36 research outputs found
Notes in Pure Mathematics & Mathematical Structures in Physics
These Notes deal with various areas of mathematics, and seek reciprocal
combinations, explore mutual relations, ranging from abstract objects to
problems in physics.Comment: Small improvements and addition
The supermassive binary black hole system OJ287
Abstract
This doctoral thesis concerns the active galactic nucleus (AGN) most often
referred to with the catalogue number OJ287. The publications in the thesis
present new discoveries of the system in the context of a supermassive
binary black hole model. In addition, the introduction discusses general
characteristics of the OJ287 system and the physical fundamentals behind
these characteristics. The place of OJ287 in the hierarchy of known types
of AGN is also discussed.
The introduction presents a large selection of fundamental physics required
to have a basic understanding of active galactic nuclei, binary black
holes, relativistic jets and accretion disks. Particularly the general relativistic
nature of the orbits of close binaries of supermassive black holes is
explored with some detail. Analytic estimates of some of the general relativistic
effects in such a binary are presented, as well as numerical methods
to calculate the effects more precisely. It is also shown how these results
can be applied to the OJ287 system.
The binary orbit model forms the basis for models of the recurring optical
outbursts in the OJ287 system. In the introduction, two physical
outburst models are presented in some detail and compared. The radiation
hydrodynamics of the outbursts are discussed and optical light curve predictions
are derived. The precursor outbursts studied in Paper III are also
presented, and tied into the model of OJ287.
To complete the discussion of the observable features of OJ287, the
nature of the relativistic jets in the system, and in active galactic nuclei in
general, is discussed. Basic physics of relativistic jets are presented, with
additional detail added in the form of helical jet models. The results of
Papers II, IV and V concerning the jet of OJ287 are presented, and their
relation to other facets of the binary black hole model is discussed.
As a whole, the introduction serves as a guide, though terse, for the
physics and numerical methods required to successfully understand and
simulate a close binary of supermassive black holes. For this purpose, the introduction necessarily combines a large number of both fundamental and
specific results from broad disciplines like general relativity and radiation
hydrodynamics. With the material included in the introduction, the publications
of the thesis, which present new results with a much narrower focus,
can be readily understood.
Of the publications, Paper I presents newly discovered optical data
points for OJ287, detected on archival astronomical plates from the Harvard
College Observatory. These data points show the 1900 outburst of
OJ287 for the first time. In addition, new data points covering the 1913
outburst allowed the determination of the start of the outburst with more
precision than was possible before. These outbursts were then successfully
numerically modelled with an N-body simulation of the OJ287 binary and
accretion disc.
In Paper II, mechanisms for the spin-up of the secondary black hole in
OJ287 via interaction with the primary accretion disc and the magnetic
fields in the system are discussed. Timescales for spin-up and alignment
via both processes are estimated. It is found that the secondary black hole
likely has a high spin.
Paper III reports a new outburst of OJ287 in March 2013. The outburst
was found to be rather similar to the ones reported in 1993 and 2004.
All these outbursts happened just before the main outburst season, and
are called precursor outbursts. In this paper, a mechanism was proposed
for the precursor outbursts, where the secondary black hole collides with
a gas cloud in the primary accretion disc corona. From this, estimates
of brightness and timescales for the precursor were derived, as well as a
prediction of the timing of the next precursor outburst.
In Paper IV, observations from the 2004–2006 OJ287 observing program
are used to investigate the existence of short periodicities in OJ287. The
existence of a _50 day quasiperiodic component is confirmed. In addition,
statistically significant 250 day and 3.5 day periods are found. Primary
black hole accretion of a spiral density wave in the accretion disc is proposed
as the source of the 50 day period, with numerical simulations supporting
these results. Lorentz contracted jet re-emission is then proposed as the
reason for the 3.5 day timescale.
Paper V fits optical observations and mm and cm radio observations of
OJ287 with a helical jet model. The jet is found to have a spine–sheath
structure, with the sheath having a much lower Lorentz gamma factor than
the spine. The sheath opening angle and Lorentz factor, as well as the helical wavelength of the jet are reported for the first time.
Tiivistelmä
Tässä väitöskirjatutkimuksessa on keskitytty tutkimaan aktiivista galaksiydintä
OJ287. Väitöskirjan osana olevat tieteelliset julkaisut esittelevät
OJ287-systeemistä saatuja uusia tuloksia kaksoismusta-aukkomallin kontekstissa.
