Search results for "equation"
showing 10 items of 4219 documents
Improving Reliability of Road Safety Estimates Based on High Correlated Accident Counts
2007
Calibrating a safety performance function (SPF) with many years of accident data creates a temporal correlation that traditional model calibration procedures cannot deal with. It is well known that generalized estimating equations (GEE) models are able to incorporate trends into accident data and thus overcome difficulties in accounting for correlation; the usual application of GEEs to safety analysis uses robust (or sandwich) estimates of regression coefficients under the independence hypothesis for the working correlation matrix. This practice is justified by the robustness of the GEE procedure against misspecification of the response correlation structure. Nevertheless, with this method…
NUMERICAL SIMULATION OF MAGNETIC DROPLET DYNAMICS IN A ROTATING FIELD
2013
Dynamics and hysteresis of an elongated droplet under the action of a rotating magnetic field is considered for mathematical modelling. The shape of droplet is found by regularization of the ill-posed initial–boundary value problem for nonlinear partial differential equation (PDE). It is shown that two methods of the regularization – introduction of small viscous bending torques and construction of monotonous continuous functions are equivalent. Their connection with the regularization of the ill-posed reverse problems for the parabolic equation of heat conduction is remarked. Spatial discretization is carried out by the finite difference scheme (FDS). Time evolution of numerical solutions …
Mathematical modelling of an elongated magnetic droplet in a rotating magnetic field
2012
Dynamics of an elongated droplet under the action of a rotating magnetic field is considered by mathematical modelling. The actual shape of a droplet is obtained by solving the initial-boundary value problem of a nonlinear singularly perturbed partial differential equation (PDE). For the discretization in space the finite difference scheme (FDS) is applied. Time evolution of numerical solutions is obtained with MATLAB by solving a large system of ordinary differential equations (ODE).
On the moving load problem in beam structures equipped with tuned mass dampers
2017
This paper proposes an original and efficient approach to the moving load problem on Euler–Bernoulli beams, with Kelvin–Voigt viscoelastic translational supports and rotational joints, and in addition, equipped with Kelvin–Voigt viscoelastic tuned mass dampers (TMDs). While supports are taken as representative of external devices such as grounded dampers or in-span supports with flexibility and damping, the rotational joints may model rotational dampers or connections with flexibility and damping arising from imperfections or damage. The theory of generalised functions is used to treat the discontinuities of the response variables, which involves deriving exact complex eigenvalues and eigen…
Estimating radiant fields in flat heterogeneous photoreactors by the six-flux model
2006
Heterogeneous photoreactor modeling is a task complicated by the integro-differential nature of the Radiation Transfer Equation (RTE) when scattering phenomena are important. In the present work, a novel “Six Flux Model” (SFM) is proposed, which may be regarded as a step forward with respect to the previously proposed “Two Flux Model” (TFM). In order to validate the newly proposed model, Monte Carlo simulations of an indefinite plane-slab photoreactor have been performed. As no simplifying assumptions are involved in this case, the information obtained may be regarded as “pseudo-experimental,” and therefore compared with the predictions of both TFM and SFM models. Results show that the nove…
JIMWLK evolution of the odderon
2016
We study the effects of a parity-odd "odderon" correlation in JIMWLK renormalization group evolution at high energy. Firstly we show that in the eikonal picture where the scattering is described by Wilson lines, one obtains a strict mathematical upper limit for the magnitude of the odderon amplitude compared to the parity even pomeron one. This limit increases with N_c, approaching infinity in the infinite N_c limit. We use a systematic extension of the Gaussian approximation including both 2- and 3-point correlations which enables us to close the system of equations even at finite N_c. In the large-N_c limit we recover an evolution equation derived earlier. By solving this equation numeric…
Modeling Networks of Probabilistic Memristors in SPICE
2021
Efficient simulation of stochastic memristors and their networks requires novel modeling approaches. Utilizing a master equation to find occupation probabilities of network states is a recent major departure from typical memristor modeling [Chaos, solitons fractals 142, 110385 (2021)]. In the present article we show how to implement such master equations in SPICE – a general purpose circuit simulation program. In the case studies we simulate the dynamics of acdriven probabilistic binary and multi-state memristors, and dc-driven networks of probabilistic binary and multi-state memristors. Our SPICE results are in perfect agreement with known analytical solutions. Examples of LTspice code are…
Psychometric Properties and Measurement Invariance by Gender of the Abbreviated Three-Item Version of the Satisfaction with Life Scale in a Colombian…
2022
(1) Background: The need to offer brief scales with items that can be answered with few response options is increasingly important in order to be able to access a broad range of the population. The three-item version of Diener’s Satisfaction with Life Scale has recently been proposed. The objective of this study is to study the psychometric properties of the three-item version of this Scale with five response options, as well as the measurement invariance by gender, in a Colombian sample; (2) Methods: A confirmatory factor model of the three items of the scale together with the Flourishing Scale has been tested, and the measurement invariance by gender of the model has been studied. The res…
Novel dual-flow perfusion bioreactor for in vitro pre-screening of nanoparticles delivery: design, characterization and testing
2021
An advanced dual-flow perfusion bioreactor with a simple and compact design was developed and evaluated as a potential apparatus to reduce the gap between animal testing and drug administration to human subjects in clinical trials. All the experimental tests were carried out using an ad hoc Poly Lactic Acid (PLLA) scaffold synthesized via Thermally Induced Phase Separation (TIPS). The bioreactor shows a tunable radial flow throughout the microporous matrix of the scaffold. The radial perfusion was quantified both with permeability tests and with a mathematical model, applying a combination of Darcy's Theory, Bernoulli's Equation, and Poiseuille's Law. Finally, a diffusion test allowed to in…
The mapping properties of the radiosity operator along an edge
2002
In this article we study the radiosity operator along an edge between two adjacent half-planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half-planes, the reflectivity coefficients and the right-hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22: 217–241). Copyright © 2002 John Wiley & Sons, Ltd.