Computers Math

From designing new airplane wings to better understanding how fuel sprays ignite in a combustion engine, researchers have long been interested in better understanding how chaotic, turbulent motions impact fluid flows under a variety of conditions. Despite decades of focused research on the topic, physicists still consider a fundamental understanding of turbulence statistics to be among the last major unsolved challenges in physics.
Due to its complexity, researchers have come to rely on a combination of experiments, semi-empirical turbulence models, and computer simulation to advance the field. Supercomputers have played an essential role in advancing researchers’ understanding of turbulence physics, but even today’s most computationally expensive approaches have limitations.
Recently, researchers at the Technical University of Darmstadt (TU Darmstadt) led by Prof. Dr. Martin Oberlack and the Universitat Politècnica de València headed by Prof. Dr. Sergio Hoyas started using a new approach for understanding turbulence, and with the help of supercomputing resources at the Leibniz Supercomputing Centre (LRZ), the team was able to calculate the largest turbulence simulation of its kind. Specifically, the team generated turbulence statistics through this large simulation of the Navier-Stokes equations, which provided the critical data base for underpinning a new theory of turbulence.
“Turbulence is statistical, because of the random behaviour we observe,” Oberlack said. “We believe Navier-Stokes equations do a very good job of describing it, and with it we are able to study the entire range of scales down to the smallest scales, but that is also the problem — all of these scales play a role in turbulent motion, so we have to resolve all of it in simulations. The biggest problem is resolving the smallest turbulent scales, which decrease inversely with Reynolds number (a number that indicates how turbulent a fluid is moving, based on a ratio of velocity, length scale, and viscosity). For airplanes like the Airbus A 380, the Reynolds number is so large and thus the smallest turbulent scales are so small that they cannot be represented even on the SuperMUC NG.”
Statistical averages show promise for closing an unending equation loop
In 2009, while visiting the University of Cambridge, Oberlack had an epiphany — while thinking about turbulence, he thought about symmetry theory, a concept that forms the fundamental basis to all areas of physics research. In essence, the concept of symmetry in mathematics demonstrates that equations can equal the same result even when being done in different arrangements or operating conditions. More

We have all seen crystals, whether a simple grain of salt or sugar, or an elaborate and beautiful amethyst. These crystals are made of atoms or molecules repeating in a symmetrical three-dimensional pattern called a lattice, in which atoms occupy specific points in space. By forming a periodic lattice, carbon atoms in a diamond, for example, break the symmetry of the space they sit in. Physicists call this “breaking symmetry.”
Scientists have recently discovered that a similar effect can be witnessed in time. Symmetry breaking, as the name suggests, can arise only where some sort of symmetry exists. In the time domain, a cyclically changing force or energy source naturally produces a temporal pattern.
Breaking of the symmetry occurs when a system driven by such a force faces a déjà vu moment, but not with the same period as that of the force. ‘Time crystals’ have in the past decade been pursued as a new phase of matter, and more recently observed under elaborate experimental conditions in isolated systems. These experiments require extremely low temperatures or other rigorous conditions to minimize undesired external influences, called noise.
In order for scientists to learn more about time crystals and employ their potential in technology, they need to find ways to produce time crystalline states and keep them stable outside the laboratory.
Cutting-edge research led by UC Riverside and published this week in Nature Communications has now observed time crystals in a system that is not isolated from its ambient environment. This major achievement brings scientists one step closer to developing time crystals for use in real-world applications.
“When your experimental system has energy exchange with its surroundings, dissipation and noise work hand-in-hand to destroy the temporal order,” said lead author Hossein Taheri, an assistant research professor of electrical and computer engineering in UC Riverside’s Marlan and Rosemary Bourns College of Engineering. “In our photonic platform, the system strikes a balance between gain and loss to create and preserve time crystals.”
The all-optical time crystal is realized using a disk-shaped magnesium fluoride glass resonator one millimeter in diameter. When bombarded by two laser beams, the researchers observed subharmonic spikes, or frequency tones between the two laser beams, that indicated breaking of temporal symmetry and creation of time crystals.
The UCR-led team utilized a technique called self-injection locking of the two lasers to the resonator to achieve robustness against environmental effects. Signatures of the temporally repeating state of this system can readily be measured in the frequency domain. The proposed platform therefore simplifies the study of this new phase of matter.
Without the need for a low temperature, the system can be moved outside a complex lab for field applications. One such application could be highly accurate measurements of time. Because frequency and time are mathematical inverses of each other, accuracy in measuring frequency enables accurate time measurement.
“We hope that this photonic system can be utilized in compact and lightweight radiofrequency sources with superior stability as well as in precision timekeeping,” said Taheri.
The open-access Nature Communications paper, “All-optical dissipative discrete time crystals,” is available here. Taheri was joined in the research by Andrey B. Matsko at NASA’s Jet Propulsion Laboratory, Lute Maleki at OEwaves Inc. in Pasadena, Calif., and Krzysztof Sacha at Jagiellonian University in Poland.
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Materials provided by University of California – Riverside. Original written by Holly Ober. Note: Content may be edited for style and length. More

