Aperiodic crystals in biology.

Biological systems display a broad palette of hierarchically ordered designs spanning over many orders of magnitude in size. Remarkably enough, periodic order, which profusely shows up in non-living ordered compounds, plays a quite subsidiary role in most biological structures, which can be appropriately described in terms of the more general aperiodic crystal notion instead. In this topical review I shall illustrate this issue by considering several representative examples, including botanical phyllotaxis, the geometry of cell patterns in tissues, the morphology of sea urchins, or the symmetry principles underlying virus architectures. In doing so, we will realize that albeit the currently adopted quasicrystal notion is not general enough to properly account for the rich structural features one usually finds in biological arrangements of matter, several mathematical tools and fundamental notions belonging to the aperiodic crystals science toolkit can provide a useful modeling framework to this end.

Base-Pairs' Correlated Oscillation Effects on the Charge Transfer in Double-Helix B-DNA Molecules.

By introducing a suitable renormalization process, the charge carrier and phonon dynamics of a double-stranded helical DNA molecule are expressed in terms of an effective Hamiltonian describing a linear chain, where the renormalized transfer integrals explicitly depend on the relative orientations of the Watson-Crick base pairs, and the renormalized on-site energies are related to the electronic parameters of consecutive base pairs along the helix axis, as well as to the low-frequency phonons' dispersion relation. The existence of synchronized collective oscillations enhancing the π-π orbital overlapping among different base pairs is disclosed from the study of the obtained analytical dynamical equations. The role of these phonon-correlated, long-range oscillation effects on the charge transfer properties of double-stranded DNA homopolymers is discussed in terms of the resulting band structure.

Thermal Emission Control via Bandgap Engineering in Aperiodically Designed Nanophotonic Devices.

Aperiodic photonic crystals can open up novel routes for more efficient photon management due to increased degrees of freedom in their design along with the unique properties brought about by the long-range aperiodic order as compared to their periodic counterparts. In this work we first describe the fundamental notions underlying the idea of thermal emission/absorption control on the basis of the systematic use of aperiodic multilayer designs in photonic quasicrystals. Then, we illustrate the potential applications of this approach in order to enhance the performance of daytime radiative coolers and solar thermoelectric energy generators.

Exploiting aperiodic designs in nanophotonic devices.

In this work we consider the role of aperiodic order-order without periodicity-in the design of different optical devices in one, two and three dimensions. To this end, we will first study devices based on aperiodic multilayered structures. In many instances the recourse to Fibonacci, Thue-Morse or fractal arrangements of layers results in improved optical properties compared with their periodic counterparts. On this basis, the possibility of constructing optical devices based on a modular design of the multilayered structure, where periodic and quasiperiodic subunits are properly mixed, is analyzed, illustrating how this additional degree of freedom enhances the optical performance in some specific applications. This line of thought can be naturally extended to aperiodic arrangements of optical elements, such as nanospheres or dielectric rods in the plane, as well as to three-dimensional photonic quasicrystals based on polymer materials. In this way, plentiful possibilities for new tailored materials naturally appear, generally following suitable optimization algorithms. Then, we present a detailed discussion on the physical properties supporting the preferential use of aperiodic devices in a number of optical applications, opening new avenues for technological innovation. Finally we suggest some related emerging topics that deserve some attention in the years to come.

Anomalous electronic transport in ξ'-Al-Pd-Mn complex metallic alloy studied by spectral conductivity analysis.

The ξ' giant-unit-cell phase of the Al-Pd-Mn alloy system exhibits an almost temperature-independent electrical conductivity with a value typical of metallic alloys, but an anomalously low thermal conductivity comparable to that of thermal insulators. The origin of the T-independent conductivity is analysed by determining the spectral conductivity function σ(E) from a combined analysis of the electrical conductivity σ(T) and the thermoelectric power S(T) using a phenomenological approach. It is found that the T-independence of the conductivity results from the specific form of the spectral conductivity, which shows very weak variation over an energy scale of several k(B)T around the Fermi level, but exhibits fine structure that yields observable effects in σ(T) and S(T).

The role of phosphorus in chemical evolution.

In this tutorial review we consider the role of phosphorus and its compounds within the context of chemical evolution in galaxies. Following an interdisciplinary approach we first discuss the position of P among the main biogenic elements by considering its relevance in most essential biochemical functions as well as its peculiar chemistry under different physicochemical conditions. Then we review the phosphorus distribution in different cosmic sites, such as terrestrial planets, interplanetary dust particles, cometary dust, planetary atmospheres and the interstellar medium (ISM). In this way we realize that this element is both scarce and ubiquitous in the universe. These features can be related to the complex nucleosynthesis of P nuclide in the cores of massive stars under explosive conditions favouring a wide distribution of this element through the ISM, where it would be ready to react with other available atoms. A general tendency towards more oxidized phosphorus compounds is clearly appreciated as chemical evolution proceeds from circumstellar and ISM materials to protoplanetary and planetary condensed matter phases. To conclude we discuss some possible routes allowing for the incorporation of phosphorus compounds of prebiotic interest during the earlier stages of solar system formation.

Long range correlations in DNA: scaling properties and charge transfer efficiency.

We address the relation between long-range correlations and charge transfer efficiency in aperiodic artificial or genomic DNA sequences. Coherent charge transfer through the highest occupied molecular orbital states of the guanine nucleotide is studied using the transmission approach, and the focus is on how the sequence-dependent backscattering profile can be inferred from correlations between base pairs.