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1.
We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable Si=±1Si=±1 on the ii-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable Jij=±1Jij=±1 describes a state of the synaptic connection between jj-th and ii-th neurons. The gauge symmetry allows for a self-coupling energy among JijJij’s such as JijJjkJkiJijJjkJki, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of JijJij, (II) a quenched model with full connections where JijJij 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).  相似文献   

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I examine the role of entropy in the transition from incoherence to phase synchronisation in the Kuramoto model of NN coupled phase oscillators on a general undirected network. In a Hamiltonian ‘action-angle’ formulation, auxiliary variables JiJi combine with the phases θiθi to determine a conserved system with a 2N2N dimensional phase space. In the vicinity of the fixed point for phase synchronisation, θi≈θjθiθj, which is known to be stable, the auxiliary variables JiJi exhibit instability  . This manifests Liouville’s Theorem in the phase synchronised regime in that contraction in the θiθi parts of phase space are compensated for by expansion in the auxiliary dimensions. I formulate an entropy rate based on the projection of the JiJi 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.  相似文献   

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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 SxSx and momentum SpSp information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the SxSx entropy as well as for the Fourier transformed wave functions, while the SpSp quantity is calculated numerically. We notice the behavior of the SxSx 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 SpSp on the width is contrary to the one for SxSx. Some interesting features of the information entropy densities ρs(x)ρs(x) and ρs(p)ρs(p) 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.  相似文献   

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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 ωpi>Ωiωpi>Ωi and ωpi<Ωiωpi<Ωi are examined, where ωpiωpi is the ion plasma frequency and ΩiΩi is the ion gyrofrequency. It is found that the soliton gets reflected more strongly when the condition ωpi>Ωiωpi>Ωi is achieved in the plasma. The effect of magnetic field is found to be more pronounced on the reflected soliton.  相似文献   

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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)ρs(x), ρs(p)ρs(p) and probability densities ρ(x)ρ(x), ρ(p)ρ(p) are illustrated with different potential range L and potential depth U  . We present analytical position information entropies SxSx for the lowest two states. We observe that the sum of position and momentum entropies SxSx and SpSp 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 SxSx increases with the potential range L, while decreases with the potential depth U  . The variation of SpSp is contrary to that of SxSx.  相似文献   

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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/νβ/ν and 1/ν1/ν 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.  相似文献   

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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)(Tc) 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×LL×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 KK limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of TcTc on anisotropic parameter KK becomes linear and in the single-ion anisotropic case, TcTc becomes independent of KK. 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=0.125α=0.125 and γ=1.75γ=1.75.  相似文献   

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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, ΔSVΔSV and change in the configuration, ΔSDΔSD were evaluated. It is found that they have similar trend as the overall entropy change in melting, and ΔSDΔSD is more dominant. Furthermore, the value of ΔSDΔSD at ambient pressure is close to Rln  2 per mole, which is the specific value of ΔSDΔSD 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 ΔSDΔSD.  相似文献   

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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)/Δxi(t)→∞vi(t)/Δxi(t) if Δxi(t)→0Δxi(t)0 where vi(t)vi(t) and Δxi(t)Δxi(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.  相似文献   

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We consider an extension of the standard model (SM) with three SU(2)SU(2) scalar doublets and discrete S3⊗Z2S3Z2 symmetries. The irreducible representation of S3S3 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(2) doublets forming a S3S3 doublet are inert. In general, in a three scalar doublet model, with or without S3S3 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.  相似文献   

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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 (LGLG), negative junction depth (NJD), substrate doping (NANA), gate metal workfunction, substrate bias (VSUBVSUB), drain bias (VDSVDS) and gate oxide permittivity (εox2εox2), 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 LGLG, NJD, NANA, gate metal workfunction and εox2εox2 for different substrate (VSUBVSUB) and drain to source (VDSVDS) 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.  相似文献   

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