Nav: Home

What atoms do when liquids and gases meet

January 24, 2019

Although this is correct on larger scales, the assumption fails on smaller scales, according to various experiments and computer simulations carried out in recent decades. In an article recently published in Nature Physics, a group of mathematicians from Universidad Carlos III de Madrid (UC3M) and Imperial College London have come up with a new approach that solves this problem.

When materials are in a solid state, their atoms are arranged in very uniform patterns, like grids, sheets and lattices. This means that, knowing the position of one atom, we can deduce the positions of all its neighbouring atoms. However, in liquids and gases, the arrangement of the atoms is very different, since they are subject to a disorderly motion. As a result of this motion, the atoms may be "locally" packed closely together for a moment, which leads to greater instantaneous density, and then separate. This only happens at microscopic scales; on larger scales, we are unable to discern this behaviour.

In order to explain these systems, the theory of capillary waves had been used successfully, which fits with the "drum skin" analogy. However, at smaller scales, this theory fails. For decades, all attempts to "adapt" it by means of small modifications have been unsuccessful and we have been unable to reproduce the experimental results and computer simulations. However, the authors of this study have found that a more microscopic (and, therefore, more fundamental) description can neatly explain these elusive results.

According to the authors of the study, the key lies in the fact that the functions that describe the arrangement of the atoms exhibit certain mathematical properties called "resonances" which, until now, had gone unnoticed. Taking these resonances into account, the mathematical consistency of the problem itself means the solution has to adopt a very particular form. "It's a completely new way of viewing the liquid-gas interface that can be applied to other systems; for example, by putting into contact two different liquids that do not mix," explains one of the authors of the study, Professor Andrew Parry, from the Mathematics Department at Imperial College London.

"The most surprising thing for us was the simplicity and neatness of the mathematics of this theory and the fact that the theoretical models that we had all used for decades turn out to be, quite unexpectedly, special cases without any significance. Who would have suspected it?" says Carlos Rascón, co-author of the study and lecturer from the Mathematics Department at UC3M.

The study has not only given rise to a consistent description of the liquid-gas fluctuations but it has also, in an indirect fashion, allowed for the discovery of a family of theoretical models that can be solved analytically, without the need to use computer numerical calculations. Models with analytical solutions are always welcome in physics because they allow for a very useful comparison with more complex models. "In truth, these new analytical models are going to involve more work for us. Perhaps it would have been better not to have discovered them," jokes Carlos Rascón.
-end-
Bibliographic reference: A.O. Parry and C. Rascón. The Goldstone Mode and Resonances in the Fluid Interfacial Region. Nature Physics. 10 December 2018 https://www.nature.com/articles/s41567-018-0361-z

Universidad Carlos III de Madrid

Related Mathematics Articles:

More democracy through mathematics
For democratic elections to be fair, voting districts must have similar sizes.
How to color a lizard: From biology to mathematics
Skin color patterns in animals arise from microscopic interactions among colored cells that obey equations discovered by Alan Turing.
Mathematics supports a new way to classify viruses based on structure
New research supports a structure-based classification system for viruses which could help in the identification and treatment of emerging viruses.
US educators awarded for exemplary teaching in mathematics
Janet Heine Barnett, Caren Diefenderfer, and Tevian Dray were named the 2017 Deborah and Franklin Tepper Haimo Award winners by the Mathematical Association of America (MAA) for their teaching effectiveness and influence beyond their institutions.
Authors of year's best books in mathematics honored
Prizes for the year's best books in mathematics were awarded to Ian Stewart and Tim Chartier by the Mathematical Association of America (MAA) on Jan.
The mathematics of coffee extraction: Searching for the ideal brew
Composed of over 1,800 chemical components, coffee is one of the most widely-consumed drinks in the world.
Even physicists are 'afraid' of mathematics
Physicists avoid highly mathematical work despite being trained in advanced mathematics, new research suggests.
Mathematics and music: New perspectives on the connections between these ancient arts
World-leading experts on music and mathematics present insights on the connections between these two ancient arts, especially as they relate to composition and performance, as well as creativity, education, and geometry.
Kindergarteners' mathematics success hinges on preschool skills
In a study funded by the National Science Foundation, researchers at the University of Missouri discovered that preschoolers who better process words associated with numbers and understand the quantities associated with these words are more likely to have success with math when they enter kindergarten.
First international mathematics research institute launched in Australia
World leaders in the mathematical sciences are visiting Melbourne for a series of research programs at Australia's first international research institute for mathematics and statistics.

Related Mathematics Reading:

Best Science Podcasts 2019

We have hand picked the best science podcasts for 2019. Sit back and enjoy new science podcasts updated daily from your favorite science news services and scientists.
Now Playing: TED Radio Hour

Digital Manipulation
Technology has reshaped our lives in amazing ways. But at what cost? This hour, TED speakers reveal how what we see, read, believe — even how we vote — can be manipulated by the technology we use. Guests include journalist Carole Cadwalladr, consumer advocate Finn Myrstad, writer and marketing professor Scott Galloway, behavioral designer Nir Eyal, and computer graphics researcher Doug Roble.
Now Playing: Science for the People

#529 Do You Really Want to Find Out Who's Your Daddy?
At least some of you by now have probably spit into a tube and mailed it off to find out who your closest relatives are, where you might be from, and what terrible diseases might await you. But what exactly did you find out? And what did you give away? In this live panel at Awesome Con we bring in science writer Tina Saey to talk about all her DNA testing, and bioethicist Debra Mathews, to determine whether Tina should have done it at all. Related links: What FamilyTreeDNA sharing genetic data with police means for you Crime solvers embraced...