13,590 research outputs found
The mathematical research of William Parry FRS
In this article we survey the mathematical research of the late William (Bill) Parry, FRS
Pattern Formation in the Early Universe
Systems that exhibit pattern formation are typically driven and dissipative.
In the early universe, parametric resonance can drive explosive particle
production called preheating. The fields that are populated then decay quantum
mechanically if their particles are unstable. Thus, during preheating, a
driven-dissipative system exists. We have shown previously that pattern
formation can occur in two dimensions in a self-coupled inflaton system
undergoing parametric resonance. In this paper, we provide evidence of pattern
formation for more realistic initial conditions in both two and three
dimensions. In the one-field case, we have the novel interpretation that these
patterns can be thought of as a network of domain walls. We also show that the
patterns are spatio-temporal, leading to a distinctive, but probably
low-amplitude peak in the gravitational wave spectrum. In the context of a
two-field model, we discuss putting power from resonance into patterns on
cosmological scales, in particular to explain the observed excess power at 100
h^{-1}Mpc, but why this seems unlikely in the absence of a period of
post-preheating inflation. Finally we note our model is similar to that of the
decay of DCCs and therefore pattern formation may also occur at RHIC and LHC.Comment: 9 pages, 11 figure
Droplet shapes on structured substrates and conformal invariance
We consider the finite-size scaling of equilibrium droplet shapes for fluid
adsorption (at bulk two-phase co-existence) on heterogeneous substrates and
also in wedge geometries in which only a finite domain of the
substrate is completely wet. For three-dimensional systems with short-ranged
forces we use renormalization group ideas to establish that both the shape of
the droplet height and the height-height correlations can be understood from
the conformal invariance of an appropriate operator. This allows us to predict
the explicit scaling form of the droplet height for a number of different
domain shapes. For systems with long-ranged forces, conformal invariance is not
obeyed but the droplet shape is still shown to exhibit strong scaling
behaviour. We argue that droplet formation in heterogeneous wedge geometries
also shows a number of different scaling regimes depending on the range of the
forces. The conformal invariance of the wedge droplet shape for short-ranged
forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.
Tricritical wedge filling transitions with short-ranged forces
We show that the 3D wedge filling transition in the presence of short-ranged
interactions can be first-order or second order depending on the strength of
the line tension associated with to the wedge bottom. This fact implies the
existence of a tricritical point characterized by a short-distance expansion
which differs from the usual continuous filling transition. Our analysis is
based on an effective one-dimensional model for the 3D wedge filling which
arises from the identification of the breather modes as the only relevant
interfacial fluctuations. From such analysis we find a correspondence between
continuous 3D filling at bulk coexistence and 2D wetting transitions with
random-bond disorder.Comment: 7 pages, 3 figures, 6th Liquid Matter Conference Proceedings (to be
published in J. Phys.: Condens. Matter
The large CP phase in B(s)-anti-B(s) mixing from primary scalar unparticles
In this letter we consider the case of primary scalar unparticle
contributions to B(d,s) mixing. With particular emphasis on the impact of the
recent hint of new physics in the measurement of the B(s) mixing phase, phi(s),
we determine the allowed parameter space and impose bounds on the unparticle
couplings.Comment: 8 pages, 8 jpeg figures, using pdflatex. Typo corrected, reference
adde
Interfacial Structural Changes and Singularities in Non-Planar Geometries
We consider phase coexistence and criticality in a thin-film Ising magnet
with opposing surface fields and non-planar (corrugated) walls. We show that
the loss of translational invariance has a strong and unexpected non-linear
influence on the interface structure and phase diagram. We identify 4
non-thermodynamic singularities where there is a qualitative change in the
interface shape. In addition, we establish that at the finite-size critical
point, the singularity in the interface shape is characterized by two distint
critical exponents in contrast to the planar case (which is characterised by
one). Similar effects should be observed for prewetting at a corrugated
substrate. Analogy is made with the behaviour of a non-linear forced oscillator
showing chaotic dynamics.Comment: 13 pages, 3 figure
Brane Gas Inflation
We consider the brane gas picture of the early universe. At later stages,
when there are no winding modes and the background is free to expand, we show
that a moving 3-brane, which we identify with our universe, can inflate even
though it is radiation-dominated. The crucial ingredients for successful
inflation are the coupling to the dilaton and the equation of state of the
bulk. If we suppose the brane initially forms in a collision of
higher-dimensional branes, then the spectrum of primordial density fluctuations
naturally has a thermal origin.Comment: 4 pages, 1 figur
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