Vlasov Model Research Articles

Vibration Analysis of Perovskite Solar Cells Resting on Porous Nanocomposite Substrate in Thermal Environment

The free vibration analysis of a perovskite solar cell (PSC) within thermal environments is studied through a quasi-3D plate model. This model is designed to account for the stretching effects and non-uniform shear strains throughout the thickness. The PSC film is represented in the model as a thin laminated plate, comprising five distinct plies: ITO, PEDOT:PSS, perovskite, PCBM, and Au. A graphene platelets reinforced composite (GPLRC) substrate, made of Poly (methyl methacrylate), is assumed to be located under the noted five layers. The GPLRC substrate is conceptualized in the model as a porous foundation with finite depth. The foundation stiffnesses are determined using a modified Vlasov model, and the equivalent Young modulus of the foundation is evaluated using a modified Halpin–Tsai model, introducing the porosity coefficient. It is also considered that the material properties of GPLRC substrates exhibit temperature dependency. For the PSC with all edges simply supported, Navier solution method is applied to obtain the frequencies and associated mode numbers. Based on the results presented in this study, an increase in the porosity and thickness of the substrate can negatively impact the frequencies of the structure. However, natural frequencies experience almost no change if the temperature rises.

Parallel expansion of a fuel pellet plasmoid

The problem of the assimilation of a cryogenic fuel pellet injected into a hot plasma is considered. Due to the transparency to ambient particles of the plasmoid, the localised region of high-density plasma created by ionisation of the ablated pellet material, electrons reach a ‘quasiequilibrium’ (QE) state which is characterised by a steady-state on the fastest collisional time scale. The simplified electron kinetic equation of the QE state is solved. Taking a velocity moment of the higher-order electron kinetic equation, which is valid on the expansion time scale, permits a fluid closure, yielding an evolution equation for the macroscopic parameters describing the QE distribution function. In contrast to the Braginskii equations, the closure does not require that electrons have a short mean free path compared with the size of density perturbations, and permits an anisotropic and highly non-Maxwellian distribution function. As the QE distribution function accounts for both trapped and passing electrons, the self-consistent electric potential that causes the expansion can be properly described, in contrast to earlier models of pellet plasmoid expansion with an unbounded potential. The plasmoid expansion is simulated using both a Vlasov model and a cold-fluid model for the ions. During the expansion plasmoid ions and electrons obtain nearly equal amounts of energy; as hot ambient electrons provide this energy in the form of collisional heating of plasmoid electrons, the expansion of a pellet plasmoid is expected to be a potent mechanism for the transfer of energy from electrons to ions on a time scale shorter than that of ion–electron thermalisation.

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad–Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.

Fourth-Order Conservative Non-splitting Semi-Lagrangian Hermite WENO Schemes for Kinetic and Fluid Simulations

AbstractWe present fourth-order conservative non-splitting semi-Lagrangian (SL) Hermite essentially non-oscillatory (HWENO) schemes for linear transport equations with applications for nonlinear problems including the Vlasov–Poisson system, the guiding center Vlasov model, and the incompressible Euler equations in the vorticity-stream function formulation. The proposed SL HWENO schemes combine a weak formulation of the characteristic Galerkin method with two newly constructed HWENO reconstruction methods. The new HWENO reconstructions are meticulously designed to strike a delicate balance between curbing numerical oscillation and introducing excessive dissipation. Mass conservation naturally holds due to the weak formulation of the semi-Lagrangian discontinuous Galerkin method and the design of the HWENO reconstructions. We apply a positivity-preserving limiter to maintain the positivity of numerical solutions when needed. Abundant benchmark tests are performed to verify the effectiveness of the proposed SL HWENO schemes.

Analysis of Settlement of an Existing Tunnel Subjected to Undercrossing Tunneling Based on the Modified Vlasov Model

Analysis of Settlement of an Existing Tunnel Subjected to Undercrossing Tunneling Based on the Modified Vlasov Model

Numerical approximation of 3D particle beams by multi-scale paraxial Vlasov-Maxwell equations

Even now, solving numerically the 3D time-dependent Vlasov-Maxwell equations is a challenging problem. Hence, it is always interesting to develop simpler but accurate approximate models. By introducing a small parameter, we derived paraxial asymptotic models that approximate these equations, allowing us to treat relativistic cases, much slower beams or even non-relativistic cases. These models are static or quasi-static and with a nth order accuracy that may be chosen as required. Here, we propose a 3D numerical approximation of this multi-scale model. It is based, for the paraxial Maxwell model, on a finite element method coupled with a Particle-In-Cell approximation of the paraxial Vlasov model. Numerical results illustrated the efficiency of the method.

