Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles

Phosphorene, the single layer counterpart of black phosphorus, is a novel two-dimensional semiconductor with high carrier mobility and a large fundamental direct band gap, which has attracted tremendous interest recently. Its potential applications in nano-electronics and thermoelectrics call for a fundamental study of the phonon transport. Here, we calculate the intrinsic lattice thermal conductivity of phosphorene by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations. The thermal conductivity of phosphorene at $300\,\mathrm{K}$ is $30.15\,\mathrm{Wm^{-1}K^{-1}}$ (zigzag) and $13.65\,\mathrm{Wm^{-1}K^{-1}}$ (armchair), showing an obvious anisotropy along different directions. The calculated thermal conductivity fits perfectly to the inverse relation with temperature when the temperature is higher than Debye temperature ($\Theta_D = 278.66\,\mathrm{K}$). In comparison to graphene, the minor contribution around $5\%$ of the ZA mode is responsible for the low thermal conductivity of phosphorene. In addition, the representative mean free path (MFP), a critical size for phonon transport, is also obtained.Comment: 5 pages and 6 figures, Supplemental Material available as http://www.rsc.org/suppdata/cp/c4/c4cp04858j/c4cp04858j1.pd

Logic of Predicates With Explicit Substitutions

This paper aims at supporting the same idea. Our justification of the claim is, however, quite different from the one offered by Girard. The latter, cf. [9], translates every sequent of the usual propositional logic (classical, or intuitionistic) into a sequent of commutative linear logic. Then one shows that a sequent can be proved classically, resp., intuitionistically, iff its translation can be proved linearly. By contrast, our embedding only works on the level of predicate logic. We show that every theory of classical logic of predicates with equality lives as a theory within a non-commutative intuitionistic substructural logic: the logic of predicates with equality and explicit substitution. Also, our explanation does not require to call upon so called exponentials --- the modalities introduced by Girard just to facilitate his embedding. Our construction is also different from other proposals to move substitutions from the level of metatheory to the theory of logic, cf. [16]. They add substitutions as modal constructions. Here, substitutions are considered new atomic formulae

A Non-monotone Logic for Reasoning about Action

A logic for reasoning about action is presented. The logic is based on the idea that explicit substitutions can be seen as atomic formul describing basic change of state of a system. The logic is non-monotone, i.e., it does not admit weakening in its presentation as a fragment of non-commutative linear logic. Potential applications of the logic are also discussed in connection to the "Frame Problem"

General Morphisms of Petri Nets (Extended Abstract)

) ? Marek A. Bednarczyk and Andrzej M. Borzyszkowski Institute of Computer Science, Gdansk Branch, Polish Acad. of Sc. Abrahama 18, 81-825 Sopot, Poland, http://www.ipipan.gda.pl Abstract. A new notion of a general morphism of Petri nets is introduced. The new morphisms are shown to properly include the morphisms considered so far. The resulting category of Petri nets is shown to admit products. Potential applications of general morphisms are indicated. 1 Introduction For mathematically oriented people Petri nets are quite complex objects. The following observation should put the above statement into a proper perspective: it took a quarter of a century from the inception of Petri nets, cf. [12], to the definition of their morphisms, cf. [14, 15]. Winskel's solution to the problem of defining a suitable notion of Petri net morphism was algebraic. He noticed that Petri nets can be viewed as certain 2-sorted algebras. Consequently, Petri net morphisms defined in [14] are homomo..

The mandala and Concurrent Realizations of Reactive Systems

The problem of finding a (functorial) concurrent realization of a reactive system by means of a labelled safe Petri net is studied. Firstly, a (functorial) construction is described that leads from the category of concrete asynchronous systems introduced by Morin to the category of labelled safe Petri nets. Then, the general problem is discussed. It is indicated that in general there are no optimal solutions, i.e., that the most concurrent realizations of a reactive system needs not exist. Nevertheless, a framework to support the process of building a concurrent realization of a reactive system is presented. The framework is based on zig-zag morphisms. 1 Introduction There is a gap between ways in which one specifies the behaviour of reactive systems and their concurrent asynchronous implementations. The former is often done by means of a brand of temporal logic. The many temporal logics used, in pure form, do not o#er any means to describe what should, and what should not be done by ..

Generalized Automata and their Net Representations

We consider two generalizations of the duality between transition systems and Petri nets. In the first, transitions are replaced by paths, that is partial functions from a fixed set \Delta to states. This allows to model continuous and/or hybrid systems when \Delta represents durations

Expressing and Verifying Temporal and Structural Properties of Mobile Agents

Logics for expressing properties of Petri hypernets, a visual formalism for modelling mobile agents, are proposed. Two classes of properties are of interest—the temporal evolution of agents and their structural correlation. In particular, we investigate how the classes can be combined into a logic capable of expressing the dynamic evolution of the structural correlation. The problem of model checking properties of a class of the logic on Petri hypernets is shown to be PSPACE-complete