Väitöskirjan johdannossa käsitellään OJ287:n yleisiä ominaisuuksia
ja niitä fysikaalisia perusilmiöitä, jotka näiden ominaisuuksien taustalla
vaikuttavat. Johdanto selvittää myös OJ287-järjestelmän sijoittumisen aktiivisten
galaksiytimien hierarkiassa.
Johdannossa käydään läpi joitakin perusfysiikan tuloksia, jotka ovat
tarpeen aktiivisten galaksiydinten, mustien aukkojen binäärien, relativististen
suihkujen ja kertymäkiekkojen ymmärtämiseksi. Kahden toisiaan kiertävän
mustan aukon keskinäisen radan suhteellisuusteoreettiset perusteet
käydään läpi yksityiskohtaisemmin. Johdannossa esitetään joitakin analyyttisiä
tuloksia tällaisessa binäärissä havaittavista suhteellisuusteoreettisista
ilmiöistä. Myös numeerisia menetelmiä näiden ilmiöiden tarkempaan
laskemiseen esitellään. Tuloksia sovelletaan OJ287-systeemiin, ja verrataan
havaintoihin.
OJ287:n mustien aukkojen ratamalli muodostaa pohjan systeemin toistuvien
optisten purkausten malleille. Johdannossa esitellään yksityiskohtaisemmin
kaksi fysikaalista purkausmallia, ja vertaillaan niitä. Purkausten
säteilyhydrodynamiikka käydään läpi, ja myös ennusteet purkausten
valokäyrille johdetaan. Johdannossa esitellään myös Julkaisussa III johdettu
prekursoripurkausten malli, ja osoitetaan sen sopivan yhteen OJ287:n
binäärimallin kanssa.
Johdanto esittelee myös relativististen suihkujen fysiikkaa sekä OJ287-
systeemiin liittyen että aktiivisten galaksiydinten kontekstissa yleisesti. Relativististen
suihkujen perusfysiikka esitellään, kuten myös malleja kierteisistä
suihkuista. Julkaisujen II, IV ja V OJ287-systeemin suihkuja koskevat
tulokset esitellään binäärimallin kontekstissa.
Kokonaisuutena johdanto palvelee suppeana oppaana, joka esittelee tarvittavan
fysiikan ja tarpeelliset numeeriset menetelmät mustien aukkojen binäärijärjestelmän ymmärtämiseen ja simulointiin. Tätä tarkoitusta varten
johdanto yhdistää sekä perustuloksia että joitakin syvällisempiä tuloksia
laajoilta fysiikan osa-alueilta kuten suhteellisuusteoriasta ja säteilyhydrodynamiikasta.
Johdannon sisältämän materiaalin avulla väitöskirjan
julkaisut, ja niiden esittämät tulokset, ovat hyvin ymmärrettävissä.
Väitöskirjan julkaisuista ensimmäinen esittelee uusia OJ287-systeemistä
saatuja havaintopisteitä, jotka on paikallistettu Harvardin yliopiston observatorion
arkiston valokuvauslevyiltä. OJ287:n vuonna 1900 tapahtunut purkaus
nähdään ensimmäistä kertaa näissä havaintopisteissä. Uudet havaintopisteet
mahdollistivat myös vuoden 1913 purkauksen alun ajoittamisen
tarkemmin kuin aiemmin oli mahdollista. Havaitut purkaukset mallinnettiin
onnistuneesti simuloimalla OJ287-järjestelmän mustien aukkojen paria
ja kertymäkiekkoa.
Julkaisussa II käsitellään mekanismeja OJ287:n sekundäärisen mustan
aukon spinin kasvamiseen vuorovaikutuksessa primäärin kertymäkiekon ja
systeemin magneettikenttien kanssa. Julkaisussa arvioidaan maksimispinin
saavuttamisen ja spinin suunnan vakiintumisen aikaskaalat kummallakin
mekanismilla. Tutkimuksessa havaitaan sekundäärin spinin olevan todennäköisesti
suuri.
Julkaisu III esittelee OJ287-systeemissä maaliskuussa 2013 tapahtuneen
purkauksen. Purkauksen havaittiin muistuttavan vuosina 1993 ja 2004 tapahtuneita
purkauksia, joita kutsutaan yhteisnimityksellä prekursoripurkaus
(precursor outburst). Julkaisussa esitellään purkauksen synnylle mekanismi,
jossa OJ287-systeemin sekundäärinen musta aukko osuu primäärisen
mustan aukon kertymäkiekon koronassa olevaan kaasupilveen. Mekanismin
avulla johdetaan arviot prekursoripurkausten kirkkaudelle ja aikaskaalalle.
