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‎assets/css/main.css‎

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‎index.html‎

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@@ -93,7 +93,7 @@ <h2> <b> Exp </b> = BFE+mSSA: finding the story being told by BFE’s </h2>
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<a href="images/fulls/plain.png" class="image"><img src="images/thumbs/4.png" alt="" /></a>
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<h2> <b> EXP </b>: applications to cosmology</h2>
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<p> <b> EXP </b> can be used to analyze structure in cosmological simulations. Members of the <b> EXP </b> Collaboration are applying
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these tools to snapshots from simulations of galaxy formation to:
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these tools to snapshots from simulations of galaxy formation to: </p>
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<ul>
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<li> Compare and contrast the signatures of filamentary accretion from halo deformation in the FIRE simulation suite
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(<a “https://ui.adsabs.harvard.edu/abs/2025ApJ...988..190A/abstract” Arora et al, 2025 </a>); </li>
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</article>
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<article class="thumb">
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<a href="images/fulls/center-2.png" class="image"><img src="images/thumbs/center-2.png" alt="" /></a>
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<h2></h2>
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<p></p>
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<h2> <b> Exp </b>: the code and the collaboration </h2>
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<p><b> Exp </b> is designed to connect: (1) theoretical descriptions of dynamics, (2) N-body simulations, and (3) data-efficient descriptions of
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their natural consequences. <b> Exp </b> provides recent developments from applied mathematics and numerical computation to represent time
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series of BFEs that describe the temporal variation of any field in space. In the context of galactic dynamics, these fields may be density,
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potential, force, velocity fields or any intrinsic field produced by simulations such as chemistry data. By combining the coefficient
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information through time using spectral analysis, we hope to discover the dynamics of galaxy evolution directly from simulations and by
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predictive comparison with observed data. </p>
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<p> The <b> Exp Collaboration</b> is exploring the applications of these tools to galactic dynamics, from the Milky Way disk to cosmological
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simulations of galaxy formation. Our team combines expertise in (i) analytic models, (ii) numerical simulations and (iii) data analysis.
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We aim to build a language that unites all three. We use <b> Basis Function Expansions (BFE) </b> to compactly summarize spatial or
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velocity features in simulations and <b> multivariate Singular Spectrum Analysis (mSSA)</b> to discover the non-linear dynamics of their
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interaction. This allows us to detect deep dynamical relationships in our simulations. The approach promises multiple connections: from
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observations to simulations to theoretical descriptions; between galactic components; and across phase-space dimensions. </p>
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</article>
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<article class="thumb">
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<a href="images/fulls/plain.png" class="image"><img src="images/thumbs/5.png" alt="" /></a>
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<h2>Basis Function Expansions for N-body Dynamical Simulations</h2>
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<p>Basis function expansions (BFEs) can be used to both run and analyze dynamical N-body simulations. The EXP
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collaboration - spearheaded by Martin Weinberg - has developed eponymous code to perform both of these
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functions. <b> Exp </b> uses BFEs to represent the potential and mass distributions of the star and dark
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matter particles of a galaxy to run simulations significantly faster than alternate techniques. The
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theory underpinning BFE simulations and the implementation are discussed in
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more detail in the <a href="https://exp-docs.readthedocs.io/en/latest/topics/multistep.html"readthedocs></a>,
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as well as these papers (<a href="https://ui.adsabs.harvard.edu/abs/1999AJ....117..629W/abstract"1></a>,
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<a href="https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.6201P/abstract"2></a>).</p>
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<p>The resulting simulations have both particle-based snapshot data and basis function information, including
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the basis and time-evolving coefficients. These data can be used together to provide unique insight into
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the underlying dynamics. <b> Exp </b> can also be run on simulations that were produced with different software,
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including cosmological simulations, to provide BFEs at each time step. See below for
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examples that use either or both of these functionalities of <b> Exp </b>.</p>
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<p> Your paper links and blurbs here!</p>
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<h2> <b> EXP</b>: applications to dynamical systems </h2>
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<p> Density/potential pairs of BFEs that are solutions to Poisson’s equation provide a natural
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language for dynamics. They are used both in simulations and analytic calculations, and
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hence can be used to link the two. </p>
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<p> In addition to its analysis framework, <b> EXP </b> includes an N-body gravitational code. The resulting
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simulations output both particle-based snapshot data and BFE information, including the basis and
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time-evolving coefficients. The theory underpinning <b> EXP </b> simulations and the implementation are
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discussed in more detail in the
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<a href="https://exp-docs.readthedocs.io/en/latest/topics/multistep.html"readthedocs></a>, as well
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as these papers (<a href="https://ui.adsabs.harvard.edu/abs/1999AJ....117..629W/abstract" Weinberg, 1999</a>,
