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Directed assembly of block polymers is rapidly becoming a viable strategy for lithographic patterning of nanoscopic features. One of the key attributes of directed assembly is that an underlying chemical or topographic substrate pattern…
The directed self-assembly (DSA) of block copolymers (BCPs) offers a highly promising approach for the fabrication of contact holes or vertical interconnect access at sub-7nm technology nodes. To fabricate circular holes with precisely…
Functional nanoparticles (NPs) have gained significant attention as a promising application in various fields, including sensor, smart coating, drug delivery, and more. Here, we propose a novel mechanism assisted by machine-learning…
The dissipative particle dynamics (DPD) simulation method has been shown to be a promising tool to study self-assembly of soft matter systems. In particular, it has been used to study block copolymer (BCP) self-assembly. However, previous…
The phase separation processes are typically modeled by Cahn-Hilliard equations. This equation was originally introduced to model phase separation in binary alloys, where phase stands for concentration of different components in alloy. When…
In this work we consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts. Specifically, we model polymer self-assembly using Self-Consistent Field Theory and…
This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…
Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential…
We numerically investigate local defectiveness control of self-assembled diblock copolymer patterns through appropriate substrate design. We use a nonlocal Cahn-Hilliard (CH) equation for the phase separation dynamics of diblock copolymers.…
Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
We propose a fast and robust scheme for the direct minimization of the Ohta-Kawasaki energy that characterizes the microphase separation of diblock copolymer melts. The scheme employs a globally convergent modified Newton method with line…
We propose a solution strategy for a multimaterial minimum compliance topology optimization problem, which consists in finding the optimal allocation of a finite number of candidate (possibly anisotropic) materials inside a reference…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
We develop a set of algorithms to solve a broad class of Design of Experiment (DoE) problems efficiently. Specifically, we consider problems in which one must choose a subset of polymers to test in experiments such that the learning of the…
In this paper, elliptic optimal control problems involving the $L^1$-control cost ($L^1$-EOCP) is considered. To numerically discretize $L^1$-EOCP, the standard piecewise linear finite element is employed. However, different from the finite…
This paper applies the N-block PCPM algorithm to solve multi-scale multi-stage stochastic programs, with the application to electricity capacity expansion models. Numerical results show that the proposed simplified N-block PCPM algorithm,…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
We develop an algorithm to solve tridiagonal systems of linear equations, which appear in implicit finite-difference schemes of partial differential equations (PDEs), being the time-dependent Schr\"{o}dinger equation (TDSE) an ideal…
An optimal control strategy is developed to construct nanostructures of desired geometry along line segments by means of directed self-assembly of charged particles. Such a control strategy determines the electric potentials of a set of…