论文标题
部分可观测时空混沌系统的无模型预测
Anomalous evolution of the magnetocaloric effect in dilute triangular Ising antiferromagnets $Tb_{1-x}Y_{x}(HCO_{2})_{3}$
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
We investigate the effects of diamagnetic doping in the solid-solution series $Tb_{1-x}Y_{x}(HCO_{2})_{3}$, in which the parent $Tb(HCO_{2})_{3}$ phase has previously been shown to host a combination of frustrated and quasi-1D physics, giving rise to a triangular Ising antiferromagnetic ground state that lacks long range 3D order. Heat capacity measurements show three key features: (i) a low temperature Schottky anomaly is observed, which is constant as a function of x; (ii) the transition temperature and associated entropy change are both surprisingly robust to diamagnetic doping; and (iii) an additional contribution at T < 0.4 K appears with increasing x. The origin of this unusual behaviour is rationalised in terms of the fragmentation of quasi-1D spin chains by the diamagnetic $Y^{3+}$ dopant. Magnetocaloric measurements show a nonlinear dependence on x. The mass-weighted magnetocaloric entropy decreases across the series from the promising values in $Tb(HCO_{2})_{3}$; however, the magnetocaloric entropy per magnetic $Tb^{3+}$ ion first decreases then increases with increasing x. Our results establish $Tb_{1-x}Y_{x}(HCO_{2})_{3}$ as a model system in which to explore the functional ramifications of dilution in a low-dimensional magnet.