Integral-type operators from Hardy space to Bloch space on the upper half-plane

The boundedness of compactness of integral-type operators from Hardy space to Bloch space on the upper half-plane $\Pi_+=\{z\in\mathbb{C}:Imz>0\}$ are characterized.Comment: 8 page

Structural signature of jamming transition in thermal amorphous systems

In thermal amorphous systems, the first peak of the pair correlation function $g(r)$ shows a maximum height $g_1^{\rm max}$ at a volume fraction $\phi=\phi_v$ that increases with the temperature. $g_1^{\rm max}$ diverges at the T=0 jamming transition at $\phi=\phi_c$. Molecular dynamics simulations show that some typical quantities, such as the pressure, bulk modulus, shear modulus, and boson peak frequency that behave power law scalings with $\phi-\phi_c$ in marginally jammed solids at T=0, all show scalings with $\phi-\phi_c$ when $\phi > \phi_v$, while the scalings break down when $\phi < \phi_v$. The presence of $g_1^{\rm max}$ is thus not only a thermal vestige of the T=0 jamming transition, but more importantly the structural signature of the jamming transition.Comment: This paper has been withdrawn by the author and replaced by the most recent paper arxiv:1112.242

Critical scalings and jamming in thermal colloidal systems

During the jamming of thermal colloids, the first peak of the pair distribution function shows a maximum height $g_1^{\rm max}$. We find that $g_1^{\rm max}$ is accompanied by significant change of material properties and thus signifies the transition from unjammed to jammed glasses. The scaling laws at $g_1^{\rm max}$ lead to scaling collapse of structural and thermodynamic quantities, indicating the criticality of the T=0 jamming transition. The physical significance of $g_1^{\rm max}$ is highlighted by its coincidence with the equality of the kinetic and potential energy and the maximum fluctuation of the coordination number. In jammed glasses, we find the strong coupling between the isostaticity and flattening of the density of vibrational states at the isostatic temperature scaled well with the compression.Comment: 5 pages, 6 figure

Probing the glass transition from structural and vibrational properties of zero-temperature glasses

We find that the density dependence of the glass transition temperature of Lennard-Jones (LJ) and Weeks-Chandler-Andersen (WCA) systems can be predicted from properties of the zero-temperature ($T=0$) glasses. Below a crossover density $\rho_s$, LJ and WCA glasses show different structures, leading to different vibrational properties and consequently making LJ glasses more stable with higher glass transition temperatures than WCA ones. Above $\rho_s$, structural and vibrational quantities of the $T=0$ glasses show scaling collapse. From scaling relations and dimensional analysis, we predict a density scaling of the glass transition temperature, in excellent agreement with simulation results. We also propose an empirical expression of the glass transition temperature using structural and vibrational properties of the $T=0$ glasses, which works well over a wide range of densities.Comment: 8 pages, 9 figure

Structural heterogeneity and its role in determining properties of disordered solids

We construct a new order parameter from the normal modes of vibration, based on the consideration of energy equipartition, to quantify the structural heterogeneity in disordered solids. The order parameter exhibits strong spatial correlations with low-temperature single particle dynamics and local structural entropy. To characterize the role of particles with the most defective local structures identified by the order parameter, we pin them and study how properties of disordered solids respond to the pinning. It turns out that these particles are responsible to the quasilocalized low-frequency vibration, instability, softening, and nonaffinity of disordered solids.Comment: 5 pages, 4 figure

