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Energy dissipation around a propagating crack is the primary mechanism for the enhanced fracture toughness in viscoelastic solids. Such dissipation is spatially non-uniform and is highly coupled to the crack propagation process due to the history-dependent nature of viscoelasticity. We present an experimental approach to map the dissipation field during crack propagation in soft viscoelastic solid. Specifically, we track randomly distributed tracer particles to measure the evolving deformation field. The measured deformation field is then put into a nonlinear constitutive model to determine the dissipation field. Our methodology was used to investigate the deformation and dissipation fields around a propagating crack in a Polyampholyte (PA) hydrogel. The deformation field measurements allowed us to assess whether the commonly assumed translational invariance in viscoelastic fracture theories holds true in practical experiments. Furthermore, by combining the obtained deformation fields with a nonlinear viscoelastic model, we captured the complete history of the dissipation field during crack propagation. We found that dissipation occurred even at material points that are a few millimeters away from the crack tip. The mapped dissipation field also enabled the separate determination of the intrinsic and dissipative components of fracture toughness for the viscoelastic hydrogel. 

We demonstrate that contrastive representation learning is a computationally efficient and flexible method to incorporate physical constraints, especially those defined by equalities, in machine-learning-based density functional design.

 

Copula is a popular method for modeling the dependence among marginal distributions in multivariate censored data. As many copula models are available, it is essential to check if the chosen copula model fits the data well for analysis. Existing approaches to testing the fitness of copula models are mainly for complete or right-censored data. No formal goodness-of-fit (GOF) test exists for interval-censored or recurrent events data. We develop a general GOF test for copula-based survival models using the information ratio (IR) to address this research gap. It can be applied to any copula family with a parametric form, such as the frequently used Archimedean, Gaussian, and D-vine families. The test statistic is easy to calculate, and the test procedure is straightforward to implement. We establish the asymptotic properties of the test statistic. The simulation results show that the proposed test controls the type-I error well and achieves adequate power when the dependence strength is moderate to high. Finally, we apply our method to test various copula models in analyzing multiple real datasets. Our method consistently separates different copula models for all these datasets in terms of model fitness.

 

The differential reflectivity (Z_DR) column is a notable polarimetric signature related to updrafts in deep moist convection. In this study, pseudo–water vapor (q_υ) observations are retrieved from observedZ_DRcolumns under the assumption that humidity is saturated within the convection whereZ_DRcolumns are detected, and are then assimilated within the 3DVar framework. The impacts of assimilating pseudo-q_υobservations fromZ_DRcolumns on short-term severe weather prediction are first evaluated for a squall-line case. Radar data analysis indicates that theZ_DRcolumns are mainly located on the inflow side of the high-reflectivity region. Assimilation of the pseudo-q_υobservations leads to an enhancement ofq_υwithin the convection, while concurrently reducing humidity in no-rain areas. Sensitivity experiments indicate that a tuned smaller observation error and a shorter horizontal decorrelation scale are optimal for a better assimilation of pseudo-q_υfromZ_DRcolumns, resulting in more stable rain rates during short-term forecasts. Additionally, a 15-min cycling assimilation frequency yields the best performance, providing the most accurate reflectivity forecast in terms of both location and intensity. Analysis of thermodynamic fields reveal that assimilatingZ_DRcolumns provides more favorable initial conditions for sustaining convection, including sustainable moisture condition, a strong cold pool, and divergent winds near the surface, consequently enhancing reflectivity and precipitation. With the optimal configuration determined from the sensitivity tests, a quantitative evaluation further demonstrates that assimilating the pseudo-q_υobservations fromZ_DRcolumns using the 3DVar method can improve the 0–3-h reflectivity and accumulated precipitation predictions of convective storms.