Crystal Symmetry

A primitive cubic unit cell with 8 corner atoms. (Created using CrystalMaker software.)

In undergraduate mechanical engineering program, students start connecting macroscopic concepts - such as temperature, pressure, stress - they learn from solid mechanics, fluid mechanics and thermodynamics with microscopic objects - bonding energy, crystallography, dislocations - when they study materials science.

One challenging topic in materials science is crystallography. It has to do with how we characterize and classify arrangements of atoms in three-dimensional space. It is mathematically abstract. We classify different atoms by paying attention to the symmetries of these arrangements.

Symmetry is not a thing, it is a process done to these atomic arrangement. The process changes an arrangement of these atoms to another arrangement without changing how these atoms relate to each other in space.

To study symmetry of atoms in a solid, we imagine the atoms to be arranged in a regular three-dimensional pattern. Because these atoms are placed periodically, we can come up with a building block, a unit volume that can be cloned as many times as required to create a solid of any size we want. This building block is called a unit cell. We call a solid that has a periodic arrangement of atoms a crystal.

One periodic way to arrange atoms in a crystal is to place them at 8 corners of a cubic unit cell. Each corner atom contributes 1/8 of an atom, so one cubic unit cell is occupied by 1 atom. We need to imagine we have other unit cells surrounding the first unit cell forming a crystal filled with atoms. For illustration, however, I just show one unit cell with 8 corner atoms (shown above). I am going to use this cubic unit cell to explain the crystal symmetry idea.

A cubic unit cell viewed squarely onto one of its 6 faces.

The picture above shows the cubic unit cell viewed squarely onto one of its 6 faces. One process that can change the arrangement shown is to rotate it by 90 degree about an axis at the center of the face. We get a new arrangement but this arrangement is identical to the before-rotation arrangement. We thus say that the cubic unit cell obeys the 90-degree-rotation symmetry. We don't call the 180-degree rotation a symmetry of the cubic unit cell since it can be reproduced by two 90-degree rotations. We don't call the 360-degree-rotation a symmetry of the cubic unit cell since it is trivial.

The 6 faces of the cubic unit cell can be divided into 3 groups, and each group has 2 faces. We can perform the 90-degree operation to each face group. So there are total 3 90-degree rotation symmetries.

Another symmetry that the cubic unit cell has is a mirror symmetry. The square face above has four mirror planes. One mirror plane exchanges the 2 left corner atoms with the 2 right corner atoms. Another mirror plane exchanges the 2 top corner atoms with the 2 bottom corner atoms. The other two mirror planes exchange the corner atoms face diagonally. Since there are those 3 groups of faces, there are thus a total of 12 mirror symmetries.

A cubic unit cell viewed along the body diagonal direction.

The cubic unit cell also has rotation and mirror symmetries operating on an axis running body diagonally as shown above. It has a 120-degree rotation symmetry. There are 3 body diagonal axes in the cubic unit cell, so there are 3 120-degree rotation symmetries.

There are also 3 mirror symmetries for each body diagonal axis, so there are 9 mirror symmetries.

A cubic unit cell viewed from the face diagonal direction.

Along the face diagonal direction, the cubic unit cell looks like above. We can rotate this picture 180-degree and the arrangement of atoms does not change. There are 2 axes of this 180-degree rotation for each face group. There are thus 6 180-degree rotation along its face diagonal axes.

There is 1 inversion symmetry about the center point of the cubic unit cell. This inversion symmetry exchanges one corner atom with another one body diagonally away from each other.

The total symmetry operations the cubic unit cell has is therefore

a) 3 90-degree rotation on its faces
b) 12 mirror symmetry operations on its faces
c) 3 120-degree rotation along its body diagonal axes.
d) 6 180-degree rotation along its face diagonal axes.
e) 1 inversion symmetry about the cubic center.

I so far identified 25 symmetry operations for the cubic unit cell. Are there others you can find?

Running for My Life

Hiking trail near Rockbound Lake, Alberta

I try to at least run once a week when things get hectic. It is better to run three times a week as it helps maintain habit. A once-a-week habit can be cruel to my body: it aches all over in the first 20 minutes.

One thing I really enjoy doing when running is emptying my mind. I don't listen to iPod when running so I can hear my rueful breathing. Huffing, puffing, and all. The beauty of it though is that the huffing and puffing focuses my mind and at the same time relaxes it. Actually I don't need to do anything; my mind just on its own relaxes and focuses on the pain I feel every step.