Non-equilibrium flow of van der Waals fluids in nano-channels

The Enskog–Vlasov equation provides a consistent description of the microscopic molecular interactions for real fluids based on the kinetic and mean-field theories. The fluid flows in nano-channels are investigated by the Bhatnagar–Gross–Krook (BGK) type Enskog–Vlasov model, which simplifies the complicated Enskog–Vlasov collision operator and enables large-scale engineering design simulations. The density distributions of real fluids are found to exhibit inhomogeneities across the nano-channel, particularly at large densities, as a direct consequence of the inhomogeneous force distributions caused by the real fluid effects including the fluid molecules' volume exclusion and the long-range molecular attraction. In contrast to the Navier–Stokes equation with the slip boundary condition, which fails to describe nano-scale flows due to the coexistence of confinement, non-equilibrium, and real fluid effects, the Enskog–Vlasov–BGK model is found to capture these effects accurately as confirmed by the corresponding molecular dynamics simulations for low and moderate fluid densities.

Reply to the discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer”

Reply to the discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer”

From Vlasov Equation to Degenerate Nonlocal Cahn-Hilliard Equation

We provide a rigorous mathematical framework to establish the hydrodynamic limit of the Vlasov model introduced in Takata and Noguchi (J. Stat. Phys. 172:880-903, 2018) by Noguchi and Takata in order to describe phase transition of fluids by kinetic equations. We prove that, when the scale parameter tends to 0, this model converges to a nonlocal Cahn-Hilliard equation with degenerate mobility. For our analysis, we introduce apropriate forms of the short and long range potentials which allow us to derive Helmhotlz free energy estimates. Several compactness properties follow from the energy, the energy dissipation and kinetic averaging lemmas. In particular we prove a new weak compactness bound on the flux.

Soil–Structure Interaction Effect on the Resistance of a Steel Frame against Progressive Collapse Using Linear Static and Nonlinear Dynamic Procedures

In recent years, increases in terrorist attacks or other unexpected explosions have shown that their effects can cause critical damages to buildings and cause partial or total collapse of buildings. This chain collapse mechanism is named a progressive collapse. Subsoil effects on a building are often ignored in studies on progressive collapse. In this study, the effect of soil–structure interaction on the risk of progressive collapse of a steel frame is investigated by using the modified Vlasov model, which has not been used in the studies on progressive collapse before. For this purpose, a steel building model was investigated. A linear static procedure (LSP) and nonlinear dynamic procedure (NDP) with alternative path method were used for the analysis of the frame. SAP2000 software was used to model subsoil effect on the frame via an interface coded in MATLAB interactively. The results from the analyses showed that the soil–structure interaction effect can significantly affect the progressive collapse resistance of the building.

Global continuation of a Vlasov model of rotating galaxies

A typical galaxy consists of a huge number of stars attracted to each other by gravity. For instance, the Milky Way has about $ 10^{11} $ stars. In the astrophysics literature such a galaxy is typically modeled by the Vlasov-Poisson system. We prove an existence theorem for axisymmetric steady states of galaxies that may rotate rapidly. Such states are given in terms of a fairly general function $ \phi $ of the particle energy and angular momentum. The set $ {\mathcal K} $ of such states form a connected set in an appropriate function space. Along the set $ {\mathcal K} $, we prove under suitable conditions that either (a) the supports of the galaxies become unbounded or (b) both the rotation speeds and the densities somewhere within the galaxy become unbounded.

Dynamic analysis of a laterally loaded rectangular pile in multilayered viscoelastic soil

Rectangular piles are usually used as the foundation for many infrastructures, but there are fewer theoretical solutions for the lateral vibration. This study presents a semi-analytical methodology for the dynamic analysis of laterally loaded rectangular pile in multi-layered viscoelastic soils. The pile-soil system is modeled as a continuum, the horizontal continuous displacement model is proposed as products of the separating variables function. The coupled governing equations for rectangular pile-soil system in the frame of Euler-Bernoulli beam and modified Vlasov model are derived with the aid of Hamilton's Variation principle and calculus of variations. The physical mechanisms of soil reaction and dynamic equilibrium equation are interpreted by employing thin-layer element of soil. The dynamic responses are solved analytically and numerically by an iterative procedure. The verification and accuracy of the research are obtained thorough comparison with the relevant examples from the literatures and finite element analysis. The effects of cross-section shapes and soil stratification on the complex dynamic response are investigated and discussed in detail.

Static Analysis of thin Rectangular Plate Resting on Elastic Foundation Using Modified Vlasov Model

A four-nodded rectangular plate bending element based on Kirchhoff theory resting on elastic foundation using modified Vlasov model. For evaluate the two soil parameter for Vlasov foundation the modulus of elasticity and Poisson ratio of the soil is assumed constant from top surface to the top of bottom rigid base. All the deformation stiffness matrix of plate and subsoil are evaluated using finite element method. A Matlab code is developed and convergence study is carried out and then some realistic cases of plate under static load on elastic foundations are solved to determine the static response. The results, thus obtained, are compared, with the available results obtained by other researchers. It behaves extremely well for thin plates and convergence rate is high.

Analytical method for the kinematic response and signal error of a downhole seismometer subjected to P-waves

This paper presents an analytical method for the steady-state kinematic response of downhole seismometers to vertically incident P-waves, based on a modified Vlasov model. The governing equations and boundary conditions of a soil–well system were obtained using Hamilton's principle. The three unknown functions were then decoupled using an iterative algorithm. The accuracy of the proposed method was validated by placing a downhole seismometer in the well and comparing the responses with previously reported results. A parametric study was performed to investigate the effects of the soil–well system properties on the kinematic response and monitoring errors of the downhole seismometer. Results indicated that the incident frequency, thickness of the foundation of the downhole seismometer, soil–well modulus ratio Ew/Es, and slenderness ratio of the downhole seismometer considerably influence the monitoring error, whereas soil damping has little effect on it.

Modeling and evaluation for large amplitude vibration and nonlinear bending of perovskite solar cell

The large amplitude vibration and nonlinear bending analyses for a perovskite solar cell (PSC) in thermal environments are presented through the plate-substrate model. The PSC film is modeled as a thin laminated plate which consists of five plies including ITO, PEDOT:PSS, perovskite, PCBM, and Au. Two kinds of graphene platelets reinforced composite (GPLRC) substrates are considered. The GPLRC substrate is modeled as a porous foundation with finite depth. The foundation stiffnesses are predicted by modified Vlasov model and the equivalent Young’s modulus of the foundation is estimated through a modified Halpin–Tsai model where the porosity coefficient is introduced. The material properties of GPLRC substrates are assumed to be temperature dependent. The thermal effect and plate-foundation interaction are involved in the governing equations which are solved by means of a two-step perturbation approach. The numerical investigations are carried out for the PSC plate rested on GPL/PMMA and GPL/Al substrates. It is shown that the substrate depth and porosity coefficient have substantial influences on the vibration response and nonlinear bending behavior of PSC plates.

Modeling and low-velocity impact analysis of perovskite solar cells resting on porous substrates reinforced by graphene platelets

A nanoplate-foundation model is proposed for the perovskite solar cells (PSCs) on porous substrates reinforced by graphene platelets (GPLs). The coating film of PSCs is modeled as a laminate plate with nano-scale thickness and consists of five plies including ITO, PEDOT: PSS, perovskite, PCBM, and Au. The GPL reinforced substrate is modeled as an elastic foundation with finite depth, and the spring stiffness is predicted by the modified Vlasov model. The equivalent Young's modulus of the GPL/Al composites is estimated through a modified Mori-Tanaka model, where the GPLs are regarded as particle reinforcements. The effect of the porosity coefficient is taken into account by a quartic polynomial. FE Modeling and low-velocity impact analysis are then carried out. It is shown that the depth and porosity coefficient of the substrate have substantial influences on the dynamic response of PSCs.

