Enhanced thermal stability and spin-lattice relaxation rate of N@C60 inside carbon nanotubes

We studied the temperature stability of the endohedral fullerene molecule, N@C60, inside single-wall carbon nanotubes using electron spin resonance spectroscopy. We found that the nitrogen escapes at higher temperatures in the encapsulated material as compared to its pristine, crystalline form. The temperature dependent spin-lattice relaxation time, T_1, of the encapsulated molecule is significantly shorter than that of the crystalline material, which is explained by the interaction of the nitrogen spin with the conduction electrons of the nanotubes.Comment: 5 pages, 4 figures, 1 tabl

Adapting Real Quantifier Elimination Methods for Conflict Set Computation

The satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e.\ obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

Satisfiability Checking and Symbolic Computation

Symbolic Computation and Satisfiability Checking are viewed as individual research areas, but they share common interests in the development, implementation and application of decision procedures for arithmetic theories. Despite these commonalities, the two communities are currently only weakly connected. We introduce a new project SC-square to build a joint community in this area, supported by a newly accepted EU (H2020-FETOPEN-CSA) project of the same name. We aim to strengthen the connection between these communities by creating common platforms, initiating interaction and exchange, identifying common challenges, and developing a common roadmap. This abstract and accompanying poster describes the motivation and aims for the project, and reports on the first activities.Comment: 3 page Extended Abstract to accompany an ISSAC 2016 poster. Poster available at http://www.sc-square.org/SC2-AnnouncementPoster.pd

Adapting Real Quantifier Elimination Methods for Conflict Set Computation

International audienceThe satisfiability problem in real closed fields is decidable. In the context of satisfiability modulo theories, the problem restricted to conjunctive sets of literals, that is, sets of polynomial constraints, is of particular importance. One of the central problems is the computation of good explanations of the unsatisfiability of such sets, i.e. obtaining a small subset of the input constraints whose conjunction is already unsatisfiable. We adapt two commonly used real quantifier elimination methods, cylindrical algebraic decomposition and virtual substitution, to provide such conflict sets and demonstrate the performance of our method in practice

Enhancement of the Electron Spin Resonance of Single-Walled Carbon Nanotubes by Oxygen Removal

We have observed a nearly fourfold increase in the electron spin resonance (ESR) signal from an ensemble of single-walled carbon nanotubes (SWCNTs) due to oxygen desorption. By performing temperature-dependent ESR spectroscopy both before and after thermal annealing, we found that the ESR in SWCNTs can be reversibly altered via the molecular oxygen content in the samples. Independent of the presence of adsorbed oxygen, a Curie-law (spin susceptibility $\propto 1/T$) is seen from $\sim$4 K to 300 K, indicating that the probed spins are finite-level species. For both the pre-annealed and post-annealed sample conditions, the ESR linewidth decreased as the temperature was increased, a phenomenon we identify as motional narrowing. From the temperature dependence of the linewidth, we extracted an estimate of the intertube hopping frequency; for both sample conditions, we found this hopping frequency to be $\sim$100 GHz. Since the spin hopping frequency changes only slightly when oxygen is desorbed, we conclude that only the spin susceptibility, not spin transport, is affected by the presence of physisorbed molecular oxygen in SWCNT ensembles. Surprisingly, no linewidth change is observed when the amount of oxygen in the SWCNT sample is altered, contrary to other carbonaceous systems and certain 1D conducting polymers. We hypothesize that physisorbed molecular oxygen acts as an acceptor ($p$-type), compensating the donor-like ($n$-type) defects that are responsible for the ESR signal in bulk SWCNTs.Comment: 14 pages, 7 figure

On Gröbner Bases in the Context of Satisfiability-Modulo-Theories Solving over the Real Numbers

We address satisfiability checking for the first-order theory of the real-closed field (RCF) using satisfiability-modulo-theories (SMT) solving. SMT solvers combine a SAT solver to resolve the Boolean structure of a given formula with theory solvers to verify the consistency of sets of theory constraints. In this paper, we report on an integration of Gröbner bases as a theory solver so that it conforms with the requirements for efficient SMT solving: (1) it allows the incremental adding and removing of polynomials from the input set and (2) it can compute an inconsistent subset of the input constraints if the Gröbner basis contains 1. We modify Buchberger’s algorithm by implementing a new update operator to optimize the Gröbner basis and provide two methods to handle inequalities. Our implementation uses special data structures tuned to be efficient for huge sets of sparse polynomials. Besides solving, the resulting module can be used to simplify constraints before being passed to other RCF theory solvers based on, e.g., the cylindrical algebraic decomposition