Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model

We obtain an exact solution for the motion of a particle driven by a spring in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. Many experiments on quasi-static driving of elastic interfaces (Barkhausen noise in magnets, earthquake statistics, shear dynamics of granular matter) exhibit the same universal behavior as this model. It also appears as a limit in the field theory of elastic manifolds. Here we discuss predictions of the ABBM model for monotonous, but otherwise arbitrary, time-dependent driving. Our main result is an explicit formula for the generating functional of particle velocities and positions. We apply this to derive the particle-velocity distribution following a quench in the driving velocity. We also obtain the joint avalanche size and duration distribution and the mean avalanche shape following a jump in the position of the confining spring. Such non-stationary driving is easy to realize in experiments, and provides a way to test the ABBM model beyond the stationary, quasi-static regime. We study extensions to two elastically coupled layers, and to an elastic interface of internal dimension d, in the Brownian force landscape. The effective action of the field theory is equal to the action, up to 1-loop corrections obtained exactly from a functional determinant. This provides a connection to renormalization-group methods.Comment: 18 pages, 3 figure

Prognostic Value of Different CMR-Based Techniques to Assess Left Ventricular Myocardial Strain in Takotsubo Syndrome

Cardiac magnetic resonance (CMR)-derived left ventricular (LV) global longitudinal strain (GLS) provides incremental prognostic information on various cardiovascular diseases but has not yet been investigated comprehensively in patients with Takotsubo syndrome (TS). This study evaluated the prognostic value of feature tracking (FT) GLS, tissue tracking (TT) GLS, and fast manual long axis strain (LAS) in 147 patients with TS, who underwent CMR at a median of 2 days after admission. Long-term mortality was assessed 3 years after the acute event. In contrast to LV ejection fraction and tissue characteristics, impaired FT-GLS, TT-GLS and fast manual LAS were associated with adverse outcome. The best cutoff points for the prediction of long-term mortality were similar with all three approaches: FT-GLS −11.28%, TT-GLS −11.45%, and fast manual LAS −10.86%. Long-term mortality rates were significantly higher in patients with FT-GLS > −11.28% (25.0% versus 9.8%; p = 0.029), TT-GLS > −11.45% (20.0% versus 5.4%; p = 0.016), and LAS > −10.86% (23.3% versus 6.6%; p = 0.014). However, in multivariable analysis, diabetes mellitus (p = 0.001), atrial fibrillation (p = 0.001), malignancy (p = 0.006), and physical triggers (p = 0.006) outperformed measures of myocardial strain and emerged as the strongest, independent predictors of long-term mortality in TS. In conclusion, CMR-based longitudinal strain provides valuable prognostic information in patients with TS, regardless of the utilized technique of assessment. Long-term mortality, however, is mainly determined by comorbidities