"With the aid of soap films we have solved variational mathematical problems, which appear in the formulation of many physical problems", explains Carlos Criado, professor at the University of Málaga, speaking to SINC. Together with his colleague Nieves Álamo, he has just published his work in the American Journal of Physics.
Soap films always adopt the shape which minimises their elastic energy, and therefore their area, so that they turn out to be ideal in the calculus of variations, "where we look for a function that minimises a certain quantity (depending on the function)", adds the researcher.
"Of course there are other ways to solve variational problems, but it turns out to be surprising, fun and educative to obtain soap films in the shape of brachistochrones, catenaries and semicircles", Criado emphasises.
The professor offers the example of the famous problem of the brachistochrone curve. What shape must a wire be in order that a ball travels down it from one end to the other (at a different height) as rapidly as possible? The answer is the brachistochrone (from the Greek brachistos, the shortest, and cronos, time), the curve of fastest descent.
New methods for old problems
The mathematician Johann Bernoulli found the answer centuries ago when he realised that it was a cycloid (the curve described by a point on a circle rolling along a line). That was the origin of the calculus of variations, which was also used in other classic problems, like that of the catenary (the shape of a chain suspended by its endpoints) and the isoperimetric curve (a curve which maximises the area it encloses).
The study shows that these calculations may be related to Plateau's problem, that is, to find the shape adopted by a soap film under certain boundary restrictions. Besides, the researchers show how to design the experiments, constraining the soap films between two surfaces in such a way as to obtain the appropriate curves.
Other Spanish researchers, like Isabel Fernández, of the University of Seville, and Pablo Mira, of the Polytechnic University of Cartagena, have succeeded in finding for the first time the solution to specific mathematical problems (the Bernstein problem in the Heisenberg space) with the help of soap films.
References: C. Criado y N. Alamo. "Solving the brachistochrone and other variational problems with soap films". American Journal of Physics 78 (12): 1400-1405, diciembre de 2010.
SINC | EurekAlert!
Explained: Why water droplets 'bounce off the walls'
27.02.2020 | University of Warwick
Scientists 'film' a quantum measurement
26.02.2020 | Stockholm University
Researchers at the University of Bayreuth have discovered an unusual material: When cooled down to two degrees Celsius, its crystal structure and electronic properties change abruptly and significantly. In this new state, the distances between iron atoms can be tailored with the help of light beams. This opens up intriguing possibilities for application in the field of information technology. The scientists have presented their discovery in the journal "Angewandte Chemie - International Edition". The new findings are the result of close cooperation with partnering facilities in Augsburg, Dresden, Hamburg, and Moscow.
The material is an unusual form of iron oxide with the formula Fe₅O₆. The researchers produced it at a pressure of 15 gigapascals in a high-pressure laboratory...
Study by Mainz physicists indicates that the next generation of neutrino experiments may well find the answer to one of the most pressing issues in neutrino physics
Among the most exciting challenges in modern physics is the identification of the neutrino mass ordering. Physicists from the Cluster of Excellence PRISMA+ at...
Fraunhofer researchers are investigating the potential of microimplants to stimulate nerve cells and treat chronic conditions like asthma, diabetes, or Parkinson’s disease. Find out what makes this form of treatment so appealing and which challenges the researchers still have to master.
A study by the Robert Koch Institute has found that one in four women will suffer from weak bladders at some point in their lives. Treatments of this condition...
The operational speed of semiconductors in various electronic and optoelectronic devices is limited to several gigahertz (a billion oscillations per second). This constrains the upper limit of the operational speed of computing. Now researchers from the Max Planck Institute for the Structure and Dynamics of Matter in Hamburg, Germany, and the Indian Institute of Technology in Bombay have explained how these processes can be sped up through the use of light waves and defected solid materials.
Light waves perform several hundred trillion oscillations per second. Hence, it is natural to envision employing light oscillations to drive the electronic...
Most natural and artificial surfaces are rough: metals and even glasses that appear smooth to the naked eye can look like jagged mountain ranges under the microscope. There is currently no uniform theory about the origin of this roughness despite it being observed on all scales, from the atomic to the tectonic. Scientists suspect that the rough surface is formed by irreversible plastic deformation that occurs in many processes of mechanical machining of components such as milling.
Prof. Dr. Lars Pastewka from the Simulation group at the Department of Microsystems Engineering at the University of Freiburg and his team have simulated such...
12.02.2020 | Event News
16.01.2020 | Event News
15.01.2020 | Event News
27.02.2020 | Life Sciences
27.02.2020 | Life Sciences
27.02.2020 | Life Sciences