Roundoff-induced attractors and reversibility in conservative two-dimensional maps

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.     

Locally solvable vector fields and Hardy spaces

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.     

Level algebras with bad properties

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.

     

Angular broadening in core‐electron spectroscopy

The role of angular broadening in quantitative core‐electron spectroscopy is investigated using an analytic approach. It is shown why, practically, this effect remains relatively small for a broad range of parameters. A correction factor is derived, suggesting that the replacement of inelastic mean free path by an effective attenuation‐length parameter is not necessarily an optimal choice. The derived expression further proposes useful insight on the contribution of leading experimental parameters and, in particular, on the sharp increase of elastic‐scattering corrections above a (depth dependent) critical angle. Copyright © 2015 John Wiley & Sons, Ltd.     

Introduction of periodic boundary conditions into UNRES force field

In this article, implementation of periodic boundary conditions (PBC) into physics‐based coarse‐grained UNited RESidue (UNRES) force field is presented, which replaces droplet‐like restraints previously used. Droplet‐like restraints are necessary to keep multichain systems together and prevent them from dissolving to infinitely low concentration. As an alternative for droplet‐like restrains cuboid PBCs with imaging of the molecules were introduced. Owing to this modification, artificial forces which arose from restraints keeping a droplet together were eliminated what leads to more realistic trajectories. Due to computational reasons cutoff and smoothing functions were introduced on the long range interactions. The UNRES force field with PBC was tested by performing microcanonical simulations. Moreover, to asses the behavior of the thermostat in PBCs Langevin and Berendsen thermostats were studied. The influence of PBCs on association pattern was compared with droplet‐like restraints on the ββα hetero tetramer 1 protein system. © 2015 Wiley Periodicals, Inc.     

浅析升钟水库右总干渠石爬明渠填方段滑坡形成的原因

本文阐述了升钟水库右总干渠石爬明渠填方段滑坡的地质环境、规模及特征，分析了渗漏对填筑土、粉砂质泥岩C、φ值的影响，论述了红层丘陵区填方输水渠道滑坡形成的原因，计算了孔隙水压力、渗透压力对填方渠堤稳定性的影响，介绍了该区的防渗整治措施。     

Stationary solutions of SPDEs and infinite horizon BDSDEs

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.     

Microstructure and mechanical behavior of UFG copper processed by ECAP following different processing regimes

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.     

Comments on “role of impurities on the primary process for f-coloring in alkali halides”

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.