Origin of the roughness exponent in elastic strings at the depinning threshold

Within a recently developed framework of dynamical Monte Carlo algorithms, we compute the roughness exponent $\zeta$ of driven elastic strings at the depinning threshold in 1+1 dimensions for different functional forms of the (short-range) elastic energy. A purely harmonic elastic energy leads to an unphysical value for $\zeta$. We include supplementary terms in the elastic energy of at least quartic order in the local extension. We then find a roughness exponent of $\zeta \simeq 0.63$, which coincides with the one obtained for different cellular automaton models of directed percolation depinning. The quartic term translates into a nonlinear piece which changes the roughness exponent in the corresponding continuum equation of motion. We discuss the implications of our analysis for higher-dimensional elastic manifolds in disordered media.Comment: 4 pages, 2 figure

Elastic String in a Random Medium

We consider a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We present evidence that the consideration of longitudinal fluctuations leads to nonlinear behavior in the equation of motion which is {\it kinematically} generated by the motion of the string. The strength of the nonlinear effects depends on the anisotropy of the medium and the distance from the depinning transition. On the other hand the consideration of restricted solid on solid conditions imposed to the growth of the string leads to a nonlinear term in the equation of motion with a {\it diverging} coefficient at the depinning transition.Comment: 9 pages, REVTEX, figures available upon request from [email protected]

Local in time master equations with memory effects: Applicability and interpretation

Non-Markovian local in time master equations give a relatively simple way to describe the dynamics of open quantum systems with memory effects. Despite their simple form, there are still many misunderstandings related to the physical applicability and interpretation of these equations. Here we clarify these issues both in the case of quantum and classical master equations. We further introduce the concept of a classical non-Markov chain signified through negative jump rates in the chain configuration.Comment: Special issue on loss of coherence and memory effects in quantum dynamics, J. Phys. B., to appea

Avalanches and Correlations in Driven Interface Depinning

We study the critical behavior of a driven interface in a medium with random pinning forces by analyzing spatial and temporal correlations in a lattice model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)]. The static and dynamic behavior of the model is related to the properties of directed percolation. We show that, due to the interplay of local and global growth rules, the usual method of dynamical scaling has to be modified. We separate the local from the global part of the dynamics by defining a train of causal growth events, or "avalanche", which can be ascribed a well-defined dynamical exponent $z_{loc} = 1 + \zeta_c \simeq 1.63$ where $\zeta_c$ is the roughness exponent of the interface. We observe that the avalanche size distribution obeys a power-law decay with an exponent $\kappa \simeq 1.25$.Comment: 7 pages, (5 figures available upon request), REVTeX, RUB-TP3-93-0

Effect of borehole stress concentration on compressional wave velocity measurements

Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could lead to a biased estimation of formation elastic properties measured from sonic logging data. To study the effect of stress concentration around a borehole on sonic logging, we first use an iterative approach, which combines a rock physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole when it is subjected to an anisotropic stress loading. Then we use the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response in a borehole. Our numerical results are consistent with published laboratory measurements of the azimuthal velocity variations caused by borehole stress concentration. Both numerical and experimental results show that the variation of P-wave velocity versus azimuth has broad maxima and cusped minima, which is different from the presumed cosine behavior. This is caused by the preference of the wavefield to propagate through a higher velocity region

Multi-Modes Phonon Softening in Two-Dimensional Electron-Lattice System

Phonon dispersion in a two-dimensional electron-lattice system described by a two-dimensional square-lattice version of Su-Schrieffer-Heeger's model and having the half-filled electronic band is studied theoretically at temperatures higher than the mean field critical temperature of the Peierls transition. When the temperature is lowered from the higher region down to the critical one, softening of multi phonon modes which have wave vectors equal to the nesting vector \vv{Q}=(\pi/a,\pi/a) with $a$ the lattice constant or parallel to \vv{Q} is observed. Although both of the transverse and longitudinal modes are softened at the critical temperature in the case of the wave vector equal to \vv{Q}, only the transverse modes are softened for other wave vectors parallel to \vv{Q}. This behavior is consistent with the Peierls distortions at lower temperatures.Comment: 10 pages, 5 Figure

Oxygen isotopes and high ^(26)Mg excesses in a U-depleted fine-grained Allende CAI

CAIs are thought to be among the first solids formed in the early Solar System (ESS). As such, they are prime samples to study when (1) investigating ESS high-temperature processes, and (2) searching for evidence of short-lived radionu-clides at the time of formation of the SS. A recent systematic study of fine-grained CAIs characterized by a Group II REE pat-tern from Allende [1], found an extremely large ^(235)U excess (δ^(235)U >50 ‰ rel. to CRM-112a) in one sample: ME-3364 3.2. The discovery of this large ^(235)U excess provides definite evidence of the existence of live ^(247)Cm in the ESS, as previously suggested by [2]. In this study, we analyzed the oxygen isotope composi-tions and Al-Mg systematics of CAI ME-3364 3.2 to constrain the conditions of its formation

^(36)Cl-^(36)S in Allende CAIs: Implication for the origins of ^(36)Cl in the early solar system

Chlorine-36 (t_(1/2)=0.3 Myr) decays to either ^(36)Ar (98%, β-) or ^(36)S (1.9%, ε and β+). This radionuclide can be produced by either charged particle irradiation [1,2] or stellar nucleosynthesis [3]. Evidence for the prior existence of ^(36)Cl in the Early Solar System (ESS) comes from radiogenic excesses of ^(36)Ar [4,5] and/or ^(36)S [6-9] in secondary phases (e.g., sodalite and wadalite) of ESS materials such as Ca, Al-rich inclusions (CAIs) and chondrules. However, the inferred initial ^(36)Cl/^(35)Cl ratios vary over three orders of magnitude among different chondrite constituents (5×10^(-6)-9×10^(-3)) [6-9]. Interestingly, although the initial ^(36)Cl/^(35)Cl ratios inferred in previous studies vary widely, all secondary phases bearing evidence for live ^(36)Cl in the ESS measured so far lack resolvable ^(26)Mg excesses due to the decay of ^(26)Al (t_(1/2) = 0.7 Myr), implying that ^(36)Cl and ^(26)Al may have been produced by different processes and/or incorporated into ESS solids at different times. Given that secondary phases may have formed late, the ^(36)S anomalies in secondary phases point to either a very high ^(36)Cl/^(35)Cl initial ratio (~10^(-2)) in the ESS, or a late irradiation scenario for the local production of ^(36)Cl (> 3 Myr after CAI formation) [9]. The elevated ESS ratio of ^(36)Cl/^(35)Cl ~10^(-2) inferred from [9] far exceeds the predictions from any model of stellar nucleosynthesis; therefore, a late irradiation scenario producing ^(36)Cl is currently the favored idea. In this framework, ^(36)Cl would be be produced in the nebular gas and then incorporated into the CAIs via aqueous alteration, which formed secondary phases

Pipe network model for scaling of dynamic interfaces in porous media

We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E {\bf 52}, 5166 (1995)]. Using simple scaling arguments, we derive a new identity among the scaling exponents in agreement with the experimental results.Comment: 13 pages, 3 figures, REVTeX, to appear in Phys. Rev. Let