CoOL and QuIeT

For the past few years, I have been helping out students with their maths. There are several topics that students would find hard to understand and one of them is: quadratic functions.

The beauty of polynomial functions is that you could visualise them on graphs. This would enhance your understanding towards the properties of the equations.

A general quadratic function has the form y= ax^2+ bx + c where a, b, c are constants and a is non zero. Since its highest order power is two, there could only be two solutions, in mathematics jargon , it is known as roots.

Quadratic functions has a discriminant expression (D= b^2-4ac) which enable us to determine whether the root is real (D = 0 or D>0) or not real or complex root (D<0).

This would be much easy to understand if the graph is sketched. There are few points to note before sketching:

1) The shape of quadratic function is a parabola - a ‘U-shaped’.

2) The coefficient of x^2 would determine whether it is a Up-U or Down-U. Whenever, the coefficient is positive, it would be a Up-U graph as I called it a ’smiley face’. So, for negative coefficient, it would be a Down-U graph and I labelled it a ’sad face’.

Now, I think you are ready to sketch. Let’s look at the various discriminant cases:

1) Real Root (Equal Root):

For instant, the function: y=x^2.It is symmetric about the y-axis, ’smiley face’ and passing through the origin. The key feature is that the graph only touches the x-axis at one point. This indicates that the roots are real and equal, hence it is equal root.

2) Real Root (Distinct Roots):

For example, the function: y = x^2 + x - 6. I would first factorise the function as: y = (x+3) (x-2). By sketching out the graph, you could then see that the function has ‘cut’ x-axis at 2 and -3. They are the distinct roots.

The important feature in for such function is that whenever you see a graph that ‘cuts’ x-axis at two points; you could tell instantly that it has two distinct roots.

3) Complex or no real root:

This function has a unique feature and it is the most easiest to distinguish with other functions. This is because the graph is ‘floating’ above x-axis. Therefore, there is no real root.

So next time when you about to solve or try to understand a quadratic equation, sketch it out and see for yourself!!

I have not been writing my blog for ages.. anyone missing me ?? mm.. :((

I am looking forward to the coming summer as i am goin to Nigeria for a summer placement.. i can’t wait for this opportunity.. This is going to be exciting and interesting.

Hope i could attach some pic in my next blog.

Making waves
Jun 8th 2006
From The Economist print edition

Energy: Converting the motion of the sea into electricity requires a
trade-off between efficiency and resilience—or does it?

THE prospects for wave power have risen and fallen, appropriately
enough, for years. But now the technology finally seems to be making
headway. Not only is the world’s first commercial wave farm due to be
switched on and connected to the electricity grid in Portugal this
summer—but an even newer type of wave-power generator could
drastically reduce the cost of extracting energy from the sea.

Wave power first attracted interest in the 1970s, when Stephen Salter
of the University of Edinburgh devised a device that converted the
motion of waves into electricity. The potential is vast: a report
published earlier this year by the Carbon Trust, an organisation set
up by the British government to help meet its targets for reducing
greenhouse-gas emissions, concluded that 20% of Britain’s electricity
could be provided by wave and tidal power. This is four times more
than previous estimates, and means that marine energy alone could
enable Britain to reach its emissions-reduction targets. In America,
meanwhile, the Department of Energy’s National Renewable Energy
Laboratory has estimated that the use of wave power on the east coast
could provide 10-25 times more electricity than the total wind
potential of the Great Plains.

Given this potential, why is it that so far, not a single commercial
wave-power generator is in operation? "The biggest problem with
wave-power generators is that they are relatively expensive," says
Keith Melton of the New and Renewable Energy Centre in Blyth, England.
Most produce electricity at a cost of between 10-20 pence (18-36
cents) per kilowatt hour (kWh), whereas electricity produced from
natural gas costs around 4p/kWh. One reason for the expense of wave
power is the need to make the equipment impervious to storm damage and
corrosion. Of the countless wave-power concepts invented over the
years, most have been heavily over-engineered to reduce the chances of
breakdown at sea. This reduces their efficiency, increasing the cost
per kWh and preventing wave power from making progress.

But now things seem to be changing. Near Póvoa de Varzim, off the
northern coast of Portugal, three 150-metre-long articulated
snake-like pontoons, called Pelamis Wave Energy Converters, are in the
final stages of being hooked up to the country’s national grid, says
Andrew Scott of Ocean Power Delivery, the firm behind them. Each one
has three power-converter modules distributed along its length, which
transform the flexing motion at the snake’s joints into electricity as
the snakes are buffeted by the waves. The three snakes are the first
stage of a planned 24-megawatt wave-power farm, which will be capable
of providing 15,000 households with power. The Pelamis’s design avoids
the trade-off between resilience and efficiency by switching to a
higher-efficiency mode in calm seas.

