Observing collective phenomena such as the movement of a flock of birds, a school of fish, or a migrating population of ungulates is a source of fascination because of the mystery behind the spontaneous formation of the aggregating behavior and the apparent cohesiveness of the movements. However, they can also be the cause of a major environmental and social problem when one thinks, for example, of the flight of a swarm of voracious locusts ravaging crops in various parts of the world and putting many communities under severe stress. Continue reading

## Author Archives: Guest Blogger

Here we consider the optimal control theory of infinite dimensional systems that has recently found interesting applications in theoretical economics so that economic models can be made more realistic. Continue reading

While I am a pure mathematician working in dynamical systems, I have always been fascinated by the mathematics of the N-body problem and its applications to celestial mechanics in general, and to the Solar system in particular. Continue reading

In June 2012, more than 3,000 daily maximum temperature records were broken or tied in the United States, according to the National Climatic Data Center (NCDC) of the US National Oceanic and Atmospheric Administration (NOAA). Meteorologists commented at that time that this number was very unusual. By comparison, in June 2013, only about 1,200 such records were broken or tied. Was that number “normal”? Continue reading

A recurrent idea in science is that the loss of stability of an equilibrium position through diffusion can lead to the creation of patterns. The idea goes back to Turing in his famous 1952 paper “On the chemical basis of morphogenesis,” which proposes a model for morphogenesis through chemical reaction-diffusion. Continue reading

What do bats and oil companies have in common? Both use active sensing methods (echolocation) in pursuit of their objectives—dinner or oil reserves. Recently, the method of Gaussian beams has become a promising alternative for asymptotic solutions to the wave equations in place of the traditional methods based on geometric optics for finding approximate short-time solutions. Continue reading

When asked to give an invited lecture at the first ever Mathematical Congress of the Americas, I jumped at the chance. This would be an opportunity to meet new colleagues from the Americas and to share my interest in mathematical ecology. Continue reading

In support of worldwide MPE2013 efforts, NSF’s Mathematical Biosciences Institute (MBI) at Ohio State University is hosting three autumn workshops aimed at the interface of mathematics and the science of sustainability. Continue reading

“It’s fire season in the forests and wildlands of America.” So began an article by Barry Cipra (“Fighting Fire with Data’). I recalled this article after hearing about the tragic events in the forest fires in Arizona earlier this week, Continue reading

Mathematics analyzes numerous aspects of financial markets and financial instruments. For the markets trading CO2 emissions, mathematics is used to decide how cap and trade rules will operate. Continue reading

The AIM workshop on exponential random network models was an experiment, bringing together people in applied social sciences, biologists, statisticians, and mathematicians who are interested in the emerging field of graph limit theory. Continue reading

No matter how surprising, outlandish, or even impossible it may seem, one of the next challenges of modern applied mathematics is the modeling of human behaviors. Continue reading

Is the Earth’s orbit stable? Will the Moon always point the same face to our planet? Will some asteroid collide with the Earth? Continue reading

The use of computational methods to explore complex social and cultural phenomena is growing ever more common. Continue reading

Vegetation patterns are a mysterious phenomenon that we can think about in the same way as patterns that form in many other contexts. What’s more, they may have importance that transcends their beauty. Continue reading

What exactly is the definition of the “social cost of carbon” (SCC)? Who is interested in determining this quantity? Who is interested in its value? Can this even be done and, if so, how accurately? Continue reading

As a large crowd gathered at CRM on Friday evening, May 10, to hear Paul Embrechts, Professor of Mathematics at the Swiss Federal Institute of Technology in Zürich (ETHZ), everyone was wondering how he would connect “Königsberg’s bridges, Holland’s dikes, and Wall Street’s downfall.” Continue reading

Today’s blog is a short blog about a “Blog on Math Blogs.” Continue reading

The National Museum of Natural History and Science of the University of Lisbon, Portugal, has added several new and significant displays to the exhibition “Forms and Formulas” in the framework of the Portuguese activities for MPE2013. Highlight is the winning entry of the MPE2013 competition, “The Sphere of the Earth,” an interactive module created by Daniel Ramos (Spain). Continue reading

