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Type: Text × Subject: Monte Carlo method ×

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    Local difference measures between complex networks for dynamical system model evaluation
    (San Francisco, CA : Public Library of Science (PLoS), 2015) Lange, S.; Donges, J.F.; Volkholz, J.; Kurths, J.
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    Few-cycle laser driven reaction nanoscopy on aerosolized silica nanoparticles
    ([London] : Nature Publishing Group UK, 2019) Rupp, Philipp; Burger, Christian; Kling, Nora G; Kübel, Matthias; Mitra, Sambit; Rosenberger, Philipp; Weatherby, Thomas; Saito, Nariyuki; Itatani, Jiro; Alnaser, Ali S.; Raschke, Markus B.; Rühl, Eckart; Schlander, Annika; Gallei, Markus; Seiffert, Lennart; Fennel, Thomas; Bergues, Boris; Kling, Matthias F.
    Nanoparticles offer unique properties as photocatalysts with large surface areas. Under irradiation with light, the associated near-fields can induce, enhance, and control molecular adsorbate reactions on the nanoscale. So far, however, there is no simple method available to spatially resolve the near-field induced reaction yield on the surface of nanoparticles. Here we close this gap by introducing reaction nanoscopy based on three-dimensional momentum-resolved photoionization. The technique is demonstrated for the spatially selective proton generation in few-cycle laser-induced dissociative ionization of ethanol and water on SiO2 nanoparticles, resolving a pronounced variation across the particle surface. The results are modeled and reproduced qualitatively by electrostatic and quasi-classical mean-field Mie Monte-Carlo (M3C) calculations. Reaction nanoscopy is suited for a wide range of isolated nanosystems and can provide spatially resolved ultrafast reaction dynamics on nanoparticles, clusters, and droplets.
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    Observation of fractional spin textures in a Heusler material
    ([London] : Nature Publishing Group UK, 2022) Jena, Jagannath; Göbel, Börge; Hirosawa, Tomoki; Díaz, Sebastián A.; Wolf, Daniel; Hinokihara, Taichi; Kumar, Vivek; Mertig, Ingrid; Felser, Claudia; Lubk, Axel; Loss, Daniel; Parkin, Stuart S.P.
    Recently a zoology of non-collinear chiral spin textures has been discovered, most of which, such as skyrmions and antiskyrmions, have integer topological charges. Here we report the experimental real-space observation of the formation and stability of fractional antiskyrmions and fractional elliptical skyrmions in a Heusler material. These fractional objects appear, over a wide range of temperature and magnetic field, at the edges of a sample, whose interior is occupied by an array of nano-objects with integer topological charges, in agreement with our simulations. We explore the evolution of these objects in the presence of magnetic fields and show their interconversion to objects with integer topological charges. This means the topological charge can be varied continuously. These fractional spin textures are not just another type of skyrmion, but are essentially a new state of matter that emerges and lives only at the boundary of a magnetic system. The coexistence of both integer and fractionally charged spin textures in the same material makes the Heusler family of compounds unique for the manipulation of the real-space topology of spin textures and thus an exciting platform for spintronic and magnonic applications.
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    Regression methods in pricing American and Bermudan options using consumption processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Belomestny, Denis; Milstein, Grigor N.; Spokoiny, Vladimir
    Here we develop methods for efficient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market model.
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    Deviational particle Monte Carlo for the Boltzmann equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Wagner, Wolfgang
    The paper describes the deviational particle Monte Carlo method for the Boltzmann equation. The approach is an application of the general ``control variates'' variance reduction technique to the problem of solving a nonlinear equation. The deviation of the solution from a reference Maxwellian is approximated by a system of positive and negative particles. Previous results from the literature are modified and extended. New algorithms are proposed that cover the nonlinear Boltzmann equation (instead of a linearized version) with a general interaction model (instead of hard spheres). The algorithms are obtained as procedures for generating trajectories of Markov jump processes. This provides the framework for deriving the limiting equations, when the number of particles tends to infinity. These equations reflect the influence of various numerical approximation parameters. Detailed simulation schemes are provided for the variable hard sphere interaction model.