We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of maps introduced by C. Moore [Phys. Rev. Lett. 64 (1990) 2354] in the context of undecidability. We calculate the time evolution of the entropy (). We exhibit the dramatic effect introduced by numerical precision. Indeed, in spite of being area-preserving maps, they present, well after the initially concentrated ensemble has spread virtually all over the phase space, unexpected pseudo-attractors (fixed-point like for the baker map, and more complex structures for the Moore map). These pseudo-attractors, and the apparent time (partial) reversibility they provoke, gradually disappear for increasingly large precision. In the case of the Moore map, they are related to zero Lebesgue-measure effects associated with the frontiers existing in the definition of the map. In addition to the above, and consistent with the results by V. Latora and M. Baranger [Phys. Rev. Lett. 82 (1999) 520], we find that the rate of the far-from-equilibrium entropy production of baker map numerically coincides with the standard Kolmogorov-Sinai entropy of this strongly chaotic system. 相似文献
We characterize the boundary value of homegeneous solutions of planar one-sided locally solvable vector fields with analytic coefficients with the property that the Lp norm of their traces is locally uniformly bounded, 0<p?1. For p≠1/n, , the boundary value must locally belong to the local Hardy space hp(R) of Goldberg while for p=1/n, , the answer calls for a new class of atomic Hardy spaces if the vector field is of infinite type at some boundary point. 相似文献
This paper can be seen as a continuation of the works contained in the recent article (J. Alg., 305 (2006), 949-956) of the second author, and those of Juan Migliore (math. AC/0508067). Our results are:
1). There exist codimension three artinian level algebras of type two which do not enjoy the Weak Lefschetz Property (WLP). In fact, for , we will construct a codimension three, type two -vector of socle degree such that all the level algebras with that -vector do not have the WLP. We will also describe the family of those algebras and compute its dimension, for each .
2). There exist reduced level sets of points in of type two whose artinian reductions all fail to have the WLP. Indeed, the examples constructed here have the same -vectors we mentioned in 1).
3). For any integer , there exist non-unimodal monomial artinian level algebras of codimension . As an immediate consequence of this result, we obtain another proof of the fact (first shown by Migliore in the above-mentioned preprint, Theorem 4.3) that, for any , there exist reduced level sets of points in whose artinian reductions are non-unimodal.
In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between valued solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. Moreover, we prove the existence and uniqueness of the solutions of BDSDEs on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary solutions (independent of any initial value) of SPDEs. The connection of the weak solutions of SPDEs and BDSDEs has independent interests in the areas of both SPDEs and BSDEs. 相似文献
Commercially pure (99.9%) copper was severe plastically deformed by equal-channel angular pressing (ECAP) following route-Bc in three different processing regimes in order to obtain ultrafine-grained (UFG) microstructures leading to improved mechanical properties. In regime-1, the billets were processed at room temperature up to eight passes. The billets were processed at 200°C up to eight passes in regime-2. Regime-3 is a hybrid regime by which the billets were deformed at 200°C up to four passes first, and these billets were then processed at room temperature for one, two and four passes. In all regimes, the ECAP processing results in a refinement of the conventionally grained (CG) initial microstructure of copper down to sub-micron level leading to a great improvement in the strength as compared to CG copper. Among the regimes applied, regime-3 was found to be the best regime for improvement in strength along with adequate ductility. The samples showed more than eight times increases in yield strength after processing in regime-3 for 4?+?4 passes, from 47?MPa for CG copper to about 408?MPa for the UFG sample. Such improvement in strength was accompanied by a 16.9% total elongation and 6% uniform elongation. The processing in regime-2 resulted in the best elongation to failure of about 22% after eight passes, but it gave the lowest strength values among others. 相似文献
Growth of the V4 centers during and after pulsed electron irradiation of KBr was measured between 77K and 200K. It is found that the growth during pulsed irradiation is clearly different from that due to the thermal motion of the H centers. Critical discussions on the mechanism of the interstitial interaction in the primary step of the Frenkel-pair creation were made. 相似文献