Anyway, in that state of mind, I always get reminded that I can only do what my mind and body can deliver optimally. Nothing more. It does not matter anymore what people see and think because I am alone running and cannot pretend I can run faster than I can. Running - as it turns out - teaches me how to maintain endurance in this game of life.

There is no need to be faster or slower since, if I pretend, it will catch up to me one way or another. So I don't envy when I see people can run faster. He must either train harder or has a better genetic material. Running teaches me not to envy what other people have and can do. Running teaches me to be happy with myself.

Running is a simple activity and gives me a lot of pleasure. I don't need to spend a lot of money to have tons of fun. Sure, I sweat a lot but those endorphins do wonder to my brain. The longer I run the less pain I feel. They also make me feel happy even if I am dog tired.

I like running since I don't have to win or lose. I am not happy when I become slower, but I like the steady pace I make. Trudging along the path. Slow meditative steps I make. It suits me just fine.

Minimize My Living Cost

One way for me to practice living simply and beatifully is to minimize my living cost. Yeah, we know that, don't we? But it is very difficult to PRACTICE it. Just LoOk ArOUnD US. We bought SO MuCH StufF and ended up not using most of them. They are parts of our collections: cards, books, shoes, jackets, and the rest. They fill up our living space and make us want a larger space. And the cycle of living large continues.

I try to instill this value to my sons. At the fundraising to help Merapi eruption victims and Mentawai tsunami victims yesterday, my eight year old son and I sold smoothie. It was his idea and I jumped in since I have been wondering how to teach him the value of MONEY = WORK. The cost was $80 for ingredients - milk, strawberry, yogurt, banana - and menu sign. It was busy 2 hours as I was making smoothies non-stop and I saw him busy receiving money. Good, I said to myself; he is learning how money is made.

We made $149 and one-half went to the fundraising cause. I doubled his profit so he made $140 as a part of the deal he would be selling the smoothie.

This morning he asked me to go to his game store to get the Little Big Planet 2 game. He brought with him old games, and some were valued at 50 cents or less. So he learned another lesson. His brother gave him $25 coupon. He figured out at the end he spent $25 from his money. GooD, I said to myself.

Minimizing my living cost also frees me to do what I want later in life. I don't want to bear a HuGE mortgage when buying home. I don't want to carry TOO much StuFF when I travel. Why create burden? Why be a BeaST of BurDEN?

If I am poor, then I Don't WoRRY too much since my cost is low. If I make some money, I can SaVE to do other THings, like TRAVELing and eXPLORing this WORLD. That's my DREAM.

Can Online Teaching Replace University Classroom?

Coffee shop in Jakarta could become a classroom for an online learning

I regularly feel the urge to write blogs from my teaching materials. I find them a good way to flush these teaching materials out of my memory bank. When I finish writing it, I feel both satisfied and tired. Much like at the end of every teaching I do in front of class.

One good thing about blogging teaching materials is that I don't have to repeat it. I can imagine saying to my imaginary online students: well, they are on my blog, please read it, and contact me if you have questions.

If students can be motivated to read the material first, then the professor-student interaction will always be Q&A sessions. Discussions take place, instead of mostly one-way communication. That would be lovely.

However, I see little incentive for students to read the material first in the classroom delivery model. Why bother? Professors are expected to deliver lectures; they get paid for doing exactly that. This classroom model is what makes university tuition fees expensive. Buildings need to be erected, full time professors need to be hired.

Which leads me to another question: Can online teaching replace classroom model? There are already many online learning materials. Youtube, Wikipedia, online universities, MIT OpenCourseWare project, and various other sites. I don't think it is difficult for any student to come up with an online study plan for a particular topic or course. I don't think either that learning math or physics online is impossible just because they are mathematical. Video, slides, phone conversations can all be delivered online.

Can an online teaching model be effective? I believe it can be more effective when it is accompanied by the Q&A sessions, or at least as effective without these Q&A sessions. The online model is clearly more efficient. It might even simplify learning process of millions of undergraduate students. What does "simplify" here mean?

Monsoon rain washing quadrangle in Department of Physics, ITB

Students might be persuaded to take fewer courses in an online learning environment since they have more freedom to tailor their individual study plans. I used to live in a dorm in my first year undergraduate and remember arts & sciences students took fewer courses than us - engineering students - since they had freedom to choose (and we don't).

Taking more courses does not mean better understanding. My engineering undergraduate years were always in a rush. Doing homeworks, assignments, term projects, preparing exams. Time moved so fast: exams came and went. I had no time to think and reflect on what I studied. I see my students now feel that way. 20 years separate us and there is no difference. I don't like it.

