1,032 research outputs found
The Role Of Forestry In Food Security
A GEM article on the role of forestry in food security.Land use practices that lead to environmental degradation are widely recognized as a principal cause of the food emergencies that occur with such tragic frequency in developing countries. It is also well known that they have put the long-term future of food supplies in jeopardy. Nevertheless, they have so far received little attention in international discussions of world food security.FA
Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases
Both the right and left eigenfunctions and eigenvalues of the linearized
homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to
the hydrodynamic modes are calculated. Also, some non-hydrodynamic modes are
identified. It is shown that below a critical value of the parameter
characterizing the inelasticity, one of the kinetic modes decays slower than
one of the hydrodynamic ones. As a consequence, a closed hydrodynamic
description does not exist in that regime. Some implications of this behavior
on the formally computed Navier-Stokes transport coefficients are discussed.Comment: Submitted to PRL (13/04/10
Shear Viscosities from the Chapman-Enskog and the Relaxation Time Approaches
The interpretation of the measured elliptic and higher order collective flows
in heavy-ion collisions in terms of viscous hydrodynamics depends sensitively
on the ratio of shear viscosity to entropy density. Here we perform a
quantitative comparison between the results of shear viscosities from the
Chapman-Enskog and relaxation time methods for selected test cases with
specified elastic differential cross sections: (i) The non-relativistic,
relativistic and ultra-relativistic hard sphere gas with angle and energy
independent differential cross section (ii) The Maxwell gas, (iii) chiral pions
and (iv) massive pions for which the differential elastic cross section is
taken from experiments. Our quantitative results reveal that (i) the extent of
agreement (or disagreement) depends sensitively on the energy dependence of the
differential cross sections employed, and (ii) stress the need to perform
quantum molecular dynamical (URQMD) simulations that employ Green-Kubo
techniques with similar cross sections to validate the codes employed and to
test the accuracy of other methods.Comment: To be submitted to PR
Settling Some Open Problems on 2-Player Symmetric Nash Equilibria
Over the years, researchers have studied the complexity of several decision
versions of Nash equilibrium in (symmetric) two-player games (bimatrix games).
To the best of our knowledge, the last remaining open problem of this sort is
the following; it was stated by Papadimitriou in 2007: find a non-symmetric
Nash equilibrium (NE) in a symmetric game. We show that this problem is
NP-complete and the problem of counting the number of non-symmetric NE in a
symmetric game is #P-complete.
In 2005, Kannan and Theobald defined the "rank of a bimatrix game"
represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be
computed in rank 1 games in polynomial time. Observe that the rank 0 case is
precisely the zero sum case, for which a polynomial time algorithm follows from
von Neumann's reduction of such games to linear programming. In 2011, Adsul et.
al. obtained an algorithm for rank 1 games; however, it does not solve the case
of symmetric rank 1 games. We resolve this problem
Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
The revised Enskog approximation for a fluid of hard spheres which lose
energy upon collision is discussed for the case that the energy is lost from
the normal component of the velocity at collision but is otherwise arbitrary.
Granular fluids with a velocity-dependent coefficient of restitution are an
important special case covered by this model. A normal solution to the Enskog
equation is developed using the Chapman-Enskog expansion. The lowest order
solution describes the general homogeneous cooling state and a generating
function formalism is introduced for the determination of the distribution
function. The first order solution, evaluated in the lowest Sonine
approximation, provides estimates for the transport coefficients for the
Navier-Stokes hydrodynamic description. All calculations are performed in an
arbitrary number of dimensions.Comment: 27 pages + 1 figur
Leading Pollicott-Ruelle Resonances and Transport in Area-Preserving Maps
The leading Pollicott-Ruelle resonance is calculated analytically for a
general class of two-dimensional area-preserving maps. Its wave number
dependence determines the normal transport coefficients. In particular, a
general exact formula for the diffusion coefficient D is derived without any
high stochasticity approximation and a new effect emerges: The angular
evolution can induce fast or slow modes of diffusion even in the high
stochasticity regime. The behavior of D is examined for three particular cases:
(i) the standard map, (ii) a sawtooth map, and (iii) a Harper map as an example
of a map with nonlinear rotation number. Numerical simulations support this
formula.Comment: 5 pages, 1 figur
Entropy flow in near-critical quantum circuits
Near-critical quantum circuits are ideal physical systems for asymptotically
large-scale quantum computers, because their low energy collective excitations
evolve reversibly, effectively isolated from the environment. The design of
reversible computers is constrained by the laws governing entropy flow within
the computer. In near-critical quantum circuits, entropy flows as a locally
conserved quantum current, obeying circuit laws analogous to the electric
circuit laws. The quantum entropy current is just the energy current divided by
the temperature. A quantum circuit made from a near-critical system (of
conventional type) is described by a relativistic 1+1 dimensional relativistic
quantum field theory on the circuit. The universal properties of the
energy-momentum tensor constrain the entropy flow characteristics of the
circuit components: the entropic conductivity of the quantum wires and the
entropic admittance of the quantum circuit junctions. For example,
near-critical quantum wires are always resistanceless inductors for entropy. A
universal formula is derived for the entropic conductivity:
\sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the
temperature, S the equilibrium entropy density and v the velocity of `light'.
The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega).
The thermal Drude weight is, universally, v^{2}S. This gives a way to measure
the entropy density directly.Comment: 2005 paper published 2017 in Kadanoff memorial issue of J Stat Phys
with revisions for clarity following referee's suggestions, arguments and
results unchanged, cross-posting now to quant-ph, 27 page
Conformal compactification and cycle-preserving symmetries of spacetimes
The cycle-preserving symmetries for the nine two-dimensional real spaces of
constant curvature are collectively obtained within a Cayley-Klein framework.
This approach affords a unified and global study of the conformal structure of
the three classical Riemannian spaces as well as of the six relativistic and
non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, both
Newton-Hooke and Galilean), and gives rise to general expressions holding
simultaneously for all of them. Their metric structure and cycles (lines with
constant geodesic curvature that include geodesics and circles) are explicitly
characterized. The corresponding cyclic (Mobius-like) Lie groups together with
the differential realizations of their algebras are then deduced; this
derivation is new and much simpler than the usual ones and applies to any
homogeneous space in the Cayley-Klein family, whether flat or curved and with
any signature. Laplace and wave-type differential equations with conformal
algebra symmetry are constructed. Furthermore, the conformal groups are
realized as matrix groups acting as globally defined linear transformations in
a four-dimensional "conformal ambient space", which in turn leads to an
explicit description of the "conformal completion" or compactification of the
nine spaces.Comment: 43 pages, LaTe
Mesoscopic constitutive relations for dilute polymer solutions
A novel approach to the dynamics of dilute solutions of polymer molecules
under flow conditions is proposed by applying the rules of mesoscopic
nonequilibrium thermodynamics (MNET). The probability density describing the
state of the system is taken to be a function of the position and velocity of
the molecules, and on a local vector parameter accounting for its deformation.
This function obeys a generalized Fokker-Planck equation, obtained by
calculating the entropy production of the system, and identifying the
corresponding probability currents in terms of generalized forces. In simple
form, this coarse-grained description allows one to derive hydrodynamic
equations where molecular deformation and diffusion effects are coupled. A
class of non-linear constitutive relations for the pressure tensor are
obtained. Particular models are considered and compared with experiments.Comment: To be published in Physica A (16 pages, 2 figures
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