Scientists have long studied how atoms and molecules structure themselves into intricate clusters. Unlocking the design secrets of nature offers lessons in engineering artificial systems that could self-assemble into desired forms.In the Jan. 29 issue of Science, a team from Harvard led by Vinothan Manoharan and Michael Brenner presents additional clues to how and why groups of atoms and molecules may favor less symmetrical and more complex, flexible geometric patterns.The answer relates to a familiar concept in physics called entropy, the ways in which particles are able to arrange themselves. The researchers first caught sight of the link by using magnetic “stick and ball” construction toys that can make varying shapes.Manoharan, associate professor of chemical engineering and physics in Harvard’s School of Engineering and Applied Sciences (SEAS) and the Department of Physics, and his colleagues used colloidal particles, a suspended chemical mixture seen in semi-solid foods such as mayonnaise, to simulate the clustering behavior of atoms and molecules.“To allow clusters to form, we put a few tiny polystyrene spheres in microscopic cylindrical wells filled with water. The particles act as ’sticky’ hard spheres and naturally cluster together just like groups of nearby interacting atoms and molecules do,” said Manoharan.The researchers expected that simple, highly symmetric shapes would arise most often. Instead, two surprising, related, and scalable phenomena arose when the number of particles used in their experiments reached six or rose above nine.Six particles can form into a symmetrical octahedron and into a more complex tri-tetrahedron shape. In terms of chemical structure, each shape results in 12 bonds, and hence, has the same amount of potential energy. With the potential energy being equal, Manoharan and colleagues thought that both shapes would occur in equal proportion. They found, however, that the tri-tetrahedron occurs 20 times more often than the octahedron.“The only possible explanation was entropy,” said Manoharan. “Most people are familiar with entropy as a measure of ‘disorder,’ but the most useful definition of entropy is simply the number of different ways a bunch of particles can arrange themselves.”Natalie Arkus, a former applied mathematics graduate student who worked with Brenner, the Glover Professor of Applied Mathematics and Applied Physics, provided a hint to solving the puzzle, as she discovered a method to calculate all the possible structures that could be formed using geometric magnetic toys made up of magnetic metal rods and silver ball bearings.Since there are more ways for the complicated tri-tetrahedron structure to form (something that can be seen by labeling the toy spheres and counting the ways they can be put together), the shape appears far more frequently than the octahedron. In general, among clusters with the same potential energy, highly symmetric structures are less likely to arise.The researchers also found that when the number of particles reaches nine or higher, entropy plays another important role.Because the number of possible structures with nine or more particles is vast, the team focused on what are called nonrigid, or flexible, structures. Nonrigidity occurs when a cluster is half octahedral and shares at least one vertex, allowing the cluster to twist without breaking or forming another bond (something also easily seen by using the toys).“Because they can move flexibly, the nonrigid clusters have high vibrational entropy,” explained Manoharan. “In cases with nine or more particles, symmetric clusters do not appear as often due to rotational entropy. The ability to rotate is useful, as it allows clusters to have extra bonds.”As a general rule, the team found that for all clusters up to eight particles and a select number of structures with up to 12, the most symmetric structures occurred the least often due to entropy.“Our findings illustrate, in a tangible way, what the concept of entropy means,” said Manohran.Looking ahead, the researchers are interested in using their results to understand the emergence of bulk crystallization, or how particles come together in the early stages of forming a crystal.Manoharan and Brenner’s co-authors included Guangnan Meng, a research associate in the Department of Physics at Harvard University, and Natalie Arkus, a graduate of SEAS and now a postdoctoral fellow at the Rockefeller University. The authors acknowledge support from theNational Science Foundation and the Defense Advanced Research Projects Agency.
