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Transmission experiments of Nd: YAG laser pulse of 25 ps and 30 ns duration through 100 μm thick silicon single crystal allow the determination of the free carrier absorption cross section, σFC = 5 × 10−18 cm2, and of the Auger decay... more
Transmission experiments of Nd: YAG laser pulse of 25 ps and 30 ns duration through 100 μm thick silicon single crystal allow the determination of the free carrier absorption cross section, σFC = 5 × 10−18 cm2, and of the Auger decay constant, γ3 = 8 × 10−31 cm6 s−1. These two parameters are used in the numerical solution of a set of coupled differential equations which describe the space and time evolution of carrier concentration, carrier energy, and lattice temperature. A comparison with time resolved reflectivity data reported in literature, allows the determination of the energy relaxation time constant, τe ≈︁ 1 ps. The validity of the thermal model used to describe laser annealing in the nanosecond regime is also discussed and justified.
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The redistribution in Bi-implanted Si was measured after irradiation with 25-ps or 35-ns Nd laser pulses by channeling effect measurements in combination with MeV He+ backscattering. For both pulse durations some of the Bi accumulated at... more
The redistribution in Bi-implanted Si was measured after irradiation with 25-ps or 35-ns Nd laser pulses by channeling effect measurements in combination with MeV He+ backscattering. For both pulse durations some of the Bi accumulated at the surface and the amount of segregation depended on the substrate orientation. The impurity redistribution was similar after nanosecond or picosecond laser pulses thus indicating that the solidification velocities were comparable for the two cases.
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Multispecies kinematic flow models with strongly degenerate diffusive corrections give rise to systems of nonlinear convection-diffusion equations of arbitrary size. Applications of these systems include models of polydisperse... more
Multispecies kinematic flow models with strongly degenerate diffusive corrections give rise to systems of nonlinear convection-diffusion equations of arbitrary size. Applications of these systems include models of polydisperse sedimentation and multiclass traffic flow. Implicit-explicit (IMEX) Runge--Kutta (RK) methods are suitable for the solution of these convection-diffusion problems since the stability restrictions, coming from the explicitly treated convective part, are much less severe than those that would be deduced from an explicit treatment of the diffusive term. These schemes usually combine an explicit RK scheme for the time integration of the convective part with a diagonally implicit one for the diffusive part. In [R. Burger, P. Mulet, and L. M. Villada, SIAM J. Sci. Comput., 35 (2013), pp. B751--B777] a scheme of this type is proposed, where the nonlinear and nonsmooth systems of algebraic equations arising in the implicit treatment of the degenerate diffusive part are solved by smoothing o...
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The Hamiltonian formulation of incompressible, inviscid fluid dynamics is recalled. Numerical methods based on this formulation have several conservation properties that make them attractive. This formulation is applied to study the... more
The Hamiltonian formulation of incompressible, inviscid fluid dynamics is recalled. Numerical methods based on this formulation have several conservation properties that make them attractive. This formulation is applied to study the interaction of a fluid with a ...
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Abstract. A Vlasov equation for bubbly flow is modified to account for local interactions between bubbles. Fluid equations are deduced in the limit where local interactions cause the system to become locally Maxwellian. The resulting... more
Abstract. A Vlasov equation for bubbly flow is modified to account for local interactions between bubbles. Fluid equations are deduced in the limit where local interactions cause the system to become locally Maxwellian. The resulting fluid equations are well posed for sufficiently ...
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... original paper by Enrico Creaco , (corresponding author) , (Post-Doctoral Researcher, Dipartimento di Ingegneria Civile e Ambientale, Università degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, Italy E-mail:... more
... original paper by Enrico Creaco , (corresponding author) , (Post-Doctoral Researcher, Dipartimento di Ingegneria Civile e Ambientale, Università degli Studi di Catania, Viale Andrea Doria 6, 95125 Catania, Italy E-mail: ecreaco@dica.unict.it) , Alberto Campisano , (Research ...
