Random walks in a random environment on a strip: a renormalization group approach

We present a real space renormalization group scheme for the problem of random walks in a random environment on a strip, which includes one-dimensional random walk in random environment with bounded non-nearest-neighbor jumps. We show that the model renormalizes to an effective one-dimensional random walk problem with nearest-neighbor jumps and conclude that Sinai scaling is valid in the recurrent case, while in the sub-linear transient phase, the displacement grows as a power of the time.Comment: 9 page

An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics

The numerical simulation of acoustic waves in complex 3D media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this field has dramatically grown in the last twenty years. However many 3D computations, especially at high frequency and/or long range, are still far beyond current reach and force researchers to resort to approximations, for example by working in 2D (plane strain) or by using a paraxial approximation. This article presents and validates a numerical technique based on an axisymmetric formulation of a spectral finite-element method in the time domain for heterogeneous fluid-solid media. Taking advantage of axisymmetry enables the study of relevant 3D configurations at a very moderate computational cost. The axisymmetric spectral-element formulation is first introduced, and validation tests are then performed. A typical application of interest in ocean acoustics showing upslope propagation above a dipping viscoelastic ocean bottom is then presented. The method correctly models backscattered waves and explains the transmission losses discrepancies pointed out in Jensen et al. (2007). Finally, a realistic application to a double seamount problem is considered.Comment: Added a reference, and fixed a typo (cylindrical versus spherical

Anomalous diffusion in disordered multi-channel systems

We study diffusion of a particle in a system composed of K parallel channels, where the transition rates within the channels are quenched random variables whereas the inter-channel transition rate v is homogeneous. A variant of the strong disorder renormalization group method and Monte Carlo simulations are used. Generally, we observe anomalous diffusion, where the average distance travelled by the particle, []_{av}, has a power-law time-dependence []_{av} ~ t^{\mu_K(v)}, with a diffusion exponent 0 \le \mu_K(v) \le 1. In the presence of left-right symmetry of the distribution of random rates, the recurrent point of the multi-channel system is independent of K, and the diffusion exponent is found to increase with K and decrease with v. In the absence of this symmetry, the recurrent point may be shifted with K and the current can be reversed by varying the lane change rate v.Comment: 16 pages, 7 figure

Bulk and Surface Stabilization Process of Metastable Li-Rich Disordered Rocksalt Oxyfluorides as Efficient Cathode Materials

Manganese based disordered rocksalt systems have attracted attention as Co-free and high capacity cathode materials for Li-ion batteries. However, for a practical application these materials are considered as metastable and exhibit too limited cyclability. In order to improve the structural stability of the disordered rocksalt Li$_{1+x}$Mn$_{2/3}$Ti$_{1/3}$O$_2$F$_x$ (0 ≤ x ≤ 1) system during cycling, we have introduced a mild temperature heat treatment process under reducing atmosphere, which is intended to overcome the structural anomalies formed during the mechanochemical synthesis. The heat-treated samples presented better electrochemical properties, which are ascribed to a structural defect mitigation process both at the surface and in the bulk, resulting in improved crystal structure stability. In addition, the optimized particle size and the smaller BET surface area induced by the recrystallization contributes to the observed enhanced performance. Among the studied compositions, the heat treated Li$_2$Mn$_{2/3}$Ti$_{1/3}$O$_2$F sample displayed better electrochemical performance with a discharge capacity of 165 mAh g$^{−1}$ after 100 cycles at 0.1 C (∼80% of the initial capacity), when combined with further conditioning of the cells. The results point explicitly towards a guided stabilization approach, which could have a beneficial effect regarding the application of DRS oxyfluoride materials for sustainable LIBs

Redetermination of di-μ-hydrido-hexa­hydridotetra­kis(tetra­hydro­furan)dialuminium(III)magnesium(II)

The structure of the title compound, [Mg(AlH4)2(C4H8O)4], has been redetermined at 150 K. The MgII ion is hexa­coordinated to four tetra­hydro­furan (THF) ligands, and two AlH4 − anions through bridging H atoms. The Al—H distances are more precise compared to those previously determined [Nöth et al. (1995 ▶). Chem. Ber. 128, 999–1006; Fichtner & Fuhr (2002 ▶). J. Alloys Compd, 345, 386–396]. The mol­ecule has twofold rotation symmetry

Toward Better Stability and Reversibility of the Mn4+^{4+}/Mn2+^{2+}Double Redox Activity in Disordered Rocksalt Oxyfluoride Cathode Materials

Cation-disordered rocksalt (DRS) materials have shown good initial reversibility and facile Li$^{+}$insertion and extraction in the structure at high rates. However, all of the Li-rich oxyfluorides introduced so far suffer from short cycle lifetimes and severe capacity fading. In the current study, we combine the strategy of using high-valent cations with partial substitution of oxygen anions by fluorine ions to achieve the optimal Mn$^{4+}$/Mn$^{2+}$ double redox reaction in the composition system Li$_{2}$Mn$_{1-x}$Ti$_{x}$O$_{2}$F (0 ≤ x ≤ 2/3). While Ti-rich compositions correlate to an O-oxidation plateau and a partial Mn$^{3+}$–Mn$^{4+}$ redox process at high voltages, owing to the presence of Ti3+ in the structure, a new composition Li$_{2}$Mn$_{2/3}$Ti$_{1/3}$O$_{2}$F with a lower amount of Ti shows better electrochemical performance with an initial high discharge capacity of 227 mAh g$^{-1}$ (1.5–4.3 V window) and a Coulombic efficiency of 82% after 200 cycles with a capacity of 136 mAh g$^{-1}$ (>462 Wh kg$^{-1}$). The structural characteristics, oxidation states, and charge-transfer mechanism have been examined as a function of composition and state of charge. The results indicate a double redox mechanism of Mn$^{4+}$/Mn$^{2+}$ in agreement with Mn–Ti structural charge compensation. The findings point to a way for designing high-capacity DRS materials with multi-electron redox reactions