The rigid body dynamics: classical and algebro-geometric integration

The basic notion for a motion of a heavy rigid body fixed at a point in three-dimensional space as well as its higher-dimensional generalizations are presented. On a basis of Lax representation, the algebro-geometric integration procedure for one of the classical cases of motion of three-dimensional rigid body - the Hess-Appel'rot system is given. The classical integration in Hess coordinates is presented also. For higher-dimensional generalizations, the special attention is paid in dimension four. The L-A pairs and the classical integration procedures for completely integrable four-dimensional rigid body so called the Lagrange bitop as well as for four-dimensional generalization of Hess-Appel'rot system are given. An $n$-dimensional generalization of the Hess-Appel'rot system is also presented and its Lax representation is given. Starting from another Lax representation for the Hess-Appel'rot system, a family of dynamical systems on $e(3)$ is constructed. For five cases from the family, the classical and algebro-geometric integration procedures are presented. The four-dimensional generalizations for the Kirchhoff and the Chaplygin cases of motion of rigid body in ideal fluid are defined. The results presented in the paper are part of results obtained in last decade.Comment: Zb. Rad.(Beogr.), 16(24), 2013 (accepted for publication); 43 page

Coordinate transformation based design of confined metamaterial structures

The coordinate transformation method is applied to bounded domains to design metamaterial devices for steering spatially confined electromagnetic fields. Both waveguide and free-space beam applications are considered as these are analogous within the present approach. In particular, we describe devices that bend the propagation direction and squeeze confined electromagnetic fields. Two approaches in non-magnetic realization of these structures are examined. The first is based on using a reduced set of material parameters, and the second on finding non-magnetic transformation media. It is shown that transverse-magnetic fields can be bent or squeezed to an arbitrary extent and without reflection using only dielectric structures.Comment: The previous version has been revised and considerably expande

Comparative studies on osmosis based encapsulation of sodium diclofenac in porcine and outdated human erythrocyte ghosts

The objective of our study was to develop controlled drug delivery system based on erythrocyte ghosts for amphiphilic compound sodium diclofenac considering the differences between erythrocytes derived from two readily available materials - porcine slaughterhouse and outdated transfusion human blood. Starting erythrocytes, empty erythrocyte ghosts and diclofenac loaded ghosts were compared in terms of the encapsulation efficiency, drug releasing profiles, size distribution, surface charge, conductivity, surface roughness and morphology. The encapsulation of sodium diclofenac was performed by an osmosis based process - gradual hemolysis. During this process sodium diclofenac exerted mild and delayed antihemolytic effect and increased potassium efflux in porcine but not in outdated human erythrocytes. FTIR spectra revealed lack of any membrane lipid disorder and chemical reaction with sodium diclofenac in encapsulated ghosts. Outdated human erythrocyte ghosts with detected nanoscale damages and reduced ability to shrink had encapsulation efficiency of only 8%. On the other hand, porcine erythrocyte ghosts had encapsulation efficiency of 37% and relatively slow drug release rate. More preserved structure and functional properties of porcine erythrocytes related to their superior encapsulation and release performances, define them as more appropriate for the usage in sodium diclofenac encapsulation process

Low-friction, wear-resistant, and electrically homogeneous multilayer graphene grown by chemical vapor deposition on molybdenum

Chemical vapour deposition (CVD) is a promising method for producing large-scale graphene (Gr). Nevertheless, microscopic inhomogeneity of Gr grown on traditional metal substrates such as copper or nickel results in a spatial variation of Gr properties due to long wrinkles formed when the metal substrate shrinks during the cooling part of the production cycle. Recently, molybdenum (Mo) has emerged as an alternative substrate for CVD growth of Gr, mainly due to a better matching of the thermal expansion coefficient of the substrate and Gr. We investigate the quality of multilayer Gr grown on Mo and the relation between Gr morphology and nanoscale mechanical and electrical properties, and spatial homogeneity of these parameters. With atomic force microscopy (AFM) based scratching, Kelvin probe force microscopy, and conductive AFM, we measure friction and wear, surface potential, and local conductivity, respectively. We find that Gr grown on Mo is free of large wrinkles that are common with growth on other metals, although it contains a dense network of small wrinkles. We demonstrate that as a result of this unique and favorable morphology, the Gr studied here has low friction, high wear resistance, and excellent homogeneity of electrical surface potential and conductivity.This is peer-reviewed version of the artcle: B. Vasić, U. Ralević, K.C. Zobenica, M.M. Smiljanić, R. Gajić, M. Spasenović, S. Vollebregt, Low-friction, wear-resistant, and electrically homogeneous multilayer graphene grown by chemical vapor deposition on molybdenum, Appl. Surf. Sci. (2019) 144792. [https://doi.org/10.1016/j.apsusc.2019.144792]Published version: [http://cer.ihtm.bg.ac.rs/handle/123456789/3347

Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear