单轴随机介质中涡旋线的脱钉和流动
Depinning and flow of a vortex line in an uniaxial random medium
摘要：
本文用数值方法和解析方法研究了单向弹性弦在三维无序介质中的动力学行为。在准静态极限下，弦在驱动方向上是超粗糙的，具有粗糙度指数$ζ_{\parallel} = 1.25\pm 0.01$、动态指数$z_{\parallel}= 1.43 \pm 0.01$、相关长度指数$ν= 1.33 \pm 0.02$、去钉扎指数$β= 0.24\pm 0.01$和雪崩大小指数$τ_{\parallel} = 1.09 \pm 0.03$。在横向上，我们发现$ζ_{\perp} = 0.5 \pm 0.01$、$z_{\perp} = 2.27 \pm 0.05$和$τ_{\perp} =1.17\pm 0.06$。我们表明，横向波动不改变临界指数的驱动方向，所预测的平面近似（PA）在1996年提出的Ertas和Kardar（EK）。我们检查PA的力-力相关，比较功能重整化群和模拟。随机键（RB）和随机场（RF）无序都产生一个普适类，与二维随机介质中的弹性弦的普适类无法区分。当满足EK的$z_{\perp}=z_{\parallel}+1/ν$和$ν=1/(2-ζ_{\parallel})$时，横向运动是布朗运动，具有由向前运动局部设置的时钟。这意味着$ζ_\perp = (2-d)/2$，不同于EK。在小的驱动速度下，局部平行位移的分布具有负偏度，而在横向上，它是高斯分布。对于大尺度，系统可以用各向异性的有效温度来描述。在快流区，两个方向上的局部位移分布变为高斯分布，有效温度对于RB为$T^{\perp}_{\tt eff}\sim 1/v$和$T^{\parallel}_{\tt eff}\sim 1/v^3$，对于RF为$T^{\perp}_{\tt eff} \approx T^{\parallel}_{\tt eff} \sim 1/v$。
英文摘要：
We study numerically and analytically the dynamics of a single directed elastic string driven through a 3-dimensional disordered medium. In the quasistatic limit the string is super-rough in the driving direction, with roughness exponent $ζ_{\parallel} = 1.25\pm 0.01$, dynamic exponent $z_{\parallel}= 1.43 \pm 0.01$, correlation-length exponent $ν= 1.33 \pm 0.02$, depinning exponent $β= 0.24\pm 0.01$, and avalanche-size exponent $τ_{\parallel} = 1.09 \pm 0.03$. In the transverse direction we find $ζ_{\perp} = 0.5 \pm 0.01$, $z_{\perp} = 2.27 \pm 0.05$, and $τ_{\perp} =1.17\pm 0.06$. We show that transverse fluctuations do not alter the critical exponents in the driving direction, as predicted by the planar approximation (PA) proposed in 1996 by Ertas and Kardar (EK). We check the PA for the force-force correlator, comparing to the functional renormalization group and simulations. Both Random-Bond (RB) and Random-Field (RF) disorder yield a single universality class, indistinguishable from the one of an elastic string in a 2-dimensional random medium. While $z_{\perp}=z_{\parallel}+1/ν$ and $ν=1/(2-ζ_{\parallel})$ of EK are satisfied, the transversal movement is that of a Brownian, with a clock set locally by the forward movement. This implies $ζ_\perp = (2-d)/2$, distinct from EK. At small driving velocities the distribution of local parallel displacements has a negative skewness, while in the transverse direction it is a Gaussian. For large scales, the system can be described by anisotropic effective temperatures. In the fast-flow regime the local displacement distributions become Gaussian in both directions and the effective temperatures vanish as $T^{\perp}_{\tt eff}\sim 1/v$ and $T^{\parallel}_{\tt eff}\sim 1/v^3$ for RB and as $T^{\perp}_{\tt eff} \approx T^{\parallel}_{\tt eff} \sim 1/v$ for RF.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