Julkaisussa johdetaan myös ennuste seuraavan prekursoripurkauksen
ajankohdalle.
Julkaisussa IV käytetään vuosina 2004–2006 kerättyjä havaintoja OJ287-
systeemistä lyhyiden jaksollisuuksien etsintään. Julkaisussa varmennetaan
systeemissä esiintyvä n. 50 päivän kvasiperiodisuus. Lisäksi tilastollisesti
merkittävät 250 päivän ja 3,5 päivän jaksollisuudet havaitaan. Julkaisussa
esitetään malli, jossa primäärisen mustan aukon kertymäkiekossa oleva spiraalitiheysaalto
aiheuttaa 50 päivän jaksollisuuden. Mallista tehty numeerinen
simulaatio tukee tulosta. Systeemin relativistisen suihkun emittoima
aikadilatoitunut säteily esitetään aiheuttajaksi 3,5 päivän jaksollisuusaikaskaalalle.
Julkaisussa V sovitetaan kierresuihkumalli OJ287-systeemistä tehtyihin optisiin havaintoihin ja millimetri- sekä senttimetriaallonpituuden radiohavaintoihin.
Suihkun rakenteen havaitaan olevan kaksijakoinen ja koostuvan
ytimestä ja kuoresta. Suihkun kuorella on merkittävästi pienempi Lorentzin
gamma-tekijä kuin suihkun ytimellä. Kuoren avautumiskulma ja Lorentztekijä
sekä suihkun kierteen aallonpituus raportoidaan julkaisussa ensimmäistä
kertaa.Siirretty Doriast
The Eightfold Way to Dissipation: Classification of Hydrodynamic Transport
Hydrodynamics is the low-energy effective field theory of any interacting quantum theory, capturing the long-wavelength fluctuations of an equilibrium Gibbs density matrix. Conventionally, one views the effective dynamics in terms of the conserved currents, which should be expressed in terms of the fluid velocity and the intensive parameters such as the temperature and chemical potential. However, not all currents allowed by symmetry are physically acceptable; one has to ensure that the second law of thermodynamics is satisfied on all physical configurations. We provide a complete solution to hydrodynamic transport at all orders in the gradient expansion compatible with the second law constraint.
The key new ingredient we introduce is the notion of adiabaticity, which allows us to take hydrodynamics off-shell. Adiabatic fluids are such that off-shell dynamics of the fluid compensates for entropy production. The space of adiabatic fluids admits a decomposition into seven distinct classes. Together with the dissipative class this establishes the eightfold way of hydrodynamic transport. Furthermore, recent results guarantee that dissipative terms beyond leading order in the gradient expansion are agnostic of the second law.
After completing the transport taxonomy, we go on to argue for a new symmetry principle, an Abelian gauge invariance that guarantees adiabaticity in hydrodynamics and serves as the emergent version of microscopic KMS conditions. We demonstrate its utility by explicitly constructing effective actions for adiabatic transport (i.e., seven out of eight classes). The theory of adiabatic fluids, we speculate, provides a useful starting point for a new framework to describe non-equilibrium dynamics. We outline briefly the crucial role of the proposed symmetry of gauged thermal translations in the construction of a Schwinger-Keldysh effective action that encompasses all of hydrodynamic transport
Core foundations, algorithms, and language design for symbolic computation in physics
This thesis presents three contributions to the field of symbolic computation, followed by their application to symbolic physics computations.
The first contribution is to interfacing systems. The Notation package, which is developed in this thesis, allows the entry and the creation of advanced notations in the Mathematica symbolic computation system. In particular, a complete and functioning notation for both Dirac's BraKet notation as well as a full tensorial notation, are given herein.
The second part of the thesis introduces a prototype based rule inheritance language paradigm that is applicable to certain advanced pattern matching rewrite rule language models. In particular, an implementation is presented for Mathematica. After detailing this language extension, it is adopted throughout the rest of the thesis.
Finally, the third major contribution is a highly efficient algorithm to canonicalize tensorial expressions. By an innovative technique this algorithm avoids the dummy index relabeling problem. Further algorithmic optimizations are then presented. The complete algorithm handles linear symmetries such as the Bianchi identities. It also fully accommodates partial derivatives as well as mixed index classes.
These advances in language and notations are extensively demonstrated on problems in quantum mechanics, angular momentum, general relativity, and quasi-spin. It is shown that the developments in this thesis lead to an extremely flexible, extensible, and powerful working environment for the expression and ensuing calculation of symbolic physics computations
Information Geometry
This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience
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