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   https://doi.org/10.1175/JAS-D-19-0320.1  

   Chen, Jie; Chavas, Daniel R. (August 2020, Journal of the Atmospheric Sciences)

   Abstract Inland tropical cyclone (TC) impacts due to high winds and rainfall-induced flooding depend strongly on the evolution of the wind field and precipitation distribution after landfall. However, research has yet to test the detailed response of a mature TC and its hazards to changes in surface forcing in idealized settings. This work tests the transient responses of an idealized hurricane to instantaneous transitions in two key surface properties associated with landfall: roughening and drying. Simplified axisymmetric numerical modeling experiments are performed in which the surface drag coefficient and evaporative fraction are each systematically modified beneath a mature hurricane. Surface drying stabilizes the eyewall and consequently weakens the overturning circulation, thereby reducing inward angular momentum transport that slowly decays the wind field only within the inner core. In contrast, surface roughening initially (~12 h) rapidly weakens the entire low-level wind field and enhances the overturning circulation dynamically despite the concurrent thermodynamic stabilization of the eyewall; thereafter the storm gradually decays, similar to drying. As a result, total precipitation temporarily increases with roughening but uniformly decreases with drying. Storm size decreases monotonically and rapidly with surface roughening, whereas the radius of maximum wind can increase with moderate surface drying. Overall, this work provides a mechanistic foundation for understanding the inland evolution of real storms in nature. 

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2. Instantaneous Polarimetry With Zak-OTFS

   https://doi.org/10.1109/TRS.2025.3625812  

   Mehrotra, Nishant; Rao_Mattu, Sandesh; Calderbank, Robert (January 2025, IEEE Transactions on Radar Systems)
3. Instantaneous SED coding over a DMC

   https://doi.org/10.1109/ISIT45174.2021.9518087  

   Guo, Nian; Kostina, Victoria (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))
4. Instantaneous Fuel Consumption Estimation Using Smartphones

   https://doi.org/10.1109/VTCFall.2019.8891261  

   Shaw, Samuel; Hou, Yunfei; Zhong, Weida; Sun, Qingquan; Guan, Tong; Su, Lu (September 2019, 2019 IEEE 90th Vehicular Technology Conference (VTC2019-Fall))
5. Instantaneous everywhere-blowup of parabolic SPDEs

   https://doi.org/10.1007/s00440-024-01263-7  

   Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia (October 2024, Probability Theory and Related Fields)

   Abstract We consider the following stochastic heat equation$$\begin{aligned} \partial _t u(t,x) = \tfrac{1}{2} \partial ^2_x u(t,x) + b(u(t,x)) + \sigma (u(t,x)) {\dot{W}}(t,x), \end{aligned}$$ $\begin{array}{c}{\partial }_{t}u(t,x)=\frac{1}{2}{\partial }_x^{2}u(t,x)+b\left(u(t,x)\right)+\sigma \left(u(t,x)\right)\dot{W}(t,x),\end{array}$defined for$$(t,x)\in (0,\infty )\times {\mathbb {R}}$$ $(t,x)\in (0,\infty )\times R$, where$${\dot{W}}$$ $\dot{W}$denotes space-time white noise. The function$$\sigma $$ $\sigma$is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the functionbis assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition$$\begin{aligned} \int _1^\infty \frac{\textrm{d}y}{b(y)}<\infty \end{aligned}$$ $\begin{array}{c}{\int }_1^{\infty }\frac{\text{d}y}{b\left(y\right)}<\infty \end{array}$implies that the solution almost surely blows up everywhere and instantaneously, In other words, the Osgood condition ensures that$$\textrm{P}\{ u(t,x)=\infty \quad \hbox { for all } t>0 \hbox { and } x\in {\mathbb {R}}\}=1.$$ $\text{P}\left\{u\right(t,x)=\infty \text{for all}t>0\text{and}x\in R\}=1.$The main ingredients of the proof involve a hitting-time bound for a class of differential inequalities (Remark 3.3), and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincaré inequalities that were developed in Chen et al. (Electron J Probab 26:1–37, 2021, J Funct Anal 282(2):109290, 2022). 

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