2017
http://publications.mfo.de/handle/mfo/1294
Wed, 12 May 2021 00:23:47 GMT2021-05-12T00:23:47ZComputing the long term evolution of the solar system with geometric numerical integrators
http://publications.mfo.de/handle/mfo/1355
Computing the long term evolution of the solar system with geometric numerical integrators
Fiorelli Vilmart, Shaula; Vilmart, Gilles
Simulating the dynamics of the Sun–Earth–Moon system
with a standard algorithm yields a dramatically
wrong solution, predicting that the Moon is ejected
from its orbit. In contrast, a well chosen algorithm
with the same initial data yields the correct behavior.
We explain the main ideas of how the evolution of
the solar system can be computed over long times
by taking advantage of so-called geometric numerical
methods. Short sample codes are provided for the
Sun–Earth–Moon system.
Wed, 27 Dec 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13552017-12-27T00:00:00ZFiorelli Vilmart, ShaulaVilmart, GillesSimulating the dynamics of the Sun–Earth–Moon system
with a standard algorithm yields a dramatically
wrong solution, predicting that the Moon is ejected
from its orbit. In contrast, a well chosen algorithm
with the same initial data yields the correct behavior.
We explain the main ideas of how the evolution of
the solar system can be computed over long times
by taking advantage of so-called geometric numerical
methods. Short sample codes are provided for the
Sun–Earth–Moon system.Spaces of Riemannian metrics
http://publications.mfo.de/handle/mfo/1352
Spaces of Riemannian metrics
Bustamante, Mauricio; Kordaß, Jan-Bernhard
Riemannian metrics endow smooth manifolds such as
surfaces with intrinsic geometric properties, for example
with curvature. They also allow us to measure
quantities like distances, angles and volumes. These
are the notions we use to characterize the “shape” of
a manifold. The space of Riemannian metrics is a
mathematical object that encodes the many possible
ways in which we can geometrically deform the shape
of a manifold.
Thu, 28 Dec 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13522017-12-28T00:00:00ZBustamante, MauricioKordaß, Jan-BernhardRiemannian metrics endow smooth manifolds such as
surfaces with intrinsic geometric properties, for example
with curvature. They also allow us to measure
quantities like distances, angles and volumes. These
are the notions we use to characterize the “shape” of
a manifold. The space of Riemannian metrics is a
mathematical object that encodes the many possible
ways in which we can geometrically deform the shape
of a manifold.Mathematics plays a key role in scientific computing
http://publications.mfo.de/handle/mfo/1351
Mathematics plays a key role in scientific computing
Shu, Chi-Wang
I attended a very interesting workshop at the research
center MFO in Oberwolfach on “Recent Developments
in the Numerics of Nonlinear Hyperbolic Conservation
Laws”. The title sounds a bit technical,
but in plain language we could say: The theme is
to survey recent research concerning how mathematics
is used to study numerical algorithms involving
a special class of equations. These equations arise
from computer simulations to solve application problems
including those in aerospace engineering, automobile
design, and electromagnetic waves in communications
as examples. This topic belongs to the general
research area called “scientific computing”.
Fri, 29 Dec 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13512017-12-29T00:00:00ZShu, Chi-WangI attended a very interesting workshop at the research
center MFO in Oberwolfach on “Recent Developments
in the Numerics of Nonlinear Hyperbolic Conservation
Laws”. The title sounds a bit technical,
but in plain language we could say: The theme is
to survey recent research concerning how mathematics
is used to study numerical algorithms involving
a special class of equations. These equations arise
from computer simulations to solve application problems
including those in aerospace engineering, automobile
design, and electromagnetic waves in communications
as examples. This topic belongs to the general
research area called “scientific computing”.Solving quadratic equations in many variables
http://publications.mfo.de/handle/mfo/1335
Solving quadratic equations in many variables
Tignol, Jean-Pierre
Fields are number systems in which every linear equation
has a solution, such as the set of all rational
numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields
have the same properties in relation with systems of
linear equations, but quadratic equations behave differently
from field to field. Is there a field in which
every quadratic equation in five variables has a solution,
but some quadratic equation in four variables
has no solution? The answer is in this snapshot.
Sat, 30 Dec 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13352017-12-30T00:00:00ZTignol, Jean-PierreFields are number systems in which every linear equation
has a solution, such as the set of all rational
numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. All fields
have the same properties in relation with systems of
linear equations, but quadratic equations behave differently
from field to field. Is there a field in which
every quadratic equation in five variables has a solution,
but some quadratic equation in four variables
has no solution? The answer is in this snapshot.Computational Optimal Transport
http://publications.mfo.de/handle/mfo/1332
Computational Optimal Transport
Solomon, Justin
Optimal transport is the mathematical discipline of
matching supply to demand while minimizing shipping
costs. This matching problem becomes extremely
challenging as the quantity of supply and demand
points increases; modern applications must cope with
thousands or millions of these at a time. Here, we
introduce the computational optimal transport problem
and summarize recent ideas for achieving new
heights in efficiency and scalability.
Thu, 21 Dec 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13322017-12-21T00:00:00ZSolomon, JustinOptimal transport is the mathematical discipline of
matching supply to demand while minimizing shipping
costs. This matching problem becomes extremely
challenging as the quantity of supply and demand
points increases; modern applications must cope with
thousands or millions of these at a time. Here, we
introduce the computational optimal transport problem
and summarize recent ideas for achieving new
heights in efficiency and scalability.A few shades of interpolation
http://publications.mfo.de/handle/mfo/1329
A few shades of interpolation
Szpond, Justyna
The topic of this snapshot is interpolation. In the
ordinary sense, interpolation means to insert something
of a different nature into something else. In
mathematics, interpolation means constructing new
data points from given data points. The new points
usually lie in between the already-known points. The
purpose of this snapshot is to introduce a particular
type of interpolation, namely, polynomial interpolation.