But the new device, called the Snapper, increases efficiency still
further. Electrical generators tend to work most efficiently when a
small force is applied at high speed—which is just the opposite of
what wave power provides, says Ed Spooner, a consultant engineer based
near Durham, in England, who invented the Snapper. His invention works
much like a typical linear generator, in which a magnet is moved up
and down inside coils of wire, inducing electrical currents in the
process. But there is a crucial difference: alongside the coils are a
second set of magnets of alternating polarity. These prevent the
central magnet from moving up and down smoothly. Instead, magnetic
forces repeatedly halt its motion, so that it moves up and down in a
jerky fashion. The resulting series of short, rapid movements is more
suitable for generating electricity than a slow, smooth movement.
Early tests suggest that it could be as much as ten times more
efficient than existing wave generators. Having spent years
floundering in the water, could wave power finally be ready to make a
splash?

The flow of the universe moves through everything. It’s in the rocks that form, get pounded into dust, and are blown away. It is the blossoming of a flower born from a seed planted in the spring. The growth cycle that every human being goes through is part of this natural flow. The current that takes us down life’s paths is this flow. When we move with it, rather than resisting, we are riding on the universal current that allows us to flow with life.

Many people live their lives struggling against this current. They try to use force or resistance to will their lives into happening the way they think it should. Others move with this flow like a sailor using the wind, trusting that the universe is taking them exactly where they need to be at all times. This flow is accessible to everyone because it moves through and around us. We are always riding this flow. It’s just a matter of whether we are willing to go with it or resist it. Choosing to go with the flow is often a matter of letting go of the notion that we need to be in control at all times. The flow is always taking you where you need to go. It’s just a matter of deciding whether you plan on taking the ride or having it take you there with you dragging your feet.

Learning to step into the flow can help you feel a connection to a force that is greater than you and is always there to support you. The decision to go with the flow can take courage because you are surrendering the notion that you need to do everything by yourself. Riding the flow of the universe can be effortless, exhilarating, and not like anything you ever expected. When you are open to being in this flow, you open yourself to possibilities that exist beyond the grasp of your control. As a child, you were naturally swept by the flow. Tears of sadness falling down your face could just as quickly turn to tears of laughter. Just the tiniest wave carrying you forward off the shores of the ocean could carry you into peals of delight. Our souls feel good when we go with the flow of the universe. All we have to do is make the choice to ride its currents.

  Finally , the first term is over !!!!! gosh is a like just finish a whole year ..well this is just a beinging of 3rd year *sigh* ‘酸 甜 苦  辣’ = taste of sour,sweet,bitter and spice all at once !!  now is time to relax, enjoy the days i left ..before the new term start again ..

Have a look at this northern light at christmas time. is pretty cool

Merry Christmas to all ChEM EnG sTudENt at UCL !!!!!

Finally, PDC coursework is done well more to come .. TP ..CRE..design … ai.. 为什么 ?? student life is so 凄惨 ? there is no life beside 大学生活.Recently, i am applying for internship and industrial placement.This is another worry.Life is up and downs. I am sure there is lots of ppl out there under the same roof as me.oh well all i can do is my best and the rest i will leave to my best friend - God.

Finally,the deadline of the report was over and some cwks were submitted this week.univ life is so busy^-^ .. never stop. cwk just keep coming.lectures notes are piling up as high as my table. this is so stress,I need a break this weekend. i want to be fresh for the coming week..as for now enjoy as much as i can

” The first tep to knowledge is to know that we are ignorant.”

Scorates (470 - 399 B.C)

”Be more concerned with your character than with your reputation because character is what you really are while reputation is merely what others think you are.”

John Wooden,coach, UCLA Bruins

”Success is measured not so much by the position one has reached in life, as by the obstacles one has overcome while trying to succeed.”

Booker T.Washington

”Success is a journey,not a destination.”

Ben Sweetland

”You can observe a lot just by watching .”

Yogi Berra,New York Yankees

”Chemical Engineers are not gentle people,they like high temperatures and high pressures.”

Steve LeBlanc

”Giving up is the ultimate tragedy.”

Robert J.Donovan

”It ain’t over ’til it’s over.”

Yogi Berra

”Research is to see what everybody else sees and to think what nobody else has thought.”

Alber Szent-Gyorgyi

”Nothing in life is to be feared.It is only to be understood.”

Marie Curie

”This is not the end.

It is not even the beginning of the end.

But it is the end of the beginning. ”

Winston Churchill