Martina Morris, a Professor of Sociology and Statistics at the University of Washington, studies the transmission of sexually transmitted diseases like HIV using network analysis. Continue reading

UCLA Professor Andrea Bertozzi is applying the powerful tools of mathematics and big data analysis for mapping crime patterns - with implications for crime prevention. Continue reading

Two recent articles, written for a general audience, provide examples from the applied mathematics literature that show how mathematics is used to model and understand the progression and propagation of certain kinds of infections. Continue reading

The workshop “Mathematical Models and Methods for Planet Earth,” organized by the Italian National Institute for Advanced Mathematics (INdAM) under the auspices of MPE2013 in Rome, May 27-29, finished a few days ago. Continue reading

The Pacific Institute for the Mathematical Sciences (PIMS) is organizing a Mathematical Biology Summer School at the University of Alberta in Edmonton, Canada, May 27-June 14, 2013, on “The Mathematics Behind Biological Invasions.”

Continue reading

In recent years, governments around the world have experimented with many different policy tools to encourage the growth of renewable energy. Continue reading

The Italian National Institute of Advanced Mathematics (INdAM) is organizing a Workshop “Mathematical models and methods for Planet Earth” in Rome, Italy, on May 27-29, 2013. Continue reading

During the week of May 13, 2013, thirty-four students from around the United States attended the Statistical and Mathematical Sciences Institute (SAMSI) Undergraduate Modeling Workshop. Continue reading

In coastal ocean, estuary, and lake systems, there is much interest in understanding, detecting, and predicting biological events. Continue reading

“Neglected Tropical Diseases” isn’t just a generic title for all the forgotten diseases in the world; it’s a specific designation on behalf of the World Health Organization for 13 particular diseases that qualify for neglected status. Collectively, these diseases infect about one sixth of the world’s population. Continue reading

This week at AIM features a MPE related workshop concerned with boundary-value problems for nonlinear dispersive evolution equations and systems. The workshop has participants with diverse interests in both the pure and applied aspects of such problems. Continue reading

There is widespread interest in finding and designing spacecraft trajectories to the Moon, Mars, other planets, or other celestial bodies (comets, asteroids), which require as little fuel as possible. Continue reading

Pressure is an important property of fluid flow, and it is known that the pressure changes continuously in the fluid domain. In the coupling of flows of different nature, however, the situation can be more complicated and discontinuities may appear in the pressure field. Continue reading

I recently had the opportunity to travel to the Antarctic peninsula on board the National Geographic Explorer. We departed out of Ushuaia, Argentina, crossed the Drake Passage and spent the better part of a week exploring the northwestern side of the Antarctic peninsula from the South Shetland Islands to just inside the Antarctic Circle in Crystal Sound. Continue reading

Brinicles are fun things to think about, but they also have broader implications. On one hand, as heat flows through them, they contribute to the energy balance in the ice pack around Antarctica. On the other hand, brinicles may have played a role in the beginnings of life on the early Earth. Continue reading

Today’s blog is an update on a story that was in the news earlier and also some comments on a recent article in the New York Review of Books. (See the blog of 4.11.2013.)

Continue reading

How fast does water flow through sand or soil? Maybe not so fast, but everyone has seen water soak into beach sand and garden soils. Most people have also noticed a concrete sidewalk soaking up a little water as rain begins to come down. But how fast does water flow through a rock? Continue reading

How precarious is the existence of the Monarch butterfly? Does personal diet affect the environment? What are the consequences of increased human life expectancy? Continue reading

Our team had begun our initial work on what we call the “berry problem”, and I was able to describe our efforts to help stakeholders in the Pajaro Valley region in California balance water needs among competing interests. Continue reading

Most buildings more than 20 years old are energy “hogs.” They take a lot of energy to heat in the winter, and they take a lot of energy to cool in the summer. The benefits of saving energy in buildings are enormous. Continue reading

Hydrogen fuel cells are of interest as an alternative energy technology. They are electrochemical systems that combine hydrogen and oxygen (from air) to produce electrical energy. They have potential for use in many applications, including automotive, stationary power and small-scale power for mobile electronics. Continue reading

