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Simulations of the generation of the atomic polarization is necessary for interpreting the second solar spectrum. For this purpose, it is important to rigorously determine the effects of the isotropic collisions with neutral hydrogen on the…
We consider blow-up solutions of a semilinear wave equation with a loglog perturbation of the power nonlinearity in the subconformal case, and show that the blow-up rate is given by the solution of the associated ODE which has the same…
Laser-driven ions have compelling properties and their potential use for medical applications has attracted a huge global interest. One of the major challenges of these applications is generating beams of the required energies. To date,…
We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization…
This paper is devoted to numerical approximations for the wave equation with a multiscale character. Our approach is formulated in the framework of the Localized Orthogonal Decomposition (LOD) interpreted as a numerical homogenization with…
Porous electrode theory (PET) provides essential insights into electrochemical states, but its computational complexity hinders real-time control and obscures scaling relations. To bridge the gap between high-fidelity simulations and…
We develop the first theoretical model for the analytical description of ion concentration polarization (ICP)-based electrokinetic molecular concentration, which had not been possible due to the extraordinary complexity of the system. We…
The polar decomposition of a matrix is a key element in the quantum linear algebra toolbox. We show that the problem of quantum polar decomposition, recently studied in Lloyd et al. [LBP+20], has a simple and concise implementation via the…
The ability of laser cooling for relativistic ion beams is investigated. For this purpose, the excitation of relativistic ions with a continuous wave and a pulsed laser is analyzed, utilizing the optical Bloch equations. The laser cooling…
Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100 terawatt-class lasers. Two different approaches to computationally efficient,…
Using laser accelerated protons or ions for various applications - for example in particle therapie or short-pulse radiographic diagnostics - requires an effective method of focusing and energy selection. We derive an analytical scaling for…
We determined bulk crystal nucleation rates in aqueous suspensions of charged spheres at low metastability. Experiments were performed in dependence on electrolyte concen-tration and for two different particle number densities. The…
The aggregation of particles in the free molecular regime is determined approximately for situations with a high degree of translational energy equilibration. The mean particle sizes develop linearly in time. Scaling relations are used to…
We present a new numerical algorithm based on a relative energy scaling for collisional kinetic equations allowing to study numerically their long time behavior, without the usual problems related to the change of scales in velocity…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
Experimental results, supported by precise modelling, demonstrate optimisation of a plasma-based injector with intermediate laser pulse energy ($<1$ J), corresponding to a normalised vector potential $a_0 = 2.15$, using ionisation injection…
The determination of the resolution of cosmological N-body simulations, i.e., the range of scales in which quantities measured in them represent accurately the continuum limit, is an important open question. We address it here using…
Motivated by the need to better understand the properties of sparse cutting-planes used in mixed integer programming solvers, the paper [2] studied the idealized problem of how well a polytope is approximated by the use of sparse valid…
Pauli-projected random gaussians are used as a representation to solve the shell model equations. The elements of the representation are chosen by a variational procedure. This scheme is particularly suited to describe cluster formation and…
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground…