Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

Entanglement relaxation of poly(1-butene) and its copolymer with ethylene detected in conventional shear rheometer and quartz resonator

This study examined linear viscoelasticity (LVE) of stereo-regular poly(1-butene) (PB) and its random copolymer with polyethylene, with number fraction of ethylene comonomer ≤10%, using a conventional shear rheometer combined with a quartz resonator. This combination resulted in the detection of LVE in a broad frequency range from Rouse region to terminal relaxation. LVE, thus, determined was fit to the double reptation model through utilizing inputting molecular weights determined by gel permeation chromatography equipped with refractive index and two-angle laser light scattering monitors, and the segmental time and entanglement molecular weight as the two fitting parameters. A quantitative prediction was finally achieved when the two fitting parameters changed systematically by the increase of ethylene content, a decrease of segmental time quantified a plasticizing effect, and a decrease of entanglement molecular weight reflected enhanced the chain flexibility. The entanglement molecular weight of the PB samples was found to be lower than those reported for stereo-irregular PB, suggesting the important effect of stereo-regularity on the chain flexibility

Microscopic modeling of energy dissipation and decoherence in nanoscale materials and devices

Primary goal of this thesis work is to develop and implement microscopic modeling strategies able to describe semiconductor-based nanomaterials and nanodevices, overcoming both the intrinsic limits of the semiclassical transport theory and the huge computational costs of non Markovian approaches. The progressive reduction of modern optoelectronic devices space-scales, triggered by the evolution on semiconductor heterostructures at the nanoscale, together with the decrease of the typical time-scales involved, pushes device miniaturization toward limits where the application of the traditional Boltzmann transport theory becomes questionable, and a comparison with more rigorous quantum transport approaches is imperative. In spite of the quantum-mechanical nature of electron and photon dynamics in the core region of typical solid-state nanodevices, the overall behavior of such quantum systems is often governed by a highly non-trivial interplay between phase coherence and dissipation/dephasing. To this aim, the crucial step is to adopt a quantum mechanical description of the carrier subsystem; this can be performed at different levels, ranging from phenomenological dissipation/decoherence models to quantum-kinetic treatments. However, due to their high computational cost, non-Markovian Green’ s-function as well as density-matrix approaches like quantum Monte Carlo techniques or quantum-kinetics are currently unsuitable for the design and optimization of new-generation nanodevices. On the other end, the Wigner-function technique is a widely used approach which, in principle, is well suited to describe an interplay between coherence and dissipation: in fact it can be regarded both as a phase space formulation of the electronic density matrix and a quantum equivalent of the classical distribution function. The evolution of this quasi-distribution function is governed by the Wigner-equation, which is usually solved by applying local spatial boundary conditions. However, such a scheme has recently shown some intrinsic limits. In this thesis work we analyze both the reasons for these unphysical features –pointing out the needing of different and purely quantum approaches– and the limits in which they should not appear, thus justifying why these problems had not been encountered in numerous quantum-transport simulations based on this procedure. For these reasons here we present a novel single-particle simulation strategy able to describe the interplay between coherence and dissipation/dephasing. In the presence of one- as well as two-body scattering mechanisms, we apply the mean-field approximation to the many-body Lindblad-type (hence, positive-definite) scattering superoperators provided by a recently proposed Markov approach, and we derive a closed equation of motion for the electronic single-particle density matrix. Although the resulting scattering superoperator turns out to be, at finite or high carrier densities, nonlinear and non-Lindblad, we prove that it is able to guarantee the positivity of the evolution (in striking contrast with conventional Markov approaches) independently of the scattering mechanisms, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices; furthermore, it may be extended to the cases of quantum systems with open spatial boundaries (in this regard, it provides a formal derivation of a recently proposed Lindblad-like device-reservoir scattering superoperator). The proposed theoretical scheme is able, one the one hand, to recover the space-dependent Boltzmann equation and, on the other, to point out the regimes where a relevant role may be played by scattering-nonlocality effects, e.g. scattering-induced variations of the spatial charge-density which may not be provided by semiclassical treatments. Supplementing our analytical investigation with a number of simulated experiments in homogeneous as well as inhomogeneous GaN-based systems, we provide a rigorous treatment of scattering nonlocality in semiconductor nanostructures: in particular, we show how the scattering-nonlocality effects (i) are particularly significant in the presence of a carrier localization on the nanometric space scale, (ii) cause a speedup of the diffusion and (iii) in superlattice structures induce, with respect to scattering-free evolutions, a suppression of coherent oscillations between adjacent wells. These genuine quantum effects may be predicted also by other simplified treatments of the dissipation/decoherence like, e.g., the Relaxation Time Approximation: the latter however turns out to be, contrary to the proposed microscopic theoretical scheme, totally nonlocal, e.g. it is unable to recover the local character of the Boltzmann collision term in the semiclassical limit and it leads, especially for the case of quasielastic dissipation processes, to a significant overestimation of the diffusion speedup