I had time to think and reflect when I only had to take 2-3 courses per term. This happened in graduate school. I started seeing connections among courses I took in undergraduate and I remembered then that my language became more simple.

Students would actually love fewer courses, I am sure, but professional associations and accreditation boards want to uphold standards. These standards often mean the course load tends to bulge over time rather than gets simpler and leaner.

The US has a market driven university system, where both private and state universities coexist. I think a "drive to simplify" in higher education will occur first in the US, not in Canada. MIT and other prestigious universities might at some point expand their online learning projects into full-fledged online teaching business branches that would compete at a local level with universities around the world. This could be one of the last globalization waves, I guess. (Well, the really last two would be really tough to implement: globalization of free labour movement and state governance.)

I don't see any possibility of self simplification within a university since the world has indeed become more complex. There are always valid arguments to add more courses, or at least keep the number of courses the way they are now. One way to simplify as a response to this pressure is to create more specific programs. Instead of simplifying, it will lead to provincialism.

Only market forces will do this; that is only pressure from students will change things around. Or when MIT and its peers start offering their undergraduate degrees locally at cheaper tuition fees. Or when companies start hiring people based more on their skills than diplomas. Who knows.

Teaching during my sabbatical in ITB, Indonesia (when I still had my hair)

Mechanical Characters of Metals

Stress-strain curve of a metal obtained from a tensile test

From its stress-strain curve we can tell a lot about mechanical properties of a metal. Such stress-strain curve is produced routinely in a tensile testing done in many labs around the world. The curve behaves linearly initially and the slope of this linear portion is equal to its Young's modulus. A rigidity of a metal can be attributed to its large Young's modulus. Aluminum is often the most optimum metal as it offers sufficient rigidity, cheap cost, and light weight.

Deformation in the linear regime is called elastic deformation since the metal would return to its original shape when the loading is removed. This elastic deformation originates from the distance change between two adjacent atoms in a crystalline metal. It is possible for a metal to be not crystalline; we say it is a polycrystalline since it is composed of many small crystals. The region between two adjoining small crystals in a polycrystalline metal is called grain boundary and can disrupt the elastic deformation process, so that the elastic deformation terminates prematurely.

In any case, elastic deformation terminates when dislocations in the metal start moving. Dislocations arise from imperfections that emerge when the metal is processed and fabricated. It is impossible to have a 100% pure elemental metal; it can easily incorporate impurity atoms - such as oxygen, nitrogen, and hydrogen - and vacancies are always present. Vacancies are atomic-size bubbles and when they bunch together they will create a dislocation. Larger or smaller impurity atoms than the host elemental metal can also create dislocations.

It takes energy to move these dislocations since they have to break chemical bonds. When they move, they have to push aside nearby atoms. This creates a friction, and thus require a minimum energy before they can move. The metal is said to develop plastic deformation when these dislocations move. The threshold energy density corresponds to the upper yield strength.

Since these dislocations are distributed randomly and are usually bunched up near grain boundaries, the stress will fluctuate rather wildly as the dislocations move. In the stress-strain curve, this region is called discontinuous yielding. A metal that does not have many dislocations will have a smooth curve around the yield strength. After the dislocations can move more easily, we get a uniform elongation in the plastic deformation region and the elongation continues until the metal breaks.

When the loading is removed, the metal no longer returns to its original shape once plastic deformation occurs. The dislocations, in other words, do not remember their original positions. The energy spent for the loading is now stored in the metal.

The maximum loading that the metal can withstand before it breaks is called tensile strength. The breaking strength is called fracture strength. The strain value at fracture strength is called fracture strain. A metal that is ductile will have a large fracture strain, i.e., large elongation.

This mechanical behavior of a metal is analogous to how a person might respond to a life stress. When the person is subjected to a small stress, he will be able to bounce back to his normal, unstressful state. He can alter his behavior and even character, however, when the stress exceeds some value. There is a stress limit as well a person can take. Characters that are used to describe mechanical behavior of a metal are similar to people's characters: strength, hardness, rigidity, toughness.

Strength has to do with how much stress a metal can take and is proportional to its tensile strength. Hardness has to do with how much stress a metal can take before it produces plastic deformation and it is thus proportional to its yield strength. Rigidity is proportional to its Young's modulus. Toughness has to do with how much energy a metal can absorb and is proportional to the area under the stress-strain curve. A person is said to be tough if he can take physical (and sometimes mental) abuses. We can learn a lot about people by studying mechanical characters of metals.

