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We develop a space-time spectral element method for topology optimization of transient heat conduction. The forward problem is discretized with summation-by-parts (SBP) operators, and interface/boundary and initial/terminal conditions are…
Flat beams feature unequal emittances in the horizontal and vertical phase space. Those beams were created successfully in lepton machines. Although a number of applications will profit also from flat hadron beams, to our knowledge they…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
The subject of this introductory course is transverse dynamics of charged particle beams in linear approximation. Starting with a discussion of the most important types of magnets and defining their multipole strengths, the linearized…
Conformational phases of a semiflexible off-lattice homopolymer model near an attractive substrate are investigated by means of multicanonical computer simulations. In our polymer-substrate model, nonbonded pairs of monomers as well as…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
Transformers are difficult to optimize with stochastic gradient descent (SGD) and largely rely on adaptive optimizers such as Adam. Despite their empirical success, the reasons behind Adam's superior performance over SGD remain poorly…
We show that allowing magnetic fields to be complex-valued leads to an improvement in the magnetic Hardy-type inequality due to Laptev and Weidl. The proof is based on the study of momenta on the circle with complex magnetic fields, which…
The behavior of orbits in charged-particle beam transport systems, including both linear and circular accelerators as well as final focus sections and spectrometers, can depend sensitively on nonlinear fringe-field and high-order-multipole…
The first order condition of the constrained minimization problem leads to a saddle point problem. A multigrid method using a multiplicative Schwarz smoother for saddle point problems can thus be interpreted as a successive subspace…
A new approach for the parallel forward modeling of transient electromagnetic (TEM) fields is presented. It is based on a family of uniform-in-time rational approximants to the matrix exponential that share a common denominator independent…
We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…
We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…
Polar molecules, in strong-field seeking states, can be transported and focused by an alternating sequence of electric field gradients that focus in one transverse direction while defocusing in the other. We show, by calculation and…
We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations…
Orbit-based methods are widespread in strong-field laser-matter interaction. They provide a framework in which photoelectron momentum distributions can be interpreted as the quantum interference between different semi-classical pathways the…
This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…
Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…
The optimal conversion of a continuous inter-particle potential to a discrete equivalent is considered here. Existing and novel algorithms are evaluated to determine the best technique for creating accurate discrete forms using the minimum…