13
11/18/2015
@1:26 PM
Partial Differential Equations
This semester I took MATH2100 which focused on ordinary differential equations (ODEs) in the first half of semester and partial differential equations (PDEs) in the second half of semester. One of the topics covered in PDEs was the one dimensional heat equation.
For some context, consider a uniform rod with length L. The temperature in the rod would be evenly distributed assuming the environment temperature stays the same and there is no heat loss from the rod. This can be represented in Figure 1 below where the x-axis is a point on the rod between 0 and L and the y-axis is the temperature at the corresponding x point.
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| Figure 1 Temperature of a rod with no heating |
Now what happens when I add a heat source like a candle at the half way point of the rod (L/2)? The temperature on the rod at the point of heating would be higher and decrease as you move further away from it. Note that temperature should be symmetrical about L/2.
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| Figure 2 Temperature of a rod with heating |
Over time, the heat will be able to distribute itself further away from the point of heating like at t = 5 and at t = 20. Eventually with sufficient time the temperature of the rod will become uniform again like in Figure 1.
This behaviour is known as heat flow and can be described mathematically! First, we need to think about the variables which affect the temperature in the rod. There are three:
- Heating source(s) and their location,
- Distance along the rod and,
- Time
We can let the function u(x,t) describe the temperature along the rod where x is a point on the rod and t denote time.
The one dimensional (1-D) heat equation is given as:
Where the subscripts are the partial derivatives of the function u (and hence the name partial differential equations).
Now we can try a possible solution:
Taking the partial derivatives:
Substitute into the 1-D heat equation:
Now we have found the mathematical function which describes the behaviour of heat flow. There are infinite solutions since A and b can be any constant and it will still work!
Unfortunately that is incorrect :(
Although the function we have found satisfies the PDE, we still need additional information. Like ODEs we need to know the initial conditions (IC) of the rod (i.e. at t = 0) and what's happening at the ends of the rod (i.e. at x = 0 and x = L), called the boundary conditions (BC) .
There are a few BCs we can consider:
- The ends are insulated
- There are ice cubes at the ends of the rod which means temperate is zero at the ends
- Or a mixture of the two
If we consider the ICs, BCs and the 1-D heat equation, there will only be one solution which satisfies all three. So for different scenarios of heat flow, there will only be one function which can model its behaviour. Personally, I find it remarkable how there can only be one solution to model heat flow for a given situation.
Another important thing to note is heat flow looks really similar to the Gaussian distribution and the heat equation can intuitively model Brownian motion. Perhaps a post for another time.
W.T
10
9/02/2014
@6:12 PM
Social Circles
In high school, students are normally stuck with one another for the next few years of their lives. It isn't necessarily a bad thing because it encourages students to befriend each other. Each class usually has roughly 25 students and there's only a few subjects to take. So chances are students will often see their friends.
At uni, it's not really the same. Classes, especially lectures can have hundreds of students and there is a lot more freedom in choosing lecture times. As a result, the probability of seeing someone you met in a lecture be in the same tutorial or practical is minuscule. Due to less time spent seeing the same people, it's difficult to make new friends.
Another challenge is sometimes friendship groups from high school transfer over to uni. The people in a friendship group already know each other. As an outsider, it can be hard to integrate yourself into that group.
At uni, I've met numerous people but most of them aren't my friends - they're more like acquaintances. I see them time to time and we exchange a few words but it never becomes anything more than that. It's a repeating cycle. I talk to new people and become acquaintances. I meet new people and become acquaintances. The end is result is always the same.
Why? There are probably a multitude of explanations. I'm introverted and naturally quiet. My hobbies aren't common and as a result people could find me boring. My mind goes blank when I'm talking to people. Consequently I can't hold conversations and people can be more selective in choosing friends at uni because they meet more people.
I've noticed throughout the years my social circle has grown larger but simultaneously I've drifted away from people and grown closer to others. I could say that uni has been one of the major factors influencing the change in my social circle. Perhaps people no longer have the time to spend with others due to new responsibilities. Maybe I don't have things in common with people I once knew. Though one thing I did learn from this is good friends are hard to come by in life.
