arXiv subjects

Lei-Han Tang

Publications and source records attributed to Lei-Han Tang.

40 records · Page 3Linked to original sources

arXiv1996

Driven Interface Depinning in a Disordered Medium

The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity $v$, which increases as $v \sim (F-F_c)^θ$ for driving forces $F$ close to its threshold value $F_c$. We consider a Langevin-type equation which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical exponents characterizing the depinning transition are obtained to the first order in $ε=4-D>0$, where $D$ is the interface dimension. The main results were published earlier [T. Nattermann et al., J. Phys. II France {\bf 2} (1992) 1483]. Here, we present details of the perturbative calculation and of the derivation of the functional flow equation for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold $F_c$, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For $ε=1$ the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions $ε= 2,3$ are larger and suggest that the roughness exponent is somewhat larger than the value $ζ= ε/ 3$ of an interface in thermal equilibrium.

cond-mat↗

arXiv1996

Vortex statistics in a disordered two-dimensional XY model

The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a number of other bond-disordered 2D systems. The vortex Hamiltonian is that of a Coulomb gas in a background of quenched random dipoles, which is capable of forming either a dielectric insulator or a plasma. We confirm a recent suggestion by Nattermann, Scheidl, Korshunov, and Li [J. Phys. I (France) {\bf 5}, 565 (1995)], and by Cha and Fertig [Phys. Rev. Lett. {\bf 74}, 4867 (1995)] that, when the variance $σ$ of random phase shifts is smaller than a critical value $σ_c$, the system is in a phase with quasi-long-range order at low temperatures, without a reentrance transition. This conclusion is reached through a nearly exact calculation of the single-vortex free energy, and a Kosterlitz-type renormalization group analysis of screening and random polarization effects from vortex-antivortex pairs. The critical strength of disorder $σ_c$ is found not to be universal, but generally lies in the range $0<σ_c<π/8$. Argument is presented to suggest that the system at $σ>σ_c$ does not possess long-range glassy order at any finite temperature. In the ordered phase, vortex pairs undergo a series of spatial and angular localization processes as the temperature is lowered. This behavior, which is common to many glass-forming systems, can be quantified through approximate mappings to the random energy model and to the directed polymer on the Cayley tree. Various critical properties at the order-disorder transition are calculated.

cond-mat↗

arXiv1994

Capillary Rise in Tubes with Sharp Grooves

Liquid in grooved capillaries, made by e.g. inserting a plate in a cylindrical tube, exhibits unusual spreading and flow properties. One example is capillary rise, where a long, upward tongue on top of the usual meniscus has been observed along the groove. We attribute the underlying mechanism to a thermodynamic instability against spreading for a (partial or complete wetting) liquid in a sharp groove whose opening angle $α$ is less than a critical value $α_c=π-2θ$. The equilibrium shape of the tongue is determined analytically. The dynamics of liquid rising is studied in the viscous regime. When the diameter of the tube is smaller than the capillary length, the center part of the meniscus rises with time $t$ following a $t^{1/2}$-law, while the tongue is truncated at a height which grows following a $t^{1/3}$-law. Sharp groove also facilitates release of gas bubbles trapped inside a capillary under the action of gravity.

cond-mat↗

arXiv1993

Avalanches and Correlations in Driven Interface Depinning

We study the critical behavior of a driven interface in a medium with random pinning forces by analyzing spatial and temporal correlations in a lattice model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)]. The static and dynamic behavior of the model is related to the properties of directed percolation. We show that, due to the interplay of local and global growth rules, the usual method of dynamical scaling has to be modified. We separate the local from the global part of the dynamics by defining a train of causal growth events, or "avalanche", which can be ascribed a well-defined dynamical exponent $z_{loc} = 1 + ζ_c \simeq 1.63$ where $ζ_c$ is the roughness exponent of the interface. We observe that the avalanche size distribution obeys a power-law decay with an exponent $κ\simeq 1.25$.

cond-mat↗