1,859 research outputs found
On the duality relation for correlation functions of the Potts model
We prove a recent conjecture on the duality relation for correlation
functions of the Potts model for boundary spins of a planar lattice.
Specifically, we deduce the explicit expression for the duality of the n-site
correlation functions, and establish sum rule identities in the form of the
M\"obius inversion of a partially ordered set. The strategy of the proof is by
first formulating the problem for the more general chiral Potts model. The
extension of our consideration to the many-component Potts models is also
given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.
Gas-plasma compressional wave coupling by momentum transfer
Pressure disturbances in a gas-plasma mixed fluid will result in a hybrid response, with magnetosonic plasma waves coupled to acoustic waves in the neutral gas. In the analytical and numerical treatment presented here, we demonstrate the evolution of the total fluid medium response under a variety of conditions, with the gas-plasma linkage achieved by additional coupling terms in the momentum equations of each species. The significance of this treatment lies in the consideration of density perturbations in such fluids: there is no 'pure' mode response, only a collective one in which elements of the characteristics of each component are present. For example, an initially isotropic gas sound wave can trigger an anisotropic magnetic response in the plasma, with the character of each being blended in the global evolution. Hence sound waves do not remain wholly isotropic, and magnetic responses are less constrained by pure magnetoplasma dynamics
Weakly nonlinear analysis of a two-species non-local advectionâdiffusion system
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advectionâdiffusion model with nonlocal advection terms describing the species movements generated by inter-species interactions. We use linear analysis to assess the stability of the constant steady state, then weakly nonlinear analysis to recover the shape and stability of non-homogeneous solutions. Since the system arises from a conservation law, the resulting amplitude equations consist of a GinzburgâLandau equation coupled with an equation for the zero mode. In particular, this means that supercritical branches from the GinzburgâLandau equation need not be stable. Indeed, we find that, depending on the parameters, bifurcations can be subcritical (always unstable), stable supercritical, or unstable supercritical. We show numerically that, when small amplitude patterns are unstable, the system exhibits large amplitude patterns and hysteresis, even in supercritical regimes. Finally, we construct bifurcation diagrams by combining our analysis with a previous study of the minimizers of the associated energy functional. Through this approach we reveal parameter regions in which stable small amplitude patterns coexist with strongly modulated solutions
Detecting minimum energy states and multi-stability in nonlocal advectionâdiffusion models for interacting species
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations, these emergent patterns sometimes appear as local minimisers of a corresponding energy functional. Here we give methods for determining the qualitative structure of local minimum energy states of a broad class of multi-species nonlocal advectionâdiffusion models, recently proposed for modelling the spatial structure of ecosystems. We show that when each pair of species respond to one another in a symmetric fashion (i.e. via mutual avoidance or mutual attraction, with equal strength), the system admits an energy functional that decreases in time and is bounded below. This suggests that the system will eventually reach a local minimum energy steady state, rather than fluctuating in perpetuity. We leverage this energy functional to develop tools, including a novel application of computational algebraic geometry, for making conjectures about the number and qualitative structure of local minimum energy solutions. These conjectures give a guide as to where to look for numerical steady state solutions, which we verify through numerical analysis. Our technique shows that even with two species, multi-stability with up to four classes of local minimum energy states can emerge. The associated dynamics include spatial sorting via aggregation and repulsion both within and between species. The emerging spatial patterns include a mixture of territory-like segregation as well as narrow spike-type solutions. Overall, our study reveals a general picture of rich multi-stability in systems of moving and interacting species
Monte Carlo study of the antiferromagnetic three-state Potts model with staggered polarization field on the square lattice
Using the Wang-Landau Monte Carlo method, we study the antiferromagnetic (AF)
three-state Potts model with a staggered polarization field on the square
lattice. We obtain two phase transitions; one belongs to the ferromagnetic
three-state Potts universality class, and the other to the Ising universality
class. The phase diagram obtained is quantitatively consistent with the
transfer matrix calculation. The Ising transition in the large nearest-neighbor
interaction limit has been made clear by the detailed analysis of the energy
density of states.Comment: accepted for publication in J. Phys.
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Editorial: summary for policymakers of the thematic assessment on pollinators, pollination and food production
Values of pollinators and pollination
1. Animal pollination plays a vital role as a regulating ecosystem service in nature. Globally, nearly 90 per cent of wild flowering plant species depend, at least in part, on the transfer of pollen by animals. These plants are critical for the continued functioning of ecosystems as they provide food, form habitats, and provide other resources for a wide range of other species.
2. More than three quarters of the leading types of global
food crops rely to some extent on animal pollination for yield and/or quality. Pollinator-dependent crops contribute to 35 per cent of global crop production volume.
3. Given that pollinator-dependent crops rely on animal pollination to varying degrees, it is estimated that 5â8 per cent of current global crop production is directly attributed to animal pollination with an annual market value of 577 billion (in 2015, United States dollars1) worldwide
The assessment report of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services on pollinators, pollination and food production
The thematic assessment of pollinators, pollination and food production carried out under the auspices of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services aims to assess animal pollination as a regulating ecosystem service underpinning food production in the context of its contribution to natureâs gifts to people and supporting a good quality of life. To achieve this, it focuses on the role of native and managed pollinators, the status and trends of pollinators and pollinator-plant networks
and pollination, drivers of change, impacts on human well-being, food production in response to pollination declines and deficits and the effectiveness of responses
Stability of trions in strongly spin-polarized two-dimensional electron gases
Low-temperature magneto-photoluminescence studies of negatively charged
excitons (X- trions) are reported for n-type modulation-doped ZnSe/Zn(Cd,Mn)Se
quantum wells over a wide range of Fermi energy and spin-splitting. The
magnetic composition is chosen such that these magnetic two-dimensional
electron gases (2DEGs) are highly spin-polarized even at low magnetic fields,
throughout the entire range of electron densities studied (5e10 to 6.5e11
cm^-2). This spin polarization has a pronounced effect on the formation and
energy of X-, with the striking result that the trion ionization energy (the
energy separating X- from the neutral exciton) follows the temperature- and
magnetic field-tunable Fermi energy. The large Zeeman energy destabilizes X- at
the nu=1 quantum limit, beyond which a new PL peak appears and persists to 60
Tesla, suggesting the formation of spin-triplet charged excitons.Comment: 5 pages (RevTex), 4 embedded EPS figs. Submitted to PRB-R
Spanning Trees on Graphs and Lattices in d Dimensions
The problem of enumerating spanning trees on graphs and lattices is
considered. We obtain bounds on the number of spanning trees and
establish inequalities relating the numbers of spanning trees of different
graphs or lattices. A general formulation is presented for the enumeration of
spanning trees on lattices in dimensions, and is applied to the
hypercubic, body-centered cubic, face-centered cubic, and specific planar
lattices including the kagom\'e, diced, 4-8-8 (bathroom-tile), Union Jack, and
3-12-12 lattices. This leads to closed-form expressions for for these
lattices of finite sizes. We prove a theorem concerning the classes of graphs
and lattices with the property that
as the number of vertices , where is a finite
nonzero constant. This includes the bulk limit of lattices in any spatial
dimension, and also sections of lattices whose lengths in some dimensions go to
infinity while others are finite. We evaluate exactly for the
lattices we considered, and discuss the dependence of on d and the
lattice coordination number. We also establish a relation connecting to the free energy of the critical Ising model for planar lattices .Comment: 28 pages, latex, 1 postscript figure, J. Phys. A, in pres
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