We demonstrate that highly surface-sensitive supersonic rare-gas (He, Ar, and Xe) atom scattering, in both the quantum and classical regimes, can probe and quantify the interlayer interactions between graphene monolayers and metal substrates in terms of the Debye temperature corresponding to the surface normal vibration, and the surface effective mass. As models of the strongly and weakly interacting graphene, we investigated two systems, graphene on Ru(0001) and Pt (111), respectively. The experimental data for Ar and Xe are compared with the results from theoretical simulations based on the classical smooth surface model. For gr/Pt(111) we find that the scattering pattern of the rare-gas beam, including the Debye-Waller attenuation of the He beam, are quite similar to that from highly oriented pyrolytic graphite (HOPG); this suggests that the graphene-Pt (111) interaction is much like a van der Waals interaction. On the contrary, for the gr/Ru(0001) system, we find a smaller Debye-Waller attenuation and a larger surface effective mass, indicating that graphene on Ru(0001) is tightly bonded to the substrate. Furthermore, asymmetrical spectral shapes in the Ar and Xe scattering spectra from gr/Ru(0001) are interpreted as a result of the lateral distribution of the interlayer interaction corresponding to the moiré pattern. It is found that the "valley" region of the moiré pattern has high effective mass reflecting stronger bonding to the substrate, contributing to the high reflectivity of the He beam reported for this system. On the other hand, the effective mass of the "hill" region is found to be similar to that of HOPG, indicating that this region is well decoupled from the substrate. These results demonstrate a unique capability of atom scattering to probe and evaluate the molecule-substrate interaction and its spatial distributions.

Supersonic He and Ar atomic beam scattering from C(60) and graphene monolayers adsorbed on a Pt(111) surface are demonstrated in order to obtain detailed insight into a gas-molecule collision that has not been studied in detail so far. The effective masses and phonon spectral densities of the monolayers seen by different projectiles are discussed based on classical models such as the hard cube model and the recently developed smooth surface model. Large effective masses are deduced for both the monolayers, suggesting collective effects of surface atoms in the single collision event. The effective Debye temperature of graphene was found to be similar to that reported in highly oriented pyrolytic graphite (HOPG), indicating that the graphene is decoupled well from the Pt substrate. A much smaller Debye-Waller factor was found for the C(60) layer, probably reflecting the strong C(60)-Pt(111) interaction.

This paper considers verification of non-deterministic higher-order functional programs. Our contribution is a novel type system in which the types are used to express and verify (conditional) safety, termination, non-safety, and non-termination properties in the presence of ∀-∃ branching behavior due to non-determinism. For instance, the judgement ⊢ e : {u :int | ϕ(u)} ∀∀ says that every evaluation of e either diverges or reduces to some integer u satisfying ϕ(u), whereas ⊢ e : {u :int | ψ (u)} ∃∀ says that there exists an evaluation of e that either diverges or reduces to some integer u satisfying ψ (u). Note that the former is a safety property whereas the latter is a counterexample to a (conditional) termination property. Following the recent work on type-based verification methods for deterministic higher-order functional programs, we formalize the idea on the foundation of dependent refinement types, thereby allowing the type system to express and verify rich properties involving program values, branching behaviors, and the combination thereof.Our type system is able to seamlessly combine deductions of both universal and existential facts within a unified framework, paving the way for an exciting opportunity for new type-based verification methods that combine both universal and existential reasoning. For example, our system can prove the existence of a path violating some safety property from a proof of termination that uses a well-foundedness termination argument. We prove that our type system is sound and relatively complete, and further, thanks to having both modes of non-determinism, we show that our types are closed under complement.

In this paper, we present a novel constraint solving method for a class of predicate Constraint Satisfaction Problems (pCSP) where each constraint is represented by an arbitrary clause of first-order predicate logic over predicate variables. The class of pCSP properly subsumes the well-studied class of Constrained Horn Clauses (CHCs) where each constraint is restricted to a Horn clause. The class of CHCs has been widely applied to verification of linear-time safety properties of programs in different paradigms. In this paper, we show that pCSP further widens the applicability to verification of branching-time safety properties of programs that exhibit finitely-branching non-determinism. Solving pCSP (and CHCs) however is challenging because the search space of solutions is often very large (or unbounded), high-dimensional, and non-smooth. To address these challenges, our method naturally combines techniques studied separately in different literatures: counterexample guided inductive synthesis (CEGIS) and probabilistic inference in graphical models. We have implemented the presented method and obtained promising results on existing benchmarks as well as new ones that are beyond the scope of existing CHC solvers.

No abstract