W.T
6
7/20/2014
@8:35 PM
Personality
Hello everyone!
One thing that I do time to time is personality quizzes. They seem to make me more conscious of the way I behave and think. Back in high school, I did a personality quiz and was labelled an INFJ. I was categorized as an INFJ until this year. I did the same quiz again and was an INTJ. I know that there are other factors that could have influenced the different personality profile like the mood I was in when taking the quiz, time of day and recent activities. I still think that I am an INFJ at the core but perhaps I've had to develop my thinking side because of my exposure to maths and engineering-like subjects in the past year.
Though the one thing that is consistent is that I'm introverted. Perhaps it is a self-fulfilling prophecy but I do need spend some time alone after social gatherings. I feel drained and exhausted after talking to people. That's one of the reasons why I don't go out as much or why I sometimes become antisocial.
I also have internal monologues and space out when I'm alone. It can happen when I'm with other people too. Often when people ask me what I'm thinking about I get startled and forget what I was thinking about. Even when I catch myself daydreaming I'll forget what I was thinking about. It can get annoying at times. Getting a bit off track now haha.
W.T
Labels: 006
5
6/17/2014
@8:25 PM
Exams
Hey everyone!
Today I finished the MATH1051 exam and that brings the exam count to ONE! I'm super excited that semester one is almost done. I just hope I can keep the momentum up and study dynamics :P Out of all my exams I'm most concerned about this last exam. I have almost no clue what the hell is happening in the dynamics part of ENGG1400 >.<
After the math exam today, I went with Roy and Liang to Pancake Manor to celebrate. I ordered a Blueberry Heaven. The highlight of the dish was the ice cream. Although the food was expensive, the servings were large enough to fill us up.
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| Seafood Crepe |
We ordered four dishes. One pancake dish for ourselves and we shared the Seafood one. I was surprised that I could finish the pancakes. I usually don't eat sweet things for lunch since I tend to get sick afterwards.
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| Blueberry Heaven |
It was my first time eating at Pancake Manor and I choked on the powdered sugar. Albeit I wasn't the only person to choke on the powdered sugar haha.
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| Strawberry pancakes and salad with Italian dressing |
I also got to use my UQ Banking Club membership. It provided us with a 10% discount. Not much but it's better than paying full price. The UQ Banking Club discounts are actually useful. For only a $3 investment, its helped me save about $10.
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| Macadamia Madness |
Apart from exams and uni life, my gaming mouse decided to die on Sunday. The left click finally broke so I can only move my cursor now. I've decided to go with a Razer DeathAdder for my next gaming mouse. It's $48 which was cheaper than I expected. I was debating on getting the Logitech G400 or the Razer DeathAdder. The difference in price is $5 from Umart. I've read great reviews for both products but the Razer DeathAdder looked cooler. If I'm not satisfied with it I can always try the Logitech G400.
Anyway, good luck with your remaining exams and congrats to those of you who are finished! :D
W.T
4
6/12/2014
@1:05 PM
SWOTVAC
Hey everyone!
This post was delayed because I've been experiencing issues with my internet. The DNS server was unresponsive -.- I managed to find a temporary solution by changing the DNS to 8.8.8.8 and 8.8.4.4. which are Google's. The internet still drops out but is much more stable than what it was before. If any of you do know a solution please message me!
So as we all know, the end of semester is approaching which also means EXAMS! The only thing stopping me from enjoying winter break is the final exams. Whenever exam season approaches I always go through a series of steps to prepare for them. I'll list them below:
1. Know the material might be on the exam
2. Gather study materials and past exam papers
2.5 Make a timetable of things I have to get done and when
3. Revise concepts if I need to and questions from specific topics
4. Past papers
One thing that annoys me is the lack of solutions to the past exam papers (except for math). Even though it encourages people to work together to compare answers I find it unsettling. The lack of a mark scheme also makes me worry a bit.
