![\"\"](\"https://www.kaggleusercontent.com/kf/73665415/eyJhbGciOiJkaXIiLCJlbmMiOiJBMTI4Q0JDLUhTMjU2In0..RMrg1JNvW6jdcNusNFAQYQ.VTmakGwibxp4Uv7R8MCR-NZk5HQpGMmGNP6tE8Qk8WrM5PPXsJe-UnNtofcJS7HlRdmsFws9QBFRN_sl3iJ8uNFdtDMTc_jB_kpjtvjfMEOgQY79Kct42qhBqNmF4U4c-vUA9Lf6X2Mc9oFjT18BDmrND_jr9B-0eGetACZCkRqncDNGfGzcJ3AzPl3mzsRiXsmeDFLsE9vHoDbQJGOeP3hx4VgzwfeBHYsmUTvrMJ9HRe-jPYRrYJQWqcxJ4Ue5Ct5fQaDb-GhfKAB3Z4ijDST3ndE263LncHzAihJqoIMN4PzRjBHdWTxsc5FQ80r6VEKpJ7Qu3ZPX8dqu40p3FO7_NlPjbbktdVpTmLO6mBuE2oG4O6oPQROFQdtQ4P_PaCu1xeuw_clfMQTHg5hvb5J69AknLfNR9a2O3-E_4D2F1f77gkYbJveAbrP418Pj_huwitM4j63kF03XwYNlZxp3yPzo7NOEgVq_NBJsdVZSnlrr35G8NBF7_aY6L48p2pgWnLTUu3EvKjPgdnmvbj1bBKeexMrhqwKZq7Ioj5jCNRiLp-mIVllE8vlFQZS9hwXJcCHmM9Sq_4NH1ijNpOIQwCAMvuZUOecxgH_dvPtJk5IJBX5YiwazDC2lxCq3XlbNeAbO2FVPkvPqBib3YaA6MOGSWrgSBRz99f9AmKJRFrxOW5wXT12GGEr5QY_J.-kCGV7bnirQ9urU4fl1VXQ/__results___files/__results___14_0.png\")
How do we go from the plus and cross polarizations (the orthogonal / diagonal waveforms returned by, e.g. seobnr simulation algorithm) to strain in the current dataset, given host comment:
\n\n\nYes, strain is defined as twice the fractional change in the interferometer arm length (so it's a ratio of lengths) and hence dimensionless.
\n
2 * hp / hc? That cannot possible be right . . .
How do we go from the plus and cross polarizations (the orthogonal / diagonal waveforms returned by, e.g. seobnr simulation algorithm) to strain in the current dataset, given host comment:
\n\n\nYes, strain is defined as twice the fractional change in the interferometer arm length (so it's a ratio of lengths) and hence dimensionless.
\n
2 * hp / hc? That cannot possible be right . . .
What cannot be possibly right? You define neither hp nor hc BTW.
", "rawMarkdown": "What cannot be possibly right? You define neither hp nor hc BTW.", "votes": null }, { "id": "1510429", "postDate": "09/12/2021 12:13:48", "content": "My apologies; by hp and cp I mean the plus and cross polarization. Since those waveforms are very sinusoidal in nature and also have phases that are mostly in sync, hp/hc produces mostly a constant line with a few a few spikes in it and not anything like the competition data.
\n
![\"\"](\"https://i.imgur.com/vjk95A2.jpg\")
\n\nhp and cp I mean the plus and cross polarization
\n
How are these correlated to arm lengths? Host discusses arm lengths, not polarization.
", "rawMarkdown": "> hp and cp I mean the plus and cross polarization\n\nHow are these correlated to arm lengths? Host discusses arm lengths, not polarization.", "votes": null }, { "id": "1510500", "postDate": "09/12/2021 13:19:13", "content": "This is my question verbatim; all the generation software produces polarizations.
", "rawMarkdown": "This is my question verbatim; all the generation software produces polarizations.", "votes": null }, { "id": "1510558", "postDate": "09/12/2021 14:26:08", "content": "And my question is why do compute polarizations ratio when host says it is the ratio of arm lengths?
