Cross over of recurrence networks to random graphs and random geometric graphs

Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.     

Where is SUSY?

The searches for supersymmetry at the Large Hadron Collider (LHC) have so far yielded only null results and have considerably tightened the bounds on the sparticle masses. This has generated some skepticism in the literature regarding the ‘naturalness of SUSY’ which qualitatively requires some sparticles to be relatively light. Re-examining some of the bounds from LHC searches, it is argued with specific examples that the above skepticism is a red herring because (i) a quantitative and universally accepted definition of ‘naturalness’ is not available and (ii) even if some conventional definitions of naturalness is accepted at their face values, the alleged tension with the apparently stringent LHC bounds wither away once the strong assumptions, by no means compelling, underlying such bounds are relaxed.     

First-principle calculations of structural,electronic, optical,elastic and thermal properties of $$\hbox {MgXAs}_{2}$$ ($$\hbox {X}=\hbox {Si}, \hbox {Ge}$$X=Si,Ge) compounds

First-principle calculations on the structural, electronic, optical, elastic and thermal properties of the chalcopyrite \(\hbox {MgXAs}_{2}\) (\(\hbox {X}=\hbox {Si}, \hbox {Ge}\)) have been performed within the density functional theory (DFT) using the full-potential linearized augmented plane wave (FP-LAPW) method. The obtained equilibrium structural parameters are in good agreement with the available experimental data and theoretical results. The calculated band structures reveal a direct energy band gap for the interested compounds. The predicted band gaps using the modified Becke–Johnson (mBJ) exchange approximation are in fairly good agreement with the experimental data. The optical constants such as the dielectric function, refractive index, and the extinction coefficient are calculated and analysed. The independent elastic parameters namely, \(C_{11}\), \(C_{12}\), \(C_{13}\), \(C_{33}\), \(C_{44}\) and \(C_{66 }\) are evaluated. The effects of temperature and pressure on some macroscopic properties of \(\hbox {MgSiAs}_{2}\) and \(\hbox {MgGeAs}_{2}\) are predicted using the quasiharmonic Debye model in which the lattice vibrations are taken into account.     

A new fractional derivative involving the normalized sinc function without singular kernel

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.     

Polarization of plane wave propagating inside elastic hexagonal system solids

Based on the reported physical parameters for hexagonal system solids,we have calculated the effects of anisotropy on polarization of plane P-wave propagation.Herein we report the results of calculations and the newly observed physical phenomena.It is found that,for a given propagation,if the polarization is parallel to the wave vector,so also to the Poynting vector.In such a case,the phase velocity is identical to the energy velocity;the quasi P-wave degenerates to a pure P-wave along the propagation.It is also noted that if the polarization is parallel to the Poynting vector but not to the wave vector,the propagating wave cannot be a pure P-wave.Furthermore,the polarization in a quasi P-wave may deviate from the wave vector for more than 45°,but the deviation from the Poynting vector is always less than 45°.The energy velocity of a quasi SV-wave can be larger than that of the quasi P-wave in some propagation directions,even though the phase velocity of a quasi SV-wave may never be larger than either the phase velocity or energy velocity of the quasi P-wave.Finally,in case of parameters ε=0 and δ*≠0,the polarization of a quasi P-wave has an observed symmetry at a 45°phase angle.The anisotropy of a hexagonal system solid determines if a pure P-wave can be created and what the propagation direction is for a plane wave propagating inside such a hexagonal system solid.     

Ideal Mixture Approximation of Cluster Size Distributions at Low Density

We consider an interacting particle system in continuous configuration space. The pair interaction has an attractive part. We show that, at low density, the system behaves approximately like an ideal mixture of clusters (droplets): we prove rigorous bounds (a) for the constrained free energy associated with a given cluster size distribution, considered as an order parameter, (b) for the free energy, obtained by minimising over the order parameter, and (c) for the minimising cluster size distributions. It is known that, under suitable assumptions, the ideal mixture has a transition from a gas phase to a condensed phase as the density is varied; our bounds hold both in the gas phase and in the coexistence region of the ideal mixture. The present paper improves our earlier results by taking into account the mixing entropy.