Anyway, good luck with your exams! See you all on the other side :D
W.T
3
6/04/2014
@11:04 PM
Hello! Today was an exciting day for a number of reasons. One of them was demo day. The task required us to construct a functional electric mining shovel (EMS) that could do four motions:
- Propel
- Swing
- Hoist
- Dump
Other constraints in the task included:
- Only using the DC motors supplied by the uni
- A maximum of four motors to be used
- A single battery could not exceed 9 volts
- The maximum dimension of the EMS could not exceed 90 cm
- A budget of $100 (including the motors)
The EMS would have to dig into a pile of chickpeas and then dump it into a remote control truck nearby. The truck would then be controlled to a nearby dump site to place material and move back to the EMS. Each group had five minute to shift as much material as they could.
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| Image courtesy of UQ |
After a grueling 13 weeks of researching, designing, building and refining Bumblebee was created!
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| Adding last minute touches to Bumblebee |
Bumblebee was mostly made out of corrugated plastic. The material was durable and lightweight which was why we initially chose it (plus I had heaps of it lying around at home anyway). We covered up the plastic with yellow paper and black tape to make it look more presentable.
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| Checking the propel motion |
Out of the four motions, we had the most trouble with the propel motion. The problem was that the wheels connected to the axle of the motors wouldn't stick properly, resulting in the wheels slipping off. It didn't help that we used six wheels instead of four, resulting in an indeterminate structure. We quickly solved the problem by moving the motorized wheels to the front because provided the EMS with more digging power and raised the front outside wheels so they wouldn't touch the ground. The outside wheels are mainly for presentation but the ones at the back provided stability.
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| Side shot of Bumblebee |
The swing motion was probably the second most troublesome motion we encountered. Our initial designs involved a pulley system with a central shaft in the middle to allow the upper structure to pivot around the shaft. Due to time constraints and lack of material we decided to directly connect the motor to a lazy susan. The initial material used to connect the motor to the lazy susan was wood. We quickly found out that the motor would wear out the hole so we used plastic from a chopping board which solved the issue.
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| The dipper, boom and wooden attachment |
For the dump motion we utilized an electrical solenoid latch system. The initial solenoid we purchased was too weak to open the latch of the dipper. Purchasing a larger solenoid solved the problem. During demo day the dipper managed to scoop on average 750 grams per pass. With 8 passes within the 5 minutes we managed to shift about six kilograms of chickpeas. In addition, the trapezoidal shape of the dipper allowed it to be easily filled
The hoist motion was done by using a winding drum inside the EMS. The initial drum was 4 cm in diameter which resulted in the dipper slowly moving down when it was hoisted to the top. Although having a larger drum would increase the hoisting speed, we decided to use a smaller drum to ensure the dipper doesn't move down on its own when hoisted up. This was done to ensure we had enough clearance height to unload the chickpeas into the truck.
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| The control system |
The control system was made from an old extension cord. We removed some the rubber covering to get the individual wires for the circuits. A lot of soldering and testing was involved when making the control system. I also realized how expensive electrical parts were. The switches we purchased were $2.95 from Jaycar. We used five switches altogether meaning we spent $14.75 on switches!
Here's a short video during one of the EMS tests.
To be honest, during the first two weeks I had no idea what the hell I was doing. We were given the task to create an electric mining shovel (EMS) under a certain criteria. Having literally no experience in this kind of stuff I didn't know where to start. At that point, I didn't even know what forces were! Fast forward another 11 weeks and I feel like I've got a decent grasp of the project and the requirements. If I had to redo this project I could probably get it done in two weeks.
W.T
Labels: 003, engineering
1
6/01/2014
@7:50 PM
A New Leaf
Hello!
Another blog is created but this time I'm solo(mid). Despite wanting to continue on the previous blog I felt that it had served its purpose for the past couple years. It had a great run and I think it is time for a new blog. My previous blogging collaborator has set up a new blog too. You can see it here.
Ever since leaving the previous blog, I've felt like I didn't have a way to archive events that happen in my life. Sure randoms on the internet would be able to find out about my life but I find sharing life experiences with people enjoyable.
Hopefully you'll get something positive out of this, whether I made you laugh or provided some insight. . I know, a short post but it'll have to do for now.
W.T
Labels: 001, 2014, first post
