Search results for "equation"
showing 10 items of 4219 documents
On the behavior of a three-dimensional fractional viscoelastic constitutive model
2016
In this paper a three-dimensional isotropic fractional viscoelastic model is examined. It is shown that if different time scales for the volumetric and deviatoric components are assumed, the Poisson ratio is time varying function; in particular viscoelastic Poisson ratio may be obtained both increasing and decreasing with time. Moreover, it is shown that, from a theoretical point of view, one-dimensional fractional constitutive laws for normal stress and strain components are not correct to fit uniaxial experimental test, unless the time scale of deviatoric and volumetric are equal. Finally, the model is proved to satisfy correspondence principles also for the viscoelastic Poisson’s ratio a…
The fixed angle scattering problem and wave equation inverse problems with two measurements
2019
We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the far field pattern generated by plane waves coming from exactly two opposite directions. This implies that a reflection symmetric potential is uniquely determined by its fixed angle scattering data. We also prove a Lipschitz stability estimate for an associated problem. Motivated by the point source inverse problem in geophysics, we show that a compactly supported potential is uniquely determined from boundary measurements of the waves generated by exactl…
Functional design of power-split CVTs: An uncoupled hierarchical optimized model
2017
Abstract This paper provides a new model for the preliminary design of compound power-split CVTs. Unlike the existing models, the presented method allows the engineers to prioritize functionality and efficiency of the transmission, while delaying the choice of the involved gear sets’ layout as long as possible. The design approach follows a specific priority order, and each step deals with one particular issue, without mutual interference. A smart design-chart eases the assessment and the comparison of the only eligible alternatives, and eventually leads to a final feasible constructive scheme, which can be an excellent concept for further optimization and implementation. Moreover, the mode…
On Using “Stochastic Learning on the Line” to Design Novel Distance Estimation Methods for Three-Dimensional Environments
2019
We consider the unsolved problem of Distance Estimation (DE) when the inputs are the x and y coordinates (i.e., the latitudinal and longitudinal positions) of the points under consideration, and the elevation/altitudes of the points specified, for example, in terms of their z coordinates (3DDE). The aim of the problem is to yield an accurate value for the real (road) distance between the points specified by all the three coordinates of the cities in question (This is a typical problem encountered in a GISs and GPSs.). In our setting, the distance between any pair of cities is assumed to be computed by merely having access to the coordinates and known inter-city distances of a small subset o…
Effects of school climate and teacher self-efficacy on job satisfaction of mostly STEM teachers: a structural multigroup invariance approach
2020
Abstract Background Identification and retention of effective teachers in STEM education play cardinal roles in teacher recruitment exercises worldwide. Studies on factors that characterize effective teachers have therefore gained popularity in recent times. Teacher self-efficacy, job satisfaction and school climate are among other factors that have attracted global attention. Thus, proper understanding of the relations between these factors is equally important. The purpose of this study is to validate and cross-validate a model of direct/indirect effects of school climate and teacher self-efficacy on job satisfaction. Results The data used for the current study are extracted from a public…
An inverse problem for the fractional Schrödinger equation in a magnetic field
2020
This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrödinger equation (FMSE): an unknown electromagnetic field in a bounded domain is uniquely determined up to a natural gauge by infinitely many measurements of solutions taken in arbitrary open subsets of the exterior. The proof is based on Alessandrini's identity and the Runge approximation property, thus generalizing some previous works on the fractional Laplacian. Moreover, we show with a simple model that the FMSE relates to a long jump random walk with weights. peerReviewed
Resolvent estimates for the magnetic Schrödinger operator in dimensions ≥2
2020
It is well known that the resolvent of the free Schrödinger operator on weighted L2 spaces has norm decaying like λ−12 at energy λ . There are several works proving analogous high frequency estimates for magnetic Schrödinger operators, with large long or short range potentials, in dimensions n≥3 . We prove that the same estimates remain valid in all dimensions n≥2 . peerReviewed
On Infiltration and Infiltration Characteristic Times
2022
In his seminal paper on the solution of the infiltration equation, Philip (1969), https://doi.org/10.1016/b978-1-4831-9936-8.50010-6 proposed a gravity time, tgrav, to estimate practical convergence time and the time domain validity of his infinite time series expansion, TSE, for describing the transient state. The parameter tgrav refers to a point in time where infiltration is dominated equally by capillarity and gravity as derived from the first two (dominant) terms of the TSE. Evidence suggests that applicability of the truncated two-term equation of Philip has a time limit requiring higher-order TSE terms to better describe the infiltration process for times exceeding that limit. Since …
Coherent master equation for laser modelocking
2020
Modelocked lasers constitute the fundamental source of optically-coherent ultrashort-pulsed radiation, with huge impact in science and technology. Their modeling largely rests on the master equation (ME) approach introduced in 1975 by Hermann A. Haus. However, that description fails when the medium dynamics is fast and, ultimately, when light-matter quantum coherence is relevant. Here we set a rigorous and general ME framework, the coherent ME (CME), that overcomes both limitations. The CME predicts strong deviations from Haus ME, which we substantiate through an amplitude-modulated semiconductor laser experiment. Accounting for coherent effects, like the Risken-Nummedal-Graham-Haken multim…
Indefinite integrals from Wronskians and related linear second-order differential equations
2021
Many indefinite integrals are derived for Bessel functions and associated Legendre functions from particular transformations of their differential equations which are closely linked to Wronskians. A large portion of the results for Bessel functions is known, but all the results for associated Legendre functions appear to be new. The method can be applied to many other special functions. All results have been checked by differentiation using Mathematica.