Problems of physics

Nayantara Bhatnagar

Water turning into ice at its freezing point or the magnetization of iron are examples of phase transitions. Properties such as volume or heat capacity change at the transition point.

Phase transitions also arise in models such as attracting and repelling particles on a lattice. The energy of such systems can be mathematically modeled, but it is difficult because of the exponential numbers of possible configurations even for a small number of particles.

Nayantara Bhatnagar is developing tools and theories to understand the locations of phase transitions in such models and their nature—whether abrupt and discontinuous or smooth from one phase to another.

She also is creating new research opportunities for graduate and undergraduate students in probability and developing mentoring programs with the goal to retain women in mathematics.

New avenues in math education

Charles Hohensee

“Backward transfer” refers to the process of new language learning interfering with (or sometimes enhancing) comprehension of a previously acquired language. But backward transfer also has been found to occur when students learn math.

As a middle-schooler begins to do quadratic equations in algebra, such as 3×2 + 6x = -10, that student may suddenly be at a loss doing previously learned linear equations, such as 4x = 20.

Charles Hohensee is exploring how negative influences of backward transfer can be minimized and the effectiveness of math instruction be increased. He will share findings at national conferences and in journals, as well as at a summer course for UD pre-service teachers and a local math teachers’ club.

Defects that matter

Anderson Janotti

Anderson Janotti develops computational models of defects in materials that are used for energy, electronics and optoelectronics applications. The ability to control the type and number of defects determines whether a given material will be suitable for various devices.

Not surprisingly, defects can be detrimental to performance, limiting the efficiency of solar cells, for example. However, defects also can be manipulated to boost desirable characteristics, which is Janotti’s focus.

By adding minute concentrations of impurities to a semiconductor such as silicon, a good insulator can be transformed into an excellent conductor, he explains. Such technology is widely used today in the microchips inside our computers, smartphones and tablets.

Go away, greenhouse gas

Bingjun Xu

Bingjun Xu wants to reduce levels of carbon dioxide, a major greenhouse gas, in a new way.
“Climate change has sparked a great deal of interest in harvesting the sun and wind to produce renewable electricity, but a major disadvantage is that these energy sources are intermittent,” he says.

Matching peak production to peak demand involves storing the harvested energy and delivering it when needed. An alternative is to use the energy as it’s produced.

Xu wants to use it to convert atmospheric CO2 into fuels and chemicals through an electrochemical process. He’ll be probing how electrodes and electrolytes interact at the molecular level to establish guiding principles for the process and for developing new devices.