71 relations: Astronomical Calculation Institute (Heidelberg University), Astronomy, Astrophysics, Avogadro constant, Barnes–Hut simulation, Baryon, Binary star, Bolshoi Cosmological Simulation, Cambridge University Press, Cold dark matter, Comoving and proper distances, Computational complexity theory, Dark matter, Dynamical system, Earth, Ergodic theory, Fast Fourier transform, Figure of the Earth, Frequency domain, Friedmann–Lemaître–Robertson–Walker metric, Frozen orbit, GADGET, Galactic halo, Galaxy filament, Galaxy formation and evolution, General relativity, Germany, Gravitational constant, Gravitational potential, Gravity, Heidelberg, Interstellar cloud, Leapfrog integration, Lepton, Lyapunov stability, Lyapunov time, Millennium Run, Moon, Multibody simulation, Multibody system, Multipole expansion, N-body problem, Natural units, Newton's law of universal gravitation, Observable universe, Octree, Ordinary differential equation, Particle Mesh, Perturbation (astronomy), Photon, ..., Physical cosmology, Physics, Poisson's equation, Princeton University Press, PSPACE, Ray tracing (graphics), Redshift, Runge–Kutta methods, S. Rao Kosaraju, Scale factor (cosmology), Sebastian von Hoerner, Smoothed-particle hydrodynamics, Solar mass, Speed of gravity, Star cluster, Structure formation, Sun, Sverre Aarseth, University of Cambridge, Virgo Consortium, Well-separated pair decomposition. Expand index (21 more) »

## Astronomical Calculation Institute (Heidelberg University)

The Astronomical Calculation Institute (Astronomisches Rechen-Institut; ARI) is a research institute in Heidelberg, Germany, dating from the 1700s.

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## Astronomy

Astronomy (from ἀστρονομία) is a natural science that studies celestial objects and phenomena.

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## Astrophysics

Astrophysics is the branch of astronomy that employs the principles of physics and chemistry "to ascertain the nature of the astronomical objects, rather than their positions or motions in space".

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## Avogadro constant

In chemistry and physics, the Avogadro constant (named after scientist Amedeo Avogadro) is the number of constituent particles, usually atoms or molecules, that are contained in the amount of substance given by one mole.

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## Barnes–Hut simulation

The Barnes–Hut simulation (Josh Barnes and Piet Hut) is an approximation algorithm for performing an ''n''-body simulation.

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## Baryon

A baryon is a composite subatomic particle made up of three quarks (a triquark, as distinct from mesons, which are composed of one quark and one antiquark).

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## Binary star

A binary star is a star system consisting of two stars orbiting around their common barycenter.

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## Bolshoi Cosmological Simulation

The Bolshoi simulation, run in 2010 on the Pleiades supercomputer at the NASA Ames Research Center, was the most accurate cosmological simulation to that date of the evolution of the large-scale structure of the universe.

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## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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## Cold dark matter

In cosmology and physics, cold dark matter (CDM) is a hypothetical form of dark matter whose particles moved slowly compared to the speed of light (the cold in CDM) since the universe was approximately one year old (a time when the cosmic particle horizon contained the mass of one typical galaxy); and interact very weakly with ordinary matter and electromagnetic radiation (the dark in CDM).

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## Comoving and proper distances

In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects.

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## Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

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## Dark matter

Dark matter is a theorized form of matter that is thought to account for approximately 80% of the matter in the universe, and about a quarter of its total energy density.

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## Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

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## Earth

Earth is the third planet from the Sun and the only astronomical object known to harbor life.

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## Ergodic theory

Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.

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## Fast Fourier transform

A fast Fourier transform (FFT) is an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.

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## Figure of the Earth

The figure of the Earth is the size and shape of the Earth in geodesy.

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## Frequency domain

In electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time.

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## Friedmann–Lemaître–Robertson–Walker metric

The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding or contracting universe that is path connected, but not necessarily simply connected.

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## Frozen orbit

In orbital mechanics, a frozen orbit is an orbit for an artificial satellite in which natural drifting due to the central body's shape has been minimized by careful selection of the orbital parameters.

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## GADGET

GADGET is a free software for cosmological N-body/SPH simulations written by Volker Springel at the Max Planck Institute for Astrophysics.

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## Galactic halo

A galactic halo is an extended, roughly spherical component of a galaxy which extends beyond the main, visible component.

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## Galaxy filament

The distribution reveals fine, filamentary structures.

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## Galaxy formation and evolution

The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous universe from a homogeneous beginning, the formation of the first galaxies, the way galaxies change over time, and the processes that have generated the variety of structures observed in nearby galaxies.

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## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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## Germany

Germany (Deutschland), officially the Federal Republic of Germany (Bundesrepublik Deutschland), is a sovereign state in central-western Europe.

