A critical analysis for the arguments in support of, and against, the traditional approach to thermodynamics of vitreous state is provided. In this approach one presumes that there is a continuous variation of the entropy in the glass-liquid transition temperature range, or a “continuous entropy approach” towards 0 K which produces a positive value of the entropy at T→ 0 K. I find that argument...

Implementation of orbital-free free-energy functionals in the Profess code and the coupling of Profess with the Quantum Espresso code are described. The combination enables orbital-free DFT to drive ab initio molecular dynamics simulations on the same footing (algorithms, thermostats, convergence parameters, etc.) as for Kohn–Sham (KS) DFT. All the non-interacting free-energy functionals implem...

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

A random composition of n appears when the points of a random closed set R ⊂ [0, 1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts K n of this composition and other related functionals under the assumption that R = φ(S •) where (S t , t ≥ 0) is a subordinator and φ : [0, ∞] → [0, 1] is a diffeomorphism. We derive the asymptotics of ...

We investigate equality cases in inequalities for Sylvester-type functionals. Namely, it was proven by Campi, Colesanti and Gronchi that the quantity ∫ x0∈K ... ∫ xn∈K [V (conv{x0, ..., xn})]dx0...dxn , n ≥ d, p ≥ 1 is maximized by triangles among all planar convex bodies K (parallelograms in the symmetric case). We show that these are the only maximizers, a fact proven by Giannopoulos for p = ...

We present a general-purpose meta-generalized gradient approximation (MGGA) exchange-correlation functional generated within the Bayesian error estimation functional framework [J. Wellendorff, K. T. Lundgaard, A. Møgelhøj, V. Petzold, D. D. Landis, J. K. Nørskov, T. Bligaard, and K. W. Jacobsen, Phys. Rev. B 85, 235149 (2012)]. The functional is designed to give reasonably accurate density func...

A random composition of n appears when the points of a random closed set R ⊂ [0, 1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts K n of this composition and other related functionals under the assumption that R = φ(S t) where (S t , t ≥ 0) is a subordinator and φ : [0, ∞] → [0, 1] is a diffeomorphism. We derive the asymptotics of ...

We have investigated the performance of popular density functionals that include van der Waals interactions for the experimentally well-characterized problem of ethene (C(2)H(4)) adsorbed on the low-index surfaces of copper. This set of functionals does not only include three van der Waals density functionals-vdwDF-PBE, vdwDF-revPBE and optB86b-vdwDF-and two dispersion-corrected functionals-Gri...