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Mathematics Of Ice To Aid Global Warming Forecasts

published on September 21st, 2007 . by Vanaja

University of Utah mathematicians have arrived at a new understanding of how salt-saturated ocean water flows through sea ice — a discovery that promises to improve forecasts of how global warming will affect polar icepacks.

In the current issue of the journal Geophysical Research Letters, math Professor Ken Golden and colleagues show that brine moving up or down through floating sea ice follows “universal transport properties.”
“It means that almost the exact same formulas describing how water flows through sedimentary rocks in the Earth’s crust apply to brine flow in sea ice, even though the microstructural details of the rocks are quite different from sea ice,” says Golden, who currently is on an Australian research ship in Antarctica.

(University of Utah mathematician Ken Golden stands in front of sea ice melt ponds in the Arctic near Barrow, Alaska. His research on sea ice’s permeability to salt water promises to help improve forecasts of the effects of global warming. )

The study suggests similar porous materials — including ice on other worlds, such as Jupiter’s icy ocean-covered moon Europa — should follow the same rules, he adds.
Golden has made several trips to Antarctica and the Arctic for his studies.

The American Geophysical Union, which publishes the journal carrying Golden’s study, says sea ice is important because it is both “an indicator and regulator of climate change; its thinning and retreat show the effects of climate warming, and its presence greatly reduces solar heating of the polar oceans.”

“Sea ice also is a primary habitat for microbial communities, sustaining marine food webs,” the group adds. “The permeability of sea ice and its ability to transport brine are important to many problems in geophysics and biology, yet remain poorly understood.”

The AGU says Golden’s study presents “a unified picture of sea ice permeability,” and how that permeability to brine flow varies with the temperature and salinity of the ice.

Icy math and climate change

“One of the most important aspects of the polar sea ice packs is the role they play in Earth’s albedo — whether Earth absorbs or reflects incoming solar radiation,” says Golden. “White sea ice reflects; the ocean absorbs. In the late spring, melt ponds [atop the ice] critically affect the albedo of the polar ice packs. The drainage of these melt ponds is again largely controlled by the permeability of the ice.”

The Intergovernmental Panel on Climate Change’s predictions “that the summer Arctic ice pack may disappear sometime during 2050-2100 depend in part on these types of considerations,” he adds. “Now that we have a much firmer understanding of how permeability depends on the variables of sea ice, namely temperature and salinity, our results can help to provide more realistic representations of sea ice in global climate models, helping to hone the predictions for world climate and the effects of warming.”

The results “can also help in understanding how polar ecosystems respond to climate change,” Golden says. “Biological processes in the polar regions depend on brine flow through sea ice. For example, the rich food webs in the polar oceans are based on algae and bacteria living in the ice, and their nutrient intake is controlled by brine flow.”

“In the Antarctic, ice formed from flooding of ice surfaces is an important component of the ice pack, and this formation is dependent on brine flow,” he adds. “Brine drainage out of sea ice and the subsequent formation of Antarctic bottom water is an important part of the world’s oceans.”
Golden says the formulas that describe brine flow through sea ice and groundwater flow through sediments arose from abstract solid-state physics models used to describe atomic-scale phenomena in metals.

“These formulas exhibit universality, meaning that the end result doesn’t depend on the details of the model or system, only on the dimension of the system,” he says. “While large classes of abstract models obey this principle, real materials often do not. So it is surprising that a complex, real material like sea ice actually obeys these formulas.”

To conduct the study, Golden and colleagues analyzed sea ice and “modeled” or simulated its behavior mathematically, and also made field and laboratory measurements of sea ice, including using X-rays to make CT-scan images of how the microscopic pore structure of ice varies with temperature.

Golden conducted the study with University of Utah colleagues Amy Heaton, a chemistry graduate student, and Jingyi Zhu, an associate professor of mathematics. Other co-authors are from the University of Alaska Fairbanks.

Courtesy: Science Daily.

Mathematician suggests extra dimensions are time-like

published on April 18th, 2007 . by Vanaja

In a recent study, mathematician George Sparling of the University of Pittsburgh examines a fundamental question pondered since the time of Pythagoras, and still vexing scientists today: what is the nature of space and time? After analyzing different perspectives, Sparling offers an alternative idea: space-time may have six dimensions, with the extra two being time-like.

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Theoretical cloaking device is created

published on April 3rd, 2007 . by Vanaja

U.S. scientists, taking a tip from Star Trek, have used nanotechnology to create a theoretical optical “cloaking” device that can make objects invisible.
The Purdue University engineers, following mathematical guidelines devised by British physicists, created the theoretical device that can render objects invisible by guiding light around anything placed inside the “cloak.”
The design uses an array of tiny needles radiating outward from a central spoke. The device would bend light around the object being cloaked. Background objects would be visible, but not the object surrounded by the cylindrical array of nano-needles, said Vladimir Shalaev, a professor of electrical and computer engineering.
The design does, however, have a major limitation: It works only for any single wavelength, and not for the entire frequency range of the visible spectrum, Shalaev said.
“But this is a first design step toward creating an optical cloaking device that might work for all wavelengths of visible light,” he said.
The research is detailed in a paper appearing this month in the journal Nature Photonics.

Copyright 2007 by United Press International. All Rights Reserved.

Ref: science daily

New Website

published on January 2nd, 2007 . by Vanaja

Today I have launched a new math help website.

Its name is

I will add some basic math topics later.

