Z(2) gauge neural network and its phase structure

We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable _Si=±1$S_i=\pm 1$ on the i$i$-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable _Jij=±1$J_{ij}=\pm 1$ describes a state of the synaptic connection between j$j$-th and i$i$-th neurons. The gauge symmetry allows for a self-coupling energy among _Jij$J_{ij}$’s such as _JijJjkJki$J_{ij}{J}_{jk}{J}_{ki}$, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of _Jij$J_{ij}$, (II) a quenched model with full connections where _Jij$J_{ij}$ is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III).     

Entropy and stability of phase synchronisation of oscillators on networks

I examine the role of entropy in the transition from incoherence to phase synchronisation in the Kuramoto model of N$N$ coupled phase oscillators on a general undirected network. In a Hamiltonian ‘action-angle’ formulation, auxiliary variables J_i$J_i$ combine with the phases θ_i${\theta }_i$ to determine a conserved system with a 2N$2N$ dimensional phase space. In the vicinity of the fixed point for phase synchronisation, θ_i≈θ_j${\theta }_i\approx {\theta }_j$, which is known to be stable, the auxiliary variables J_i$J_i$ exhibit instability  . This manifests Liouville’s Theorem in the phase synchronised regime in that contraction in the θ_i${\theta }_i$ parts of phase space are compensated for by expansion in the auxiliary dimensions. I formulate an entropy rate based on the projection of the J_i$J_i$ onto eigenvectors of the graph Laplacian that satisfies Pesin’s Theorem. This leads to the insight that the evolution to phase synchronisation of the Kuramoto model is equivalent to the approach to a state of monotonically increasing entropy. Indeed, for unequal intrinsic frequencies on the nodes, the networks that achieve the closest to exact phase synchronisation are those which enjoy the highest entropy production. I compare numerical results for a range of networks.     

Quantum information entropies for position-dependent mass Schrödinger problem

The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S_x$S_x$ and momentum S_p$S_p$ information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S_x$S_x$ entropy as well as for the Fourier transformed wave functions, while the S_p$S_p$ quantity is calculated numerically. We notice the behavior of the S_x$S_x$ entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S_p$S_p$ on the width is contrary to the one for S_x$S_x$. Some interesting features of the information entropy densities ρ_s(x)${\rho }_s\left(x\right)$ and ρ_s(p)${\rho }_s\left(p\right)$ are demonstrated. In addition, the Bialynicki-Birula–Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases.     

Magnetic field contribution to soliton propagation and reflection in an inhomogeneous plasma

The propagation and reflection characteristics of an ion acoustic soliton are studied in an inhomogeneous plasma through two coupled equations of the KdV family, and the contribution of external static magnetic field is evaluated. The incident and reflected solitons behave oppositely with the angle ψ   between the directions of magnetic field and the wave propagation. Two cases of ω_pi>Ωi${\omega }_{pi}>{\Omega }_i$ and ω_pi<Ωi${\omega }_{pi}<{\Omega }_i$ are examined, where ω_pi${\omega }_{pi}$ is the ion plasma frequency and Ωi${\Omega }_i$ is the ion gyrofrequency. It is found that the soliton gets reflected more strongly when the condition ω_pi>Ωi${\omega }_{pi}>{\Omega }_i$ is achieved in the plasma. The effect of magnetic field is found to be more pronounced on the reflected soliton.     

Quantum information entropies for a squared tangent potential well

The particle in a symmetrical squared tangent potential well is studied by examining its Shannon information entropy and standard deviations. The position and momentum information entropy densities _ρs(x)${\rho }_s(x)$, _ρs(p)${\rho }_s(p)$ and probability densities ρ(x)$\rho (x)$, ρ(p)$\rho (p)$ are illustrated with different potential range L and potential depth U  . We present analytical position information entropies _Sx$S_x$ for the lowest two states. We observe that the sum of position and momentum entropies _Sx$S_x$ and _Sp$S_p$ expressed by Bialynicki-Birula–Mycielski (BBM) inequality is satisfied. Some eigenstates exhibit entropy squeezing in the position. The entropy squeezing in position will be compensated by an increase in momentum entropy. We also note that the _Sx$S_x$ increases with the potential range L, while decreases with the potential depth U  . The variation of _Sp$S_p$ is contrary to that of _Sx$S_x$.     

Critical properties of contact process on the Apollonian network

We investigate an epidemic spreading process by means of a computational simulation on the Apollonian network, which is simultaneously small-world, scale-free, Euclidean, space-filling and matching graphs. An analysis of the critical behavior of the Contact Process (CP) is presented using a Monte Carlo method. Our model shows a competition between healthy and infected individuals in a given biological or technological system, leading to a continuous phase transition between the active and inactive states, whose critical exponents β/_ν⊥$\beta /{\nu }_{\perp }$ and 1/_ν⊥$1/{\nu }_{\perp }$ are calculated. Employing a finite-size scaling analysis, we show that the continuous phase transition belongs to the mean-field directed percolation universality class in regular lattices.     