This week (April 14-20) is National Environmental Education Week. Monday April 22 is Earth Day! On that day, the U.S. Department of Education will announce the winners of the second annual Green Ribbon School awards. Continue reading

In January of 2011, AIM held a Sustainability Problems workshop, with the goal of bringing together mathematicians and industry representatives to work on a variety of sustainability problems, including renewable energy, air quality, water management, and other environmental issues. Continue reading

An exciting aspect of the relationship between mathematics and biology is the potential — the expectation even — that biology will provide the impetus for new mathematics, and that the feedback loop between mathematics and biology will be at least as influential and exciting as the one mathematics and physics has enjoyed for over 2000 years.

Continue reading

It was unusually warm and windy for early April. We piled into the toasty lecture hall with drinks and sandwich wraps in hand. Dr. Smith, with his shock of white hair and the thin frame of a marathon runner, shed his sport jacket as he recounted the 2003 European heat wave. Continue reading

Mathematical modeling and data analysis play a critical role in the mathematics of Planet Earth. Continue reading

The Next Generation Science Standards have just been released. They propose that climate change be an integral part of science education starting already in middle school. Continue reading

Last Friday, the Wall Street Journal published an essay by E.O. Wilson that has since generated much discussion from readers (229 comments to date) on the WSJ website and also among mathematicians. Continue reading

A lake that used to be clear, with a rich vegetation and a diverse aquatic life, suddenly becomes turbid, with much less vegetation and only bottom dwelling fish remaining. It turns out that the change comes from increased nutrient loading, but when the runoff leading to the nutrient inflow is reduced, the lake doesn’t become clear again - it remains murky. Continue reading

Please join us at the World Conference on Natural Resource Modeling. This annual meeting is run by the Resource Modeling Association. In June 2013, the conference will be held at Cornell University. Continue reading

Last week I attended “MECC 2013” – the International Conference and Advanced School Planet Earth, Mathematics of Energy and Climate Change, Portugal, 21-28 March 2013. Continue reading

Mathematical models can be used to study the spread of technological innovations among individuals connected to each other by a network of peer-to-peer influences, such as in a physical community or neighborhood. Continue reading

As the energy needs are expected to surpass the energy content found in available fossil-fuel resources in this century, interest in renewable energy sources has increased in the past decade. One area of interest is in geothermal energy harvesting. Continue reading

April is Mathematics Awareness Month (MAM). This year’s theme is **Mathematics of Sustainability**, which explores how mathematics helps us better understand these complex questions. Continue reading

A distinguished panel of experts, gathered by the National Academies, has recently produced a very interesting and informative publication: Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. This publication was released by the National Academies in advance of their report The Mathematical Sciences in 2025, developed with support from the National Science Foundation. Continue reading

This morning I heard a lecture by Rick Anthes, president emeritus of UCAR, former director of NCAR. His talk was entitled “Butterflies and Demons,” and the subject was predictability of weather and climate. He was a witness to, and participant in the development of numerical weather prediction in the form it exists today at weather centers worldwide. It was a particularly interesting and provocative talk.

Continue reading

Last Saturday, at the Association for Women in Mathematics (AWM) Research Symposium at Santa Clara University, Inez Fung gave a wonderful spirited lecture on “Climate Math.” Continue reading

For the past nine weeks, I had the privilege to teach a Massive Open Online Course(MOOC) on image and video processing. Continue reading

This month marks the 50th anniversary of the 1963 publication of Ed Lorenz’s groundbreaking paper, *“Deterministic Nonperiodic Flow,”* in the Journal of Atmospheric Science. This seminal work, now cited more than 11,000 times, inspired a generation of mathematicians and physicists to embrace the nonlinearity governing our complex world. Continue reading

It took approximately 40 years for the community of mathematicians to become aware of the various difficulties facing human society in the near future and to accept to work on these questions. Continue reading