Washington Hall rang with laughter Monday evening from first-year Moreau First Year Experience students who had gathered to watch and participate in Sex Signals, an annual improvisational comedy show sponsored by the Gender Relations Center (GRC) that aims to educate and inspire student discussion about sex, relationships and consent.The show was introduced to Notre Dame five years ago, but it is the first year the GRC is partnering with the Moreau program to allow students to receive ten extra credit points for their attendance, GRC director Christine Gebhardt said in an email. Poncho Ortega | The Observer Jessamyn Fitzpatrick, left, and Vincent Banks of Catharsis Production perform during ‘Sex Signals’ Monday night. The Gender Relations Center program aims to create a culture of consent.“This year we revised the design of the first two weeks to be more conversation based and included the opportunity for Sex Signals, which uses humor, case studies and audience participation,” Gebhardt said. “It is our hope that the extra credit will give students an incentive to make the event a priority, as it is our institution’s way of acknowledging how the conversation should not merely happen in class but throughout our campus.”Vincent Banks and Jessamyn Fitzpatrick of Catharsis Productions — the Chicago-based performance group running Sex Signals, launched into a discussion about sexual relationships in a campus setting —“How many of you had sex ed classes in high school?” Banks asked the audience.A majority of students raised their hands.“What did you learn in those classes?” he asked.Students shouted out their answers.“Did anyone learn how to have sex. — other than from porn” Banks said half-jokingly in response.Throughout their hour and 15 minute performance, Banks and Fitzpatrick interacted with their audience as they acted out three hypothetical scenarios representative of real-life situations — flirting at a party, sexual harassment at a gym and dealing with people who make excuses for sexual assault in the name of friendship. The acts were used as teaching tools to break stereotypes, explain gender spectrums, clearly define consent, fight against victim-blaming and encourage bystander intervention.Towards the end of the program, the performers called for students to “raise the bar” on campus by making a culture of consent so normal that it would force those who do not ask for it to stand out.First year Danielle Slevin attended the performance with her friend and — fellow first year — Helton Rodriguez.“I felt that it was really empowering and really moving, especially to be in a room full of kids who might have experiences similar to mine or who feel the way I do. … I have friends who have been affected, whether it’s being uncomfortable at parties, or things that have escalated to more serious situations that were usually induced by alcohol,” Slevin said. “It’s a serious thing that is present on this campus, and it’s something that should be spoken about.”Rodriguez, who participated during the show, said he reflected on how the issues presented in the show were present in his life.“Whenever I have girls over at my dorm to study, I always have to ask if they’re comfortable walking home alone,” he said. “And it’s just kind of a sucky part of life.”He feels that Notre Dame’s strong Catholic identity can reinforce values preventing sexual assault, but also can make the topic a taboo to talk about.“I think, regardless, it’s problem on campus,” he said. “You can argue whether or not it’s harder or easier to talk about, but you have to talk about it.”Editor‘s note: A previous version of this article used the incorrect gender pronouns when referring to a student on first mention. The Observer regrets this error.Tags: Gender Relations Center, Moreau First Year Experience, Sex Signals, sexual assault
The Trojans responded to their first loss of the season with one of their most lively practices yet. It was visibly louder, as coaches and players shouted words of encouragement to each other.“I can help the run game by being a vocal guy to get the offensive line together,” said redshirt senior quarterback Cody Kessler, after Tuesday’s practice. “I think getting in on the sideline and getting them pumped up, which I have been trying to do a lot.”After a 41-31 loss to Stanford, this close-knit USC team is stressing accountability as key to moving on.“Guys admit that they are wrong and learn from it and then move on,” Kessler said. “And it’s cool, you can call them out in the meeting room, and then they respond to it. Instead of putting their head down or being upset, they stand up and let the guys know that they will fix it. And that is what you need to be successful after a loss.”Kessler continued his impressive play this season against Stanford, completing 25 of 32 passes for 272 yards with three touchdowns and no interceptions. Unfortunately, his counterpart, Kevin Hogan, did as well. Without adequate pressure from the Trojan defense, he completed 18 of 23 passes for 279 yards and two touchdowns.“The problem, when we missed [Hogan] our rush lane integrity was not good, and we allowed for him to escape the pocket whether it was on the perimeter or through the b-gap on a couple of other instances that he took advantage of and hurt us on,” head coach Steve Sarkisian said. “So that is what we need to clean up. We are trying to go sack the quarterback, and we are going to continue [making] him uncomfortable.”Not only did the Trojans allow Stanford to throw the ball, they also allowed their rushing attack, led by freshman Christian McCaffrey, 115 yards. The USC defense allowed Stanford to score on seven of its nine possessions and convert eight of 12 third down conversions.“I just felt like in the run game, we didn’t knock back the line of scrimmage enough,” Sarkisian said. “I felt like the game was played too much on the line of scrimmage or on our side of the line of scrimmage. We didn’t have enough tackles for losses or penetrations. We had a couple, but not nearly enough against a quality opponent on first and 10.”Along with Kessler’s performance, another positive takeaway’s from Saturday’s game was evidently USC’s run game, which the coaches emphasized last week was essential in defeating Stanford. Though the game plan worked well early on, as USC scored touchdowns on three of its first four possessions, Hogan’s play on third down often left the USC running backs on the sideline. The Trojan offense scored only 10 points over the final 39 minutes and 29 seconds.Third downs continued to be an issue for the USC offense too, in a game that Stanford dominated in time of possession and number of plays run.“I thought we got a little bit better on third down with the 40 percent, on four out of 10. But our mark is always 50 percent or better,” offensive coordinator Clay Helton said. “Our job right now is to score every time we get the ball, and that is what we tell the offense. Our job was to score 42 that night.”While the Trojans did score 31 points, they will have to prepare for games with similarly high scores in the pass-happy Pac-12, which will certainly be a challenge against an Arizona State pass defense that is ranked ninth in the nation.“In the second half, score more points, double the opponents score and establish the run,” said running back Tre Madden, when asked how USC’s offense can improve heading into the desert. “Being physical and being able to put the game away. And that is what we are going to focus on.”“We didn’t expect to lose, but it’s football,” said Madden, who left Saturday’s game with a calf injury.Madden said he will be fully able to play against Arizona State.“They wanted to win, obviously, and we just have to move on and focus on this next Pac-12 South game, because all of our goals are still in front of us,” he said. “We’re just trying to take it week by week.”