", "rawMarkdown": "And my question is why do compute polarizations ratio when host says it is the ratio of arm lengths?", "votes": null }, { "id": "1510589", "postDate": "09/12/2021 14:55:05", "content": "Let me try to clarify things with going into too much depth. The important distinction is whether we're thinking about what strain physically is or how we model it in the interferometer.
\nWhat we detect is the relative change in the length of the arms of the interferometer caused by a gravitational wave. Since we know the length of arms of the interferometer (L), if the length changes, we can then measure the strain (h): $$h =\\frac{\\Delta L}{L}.$$
\nHowever, when we analyse the data we don't think about tit his way. We instead model the strain data from the interformeter as a combination of signal and noise $$h = h_{signal} + h_{noise}.$$
\nWe then have to define what we mean by signal, this could a number of different astrophysical sources, but this challenge is for binary black holes (BBH), so (h_{signal}) is modelled as the signal from a BBH. This is where the polarisation comes in.
\nGravitational waves have two polarisations that we call plus (h_{+}) and cross (h_{\\times}). A BBH will emit both polarisations and the interferometers respond differently to each, so we typically model the signals in terms of the two polarisations. If we put this all together, we can define the signal as:
\n$$h_{signal} = F_{\\times}(\\theta)h_{\\times}(\\theta) + F_{+}(\\theta)h_{+}(\\theta),$$
\nwhere (F_{\\times,+}) are antenna patterns that describe how the interferometer responds to each polarisation and (\\theta) are the parameters of signal (\\theta), such as masses, location on the sky etc.
\nHope this helps and I'll try to answer any more questions you might have about this.
\nFor those interested and with a mathematical/physics background, these lecture notes cover more the details.
", "rawMarkdown": "Let me try to clarify things with going into too much depth. The important distinction is whether we're thinking about what strain physically is or how we model it in the interferometer.\n\nWhat we detect is the relative change in the length of the arms of the interferometer caused by a gravitational wave. Since we know the length of arms of the interferometer (L), if the length changes, we can then measure the strain (h): $$h =\\frac{\\Delta L}{L}.$$\n\nHowever, when we analyse the data we don't think about tit his way. We instead model the strain data from the interformeter as a combination of signal and noise $$h = h_{signal} + h_{noise}.$$\n\nWe then have to define what we mean by signal, this could a number of different astrophysical sources, but this challenge is for binary black holes (BBH), so (h_{signal}) is modelled as the signal from a BBH. This is where the polarisation comes in. \n\nGravitational waves have two polarisations that we call plus (h_{+}) and cross (h_{\\times}). A BBH will emit both polarisations and the interferometers respond differently to each, so we typically model the signals in terms of the two polarisations. If we put this all together, we can define the signal as:\n\n$$h_{signal} = F_{\\times}(\\theta)h_{\\times}(\\theta) + F_{+}(\\theta)h_{+}(\\theta),$$\n\nwhere (F_{\\times,+}) are antenna patterns that describe how the interferometer responds to each polarisation and (\\theta) are the parameters of signal (\\theta), such as masses, location on the sky etc.\n\nHope this helps and I'll try to answer any more questions you might have about this.\n\nFor those interested and with a mathematical/physics background, [these lecture notes](https://dcc.ligo.org/public/0106/T1300666/003/Whelan_notes.pdf) cover more the details.", "votes": null }, { "id": "1510596", "postDate": "09/12/2021 14:59:56", "content": "Thank you!
", "rawMarkdown": "Thank you!", "votes": null }, { "id": "1511492", "postDate": "09/13/2021 13:20:47", "content": "not sure if this would help.
\nit is a lecture notes that I have been following
\nhttp://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf
page 10 and 11 shows equation for chirp waveform
", "rawMarkdown": "not sure if this would help.\nit is a lecture notes that I have been following\nhttp://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf\n\npage 10 and 11 shows equation for chirp waveform", "votes": null }, { "id": "1559708", "postDate": "10/27/2021 07:08:25", "content": "Hey All,
\nThank you all for taking part in our competition. The participation has been overwhelmingly positive. We are currently conducting a survey to gauge the demographic and outreach achieved. Kindly spare 2min and fill in this survey https://forms.gle/QP9L16niPexozyhu5.