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.     

Improving the understanding of the melting curve of tantalum at extreme pressures through the pressure dependence of fusion volume and entropy

Molecular dynamics simulations of the melting curve of tantalum for the pressure range 0–300 GPa are reported. The calculated melting curve agrees well with shock wave measurements and other calculations, but disagrees strongly with the diamond anvil cell data at high pressure. Calculated results for the pressure dependence of the fusion volume and entropy show that the pressure dependence of melting temperature approximately followed the Clausius–Clapeyron relation, and the slope of melting curve is mainly due to the variation of fusion volume. Entropy change due to latent volume change in melting, ΔS_V$\mathrm{\Delta }{S}_V$ and change in the configuration, ΔS_D$\mathrm{\Delta }{S}_D$ were evaluated. It is found that they have similar trend as the overall entropy change in melting, and ΔS_D$\mathrm{\Delta }{S}_D$ is more dominant. Furthermore, the value of ΔS_D$\mathrm{\Delta }{S}_D$ at ambient pressure is close to Rln  2 per mole, which is the specific value of ΔS_D$\mathrm{\Delta }{S}_D$ predicted by the Rln2 rule, while it decreases when pressure goes from 50 to 300 GPa. The analysis of the pair distribution function at extreme pressure shows that the change of configuration on melting decreases with increasing pressure, which supports the pressure dependence of ΔS_D$\mathrm{\Delta }{S}_D$.     

Multiple-vehicle collision induced by a sudden stop in traffic flow

We study the dynamic process of the multiple-vehicle collision when a vehicle stops suddenly in a traffic flow. We apply the optimal-velocity model to the vehicular motion. If a vehicle does not decelerate successfully, it crashes into the vehicle ahead with a residual speed. The collision criterion is presented by _vi(t)/Δ_xi(t)→∞$v_i(t)/\mathrm{\Delta }{x}_i(t)\to \infty$ if Δ_xi(t)→0$\mathrm{\Delta }{x}_i(t)\to 0$ where _vi(t)$v_i(t)$ and Δ_xi(t)$\mathrm{\Delta }{x}_i(t)$ are the speed and headway of vehicle i at time t. The number of crumpled vehicles depends on the initial velocity, the sensitivity, and the initial headway. We derive the region map (or phase diagram) for the multiple-vehicle collision.     

A model with two inert scalar doublets

We consider an extension of the standard model (SM) with three SU(2)$SU\left(2\right)$ scalar doublets and discrete S₃⊗Z₂$S_3\otimes {\mathbb{Z}}_2$ symmetries. The irreducible representation of S₃$S_3$ has a singlet and a doublet, and here we show that the singlet corresponds to the SM-like Higgs and the two additional SU(2)$SU\left(2\right)$ doublets forming a S₃$S_3$ doublet are inert. In general, in a three scalar doublet model, with or without S₃$S_3$ symmetry, the diagonalization of the mass matrices implies arbitrary unitary matrices. However, we show that in our model these matrices are of the tri-bimaximal type. We also analyzed the scalar mass spectra and the conditions for the scalar potential is bounded from below at the tree level. We also discuss some phenomenological consequences of the model.     

TCAD assessment of Gate Electrode Workfunction Engineered Recessed Channel (GEWE-RC) MOSFET and its multi-layered gate architecture,Part II: Analog and large signal performance evaluation

Part I of this paper dealt with the hot carrier reliability evaluation of Gate Electrode Workfunction Engineered Recessed Channel (GEWE-RC) MOSFET involving channel recession and gate electrode workfunction engineering integration onto the conventional MOSFET, using an ATLAS device simulator. It was demonstrated that with the gate stack architecture incorporated onto the GEWE-RC MOSFET and tuning of various structural design parameters such as gate length (_LG$L_G$), negative junction depth (NJD), substrate doping (_NA$N_A$), gate metal workfunction, substrate bias (_VSUB$V_{SUB}$), drain bias (_VDS$V_{DS}$) and gate oxide permittivity (_εox2${\epsilon }_{ox2}$), excellent hot carrier immunity can be achieved in terms of conduction band offset, reduced electron velocity, electron temperature, hot electron injected gate current and impact ionization substrate current. This paper focuses on the analog and large signal performance metrics in terms of linearity, intermodulation distortion, device efficiency and speed-to-power dissipation design parameters. Moreover, the paper also discusses the effect of gate stack architecture and various design parameters such as _LG$L_G$, NJD, _NA$N_A$, gate metal workfunction and _εox2${\epsilon }_{ox2}$ for different substrate (_VSUB$V_{SUB}$) and drain to source (_VDS$V_{DS}$) voltages. The work, thus, proves the effectiveness of GEWE-RC for RFICs with a higher efficiency, better linearity performance; and designing and modeling of power amplifiers.