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In this work, we apply a phase-field modeling framework to elucidate the interplay between nucleation and kinetics in the dynamic evolution of twinning interfaces. The key feature of this phase-field approach is the ability to transparently and explicitly specify nucleation and kinetic behavior in the model, in contrast to other regularized interface models. We use this to study 2 distinct problems where it is essential to explicitly specify the kinetic and nucleation behavior governing twin evolution. First, we study twinning interfaces in 2-d. When these interfaces are driven to move, we find that significant levels of twin nucleation occur ahead of the moving interface. Essentially, the finite interface velocity and the relaxation time of the stresses ahead of the interface allows for nucleation to occur before the interface is able to propagate to that point. Second, we study the growth of needle twins in antiplane elasticity. We show that both nucleation and anisotropic kinetics are essential to obtain predictions of needle twins. While standard regularized interface approaches do not permit the transparent specification of anisotropic kinetics, this is readily possible with the phase-field approach that we have used here. 

Abstract We briefly compare the structure of two classes of popular models used to describe poro-mechanics and chemo-mechanics, wherein a fluid phase is transported within a solid phase. The multiplicative deformation decomposition has been successfully used to model permanent inelastic shape change in plasticity, solid–solid phase transformation, and thermal expansion, which has motivated its application to poro-mechanics and chemo-mechanics. However, the energetic decomposition provides a more transparent structure and advantages, such as to couple to phase-field fracture, for models of poro-mechanics and chemo-mechanics. 

Optical metasurfaces consist of densely arranged unit cells that manipulate light through various light confinement and scattering processes. Due to its unique advantages, such as high performance, small form factor and easy integration with semiconductor devices, metasurfaces have been gathering increasing attention in fields such as displays, imaging, sensing and optical computation. Despite advances in fabrication and characterization, a viable design prediction for suitable optical response remains challenging for complex optical metamaterial systems. The computation cost required to obtain the optimal design exponentially grows as the design complexity increases. Furthermore, the design prediction is challenging since the inverse problem is often ill-posed. In recent years, deep learning (DL) methods have shown great promise in the area of inverse design. Inspired by this and the capability of DL to produce fast inference, we introduce a physics-informed DL framework to expedite the computation for the inverse design of metasurfaces. Addition of the physics-based constraints improve generalizability of the DL model while reducing data burden. Our approach introduces a tandem DL architecture with physics-based learning to alleviate the nonuniqueness issue by selecting designs that are scientifically consistent, with low error in design prediction and accurate reconstruction of optical responses. To prove the concept, we focus on the inverse design of a representative plasmonic device that consists of metal gratings deposited on a dielectric film on top of a metal substrate. The optical response of the device is determined by the geometrical dimensions as well as the material properties. The training and testing data are obtained through Rigorous Coupled-Wave Analysis (RCWA), while the physics-based constraint is derived from solving the electromagnetic (EM) wave equations for a simplified homogenized model. We consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. Our model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input. The model is also able to predict design with accuracy up to 96% and optical response reconstruction accuracy of 99% for optical response of a single wavelength of light as input. 

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples. To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability. We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods.

 

Liquid Crystalline Elastomers (LCEs) are active materials that are of interest due to their programmable response to various external stimuli such as light and heat. When exposed to these stimuli,...