Theory and applications of the Vlasov equation

Forty articles have been recently published in EPJD as contributions to the topical issue "Theory and applications of the Vlasov equation". The aim of this topical issue was to provide a forum for the presentation of a broad variety of scientific results involving the Vlasov equation. In this editorial, after some introductory notes, a brief account is given of the main points addressed in these papers and of the perspectives they open.Comment: Editoria

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

Viscoplastic simple shear at finite strains

The equations governing the simple shear deformation of an incompressible inelastic material undergoing finite strain are derived in this paper. The constitutive assumptions are kept in their most general form to allow the incorporation of widely used viscoplastic or viscoelastic models from the literature. It is shown that, while for a hyperelastic material the simple shear problem is completely determined by a single parameter, the amount of shear, in the viscoplastic case, the elastic deformation is the superposition of a triaxial stretch and a simple shear, whose determination requires the solution of three coupled nonlinear evolution equations. We evaluate such a solution for different material models and compare it with three-dimensional finite element simulations to assess its accuracy. We further assess the performance of these models using experimental data from filled rubber, focusing on their ability to capture the observed behaviour, such as the well-known Payne effect. Additionally, we extend our simple shear solution to address torsion and the extension of thin-walled cylinders. These derivations and analyses offer valuable insights for experimentalists engaged in the mechanical characterization of soft materials

Response to Comment on `Undamped electrostatic plasma waves' [Phys. Plasmas 19, 092103 (2012)]

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment

Biphonons in the Klein-Gordon lattice

A numerical approach is proposed for studying the quantum optical modes in the Klein-Gordon lattices where the energy contribution of the atomic displacements is non-quadratic. The features of the biphonon excitations are investigated in detail for different non-quadratic contributions to the Hamiltonian. The results are extended to multi-phonon bound states.Comment: Comments and suggestions are welcom

Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation

We here discuss the emergence of Quasi Stationary States (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian Mean Field (HMF) model, numerical simulations are performed based on both the original $N$-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bell's theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particles correlations.Comment: 5 pages, 3 figure

Effect of wetting layers on the strain and electronic structure of InAs self-assembled quantum dots

The effect of wetting layers on the strain and electronic structure of InAs self-assembled quantum dots grown on GaAs is investigated with an atomistic valence-force-field model and an empirical tight-binding model. By comparing a dot with and without a wetting layer, we find that the inclusion of the wetting layer weakens the strain inside the dot by only 1% relative change, while it reduces the energy gap between a confined electron and hole level by as much as 10%. The small change in the strain distribution indicates that strain relaxes only little through the thin wetting layer. The large reduction of the energy gap is attributed to the increase of the confining-potential width rather than the change of the potential height. First-order perturbation calculations or, alternatively, the addition of an InAs disk below the quantum dot confirm this conclusion. The effect of the wetting layer on the wave function is qualitatively different for the weakly confined electron state and the strongly confined hole state. The electron wave function shifts from the buffer to the wetting layer, while the hole shifts from the dot to the wetting layer.Comment: 14 pages, 3 figures, and 3 table

Twenty years of distributed port-Hamiltonian systems:A literature review

The port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on different research focuses ranging from modeling, discretization, control and theoretical foundations. This literature review highlights the wide applicability of the pH systems theory to complex systems with multi-physical domains using the same tools and language. We also supplement this article with a bibliographical database including all papers reviewed in this paper classified in their respective groups

Interwell relaxation times in p-Si/SiGe asymmetric quantum well structures: the role of interface roughness

We report the direct determination of nonradiative lifetimes in Si∕SiGe asymmetric quantum well structures designed to access spatially indirect (diagonal) interwell transitions between heavy-hole ground states, at photon energies below the optical phonon energy. We show both experimentally and theoretically, using a six-band k∙p model and a time-domain rate equation scheme, that, for the interface quality currently achievable experimentally (with an average step height ⩾1 Å), interface roughness will dominate all other scattering processes up to about 200 K. By comparing our results obtained for two different structures we deduce that in this regime both barrier and well widths play an important role in the determination of the carrier lifetime. Comparison with recently published experimental and theoretical data obtained for mid-infrared GaAs∕AlxGa1−xAs multiple quantum well systems leads us to the conclusion that the dominant role of interface roughness scattering at low temperature is a general feature of a wide range of semiconductor heterostructures not limited to IV-IV material

Optimal energy shaping via neural approximators

We introduce optimal energy shaping as an enhancement of classical passivity-based control methods. A promising feature of passivity theory, alongside stability, has traditionally been claimed to be intuitive performance tuning along the execution of a given task. However, a systematic approach to adjust performance within a passive control framework has yet to be developed, as each method relies on few and problem-specific practical insights. Here, we cast the classic energy-shaping control design process in an optimal control framework; once a task-dependent performance metric is defined, an optimal solution is systematically obtained through an iterative procedure relying on neural networks and gradient-based optimization. The proposed method is validated on state-regulation tasks