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Isoporous membranes made from diblock copolymers have numerous applications, including water treatment and protein separation, and are successfully produced at a laboratory scale under controlled conditions. However, achieving optimal…
We study both experimentally and theoretically the self-assembly of binary block copolymers in dilute solution, where self-assembly is triggered by changing the solvent from the common good solvent THF to the selective solvent water, and…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…
Block copolymer self-assembly is a fundamental process in which incompatible blocks spontaneously form organized microstructures with broad practical applications. Classical understanding is that the domain spacing is limited by the contour…
The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying…
The development of new materials typically involves a process of trial and error, guided by insights from past experimental and theoretical findings. The inverse design approach for soft-matter systems has the potential to optimize specific…
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with…
As an increasingly powerful technique in integrated photonics, inverse design uses optimization algorithms to automatically create compact, high-performance photonic structures, often yielding non-intuitive layouts far more compact than…
The fabrication of versatile building blocks that are reliably self-assemble into desired ordered and disordered phases is amongst the hottest topics in contemporary material science. To this end, microscopic units of varying complexity,…
Self-closing assembly is prone to polymorphism due to thermally-excited bending fluctuations, which permit the formation of off-target assemblies at the point of self-closure. One way to overcome this source of polymorphism is to use…
One of the challenges of self-assembling finite-sized colloidal aggregates with a sought morphology is the necessity of precisely sorting the position of the colloids at the microscopic scale to avoid the formation of off-target structures.…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained…
A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh…
The kinetic paths of structural evolution and formation of block copolymer (BCP) particles are explored using dynamic self-consistent field theory (DSCFT). It is shown that the process-directed self-assembly of BCP immersed in a poor…
State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to…
Controlling the topology of structures self-assembled from a set of heterogeneous building blocks is highly desirable for many applications, but is poorly understood theoretically. Here we show that the thermodynamic theory of self-assembly…
The design of specified nonlinear mechanical responses into a structure or material is a highly sought after capability, which would have a significant impact in areas such as wave tailoring in metamaterials, impact mitigation, soft…
Field-theoretical method is efficient in predicting the assembling structures of polymeric systems. However, for the polymer/nanoparticle mixture, the continuous density description is not suitable to capture the realistic assembly of…