By finding local minima of an enthalpy-like energy, we can generate jammed packings of frictionless spheres under constant shear stress σ and obtain the yield stress σy by sampling the potential energy landscape. For three-dimensional systems with harmonic repulsion, σy satisfies the finite size scaling with the limiting scaling relation σy ∼ φ − φ c,∞ , where φ c,∞ is the critical volume fraction of the jamming transition at σ = 0 in the thermodynamic limit. The width or uncertainty of the yield stress decreases with decreasing φ and decays to zero in the thermodynamic limit. The finite size scaling implies a length ξ ∼ (φ − φ c,∞ ) −ν with ν = 0.81 ± 0.05, which turns out to be a robust and universal length scale exhibited as well in the finite size scaling of multiple quantities measured without shear and independent of particle interaction. Moreover, comparison between our new approach and quasi-static shear reveals that quasi-static shear tends to explore low-energy states.PACS numbers: 61.43. Bn,61.43.Fs At zero temperature and shear stress, a packing of frictionless spheres interacting via repulsions jams into a disordered solid when its volume fraction φ exceeds a critical value φ c at the so-called Point J [1][2][3]. As a simplified model to understand the noncrystalline liquid-solid transition of various materials including granular materials, foams, colloids, emulsions, and glasses, jammed packings of frictionless spheres exhibit interesting but unusual critical behaviors at Point J [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].In addition to the volume fraction, shear stress σ and temperature T have been proposed as the other two control parameters to cause generalized jamming transition, i.e. yielding and glass transition [1]. A jammed solid remains rigid when subject to a shear stress smaller than the yield stress σ y , while it unjams and flows otherwise. It has been shown that the yield stress of the T = 0 jammed solids decreases with decreasing the volume fraction and vanishes at Point J [7,12,18,19]. This is different from the glass transition temperature at which a supercooled liquid is supposed to freeze into a glass, through the fact that in the T = 0 limit glass transition occurs at a volume fraction lower than φ c [20][21][22][23][24][25][26]. Therefore, Point J is more relevant to the volume fraction and shear stress than to the temperature. Jammed packings of frictionless spheres under applied shear stress thus serve as typical systems to study the criticality of Point J [7,8,12].In most of the previous simulations, the yield stress of a jammed solid has been defined as either the average shear stress of the quasi-static shear flow in which the shear stress is not a controllable parameter [18,19,27,28] or the critical shear stress extrapolated from nonequilibrium molecular dynamics simulations above which the system loses shear rigidity and flows forever [18,28]. In the potential energy landscape perspective, the yield stress corresponds to the critical shear stress above whic...

The anti-and positive correlations between X-ray photon index and Eddington-scaled X-ray luminosity were found in decay phase of X-ray binary outbursts and a sample of active galactic nuclei in former works. We further systematically investigate the evolution of X-ray spectral index, along the X-ray flux and Eddington ratio in eight outbursts of four black-hole X-ray binaries, where all selected outbursts have observational data from Rossi X-ray Timing Explorer in both rise and decay phases. In the initial rise phase, the X-ray spectral index is anti-correlated with the flux, and the X-ray spectrum quickly softens when the X-ray flux is approaching the peak value. In the decay phase, the X-ray photon index and the flux follow two different positive correlations, and they become anti-correlated again when the X-ray flux is below a critical value, where the anti-correlation part follow the same trend as that found in the initial rise phase. Compared with other X-ray binaries, GRO J1655-40 has an evident lower critical Eddington ratio for the anti-and positive transition, which suggests that its black-hole mass and distance are not well constrained or its intrinsic physic is different.

We find that unjammed packings of frictionless particles with rather weak attraction can always be driven into solidlike states by shear. The structure of shear-driven solids evolves continuously with packing fraction from gel-like to jamminglike, but is almost independent of the shear stress. In contrast, both the density of vibrational states (DOVS) and force network evolve progressively with the shear stress. There exists a packing fraction independent shear stress σ_{c}, at which the shear-driven solids are isostatic and have a flattened DOVS. Solidlike states induced by a shear stress greater than σ_{c} possess properties of marginally jammed solids and are thus strictly defined shear jammed states. Below σ_{c}, shear-driven solids with rather different structures are all under isostaticity and share common features in the DOVS and force network. Our study leads to a jamming phase diagram for weakly attractive particles, which reveals the significance of the shear stress in determining properties of shear-driven solids and the connections and distinctions between jamminglike and gel-like states.