A True Love Story

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Peter Chang

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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.

$Poster_density_driven_with_fracture_MLMC.pdf$ $Poster_density_driven_with_fracture_MLMC.pdf$

Poster_density_driven_with_fracture_MLMC.pdf

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This PowerPoint presentation provides an in-depth analysis of "The Ball Poem" by John Berryman. It covers the poem's themes, literary devices, and the author's background, offering a comprehensive understanding of the text. Ideal for students, teachers, and poetry enthusiasts, this presentation delves into the emotional and philosophical dimensions of the poem, highlighting its relevance to the human experience of loss and resilience. Discussion questions and personal response prompts are included to encourage further engagement and reflection.

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The Department of Emergency Medicine at Carolinas Medical Center is passionate about education! Dr. Michael Gibbs is a world-renowned clinician and educator and has helped guide numerous young clinicians on the long path of Mastery of Emergency Medical Care. With his oversight, the EMGuideWire team aim to help augment our understanding of emergent imaging. You can follow along with the EMGuideWire.com team as they post these educational, self-guided radiology slides or you can also use this section to learn more in-depth about specific conditions and diseases. This Radiology Reading Room pertains to Sternal Fractures and Dislocations and is brought to you by Carrie Bissell, MD, Aaron Fox, MD, Kendrick Lim, MD, Stephanie Jensen, MD, and Olivia Rice, MD. It is has special guest editor: Sean Dieffenbaugher, MD and Laurence Kempton, MD

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$Poster_density_driven_with_fracture_MLMC.pdf$ $Poster_density_driven_with_fracture_MLMC.pdf$

Poster_density_driven_with_fracture_MLMC.pdf

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ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...

A True Love Story

1. A True Love Story

2. He is Sin

3. He was through the web --

4. To look for

5. one of the girls

6. who is suitable for him.

7. And he met her.

8. She is ---

9. beautiful

10. understanding

11. and gentle.

12. They always chat.

13. As time goes by ---

14. They fell in love.

15. Sin was very ----

16. Caring----

17.

18. One day ----

19. She left him.

20. He didn’t know what was the problem.

21.

22. He was sad.

23. After a few months----

24. He got a phone call.

25. He was very shocked to hear ---

26. She was dead.

27. It was cancer.

28. Took away her life .

29. He was very sad.

30. And he left the city.

31. Because there he had many sad memories.

32. The end

A True Love Story

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A True Love Story