the magnetic vortex of type-II superconductors. We study the confinement of the field lines due to the superconducting state and calculate the effective potential between the two monopoles. The monopoles can be simulated in a real experiment inserting two long and thin magnetic rods. At short distances the potential is Coulombic and at large distances the potential is linear, as previously determined solving the Ginzburg-Landau equations. The magnetic field lines and the string tension are also studied as a function of the temperature T. Because we take into account the explicit fermionic degrees of freedom, this work may open new perspectives to the breaking of chiral symmetry or to colour superconductivity.     

Formation of ferrocyanides-IV Th(IV), Nd(III), UO(2)(II) and Hg(II)

The stoichiometry of the reaction between ferrocyanide and thorium, neodymium, uranyl ion and mercury(II) has been investigated. The first three give single products irrespective of the order of addition of the reagents, but the last does not. If mercury(II) is added to ferrocyanide Hg(2)Fe(CN)(6) is obtained, but if ferrocyanide is added to mercury(II) various cyanide complexes of mercury are formed. The K(sp) values for the precipitates are reported.     

The reactions of iminosulfur difluorides and chlorine monofluoride

The reactions of perfluoroalkyl- and perfluoroacyl-iminosulfur difluorides with chlorine monofluoride result in the preparation of perfluoroalkyldichloroamines and a new class of compounds N,N-dichloroperfluoroamides, R_fC(O)NCl₂, via the elimination of SF₄. The amides, FC(O)NCl₂ and CF₃C(O)NCl₂, in addition to 1,2-bis-(dichloroamino)tetrafluoroethane, Cl₂NCF₂CF₂NCl₂, are reported and characterized. The reactions of CIF with other sulfur(IV) imines proceed in an analogous manner to form perfluoroalkyl-dichloroamines via the elimination of the corresponding sulfur(IV) fluoride.     

Møller-Plesset (MP2) perturbation theory for large molecules

Summary A novel formulation of MP2 theory is presented which starts from the Laplace transform MP2 ansatz, and subsequently moves from a molecular orbital (MO) representation to an atomic orbital (AO) representation. Consequently, the new formulation is denoted AO-MP2. As in traditional MP2 approaches electron repulsion integrals still need to be transformed. Strict bounds on the individual MP2 energy contribution of each intermediate four-index quantity allow to screen off numerically insignificant integrals with a single threshold parameter. Implicit in our formulation is a bound to two-particle density matrix elements. For small molecules the computational cost for AO-MP2 calculations is about a factor of 100 higher than for traditional MO-based approaches, but due to screening the computational effort in larger systems will only grow with the fourth power of the size of the system (or less) as is demonstrated both in theory and in application. MP2 calculations on (non-metallic) crystalline systems seem to be a feasible extension of the Laplace transform approach. In large molecules the AO-MP2 ansatz allows massively parallel MP2 calculations without input/output of four-index quantities provided that each processor has in-core memory for a limited number of two-index quantities. Energy gradient formulas for the AO-MP2 approach are derived.Dedicated to Prof. W. Kutzelnigg whose books on theoretical chemistry aroused my interest in this field