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Driven by synthetic advances combined with the ability of processing and characterization methods, multi-stimulus responsive (MSR) polymers offer technological opportunities with significant societal impacts. The purpose of this perspective is not to itemize every possible MSR polymer system but instead to highlight recent advances along with current and future trends that redefined modern polymer science. In the context of spatiotemporal and energetic requirements, this perspective explores multi-stimulus responses driven by compositional, structural, and hierarchical macromolecular arrangements, where multi-stimulus may be achieved by combining mechano-responsiveness, pH changes, electromagnetic radiation, magnetic/electric fields, redox reactions, humidity and temperature changes, solvents and gases, or biologically triggered responses. Multi-stimulus responses may be orthogonal, competitive, or synergistic and governed by the redefined principles in developing polymers with signaling and communications, encoding phenotypic properties with precisely defined sequences, programmable assembly/disassembly, and recognition attributes, and MSR materials will pave the next generations of ingenious technological advances with living-like attributes. 

Abstract We develop a new finite difference method for the wave equation in second order form. The finite difference operators satisfy a summation-by-parts (SBP) property. With boundary conditions and material interface conditions imposed weakly by the simultaneous-approximation-term (SAT) method, we derive energy estimates for the semi-discretization. In addition, error estimates are derived by the normal mode analysis. The proposed method is termed as energy-based because of its similarity with the energy-based discontinuous Galerkin method. When imposing the Dirichlet boundary condition and material interface conditions, the traditional SBP-SAT discretization uses a penalty term with a mesh-dependent parameter, which is not needed in our method. Furthermore, numerical dissipation can be added to the discretization through the boundary and interface conditions. We present numerical experiments that verify convergence and robustness of the proposed method. 

Known for their adaptability to surroundings, the capability of transport control of molecules, or the ability to convert one type of energy to another as a result of external or internal stimuli, responsive polymers play a significant role in advancing scientific discoveries that may lead to an array of diverse applications. This review outlines recent advances in the developments of selected commodity polymers equipped with stimuli‐responsiveness to temperature, pH, ionic strength, enzyme or glucose levels, carbon dioxide, water, redox agents, electromagnetic radiation, or electric and magnetic fields. Utilized diverse applications ranging from drug delivery to biosensing, dynamic structural components to color‐changing coatings, this review focuses on commodity acrylics, epoxies, esters, carbonates, urethanes, and siloxane‐based polymers containing responsive elements built into their architecture. In the context of stimuli‐responsive chemistries, current technological advances, as well as a critical outline of future opportunities and applications, are also tackled. 

Abstract An explicit spectrally accurate order-adaptive Hermite-Taylor method for the Schrödinger equation is developed. Numerical experiments illustrating the properties of the method are presented. The method, which is able to use very coarse grids while still retaining high accuracy, compares favorably to an existing exponential integrator – high order summation-by-parts finite difference method.