3,195 research outputs found
Universality in snowflake aggregation
Aggregation of ice crystals is a key process governing precipitation. Individual ice crystals exhibit considerable diversity of shape, and a wide range of physical processes could influence their aggregation; despite this we show that a simple computer model captures key features of aggregate shape and size distribution reported recently from cirrus clouds. The results prompt a new way to plot the experimental size distributions leading to remarkably good dynamical scaling. That scaling independently confirms that there is a single dominant aggregation mechanism at play, albeit our model (based on undeflected trajectories to contact) does not capture its form exactly
Equation of motion approach to the Hubbard model in infinite dimensions
We consider the Hubbard model on the infinite-dimensional Bethe lattice and
construct a systematic series of self-consistent approximations to the
one-particle Green's function, . The first
equations of motion are exactly fullfilled by and the
'th equation of motion is decoupled following a simple set of decoupling
rules. corresponds to the Hubbard-III approximation. We
present analytic and numerical results for the Mott-Hubbard transition at half
filling for .Comment: 10pager, REVTEX, 8-figures not available in postscript, manuscript
may be understood without figure
Emergence in holographic scenarios for gravity
'Holographic' relations between theories have become an important theme in
quantum gravity research. These relations entail that a theory without gravity
is equivalent to a gravitational theory with an extra spatial dimension. The
idea of holography was first proposed in 1993 by Gerard 't Hooft on the basis
of his studies of evaporating black holes. Soon afterwards the holographic
'AdS/CFT' duality was introduced, which since has been intensively studied in
the string theory community and beyond. Recently, Erik Verlinde has proposed
that even Newton's law of gravitation can be related holographically to the
`thermodynamics of information' on screens. We discuss these scenarios, with
special attention to the status of the holographic relation in them and to the
question of whether they make gravity and spacetime emergent. We conclude that
only Verlinde's scheme straightfowardly instantiates emergence. However,
assuming a non-standard interpretation of AdS/CFT may create room for the
emergence of spacetime and gravity there as well
Nontrivial Polydispersity Exponents in Aggregation Models
We consider the scaling solutions of Smoluchowski's equation of irreversible
aggregation, for a non gelling collision kernel. The scaling mass distribution
f(s) diverges as s^{-tau} when s->0. tau is non trivial and could, until now,
only be computed by numerical simulations. We develop here new general methods
to obtain exact bounds and good approximations of . For the specific
kernel KdD(x,y)=(x^{1/D}+y^{1/D})^d, describing a mean-field model of particles
moving in d dimensions and aggregating with conservation of ``mass'' s=R^D (R
is the particle radius), perturbative and nonperturbative expansions are
derived.
For a general kernel, we find exact inequalities for tau and develop a
variational approximation which is used to carry out the first systematic study
of tau(d,D) for KdD. The agreement is excellent both with the expansions we
derived and with existing numerical values. Finally, we discuss a possible
application to 2d decaying turbulence.Comment: 16 pages (multicol.sty), 6 eps figures (uses epsfig), Minor
corrections. Notations improved, as published in Phys. Rev. E 55, 546
Molecular oxygen as a signaling component in plant development
While traditionally hypoxia has been studied as a detrimental component of flooding stress, the last decade has flourished with studies reporting the involvement of molecular oxygen availability in plant developmental processes. Moreover, proliferating and undifferentiated cells from different plant tissues were found to reside in endogenously generated hypoxic niches. Thus, stress-associated acute hypoxia may be distinguished from constitutively generated chronic hypoxia. The Cys/Arg branch of the N-degron pathway assumes a central role in integrating oxygen levels resulting in proteolysis of transcriptional regulators that control different aspects of plant growth and development. As a target of this pathway, group VII of the Ethylene Response Factor (ERF-VII) family has emerged as a hub for the integration of oxygen dynamics in root development and during seedling establishment. Additionally, vegetative shoot meristem activity and reproductive transition were recently associated with oxygen availability via two novel substrates of the N-degron pathways: VERNALISATION 2 (VRN2) and LITTLE ZIPPER 2 (ZPR2). Together, these observations support roles for molecular oxygen as a signalling molecule in plant development, as well as in essential metabolic reactions. Here, we review recent findings regarding oxygen-regulated development, and discuss outstanding questions that spring from these discoveries
Fluctuation-driven insulator-to-metal transition in an external magnetic field
We consider a model for a metal-insulator transition of correlated electrons
in an external magnetic field. We find a broad region in interaction and
magnetic field where metallic and insulating (fully magnetized) solutions
coexist and the system undergoes a first-order metal-insulator transition. A
global instability of the magnetically saturated solution precedes the local
ones and is caused by collective fluctuations due to poles in electron-hole
vertex functions.Comment: REVTeX 4 pages, 3 PS figure
Renormalisation-theoretic analysis of non-equilibrium phase transitions II: The effect of perturbations on rate coefficients in the Becker-Doring equations
We study in detail the application of renormalisation theory to models of
cluster aggregation and fragmentation of relevance to nucleation and growth
processes. In particular, we investigate the Becker-Doring (BD) equations,
originally formulated to describe and analyse non-equilibrium phase
transitions, but more recently generalised to describe a wide range of
physicochemical problems. We consider here rate coefficients which depend on
the cluster size in a power-law fashion, but now perturbed by small amplitude
random noise. Power-law rate coefficients arise naturally in the theory of
surface-controlled nucleation and growth processes. The noisy perturbations on
these rates reflect the effect of microscopic variations in such mean-field
coefficients, thermal fluctuations and/or experimental uncertainties. In the
present paper we generalise our earlier work that identified the nine classes
into which all dynamical behaviour must fall by investigating how random
perturbations of the rate coefficients influence the steady-state and kinetic
behaviour of the coarse-grained, renormalised system. We are hence able to
confirm the existence of a set of up to nine universality classes for such BD
systems.Comment: 30 pages, to appear in J Phys A Math Ge
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