MIT Open Access Articleshttps://hdl.handle.net/1721.1/494332021-03-05T09:53:36Z2021-03-05T09:53:36ZLyapunov Exponent of Rank One Matrices: Ergodic Formula and Inapproximability of the Optimal DistributionAltschuler, Jason MParrilo, Pablo Ahttps://hdl.handle.net/1721.1/1300872021-03-04T22:38:48Z2020-03-01T00:00:00ZLyapunov Exponent of Rank One Matrices: Ergodic Formula and Inapproximability of the Optimal Distribution
Altschuler, Jason M; Parrilo, Pablo A
The Lyapunov exponent corresponding to a set of square matrices A = {A 1 , ... , A n } and a probability distribution p over {1, ... , n} is λ(A, p) := lim k→∞ 1/k E log ||A σk ⋯ A σ2 A σ1 ||, where σ i are i.i.d. according to p. This quantity is of fundamental importance to control theory since it determines the asymptotic convergence rate e λ(A,p) of the stochastic linear dynamical system x k+1 = A σk x k . This paper investigates the following “design problem”: given A, compute the distribution p minimizing λ(A, p). Our main result is that it is NP-hard to decide whether there exists a distribution p for which λ(A, p) <; 0, i.e. it is NP-hard to decide whether this dynamical system can be stabilized. This hardness result holds even in the “simple” case where A contains only rank-one matrices. Somewhat surprisingly, this is in stark contrast to the Joint Spectral Radius - the deterministic kindred of the Lyapunov exponent - for which the analogous optimization problem over switching rules is known to be exactly computable in polynomial time for rank-one matrices. To prove this hardness result, we first observe that the Lyapunov exponent of rank-one matrices admits a simple formula and in fact is a quadratic form in p. Hardness of the design problem is shown through a reduction from the Independent Set problem. Along the way, simple examples are given illustrating that p → λ(A, p) is neither convex nor concave in general, and a connection is made to the fact that the Martin distance on the (1, n) Grassmannian is not a metric.
2020-03-01T00:00:00ZEditors' Choice—Coating-Dependent Electrode-Electrolyte Interface for Ni-Rich Positive Electrodes in Li-Ion BatteriesKarayaylali, PinarTatara, RyoichiZhang, YiruiChan, Kuei-LinYu, YangGiordano, LiviaMaglia, FilippoJung, RolandLund, IsaacShao-Horn, Yanghttps://hdl.handle.net/1721.1/1300862021-03-05T05:59:19Z2019-03-01T00:00:00ZEditors' Choice—Coating-Dependent Electrode-Electrolyte Interface for Ni-Rich Positive Electrodes in Li-Ion Batteries
Karayaylali, Pinar; Tatara, Ryoichi; Zhang, Yirui; Chan, Kuei-Lin; Yu, Yang; Giordano, Livia; Maglia, Filippo; Jung, Roland; Lund, Isaac; Shao-Horn, Yang
Surface chemistry modification of positive electrodes has been used widely to decrease capacity loss during Li-ion battery cycling. Recent work shows that coupled LiPF6 decomposition and carbonate dehydrogenation is enhanced by increased metal-oxygen covalency associated with increasing Ni and/or lithium de-intercalation in metal oxide electrode, which can be responsible for capacity fading of Ni-rich oxide electrodes. Here we examined the reactivity of lithium nickel, manganese, cobalt oxide (LiNi[subscript 0.6]Mn[subscript 0.2]Co[subscript 0.2]O[subscript 2], NMC622) modified by coating of Al[subscript 2]O[subscript 3], Nb[subscript 2]O[subscript 5] and TiO[subscript 2] with a 1 M LiPF[subscript 6] carbonate-based electrolyte. Cycling measurements revealed that Al[subscript 2]O[subscript 3]-coated NMC622 showed the least capacity loss during cycling to 4.6 VLi compared to Nb[subscript 2]O[subscript 5]-, TiO[subscript 2]- coated and uncoated NMC622, which was in agreement with smallest electrode impedance growth during cycling from electrochemical impedance spectroscopy (EIS). Ex-situ infrared spectroscopy of charged Nb[subscript 2]O[subscript 5]- and TiO[subscript 2]-coated NMC622 