A hidden rule in metal sulfide fullerenes: A case study of Sc2S@C88

To elucidate the structure of a compound is a necessary step for its practical applications. To study the structure and properties of metal sulfide fullerene Sc₂S@C₈₈ detected by mass spectrometry, 11 194 isomers of C₈₈ and 33 isomers of Sc₂S@C₈₈ were systematically examined by density functional theory calculations. The calculations show that the two lowest‐energy isomers are Sc₂S@C₈₈:81 738 (IPR‐35) and Sc₂S@C₈₈:81 735 (IPR‐32), followed by Sc₂S@C₈₈:81 729 (IPR‐26), Sc₂S@C_88:81 712 (IPR‐9), and Sc₂S@C_88:81 733 (IPR‐30). Structural analysis shows that the first two energetically favored isomers are bridged by the third and fifth energetically favored isomers, which can transfer into each other via direct Stone–Wales rotation. The calculations of temperature effect show that the first two favored isomers become dominant forms of Sc₂S@C₈₈ with decreasing temperature and may coexist in the soot. This structural convertibility among favored isomers of Sc₂S@C₈₈ suggest a hidden rule that birds of a feather flock together in metal sulfide fullerenes. This rule may decrease the range of candidate cages for the structural identification of a metal sulfide fullerene. IR spectra are simulated for helping the future experimental identification of Sc₂S@C₈₈.     

Giant magnetoresistance of coiling polymers

We examine the magnetoresistance (MR) of conducting polymers with interest paid on the role of structural flexibility. Through Monte Carlo simulation and Green function method, we evaluate the electric transmission for a variety of polymer configurations. It is found that for a single polymer the transmission displays a complex oscillation and also a parity-dependent periodicity. For an ensemble of polymers the averaged transmission yields the nonlinear behavior of MR under varying magnetic fields. Interestingly, more flexible polymers are shown to achieve higher MR, depending on the population and the size of the loops.     

Collective dynamics of genetic oscillators with cell-to-cell communication: a study case of signal integration

This paper investigates the effect of integration of intracellular and extracellular signals on collective dynamics based on a multicellular system with cell-to-cell communication. Using a mathematical model of genetic repressilators coupled to quorum sensing, we show that the changes in parameters of a certain kind of cis-regulatory input function that quantifies the signal integration can lead to the change of coupling type from phase-attractive to phase-repulsive coupling or vice versa. Consequently, the multicellular system can exhibit, in both coupling cases, different collective behaviors in terms of synchronization and clustering. We give a general method of determining coupling type, elucidate the mechanism of generating these phenomena and present a criterion for stability of cluster states, mainly by analyzing phase interaction functions.     

ON J-SELFADJOINT EXTENSION OF THE PRODUCT OF TWO nTH-ORDER J-SYMMETRIC ORDINARY DIFFERENTIAL OPERATORS ON [a,b]

The problem of J-selfadjointness of the product of two nth-order J-symmetric operators on [a,b] is studied. We give a condition to ensure that the product operator is a J-selfadjoint extension.     

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two suffcient and necessary conditions for such graphs to be 1- or 2-arc-regular are given and based on the conditions, several infinite families of 1-or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.     

Medium modified fragmentation function: equivalence of the ACSX and QW formalisms in the high-Q2 region

We study the medium modified fragmentation function in high-energy heavy-ion collisions. We show that the ACSX and QW formalisms are equivalent to each other in the high-Q² limit in both theoretical and numerical aspects.     

MR microscopy of micron scale structures

Magnetic resonance (MR) microscopy of up to 1–5-μm resolutions have been reported previously. The tested phantom structures, however, had widths one order of magnitude bigger than the reported resolutions, e.g., spherical beads or capillary tubes of tens-of-micron diameters or wall thicknesses have been imaged. In this study, we fabricated structures having a few micron widths on a silicon wafer and imaged them using our 1-μm-resolution MR microscopy at 14.1 T. Micron scale width structures were, for the first time, resolved by MR microscopy.