4,247 research outputs found
On the emergence of random initial conditions in fluid limits
The paper presents a phenomenon occurring in population processes that start
near zero and have large carrying capacity. By the classical result of
Kurtz~(1970), such processes, normalized by the carrying capacity, converge on
finite intervals to the solutions of ordinary differential equations, also
known as the fluid limit. When the initial population is small relative to
carrying capacity, this limit is trivial. Here we show that, viewed at suitably
chosen times increasing to infinity, the process converges to the fluid limit,
governed by the same dynamics, but with a random initial condition. This random
initial condition is related to the martingale limit of an associated linear
birth and death process
A law of large numbers approximation for Markov population processes with countably many types
When modelling metapopulation dynamics, the influence of a single patch on
the metapopulation depends on the number of individuals in the patch. Since the
population size has no natural upper limit, this leads to systems in which
there are countably infinitely many possible types of individual. Analogous
considerations apply in the transmission of parasitic diseases. In this paper,
we prove a law of large numbers for rather general systems of this kind,
together with a rather sharp bound on the rate of convergence in an
appropriately chosen weighted norm.Comment: revised version in response to referee comments, 34 page
Einstein gravity as a 3D conformally invariant theory
We give an alternative description of the physical content of general
relativity that does not require a Lorentz invariant spacetime. Instead, we
find that gravity admits a dual description in terms of a theory where local
size is irrelevant. The dual theory is invariant under foliation preserving
3-diffeomorphisms and 3D conformal transformations that preserve the 3-volume
(for the spatially compact case). Locally, this symmetry is identical to that
of Horava-Lifshitz gravity in the high energy limit but our theory is
equivalent to Einstein gravity. Specifically, we find that the solutions of
general relativity, in a gauge where the spatial hypersurfaces have constant
mean extrinsic curvature, can be mapped to solutions of a particular gauge
fixing of the dual theory. Moreover, this duality is not accidental. We provide
a general geometric picture for our procedure that allows us to trade foliation
invariance for conformal invariance. The dual theory provides a new proposal
for the theory space of quantum gravity.Comment: 27 pages. Published version (minor changes and corrections
Finite Density Fat QCD
Lattice formulation of Finite Baryon Density QCD is problematic from computer
simulation point of view; it is well known that for light quark masses the
reconstructed partition function fails to be positive in a wide region of
parameter space. For large bare quark masses, instead, it is possible to obtain
more sensible results; problems are still present but restricted to a small
region. We present evidence for a saturation transition independent from the
gauge coupling and for a transition line that, starting from the
temperature critical point at , moves towards smaller with
increasing as expected from simplified phenomenological arguments.Comment: 14 pages, 10 figure
\u3ci\u3eGNATHABELODON THORPEI\u3c/i\u3e, gen. et sp. nov. A new mud-grubbing Mastodon
In February, 1932, while opening a gravel pit to get material for highway construction, the skull, tusks, and mandible of a new longirostral mastodont were found by Robert Arnold on his ranch, Sec. 24, T. 12 S., R. 22 W., 1 1/2 miles due east of Ogallah, Trego County, western Kansas. This point is located about 20 miles west and three miles north of Hays, the seat of the Fort Hays Kansas State College, in the museum of which the above mentioned specimen is mounted and exhibited. When unexpectedly exposed by Mr. Arnold and his associates, the great skull was perfect, and had one tusk in place with the other lying near by. The mandible likewise was complete throughout. The skull, jaw, and tusks were of ivory whiteness, and of substantial outward appearance, and gave little warning of their fragile nature. While they were undermining this great skull it collapsed, and the fragments were lost, with the exception of the larger pieces, such as the palatine region with the upper molars, and the very base of the skull with both occipital condyles
Quenched QCD at finite density
Simulations of quenched at relatively small but {\it nonzero} chemical
potential on lattices indicate that the nucleon
screening mass decreases linearly as increases predicting a critical
chemical potential of one third the nucleon mass, , by extrapolation.
The meson spectrum does not change as increases over the same range, from
zero to . Past studies of quenched lattice QCD have suggested that
there is phase transition at . We provide alternative
explanations for these results, and find a number of technical reasons why
standard lattice simulation techniques suffer from greatly enhanced
fluctuations and finite size effects for ranging from to
. We find evidence for such problems in our simulations, and suggest
that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte
The non-zero baryon number formulation of QCD
We discuss the non-zero baryon number formulation of QCD in the quenched
limit at finite temperature. This describes the thermodynamics of gluons in the
background of static quark sources. Although a sign problem remains in this
theory, our simulation results show that it can be handled quite well
numerically. The transition region gets shifted to smaller temperatures and the
transition region broadens with increasing baryon number. Although the action
is in our formulation explicitly Z(3) symmetric the Polyakov loop expectation
value becomes non-zero already in the low temperature phase and the heavy quark
potential gets screened at non-vanishing number density already this phase.Comment: LATTICE99(Finite Temperature and Density), Latex2e using espcrc2.sty,
3 pages, 7 figure
Imaginary chemical potential and finite fermion density on the lattice
Standard lattice fermion algorithms run into the well-known sign problem at
real chemical potential. In this paper we investigate the possibility of using
imaginary chemical potential, and argue that it has advantages over other
methods, particularly for probing the physics at finite temperature as well as
density. As a feasibility study, we present numerical results for the partition
function of the two-dimensional Hubbard model with imaginary chemical
potential.
We also note that systems with a net imbalance of isospin may be simulated
using a real chemical potential that couples to I_3 without suffering from the
sign problem.Comment: 9 pages, LaTe
Triangleland. I. Classical dynamics with exchange of relative angular momentum
In Euclidean relational particle mechanics, only relative times, relative
angles and relative separations are meaningful. Barbour--Bertotti (1982) theory
is of this form and can be viewed as a recovery of (a portion of) Newtonian
mechanics from relational premises. This is of interest in the absolute versus
relative motion debate and also shares a number of features with the
geometrodynamical formulation of general relativity, making it suitable for
some modelling of the problem of time in quantum gravity. I also study
similarity relational particle mechanics (`dynamics of pure shape'), in which
only relative times, relative angles and {\sl ratios of} relative separations
are meaningful. This I consider firstly as it is simpler, particularly in 1 and
2 d, for which the configuration space geometry turns out to be well-known,
e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail.
Secondly, the similarity model occurs as a sub-model within the Euclidean
model: that admits a shape--scale split. For harmonic oscillator like
potentials, similarity triangleland model turns out to have the same
mathematics as a family of rigid rotor problems, while the Euclidean case turns
out to have parallels with the Kepler--Coulomb problem in spherical and
parabolic coordinates. Previous work on relational mechanics covered cases
where the constituent subsystems do not exchange relative angular momentum,
which is a simplifying (but in some ways undesirable) feature paralleling
centrality in ordinary mechanics. In this paper I lift this restriction. In
each case I reduce the relational problem to a standard one, thus obtain
various exact, asymptotic and numerical solutions, and then recast these into
the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure
Method comparisons, influence of the number, distribution and range of samples on performance claims
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