Optimality in self-organized molecular sorting
We introduce a simple physical picture to explain the process of molecular sorting, whereby specific
proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this
purpose, we formulate a model based on the coupling of spontaneous molecular aggregation with vesicle
nucleation. Its implications are studied by means of a phenomenological theory describing the diffusion of
molecules toward multiple sorting centers that grow due to molecule absorption and are extracted when
they reach a sufficiently large size. The predictions of the theory are compared with numerical simulations
of a lattice-gas realization of the model and with experimental observations. The efficiency of the
distillation process is found to be optimal for intermediate aggregation rates, where the density of sorted
molecules is minimal and the process obeys simple scaling laws. Quantitative measures of endocytic
sorting performed in primary endothelial cells are compatible with the hypothesis that these optimal
conditions are realized in living cells.
We present a molecular dynamics (MD) study of size effect on the crystal nuclei geometry, formation and growth in supercooled tantalum film. The process is studied in a set of MD trajectories that are obtained by ultrafast cooling from the stable liquid phase to the temperature below the glass transition temperature. We describe the nucleation process by two morphological parameters. Along with the nucleus size, we analyze the asphericity that is a measure of deviation of crystal nuclei from idealized spherical form. This method allows to demonstrate that there are two paths for crystal nucleus shape and size evolution. The first path is crystal growth through high asphericity values. We show that this is caused by coalescence of the crystals. This mechanism is not affected by the size of the system. The second path is formation of long-lived crystal clusters that do not lead to the crystallization of the whole system on the MD simulation timescale. We demonstrate that such clusters have common geometric features which strongly depend on the system size.
Formation of carbon nanoparticles is an important type of complex non-equilibrium processes that require precise atomistic theoretical understanding. In this work, we consider the process of ultrafast cooling of pure carbon gas that results in nucleation of an onion-like fullerene. The model is based on molecular dynamics simulation with the interaction between carbon atoms described via a reactive ReaxFF model. We study the consecutive stages of fullerene-like nanoparticle formation and identify the corresponding temperature ranges. Analysis of hybridization and graphitization reveals the underlying microscopic mechanisms connected with rearrangements of dihedral angles and density changes.
Molecular dynamics with reactive interatomic potentials is the only computationally feasible approach for modeling at the atomistic level the formation of carbon nanoparticles from gas state. Such models require thousands of atoms and millions of time steps that is beyond the current capabilities of first principles electronic structure calculations. A continuously growing variety of available reactive interatomic potentials for carbon requires their careful validation for a particular molecular system and pressure-temperature conditions. In this work we consider a generic example process of carbon nanoparticle formation at cooling of the gas phase and compare different AIREBO and ReaxFF reactive models. Three main processes of clusterization, change of hybridization and graphitization are analysed and used for comparison of potentials. Ab initio density functional theory and parameterized density functional tight-binding calculations together with experimental data available are used for validation of the reactive models considered.We highlight the detected problems of some well-known reactive potentials and conclude with three models that can be selected as the best options for molecular dynamics simulations of pure carbon nanoparticle formation.
The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.
Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.