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<a href="https://ui.adsabs.harvard.edu/abs/2022MNRAS.510.6201P/abstract" Peterxen, Weinberg & Katz, 2022></a>).</p>
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<p> The collaboration has applied <b> EXP </b> to various simulations to: </p>
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<ul>
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<li> Follow the evolution of galactic bars (<a”https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.5408W/abstract” Weinberg & Petersen 2020</a>),
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as well as its interaction with a dark matter halo (<a “https://ui.adsabs.harvard.edu/abs/2025arXiv251009751H/abstract” Hunt et al, 2025></a>)</li>
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<li> Distinguish intrinsic halo instabilities from evolution driven by disk/halo coupling in the simulation of an isolated galaxy
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(https://ui.adsabs.harvard.edu/abs/2023MNRAS.521.1757J/abstract Johnson, Petersen et al 2023);</li>
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<li> Isolate the signatures of multiple interacting satellites in a simulated galactic disk (Petersen et al 2025, in prep);</li>
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<li> Connect features found in phase-space local patches of a simulated disk into global structures (Tavangar et al 2025, in prep);</li>
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<li> Characterize the morphological transformation of the SMC and LMC as they orbit our Milky Way (Rathore et al 2025, in prep)</li>
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</ul>
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</article>
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<a href="images/fulls/plain.png" class="image"><img src="images/thumbs/8.png" alt="" /></a>
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</article>
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<article class="thumb">
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<a href="images/fulls/plain.png" class="image"><img src="images/thumbs/9.png" alt="" /></a>
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<h2>Basis Function Expansions for Sonification</h2>
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<p>The light profile of a galaxy image can be described with a Fourier-Laguerre basis function expansion.
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The resulting expansion has both angular (Fourier, m) terms and radial (Laguerre, n) terms and a series
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of coefficient weights. While we typically plot these terms and weights for a visual representation, we
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can also present these same data with sounds. In plotting these data, we might decide that the n-terms
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are along the x-axis and the m-terms are along the y-axis, with the coefficient values making a heatmap.
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Similarly, we could choose to map the n-terms to notes on a given scale, the m-terms to octaves, and the
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coefficient amplitudes to volume. This mapping of data to sound is called sonification.</p>
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<p> We are pioneering the use of basis function expansions for sonfication. As part of this work, we have
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created a GalaxyZoo project to determine the efficacy of classifying galaxy morphology through sounds,
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or aural classification. Check out the project here (LINK COMING SOON) to test your own aural
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classification skills! </p>
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<h2> Looking Forward</h2>
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<ul>
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<li>Time series analyses more generally </li>
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<ul>
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<li>DMD</li>
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<li>Advanced mSSA techniques</li>
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</ul>
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<li>Other fields in galaxies</li>
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<ul>
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<li>Velocity</li>
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<li>Chemistry</li>
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<li>Ages</li>
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</ul>
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<li>Other applications beyond galaxies</li>
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<ul>
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<li>Accretion disks</li>
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<li>Planetary disks</li>
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<li>Astrophysical Plasmas</li>
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<li>Proto-stellar disks</li>
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</ul>
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</ul>
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</article>
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<a href="images/fulls/plain.png" class="image"><img src="images/thumbs/7.png" alt="" /></a>
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<p>If you want to want to learn more about mSSA, check out this <a href="https://michael-petersen.github.io/papers/mssa/MSSA-Tutorial-Slideshow.slides.html#/">webpage</a> and these papers:
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<a href="https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.5408W/abstract">1</a> and
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<a href="https://ui.adsabs.harvard.edu/abs/2023MNRAS.521.1757J/abstract">2</a> (see also the
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<a href = "https://exp-docs.readthedocs.io/en/latest/topics/ssa.html">EXP readthedocs</a> for more information) </p>
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<a href = "https://exp-docs.readthedocs.io/en/latest/topics/ssa.html"><b> EXP </b> readthedocs</a> for more information) </p>
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</dl>
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<p> Add more links, pedagogical stuff, etc .... </p>
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</article>
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</div>
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<div>
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<section>
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<h2>Get to know us</h2>
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<p>The EXP collaboration is developing the next generation of tools for galactic dynamics to tackle disequilibrium dynamics.
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<p>The <b> EXP </b> collaboration is developing the next generation of tools for galactic dynamics to tackle disequilibrium dynamics.
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Our team combines expertise in (i) analytic models, (ii) numerical simulations and (iii) data analysis.
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We use basis function expansions as a common language that unites all three of these realms of expertise.
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Looking forward, our proposed tools have the potential

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