Search results for "solution"
showing 10 items of 5638 documents
The analysis of dielectric relaxation phenomena with the inverse Fourier transformation
1993
Abstract A method to determine the distribution of relaxation times directly from dielectric loss spectra is presented. The method is based upon a deconvolution procedure: the Fourier transform of the loss factor is divided by sech( π 2 f ) and then, via an inverse Fourier transformation, transformed into the time domain. Limitations and possible improvements of the method are discussed. It is shown that the present method is able to reveal local relaxation processes not perceptible in the loss factor spectrum. With stimulated noise-free data, the resolution of the method is one third of a decade on a logarithmic relaxation timescale.
Accessing fast magnetization dynamics by XPEEM: Status and perspectives
2006
Abstract Being already well established as a versatile technique for high-resolution static magnetic domain imaging, X-ray photoemission electron microscopy (XPEEM) is now also capturing the field of time-resolved magnetic investigations. Using appropriate operation modes at synchrotron radiation sources, a time resolution of 10 ps and less can be achieved in recent magnetodynamics studies, giving access even to phenomena involving precessional processes.
Inductance Calculations for Circular Coils of Rectangular Cross Section and Parallel Axes Using Bessel and Struve Functions
2010
A simple method for calculating the mutual and self inductances of circular coils of rectangular cross section and parallel axes is presented. The method applies to non-coaxial as well as coaxial coils, and self inductance can be calculated by considering two identical coils which coincide in space. It is assumed that current density is homogeneous in the coil windings. The inductances are given in terms of one-dimensional integrals involving Bessel and Struve functions, and an exact solution is given for one of these integrals. The remaining terms can be evaluated numerically to great accuracy using computer packages such as Mathematica. The method is compared with other exact methods for …
Indicators of Errors for Approximate Solutions of Differential Equations
2014
Error indicators play an important role in mesh-adaptive numerical algorithms, which currently dominate in mathematical and numerical modeling of various models in physics, chemistry, biology, economics, and other sciences. Their goal is to present a comparative measure of errors related to different parts of the computational domain, which could suggest a reasonable way of improving the finite dimensional space used to compute the approximate solution. An “ideal” error indicator must possess several properties: efficiency, computability, and universality. In other words, it must correctly reproduce the distribution of errors, be indeed computable, and be applicable to a wide set of approxi…
On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain
2021
Abstract We study the wave inequality with a Hardy potential ∂ t t u − Δ u + λ | x | 2 u ≥ | u | p in ( 0 , ∞ ) × Ω , $$\begin{array}{} \displaystyle \partial_{tt}u-{\it\Delta} u+\frac{\lambda}{|x|^2}u\geq |u|^p\quad \mbox{in } (0,\infty)\times {\it\Omega}, \end{array}$$ where Ω is the exterior of the unit ball in ℝ N , N ≥ 2, p > 1, and λ ≥ − N − 2 2 2 $\begin{array}{} \displaystyle \left(\frac{N-2}{2}\right)^2 \end{array}$ , under the inhomogeneous boundary condition α ∂ u ∂ ν ( t , x ) + β u ( t , x ) ≥ w ( x ) on ( 0 , ∞ ) × ∂ Ω , $$\begin{array}{} \displaystyle \alpha \frac{\partial u}{\partial \nu}(t,x)+\beta u(t,x)\geq w(x)\quad\mbox{on } (0,\infty)\times \partial{\it\Omega}, \e…
Location of transition states and stable intermediates by MINIMAX/MINIMI optimization of synchronous transit pathways
1983
The MINIMAX/MINIMI concept for the location of transition states and/or stable intermediates of chemical reactions is introduced, based on the synchronous transit method. According to this strategy, minimization of quadratic synchronous transit path maxima or minima is achieved by constrained exhaustive optimization of internal coordinates. The method and its efficiency are demonstrated for two-dimensional model surfaces as well as for thermally allowed electrocyclic interconversions of cyclopropyl-/allyl-cation and cyclobutene-/butadiene (gauche) within the framework of MNDO-SCF calculations. Thus, in both cases a direct comparison with the exact solution determined by minimization of the …
Production of highly charged metal ion beams from organic metal compounds at RIKEN 18 GHz ECRIS
1997
Abstract Intense beams of highly charged metal ions (e.g., 80 μA for Fe13+) are successfully extracted from the 18 GHz ECR Ion Source at RIKEN by feeding vapors of organic metal compounds at room temperature into the ECR plasma chamber: by MIVOC method. The beam intensity of particular metal ion is strongly dependent on the microwave power and served compounds.
A comparative study of SPCTRAL2 and SMARTS2 parameterised models based on spectral irradiance measurements at Valencia, Spain
1998
Abstract Results obtained using the parametric models SPCTRAL2 and SMARTS2 for the urban area of Valencia, Spain, have been analysed and compared with experimental measurements at ground level obtained with two Li-cor 1800 spectroradiometers with a 6 nm resolution. The study used two different input parameters in both models for the aerosol characterisation: the aerosol optical thickness at 0.5 μ m, τ a λ (0.5) , and the Angstrom turbidity coefficient β . The results obtained show that both algorithms reproduce quite correctly the spectral irradiance experimental values when an urban aerosol model parameterised by the τ a λ (0.5) value is considered. In all the cases the deviations are low…
Pattern projection for subpixel resolved imaging in microscopy.
2006
In this paper, we present a new approach providing super resolved images exceeding the geometrical limitation given by the detector pixel size of the imaging camera. The concept involves the projection of periodic patterns on top of the sample, which are then investigated under a microscope. Combining spatial scanning together with proper digital post-processing algorithm yields the improved geometrical resolution enhancement. This new method is especially interesting for microscopic imaging when the resolution of the detector is lower than the resolution due to diffraction.
Transmission Microscopy with Nanometer Resolution Using a Deterministic Single Ion Source.
2015
We realize a single particle microscope by using deterministically extracted laser-cooled ^{40}Ca^{+} ions from a Paul trap as probe particles for transmission imaging. We demonstrate focusing of the ions to a spot size of 5.8±1.0 nm and a minimum two-sample deviation of the beam position of 1.5 nm in the focal plane. The deterministic source, even when used in combination with an imperfect detector, gives rise to a fivefold increase in the signal-to-noise ratio as compared with conventional Poissonian sources. Gating of the detector signal by the extraction event suppresses dark counts by 6 orders of magnitude. We implement a Bayes experimental design approach to microscopy in order to ma…