pellets (without carbon nor binder) revealed blue peak shifts of 10 cm[superscript −1], indicative of dehydrogenation of ethylene carbonate (EC), but not for Al[subscript 2]O[subscript 3]-coated NMC622. X-ray Photoelectron Spectroscopy (XPS) of charged TiO[subscript 2]-coated NMC622 electrodes (carbon-free and binder-free) showed greater salt decomposition with the formation of lithium-nickel-titanium oxyfluoride species, which was in agreement with ex-situ infrared spectroscopy showing greater blue shifts of P-F peaks with increased charged voltages, indicative of species with less F-coordination than salt PF[subscript 6][superscript −] anion on the electrode surface. Greater salt decomposition was coupled with the increasing dehydrogenation of EC with higher coating content on the surface. This work shows that Al[subscript 2]O[subscript 3] coating on NMC622 is the most effective in reducing carbonate dehydrogenation and accompanied salt decomposition and rendering minimum capacity loss relative to TiO[subscript 2] and Nb[subscript 2]O[subscript 5] coating.
2019-03-01T00:00:00ZBreaking the power law: Multiscale simulations of self-ion irradiated tungstenJin, MiaomiaoPermann, CodyShort, Michael P.https://hdl.handle.net/1721.1/1300852021-03-04T17:00:22Z2018-06-01T00:00:00ZBreaking the power law: Multiscale simulations of self-ion irradiated tungsten
Jin, Miaomiao; Permann, Cody; Short, Michael P.
The initial stage of radiation defect creation has often been shown to follow a power law distribution at short time scales, recently so with tungsten, following many self-organizing patterns found in nature. The evolution of this damage, however, is dominated by interactions between defect clusters, as the coalescence of smaller defects into clusters depends on the balance between transport, absorption, and emission to/from existing clusters. The long-time evolution of radiation-induced defects in tungsten is studied with cluster dynamics parameterized with lower length scale simulations, and is shown to deviate from a power law size distribution. The effects of parameters such as dose rate and total dose, as parameters affecting the strength of the driving force for defect evolution, are also analyzed. Excellent agreement is achieved with regards to an experimentally measured defect size distribution at 30 K. This study provides another satisfactory explanation for experimental observations in addition to that of primary radiation damage, which should be reconciled with additional validation data.
2018-06-01T00:00:00ZMacroscopic Ionic Flow in a Superionic Conductor Na+ β-Alumina Driven by Single-Cycle Terahertz PulsesMinami, YasuoOfori-Okai, Benjamin KwasiSivarajah, PrasahntKatayama, IkufumiTakeda, JunNelson, Keith AdamSuemoto, Tohruhttps://hdl.handle.net/1721.1/1300842021-03-05T05:54:51Z2020-04-01T00:00:00ZMacroscopic Ionic Flow in a Superionic Conductor Na+ β-Alumina Driven by Single-Cycle Terahertz Pulses
Minami, Yasuo; Ofori-Okai, Benjamin Kwasi; Sivarajah, Prasahnt; Katayama, Ikufumi; Takeda, Jun; Nelson, Keith Adam; Suemoto, Tohru
Ionic motion significantly contributes to conductivity in devices such as memory, switches, and rechargeable batteries. In our work, we experimentally demonstrate that intense terahertz electric-field transients can be used to manipulate ions in a superionic conductor, namely Na+ β-alumina. The cations trapped in the local potential minima are accelerated using single-cycle terahertz pulses, thereby inducing a macroscopic current flow on a subpicosecond timescale. Our results clearly show that single-cycle terahertz pulses can be used to significantly modulate the nature of superionic conductors and could possibly serve as a basic tool for application in future electronic devices.
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