One of the most famous images in Japanese art is the Great Wave off Kanagawa, a woodblock print by the Japanese artist Hokusai. The print is also famous in mathematics: the structure of the breaking wave at its crest illustrates features of self-similarity, and the large amplitude of the wave has led it to be interpreted as a rogue wave generated from nonlinear wave effects. Continue reading

While the European launch of MPE2013 was taking place at the UNESCO Headquarters in Paris, a youth festival was taking place in Lisbon at “Pavilhão do Conhecimento,” the largest science center in Portugal, with hundred of pupils participating in mathematics popularization activities directly or indirectly related to the mathematics of planet earth for schools. Continue reading

March 11, marks two years from the 2011 9.0 earthquake, with epicenter located off the coast of Japan, which caught the world by surprise, including expert seismologists. Continue reading

Sub-Sahara Africa is the epicenter for both the HIV epidemic and poverty. Continue reading

On Monday, March 4, Emily Shuckburgh delivered the second of the MPE2013-Simons Public Lecture Series talk, “Climate disruption: what math and science have to say” at the Palace of Fine Arts in San Francisco. Continue reading

On March 5, at 9:00 am, the first visitors started to explore the 20 modules of the first MPE exhibition at the UNESCO Headquarters in Paris. Continue reading

Twenty-nine entries were submitted for the competition for modules for a virtual exhibition Continue reading

Though waves of one sort or another are a ubiquitous part of our daily experience, we have to get on with our lives, and therefore tend not to think of the wavelike nature of daily phenomena. Those fortunate among us who can escape to the shore on a hot August week can then take the time to observe the sea and the waves she sends us. Continue reading

This past week at AIM Mark Ablowitz told me about an interesting article (with beautiful pictures) he wrote with Douglas Baldwin called “Nonlinear shallow ocean-wave silicon interactions on flat beaches.” The propagation of these waves may contribute to the growth of tsunami waves. Continue reading

A small research group has been meeting at the American Institute of Mathematics (AIM) in Palo Alto, CA, during the week of Feb. 18-22 to work on integrable systems of nonlinear Schroedinger type, a special class of nonlinear partial differential equations (PDEs). Continue reading

One of the reasons for designating 2013 as the year of “Mathematics of Planet Earth” is to showcase the work done by mathematics in application areas like climate, ocean, and earth sciences. The SIAM Conference on CS&E, which begins on February 25th, contains many sessions relevant to MPE 2013. Continue reading

I was planning to send an update every day from the data assimilation workshop at the Banff Center, but I’ve been so busy here that by the time I get back to my room I’m ready to collapse. The Banff Center is the best place I know of for a workshop. It’s almost like working hard and being on vacation at the same time, with the benefits of both. Continue reading

I was planning to send an update every day from the data assimilation workshop at the Banff Center, but I’ve been so busy here that by the time I get back to my room I’m ready to collapse. The Banff Center is the best place I know of for a workshop. It’s almost like working hard and being on vacation at the same time, with the benefits of both. Continue reading

The close approach of the asteroid that we have all read about in the newspapers represents something of a coincidence for me as I prepare for the data assimilation workshop in Banff this coming week. Continue reading

“Science without data is science-fiction.” This was on of the boldest (if more facetious…) statements heard at the workshop “Models and Methods in Ecology and Epidemiology (M2E2)” held at CRM last week. Speakers from very diverse backgrounds presented a wide rage of mathematical models developed to better understand the dynamics and propagation mechanisms of, amongst others, Avian Flu, Lyme Disease and the West Nile virus. Throughout the presentations, the pervasive role played by data incorporation in the models was emphasized, and the equally important organization of model development as a team effort was underlined. Continue reading

You would be forgiven for not initially recognizing some of the high-level similarities between the practice of research in sciences such as physics and research in ornithology. One basic similarity is that we are all constrained in what we can measure. Quantum physics has its uncertainty principle that describes limits on what can be measured. Ornithologists are at times limited in what they can measure by the very things that they are trying to observe: birds will sometimes actively avoid detection. Continue reading

One hears occasionally in the popular media that one possible consequence of global warming might be the disappearance of the Gulf Stream. This makes physical oceanographers cringe. The Gulf Stream and its analogs in other ocean basins exist for fundamental physical reasons. Climate change may well bring changes in the Gulf Stream. It may not be in the same place, may not be of the same strength or have the same temperature and salinity characteristics, but as long as the continents bound the great ocean basins, the sun shines, the earth turns toward the east and the wind blows in response, there will be a Gulf Stream. Continue reading

A scientific workshop, as part of the pan-Canadian MPE2013 thematic program “Models and Methods in Ecology, Epidemiology and Public Health (M2E2)”, started at CRM today. The workshop, focusing on models and methods in ecology and epidemiology, was designed to initiate … Continue reading

I have been involved with MPE2013 activities since the first organizing workshop was held at AIM in March of 2011, not as a mathematician with MPE areas of interest, but more as an institute staff member helping to bring about … Continue reading

It is increasingly clear that we are initiating a sequence of dramatic events across our planet. They include habitat loss, an increased rate of extinction, global warming, the melting of ice caps and permafrost, an increase in extreme weather events, … Continue reading

Prepared by Ali Nadim (Claremont Graduate University) and Ami Radunskaya (Pomona College) What do green buildings, environmental toxins, sources of ozone pollution in the atmosphere, and infrastructure planning for electrical power have in common? They were all topics of intense … Continue reading

A workshop is taking place this week at the American Institute of Mathematics (AIM) in Palo Alto, California, on “Stochastics in Geophysical Fluid Dynamics: Mathematical foundations and physical underpinnings.” This workshop is co-organized by Nathan Glatt-Holtz (Institute of Mathematics and … Continue reading

A book review in the January 11 issue of Science magazine begins with a wonderful line: “It is not often that mathematical theory is tested with a machine gun.” The book under review is “How Species Interact: Altering the Standard … Continue reading

I have wanted to run this story down since I saw the reference in Lamb’s Hydrodynamics to a paper by G. I. Taylor that contains a description of what oceanic and atmospheric scientists call “Ekman layers.” Physical oceanographers learn early … Continue reading

This session, organized by Thomas Bellsky, Arizona State University, and Lewis Mitchell, University of Vermont, focused on applications of data assimilation to climate issues. It opened with a talk by Chris Jones of the University of North Carolina at Chapel … Continue reading

In concert with the MPE 2013 initiative, the NSF’s Mathematical Biosciences Institute (MBI) at Ohio State will host the Keyfitz Centennial Symposium on Mathematical Demography in June 2013, cosponsored by the OSU Institute for Population Research (IPR). The main goal … Continue reading

I am attending the Joint Mathematics Meetings in San Diego, where I was convinced to help organize a special session on environmental mathematics focused on evaluating past climate changes and modeling of future variations. I am a meteorologist by training … Continue reading

I was thrilled to get your last letter. I’m glad to see you are looking at some of the references I sent you last time. Figuring out who is responsible for higher atmospheric levels and how to respond to climate … Continue reading

In January I am normally in a southern US city attending the American Meteorological Society annual meeting. This week, I am in San Diego attending a different AMS – the American Mathematical Society Joint Mathematics Meetings. I am helping to … Continue reading

Doing your school research paper on climate change sounds like a great idea! Let me see if I can get you started. I’ll even put a few references at the end in case you want to look those up for … Continue reading

It is often the case that at the end of one of my talks about some aspect of climate research or about the development of tools for the analysis of climate I get asked questions regarding global warming. Whether global … Continue reading

Upon encountering a mathematics topic such as logarithms, students in typical introductory mathematics classes often ask “When will I ever use this math?” Without seeing relevant applications, students lose motivation and without motivation, they struggle to learn the concepts. In … Continue reading

As we enter the new year, SIAM — along with more than one hundred universities, research institutes, and other scientific organizations —is thrilled to be a part of Mathematics of Planet Earth 2013. It is an exciting year-long program dedicated … Continue reading

Unprecedented in its all encompassing scope and geographic reach, the MPE2013 year brings to the forefront the universality of mathematics, with the hopes of making the general public aware of the insights it provides into many human endeavors, of its … Continue reading