On the retention of high-energy protons and nuclei with charges Z or equal to 2 in large solar flares after the process of their acceleration

Data which suggest that the protons with energies of up to several GeV should be retained on the Sun after the process of their acceleration are presented. The protons are on the average retained for 15 min, irrespectively of the solar flare heliolatitude and of the accelerated particle energy ranging from 100 MeV to several GeV. It is suggested that the particles are retained in a magnetic trap formed in a solar active region. No Z or = 2 nuclei of solar origin during large solar flares. The absence of the 500 MeV/nucleon nuclei with Z or = 2 may be due to their retention in the magnetic trap which also retains the high-energy protons. During the trapping time the approx. 500 MeV/nucleon nuclei with Z or = 2 may escape due to nuclear interactions and ionization loss

Statistics of layered zigzags: a two-dimensional generalization of TASEP

A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted minimal local height gradient. We demonstrate that the coarse-grained behavior of this model is described by the two-dimensional Kardar-Parisi-Zhang equation. The coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow-density curve, the so called `fundamental' diagram. A conjecture concerning the analytical form of this flow-density curve is presented and is verified numerically.Comment: 5 pages, 4 figure

Random Operator Approach for Word Enumeration in Braid Groups

We investigate analytically the problem of enumeration of nonequivalent primitive words in the braid group B_n for n >> 1 by analysing the random word statistics and the target space on the basis of the locally free group approximation. We develop a "symbolic dynamics" method for exact word enumeration in locally free groups and bring arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations. We consider the connection of these problems with the conventional random operator theory, localization phenomena and statistics of systems with quenched disorder. Also we discuss the relation of the particular problems of random operator theory to the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl. Phys. B [PM

Ballistic deposition patterns beneath a growing KPZ interface

We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the randomly forced continuous Burgers equation. This allows to identify the characteristic structures in the bulk of a growing aggregate ("clusters" and "crevices") with minimizers and shocks in the Burgers turbulence, and to introduce a new kind of equipped Airy process for ballistic growth. We dub it the "hairy Airy process" and investigate its statistics numerically. We also identify scaling laws that characterize the ballistic deposition patterns in the bulk: the law of "thinning" of the forest of clusters with increasing height, the law of transversal fluctuations of cluster boundaries, and the size distribution of clusters. The corresponding critical exponents are determined exactly based on the analogy with the Burgers turbulence and simple scaling considerations.Comment: 10 pages, 5 figures. Minor edits: typo corrected, added explanation of two acronyms. The text is essentially equivalent to version

Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment

Using angle-resolved photoelectron spectroscopy and ab-initio GW calculations, we unambiguously show that the widely investigated three-dimensional topological insulator Bi2Se3 has a direct band gap at the Gamma point. Experimentally, this is shown by a three-dimensional band mapping in large fractions of the Brillouin zone. Theoretically, we demonstrate that the valence band maximum is located at the Brillouin center only if many-body effects are included in the calculation. Otherwise, it is found in a high-symmetry mirror plane away from the zone center.Comment: 8 pages, 4 figure

Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice

The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random knot diagram was represented by a partition function of the Potts model with a random configuration of ferro- and antiferromagnetic bonds, which allowed the probability distribution of the random dense knots on a flat square lattice over topological classes to be studied. A topological class is characterized by the highest power of the Kauffman polynomial invariant and interpreted as the free energy of a q-component Potts spin system for q->infinity. It is shown that the highest power of the Kauffman invariant is correlated with the minimum energy of the corresponding Potts spin system. The probability of the lattice knot distribution over topological classes was studied by the method of transfer matrices, depending on the type of local junctions and the size of the flat knot diagram. The obtained results are compared to the probability distribution of the minimum energy of a Potts system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references added

Rotated multifractal network generator

The recently introduced multifractal network generator (MFNG), has been shown to provide a simple and flexible tool for creating random graphs with very diverse features. The MFNG is based on multifractal measures embedded in 2d, leading also to isolated nodes, whose number is relatively low for realistic cases, but may become dominant in the limiting case of infinitely large network sizes. Here we discuss the relation between this effect and the information dimension for the 1d projection of the link probability measure (LPM), and argue that the node isolation can be avoided by a simple transformation of the LPM based on rotation.Comment: Accepted for publication in JSTA

Space-charge mechanism of aging in ferroelectrics: an exactly solvable two-dimensional model

A mechanism of point defect migration triggered by local depolarization fields is shown to explain some still inexplicable features of aging in acceptor doped ferroelectrics. A drift-diffusion model of the coupled charged defect transport and electrostatic field relaxation within a two-dimensional domain configuration is treated numerically and analytically. Numerical results are given for the emerging internal bias field of about 1 kV/mm which levels off at dopant concentrations well below 1 mol%; the fact, long ago known experimentally but still not explained. For higher defect concentrations a closed solution of the model equations in the drift approximation as well as an explicit formula for the internal bias field is derived revealing the plausible time, temperature and concentration dependencies of aging. The results are compared to those due to the mechanism of orientational reordering of defect dipoles.Comment: 8 pages, 4 figures. accepted to Physical Review

NN potentials from inverse scattering in the J-matrix approach

An approximate inverse scattering method [7,8] has been used to construct separable potentials with the Laguerre form factors. As an application, we invert the phase shifts of proton-proton in the $^1S_0$ and $^3P_2-^3F_2$ channels and neutron-proton in the $^3S_1-^3D_1$ channel elastic scattering. In the latter case the deuteron wave function of a realistic $np$ potential was used as input.Comment: LaTex2e, 17 pages, 3 Postscript figures; corrected typo