Abstract: Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way.

Abstract: Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

Abstract: Fibonacci numbers are a very popular subject in mathematics, culture and science. A major open question is why the ancient Greeks overlooked this series, while they were very familiar with the golden mean and division in extreme and mean ratio. Furthermore, they could compute the square root of five to a high degree of precision using Theon 's ladder. This fact is based on tables built with side and diagonal numbers, and it is a simple and incredibly efficient method to compute roots of integers, though it is little known even now among most of the experts. The biologist D 'Arcy Wentworth Thompson showed that the same method could be used to generate the Fibonacci series using a simple shift in the computation of the tables. He argues, quite convincingly, that the ancient Greeks could not have overlooked this. Actually, the same method can be used to generate all possible regular phyllotaxis patterns.

Abstract: Our scientific and technological worldviews are largely dominated by the concepts of entropy and complexity. Originating in 19th-century thermodynamics, the concept of entropy merged with information in the last century, leading to definitions of entropy and complexity by Kolmogorov, Shannon and others. In its simplest form, this worldview is an application of the normal rules of arithmetic. In this worldview, when tossing a coin, a million heads or tails in a row is theoretically possible, but impossible in practice and in real life. On this basis, the impossible (in the binary case, the outermost entries of Pascal's triangle xn and yn for large values of n) can be safely neglected, and one can concentrate fully on what is common and what conforms to the law of large numbers, in fields ranging from physics to sociology and everything in between. However, in recent decades it has been shown that what is most improbable tends to be the rule in nature. Indeed, if one combines the outermost entries xn and yn with the normal rules of arithmetic, either addition or multiplication, one obtains Lamé curves and power laws respectively. In this article, some of these correspondences are highlighted, leading to a double conclusion. First, Gabriel Lamé's geometric footprint in mathematics and the sciences is enormous. Second, conic sections are at the core once more. Whereas mathematics so far has been exclusively the language of patterns in the sciences, the door is opened for mathematics to also become the language of the individual. The probabilistic worldview and Lamé's footprint can be seen as dual methods. In this context, it is to be expected that the notions of information, complexity, simplicity and redundancy benefit from this different viewpoint.

Abstract: We provide experimental evidence for the existence of ferromagnetism in bilayers of Pd/C-60 which is supported by theoretical calculations based on density functional theory (DFT). The observed ferromagnetism is surprising as C-60 and Pd films are both non-ferromagnetic in the non-interacting limit. Magnetization (M) versus applied field (H) data acquired at different temperatures (T) show magnetic hysteresis with typical coercive fields (H-c) on the order of 50 Oe. From the temperature-dependent magnetization M(T) we extract a Curie temperature (T-c >= 550 K) using Bloch-like power law extrapolations to high temperatures. Using DFT calculations we investigated all plausible scenarios for the interaction between the C-60 molecules and the Pd slabs, Pd single atoms and Pd clusters. DFT shows that while the C-60 molecules are nonmagnetic, Pd films have a degenerate ground state that subject to a weak perturbation, can become ferromagnetic. Calculations also show that the interaction of C-60 molecules with excess Pd atoms and with sharp edges of a Pd slab is the most likely configuration that render the system ferromagnetic Interestingly, the calculated charge transfer (0.016 e per surface Pd atom, 0.064 e per Pd for intimate contact region) between C-60 and Pd does not appear to play an important role. (C) 2013 Elsevier B.V. All rights reserved.

Abstract: Brownian transport of self-propelled overdamped microswimmers (like Janus particles) in a two-dimensional periodically compartmentalized channel is numerically investigated for different compartment geometries, boundary collisional dynamics, and particle rotational diffusion. The resulting time-correlated active Brownian motion is subject to rectification in the presence of spatial asymmetry. We prove that ratcheting of Janus particles can be orders of magnitude stronger than for ordinary thermal potential ratchets and thus experimentally accessible. In particular, autonomous pumping of a large mixture of passive particles can be induced by just adding a small fraction of Janus particles.

Abstract: Van der Waals (vdW) interaction between two-dimensional crystals (2D) can trap substances in high pressurized (of order 1 GPa) on nanobubbles. Increasing the adhesion between the 2D crystals further enhances the pressure and can lead to a phase transition of the trapped material. We found that the shape of the nanobubble can depend critically on the properties of the trapped substance. In the absence of any residual strain in the top 2D crystal, flat nanobubbles can be formed by trapped long hydrocarbons (that is, hexadecane). For large nanobubbles with radius 130 nm, our atomic force microscopy measurements show nanobubbles filled with hydrocarbons (water) have a cylindrical symmetry (asymmetric) shape which is in good agreement with our molecular dynamics simulations. This study provides insights into the effects of the specific material and the vdW pressure on the microscopic details of graphene bubbles.

Abstract: The structural and mechanical properties of N-doped graphene (NG) are investigated using reactive force field (ReaxFF) potentials in large-scale molecular dynamics simulations. We found that ripples, which are induced by the dopants, change the roughness of NG, which depends on the number of dopants and their local arrangement. For any doping ratio N/C, the NG becomes ferroelectric with a net dipole moment. The formation energy increases nonlinearly with N/C ratio, while the Young's modulus, tensile strength, and intrinsic strain decrease with the number of dopants. Our results for the structural deformation and the thermoelectricity of the NG sheet are in good agreement with recent experiments and ab initio calculations.

Abstract: Cold atmospheric pressure plasma jets (plasma) operated in ambient air provide a rich source of reactive oxygen and nitrogen species (RONS), which are known to influence biological processes important in disease. In the plasma treatment of diseased tissue such as subcutaneous cancer tumors, plasma RONS need to first traverse an interface between the plasma-skin surface and second be transported to millimeter depths in order to reach deep-seated diseased cells. However, the mechanisms in the plasma generation of RONS within soft tissues are not understood. In this study, we track the plasma jet delivery of RONS into a tissue model target and we delineate two processes: through target delivery of RONS generated (primarily) in the plasma jet and in situ RONS generation by UV photolysis within the target. We demonstrate that UV photolysis promotes the rapid generation of RONS in the tissue model target’s surface after which the RONS are transported to millimeter depths via a slower molecular process. Our results imply that the flux of UV photons from plasma jets is important for delivering RONS through seemingly impenetrable barriers such as skin. The findings have implications not only in treatments of living tissues but also in the functionalization of soft hydrated biomaterials such as hydrogels and extracellular matrix derived tissue scaffolds.