A note on the connection between nonextensive entropy and hh-derivative

In order to study as a whole the major part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the \textit{h}-derivative which generalizes the conventional Newton-Leibniz calculus. This new entropy, $S_{h,h'}$, is proved to describe the non-extensive systems and recover several types of the well-known non-extensive entropic expressions, such as the Tsallis entropy, the Abe entropy, the Shafee entropy, the Kaniadakis entropy and even the classical Boltzmann\,--\,Gibbs one. As a generalized entropy, its corresponding properties are also analyzed.Comment: 6 pages, 1 figur

Thermoelectric properties of (an-)isotropic QGP in magnetic fields

The Seebeck effect and the Nernst effect, reflecting the appearances of a longitudinal electric field and a transverse electric field, $E_{x}$ and $E_{y}$, respectively, induced by a longitudinal thermal gradient, are studied in QGP at a perpendicular magnetic field placed in $z$-axis. We calculate the associated Seebeck coefficient ($S_{xx}$) and Nernst signal ($N$) using the relativistic Boltzmann equation under the relaxation time approximation. In an isotropic QGP, the influences of magnetic field ($B$) and quark chemical potential ($\mu_{q}$) on these thermoelectric transport coefficients are investigated. In the presence (absence) of weak magnetic field, we find $S_{xx}$ for a fixed $\mu_{q}$ is negative (positive) in sign, indicating that the dominant carriers for converting heat gradient to electric field are negatively (positively) charged quarks. The absolute value of $S_{xx}$ decreases with increasing temperature. Unlike $S_{xx}$, the sign of $N$ is independent of charge carrier type, and its thermal behavior displays a peak structure. In the presence of strong magnetic field, the motions of (anti-)quarks perpendicular to magnetic field can be quantized, only the Seebeck coefficient along the direction of magnetic field, $S_{zz}$, is concentrated. Our results show that the value of $S_{zz}$ at a fixed $\mu_{q}$ in lowest Landau level (LLL) approximation always remains positive. Within the effect of high Landau levels, $S_{zz}$ exhibits a thermal structure similar to that in LLL approximation. As Landau level increases further, $S_{zz}$ decreases and even its sign changes from positive to negative. The computation of these thermoelectric transport coefficients are also extended to a medium with momentum-anisotropy induced by initial spatial expansion as well as strong magnetic field.Comment: 20 pages, 7 figure

Multijet topology in high-energy nuclear collisions: jet broadening

This work presents the first theoretical investigation of the medium modification of jet broadening as an event-shape observable in multijet final states due to jet quenching in high-energy nuclear collisions. The partonic spectrum of $pp$ collisions with next-to-leading order (NLO) accuracy at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV is provided by the POWHEG$+$PYTHIA8 event generator, while the linear Boltzmann transport (LBT) model is utilized to investigate the energy loss of fast partons as they traverse through the hot and dense QCD medium. We present the jet broadening distributions in multijet final states for both $pp$ and PbPb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, then observe an enhancement at the small jet broadening region and suppression at the large jet broadening region in PbPb collisions relative to that in $pp$. This suggests that medium modification with parton energy loss in the QGP leads to a more concentrated energy flow in all observed multijet events in PbPb reactions. We also demonstrate that the intertwining of two effects, the jet number reduction and the restructured contribution, results in the novel behavior of nuclear modification of the jet broadening observable in PbPb collisions.Comment: 9 pages, 6 figures, 2 table

Suppression of Superconducting Critical Current Density by Small Flux Jumps in MgB2MgB_2 Thin Films

By doing magnetization measurements during magnetic field sweeps on thin films of the new superconductor $MgB_2$, it is found that in a low temperature and low field region small flux jumps are taking place. This effect strongly suppresses the central magnetization peak leading to reduced nominal superconducting critical current density at low temperatures. A borderline for this effect to occur is determined on the field-temperature (H-T) phase diagram. It is suggested that the small size of the flux jumps in films is due to the higher density of small defects and the relatively easy thermal diffusion in thin films in comparison with bulk samples.Comment: 7 figures Phys. Rev. B accepted scheduled issue: 01 Feb 200