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Wavelets and Partial Differential Equations.- What is a Wavelet?.- The Fundamental Property of Wavelets.- Wavelets for Partial Differential Equations.- High-Order Shock-Capturing Schemes for Balance Laws.- Upwind Scheme for Systems.- The... more
Wavelets and Partial Differential Equations.- What is a Wavelet?.- The Fundamental Property of Wavelets.- Wavelets for Partial Differential Equations.- High-Order Shock-Capturing Schemes for Balance Laws.- Upwind Scheme for Systems.- The Numerical Flux Function.- Nonlinear Reconstruction and High-Order Schemes.- Central Schemes.- Systems with Stiff Source.- Discontinuous Galerkin Methods: General Approach and Stability.- Time Discretization.- Discontinuous Galerkin Method for Conservation Laws.- Discontinuous Galerkin Method for Convection-Diffusion Equations.- Discontinuous Galerkin Method for PDEs Containing Higher-Order Spatial Derivatives.
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In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media... more
In recent years kinetic theory has developed in many areas of the physical sciences and engineering, and has extended the borders of its traditional fields of application. New applications in traffic flow engineering, granular media modeling, and polymer and phase transition physics have resulted in new numerical algorithms which depart from traditional stochastic Monte--Carlo methods. This monograph is a self-contained presentation of such recently developed aspects of kinetic theory, as well as a comprehensive account of the ...
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Google, Inc. (search). ...
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Research Interests: Mathematics, Applied Mathematics, Computer Science, Finite Volume Methods, Nonlinear hyperbolic equations, and 8 moreNumerical Analysis, Discretization, Historic conservation law, Numerical Analysis and Computational Mathematics, High Order Accuracy, Runge Kutta, System of Equation Linear Equations, and Runge Kutta Methods
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In this paper we present a novel technique for the simulation of moving boundaries and moving rigid bodies immersed in a rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The rarefied gas is simulated by... more
In this paper we present a novel technique for the simulation of moving boundaries and moving rigid bodies immersed in a rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The rarefied gas is simulated by solving the Bhatnagar-Gross-Krook (BGK) model for the Boltzmann equation of rarefied gas dynamics. The BGK model is solved by an Arbitrary Lagrangian-Eulerian (ALE) method, where grid-points/particles are moved with the mean velocity of the gas. The computational domain for the rarefied gas changes with time due to the motion of the boundaries. To allow a simpler handling of the interface motion we have used a meshfree method based on a least-square approximation for the reconstruction procedures required for the scheme. We have considered a one way, as well as a two-way coupling of boundaries/rigid bodies and gas flow. The numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann ...
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In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid... more
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid points, does not necessarily conserve the total mass. To ensure mass conservation, we propose a conservative correction procedure based on a flux difference form. Such procedure guarantees local mass conservation, while introducing time step constraints for stability. We theoretically investigate such stability constraints from an ODE point of view by assuming exact evaluation of spatial differential operators and from the Fourier analysis for linear PDEs. The scheme is tested by classical two dimensional linear passive-transport problems, such as linear advection, rotation and swirling deformation. The scheme is applied to solve the nonlinear Vlasov-Poisson system using a a high order tracing mechanism proposed in [Qiu and Russo, 2016]. Such high or...
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We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered (2p + 1)-point stencils,... more
We present a new family of high-order shock-capturing finite difference numerical methods for systems of conservation laws. These methods, called Adaptive Compact Approximation Taylor (ACAT) schemes, use centered (2p + 1)-point stencils, where p may take values in {1, 2, ..., P} according to a new family of smoothness indicators in the stencils. The methods are based on a combination of a robust first order scheme and the Compact Approximate Taylor (CAT) methods of order 2p-order, p=1,2,..., P so that they are first order accurate near discontinuities and have order 2p in smooth regions, where (2p +1) is the size of the biggest stencil in which large gradients are not detected. CAT methods, introduced in <cit.>, are an extension to nonlinear problems of the Lax-Wendroff methods in which the Cauchy-Kovalesky (CK) procedure is circumvented following the strategy introduced in <cit.> that allows one to compute time derivatives in a recursive way using high-order centered di...