\nThank you all,
\nRegards,
\nChris
What cannot be possibly right? You define neither hp nor hc BTW.
", "votes": null, "replies": [ { "id": 1510429, "author_name": "authman", "author_url": "", "post_date": "09/12/2021 12:13:48", "content": "My apologies; by hp and cp I mean the plus and cross polarization. Since those waveforms are very sinusoidal in nature and also have phases that are mostly in sync, hp/hc produces mostly a constant line with a few a few spikes in it and not anything like the competition data.
\n
\n\nhp and cp I mean the plus and cross polarization
\n
How are these correlated to arm lengths? Host discusses arm lengths, not polarization.
", "votes": null, "replies": [] }, { "id": 1510500, "author_name": "authman", "author_url": "", "post_date": "09/12/2021 13:19:13", "content": "This is my question verbatim; all the generation software produces polarizations.
", "votes": null, "replies": [] }, { "id": 1510558, "author_name": "cpmpml", "author_url": "", "post_date": "09/12/2021 14:26:08", "content": "And my question is why do compute polarizations ratio when host says it is the ratio of arm lengths?
", "votes": null, "replies": [] } ] }, { "id": 1510589, "author_name": "michaeljwill", "author_url": "", "post_date": "09/12/2021 14:55:05", "content": "Let me try to clarify things with going into too much depth. The important distinction is whether we're thinking about what strain physically is or how we model it in the interferometer.
\nWhat we detect is the relative change in the length of the arms of the interferometer caused by a gravitational wave. Since we know the length of arms of the interferometer (L), if the length changes, we can then measure the strain (h): $$h =\\frac{\\Delta L}{L}.$$
\nHowever, when we analyse the data we don't think about tit his way. We instead model the strain data from the interformeter as a combination of signal and noise $$h = h_{signal} + h_{noise}.$$
\nWe then have to define what we mean by signal, this could a number of different astrophysical sources, but this challenge is for binary black holes (BBH), so (h_{signal}) is modelled as the signal from a BBH. This is where the polarisation comes in.
\nGravitational waves have two polarisations that we call plus (h_{+}) and cross (h_{\\times}). A BBH will emit both polarisations and the interferometers respond differently to each, so we typically model the signals in terms of the two polarisations. If we put this all together, we can define the signal as:
\n$$h_{signal} = F_{\\times}(\\theta)h_{\\times}(\\theta) + F_{+}(\\theta)h_{+}(\\theta),$$
\nwhere (F_{\\times,+}) are antenna patterns that describe how the interferometer responds to each polarisation and (\\theta) are the parameters of signal (\\theta), such as masses, location on the sky etc.
\nHope this helps and I'll try to answer any more questions you might have about this.
\nFor those interested and with a mathematical/physics background, these lecture notes cover more the details.
", "votes": null, "replies": [ { "id": 1510596, "author_name": "cpmpml", "author_url": "", "post_date": "09/12/2021 14:59:56", "content": "Thank you!
", "votes": null, "replies": [] } ] }, { "id": 1511492, "author_name": "hengck23", "author_url": "", "post_date": "09/13/2021 13:20:47", "content": "not sure if this would help.
\nit is a lecture notes that I have been following
\nhttp://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf
page 10 and 11 shows equation for chirp waveform
", "votes": null, "replies": [] }, { "id": 1559708, "author_name": "zerafachris", "author_url": "", "post_date": "10/27/2021 07:08:25", "content": "Hey All,
\nThank you all for taking part in our competition. The participation has been overwhelmingly positive. We are currently conducting a survey to gauge the demographic and outreach achieved. Kindly spare 2min and fill in this survey https://forms.gle/QP9L16niPexozyhu5.
\nThank you all,
\nRegards,
\nChris