Percolation study for the capillary ascent of a liquid through a granular soil

Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length {\lambda} of the capillary bridges among grains. Low {\lambda} generate a disconnect structure, with small clusters everywhere. On the contrary, for high {\lambda}, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of {\lambda} on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold {\lambda}_{c} = (0.049 \pm 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length {\nu} = (0.830 \pm 0.051), suggesting that the percolation transition falls into the universality class of ordinary percolation

Atomic Effective Pseudopotentials for Semiconductors

We derive an analytic connection between the screened self-consistent effective potential from density functional theory (DFT) and atomic effective pseudopotentials (AEPs). The motivation to derive AEPs is to address structures with thousands to hundred thousand atoms, as given in most nanostructures. The use of AEPs allows to bypass a self-consistent procedure and to address eigenstates around a certain region of the spectrum (e.g., around the band gap). The bulk AEP construction requires two simple DFT calculations of slightly deformed elongated cells. The ensuing AEPs are given on a fine reciprocal space grid, including the small reciprocal vector components, are free of parameters, and involve no fitting procedure. We further show how to connect the AEPs of different bulk materials, which is necessary to obtain accurate band offsets. We derive a total of 20 AEPs for III-V, II-VI and group IV semiconductors and demonstrate their accuracy and transferability by comparison to DFT calculations of strained bulk structures, quantum wells with varying thickness, and semiconductor alloys.Comment: 10 pages, 5 figures, submitted to PR

Resonance enhancement of particle production during reheating

We found a consistent equation of reheating after inflation, which shows that for small quantum fluctuations the frequencies of resonance are slighted different from the standard ones. Quantum interference is taken into account and we found that at large fluctuations the process mimics very well the usual parametric resonance but proceed in a different dynamical way. The analysis is made in a toy quantum mechanical model and we discuss further its extension to quantum field theory.Comment: 4 pages, 4 figures(eps), using RevTe

Degree of Quantumness in Quantum Synchronization

We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators

R^2-corrections to Chaotic Inflation

Scalar density cosmological perturbations, spectral indices and reheating in a chaotic inflationary universe model, in which a higher derivative term is added, are investigated. This term is supposed to play an important role in the early evolution of the Universe, specifically at times closer to the Planck era.Comment: 14 pages, accepted for publication in MPL

Asymptotic and Non-asymptotic Results in the Approximation by Bernstein Polynomials

This paper deals with the approximation of functions by the classical Bernstein polynomials in terms of the Ditzian–Totik modulus of smoothness. Asymptotic and non-asymptotic results are respectively stated for continuous and twice continuously differentiable functions. By using a probabilistic approach, known results are either completed or strengthened

On the Uniqueness Conjecture for the Maximum Stirling Numbers of the Second Kind

The Stirling numbers of the second kind S(n,  k) satisfy S(n, 0)<¿<S(n, kn)=S(n, kn+1)>¿>S(n, n).A long standing conjecture asserts that there exists no n= 3 such that S(n, kn) = S(n, kn+ 1). In this note, we give a characterization of this conjecture in terms of multinomial probabilities, as well as sufficient conditions on n ensuring that S(n, kn) > S(n, kn+ 1). © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG

A load-based approach for optimizing a packed-bed thermal store

This paper presents a load-based optimization approach for improving the efficiency of a packed bed. The optimization is based on splitting the work-cycle of the thermal store into two frequency components: low and high. A packed bed is designed for each one of the two profiles. A packed bed can be customised much better for a duty-cycle that contains a narrow range of frequencies.The case study presented considers a 24 h working-cycle (12 h charge / 12 h discharge) with a 10 MW peak power and an exergy storage requirement of 33.3 MW h (76.3 MW h of heat). A packed bed was optimized for this duty-cycle using a one dimensional model that varies the aspect ratio and the rock size. This packed bed is the ‘reference case’ for the study. The aim of the load-based optimization is to create a two-bed system that achieves lower exergy losses than the reference case while keeping the overall storage capacity constant.A sign-preserving filter is used as the signal-splitting tool. Numerous different work-cycle “splits” are explored. Results show that the exergy losses of the packed bed can be considerably reduced. The optimum work-cycle split considers a low-frequency packed bed that supplies 85% of the storage capacity and a high-frequency packed bed that provides the remaining 15%. The combined losses of the two packed beds are 644 kW h, which represents a reduction of 25.5% in comparison to the exergy losses of the reference case. The study demonstrates that the “load-based optimization” allows replacing a packed bed with an equivalent but more efficient two-bed system at almost no additional cost