Two Novel Vlasov Models for Bending Analysis of Finite-Length Beams Embedded in Elastic Foundations

The issue of soil–structure interaction (SSI) is essentially to analyze the influence of complex media on the mechanical behavior of supported structures. With the development of underground space, geological structures and space constraints put forward higher requirements for foundations and buildings. In this paper, the effects of soil heterogeneity and embedment depth on the bending of finite-length beams embedded in two novel Vlasov elastic foundations are investigated. Firstly, the constitutive relations of subsoil are simulated by Gibson and transversely isotropic soils, and the type of elastic foundation is described by the modified Vlasov model. Then, based on variational principles, the governing differential equations for the deformation and attenuation parameters of beams embedded in elastic foundations are derived by taking the variation of the minimum potential energy of the system, and the characteristic coefficient related to the embedment depth is introduced. Finally, the mechanical performance of the beam and foundation is obtained by an iterative technique and the Fourier series method, and an extensive parametric study is performed to examine influence of some basic parameters on the deformation and internal forces of the system. The results show that the mathematical expressions of two refined elastic models are in good agreement with those of the traditional Vlasov foundation after degradation. The iterative technique based on the principles of solid mechanics can be employed to obtain more reliable model parameters. More importantly, with the increase in the embedment depth, the mechanical responses of the beam and subgrade forces decrease. The main reason is that the restraint effect of the soil media around structures, which leads to the reduction of the characteristic coefficient affecting the displacement of beams. Moreover, the heterogeneity of soil, including Gibson characteristics and transverse isotropy, should be considered according to specific working conditions in civil engineering.

Discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer” by Volkan Isbuga, Mehmet Cerezci and M. Zulfu Asik

Discussion on “The modified Vlasov model on a nonhomogeneous and nonlinear soil layer” by Volkan Isbuga, Mehmet Cerezci and M. Zulfu Asik

The modified Vlasov model on a nonhomogeneous and nonlinear soil layer

This study presents a novel approach to account for the soil nonlinearity of nonhomogeneous soil deposits in foundation deflection analyses in the context of a modified Vlasov foundation model. We present an extension of the previously proposed formulation by developing a new formulation employing an improved algorithm that takes the modulus degradation curves at varying strain levels into account in an iterative manner. This new model, which takes the nonlinear soil behavior into account, was first verified against a linear elastic soil model given in the literature to ensure that the new model algorithm can capture the original solution when the soil behavior is assumed to be linear elastic. Later, the experimental data reported in the literature for a specific type of dense and loose sands were used in the example analyses. Example problems were considered for different cases, which presented (i) how the model captures nonlinear behavior and (ii) the significant effect of the nonlinear soil behavior. The result of the new model was also compared with the finite element model results, assuming elastoplastic soil. The results obtained from both models match well, especially for the maximum deflection value, provided that laterally constrained sections underneath the foundation are used.

A fourth-order conservative semi-Lagrangian finite volume WENO scheme without operator splitting for kinetic and fluid simulations

In this paper, we present a fourth-order conservative semi-Lagrangian (SL) finite volume (FV) weighted essentially non-oscillatory (WENO) scheme without operator splitting for two-dimensional linear transport equations with applications in kinetic models including the nonlinear Vlasov–Poisson system, the guiding center Vlasov model and the incompressible Euler equation in the vorticity-stream function formulation. To achieve fourth-order accuracy in space, two main ingredients are proposed in the SL FV formulation. Firstly, we introduce a so-called cubic-curved quadrilateral upstream cell and applying an efficient clipping method to evaluate integrals on upstream cells. Secondly, we construct a new WENO reconstruction operator, which recovers a P3 polynomial from neighboring cell averages. Mass conservation is accomplished with the mass conservative nature of the reconstruction operator and the SL formulation. A positivity-preserving limiter is applied to maintain the positivity of the numerical solution wherever appropriate. For nonlinear kinetic models, the SL scheme is coupled with a fourth-order Runge–Kutta exponential integrator for high-order temporal accuracy. Extensive benchmarks are tested to verify the designed properties.