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## Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

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## Gravitational potential

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object.

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## Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

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## Heidelberg

Heidelberg is a college town in Baden-Württemberg situated on the river Neckar in south-west Germany.

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## Interstellar cloud

An interstellar cloud is generally an accumulation of gas, plasma, and dust in our and other galaxies.

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## Leapfrog integration

In mathematics leapfrog integration is a method for numerically integrating differential equations of the form or equivalently of the form particularly in the case of a dynamical system of classical mechanics.

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## Lepton

In particle physics, a lepton is an elementary particle of half-integer spin (spin) that does not undergo strong interactions.

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## Lyapunov stability

Various types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems.

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## Lyapunov time

In mathematics, the Lyapunov time is the characteristic timescale on which a dynamical system is chaotic.

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## Millennium Run

The Millennium Run, or Millennium Simulation (referring to its size) is a computer N-body simulation used to investigate how the distribution of matter in the Universe has evolved over time, in particular, how the observed population of galaxies was formed.

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## Moon

The Moon is an astronomical body that orbits planet Earth and is Earth's only permanent natural satellite.

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## Multibody simulation

Multibody simulation (MBS) is a method of numerical simulation in which multibody systems are composed of various rigid or elastic bodies.

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## Multibody system

Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements.

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## Multipole expansion

A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere.

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## N-body problem

In physics, the -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.

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## Natural units

In physics, natural units are physical units of measurement based only on universal physical constants.

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## Newton's law of universal gravitation

Newton's law of universal gravitation states that a particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

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## Observable universe

The observable universe is a spherical region of the Universe comprising all matter that can be observed from Earth at the present time, because electromagnetic radiation from these objects has had time to reach Earth since the beginning of the cosmological expansion.

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## Octree

An octree is a tree data structure in which each internal node has exactly eight children.

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## Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.

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## Particle Mesh

Particle Mesh (PM) is a computational method for determining the forces in a system of particles.

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## Perturbation (astronomy)

In astronomy, perturbation is the complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body.

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## Photon

The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force (even when static via virtual particles).

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## Physical cosmology

Physical cosmology is the study of the largest-scale structures and dynamics of the Universe and is concerned with fundamental questions about its origin, structure, evolution, and ultimate fate.

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## Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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## Poisson's equation

In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics.

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## Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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## PSPACE

In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space.

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## Ray tracing (graphics)

In computer graphics, ray tracing is a rendering technique for generating an image by tracing the path of light as pixels in an image plane and simulating the effects of its encounters with virtual objects.

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## Redshift

In physics, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the spectrum.

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## Runge–Kutta methods

In numerical analysis, the Runge–Kutta methods are a family of implicit and explicit iterative methods, which include the well-known routine called the Euler Method, used in temporal discretization for the approximate solutions of ordinary differential equations.

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## S. Rao Kosaraju

Sambasiva Rao Kosaraju is a professor of computer science at Johns Hopkins University, and division director for Computing & Communication Foundations at the National Science Foundation.

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## Scale factor (cosmology)

The relative expansion of the universe is parametrized by a dimensionless scale factor a. Also known as the cosmic scale factor or sometimes the Robertson–Walker scale factor, this is a key parameter of the Friedmann equations.

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## Sebastian von Hoerner

Sebastian Rudolf Karl von Hoerner (15 April 1919 – 7 January 2003) was a German astrophysicist and radio astronomer.

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## Smoothed-particle hydrodynamics

Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows.

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## Solar mass

The solar mass is a standard unit of mass in astronomy, equal to approximately.

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## Speed of gravity

In classical theories of gravitation, the changes in a gravitational field propagate.

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## Star cluster

Star clusters are groups of stars.

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## Structure formation

In physical cosmology, structure formation is the formation of galaxies, galaxy clusters and larger structures from small early density fluctuations.

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## Sun

The Sun is the star at the center of the Solar System.

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## Sverre Aarseth

Sverre Johannes Aarseth, (born 20 July 1934) is a research scientist at the Institute of Astronomy at the University of Cambridge.

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## University of Cambridge

The University of Cambridge (informally Cambridge University)The corporate title of the university is The Chancellor, Masters, and Scholars of the University of Cambridge.

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## Virgo Consortium

The Virgo Consortium was founded in 1994 for Cosmological Supercomputer Simulations in response to the UK's High Performance Computing Initiative.

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## Well-separated pair decomposition

In computational geometry, a well-separated pair decomposition (WSPD) of a set of points S \subset \mathbb^d, is a sequence of pairs of sets (A_i, B_i), such that each pair is well-separated, and for each two distinct points p, q \in S, there exists precisely one pair which separates the two.

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## Redirects here:

N body simulation, N-body, N-body cosmological simulation, N-body simulations.

## References

[1] https://en.wikipedia.org/wiki/N-body_simulation