Please visit my site MATH SUPPORTER.COM

Division by ‘0′-The problem is solved

published on December 10th, 2006 . by Vanaja

Schoolchildren from Caversham have become the first to learn a brand new theory that dividing by zero is possible using a new number - ‘nullity’. But the suggestion has left many mathematicians cold.
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Geometry in Court

published on December 4th, 2006 . by Vanaja

In real life, math can be relevant in the courtroom or come up in legal disputes.

Last year, the Pythagorean theorem was a deciding factor in a case before the New York State Court of Appeals. A man named James Robbins was convicted of selling drugs within 1,000 feet of a school. In the appeal, his lawyers argued that Robbins wasn’t actually within the required distance when caught and so should not get the stiffer penalty that school proximity calls for.

The arrest occurred on the corner of Eighth Avenue and 40th Street in Manhattan. The nearest school, Holy Cross, is on 43rd Street between Eighth and Ninth Avenues.

Law enforcement officials applied the Pythagorean theorem to calculate the straight-line distance between the two points. They measured the distance up Eighth Avenue (764 feet) and the distance to the church along 43rd Street (490 feet), using the data to find the length of the hypotenuse, 907.63 feet.

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Approach To School Affects How Girls Compare With Boys In Math

published on November 2nd, 2006 . by Vanaja

More women are pursuing higher education and doctoral degrees than ever before, but women still are rare in the math-oriented professions. Yet, researchers say, girls perform just as well as boys on achievement tests and tend to earn better grades in math than do boys during the earlier school years.

A new study in the journal Developmental Psychology indicates that how girls and boys approach their schooling underlies the differences in math grades. It also suggests that although the girls’ approach to school may give them an edge in the grades they earn in math, it may not buy them much when it comes to math scores on achievement tests because girls are not more confident than the boys about their skills in math.

The study examined 518 boys and girls as they went through fifth and seventh grades in three primarily white, middle- to upper-class school districts in Illinois. Using children’s reports, researchers looked at how the children approached their schoolwork, including their goals and in-class behavior. The children also reported on how confident they were about their ability to do well in math. Researchers also reviewed the young students’ grades and achievement test scores in math.

In the classroom, girls outperformed boys at both time points of the study, with the girls’ grades rising over time, while the boys’ grades remained the same, said Eva Pomerantz, a professor of psychology at the University of Illinois at Urbana-Champaign. The study was part of the doctoral work done by Gwen A. Kenney-Benson, who now is at Allegheny College in Pennsylvania.

Concerns with outperforming others and engaging in disruptive behaviors while in the classroom, both of which characterized boys more than girls, were tied to lower grades in math by the researchers.

“This was due in large part to the fact that such competitive and disruptive leanings were associated with decrements in learning strategies such as preparing for tests, seeking help, and persisting even when things were challenging that led to higher grades,” Pomerantz said.

Girls consistently used these learning strategies more than the boys did, the researchers found. It appears that, in contrast to boys, girls are more concerned with learning than with outperforming their classmates. They also engaged in less disruptive classroom behavior. As a consequence, girls used more focused learning strategies, giving them an edge over boys in terms of grades, Pomerantz said.

The researchers noted that the differences in grades between girls and boys disappeared once children’s concerns with learning versus outperforming others, engagement in disruptive behavior and learning strategies were taken into account.

At achievement test time, however, girls’ lost their advantage in math; their scores were the same as those of boys. After examining various factors, what stood out, Pomerantz said, was children’s confidence in their ability to do well in math.

In the classroom, she said, children may be less likely to feel that they will be judged based on their gender, believing instead that their own behavior, knowledge and effort will determine their grades. Thus, she added, the girls’ approach to schoolwork will pay off in the classroom, while the boys’ approach will not. It also could be, the researchers theorized, that higher grades given to the girls reflect rewards from their teachers for better behavior.

During achievement tests, the researchers suggest, the environment changes. Removed for girls is the familiarity of the classroom, which is replaced with uncertainty and increased stress. In such a situation, confidence mattered more than in the classroom.

Because confidence was found to be a predictor of scores on math achievement tests, Pomerantz said, girls may not have kept the edge they had while in the classroom because confidence levels did not differ along gender lines.

It may be that while many girls are going on into higher education, they continue to steer away from “stereotypically masculine fields, such as science and engineering” because the “more competitive environment of these fields is not a good fit with how girls approach school,” the researchers wrote.

“Consequently, even if the topic is of interest,” Pomerantz said, “the girls’ more learning-oriented approach may not match the work environment, where the atmosphere in these fields may provide a better fit to boys’ more competitive approach.”

Courtesy: Science News

How to send me your math problems?

published on October 2nd, 2006 . by Vanaja

My readers are asking me, how they can type math symbols when sending questions. You can use any of the following methods.

  1. For those who are having a scanner. You can write your questions in a paper and scan it and save it as a JPGE file. Attach this file with your E-mail and send it to me at: [email protected]
  2. If you don’t have a scanner, you can send it as a word file. For typing Math symbols you can use Equation Editor. If you are using MS word it is already there. In the tool bar, click insert. Now you can see object option. Click object. In the ‘create new’ option, select Microsoft equation. With this you can type the Math symbols you want. Save your question as a .doc file and attach it with your E-mail and send it to me at: [email protected].

I have mentioned about my service in an earlier post . Please read that before sending the questions. Read that here

If you have Math Type you can use that also.