Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and R\"{o}ssler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $N \times N$ matrices in $R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.Comment: 35 pages, 4 figures, LaTe

Toxicity and cellular uptake of gold nanoparticles: what we have learned so far?

Gold nanoparticles have attracted enormous scientific and technological interest due to their ease of synthesis, chemical stability, and unique optical properties. Proof-of-concept studies demonstrate their biomedical applications in chemical sensing, biological imaging, drug delivery, and cancer treatment. Knowledge about their potential toxicity and health impact is essential before these nanomaterials can be used in real clinical settings. Furthermore, the underlying interactions of these nanomaterials with physiological fluids is a key feature of understanding their biological impact, and these interactions can perhaps be exploited to mitigate unwanted toxic effects. In this Perspective we discuss recent results that address the toxicity of gold nanoparticles both in vitro and in vivo, and we provide some experimental recommendations for future research at the interface of nanotechnology and biological systems

Global dynamic scenarios in a discrete-time model of renewable resource exploitation: a mathematical study

We consider the two-dimensional map introduced in Bischi et al. (J Differ Equ Appl 21(10):954–973, 2015) formulated as a model for a renewable resource exploitation process in an evolutionary setting. The global dynamic scenarios displayed by the model are not so often encountered in smooth two-dimensional dynamical systems. We explain the occurrence of such scenarios at the light of the theory of noninvertible maps. Moreover, complex structures of basins of attraction of coexisting invariant sets are observed. We analyze such structures by examining stability properties of chaotic sets, in the case in which a non-topological Milnor attractor is present. Stability changes of a chaotic set occur through global bifurcations (such as riddling and blowout) and are detected by means of the study of the spectrum of Lyapunov exponents associated with the set

Clay-mineral and grain-size distributions in surface sediments of the White Sea (Arctic Ocean): indicators of sediment sources and transport processes

In this study, the grain-size and clay-mineral compositions of 73 surface sediment samples collected in a variety of environmental settings in the White Sea are presented to characterize recent sedimentation processes, reconstruct transport pathways, and identify potential source areas of the terrigenous components. Areas >100 m deep are invariably characterized by silty clay, whereas areas <100 m deep exhibit more heterogeneous grain-size compositions plausibly explained by coastal erosion and (re-)distribution mechanisms, particularly tidal currents. The dominance of sand in the estuarine areas of the Onega and Dvina rivers as well as toward Gorlo Strait connecting the White Sea with the Barents Sea, is attributed to increased current speeds. Illite and smectite are the dominant clay minerals in recent sediments of the southwestern and eastern White Sea sectors, respectively. Their distribution patterns largely depend on the geology of the source areas and mirror surface circulation patterns, especially in Dvina Bay. Smectite is a key clay mineral in White Sea surface sediments as it reveals the dominating influence of the Northern Dvina's runoff on sedimentation and water circulation throughout the basin of the sea. In comparison to other Eurasian shelf seas, the White Sea is characterized by a greater diversity of clay-mineral assemblages, which range from illite- to smectite-dominated sectors containing variable amounts of chlorite and kaolinite