All Season Runner

What I got after a 1 hour, -25 C running in Calgary

Yesterday I took my best friend for winter gear shopping. It reminds me of my learning to find the best running gear for different weathers. It took probably a year for me to feel confident in deciding what to wear while running in all 4 seasons. To make things worse, Calgary is notorious for its daily weather changes. It is not unusual in the summer to have -4 C in early morning and 20 C at noon. People who have lived in Calgary long enough will say they have seen snow in all months of a year.

So I was happy to share my experience with him since he also does not enjoy exercising in a gym. I don't like exercising in a gym; I tried and gave up. Running in a treadmill bores me. Running in a loop bores me too. Outdoor is the only choice for me.

The toughest running gear decision to make is of course for winter. There are two variables I have to pay attention to: temperature and wind speed. I divide the temperature in 2 ranges. My body feels the range 0 to -15 C differently from the range -15 to -30 C. If the wind really picks up though, the -15 C temperature can feel like -30 C. I always check the weather before heading out. You have to try these ranges yourself and change them according to how your body responds.

I wear 3 layers for the warmer (0 to -15 C) range. The base layer is a short-sleeve polyester T-shirt. I never wear cotton as it retains sweat. The second layer is a thin thermal insulator, such as a merino wool zippered sweater. Having a zipper is useful since I can regulate my core body temperature. The third layer is the outside layer and acts to block wind. A light nylon wind breaker jacket will do for me. Warm toque and gloves are essential. I wear light running tights.

For the colder (-15 to -30 C) range I wear a long-sleeve polyester T-shirt as the base layer. The second layer is the same: a merino wool zippered sweater. The third layer is a thin soft shell jacket to provide additional thermal insulation. The outer layer remains the light wind breaker jacket. Warm toque and super-warm gloves are essential. Warmer running tights are required and I usually wear my cold winter biking tights.

I run a one-way route and come home using an LRT. The safer way is to run a loop so that you don't need to worry about removing sweat after running. I prefer a long, scenic route so I have to suffer a bit when walking from LRT to home with wet clothing (sometimes in a -20 C weather).

I don't need to bring water if I run for 1 hour. For a two-hour running I buy water from convenience store when running in city; it is more practical and water can freeze easily if I don't use a heavy insulated bottle. I am a minimalist runner.

My fall (15 to 0 C) running gear consists of the merino wool sweater and the short-sleeve T-shirt. Or the wind breaker jacket and the short-sleeve T-shirt. I wear the latter if rain is forecast. I find this temperature range is the best running temperature. It doesn't overheat my body and I can run faster. I definitely wear running shorts if the temperature hovers around 10 C or warmer. Toque is not needed. Light gloves are only when temperature is around 0 C.

Summer running gear (15 C or above) is downright minimalist: sleeveless T-shirt and running shorts. When the temperature reaches 30 C or hotter though, bring water. I use a Camelbak when running for 1-2 hours in Indonesia. Sunglasses and a hat might help.

How about shoes? I swear by Asics shoes. That's it, it is a marriage for life. I love Gel Trabuco and Gel Kahana series. They are good for Indonesian summer and Canadian winter. It dries quickly in rains and does not slip easily in packed snow and ice. I use two socks for winter: the inside is the low-friction socks to prevent blisters and the outside is a light insulating kind.

Outsmarted

Winter in Oklahoma

The place I stayed in Oklahoma did not have an internet connection. There was no ethernet plug, no modem connection, no wireless. Two wireless networks my laptop scanned were password protected. The only time I had connection was when I had breaks during work. It was like that for the three days I was there.

I felt I was disconnected from the world. I could not read online newspaper articles, google information, update my blogs, check friends on Facebook, and get emails continuously. I was not able to check online maps, so I found it very difficult to familiarize with streets and directions around the places I stayed and went. I felt I didn't know what was going on in the world. Instantly.

Black Angus cows; they are cute, aren't they?

I felt lonely and turned on teve to accompany me in the evening while making presentation slides. I think that is what internet - all communication technologies in general - does. It makes me weaker to fight loneliness. I cannot stand being alone. The internet becomes a close friend. It makes me feel I always have someone to talk to when around it and I crave it when it isn't around.

I sold my smartphone last year. It made me check emails, chats, Facebook status and comments everytime. It ruled me. It wasn't good. I remember that as I tell myself it is actually good to not have internet connection sometimes. It is true. I am more productive.

I learned also that I was better suited to using paper in most information recording and retrieval activities. I use a paper calendar, for example. I can scan quickly my weekly schedule without having to scroll a tiny screen. I can write down quickly with my hand what I plan to do. No need for a keyboard. I always think my cursive handwriting is neat anyway.

Percuma

yang tampak sudah hilang

yang hilang bersatu awam

yang awam berupa suci

yang suci menabur pedih

yang pedih berlalu pergi

yang pergi diam kembali

Bukan Waktu Biasa

Bryce Canyon National Park, Utah

Sekali kamu teriak
Kan kutampar telak
Walau tangan kita
Berlumur darah

Ini bukan waktu biasa
Berdua menari kaca
Menentang arus
Menghantam baja

Bualanmu kali ini
Aku mau dengar
Lalu kita terjun
Berpisah semua

Tahan napasmu
Lupakan yang enak
Selamat datang
Abadi slamanya

Contact Point of a Rolling Tire Does Not Move

How to read tire codes. Copied from this website that has additional info on tire.

That's right. Although a tire moves, the contact point between the tire and the surface does not move. This fact often confuses students. They see the tire gains distance as it moves, so how come the contact point of a tire does not move while the tire gains distance? Let me offer a simple explanation to this problem.

When a tire rolls and completes one full revolution over a time interval t, its perimeter covers a distance of 2πR, where R is the tire radius. The speed v of the tire is equal to the distance covered 2πR divided by the time interval t. That is, v = (2π/t)R. The quantity (2π/t) is called angular velocity and is typically denoted as ω.

The tire speed ωR causes the tire to gain distance. It moves. The center of the tire also moves with this speed, which can be confirmed by experiment. The contact point moves and gains distance as well. But the speed of the contact point is zero (i.e., it does not move). How come?

The key to understand this confusion is that a single point on the tire perimeter touches the surface only once every one full revolution. When it touches the surface, it becomes the contact point. But it leaves the surface as soon as it touches it. This contact point thus has zero velocity as it never moves relative to the surface. It just touches and goes fleetingly. If you follow the path of motion of this point, you get a curve called cycloid (click for animation).

Since there is always available one point on the tire perimeter touching the surface as the tire rolls, then you can always match one such contact point - that does not move - with the center of the tire that moves with the speed ωR. Hence, the statement that the contact point of a rolling tire does not move.

Beauty & simplicity

Suwuk Beach, Central Java, Indonesia

I haven't talked about what beauty & simplicity mean to me. Let me explain.

I am in awe of beauty. Beautiful math. Beautiful food. Beautiful creatures, big and small. Beautiful nature. I am nervous around them as I appreciate them. I eat beautiful food quickly as a result. Does beautiful food taste good? From my experience it always does.

Beauty is difficult to quantify, maybe it has to do with symmetry when looking at a geometrical pattern. Or proportion when glancing at a female body. Or elegance for a math equation. But symmetry, proportion, and elegance need further elaboration. So there you go.

But beauty can create or require excess. It can become gaudy, lavish. This excess needs to go.

Simplicity removes the excess. Simplicity for me suggests quality and functionality.

Beauty tends to overwhelm. Simplicity aims to clarify. Beauty shows up willingly in nature, people, things, although we still prefer to pay a lot of money to get it. Simplicity needs work but saves money.

Let me give an example. One of my postings is about whether an all wheel drive car is needed for Canadian winter driving. A beautiful solution would be just that: "symmetrical all wheel drive" motto of one car manufacturer says it all. It is not simple though: the engine drives all four wheels, is heavier, and is more expensive and less fuel efficient. Can it be simplified? I found out yes. Winter tires simplify it.

When beauty and simplicity come together, it is simply beautiful!

Car & Tire for Canadian Winter

Near Golden, BC, on Trans Canada Highway

I finally got to drive Calgary-Vancouver (click for map) in winter 2010. I saw at least 10 accidents along Trans-Canada Highway and most of them were roll over accidents, suggesting tire slip as the primary cause. I have experienced bad snow storms while driving, although luckily not during the Calgary-Vancouver trip.

It started interesting between Lake Louise and Revestoke, which is about 230 km stretch. The divided highway from Calgary is no more and there are a lot of trailer trucks as the Trans-Canada Highway is the only major land route to Vancouver. A steep 6% downhill grade stretch at the Kicking Horse Pass greeted us. Reaching Golden, the drive got even more challenging as we approached Rogers Pass which is one of the world's most avalanche prone areas. The grade continued around 6% mostly uphill for about 30 minutes until we reached Rogers Pass. There are 7 avalanche-protection tunnels in this area. I felt the remoteness of this area especially when driving at night. Between Revelstoke and Kamloops, the road levels off somewhat but it meanders wildly around Shuswap Lake. We experienced the steep grade (6-8%) again along the Coquihalla Highway between Kamloops and Hope. Once you reach Hope, it is another 150 km, mostly flat, to Vancouver.

Winter tire is a must for Canadian winter driving

There are several lessons I learned from this experience that I want to share with you.


Do I need a four wheel drive or all wheel drive car for the Calgary-Vancouver winter drive? No. I had been wanting to buy an all wheel drive car for such winter drive, but I found out that it is not necessary. The main reason a front wheel drive is sufficient is that the Trans-Canada Highway is relatively well-maintained and I did not encounter a 100% off-road condition. I won't recommend a rear wheel drive car, however, since it drifts more easily and you may not have enough time to correct it when moving at a high speed on a highway.

Do I need to use winter tires for the Calgary-Vancouver winter drive? Yes. There are in fact several warning signs along the Highway that you need winter tires during winter months (October through May for Canadian Rockies, thank you very much). There is a physics to this. The minimum coefficient of friction between tire and road to maintain a no-slip rolling tire is approximately equal to a third of the road grade. The factor 1/3 comes from the fact that the tire both rolls and its center of mass moves.

A 9% road grade thus requires a minimum static coefficient of friction of 0.03 in order for a rolling tire not to slip. The coefficient of friction between rubber and a bare asphalt - occuring mostly in summer - is 0.25 or larger. When snow covers the asphalt road, the coefficient of friction can dip to 0.05-0.1. It is thus clear that winter tires are required.

Winter tires are also required to protect from slip when the car accelerates or decelerates. Without hitting a gas pedal or brakes, the maximum downhill no-slip acceleration is almost linearly proportional to the vehicle's mass. This maximum downhill acceleration, however, also depends inversely proportional to the vehicle's tire radius. Still, a truck or an SUV can accelerate without slip faster than a subcompact car since the mass ratio of a truck v. a subcompact car is larger than their tire radius ratio.

I drive a compact car, so I know I won't be able to accelerate as fast. I thus have to apply brakes when going downhill to prevent slipping. Applying brakes can induce slip on its own if too sudden, so braking must be gentle. There is nothing wrong with the car. It is just physics.

When you hit the gas pedal or the brake pedal, you apply torque to the tires. The vehicle dynamics changes a lot. Tire design becomes important. (In tech speak, tire's moment of inertia becomes important.) When going downhill, applying brakes increases the minimum coefficient of friction to maintain a no-slip condition, thus destabilizes the vehicle. In other words, decelerating a vehicle too suddenly can cause slip to occur. This is I think the most common mistake a lot of people make when driving in winter. They hit the brake too suddenly and slip ensues.

My math shows that accelerating a bit while going downhill stabilizes the vehicle, i.e., reduces the minimum coefficient of friction. But, accelerating too much can cause slip, so I won't recommend accelerating on downhill. For me this practically means I do not need to panic when going downhill by applying brakes. This requires me to get to the appropriate speed before the downhill stretch begins.

When going uphill, the converse is true. Braking a bit will stabilize the vehicle, but of course I do not want to lose the vehicle's momentum. Hitting a gas pedal destabilizes the vehicle.

The destabilizing effect of accelerating while going uphill and generally downhill shows that it is important to mantain a constant speed on a snow covered road. In fact, a simple strategy I use for winter driving is to maintain car's momentum. It means I do not make sudden swerves, turns, and brakes.

Which other car attributes do I have to pay attention to? Bright head lights and bring enough winter windshield wiper fluid. Bright head lights are essential when you drive at night. It is likely you will drive more than 12 hours to cover the Calgary-Vancouver distance in winter. One keyword here: visibility. You want to be seen clearly by other vehicles and you want to see the road very clearly when the weather is really bad. I also brought blankets, down parkas, snow shovel, snack, drinking water, matches, and even camping stoves and fuel in case of emergency on the road.

Do I still need an all wheel drive car for a winter drive? Only if I want to venture out into a secondary road or lower, that receives no or little snow plowing. For me the main advantage an AWD has over an FWD is a lower risk of traction loss. When I drive over a well maintained road this risk is small. The lower the vehicle speed is the higher risk the traction loss has. Quantitatively, the risk is proportional to the ratio between the wheelbase and the distance between snow covered areas along the road.