1,607 research outputs found
Soccer: is scoring goals a predictable Poissonian process?
The non-scientific event of a soccer match is analysed on a strictly
scientific level. The analysis is based on the recently introduced concept of a
team fitness (Eur. Phys. J. B 67, 445, 2009) and requires the use of
finite-size scaling. A uniquely defined function is derived which
quantitatively predicts the expected average outcome of a soccer match in terms
of the fitness of both teams. It is checked whether temporary fitness
fluctuations of a team hamper the predictability of a soccer match.
To a very good approximation scoring goals during a match can be
characterized as independent Poissonian processes with pre-determined
expectation values. Minor correlations give rise to an increase of the number
of draws. The non-Poissonian overall goal distribution is just a consequence of
the fitness distribution among different teams. The limits of predictability of
soccer matches are quantified. Our model-free classification of the underlying
ingredients determining the outcome of soccer matches can be generalized to
different types of sports events
Numerical experiments of adjusted BSSN systems for controlling constraint violations
We present our numerical comparisons between the BSSN formulation widely used
in numerical relativity today and its adjusted versions using constraints. We
performed three testbeds: gauge-wave, linear wave, and Gowdy-wave tests,
proposed by the Mexico workshop on the formulation problem of the Einstein
equations. We tried three kinds of adjustments, which were previously proposed
from the analysis of the constraint propagation equations, and investigated how
they improve the accuracy and stability of evolutions. We observed that the
signature of the proposed Lagrange multipliers are always right and the
adjustments improve the convergence and stability of the simulations. When the
original BSSN system already shows satisfactory good evolutions (e.g., linear
wave test), the adjusted versions also coincide with those evolutions; while in
some cases (e.g., gauge-wave or Gowdy-wave tests) the simulations using the
adjusted systems last 10 times as long as those using the original BSSN
equations. Our demonstrations imply a potential to construct a robust evolution
system against constraint violations even in highly dynamical situations.Comment: to be published in PR
Development of laser pulse sampled DC voltammetry and its application to the determination of glucose
ArticleBUNSEKI KAGAKU. 57(1): 61-65 (2008)journal articl
Advantages of modified ADM formulation: constraint propagation analysis of Baumgarte-Shapiro-Shibata-Nakamura system
Several numerical relativity groups are using a modified ADM formulation for
their simulations, which was developed by Nakamura et al (and widely cited as
Baumgarte-Shapiro-Shibata-Nakamura system). This so-called BSSN formulation is
shown to be more stable than the standard ADM formulation in many cases, and
there have been many attempts to explain why this re-formulation has such an
advantage. We try to explain the background mechanism of the BSSN equations by
using eigenvalue analysis of constraint propagation equations. This analysis
has been applied and has succeeded in explaining other systems in our series of
works. We derive the full set of the constraint propagation equations, and
study it in the flat background space-time. We carefully examine how the
replacements and adjustments in the equations change the propagation structure
of the constraints, i.e. whether violation of constraints (if it exists) will
decay or propagate away. We conclude that the better stability of the BSSN
system is obtained by their adjustments in the equations, and that the
combination of the adjustments is in a good balance, i.e. a lack of their
adjustments might fail to obtain the present stability. We further propose
other adjustments to the equations, which may offer more stable features than
the current BSSN equations.Comment: 10 pages, RevTeX4, added related discussion to gr-qc/0209106, the
version to appear in Phys. Rev.
Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime
In order to find a way to have a better formulation for numerical evolution
of the Einstein equations, we study the propagation equations of the
constraints based on the Arnowitt-Deser-Misner formulation. By adjusting
constraint terms in the evolution equations, we try to construct an
"asymptotically constrained system" which is expected to be robust against
violation of the constraints, and to enable a long-term stable and accurate
numerical simulation. We first provide useful expressions for analyzing
constraint propagation in a general spacetime, then apply it to Schwarzschild
spacetime. We search when and where the negative real or non-zero imaginary
eigenvalues of the homogenized constraint propagation matrix appear, and how
they depend on the choice of coordinate system and adjustments. Our analysis
includes the proposal of Detweiler (1987), which is still the best one
according to our conjecture but has a growing mode of error near the horizon.