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ABSTRACT
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Abstract. In this paper we give an overview of Implicit-Explicit Runge-Kutta schemes applied to hyperbolic systems with stiff relaxation. In particular, we focus on some recent results on the uniform accuracy for hyperbolic systems with... more
Abstract. In this paper we give an overview of Implicit-Explicit Runge-Kutta schemes applied to hyperbolic systems with stiff relaxation. In particular, we focus on some recent results on the uniform accuracy for hyperbolic systems with stiff relaxation [6], and hyperbolic system with diffusive relaxation [7, 5, 4]. In the latter case, we present an original application to a model problem arising in Extended Thermodynamics. Key words. RungeKutta methods, stiff problems, hyperbolic systems with relaxation, diffusion equations. 1. Introduction. Many
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Abstract. In this paper we consider a new formulation of implicit-explicit (IMEX) methods for the numerical discretization of time dependent partial differential equations. We construct several semi-implicit Runge-Kutta methods up to... more
Abstract. In this paper we consider a new formulation of implicit-explicit (IMEX) methods for the numerical discretization of time dependent partial differential equations. We construct several semi-implicit Runge-Kutta methods up to order three. This approach is particularly suited for problems where the stiff and non-stiff components cannot be well separated. We present different numerical simulations for reaction-diffusion, convection diffusion and nonlinear diffusion system of equations. Finally, we conclude by a stability analysis of the schemes for linear problems. Contents
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In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method for the numerical solution of ODEs is presented. This methods can be regarded as an approximate formulation of the Taylor methods and it follows an approach that... more
In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method for the numerical solution of ODEs is presented. This methods can be regarded as an approximate formulation of the Taylor methods and it follows an approach that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their high order derivatives, are needed. In this reference, the absolute stability region of the new methods is conjectured to be coincident with that of their exact counterparts. There is also a conjecture about their relationship with Runge-Kutta methods. In this work we answer positively both conjectures.
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In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the... more
In this paper, we propose a new semi-Lagrangian scheme for the polyatomic ellipsoidal BGK model. In order to avoid time step restrictions coming from convection term and small Knudsen number, we combine a semi-Lagrangian approach for the convection term with an implicit treatment for the relaxation term. We show how to explicitly solve the implicit step, thus obtaining an efficient and stable scheme for any Knudsen number. We also derive an explicit error estimate on the convergence of the proposed scheme for every fixed value of the Knudsen number.
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In this paper we present a novel technique for the simulation of moving boundaries and moving rigid bodies immersed in a rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The rarefied gas is simulated by... more
In this paper we present a novel technique for the simulation of moving boundaries and moving rigid bodies immersed in a rarefied gas using an Eulerian-Lagrangian formulation based on least square method. The rarefied gas is simulated by solving the Bhatnagar-Gross-Krook (BGK) model for the Boltzmann equation of rarefied gas dynamics. The BGK model is solved by an Arbitrary Lagrangian-Eulerian (ALE) method, where grid-points/particles are moved with the mean velocity of the gas. The computational domain for the rarefied gas changes with time due to the motion of the boundaries. To allow a simpler handling of the interface motion we have used a meshfree method based on a least-square approximation for the reconstruction procedures required for the scheme. We have considered a one way, as well as a two-way coupling of boundaries/rigid bodies and gas flow. The numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann ...
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Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine... more
Most numerical schemes proposed for solving BGK models for rarefied gas dynamics are based on the discrete velocity approximation. Since such approach uses fixed velocity grids, one must secure a sufficiently large domain with fine velocity grids to resolve the structure of distribution functions. When one treats high Mach number problems, the computational cost becomes prohibitively expensive. In this paper, we propose a velocity adaptation technique in the semi-Lagrangian framework for BGK model. The velocity grid will be set locally in time and space, according to mean velocity and temperature. We apply a weighted minimization approach to impose conservation. We presented several numerical tests that illustrate the effectiveness of our proposed scheme.