Performance evaluation of on-chip wavelength conversion based on InP/In1−x_{1-x}Gax_xAsy_yP1−y_{1-y} semiconductor waveguide platforms

We propose and design the high confinement InP/In1-xGaxAsyP1-y semiconductor waveguides and report the results of effective wavelength conversion based on this platform. Efficient confinement and mode field area fluctuation at different wavelength is analyzed to achieve the high nonlinear coefficient. The numerical results show that nearly zero phase-mismatch condition can be satisfied through dispersion tailoring of InP/In1-xGaxAsyP1-y waveguides, and the wavelength conversion ranging over 40 nm with the maximum conversion efficiency -26.3 dB is achieved for fixing pump power 100 mW. Meanwhile, the influences of the doping parameter y and pumping wavelength on the bandwidth and conversion efficiency are also discussed and optimized. It is indicated the excellent optical properties of the InP/In1-xGaxAsyP1-y waveguides and pave the way towards direct integration telecom band devices on stand semiconductor platforms.Comment: 21 page

Jet radius and momentum splitting fraction with dynamical grooming in heavy-ion collisions

We investigate the medium modifications of momentum splitting fraction and groomed jet radius with both dynamical grooming and soft drop algorithms in heavy-ion collisions. In the calculation, the partonic spectrum of initial hard scattering in p+p collisions is provided by the event generator PYTHIA 8, and the energy loss of fast parton traversing in a hot/dense QCD medium is simulated with the Linear Boltzmann Transport (LBT) model. We predict the normalized distributions of the groomed jet radius $\theta_g$ and momentum splitting fraction $z_g$ with the dynamical grooming algorithm in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV, then compare these quantities in dynamical grooming at $a=0.1$, with that in soft drop at $z_{\mathrm{cut}} = 0.1$ and $\beta = 0$. It is found that the normalized distribution ratios Pb+Pb/p+p with respect to $z_g$ in $z_{\mathrm{cut}} = 0.1$, $\beta = 0$ soft drop case are close to unity and those in $a=0.1$ dynamical grooming case show enhancement at small $z_g$, and Pb+Pb/p+p with respect to $\theta_g$ in the dynamical grooming case demonstrate weaker modification than those in the soft drop counterparts. We further calculate the groomed jet number averaged momentum splitting fraction $\rm \langle z_g \rangle_{jets}$ and averaged groomed jet radius $\rm \langle \theta_g \rangle_{jets}$ in p+p and A+A for both grooming cases in three $p^{\rm ch, jet}_{\rm T}$ intervals, and find that the originally generated well balanced groomed jets will become more momentum imbalanced and less jet size narrowing due to jet quenching, and weaker medium modification of $z_g$ and $\theta_g$ in $a =0.1$ dynamical grooming case than in the soft drop counterparts.Comment: 7 pages, 3 figures, 2 table

Anti-plane interfacial crack with functionally graded coating: static and dynamic

The anti-plane displacement discontinuity method is applied to establish the Fredholm integral equation of the first kind for the orthotropic Functionally Graded Material (FGM) coatings subjected to static/dynamic shears. The shear modulus and mass density are assumed to vary exponentially through the thickness. The static and dynamic fundamental solutions with anti-plane displacement discontinuity are derived for orthotropic FGM coating by using Fourier transform method and Laplace transform method. It has been shown that the transformed fundamental solution with orthotropic coatings has the same order of hyper-singularity as in the static case, i.e. O(1/r2), and the Chebyshev polynomials of the second kind are used to solve the integral equations numerically. The time dependent stress intensity factors are obtained directly from the coefficients of the Chebyshev polynomials with the aid of Durbin’s Laplace transform inversion method. A comparative study of FGM versus homogeneous coating is conducted, and the dependence of the stress intensity factors in the coating/substrate system on the material property (orthotropic) and thickness of coating is examined. Two examples including the static/dynamic loads are given as benchmarks for the numerical methods and application in composite engineering