91,670 research outputs found
Two-loop critical mass for Wilson fermions
We have redone a recent two-loop computation of the critical mass for Wilson
fermions in lattice QCD by evaluating Feynman integrals with the
coordinate-space method. We present the results for different types of infrared
regularization. We confirm both the previous numerical estimates and the power
of the coordinate-space method whenever high accuracy is needed.Comment: 13 LaTeX2e pages, 2 ps figures include
Dynamical chiral symmetry breaking and a critical mass
On a bounded, measurable domain of non-negative current-quark mass, realistic
models of QCD's gap equation can simultaneously admit two inequivalent
dynamical chiral symmetry breaking (DCSB) solutions and a solution that is
unambiguously connected with the realisation of chiral symmetry in the Wigner
mode. The Wigner solution and one of the DCSB solutions are destabilised by a
current-quark mass and both disappear when that mass exceeds a critical value.
This critical value also bounds the domain on which the surviving DCSB solution
possesses a chiral expansion. This value can therefore be viewed as an upper
bound on the domain within which a perturbative expansion in the current-quark
mass around the chiral limit is uniformly valid for physical quantities. For a
pseudoscalar meson constituted of equal mass current-quarks, it corresponds to
a mass m_{0^-}~0.45GeV. In our discussion we employ properties of the two DCSB
solutions of the gap equation that enable a valid definition of in
the presence of a nonzero current-mass. The behaviour of this condensate
indicates that the essentially dynamical component of chiral symmetry breaking
decreases with increasing current-quark mass.Comment: 9 pages, 7 figures. Minor wording change
Statistics of statisticians: Critical mass of statistics and operational research groups in the UK
Using a recently developed model, inspired by mean field theory in
statistical physics, and data from the UK's Research Assessment Exercise, we
analyse the relationship between the quality of statistics and operational
research groups and the quantity researchers in them. Similar to other academic
disciplines, we provide evidence for a linear dependency of quality on quantity
up to an upper critical mass, which is interpreted as the average maximum
number of colleagues with whom a researcher can communicate meaningfully within
a research group. The model also predicts a lower critical mass, which research
groups should strive to achieve to avoid extinction. For statistics and
operational research, the lower critical mass is estimated to be 9 3. The
upper critical mass, beyond which research quality does not significantly
depend on group size, is about twice this value
Impact of critical mass on the evolution of cooperation in spatial public goods games
We study the evolution of cooperation under the assumption that the
collective benefits of group membership can only be harvested if the fraction
of cooperators within the group, i.e. their critical mass, exceeds a threshold
value. Considering structured populations, we show that a moderate fraction of
cooperators can prevail even at very low multiplication factors if the critical
mass is minimal. For larger multiplication factors, however, the level of
cooperation is highest at an intermediate value of the critical mass. The
latter is robust to variations of the group size and the interaction network
topology. Applying the optimal critical mass threshold, we show that the
fraction of cooperators in public goods games is significantly larger than in
the traditional linear model, where the produced public good is proportional to
the fraction of cooperators within the group.Comment: 4 two-column pages, 4 figures; accepted for publication in Physical
Review
Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag
The Nonlinear stability of triangular equilibrium points has been discussed
in the generalised photogravitational restricted three body problem with
Poynting-Robertson drag. The problem is generalised in the sense that smaller
primary is supposed to be an oblate spheroid. The bigger primary is considered
as radiating. We have performed first and second order normalization of the
Hamiltonian of the problem. We have applied KAM theorem to examine the
condition of non-linear stability. We have found three critical mass ratios.
Finally we conclude that triangular points are stable in the nonlinear sense
except three critical mass ratios at which KAM theorem fails.Comment: Including Poynting-Robertson Drag the triangular equilibrium points
are stable in the nonlinear sense except three critical mass ratios at which
KAM theorem fail
A one-dimensional Keller-Segel equation with a drift issued from the boundary
We investigate in this note the dynamics of a one-dimensional Keller-Segel
type model on the half-line. On the contrary to the classical configuration,
the chemical production term is located on the boundary. We prove, under
suitable assumptions, the following dichotomy which is reminiscent of the
two-dimensional Keller-Segel system. Solutions are global if the mass is below
the critical mass, they blow-up in finite time above the critical mass, and
they converge to some equilibrium at the critical mass. Entropy techniques are
presented which aim at providing quantitative convergence results for the
subcritical case. This note is completed with a brief introduction to a more
realistic model (still one-dimensional).Comment: short version, 8 page
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