Instability and reorientation of block copolymer microstructure by imposed electric fields

Efficient numerical approaches with accelerated graphics processing unit (GPU) computations for Poisson problems and Cahn-Hilliard equations

In this computational paper, we focused on the efficient numerical implementation of semi-implicit methods for models in materials science. In particular, we were interested in a class of nonlinear higher-order parabolic partial differential equations. The Cahn-Hilliard (CH) equation was chosen as a benchmark problem for our proposed methods. We first considered the Cahn-Hilliard equation with a convexity-splitting (CS) approach coupled with a backward Euler approximation of the time derivative and tested the performance against the bi-harmonic-modified (BHM) approach in terms of accuracy, order of convergence, and computation time. Higher-order time-stepping techniques that allow for the methods to increase their accuracy and order of convergence were then introduced. The proposed schemes in this paper were found to be very efficient for 2D computations. Computed dynamics in 2D and 3D are presented to demonstrate the energy-decreasing property and overall performance of the methods for longer simulation runs with a variety of initial conditions. In addition, we also present a simple yet powerful way to accelerate the computations by using MATLAB built-in commands to perform GPU implementations of the schemes. We show that it is possible to accelerate computations for the CH equation in 3D by a factor of 80, provided the hardware is capable enough.

Lithium-Battery Anode Gains Additional Functionality for Neuromorphic Computing through Metal-Insulator Phase Separation

Specialized hardware for neural networks requires materials with tunable symmetry, retention, and speed at low power consumption. The study proposes lithium titanates, originally developed as Li-ion battery anode materials, as promising candidates for memristive-based neuromorphic computing hardware. By using ex- and in operando spectroscopy to monitor the lithium filling and emptying of structural positions during electrochemical measurements, the study also investigates the controlled formation of a metallic phase (Li₇ Ti₅ O₁₂ ) percolating through an insulating medium (Li₄ Ti₅ O₁₂ ) with no volume changes under voltage bias, thereby controlling the spatially averaged conductivity of the film device. A theoretical model to explain the observed hysteretic switching behavior based on electrochemical nonequilibrium thermodynamics is presented, in which the metal-insulator transition results from electrically driven phase separation of Li₄ Ti₅ O₁₂ and Li₇ Ti₅ O₁₂ . Ability of highly lithiated phase of Li₇ Ti₅ O₁₂ for Deep Neural Network applications is reported, given the large retentions and symmetry, and opportunity for the low lithiated phase of Li₄ Ti₅ O₁₂ toward Spiking Neural Network applications, due to the shorter retention and large resistance changes. The findings pave the way for lithium oxides to enable thin-film memristive devices with adjustable symmetry and retention.