Search Results (5)

The primary objective of this study is the computation of the matching polynomials of a number of symmetric, semisymmetric, double group graphs, and solids in third and higher dimensions. Such computations of matching polynomials are extremely challenging problems due to the computational and combinatorial complexity of the problem. We also consider a series of recursive graphs possessing symmetries such as D_2h-polyacenes, wheels, and fans. The double group graphs of the Möbius types, which find applications in chemically interesting topologies and stereochemistry, are considered for the matching polynomials. Hence, the present study features a number of vertex- or edge-transitive regular graphs, Archimedean solids, truncated polyhedra, prisms, and 4D and 5D polyhedra. Such polyhedral and Möbius graphs present stereochemically and topologically interesting applications, including in chirality, isomerization reactions, and dynamic stereochemistry. The matching polynomials of these systems are shown to contain interesting combinatorics, including Stirling numbers of both kinds, Lucas polynomials, toroidal tree-rooted map sequences, and Hermite, Laguerre, Chebychev, and other orthogonal polynomials. Full article

The metastable vaterite polymorph of calcium carbonate (CaCO₃) holds significant practical importance, particularly in regenerative medicine, drug delivery, and various personal care products. Controlling the size and morphology of vaterite particles is crucial for biomedical applications. This study explored the synergistic effect of ultrasonic (US) irradiation and acidic amino acids on CaCO₃ synthesis, specifically the size, dispersity, and crystallographic phase of curved-edge vaterite with chiral toroids (chiral-curved vaterite). We employed 40 kHz US irradiation and introduced L- or D-aspartic acid as an additive for the formation of spheroidal chiral-curved vaterite in an aqueous solution of CaCl₂ and Na₂CO₃ at 20 ± 1 °C. Chiral-curved vaterites precipitated through mechanical stirring (without US irradiation) exhibited a particle size of approximately 15 μm, whereas those formed under US irradiation were approximately 6 μm in size and retained their chiral topoid morphology. When a fluorescent dye was used for the analysis of loading efficiency, the size-reduced vaterites with chiral morphology, produced through US irradiation, exhibited a larger loading efficiency than the vaterites produced without US irradiation. These results hold significant value for the preparation of biomimetic chiral-curved CaCO₃, specifically size-reduced vaterites, as versatile biomaterials for material filling, drug delivery, and bone regeneration. Full article

Orientational structures of polymer-dispersed cholesteric liquid crystal under homeotropic anchoring and their transformations under the action of an electric field are studied. The switching of cholesteric droplets between different topological states are experimentally and theoretically demonstrated. Structures with ${\lambda }^{+1/2}$-disclination are found and considered. These structures are formed during the transformation of a twisted toroidal configuration induced by a decrease in the electric field when a relative chiral parameter $N_0>6.3$. The transformation of the initial structure with a bipolar distribution of the helix axis into a twisted toroidal configuration and then into a structure with ${\lambda }^{+1/2}$-disclination is investigated in detail. The behavior of these structures under the influence of an external electric field, as well as the appearance of structures with ${\lambda }^{-1/2}$-disclination, are studied. Obtained results are promising for the development of optical materials with programmable properties. Full article

There are still grey areas in the understanding of the myoarchitecture of the ventricular mass. This is despite the progress of investigation methods since the beginning of the 21st century (diffusion tensor magnetic resonance imaging, microcomputed tomography, and polarised light imaging). The objective of this article is to highlight the specificities and the limitations of polarised light imaging (PLI) of the unstained myocardium embedded in methyl methacrylate (MMA). Thus, to better differentiate our method from other PLI modes, we will refer to it by the acronym PLI-MMA. PLI-MMA shows that the myosin mesh of the compact left ventricular wall behaves like a biological analogous of a nematic chiral liquid crystal. Results obtained by PLI-MMA are: the main direction of the myosin molecules contained in an imaged voxel, the crystal liquid director n, and a regional isotropy index RI that is an orientation tensor, the equivalent of the crystal liquid order parameter. The vector n is collinear with the first eigenvector of diffusion tensor imaging (DTI-MRI). The RI has not been confounded with the diffusion tensor of DTI that gives information about the three eigenvectors of the ellipsoid of diffusion. PLI-MMA gives no information about the collagen network. The physics of soft matter has allowed the revisiting of Streeter’s conjecture on the myoarchitecture of the compact left ventricular wall: “geodesics on a nested set of toroidal surfaces”. Once the torus topology is understood, this characterisation of the myoarchitecture is more accurate and parsimonious than former descriptions. Finally, this article aims to be an enthusiastic invitation to a transdisciplinary approach between physicists of liquid crystals, anatomists, and specialists of imaging. Full article

The creation of metastable particle-like structures in frustrated (unwound) chiral nematic film containing light-absorbing additive is studied. It is shown that such localized structures can be generated by the thermo-optical action of a focused laser beam or arise spontaneously at a phase transition from an isotropic to a liquid crystal state. Observed axisymmetric patterns resemble cholesteric spherulites with toroidal double-twisted director-field configuration. Full article