Anion reorientations and cation diffusion in a carbon-substituted sodium nido-borate Na-7,9-C2B9H12: 1H and 23Na NMR studies

Polyhydroborate-based salts of lithium and sodium have attracted much recent interest as promising solid-state electrolytes for energy-related applications. A member of this family, sodium dicarba-nido-undecahydroborate Na-7,9-C2B9H12 exhibits superionic conductivity above its order-disorder phase transition temperature, ∼360 K. To investigate the dynamics of the anions and cations in this compound at the microscopic level, we have measured the 1H and 23Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rates over the temperature range of 148–384 K. It has been found that the transition from the low-T ordered to the high-T disordered phase is accompanied by an abrupt, several-orders-of-magnitude acceleration of both the reorientational jump rate of the complex anions and the diffusive jump rate of Na+ cations. These results support the idea that reorientations of large [C2B9H12]− anions can facilitate cation diffusion and, thus, the ionic conductivity. The apparent activation energies for anion reorientations obtained from the 1H spin-lattice relaxation data are 314 meV for the ordered phase and 272 meV for the disordered phase. The activation energies for Na+ diffusive jumps derived from the 23Na spin-lattice relaxation data are 350 and 268 meV for the ordered and disordered phases, respectively.

Integrability of the Multi-Species TASEP with Species-Dependent Rates

Assume that each species l has its own jump rate bl in the multi-species totally asymmetric simple exclusion process. We show that this model is integrable in the sense that the Bethe ansatz method is applicable to obtain the transition probabilities for all possible N-particle systems with up to N different species.

HYDROSTATIC LIMIT FOR THE SYMMETRIC EXCLUSION PROCESS WITH LONG JUMPS: SUPER-DIFFUSIVE CASE

Hydrostatic behavior for the one dimensional exclusion process with long jumps in contact with infinite reservoirs at different densities are derived. The jump rate is described by a transition probability $p$ which is proportional to $\vert \cdot\vert ^{-(\gamma +1)}$ for $1<\gamma<2$ (super-diffusive case). The reservoirs add or remove particles with rate proportional to $ \kappa>0$.

Invariant measures of interacting particle systems: Algebraic aspects

Consider a continuous time particle system ηt = (ηt(k), k ∈ 𝕃), indexed by a lattice 𝕃 which will be either ℤ, ℤ∕nℤ, a segment {1, ⋯ , n}, or ℤd, and taking its values in the set Eκ𝕃 where Eκ = {0, ⋯ , κ − 1} for some fixed κ ∈{∞, 2, 3, ⋯ }. Assume that the Markovian evolution of the particle system (PS) is driven by some translation invariant local dynamics with bounded range, encoded by a jump rate matrix ⊤. These are standard settings, satisfied by the TASEP, the voter models, the contact processes. The aim of this paper is to provide some sufficient and/or necessary conditions on the matrix ⊤ so that this Markov process admits some simple invariant distribution, as a product measure (if 𝕃 is any of the spaces mentioned above), the law of a Markov process indexed by ℤ or [1, n] ∩ ℤ (if 𝕃 = ℤ or {1, …, n}), or a Gibbs measure if 𝕃 = ℤ/nℤ. Multiple applications follow: efficient ways to find invariant Markov laws for a given jump rate matrix or to prove that none exists. The voter models and the contact processes are shown not to possess any Markov laws as invariant distribution (for any memory m). (As usual, a random process X indexed by ℤ or ℕ is said to be a Markov chain with memory m ∈ {0, 1, 2, ⋯ } if ℙ(Xk ∈ A | Xk−i, i ≥ 1) = ℙ(Xk ∈ A | Xk−i, 1 ≤ i ≤ m), for any k.) We also prove that some models close to these models do. We exhibit PS admitting hidden Markov chains as invariant distribution and design many PS on ℤ2, with jump rates indexed by 2 × 2 squares, admitting product invariant measures.

An Empirical Analysis of Bitcoin Price Jump Risk

Given that there are both continuous and discontinuous components in the movement of asset prices, existing asset pricing models that assume only continuous price movements should be revised. In this paper, we explore the features of jumps, which are discontinuous movements, by examining Bitcoin pricing. First, we identify jumps in the Bitcoin price on a daily basis, applying a non-parametric methodology and then break down the Bitcoin total rate of return into a jump rate of return and a continuous rate of return. In our empirical analysis, price jumps turn out to be independent of volatility. Moreover, the jumps in the Bitcoin price do not appear at regular intervals; rather, they tend to be concentrated in clusters during special periods, implying that once an economic crisis occurs, the crisis will last for a long time due to contagion effects and the economy will take a considerable amount of time to recover fully. Further, the contribution of the jump rate of return to the total rate of return of the Bitcoin price is lower than the contribution of the continuous return, implying that the pursuit of sustainable returns rather than large but temporary returns will improve the total rate of return over the long term. Finally, more jumps are observed when trading volume is lower, implying that market illiquidity drives discontinuous movement in asset prices. Overall, the features of jump risk are like two sides of the same coin and jump risks are expected to have a significant effect on asset pricing, suggesting that consideration of jumps is essential for risk management as well as asset pricing.

The thermodynamics and kinetics of iodine vacancies in the hybrid perovskite methylammonium lead iodide

A quantitative description of the ionic conductivity of MAPbI3 is built on two pillars: knowledge of the iodine-vacancy jump rate and of the density of iodine defects.