6,401 research outputs found
Damping of an oscillating scalar field indirectly coupled to a thermal bath
The damping process of a homogeneous oscillating scalar field that indirectly
interacts with a thermal bath through a mediator field is investigated over a
wide range of model parameters. We consider two types of mediator fields, those
that can decay to the thermal bath and those that are individually stable but
pair annihilate. The former case has been extensively studied in the literature
by treating the damping as a local effect after integrating out the assumed
close-to-equilibrium mediator field. The same approach does not apply if the
mediator field is stable and freezes out of equilibrium. To account for the
latter case, we adopt a non-local description of damping that is only
meaningful when we consider full half-oscillations of the field being damped.
The damping rates of the oscillating scalar field and the corresponding heating
rate of the thermal bath in all bulk parameter regions are calculated in both
cases, corroborating previous results in the direct decay case. Using the
obtained results, the time it takes for the amplitude of the scalar field to be
substantially damped is estimated.Comment: 39 pages, 9 figures, 1 table; typos corrected, references adde
RESOURCE OR NUISANCE? MANAGING AFRICAN ELEPHANTS AS A MULTI-USE SPECIES
Increasing human interference with natural systems causes us to re-think our perception of wildlife species and the economic choices society makes with regards to their management. Accordingly, we generalize existing 'bioeconomic' models by proposing an economically-based classification of species. The theoretical model is applied to the case of African elephant management. We demonstrate that the classification of the steady state population of a species depends on both species' density and economic factors. Our main results are threefold. First, we demonstrate the classification-dependent possibility of multiple equilibria and perverse comparative statics for multi-use species. Second, upon comparing the optimal stock of a multi-use species to the stock under an open access regime, we find that the ranking in terms of abundance is ambiguous. Finally, and consistent with existing literature on resource management in a second-best world, our case study supports the idea that trade measures have ambiguous effects on wildlife abundance under open access.Resource /Energy Economics and Policy,
Lyapunov Exponents of Two Stochastic Lorenz 63 Systems
Two different types of perturbations of the Lorenz 63 dynamical system for
Rayleigh-Benard convection by multiplicative noise -- called stochastic
advection by Lie transport (SALT) noise and fluctuation-dissipation (FD) noise
-- are found to produce qualitatively different effects, possibly because the
total phase-space volume contraction rates are different. In the process of
making this comparison between effects of SALT and FD noise on the Lorenz 63
system, a stochastic version of a robust deterministic numerical algorithm for
obtaining the individual numerical Lyapunov exponents was developed. With this
stochastic version of the algorithm, the value of the sum of the Lyapunov
exponents for the FD noise was found to differ significantly from the value of
the deterministic Lorenz 63 system, whereas the SALT noise preserves the Lorenz
63 value with high accuracy. The Lagrangian averaged version of the SALT
equations (LA SALT) is found to yield a closed deterministic subsystem for the
expected solutions which is found to be isomorphic to the original Lorenz 63
dynamical system. The solutions of the closed chaotic subsystem, in turn, drive
a linear stochastic system for the fluctuations of the LA SALT solutions around
their expected values.Comment: 19 pages, 4 figures, comments always welcome
Renormalization automated by Hopf algebra
It was recently shown that the renormalization of quantum field theory is
organized by the Hopf algebra of decorated rooted trees, whose coproduct
identifies the divergences requiring subtraction and whose antipode achieves
this. We automate this process in a few lines of recursive symbolic code, which
deliver a finite renormalized expression for any Feynman diagram. We thus
verify a representation of the operator product expansion, which generalizes
Chen's lemma for iterated integrals. The subset of diagrams whose forest
structure entails a unique primitive subdivergence provides a representation of
the Hopf algebra of undecorated rooted trees. Our undecorated Hopf
algebra program is designed to process the 24,213,878 BPHZ contributions to the
renormalization of 7,813 diagrams, with up to 12 loops. We consider 10 models,
each in 9 renormalization schemes. The two simplest models reveal a notable
feature of the subalgebra of Connes and Moscovici, corresponding to the
commutative part of the Hopf algebra of the diffeomorphism group:
it assigns to Feynman diagrams those weights which remove zeta values from the
counterterms of the minimal subtraction scheme. We devise a fast algorithm for
these weights, whose squares are summed with a permutation factor, to give
rational counterterms.Comment: 22 pages, latex, epsf for figure
Dynamics of clade diversification on the morphological hypercube
Understanding the relationship between taxonomic and morphological changes is
important in identifying the reasons for accelerated morphological
diversification early in the history of animal phyla. Here, a simple general
model describing the joint dynamics of taxonomic diversity and morphological
disparity is presented and applied to the data on the diversification of
blastozoans. I show that the observed patterns of deceleration in clade
diversification can be explicable in terms of the geometric structure of the
morphospace and the effects of extinction and speciation on morphological
disparity without invoking major declines in the size of morphological
transitions or taxonomic turnover rates. The model allows testing of hypotheses
about patterns of diversification and estimation of rates of morphological
evolution. In the case of blastozoans, I find no evidence that major changes in
evolutionary rates and mechanisms are responsible for the deceleration of
morphological diversification seen during the period of this clade's expansion.
At the same time, there is evidence for a moderate decline in overall rates of
morphological diversification concordant with a major change (from positive to
negative values) in the clade's growth rate.Comment: 8 pages, Latex, 2 postscript figures, submitted to Proc.R.Soc.Lond.
Mobility, fitness collection, and the breakdown of cooperation
The spatial arrangement of individuals is thought to overcome the dilemma of cooperation: When cooperators engage in clusters, they might share the benefit of cooperation while being more protected against noncooperating individuals, who benefit from cooperation but save the cost of cooperation. This is paradigmatically shown by the spatial prisoner's dilemma model. Here, we study this model in one and two spatial dimensions, but explicitly take into account that in biological setups, fitness collection and selection are separated processes occurring mostly on vastly different time scales. This separation is particularly important to understand the impact of mobility on the evolution of cooperation. We find that even small diffusive mobility strongly restricts cooperation since it enables noncooperative individuals to invade cooperative clusters. Thus, in most biological scenarios, where the mobility of competing individuals is an irrefutable fact, the spatial prisoner's dilemma alone cannot explain stable cooperation, but additional mechanisms are necessary for spatial structure to promote the evolution of cooperation. The breakdown of cooperation is analyzed in detail. We confirm the existence of a phase transition, here controlled by mobility and costs, which distinguishes between purely cooperative and noncooperative absorbing states. While in one dimension the model is in the class of the voter model, it belongs to the directed percolation universality class in two dimensions. DOI: 10.1103/PhysRevE.87.04271
Coevolutionary Investments in Human Speech and Trade
We propose a novel explanation for the emergence of language in modern humans, and the lack thereof in other hominids. A coevolutionary process, where trade facilitates speech and speech facilitates trade, driven by expectations and potentially influenced by geography, gives rise to multiple stable development trajectories. While the trade-speech equilibrium is not an inevitable outcome for modern humans, we do find that it is a relatively likely result given that our species evolved in Africa under climatic conditions supporting relatively high population densities.Institutional and Behavioral Economics,
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