315 research outputs found
Parallel Algorithm and Dynamic Exponent for Diffusion-limited Aggregation
A parallel algorithm for ``diffusion-limited aggregation'' (DLA) is described
and analyzed from the perspective of computational complexity. The dynamic
exponent z of the algorithm is defined with respect to the probabilistic
parallel random-access machine (PRAM) model of parallel computation according
to , where L is the cluster size, T is the running time, and the
algorithm uses a number of processors polynomial in L\@. It is argued that
z=D-D_2/2, where D is the fractal dimension and D_2 is the second generalized
dimension. Simulations of DLA are carried out to measure D_2 and to test
scaling assumptions employed in the complexity analysis of the parallel
algorithm. It is plausible that the parallel algorithm attains the minimum
possible value of the dynamic exponent in which case z characterizes the
intrinsic history dependence of DLA.Comment: 24 pages Revtex and 2 figures. A major improvement to the algorithm
and smaller dynamic exponent in this versio
Landscape statistics of the p-spin Ising model
The statistical properties of the local optima (metastable states) of the
infinite range Ising spin glass with p-spin interactions in the presence of an
external magnetic field h are investigated analytically. The average number of
optima as well as the typical overlap between pairs of identical optima are
calculated for general p. Similarly to the thermodynamic order parameter, for
p>2 and small h the typical overlap q_t is a discontinuous function of the
energy. The size of the jump in q_t increases with p and decreases with h,
vanishing at finite values of the magnetic field.Comment: 12 pages,te
Facing metal stress by multiple strategies: morphophysiological responses of cardoon (Cynara cardunculus L.) grown in hydroponics
The contamination of environments by heavy metals has become an urgent issue causing undesirable accumulations and severe damages to agricultural crops, especially cadmium and lead which are among the most widespread and dangerous metal pollutants worldwide. The selection of proper species is a crucial step in many plant-based restoration approaches; therefore, the aim of the present work was to check for early morphophysiological responsive traits in three cultivars of Cynara cardunculus (Sardo, Siciliano, and Spagnolo), helping to select the best performing cultivar for phytoremediation. For all three tested cultivars, our results indicate that cardoon displays some morphophysiological traits to face Cd and Pb pollution, particularly at the root morphology level, element uptake ability, and photosynthetic pigment content. Other traits show instead a cultivar-specific behavior; in fact, stomata plasticity, photosynthetic pattern, and antioxidant power provide different responses, but only Spagnolo cv. achieves a successful strategy attaining a real resilience to metal stress. The capacity of Spagnolo plants to modify leaf structural and physiological traits under heavy metal contamination to maintain high photosynthetic efficiency should be considered an elective trait for its use in contaminated environments
Fractal geometry of spin-glass models
Stability and diversity are two key properties that living entities share
with spin glasses, where they are manifested through the breaking of the phase
space into many valleys or local minima connected by saddle points. The
topology of the phase space can be conveniently condensed into a tree
structure, akin to the biological phylogenetic trees, whose tips are the local
minima and internal nodes are the lowest-energy saddles connecting those
minima. For the infinite-range Ising spin glass with p-spin interactions, we
show that the average size-frequency distribution of saddles obeys a power law
, where w=w(s) is the number of minima that can be
connected through saddle s, and D is the fractal dimension of the phase space
Characteristic distributions of finite-time Lyapunov exponents
We study the probability densities of finite-time or \local Lyapunov
exponents (LLEs) in low-dimensional chaotic systems. While the multifractal
formalism describes how these densities behave in the asymptotic or long-time
limit, there are significant finite-size corrections which are coordinate
dependent. Depending on the nature of the dynamical state, the distribution of
local Lyapunov exponents has a characteristic shape. For intermittent dynamics,
and at crises, dynamical correlations lead to distributions with stretched
exponential tails, while for fully-developed chaos the probability density has
a cusp. Exact results are presented for the logistic map, . At
intermittency the density is markedly asymmetric, while for `typical' chaos, it
is known that the central limit theorem obtains and a Gaussian density results.
Local analysis provides information on the variation of predictability on
dynamical attractors. These densities, which are used to characterize the {\sl
nonuniform} spatial organization on chaotic attractors are robust to noise and
can therefore be measured from experimental data.Comment: To be appear in Phys. Rev
Curvature fluctuations and Lyapunov exponent at Melting
We calculate the maximal Lyapunov exponent in constant-energy molecular
dynamics simulations at the melting transition for finite clusters of 6 to 13
particles (model rare-gas and metallic systems) as well as for bulk rare-gas
solid. For clusters, the Lyapunov exponent generally varies linearly with the
total energy, but the slope changes sharply at the melting transition. In the
bulk system, melting corresponds to a jump in the Lyapunov exponent, and this
corresponds to a singularity in the variance of the curvature of the potential
energy surface. In these systems there are two mechanisms of chaos -- local
instability and parametric instability. We calculate the contribution of the
parametric instability towards the chaoticity of these systems using a recently
proposed formalism. The contribution of parametric instability is a continuous
function of energy in small clusters but not in the bulk where the melting
corresponds to a decrease in this quantity. This implies that the melting in
small clusters does not lead to enhanced local instability.Comment: Revtex with 7 PS figures. To appear in Phys Rev
Rupture by damage accumulation in rocks
The deformation of rocks is associated with microcracks nucleation and
propagation, i.e. damage. The accumulation of damage and its spatial
localization lead to the creation of a macroscale discontinuity, so-called
"fault" in geological terms, and to the failure of the material, i.e. a
dramatic decrease of the mechanical properties as strength and modulus. The
damage process can be studied both statically by direct observation of thin
sections and dynamically by recording acoustic waves emitted by crack
propagation (acoustic emission). Here we first review such observations
concerning geological objects over scales ranging from the laboratory sample
scale (dm) to seismically active faults (km), including cliffs and rock masses
(Dm, hm). These observations reveal complex patterns in both space (fractal
properties of damage structures as roughness and gouge), time (clustering,
particular trends when the failure approaches) and energy domains (power-law
distributions of energy release bursts). We use a numerical model based on
progressive damage within an elastic interaction framework which allows us to
simulate these observations. This study shows that the failure in rocks can be
the result of damage accumulation
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