7,229 research outputs found
Asymptotic direction of random walks in Dirichlet environment
In this paper we generalize the result of directional transience from
[SabotTournier10]. This enables us, by means of [Simenhaus07], [ZernerMerkl01]
and [Bouchet12] to conclude that, on Z^d (for any dimension d), random walks in
i.i.d. Dirichlet environment, or equivalently oriented-edge reinforced random
walks, have almost-surely an asymptotic direction equal to the direction of the
initial drift, unless this drift is zero. In addition, we identify the exact
value or distribution of certain probabilities, answering and generalizing a
conjecture of [SaTo10].Comment: This version includes a second part, proving and generalizing
identities conjectured in a previous paper by C.Sabot and the autho
Approximation of dynamical systems using S-systems theory : application to biological systems
In this paper we propose a new symbolic-numeric algorithm to find positive
equilibria of a n-dimensional dynamical system. This algorithm implies a
symbolic manipulation of ODE in order to give a local approximation of
differential equations with power-law dynamics (S-systems). A numerical
calculus is then needed to converge towards an equilibrium, giving at the same
time a S-system approximating the initial system around this equilibrium. This
algorithm is applied to a real biological example in 14 dimensions which is a
subsystem of a metabolic pathway in Arabidopsis Thaliana
The Mahāvastu and the Vinayapiṭaka of the Mahāsāṃghika-Lokottaravādins
International audienc
First-order transitions in glasses and melts induced by solid superclusters nucleated and melted by homogeneous nucleation instead of surface melting
Supercooled liquids give rise, by homogeneous nucleation, to solid
superclusters acting as building blocks of glass, ultrastable glass, and
glacial glass phases before being crystallized. Liquid-to-liquid phase
transitions begin to be observed above the melting temperature Tm as well as
critical undercooling depending on critical overheating (Tm-T)/Tm. Solid nuclei
exist above Tm and melt by homogeneous nucleation of liquid instead of surface
melting. The Gibbs free energy change predicted by the classical nucleation
equation is completed by an additional enthalpy which stabilize these solid
entities during undercooling. A two-liquid model, using this renewed equation,
predicts the new homogeneous nucleation temperatures inducing first-order
transitions, and the enthalpy and entropy of new liquid and glass phases. These
calculations are successfully applied to ethylbenzene, triphenyl phosphite,
d-mannitol, n-butanol, Zr41.2Ti13.8Cu12.5Ni10Be22.5, Ti34Zr11Cu47Ni8, and
Co81.5B18.5. A critical supercooling and overheating rate (Tm-T)/Tm = 0.198 of
liquid elements is predicted in agreement with experiments on Sn droplets.Comment: 41 pages, 21 figures, submitted to "chemical physics
Automatic polishing process of plastic injection molds on a 5-axis milling center
The plastic injection mold manufacturing process includes polishing
operations when surface roughness is critical or mirror effect is required to
produce transparent parts. This polishing operation is mainly carried out
manually by skilled workers of subcontractor companies. In this paper, we
propose an automatic polishing technique on a 5-axis milling center in order to
use the same means of production from machining to polishing and reduce the
costs. We develop special algorithms to compute 5-axis cutter locations on
free-form cavities in order to imitate the skills of the workers. These are
based on both filling curves and trochoidal curves. The polishing force is
ensured by the compliance of the passive tool itself and set-up by calibration
between displacement and force based on a force sensor. The compliance of the
tool helps to avoid kinematical error effects on the part during 5-axis tool
movements. The effectiveness of the method in terms of the surface roughness
quality and the simplicity of implementation is shown through experiments on a
5-axis machining center with a rotary and tilt table
Random walks in Dirichlet environment: an overview
Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in
Random Environment (RWRE) on where the transition probabilities are
i.i.d. at each site with a Dirichlet distribution. Hence, the model is
parametrized by a family of positive weights ,
one for each direction of . In this case, the annealed law is that
of a reinforced random walk, with linear reinforcement on directed edges. RWDE
have a remarkable property of statistical invariance by time reversal from
which can be inferred several properties that are still inaccessible for
general environments, such as the equivalence of static and dynamic points of
view and a description of the directionally transient and ballistic regimes. In
this paper we give a state of the art on this model and several sketches of
proofs presenting the core of the arguments. We also present new computation of
the large deviation rate function for one dimensional RWDE.Comment: 35 page
Non-fixation for Biased Activated Random Walks
We prove that the model of Activated Random Walks on Z^d with biased jump
distribution does not fixate for any positive density, if the sleep rate is
small enough, as well as for any finite sleep rate, if the density is close
enough to 1. The proof uses a new criterion for non-fixation. We provide a
pathwise construction of the process, of independent interest, used in the
proof of this non-fixation criterion
Regularity for the near field parallel refractor and reflector problems
We prove local estimates of solutions for the parallel
refractor and reflector problems under local assumptions on the target set
, and no assumptions are made on the smoothness of the densities.Comment: 32 pages, three figure
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