Some examples are snapshots of a maximally sliced Schwarzschild black hole. The
predictions here may help the community to make further improvements.Comment: 23 pages, RevTeX4, many figures. Revised version. Added subtitle,
reduced figures, rephrased introduction, and a native checked. :-
Constraint propagation in the family of ADM systems
The current important issue in numerical relativity is to determine which
formulation of the Einstein equations provides us with stable and accurate
simulations. Based on our previous work on "asymptotically constrained"
systems, we here present constraint propagation equations and their eigenvalues
for the Arnowitt-Deser-Misner (ADM) evolution equations with additional
constraint terms (adjusted terms) on the right hand side. We conjecture that
the system is robust against violation of constraints if the amplification
factors (eigenvalues of Fourier-component of the constraint propagation
equations) are negative or pure-imaginary. We show such a system can be
obtained by choosing multipliers of adjusted terms. Our discussion covers
Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also
mention the so-called conformal-traceless ADM systems.Comment: 11 pages, RevTeX, 2 eps figure
Generation of scalar-tensor gravity effects in equilibrium state boson stars
Boson stars in zero-, one-, and two-node equilibrium states are modeled
numerically within the framework of Scalar-Tensor Gravity. The complex scalar
field is taken to be both massive and self-interacting. Configurations are
formed in the case of a linear gravitational scalar coupling (the Brans-Dicke
case) and a quadratic coupling which has been used previously in a cosmological
context. The coupling parameters and asymptotic value for the gravitational
scalar field are chosen so that the known observational constraints on
Scalar-Tensor Gravity are satisfied. It is found that the constraints are so
restrictive that the field equations of General Relativity and Scalar-Tensor
gravity yield virtually identical solutions. We then use catastrophe theory to
determine the dynamically stable configurations. It is found that the maximum
mass allowed for a stable state in Scalar-Tensor gravity in the present
cosmological era is essentially unchanged from that of General Relativity. We
also construct boson star configurations appropriate to earlier cosmological
eras and find that the maximum mass for stable states is smaller than that
predicted by General Relativity, and the more so for earlier eras. However, our
results also show that if the cosmological era is early enough then only states
with positive binding energy can be constructed.Comment: 20 pages, RevTeX, 11 figures, to appear in Class. Quantum Grav.,
comments added, refs update
Hyperbolic formulations and numerical relativity II: Asymptotically constrained systems of the Einstein equations
We study asymptotically constrained systems for numerical integration of the
Einstein equations, which are intended to be robust against perturbative errors
for the free evolution of the initial data. First, we examine the previously
proposed "-system", which introduces artificial flows to constraint
surfaces based on the symmetric hyperbolic formulation. We show that this
system works as expected for the wave propagation problem in the Maxwell system
and in general relativity using Ashtekar's connection formulation. Second, we
propose a new mechanism to control the stability, which we call the ``adjusted
system". This is simply obtained by adding constraint terms in the dynamical
equations and adjusting its multipliers. We explain why a particular choice of
multiplier reduces the numerical errors from non-positive or pure-imaginary
eigenvalues of the adjusted constraint propagation equations. This ``adjusted
system" is also tested in the Maxwell system and in the Ashtekar's system. This
mechanism affects more than the system's symmetric hyperbolicity.Comment: 16 pages, RevTeX, 9 eps figures, added Appendix B and minor changes,
to appear in Class. Quant. Gra
Non-equilibrium Studies in Switching Arc Plasmas in Japan
This paper briefly introduce research work examples of non-equilibrium studies in switching arcs. In understanding arc behavior, one often assumes local thermodynamic equilibrium (LTE) condition in the arc plasma. However, actual arc plasmas are not completely and not always in LTE state because of strong temperature change temporally and spatially, and high electric field application etc. Recently, we have a collaboration work in numerical simulations and experimental approaches for decaying arcs without LTE assumption. First, our numerical model is presented for decaying arcs without chemical equilibrium assumption. Secondly, two experimental methods are introduced for measuring electron density in decaying arcs without LTE assumption: Laser Thomson Scattering method and the Schack-Hartmann method. Finally, comparison results is shown between the LTE simulation, the chemically non-equilibrium simulation, and the above experimental measurements
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