The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations u...

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disc. A two-dimensional corotating slice in the azimuthal–vertical plane of the disc is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, wh...

Grazing flow passing over the quiescent fluid inside the cavity of a Helmholtz resonator can excite the resonator. When the frequency of the instabilities within the shear layer is near the natural frequency of the resonator then flow-excited resonance will occur. This process causes self-sustained periodic oscillations of the flow over the orifice of the resonator. Quantitative numerical predi...

Babak Mostaghaci1,2, Arash Hanifi3, Brigitta Loretz1 and Claus-Michael Lehr1,4 1Dept. of Drug Delivery (DDEL), Helmholtz-Institute for Pharmaceutical Research Saarland (HIPS), Helmholtz Centre for Infectious Research (HZI) Saarland University, Saarbruecken 2Biomaterials Group, Materials Engineering Department Isfahan University of Technology, Isfahan 3Tissue Imaging and Spectroscopy Lab, Bioeng...

We consider three problems for the Helmholtz equation in interior and exterior domains in R, (d = 2, 3): the exterior Dirichlet-to-Neumann and Neumann-to-Dirichlet problems for outgoing solutions, and the interior impedance problem. We derive sharp estimates for solutions to these problems that, in combination, give bounds on the inverses of the combined-field boundary integral operators for ex...

1 Department of Neurology, Ulm University, Ulm, Germany 2 Department of Pharmacology and Clinical Neuroscience, Umeå University, Umeå, Sweden 3 Virtual Helmholtz Institute RNA Dysmetabolism in Amyotrophic Lateral Sclerosis and Fronto-Temporal Dementia, Germany 4 Institute of Human Genetics, Ulm University, Ulm, Germany 5 Institute of Human Genetics, Helmholtz Zentrum München, Neuherberg, German...

Driven by both empirical knowledge and mathematical reasoning, Helmholtz made extraordinary contributions to natural philosophy, including both imaging and vision science. Fundamentally important examples include the Helmholtz theorem and the Helmholtz equation, which describe vector and scalar properties of light fields. The first informs us that fields are derived from point and current sourc...