Related papers: An efficient method for computing stationary state…
In this paper, a methodology to calculate the sensitivity of the least stable modes of fluid-structure interaction systems with respect to local forces is presented. We make use of the adjoint equations of the flow-structure coupled system…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
We introduce a Phase Field Crystal (PFC) model for particles with n-fold rotational symmetry in two dimensions. Our approach is based on a free energy functional that depends on the reduced one-particle density, the strength of the…
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time…
Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elasticity, face inherent limitations in modeling…
In this work, we propose a data-driven method to discover the latent space and learn the corresponding latent dynamics for a collisional-radiative (CR) model in radiative plasma simulations. The CR model, consisting of high-dimensional…
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…
This paper is concerned with $\textit{ab initio}$ crystal structure relaxation under a fixed unit cell volume, which is a step in calculating the static equations of state and forms the basis of thermodynamic property calculations for…
In this work, we develop an accelerated sharp-interface method based on (Hu et al., JCP, 2006) and (Luo et al., JCP, 2015) for multiphase flows simulations. Traditional multiphase simulation methods use the minimum time step of all fluids…
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the…
This paper deals with the gradient stability and the gradient stabilizability of Caputo time fractional diffusion linear systems. First, we give sufficient conditions that allow the gradient Mittag-Leffler and strong stability, where we use…
We consider a modification of the so-called phase-field crystal (PFC) equation introduced by K.R. Elder et al. This variant has recently been proposed by P. Stefanovic et al. to distinguish between elastic relaxation and diffusion time…
Synchronization is essential for the operation of AC power systems: All generators in the power grid must rotate with fixed relative phases to enable a steady flow of electric power. Understanding the conditions for and the limitations of…
Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic…
The positive definiteness of discrete time-fractional derivatives is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models. A novel technique is proposed to estimate the minimum eigenvalue of…
Exact characterization of phase transitions requires sufficient configurational sampling, necessitating efficient and accurate potential energy surfaces. Molecular force fields with computational efficiency and physical interpretability are…
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
In this paper we study proximal conditional-gradient (CG) and proximal gradient-projection type algorithms for a block-structured constrained nonconvex optimization model, which arises naturally from tensor data analysis. First, we…
Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we…