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In this paper we give an overview of Implicit-Explicit Runge-Kutta schemes applied to hyperbolic systems with stiff relaxation. In particular, we focus on some recent results on the uniform accuracy for hyperbolic systems with stiff... more
In this paper we give an overview of Implicit-Explicit Runge-Kutta schemes applied to hyperbolic systems with stiff relaxation. In particular, we focus on some recent results on the uniform accuracy for hyperbolic systems with stiff relaxation [6], and hyperbolic system with diffusive relaxation [7, 5, 4]. In the latter case, we present an original application to a model problem arising in Extended Thermodynamics.
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In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL... more
In this paper, we propose a new high order semi-implicit scheme for the all Mach full Euler equations of gas dynamics. Material waves are treated explicitly, while acoustic waves are treated implicitly, thus avoiding severe CFL restrictions for low Mach flows. High order accuracy in time is obtained by semi-implicit temporal integrator based on the IMEX RungeKutta (IMEX-RK) framework. High order in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions adapted to the semi-implicit IMEX-RK time discretization. Type A IMEX schemes are constructed to handle not well-prepared initial conditions. Besides, these schemes are proven to be asymptotic preserving and asymptotically accurate as the Mach number vanishes for well-prepared initial conditions. Divergence-free property of the time-discrete schemes is proved. The proposed scheme can also well capture discontinuous solutions in the compressible regime, especially for two dimensional Riemann proble...
In this paper a new family of high-order finite-difference shock-capturing central schemes for hyperbolic systems with stiff source is presented. The schemes are based on recently developed finite difference discretization on staggered... more
In this paper a new family of high-order finite-difference shock-capturing central schemes for hyperbolic systems with stiff source is presented. The schemes are based on recently developed finite difference discretization on staggered grids, coupled with implicit-explicit (IMEX) time discretization for an efficient treatment of the source term. Numerical tests show the robustness and accuracy of the method, for a wide range of the stiffness parameter.
Consistent BGK models for inert mixtures are compared, first in their kinetic behavior and then versus the hydrodynamic limits that can be derived in different collision-dominated regimes. The comparison is carried out both analytically... more
Consistent BGK models for inert mixtures are compared, first in their kinetic behavior and then versus the hydrodynamic limits that can be derived in different collision-dominated regimes. The comparison is carried out both analytically and numerically, for the latter using an asymptotic preserving semi-Lagrangian scheme for the BGK models. Application to the plane shock wave in a binary mixture of noble gases is also presented.
In this article, we develop and analyse a new spectral method to solve the semi-classical Schrödinger equation based on the Gaussian wave-packet transform (GWPT) and Hagedorn’s semi-classical wavepackets (HWP). The GWPT equivalently... more
In this article, we develop and analyse a new spectral method to solve the semi-classical Schrödinger equation based on the Gaussian wave-packet transform (GWPT) and Hagedorn’s semi-classical wavepackets (HWP). The GWPT equivalently recasts the highly oscillatory wave equation as a much less oscillatory one (the w equation) coupled with a set of ordinary differential equations governing the dynamics of the so-called GWPT parameters. The Hamiltonian of the w equation consists of a quadratic part and a small non-quadratic perturbation, which is of order O( √ ε), where ε ≪ 1 is the rescaled Planck’s constant. By expanding the solution of the w equation as a superposition of Hagedorn’s wave-packets, we construct a spectral method while the O( √ ε) perturbation part is treated by the Galerkin approximation. This numerical implementation of the GWPT avoids imposing artificial boundary conditions and facilitates rigorous numerical analysis. For arbitrary dimensional cases, we establish how...
In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property,... more
In this work, we propose a class of high order semi-Lagrangian scheme for a general consistent BGK model for inert gas mixtures. The proposed scheme not only fulfills indifferentiability principle, but also asymptotic preserving property, which allows us to capture the behaviors of hydrodynamic limit models. We consider two hydrodynamic closure which can be derived from the BGK model at leading order: classical Euler equations for number densities, global velocity and temperature, and a multi-velocities and temperatures Euler system. Numerical simulations are performed to demonstrate indifferentiability principle and asymptotic preserving property of the proposed conservative semi-Lagrangian scheme to the Euler limits.
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In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced... more
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature...