Karl Kuhn- Basic Physics A self teaching guide

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Kenny Weirich

Basic Physics Books

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Karl Kuhn- Basic Physics A self teaching guide

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In this session, we explore three sensory strategies for supporting dysregulated children. These ideas are helpful for supporting autistic children, those with ADHD and many others. You can access a video walkthrough and other resources here on my blog: https://www.pookyknightsmith.com/bitesize-cpdsensory-strategies-for-dysregulated-children -- For more information about my speaking and training work, visit: https://www.pookyknightsmith.com/speaking/

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The Walking Dead comic book volume 1, Days Gone Bye The Walking Dead centers around Rick Grimes, a former police officer who was shot in the line of duty and wakes up from a coma after the world has succumbed to the zombie plague. Dazed from months in the hospital, and confused as to why he can't find anyone alive, he makes his way home only to find his wife and son missing. He packs up supplies from his station and travels to Atlanta in search of his family after hearing the cities would be safe (heard from Morgan and Duane Jones, his previous neighbors). Arriving in the city on horseback, Rick is overcome by a horde of zombies and narrowly escapes death with the aid of another survivor named Glenn, who has been scavenging the city for supplies. Glenn takes Rick back to his camp just outside of town where Rick's wife Lori and son Carl happen to be living, alive and well. His partner and best friend Shane had taken Lori and Carl to the outskirts of Atlanta to wait for rescue by the US Government. There they found a small group of survivors.

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Poster to be presented at Stochastic Numerics and Statistical Learning: Theory and Applications Workshop 2024, Kaust, Saudi Arabia, https://cemse.kaust.edu.sa/stochnum/events/event/snsl-workshop-2024. In this work we have considered a setting that mimics the Henry problem \cite{Simpson2003,Simpson04_Henry}, modeling seawater intrusion into a 2D coastal aquifer. The pure water recharge from the ``land side'' resists the salinisation of the aquifer due to the influx of saline water through the ``sea side'', thereby achieving some equilibrium in the salt concentration. In our setting, following \cite{GRILLO2010}, we consider a fracture on the sea side that significantly increases the permeability of the porous medium. The flow and transport essentially depend on the geological parameters of the porous medium, including the fracture. We investigated the effects of various uncertainties on saltwater intrusion. We assumed uncertainties in the fracture width, the porosity of the bulk medium, its permeability and the pure water recharge from the land side. The porosity and permeability were modeled by random fields, the recharge by a random but periodic intensity and the thickness by a random variable. We calculated the mean and variance of the salt mass fraction, which is also uncertain. The main question we investigated in this work was how well the MLMC method can be used to compute statistics of different QoIs. We found that the answer depends on the choice of the QoI. First, not every QoI requires a hierarchy of meshes and MLMC. Second, MLMC requires stable convergence rates for $\EXP{g_{\ell} - g_{\ell-1}}$ and $\Var{g_{\ell} - g_{\ell-1}}$. These rates should be independent of $\ell$. If these convergence rates vary for different $\ell$, then it will be hard to estimate $L$ and $m_{\ell}$, and MLMC will either not work or be suboptimal. We were not able to get stable convergence rates for all levels $\ell=1,\ldots,5$ when the QoI was an integral as in \eqref{eq:integral_box}. We found that for $\ell=1,\ldots 4$ and $\ell=5$ the rate $\alpha$ was different. Further investigation is needed to find the reason for this. Another difficulty is the dependence on time, i.e. the number of levels $L$ and the number of sums $m_{\ell}$ depend on $t$. At the beginning the variability is small, then it increases, and after the process of mixing salt and fresh water has stopped, the variance decreases again. The number of random samples required at each level was estimated by calculating the decay of the variances and the computational cost for each level. These estimates depend on the minimisation function in the MLMC algorithm. To achieve the efficiency of the MLMC approach presented in this work, it is essential that the complexity of the numerical solution of each random realisation is proportional to the number of grid vertices on the grid levels.

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