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- ItemMixed Cu-Fe Sulfides Derived from Polydopamine-Coated Prussian Blue Analogue as a Lithium-Ion Battery Electrode(Washington, DC : ACS Publications, 2022) Bornamehr, Behnoosh; Presser, Volker; Husmann, SamanthaBatteries employing transition-metal sulfides enable high-charge storage capacities, but polysulfide shuttling and volume expansion cause structural disintegration and early capacity fading. The design of heterostructures combining metal sulfides and carbon with an optimized morphology can effectively address these issues. Our work introduces dopamine-coated copper Prussian blue (CuPB) analogue as a template to prepare nanostructured mixed copper-iron sulfide electrodes. The material was prepared by coprecipitation of CuPB with in situ dopamine polymerization, followed by thermal sulfidation. Dopamine controls the particle size and favors K-rich CuPB due to its polymerization mechanism. While the presence of the coating prevents particle agglomeration during thermal sulfidation, its thickness demonstrates a key effect on the electrochemical performance of the derived sulfides. After a two-step activation process during cycling, the C-coated KCuFeS2electrodes showed capacities up to 800 mAh/g at 10 mA/g with nearly 100% capacity recovery after rate handling and a capacity of 380 mAh/g at 250 mA/g after 500 cycles.
- ItemLarge deviations for the capacity in dynamic spatial relay networks(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Hirsch, Christian; Jahnel, BenediktWe derive a large deviation principle for the space-time evolution of users in a relay network that are unable to connect due to capacity constraints. The users are distributed according to a Poisson point process with increasing intensity in a bounded domain, whereas the relays are positioned deterministically with given limiting density. The preceding work on capacity for relay networks by the authors describes the highly simplified setting where users can only enter but not leave the system. In the present manuscript we study the more realistic situation where users leave the system after a random transmission time. For this we extend the point process techniques developed in the preceding work thereby showing that they are not limited to settings with strong monotonicity properties.
- ItemSpace-time large deviations in capacity-constrained relay networks(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hirsch, Christian; Jahnel, Benedikt; Patterson, RobertWe consider a single-cell network of random transmitters and fixed relays in a bounded domain of Euclidean space. The transmitters arrive over time and select one relay according to a spatially inhomogeneous preference kernel. Once a transmitter is connected to a relay, the connection remains and the relay is occupied. If an occupied relay is selected by another transmitters with later arrival time, this transmitter becomes frustrated. We derive a large deviation principle for the space-time evolution of frustrated transmitters in the high-density regime.
- ItemHomogeneous nucleation for Glauber and Kawasaki dynamics in large volumes at low temperatures(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Bovier, Anton; Hollander, Frank den; Spitoni, CristianIn this paper we study metastability in large volumes at low temperatures. We consider both Ising spins subject to Glauber spin-flip dynamics and lattice gas particles subject to Kawasaki hopping dynamics. Let $b$ denote the inverse temperature and let $L_b subset Z^2$ be a square box with periodic boundary conditions such that $lim_btoinfty L_b =infty$. We run the dynamics on $L_b$ starting from a random initial configuration where all the droplets (= clusters of plus-spins, respectively, clusters of particles) are small. For large $b$, and for interaction parameters that correspond to the metastable regime, we investigate how the transition from the metastable state (with only small droplets) to the stable state (with one or more large droplets) takes place under the dynamics. This transition is triggered by the appearance of a single emphcritical droplet somewhere in $L_b$. Using potential-theoretic methods, we compute the emphaverage nucleation time (= the first time a critical droplet appears and starts growing) up to a multiplicative factor that tends to one as $btoinfty$. It turns out that this time grows as $Ke^Gammab/ L_b $ for Glauber dynamics and $Kb e^Gammab/ L_b $ for Kawasaki dynamics, where $Gamma$ is the local canonical, respectively, grand-canonical energy to create a critical droplet and $K$ is a constant reflecting the geometry of the critical droplet, provided these times tend to infinity (which puts a growth restriction on $ L_b $). The fact that the average nucleation time is inversely proportional to $ L_b $ is referred to as emphhomogeneous nucleation, because it says that the critical droplet for the transition appears essentially independently in small boxes that partition $L_b$.
- ItemMetastability : a potential theoretic approach(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2005) Bovier, AntonMetastability is an ubiquitous phenomenon of the dynamical behaviour of complex systems. In this talk, I describe recent attempts towards a model-independent approach to metastability in the context of reversible Markov processes. I will present an outline of a general theory, based on careful use of potential theoretic ideas and indicate a number of concrete examples where this theory was used very successfully. I will also indicate some challenges for future work.
- ItemSharp asymptotics for metastability in the random field Curie-Weiss model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Bianchi, Alessandra; Bovier, Anton; Ioffe, DmitryIn this paper we study the metastable behavior of one of the simplest disordered spin system, the random field Curie-Weiss model. We will show how the potential theoretic approach can be used to prove sharp estimates on capacities and metastable exit times also in the case when the distribution of the random field is continuous. Previous work was restricted to the case when the random field takes only finitely many values, which allowed the reduction to a finite dimensional problem using lumping techniques. Here we produce the first genuine sharp estimates in a context where entropy is important.