abstract

Algorithms for search of communities in networks usually consist in discrete variations of links. Here we discuss a flow method, driven by a set of differential equations. Two examples are demonstrated in detail. First is a partition of a signed graph into two parts, where the proposed equations are interpreted in terms of removal of a cognitive dissonance by agents placed in the network nodes. There, the signs and values of links refer to positive or negative interpersonal relationships of different strength. Second is an application of a method akin to the previous one, dedicated to communities identification, to the Sierpiński triangle of finite size. During the time evolution, the related graphs are weighted; yet at the end, the discrete character of links is restored. In the case of the Sierpiński triangle, the method is supplemented by adding a small noise to the initial connectivity matrix. By breaking the symmetry of the network, this allows to a successful handling of overlapping nodes.

abstract

This paper focuses on a new coupled (\(2+1\))-dimensional Burgers equations. The shock wave solution is obtained by the aid of ansatz method. There are several constraint conditions which guarantee the existence of the derived solutions. Subsequently, the simplified Hirota bilinear method, established by Hereman, is applied to construct soliton solutions to the equation. Finally, the classic Lie symmetry analysis is employed to generate a class of new solutions to the equation based on the solutions obtained earlier by ansatz and simplified Hirota bilinear methods.

abstract

Using the continuous-time random walk (CTRW) approach, we study the phenomenon of relaxation of two-state systems whose elements evolve according to a dichotomous process. Two characteristics of relaxation, the probability density function of the waiting times difference and the relaxation law, are of our particular interest. For systems characterized by the Erlang distributions of waiting times, we consider different regimes of relaxation and show that, under certain conditions, the relaxation process can be non-monotonic. By studying the asymptotic behavior of the relaxation process, we demonstrate that heavy and superheavy tails of waiting time distributions correspond to slow and superslow relaxation, respectively.

abstract

In the present paper, we address the Schrödinger-type eigenvalue problems for \(H=T+V\), where a kinetic term \(T=T_m\) is a manifestly nonlocal quasirelativistic energy operator \(T_m = \sqrt {-\hbar ^2c^2 {\mit \Delta } + m^2c^4} - mc^2\), where the whole mass \(m\in (0,\infty )\) range is admitted. We are primarily interested in a simple confining enclosure where \(V(x)\) refers to a finite well of an arbitrary depth. As a useful test model, preceding the finite well analysis, we consider the case of the harmonic attraction. We analyze spectral solutions, e.g. infer detailed eigenvalue and eigenfunction (shapes) data of the pertinent nonlocal quantum systems. We focus on their \(m\)-dependence and specifically on their low mass regime, which can be directly compared with existing \(m=0\) spectral solutions for the Cauchy oscillator and the infinite Cauchy well. To this end, an efficient spectrum generating algorithm is implemented. All computations are carried out directly in the configuration space which entails a proper assessment and control of the spatial nonlocality impact on simulation outcomes, e.g. explicit nonlocally induced eigenvalues and eigenfunctions.

abstract

This paper presents the studies of the background contribution to the \(H \rightarrow 4l\) searches originating from the processes of off-shell (virtual) photon emissions and their conversions into lepton pairs accompanying the production of \(Z/\gamma ^*\)-bosons at the LHC. They extend the analyses of the irreducible background presented in the ATLAS and CMS Higgs papers [Phys. Lett. B716, 1 (2012); Phys. Lett. B726, 88 (2013); Phys. Rev. D90, 052004 (2014); CERN-PH-EP-2014-170, to appear in Phys. Rev. D; Phys. Lett. B716, 30 (2012); Phys. Rev. D89, 92007 (2014)] by taking into account the emissions of off-shell photons by parton showers. Including these effects does not change significantly the Higgs-searches background level, provided that the transverse momentum of each of the final-state leptons is restricted to the range of \(p_{\mathrm {T}, l} \gt 7\) GeV. In the kinematical region extended towards lower lepton transverse momenta, the parton-shower contribution becomes important. A measurement method for pinning down the parton-shower effects has been proposed.

abstract

The Bogomolny decompositions (Bogomolny equations) for the gauged \(O(3)\) nonlinear “sigma” model (in this paper, we call it shortly as: gauged \(O(3)\) “sigma” model) and for the gauged baby Skyrme models: restricted and full one, in (\(2+0\))-dimensions, are derived, for some general classes of the potentials. The conditions, which must be satisfied by the potentials, for each of these mentioned models, are also derived.

abstract

Correlations between the energy, charge and the deflection angle of the projectile-like fragments were studied for the \(^{136}\)Xe + \(^{209}\)Bi reaction at \(E/A = 28\) and 62 MeV. These correlations are seen to exhibit features characteristic of dissipative orbiting, commonly found at bombarding energies of a few MeV/nucleon above the interaction barrier, but also reported in the Fermi-energy domain. It was found, that in the studied bombarding energy range, the reaction cross section is still dominated by the dissipative binary reactions of well defined projectile- and target-like fragments.

abstract

Angular distributions of deuterons elastically and inelastically scattered on \(^{7}\)Li nuclei with excitation of the 0.478 MeV (\(J^{\pi } = 1/2^{-}\)) level, and tritons from the \(^{7}\)Li(\(d, t\))\(^{6}\)Li reaction, corresponding to transitions to the ground (\(J^{\pi } = 1^{+}\)) and low-lying excited states (\(J^{\pi } = 3^{+}\) and \(0^{+}\)) of the \(^{6}\)Li nucleus were measured at the 25 MeV energy. The experimental data were analyzed within the framework of the coupled reaction channels and a modified distorted-wave methods. The values of the spectroscopic factors and the asymptotic normalization coefficients for the \(^{7}\)Li \(\rightarrow \) \(^{6}\)Li + \(n\) vertex were extracted.

abstract

The static nucleus–nucleus potential and the energy-dependent nucleus–nucleus potential are used to address the sub-barrier fusion reactions. The static nucleus–nucleus potential systematically fails to recover the experimental data of \(_{\ \ \ 16}^{32,36}\)S\(+^{90}_{40}\)Zr systems. However, the energy-dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one-dimen-sional Wong formula accurately addresses the sub-barrier fusion enhancement of these systems. The role of the inelastic surface excitations of collision partners in the fusion dynamics is entertained within the context of coupled channel calculations performed by using coupled channel code CCFULL. It is worth noting here that the energy dependence in nucleus–nucleus potential simulates the effects of inelastic surface excitations of colliding nuclei in the sub-barrier fusion enhancement of \(_{\ \ \ 16}^{32,36}\)S\(+^{90}_{40}\)Zr systems.

abstract

Information properties of co-processing model on communication networks are investigated in this paper. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are achieved to disclose the formation. Considering the influence of a node to the global dynamical behavior, co-processing centrality is introduced for each node, which determines the relative importance of nodes and exhibits the capability that a node communicates information with its neighbor environment over the network in the diffusion process. Furthermore, a new parameter, co-processing entropy, is proposed to measure the interplay between co-processing centrality and diffusion dynamics. At last, the information function of the co-processing model is investigated to deeply detect the properties of the diffusion process. The experimental results on large-scale complex networks with Poisson distribution confirm our analytical prediction.