<> Thinking and understanding

<> Problem center : Simulation modeling of sandcastle survival time

<> Topic requirements :

Basic sandcastle model .
First, models with different 3D shapes need to satisfy the same basic conditions ① Distance from water ② Sand type ③ Water sediment ratio .

Details of the problem : You need to define the distance between the water area and the sandcastle ( Hereinafter referred to as water Castle distance ), The standard of sandcastle destruction , The shape type of sand castle , Quantitative influence of water wave scouring ( At the same time, the interaction of each scour on the last scour is considered ), Maximum stress obtained by different water and sediment combinations ( Professional foundation of civil engineering is required ) etc. , The nonlinear model of sandcastle state and the above variables is constructed , Each variable is a function of time .

Optimization model

The second question is relatively simple , Simple questions should be well done . Control the distance between water tanks , sunshine , Wind erosion and other related factors , The sand castle of each shape is optimized , The specific range of optimum water sediment ratio , Note that these variables may be a function of the water sediment ratio .


Sand castle model considering the influence of rain . Construction of impact model of rainwater impact , Also established as a function of time , Add it to the model of question 1 , To evaluate the life length of sandbars with different three-dimensional shapes before and after considering this factor .( The cone may be the best structure in this case , In the problem, one is not the best )

Then think about other ideas ! Combination of different shapes , Add a wall to the sandcastle , Drainage ditch … It is suggested that students who have no beach experience should have a brainstorming session . There is no imperfect model to improve the specific model , Make sandcastle life cycle longer .


Write a copy 1-2 Page article , Express your conclusion in simple and easy to understand to the readers of the magazine , What kind of sand castle gives children a sense of accomplishment , How many years can it exist without human intervention … Pay attention to the expression of preciseness and connotation .

* The highlight of this problem is the visual representation of the model , For example, the evolution of different life cycles of each three-dimensional sandcastle , A single factor ( rainfall ) The influence evolution of .
<> Translation of original title

<> original text

2020 MCM Weekend 2
Problem B: The Longest Lasting Sandcastle(s)
Wherever there are recreational sandy ocean beaches in the world, there seem
to be children (and
adults) creating sandcastles on the seashore. Using tools, toys, and
imagination, beach goers
create sandcastles that range from simple mounds of sand to complicated
replicas of actual
castles with walls, towers, moats, and other features that mimic real
castles. In all these, one
typically forms an initial foundation consisting of a single, nondescript
mound of wetted sand,
and then proceeds to cut and shape this base into a recognizable
3-dimensional geometric shape
upon which to build the more castle-defining features.
Inevitably, the inflow of ocean waves coupled with rising tides erodes
sandcastles. It appears,
however, that not all sandcastles react the same way to waves and tides, even
if built roughly the
same size and at roughly the same distance from the water on the same beach.
Consequently, one
wonders if there exists a best 3-dimensional geometric shape to use for a
sandcastle foundation.

* Construct a mathematical model to identify the best 3-dimensional geometric
shape to use as a
sandcastle foundation that will last the longest period of time on a seashore
that experiences
waves and tides under the following conditions:
 built at roughly the same distance from the water on the same beach, and
 built using the same type of sand, roughly the same amount of sand, and the
same waterto-sand proportion.
* Using your model, determine an optimal sand-to-water mixture proportion for
the castle
foundation, assuming you use no other additives or materials (e.g. plastic or
wooden supports,
stones, etc.).
* Adjust your model as needed to determine how the best 3-dimensional
sandcastle foundation
you identified in requirement 1 is affected by rain, and whether it remains
the best 3-dimensional
geometric shape to be used as a castle foundation when it is raining.
* What other strategies, if any, might you use to make your sandcastle last
* Finally, write an informative, one- to two-page article describing your
model and its results for
publication in the vacation magazine: Fun in the Sun, whose readers are
mainly non-technical.
Your submission should consist of:
 One-page Summary Sheet
 Table of Contents
 One- to Two-page Article
 Your solution of no more than 20 pages, for a maximum of 24 pages with your
table of contents, and article.
Note: Reference List and any appendices do not count toward the page limit
and should appear
after your completed solution. You should not make use of unauthorized images
and materials
whose use is restricted by copyright laws. Ensure you cite the sources for
your ideas and the
materials used in your report.

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