Cellular Models of Nonlinear Flux Flow, Vortex Rivers, and Noise

[00:74613]许多失去平衡的颗粒系统表现出非线性输运，其中动力学是间歇性的，或被雪崩打断。这些崩溃事件可能很小，或者是灾难性的（系统范围内的），或者雪崩可能表现出缩放行为。了解颗粒物体雪崩的动力学对包括磁聚变、超导和互联网流量在内的各种学科具有基础的理论和技术重要性。描述雪崩现象的许多理论努力都集中在离散的细胞模型的行为上，如沙堆模型，这些模型自然地结合了物体的粒度和破裂过程的阈值性质。这些模型通常具有在数值上易于处理的额外好处，因此可以在一定长度和时间尺度范围内研究它们的行为，这对于检测缩放是否存在以及确定通用性是必要的。然而，到目前为止，将这些简单的模型与真实的物理系统联系起来，以评估它们的准确性、通用性和预测能力，收效甚微。该基金旨在通过构建离散的细胞模型来研究II型超导体驱动的涡流的非线性传输特性，并与实验建立具体的、可量化的联系，从而解决这一基本问题。众所周知，涡旋的排斥性相互作用与无序引起的吸引钉住相结合，导致超导体中出现一堆量子化的涡旋，使人联想到一堆沙子。因此，人们很自然地要问，沙桩类型的元胞模型能否准确地描述旋涡桩的大尺度行为。此外，涡流动力学提供了一个理想的测试平台，因为大量的实验工作表征了内部磁场剖面、使用微霍尔探头的内部雪崩分布、纵向和横向噪声测量、电流-电压特性、热激活磁流变动力学、磁松弛、大电流下的动态跃迁等。这项研究是对在同一系统上进行的分子动力学模拟的补充。这里产生的结果可以定量地与使用MD获得的有价值的结果进行比较，但这里不寻求微观上真实的模型；相反，将开发粗粒度的离散模型来尝试捕获相同的大规模行为。从实际的角度来看，这里使用的模型可以在更大的长度和时间尺度上进行数值研究，从而可以使用有限尺寸的缩放方法，并将其分类为普遍性类。从理论的角度来看，如果这种细胞模型能够被证明是准确的，它们就提供了与漩涡动力学相关的现象的更一般的描述，这可能在其他系统中观察到，并导致更好地理解与雪崩相关的非线性传输现象。这项研究涉及休斯顿大学和伦敦帝国理工学院的合作。许多失去平衡的颗粒系统表现出非线性输运，其中动力学是间歇性的，或被雪崩打断。这些崩溃事件可能很小，或者是灾难性的（系统范围内的），或者雪崩可能表现出缩放行为。了解颗粒物体雪崩的动力学对包括磁聚变、超导和互联网流量在内的各种学科具有基础的理论和技术重要性。描述雪崩现象的许多理论努力都集中在离散的细胞模型的行为上，如沙堆模型，这些模型自然地结合了物体的粒度和破裂过程的阈值性质。这些模型通常具有在数值上易于处理的额外好处，因此可以在一定长度和时间尺度范围内研究它们的行为，这对于检测缩放是否存在以及确定通用性是必要的。然而，到目前为止，将这些简单的模型与真实的物理系统联系起来，以评估它们的准确性、通用性和预测能力，收效甚微。该基金旨在通过构建离散的细胞模型来研究II型超导体驱动的涡流的非线性传输特性，并与实验建立具体的、可量化的联系，从而解决这一基本问题。众所周知，涡旋的排斥性相互作用与无序引起的吸引钉住相结合，导致超导体中出现一堆量子化的涡旋，使人联想到一堆沙子。因此，人们很自然地要问，沙桩类型的元胞模型能否准确地描述旋涡桩的大尺度行为。此外，涡流动力学提供了一个理想的测试平台，因为大量的实验工作表征了内部磁场剖面、使用微霍尔探头的内部雪崩分布、纵向和横向噪声测量、电流-电压特性、热激活磁流变动力学、磁松弛、大电流下的动态跃迁等。这项研究是对在同一系统上进行的分子动力学模拟的补充。这里产生的结果可以定量地与使用MD获得的有价值的结果进行比较，但这里不寻求微观上真实的模型；相反，将开发粗粒度的离散模型来尝试捕获相同的大规模行为。从实际的角度来看，这里使用的模型可以在更大的长度和时间尺度上进行数值研究，从而可以使用有限尺寸的缩放方法，并将其分类为普遍性类。从理论的角度来看，如果这种细胞模型能够被证明是准确的，它们就提供了与漩涡动力学相关的现象的更一般的描述，这可能在其他系统中观察到，并导致更好地理解与雪崩相关的非线性传输现象。这项研究涉及休斯顿大学和伦敦帝国理工学院的合作

0074613BasslerMany granular systems that are driven out of equilibrium exhibit nonlinear transport, where the dynamics is intermittent, or punctuated by avalanches. These breakdown events can be small, or catastrophic (system-wide), or the avalanches can exhibit scaling behavior. Understanding the dynamics of avalanches of granular objects is of fundamental theoretical and technological importance to a variety of subjects including magnetic fusion, superconductivity, and internet traffic. Much of the theoretical effort to describe avalanche phenomena has focussed on the behavior of discrete, cellular models, such as sandpile models, which naturally incorporate both the granularity of the objects and the threshold nature of the breakdown process. These models often have the added benefit of being numerically tractable, so that it is possible to study their behavior over a range of length and time scales, which is necessary to detect the presence or absence of scaling, and to determine universality. However, there has been little success, thus far, connecting those simple models with real physical systems to assess their accuracy, generality, and predictive power. This grant aims to address this fundamental problem by constructing discrete, cellular models to study the nonlinear transport properties of vortices driven through a type II superconductor, and making specific, quantifiable connection with experiments. As is well known, the repulsive interaction of vortices combined with attractive pinning due to disorder leads to a pile of quantized vortices in the superconductor, reminiscent of a pile of sand. So it is natural to ask if a sandpile type of cellular model can accurately describe the large scale behavior of the vortex pile. Furthermore, vortex dynamics provides an ideal test bed because of the large body of experimental work characterizing the internal magnetic field profile, the distribution of internal avalanches using micro-Hall probes, longitudinal and traverse noise measurements, current-voltage characteristics, thermally activated flux creep dynamics, magnetic relaxation, dynamical transitions at high currents, etc. This research is complementary to molecular dynamics simulations that have been performed on this same system. The results generated