Related papers: A computationally efficient method to solve the Ta…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…
We study numerically the reflectivity of three-dimensional (3D) photonic crystals with a complete 3D photonic band gap, with the aim to interpret recent experiments. We employ the finite element method to study crystals with the cubic…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this paper we investigate x-ray and $\gamma$-ray propagation in crystals having a constant strain gradient and flat or cylindrical surfaces. When a displacement field is present, we solve the Takagi-Taupin equations either by the…
We introduce a systematic approach that enables two robust methods for performing terahertz time-domain spectroscopy in reflection geometry. Using the Kramers-Kronig relations in connection to accurate experimental measurements of the…
An extension of the Kramers-Kronig method for treatment of polarized infrared reflectance spectra from the face of low-symmetry crystals, where directions of principal dielectric axes depend on frequency, is proposed. It is shown, how to…
This paper presents a convolution tensor decomposition based model reduction method for solving the Allen-Cahn equation. The Allen-Cahn equation is usually used to characterize phase separation or the motion of anti-phase boundaries in…
A dispersive analysis of $\eta\to 3\pi$ decays has been performed in the past by many authors. The numerical analysis of the pertinent integral equations is hampered by two technical difficulties: i) The angular averages of the amplitudes…
This paper presents a new method to obtain the deformation distribution on the main reflector of an antenna only by measuring the electric intensity on a spherical surface with the focal point as the center of the sphere, regardless of…
In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the…
Using the spectral approach, we analyze the effective properties of a composite which deviates slightly from periodicity. We find that, when the inclusions are randomly displaced from their equilibrium positions, the sharp resonances seen…
High quality micro- and nano-mechanical resonators are widely used in sensing, communications and timing, and have future applications in quantum technologies and fundamental studies of quantum physics. Crystalline thin-films are…
In this paper, we prove that there exists a unique strong solution to reflecting stochastic differential equations with merely measurable drift giving an affirmative answer to the longstanding problem. This is done through Zvonkin…
The equations for calculating diffraction profiles for bent crystals are revisited for both meridional and sagittal bending. Two approximated methods for computing diffraction profiles are treated: multilamellar and Penning-Polder. A common…
Recently it has been shown that the modules and phase of complex reflection coefficient can be determined by using a magnetic substrate and polarized neutrons. Several other methods have also been worked out based on measurement of…
The time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional…
The prediction of Debye-Scherrer diffraction patterns from strained samples is typically conducted in the small strain limit. Although valid for small deviations from the hydrostat (such as the conditions of finite strength typically…
Spatially resolved strain measurements are crucial to understanding the properties of engineering materials. Although strain measurements utilizing techniques such as transmission electron microscopy and electron backscatter diffraction…
A new numerical method is developed for solution of the Gel'fand - Levitan - Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering…