5,595 research outputs found
Reply to comment on "Towards a quantitative kinetic theory of polar active matter" by Bertin et al
A reply on the comment of Bertin, Chate, Ginelli, Gregoire, Leonard and
Peshkov, arxiv:1404.3950v1, in this special issue
Large density expansion of a hydrodynamic theory for self-propelled particles
Recently, an Enskog-type kinetic theory for Vicsek-type models for
self-propelled particles has been proposed [T. Ihle, Phys. Rev. E 83, 030901
(2011)]. This theory is based on an exact equation for a Markov chain in phase
space and is not limited to small density. Previously, the hydrodynamic
equations were derived from this theory and its transport coefficients were
given in terms of infinite series. Here, I show that the transport coefficients
take a simple form in the large density limit. This allows me to analytically
evaluate the well-known density instability of the polarly ordered phase near
the flocking threshold at moderate and large densities. The growth rate of a
longitudinal perturbation is calculated and several scaling regimes, including
three different power laws, are identified. It is shown that at large
densities, the restabilization of the ordered phase at smaller noise is
analytically accessible within the range of validity of the hydrodynamic
theory. Analytical predictions for the width of the unstable band, the maximum
growth rate and for the wave number below which the instability occurs are
given. In particular, the system size below which spatial perturbations of the
homogeneous ordered state are stable is predicted to scale with
where is the average number of collision partners. The typical time scale
until the instability becomes visible is calculated and is proportional to M
Discussion on Peshkov et al., "Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models"
A discussion on the contribution of Peshkov, Bertin, Ginelli and Chate,
arxiv:1404.3275v1, in this special issue
Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
A ring-kinetic theory for Vicsek-style models of self-propelled agents is
derived from the exact N-particle evolution equation in phase space. The theory
goes beyond mean-field and does not rely on Boltzmann's approximation of
molecular chaos. It can handle pre-collisional correlations and cluster
formation which both seem important to understand the phase transition to
collective motion. We propose a diagrammatic technique to perform a small
density expansion of the collision operator and derive the first two equations
of the BBGKY-hierarchy. An algorithm is presented that numerically solves the
evolution equation for the two-particle correlations on a lattice. Agent-based
simulations are performed and informative quantities such as orientational and
density correlation functions are compared with those obtained by ring-kinetic
theory. Excellent quantitative agreement between simulations and theory is
found at not too small noises and mean free paths. This shows that there is
parameter ranges in Vicsek-like models where the correlated closure of the
BBGKY-hierarchy gives correct and nontrivial results. We calculate the
dependence of the orientational correlations on distance in the disordered
phase and find that it seems to be consistent with a power law with exponent
around -1.8, followed by an exponential decay. General limitations of the
kinetic theory and its numerical solution are discussed
Transport coefficients of multi-particle collision algorithms with velocity-dependent collision rules
Detailed calculations of the transport coefficients of a recently introduced
particle-based model for fluid dynamics with a non-ideal equation of state are
presented. Excluded volume interactions are modeled by means of biased
stochastic multiparticle collisions which depend on the local velocities and
densities. Momentum and energy are exactly conserved locally. A general scheme
to derive transport coefficients for such biased, velocity dependent collision
rules is developed. Analytic expressions for the self-diffusion coefficient and
the shear viscosity are obtained, and very good agreement is found with
numerical results at small and large mean free paths. The viscosity turns out
to be proportional to the square root of temperature, as in a real gas. In
addition, the theoretical framework is applied to a two-component version of
the model, and expressions for the viscosity and the difference in diffusion of
the two species are given.Comment: 31 pages, 8 figures, accepted by J. Phys. Cond. Matte
Spin susceptibility and magnetic short-range order in the Hubbard model
The uniform static spin susceptibility in the paraphase of the one-band
Hubbard model is calculated within a theory of magnetic short--range order
(SRO) which extends the four-field slave-boson functional-integral approach by
the trans- formation to an effective Ising model and the self-consistent
incorporation of SRO at the saddle point. This theory describes a transition
from the paraphase without SRO for hole dopings to a
paraphase with anti- ferromagnetic SRO for . In this region the susceptibility consists of interrelated
`itinerant' and `local' parts and increases upon doping. The zero--temperature
susceptibility exhibits a cusp at and reduces to the usual
slave-boson result for larger dopings. Using the realistic value of the
on--site Coulomb repulsion for LSCO, the peak position () as well as the doping dependence reasonably agree with low--temperature
susceptibility experiments showing a maximum at a hole doping of about 25\%.Comment: 4 pages, 1 Postscript figure, revtex-style, accepted for publishing:
Phys. Rev. B, 54, ... (1996
Seasonal Asymmetric Price Transmission in Ghanaian Tomato Markets: Adapting Johansen’s Estimation Method
We assess market integration and price transmission of perishable agricultural produce in Sub-Saharan Africa by studying Ghanaian tomato markets which are characterized by pronounced seasonality in production and trade flows. We analyse the tomato markets of Ghana by simultaneously regarding its five most important markets, Navrongo, Techiman, Kumasi, Tamale and Accra, in a multivariate asymmetric price transmission framework. The estimation of the model is based on a unique dataset and on a modified version of the Johansen estimation procedure which is suitable for estimating such multivariate models. We estimate the price transmission parameters for four regimes which are a combination of the seasonal patterns in trade flows and asymmetries in the longrun price equilibrium between the most important production region (Techiman) and the most important consumption centre for tomatoes (Accra). We find strong evidence for integration of the five markets. In general, price transmission appears to be fast. Disequilibria mainly trigger price responses in the two production regions of Navrongo and Techiman. The regimes are found to matter for the whole system of tomato markets. Disequilibrium is shown to spillover between the price relationships. Consequently, tomato markets in Ghana appear to be integrated and function very well since price signals are rapidly passed through the country.asymmetric price transmission, cointegration, Ghana, regime-dependent model, seasonality, tomato, vector error-correction model, Crop Production/Industries, Demand and Price Analysis, C32, Q11, Q13, F14, F15,
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