“每日科技报告”第12期 Mathematical Model Aids Big Bang Supercomputer Research

sea_star666

Scientists have made many discoveries about the origins of our 13billion-year-old universe. But many scientific mysteries remain. Whatexactly happened during the Big Bang, when rapidly evolving physicalprocesses set the stage for gases to form stars, planets and galaxies?Now astrophysicists using supercomputers to simulate the Big Bang havea new mathematical tool to unravel those mysteries, says Daniel R.Reynolds, assistant professor of mathematics at SMU.

A representation of the evolution of the universe over 13.7 billionyears. The far left depicts the earliest moment we can now probe, whena period of "inflation" produced a burst of exponential growth in theuniverse. (Size is depicted by the vertical extent of the grid in thisgraphic.) For the next several billion years, the expansion of theuniverse gradually slowed down as the matter in the universe pulled onitself via gravity. More recently, the expansion has begun to speed upagain as the repulsive effects of dark energy have come to dominate theexpansion of the universe. The afterglow light seen by WMAP was emittedabout 380,000 years after inflation and has traversed the universelargely unimpeded since then. The conditions of earlier times areimprinted on this light; it also forms a backlight for laterdevelopments of the universe.

Reynolds collaborated with astrophysicists at the University ofCalifornia at San Diego as part of a National Science Foundationproject to simulate cosmic reionization, the time from 380,000 years to400 million years after the universe was born.
Together the scientists built a computer model of events during the"Dark Ages" when the first stars emitted radiation that altered thesurrounding matter, enabling light to pass through. The team tested itsmodel on two of the largest existing NSF supercomputers, "Ranger" atthe University of Texas at Austin and "Kraken" at the University ofTennessee.The new mathematical model tightly couples a myriad of physicalprocesses present during cosmic reionization, such as gas motion,radiation transport, chemical kinetics and gravitational accelerationdue to star clustering and dark matter dynamics, Reynolds says.

The key characteristic of the model that differentiates it from competing work is that the researchers focused on enforcing a very tight coupling in the model between the different physical processes.
"By forcing the computational methods to tightly bind theseprocesses together, our new model allows us to generate simulationsthat are highly accurate, numerically stable and computationallyscalable to the largest supercomputers available," Reynolds says.
They presented their research at a Texas Cosmology Network Meetingat UT in late October. Reynolds' mathematical research also waspublished as "Self-Consistent Solution of CosmologicalRadiation-Hydrodynamics and Chemical Ionization" in the October issueof the "Journal of Computational Physics."
Simulation models typically consist of a complex bundle ofmathematical equations representing physical processes. The equationsare integrated to reflect interaction of the physical processes. Onlysupercomputers can simultaneously solve the equations. Scientificintuition and creativity come into play by developing the base modelwith equations with the best parameters, Reynolds says. Variables canbe altered to describe different scenarios that might have occurred.The objective is to develop a simulation model with results that mostclosely resemble telescope observations and that predict a universethat looks like what we have. If that happens, scientists havediscovered the set of physical processes that existed at the birth ofthe universe as it was evolving from one instant to the next.
Physical processes include the heating of various gases, gravity,the conservation of mass, the conservation of momentum, theconservation of energy, expansion of the universe, the transport ofradiation, and the chemical ionization of different species such asHydrogen and Helium, the primary elements present at the beginning ofthe universe. An additional equation running in the backgrounddescribes and models the dynamics of dark matter -- the majority of thematter in the universe -- which gives rise to gravity and is attributedwith helping the universe form stars, planets and galaxies.
"Supercomputers are so big, they hold so much data, you can buildmodels that work with many processes at one time," Reynolds says. "Alot of these processes behave nonlinearly. When they are put together,they inhibit each other, feed off each other, so you end up with manydifferent processes when they are put together."
A direct consequence of the tight coupling that the researchersenforce in their model is that the resulting system of equations ismuch more complex than those that must be solved by other models,Reynolds says."This ** describes both how we form the coupled model, as well asthe mathematical methods that enable us to solve the systems ofequations that result. These include methods that accurately track thedifferent time scales of each process, which often occur at rates thatvary by orders of magnitude," he says. "However, perhaps the mostimportant contribution of this ** is our description of how we posethe complex interaction of different models as a nonlinear problem withpotentially billions of equations and unknowns, and solve that problemusing new algorithms designed for next-generation supercomputers. Weconclude by demonstrating that the new model lives up to the ideal,providing an approach that allows high accuracy, stability andscalability on a suite of difficult test problems."

sarah2014

~嗯嗯，还是先占座~
吼吼吼吼吼吼
Q1：afterglow light是什么啊？稍稍解释下呗，没有摆到。

yjh3207

占个座，有空慢慢看~~~~~~~~哇咔咔

sunchunghwa

看看。。。。。。。。。。。。。。。

sunchunghwa

数学是好东西。。。。多学习。。。。

wuhao080910

你找这些东西肯定可以提高英语了

明心见性

先收藏着，以后有空，在慢慢看。

liuxn_2005

看看。。。。。。。。。。。。。。。