The brain has neurons that fire specifically during certain mathematical operations. This is shown by a recent study conducted by the Universities of Tübingen and Bonn. The findings indicate that some of the neurons detected are active exclusively during additions, while others are active during subtractions. They do not care whether the calculation instruction is written down as a word or a symbol. The results have now been published in the journal Current Biology.
Most elementary school children probably already know that three apples plus two apples add up to five apples. However, what happens in the brain during such calculations is still largely unknown. The current study by the Universities of Bonn and Tübingen now sheds light on this issue.
The researchers benefited from a special feature of the Department of Epileptology at the University Hospital Bonn. It specializes in surgical procedures on the brains of people with epilepsy. In some patients, seizures always originate from the same area of the brain. In order to precisely localize this defective area, the doctors implant several electrodes into the patients. The probes can be used to precisely determine the origin of the spasm. In addition, the activity of individual neurons can be measured via the wiring.
Some neurons fire only when summing up
Five women and four men participated in the current study. They had electrodes implanted in the so-called temporal lobe of the brain to record the activity of nerve cells. Meanwhile, the participants had to perform simple arithmetic tasks. “We found that different neurons fired during additions than during subtractions,” explains Prof. Florian Mormann from the Department of Epileptology at the University Hospital Bonn.
It was not the case that some neurons responded only to a “+” sign and others only to a “-” sign: “Even when we replaced the mathematical symbols with words, the effect remained the same,” explains Esther Kutter, who is doing her doctorate in Prof. Mormann’s research group. “For example, when subjects were asked to calculate ‘5 and 3’, their addition neurons sprang back into action; whereas for ‘7 less 4,’ their subtraction neurons did.”
This shows that the cells discovered actually encode a mathematical instruction for action. The brain activity thus showed with great accuracy what kind of tasks the test subjects were currently calculating: The researchers fed the cells’ activity patterns into a self-learning computer program. At the same time, they told the software whether the subjects were currently calculating a sum or a difference. When the algorithm was confronted with new activity data after this training phase, it was able to accurately identify during which computational operation it had been recorded.
Prof. Andreas Nieder from the University of Tübingen supervised the study together with Prof. Mormann. “We know from experiments with monkeys that neurons specific to certain computational rules also exist in their brains,” he says. “In humans, however, there is hardly any data in this regard.” During their analysis, the two working groups came across an interesting phenomenon: One of the brain regions studied was the so-called parahippocampal cortex. There, too, the researchers found nerve cells that fired specifically during addition or subtraction. However, when summing up, different addition neurons became alternately active during one and the same arithmetic task. Figuratively speaking, it is as if the plus key on the calculator were constantly changing its location. It was the same with subtraction. Researchers also refer to this as “dynamic coding.”
“This study marks an important step towards a better understanding of one of our most important symbolic abilities, namely calculating with numbers,” stresses Mormann. The two teams from Bonn and Tübingen now want to investigate exactly what role the nerve cells found play in this.
The study was funded by the German Research Foundation (DFG) and the Volkswagen Foundation.
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Materials provided by University of Bonn. Note: Content may be edited for style and length. More

