Ax Dynamics
Cre Wallace
Note: the text of this page is from my original website, and I haven't updated it in a while. Make sure you look at the physics category for all of the articles related to rigid body dynamics.
I started getting interested in high end physical simulation for gamessometime in 1995. Since I didn't know anything about physics or knowany real math (I had calculus in high school and enjoyed it, but hadforgotten most of it), I had to teach myself everything from scratch.Let me just say it was a total blast. I highly recommend everyonetaking the time to learn something really big and new every once in awhile, in addition to all the little things we're all [hopefully]learning every day. As a bonus, it seems that the more we learn, thefaster we're able to learn even newer things, which makes the wholeprocess even more pleasurable.
As much fun as I had figuring this stuff out, I sure would haveappreciated some references and articles aimed at my level when I wasstarting. So, I've created this web page in the hopes I can helpeveryone else get past those difficult first steps.
I wrote a total of four articles about rigid body dynamics for Game Developer Magazine. I've posted them as PDF files, so theylook just like they do in the magazine. There are downsides to PDF,however, including the general way in which Acrobat sucks at lettingyou navigate through documents (it's clear Adobe thinks a monitor is alowres printer), and perhaps more seriously, the way some of theequations came out garbled. However, you should think of the latterproblem as a challenge to figure out the correct equations! [Ifpeople complain enough I'll figure out how to fix them.] Pleaserespect the copyright information in the front of each article.
Four articles, no matter how long, are just not enough to do justiceto rigid body dynamics. If you plan on using real dynamics in yourgame, you simply have to read my Physics References. The3D sample application below shows the beginnings ofsome really cool technology, but you'll have to take the initiative toteach yourself more math and physics to turn it into a production qualitysimulator.
Remember, these are just sample programs, not the ultimate physicssimulators. They're really just a translation of the equations in myarticles into code, so don't expect too much. They're fun to playwith and change, but you'll have a lot of your own work to do beforeyou can use this stuff in a production quality game. These apps willget you started, but not much more than that.
The most obvious thing the samples are missing is inter-body collisions. They don't do collision detection between bodies, but only betweenbodies and the world. It wouldn't be too hard to add a very simplediscrete collision detector, but I didn't have time.
The second biggest problem is the lame integrator used in both apps.Both samples are relatively unstable because I'm using the simplestEuler integrator. If you play with the spring and dampingcoefficients you'll quickly see how tweaky they are with relation tothe timestep with this cheesy integrator. There are tons of books on numerical integration to helpyou fix this problem.
The overarching Panel obective is to advance our basic understanding of atmosphere-ocean climate dynamics using observations and models and to determine the role of climate dynamics in shaping climate variability and change on seasonal to centennial time scales. Specific activities will, in the first instance, be organized around three areas
MultiSector Dynamics seeks to advance scientific understanding of the complex interactions, interdependencies, and co-evolutionary pathways of human and natural systems, including interdependencies among sectors and infrastructures. This includes advancing relevant socio-economic, risk analysis, and complex decision theory methods to lead insights into earth system science, while emphasizing the development of interoperable data, modeling, and analysis tools for integration within flexible modeling frameworks.
Scientific insights and tools emerging from MultiSector Dynamics hold significant potential to inform next-generation U.S. infrastructure and new development pathways for improved energy and economic security, including implications of and for technological and systems innovations.
There is a particular emphasis on understanding the energy-water-land nexus under both realistic and idealized forcing scenarios, including the evaluation of scale-aware processes and probabilistic uncertainties that can lead to instability through thresholds and tipping points.
Besides the focus to understand the system dynamics governing interdependencies within the natural-human system, this area seeks to advance scientists' understanding of system nonlinearity and instability associated with multiple stressors that can lead to cascading failures in connected sectors and systems. An important characteristic of nonlinearity and system failure is the probabilistic interdependence near thresholds associated with extreme weather, severe drought, and infrastructure vulnerability. Consequently, MultiSector Dynamics supports the development of interoperable tools and methods for integration with agile, flexible earth system modeling frameworks, revealing a basic understanding of different levels of complexity required to analyze interdependency.
Announcements are posted on the DOE Office of Science Grants and Contracts Website and at grants.gov. Information about preparing and submitting applications, as well as the DOE Office of Science merit review process, is available at the DOE Office of Science Grants and Contracts Website. For current announcements visit BER Funding Opportunities.
MultiSector Dynamics efforts are necessary to understand the nonlinear science involving natural-human interdependency and feedbacks on the earth system. This program area helps shape fundamental understanding of complex stressors on human systems and infrastructure, vulnerabilities and risks at the energy-water-land nexus, multisector dynamics, and more generally, implications for regional and global economic development in the face of changing weather patterns and extremes, advances in technology, availability of natural resources, and feedbacks to natural systems, including regional and global climates.
Our mission is to create and make accessible novel data on the dynamics of the labor markets, we work with research networks and statistical agencies, developing appropriate statistics to inform policy makers, researchers, and simply people seeking knowledge. We emphasize and meet the requirements of stakeholders: users as well as providers, balancing the utility of the data with the confidentiality of the people and businesses whose activities the data describe.
The Labor Dynamics Institute goals are trifold. We study and improve labor market outcomes of workers; more generally we improve access to and understanding of data sources for the study of the labor market; and improve the transparency and accessibility of economics research to enhance its credibility.
We investigate effective labor market outcomes for workers. Current projects feature creating, maintaining, and enhancing job search tools with the goal of observing outcomes of such interventions for workers. We are building collaborations with Computer and Data Scientists at both faculty and student level to enhance research into this field. We have examined existing online platforms to understand features and how employers use them. We also advocate advancing changes in employer records at the federal level to enable measurement of outcomes not previously possible..
We seek to improve access to data at multiple levels. Our leadership and affiliates serve on National Academies panels and committees at government agencies in the United States and Canada that are tasked with enabling easier and enhanced access to comprehensive confidential administrative data for research. Our affiliate Erica Groshen is a leading advocate for a U.S. "21st Century National Data Infrastructure." Better data access contributes to our other goals. It enables more comprehensive scrutiny of academic research when data cannot be published, supporting integrity even where transparency is limited.
We house leading practice and research to make economics more transparent and reproducible. LDI's Reproducibility Lab conducts reproducibility verifications for American Economic Association's Data Editor. We coordinate and share expertise with colleagues in economics, sociology, political science, program evaluation, demography, and computer science at Cornell and elsewhere to improve infrastructure, methods, and standards. Our projects also pursue development of new standards and tools to enhance transparency.
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To resolve epithelial and immune cell responses over time from SARS-CoV-2 exposure, we conducted a human SARS-CoV-2 challenge study7. In this model, young adults seronegative for SARS-CoV-2 spike protein were intranasally inoculated with a wild-type pre-Alpha SARS-CoV-2 virus strain (SARS-CoV-2/human/GBR/484861/2020) in a controlled environment. Before challenge, volunteers underwent extensive screening to exclude risk factors for severe disease and to eliminate confounding effects of comorbidities. As risk mitigation and to maximize physiological relevance, participants were inoculated with the lowest culture-quantifiable inoculum dose of 10 tissue culture infectious dose 50 (TCID50). There were no serious adverse events and all symptoms were resolved in the participants selected for this single-cell data cohort.
We studied local and systemic immune responses at single-cell resolution in 16 participants. The highly controlled nature of this experimental model enabled baseline measurements on the day before inoculation. This was followed by detailed time series analyses ( ) of cellular responses after inoculation and subsequent infection, both systemically in blood and locally in the nasopharynx, to decipher antiviral responses against SARS-CoV-2 in a precise time-resolved manner.
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