here can be compared quantitatively with the valuable results obtained using MD, but a microscopically realistic model is not sought here; instead, coarse grained, discrete models will be developed to try to capture the same large scale behavior. From a practical viewpoint, the models used here can be studied numerically at significantly larger length and time scales, enabling the use of finite size scaling methods, and the classification into universality classes. From a theoretical viewpoint, if such cellular models can be shown to be accurate, they provide a more general description of the phenomena associated with vortex dynamics, which can possibly be observed in other systems, and lead to a better understanding of nonlinear transport phenomena associated with avalanches.This research involves collaborations between the University of Houston and Imperial College, London.%%%Many granular systems that are driven out of equilibrium exhibit nonlinear transport, where the dynamics is intermittent, or punctuated by avalanches. These breakdown events can be small, or catastrophic (system-wide), or the avalanches can exhibit scaling behavior. Understanding the dynamics of avalanches of granular objects is of fundamental theoretical and technological importance to a variety of subjects including magnetic fusion, superconductivity, and internet traffic. Much of the theoretical effort to describe avalanche phenomena has focussed on the behavior of discrete, cellular models, such as sandpile models, which naturally incorporate both the granularity of the objects and the threshold nature of the breakdown process. These models often have the added benefit of being numerically tractable, so that it is possible to study their behavior over a range of length and time scales, which is necessary to detect the presence or absence of scaling, and to determine universality. However, there has been little success, thus far, connecting those simple models with real physical systems to assess their accuracy, generality, and predictive power. This grant aims to address this fundamental problem by constructing discrete, cellular models to study the nonlinear transport properties of vortices driven through a type II superconductor, and making specific, quantifiable connection with experiments. As is well known, the repulsive interaction of vortices combined with attractive pinning due to disorder leads to a pile of quantized vortices in the superconductor, reminiscent of a pile of sand. So it is natural to ask if a sandpile type of cellular model can accurately describe the large scale behavior of the vortex pile. Furthermore, vortex dynamics provides an ideal test bed because of the large body of experimental work characterizing the internal magnetic field profile, the distribution of internal avalanches using micro-Hall probes, longitudinal and traverse noise measurements, current-voltage characteristics, thermally activated flux creep dynamics, magnetic relaxation, dynamical transitions at high currents, etc. This research is complementary to molecular dynamics simulations that have been performed on this same system. The results generated here can be compared quantitatively with the valuable results obtained using MD, but a microscopically realistic model is not sought here; instead, coarse grained, discrete models will be developed to try to capture the same large scale behavior. From a practical viewpoint, the models used here can be studied numerically at significantly larger length and time scales, enabling the use of finite size scaling methods, and the classification into universality classes. From a theoretical viewpoint, if such cellular models can be shown to be accurate, they provide a more general description of the phenomena associated with vortex dynamics, which can possibly be observed in other systems, and lead to a better understanding of nonlinear transport phenomena associated with avalanches.This research involves collaborations between the University of Houston and Imperial College, London.***