Scientists have created the first ever 2D map of the Overhauser field in organic LEDs, shedding light on the challenges we face in designing accurate quantum-based technologies
Television used to be known as ‘the idiot box’. But the organic LEDs found in modern flat screens are far from stupid.
In fact, they’re helping us to draw a map that could unlock the quantum future. No wonder they’re now called smart TVs.
The emerging concept of quantum sensing has the potential to surpass existing technology in areas ranging from electronics and magnetic field detection to microscopy, global positioning systems and seismology.
By taking advantage of quantum mechanics, new devices could be designed with unprecedented sensitivity and functionality.
But for this to happen, greater understanding is required of the role played by spin, a fundamental quantum property of subatomic particles such as electrons. More

A research team from the Department of Physics, the University of Hong Kong (HKU) has developed a new algorithm to measure entanglement entropy, advancing the exploration of more comprehensive laws in quantum mechanics, a move closer towards actualisation of application of quantum materials.
This pivotal research work has recently been published in Physical Review Letters.
Quantum materials play a vital role in propelling human advancement. The search for more novel quantum materials with exceptional properties has been pressing among the scientific and technology community.
2D Moire materials such as twisted bilayer graphene are having a far-reaching role in the research of novel quantum states such as superconductivity which suffers no electronic resistance. They also play a role in the development of “quantum computers” that vastly outperforming the best supercomputers in existence.
But materials can only arrive at “quantum state” , i.e. when thermal effects can no longer hinder quantum fluctuations which trigger the quantum phase transitions between different quantum states or quantum phases, at extremely low temperatures (near Absolute Zero, -273.15°C) or under exceptional high pressure. Experiments testing when and how atoms and subatomic particles of different substances “communicate and interact with each other freely through entanglement” in quantum state are therefore prohibitively costly and difficult to execute.
The study is further complicated by the failure of classical LGW (Landau, Ginzburg, Wilson) framework to describe certain quantum phase transitions, dubbed Deconfined Quantum Critical Points (DQCP). The question then arises whether DQCP realistic lattice models can be found to resolve the inconsistencies between DQCP and QCP. Dedicated exploration of the topic produces copious numerical and theoretical works with conflicting results, and a solution remains elusive. More

Combining centuries-old traditional mandala colouring with cutting-edge computing and brain sensing technologies could lead to new ways of helping people achieve mindfulness.
Mandalas are geometric configurations of shapes that have their origins in Buddhist traditions. The colouring of mandala shapes is increasingly popular as a way for people to attempt ‘mindfulness’, a way of being present in the moment, and which has been associated with helping people to improve their mental health and wellbeing.
Human-computer interaction researchers from Lancaster University have developed a new prototype that can monitor people’s brain signals while they are colouring mandalas and produce real-time feedback on a peripheral display to represent levels of mindfulness.
The researchers, who specialise in thinking about how new computing technologies can be designed to help people, believe systems like these could be developed to aid the learning, and training, of focused attention mindfulness techniques and help people deal with stress, depression and other affective health disorders.
In the first part of their study, the researchers interviewed experienced mandala practicioners to find out about the special qualities of mandala colouring, and how they can be used to achieve mindfulness, and based the prototype on their findings.
The prototype, called ‘Anima’, included a tablet device for users to colour mandala shapes, a wearable EEG headset* that reads wearers’ brain signals, and a second display in the shape of an artists’ palette, that is placed in the user’s periphery. More