On the Grain-Modified Magnetic Diffusivities in Protoplanetary Disks

Weakly ionized protoplanetary disks (PPDs) are subject to non-ideal-magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect and ambipolar diffusion (AD), and the resulting magnetic diffusivities ($\eta_O, \eta_H$ and $\eta_A$) largely control the disk gas dynamics. The presence of grains not only strongly reduces disk ionization fraction, but also modify the scalings of $\eta_H$ and $\eta_A$ with magnetic field strength. We derive analytically asymptotic expressions of $\eta_H$ and $\eta_A$ in both strong and weak field limits and show that towards strong field, $\eta_H$ can change sign (at a threshold field strength $B_{\rm th}$), mimicking a flip of field polarity, and AD is substantially reduced. Applying to PPDs, we find that when small $\sim0.1$ ($0.01$)$\mu$m grains are sufficiently abundant [mass ratio $\sim0.01$ ($10^{-4}$)], $\eta_H$ can change sign up to $\sim2-3$ scale heights above midplane at modest field strength (plasma $\beta\sim100$) over a wide range of disk radii. Reduction of AD is also substantial towards the AD dominated outer disk and may activate the magneto-rotational instability. We further perform local non-ideal MHD simulations of the inner disk (within 10 AU) and show that with sufficiently abundant small grains, magnetic field amplification due to the Hall-shear instability saturates at very low level near the threshold field strength $B_{\rm th}$. Together with previous studies, we conclude by discussing the grain-abundance-dependent phenomenology of PPD gas dynamics.Comment: 12 pages, 6 figures. submitted to Ap

Understanding the Low-Frequency Modes in Disordered Systems at Single-Particle Level

Normal modes provide a fundamental basis for understanding crucial properties of solids, such as the thermal conductivity, the heat capacity and the sound propagation. While the normal modes are excellently described by plane waves in crystals, they are far less understood in disordered systems, due to the great difficulties in characterizing the heterogeneous vibrational behaviors. Using charged colloids with long-range repulsion, we successfully make different disordered systems without any contact friction, whose normal modes can be visualized at single-particle level. In these systems, we directly tackle the long-time outstanding puzzle in condensed matter physics: the microscopic origin of the low-frequency modes in disordered systems. For the first time, we experimentally clarify that the low-frequency modes are caused by the collective resonance of relatively disordered particles (or soft structures) coupled with long-wavelength transverse excitations, settling this puzzle at single-particle level. Next to these low-frequency modes in the density of states, we also observe a plateau due to isostaticity, verifying the fundamental prediction of jamming model. Moreover, we reveal the intrinsic correlation between the low-frequency modes and the real dynamics, which may lead to a universal mechanism for aging, melting and yielding.Comment: 14 pages, 4 figure

Signatures of shear thinning-thickening transition in dense athermal shear flows

In non-equilibrium molecular dynamics simulations of dense athermal shear flows, we observe the transition from shear thinning to shear thickening at a crossover shear rate $\dot\gamma_c$. Shear thickening occurs when $\frac{{\rm d (ln} T_g)}{{\rm d (ln}\dot\gamma)}>2$ with $T_g$ the granular temperature. At the transition, the pair distribution function shows the strongest anisotropy. Meanwhile, the dynamics undergo apparent changes, signified by distinct scaling behaviors of the mean squared displacement and relaxation time on both sides of $\dot\gamma_c$. These features serve as robust signatures of the shear thinning-thickening transition.Comment: 5 pages, 3 figure

Jamming of packings of frictionless particles with and without shear

By minimizing the enthalpy of packings of frictionless particles, we obtain jammed solids at desired pressures and hence investigate the jamming transition with and without shear. Typical scaling relations of the jamming transition are recovered in both cases. In contrast to systems without shear, shear-driven jamming transition occurs at a higher packing fraction and the jammed solids are more rigid with an anisotropic force network. Furthermore, by introducing the macro-friction coefficient, we propose an explanation of the packing fraction gap between sheared and non-sheared systems at fixed pressure.Comment: 6 pages, 5 figure

Squeezed back-to-back correlations of bosons with nonzero widths in relativistic heavy-ion collisions

We derive the formulas for calculating the squeezed back-to-back correlation (SBBC) between a boson and antiboson with nonzero width produced in relativistic heavy-ion collisions. The SBBCs of $D^0$ and $\phi$ mesons with finite in-medium widths are studied. We find that the finite width can change the pattern of the SBBC function of $D^0{\bar D}^0$ with respect to mass. However, the SBBC function of $\phi\phi$ is insensitive to the width. In the high-particle-momentum region, the SBBC function of $\phi\phi$ increases with particle momentum rapidly and can exceed that of $D^0{\bar D}^0$ whether the width is nonzero or not.Comment: 5 pages, 2 figures, accepted for publication in Phys. Rev.