Ab initio simulations of α- and β-ammonium carbamate (NH₄·NH₂CO₂), and the thermal expansivity of deuterated α-ammonium carbamate from 4.2 to 180 K by neutron powder diffraction

Experimental and computational studies of ammonium carbamate have been carried out, with the objective of studying the elastic anisotropy of the framework manifested in (i) the thermal expansion and (ii) the compressibility; furthermore, the relative thermodynamic stability of the two known polymorphs has been evaluated computationally. Using high-resolution neutron powder diffraction data, the crystal structure of α-ammonium carbamate (ND4·ND2CO2) has been refined [space group Pbca, Z = 8, with a = 17.05189 (15), b = 6.43531 (7), c = 6.68093 (7) Å and V = 733.126 (9) Å^{3} at 4.2 K] and the thermal expansivity of α-ammonium carbamate has been measured over the temperature range 4.2-180 K. The expansivity shows a high degree of anisotropy, with the b axis most expandable. The ab initio computational studies were carried out on the α- and β-polymorphs of ammonium carbamate using density functional theory. Fitting equations of state to the P(V) points of the simulations (run athermally) gave the following values: V0 = 744 (2) Å^{3} and bulk modulus K0 = 16.5 (4) GPa for the α-polymorph, and V0 = 713.6 (5) Å^{3} and K0 = 24.4 (4) GPa for the β-polymorph. The simulations show good agreement with the thermoelastic behaviour of α-ammonium carbamate. Both phases show a high-degree of anisotropy; in particular, α-ammonium carbamate shows unusual compressive behaviour, being determined to have negative linear compressibility (NLC) along its a axis above 5 GPa. The thermodynamically stable phase at ambient pressure is the α-polymorph, with a calculated enthalpy difference with respect to the β-polymorph of 0.399 kJ mol^{-1}; a transition to the β-polymorph could occur at ∼0.4 GPa

Transport models and advanced numerical simulation of silicon-germanium heterojunction bipolar transistors

Applications in the emerging high-frequency markets for millimeter wave applications more and more use SiGe components for cost reasons. To support the technology effort, a reliable TCAD platform is required. The main issue in the simulation of scaled devices is related to the limitations of the physical models used to describe charge carrier transport. Inherent approximations in the HD formalism are discussed over different technology nodes, providing for the first time a complete survey of HD models capability and restrictions with scaling for simulation of SiGe HBTs. Moreover, a complete set of models for transport parameters of SiGe HBTs is reported, including low-field mobility, energy relaxation time, saturation velocity, high-field mobility and effective density of state. Implementation in a commercial device simulator is drawn and findings are compared with simulation results obtained using a standard set of models and with trustworthy results (i.e. MC and SHE simulation results and experimental data), validating proposed models and clarifying their reliability and accuracy over different technologies. Finally, electrical breakdown phenomena in SiGe HBTs are analyzed: a novel complete model for multiplication factor is reported and validated by experimental results; new M model provides an exhaustive accuracy over a wide range of collector voltages

SMALL POLARONS IN REAL CRYSTALS - CONCEPTS AND PROBLEMS

Much of small polaron theory is based on highly idealized models, often essentially a continuum description with a single vibrational frequency. These models ignore much of the wealth of experimental data, which find interpretation in many atomistic simulations. We review here a range of properties of small polarons in real, rather than model, systems. The phenomena fall into three main classes: (i) the mechanisms and dynamics of self-trapping of polarons; (ii) static properties-the relative energies of large and small polarons, the optical transitions expected, their effect on positions of other ions and on lattice vibrations, their population in thermal equilibrium, and so on; (iii) small polaron hopping and diffusion. We discuss the key concepts and methods of calculation of polarons, and explore the properties of self-trapped holes and excitons in ionic crystals, and those of an excess electron in liquid water

Development of filtered Euler–Euler two-phase model for circulating fluidised bed: High resolution simulation, formulation and a priori analyses

Euler–Euler two-phase model simulations are usually performed with mesh sizes larger than the smallscale structure size of gas–solid flows in industrial fluidised beds because of computational resource limitation. Thus, these simulations do not fully account for the particle segregation effect at the small scale and this causes poor prediction of bed hydrodynamics. An appropriate modelling approach accounting for the influence of unresolved structures needs to be proposed for practical simulations. For this purpose, computational grids are refined to a cell size of a few particle diameters to obtain mesh-independent results requiring up to 17 million cells in a 3D periodic circulating fluidised bed. These mesh-independent results are filtered by volume averaging and used to perform a priori analyses on the filtered phase balance equations. Results show that filtered momentum equations can be used for practical simulations but must take account of a drift velocity due to the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and particle sub-grid stresses due to the filtering of the non-linear convection term. This paper proposes models for sub-grid drift velocity and particle sub-grid stresses and assesses these models by a priori tests