This will be explained starting from basic ideas
that go back to the ancient Babylonians and Greeks,
and will arrive at subjects of current research activity.
Thu, 07 Dec 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13292017-12-07T00:00:00ZSzpond, JustynaThe topic of this snapshot is interpolation. In the
ordinary sense, interpolation means to insert something
of a different nature into something else. In
mathematics, interpolation means constructing new
data points from given data points. The new points
usually lie in between the already-known points. The
purpose of this snapshot is to introduce a particular
type of interpolation, namely, polynomial interpolation.
This will be explained starting from basic ideas
that go back to the ancient Babylonians and Greeks,
and will arrive at subjects of current research activity.Closed geodesics on surfaces and Riemannian manifolds
http://publications.mfo.de/handle/mfo/1328
Closed geodesics on surfaces and Riemannian manifolds
Radeschi, Marco
Geodesics are special paths in surfaces and so-called
Riemannian manifolds which connect close points
in the shortest way. Closed geodesics are geodesics
which go back to where they started. In this snapshot
we talk about these special paths, and the efforts to
find closed geodesics.
Thu, 07 Dec 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13282017-12-07T00:00:00ZRadeschi, MarcoGeodesics are special paths in surfaces and so-called
Riemannian manifolds which connect close points
in the shortest way. Closed geodesics are geodesics
which go back to where they started. In this snapshot
we talk about these special paths, and the efforts to
find closed geodesics.Molecular Quantum Dynamics
http://publications.mfo.de/handle/mfo/1313
Molecular Quantum Dynamics
Hagedorn, George A.; Lasser, Caroline
We provide a brief introduction to some basic ideas
of Molecular Quantum Dynamics. We discuss the
scope, strengths and main applications of this field
of science. Finally, we also mention open problems
of current interest in this exciting subject.
Tue, 24 Oct 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13132017-10-24T00:00:00ZHagedorn, George A.Lasser, CarolineWe provide a brief introduction to some basic ideas
of Molecular Quantum Dynamics. We discuss the
scope, strengths and main applications of this field
of science. Finally, we also mention open problems
of current interest in this exciting subject.Mathematische Modellierung von Krebswachstum
http://publications.mfo.de/handle/mfo/1311
Mathematische Modellierung von Krebswachstum
Engwer, Christian; Knappitsch, Markus
Krebs ist eine der größten Herausforderungen der modernen
Medizin. Der WHO zufolge starben 2012 weltweit
8,2 Millionen Menschen an Krebs. Bis heute sind
dessen molekulare Mechanismen nur in Teilen verstanden,
was eine erfolgreiche Behandlung erschwert.
Mathematische Modellierung und Computersimulationen
können helfen, die Mechanismen des Tumorwachstums
besser zu verstehen. Sie eröffnen somit
neue Chancen für zukünftige Behandlungsmethoden.
In diesem Schnappschuss steht die mathematische
Modellierung von Glioblastomen im Fokus, einer Klasse
sehr agressiver Tumore im menschlichen Gehirn.
Tue, 17 Oct 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13112017-10-17T00:00:00ZEngwer, ChristianKnappitsch, MarkusKrebs ist eine der größten Herausforderungen der modernen
Medizin. Der WHO zufolge starben 2012 weltweit
8,2 Millionen Menschen an Krebs. Bis heute sind
dessen molekulare Mechanismen nur in Teilen verstanden,
was eine erfolgreiche Behandlung erschwert.
Mathematische Modellierung und Computersimulationen
können helfen, die Mechanismen des Tumorwachstums
besser zu verstehen. Sie eröffnen somit
neue Chancen für zukünftige Behandlungsmethoden.
In diesem Schnappschuss steht die mathematische
Modellierung von Glioblastomen im Fokus, einer Klasse
sehr agressiver Tumore im menschlichen Gehirn.Aperiodic Order and Spectral Properties
http://publications.mfo.de/handle/mfo/1310
Aperiodic Order and Spectral Properties
Baake, Michael; Damanik, David; Grimm, Uwe
Periodic structures like a typical tiled kitchen floor
or the arrangement of carbon atoms in a diamond
crystal certainly possess a high degree of order. But
what is order without periodicity? In this snapshot,
we are going to explore highly ordered structures that
are substantially nonperiodic, or aperiodic. As we
construct such structures, we will discover surprising
connections to various branches of mathematics, materials
science, and physics. Let us catch a glimpse
into the inherent beauty of aperiodic order!
Thu, 14 Sep 2017 00:00:00 GMThttp://publications.mfo.de/handle/mfo/13102017-09-14T00:00:00ZBaake, MichaelDamanik, DavidGrimm, UwePeriodic structures like a typical tiled kitchen floor
or the arrangement of carbon atoms in a diamond
crystal certainly possess a high degree of order. But
what is order without periodicity? In this snapshot,
we are going to explore highly ordered structures that
are substantially nonperiodic, or aperiodic. As we
construct such structures, we will discover surprising
connections to various branches of mathematics, materials
science, and physics. Let us catch a glimpse
into the inherent beauty of aperiodic order!