Empowering small, humanoid-sensing robots to take a patient’s blood pressure — using only a simple touch — is Simon Fraser University researcher Woo Soo Kim’s latest health care technology development.
Based on the intricacies of origami — and inspired by the movements of nature’s leeches — his research is advancing how robots could carry out basic health care tasks in certain conditions, including in remote regions, or where minimal personal contact is needed, such as during pandemics. The research is published in the journal npj Flexible Electronics from Nature Publishing Group.
Together with PhD student Tae-Ho Kim and a team in SFU’s Additive Manufacturing Lab, Kim and researchers have replaced the traditional blood pressure procedure by replicated the folding mechanisms of the leech in their design of 3-D printable origami sensors. The leech-inspired origami (LIO) sensors can be integrated onto the fingertips of a humanoid-sensing robot.
“Our origami-inspired dry electrode has unique characteristics such as suction for grasping and foldability inspired by nature,” says Kim, a professor and associate director of SFU’s School of Mechatronic Systems Engineering. “In keeping with nature, we saw that in addition to the complex mechanisms of a leech’s adhesive feature, these creatures have an expandable posterior sucker and body, while its organs expand and shrink appropriately to maintain better adhesion to its victim. Incorporating this point of view, we found that origami can achieve similar motions and also be customized.”
How It Works
The LIO sensors integrated onto the robot’s fingertips can be positioned on the patient’s chest. Blood pressure is monitored and estimated by combining data from electrocardiogram (ECG)and photoplethysmogram (PPG) readings, as recorded by sensors on the fingers of each hand respectively.
Using predetermined algorithms, the signals from the paired sensors can generate a patient’s systolic and diastolic blood pressure without using the traditional cuff-based digital sphygmomanometer.
Kim’s earlier work involved programming sensing robots to measure other human physiological signals, such as those from an electrocardiogram (which monitors heart rate), temperature and respiration rate.
“Robotics offers a promising method to mitigate risk and improve patient care effectiveness and quality as focused remote healthcare technology,” says Kim. The researchers plan further trials of their new process and are developing the next generation of sensors, which they hope will lead to its biomedically meaningful implementation.
“Blood pressure monitoring is an essential medical diagnostic tool for many chronic diseases and overall good health. The use of sensing robots in medical healthcare systems has substantial advantages because they can assist health care workers in monitoring patient vital signs while creating a friendly environment for those patients who may need to be isolated.”
Kim believes that robotics can provide a future platform or bridge between medical personnel and remote patients with “the potential to play an essential role in the new era of remote healthcare.”
The research is partially supported by a Discovery and Accelerator Supplement Grant, funded by the Natural Sciences and Research Council of Canada (NSERC).
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Materials provided by Simon Fraser University. Note: Content may be edited for style and length. More

For more than a century written language was seen by anthropologists and other social scientists as a definitional feature of societal complexity or “advancement” (a term that is tinged with colonialism and racism). But in a new study in the Journal of Social Computing, researchers have found that societies don’t need written languages to be large or have complex governments. In a systematic, comparative survey of precolonial Mesoamerican societies, the study’s authors found that some large population centers had written systems of communication, but others did not. At the same time, the centers that had more elaborate computational and writing systems tended to be more autocratic (top-down ruler-dominated governance) than the ones without.
“The development of writing was thought to be a characteristic of civilizations or large-scale societies,” says Gary Feinman, the MacArthur curator of anthropology at Chicago’s Field Museum and the study’s first author. “Our findings both question and refine that long-entrenched assumption by illustrating that the relationship between the scale of social networks and computation systems also must take into account how people were organized and the resultant networks of communication. This relationship is not simply a matter of efficiency; history and how people were organized and communicated are key.”
The upshot, Feinman says, is that “in pre-Hispanic Mesoamerica, the overall elaboration of computational systems like writing, mathematics, and calendars are not directly correlated with the scale of societies. They do not necessarily become more elaborate or efficient over time.”
“Many of the dominant paradigms in the study of the human past have a Western or Eurasian bias that does not hold up to close scrutiny with data from other parts of the world. Being primarily Americanists, we know that certain favored models don’t work for the Western Hemisphere,” says co-author David Carballo of Boston University. Some of the largest Indigenous empires in the Americas had no written language, and “these cases, which seem anomalous in a Eurasian context, prompted us to prompted us to probe why people wrote and what sorts of things they wrote about, rather than assuming a close correlation with other forms of social complexity.”
For the study, Feinman and Carballo compared large population centers in what’s now Mexico and Central America from 1250 BCE to 1520 CE, looking at factors like population size, the size of the area governed, and political organization. Even in societies without written records, researchers are able to determine political structure by examining the archaeological remains of buildings and features like palaces. By comparing the remains of residences, public buildings, settlement layout, burial contexts, and monuments, researchers are able to glean information about how a society was governed and how power and wealth were distributed.
Feinman and Carballo then cross-referenced these data points with the computational systems (writing, mathematics, and calendars) used by the populations of these settlements. The relationships they found between writing and societal complexity were, in a word, complex. There wasn’t a clear linear relationship between the size of a society and whether it had writing. But they did find a link between writing and political organization. Writing tended to appear more often in societies with autocratic rulers (think all-powerful leaders) than in societies where power was more evenly shared. More