Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra.

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Theoretical Study of the Exciton Binding Energy and Exciton Absorption in Different Hyperbolic-Type Quantum Wells under Applied Electric, Magnetic, and Intense Laser Fields.

In this study, we investigated the exciton binding energy and interband transition between the electron and heavy-hole for the single and double quantum wells which have different hyperbolic-type potential functions subject to electric, magnetic, and non-resonant intense laser fields. The results obtained show that the geometric shapes of the structure and the applied external fields are very effective on the electronic and optical properties. In the absence of the external fields, the exciton binding energy is a decreasing function of increasing well sizes except for the strong confinement regime. Therefore, for all applied external fields, the increase in the well widths produces a red-shift at the absorption peak positions. The magnetic field causes an increase in the exciton binding energy and provides a blue-shift of the absorption peak positions corresponding to interband transitions. The effect of the electric field is quite pronounced in the weak confinement regime, it causes localization in opposite directions of the quantum wells of the electron and hole, thereby weakening the Coulomb interaction between them, causing a decrease in exciton binding energy, and a red-shift of the peak positions corresponding to the interband transitions. Generally, an intense laser field causes a decrease in the exciton binding energy and produces a red-shift of the peak positions corresponding to interband transitions.

Distortion-controlled isotropic swelling: numerical study of free boundary swelling patterns.

Modern fabrication tools have now provided a number of platforms for designing flat sheets that, by virtue of their nonuniform growth, can buckle and fold into target three-dimensional structures. Theoretically, there is an infinitude of growth patterns that can produce the same shape, yet almost nothing is understood about which of these many growth patterns is optimal from the point of view of experiment, and few can even be realized at all. Here, we ask the question: what is the optimal way to design isotropic growth patterns for a given target shape? We propose a computational algorithm to produce optimal growth patterns by introducing cuts into the target surfaces. Within this framework, we propose that the patterns requiring the fewest or shortest cuts produce the best approximations to the target shape at finite thickness. The results are tested by simulation on spherical surfaces, and new challenges are highlighted for surfaces with both positive and negative Gaussian curvatures.

Exciton properties in zincblende InGaN-GaN quantum wells under the effects of intense laser fields.

: In this work, we study the exciton states in a zincblende InGaN/GaN quantum well using a variational technique. The system is considered under the action of intense laser fields with the incorporation of a direct current electric field as an additional external probe. The effects of these external influences as well as of the changes in the geometry of the heterostructure on the exciton binding energy are discussed in detail.