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A fundamental allotrope of carbon that has drawn significant interest in the fields of nanoscience, nanotechnology, condensed matter physics and chemistry, biological physics, materials science and technology, mechanical and electrical sciences, biomedical engineering, and most recently, medical nanotechnology, and nanoneuroscience. Fullerenes are another important allotrope of carbon in addition to graphite, diamond, and nanotubes. The use of molecular topological indices is crucial for bridging the gap between theoretical and practical aspects of chemical characteristics. In recent years, topological indices have been used to investigate the chemical and physical characteristics of fullerenes. This paper uses the $R$ molecular topological index to present topological modeling of the binding energies, heats of formation, shape resonances, and Ramsauer-Townsend minima of fullerenes.

For analyzing the flow field and topological structure of hemispherical parachute in low angles of attack, a fluid-structure interaction (FSI) simulation technique is established to decide the shape of the hemispherical parachute during terminal descent. In the fluid simulation, the semi-implicit method for pressure-linked equations consistent (SIMPLEC) algorithm is introduced to solve shear stress transport (SST) k–ω turbulence Navier–Stokes (N–S) Equations. This method is proved to be efficient and stable by the experiment and corresponding numerical simulation. After obtaining the stable shape of the canopy, the parachute in different angles and velocities are considered.

We present a simplified treatment of templates used to summarize the topological properties of chaotic attractors bounded by a genus-1 torus. The reduction is based on determinism and flow continuity, which impose tight relations between torsions of each branch, rotations between pairs of branches and the order in which they join at the branch line. This way, the number of integer parameters necessary to characterize a template can be reduced. Apart from the purely theoretical interest, the new treatment simplifies the procedure for template determination starting from a time series, with a consequential save in computation time.

The simplest electronic circuit with a memristor was recently proposed. Chaotic attractors solution to this memristive circuit are topologically characterized and compared to Rössler-like attractors.

The topological analysis of chaotic attractor by means of template is rather well established for simple attractors as solution to the Rössler system. Lorenz-like attractors are already slightly more complicated because they are bounded by a genus-3 bounding torus, implying the necessity to use a two-component Poincaré section. In this paper, we enriched the concept of linking matrix to correctly describe an algebraic template for an attractor with (g - 1) components of Poincaré section and whose bounding torus has g interior holes aligned. An example with g = 5 — a multispiral attractor — is explicitly treated.

Metabolic networks are composed of several functional modules, reproducing metabolic pathways and describing the entire cellular metabolism of an organism. In the last decade, an enormous interest has grown for the study of tolerance to errors and attacks in metabolic networks. Studies on their robustness have suggested that metabolic networks are tolerant to errors, but very vulnerable to targeted attacks against highly connected nodes. However, many findings on metabolic networks suggest that the above classification is too simple and imprecise, since hub node attacks can be by-passed if alternative metabolic paths can be exploited. On the contrary, non-hub nodes attacks can affect cell survival when the node is the only path within a functional module. In this paper an integrated approach for metabolic networks robustness analysis is presented. With more details, statistical, topological, and functional analysis are used together to evaluate metabolic network behavior under normal operation conditions and under random or targeted attacks. Two real biological metabolic networks have been used to test the effectiveness of the proposed approach.