Search results for "Parametric"
showing 10 items of 980 documents
Crack growth in fillet welded steel joints subjected to membrane and bending loading modes
2020
Abstract The present paper presents the results from extensive studies of the fatigue damage evolution in fillet welded steel joints subjected to Constant Amplitude (CA) stress under membrane and bending loading modes. The welded joints in question are F class details (category 71) with plate thicknesses ranging from 25 to 32 mm. The steel quality is a medium strength carbon manganese steel. Crack growth histories for the shallow semi-elliptical shaped cracks emanating from the weld toe are obtained by an Alternating Current Potential Drop (ACPD) technique. These growth histories are presented in detail and modelled by Linear Elastic Facture Mechanics (LEFM). The calculations follow the rec…
Thalamic Network Oscillations Synchronize Ontogenetic Columns in the Newborn Rat Barrel Cortex
2013
Neocortical areas are organized in columns, which form the basic structural and functional modules of intracortical information processing. Using voltage-sensitive dye imaging and simultaneous multi-channel extracellular recordings in the barrel cortex of newborn rats in vivo, we found that spontaneously occurring and whisker stimulation-induced gamma bursts followed by longer lasting spindle bursts were topographically organized in functional cortical columns already at the day of birth. Gamma bursts synchronized a cortical network of 300-400 µm in diameter and were coherent with gamma activity recorded simultaneously in the thalamic ventral posterior medial (VPM) nucleus. Cortical gamma b…
Construction of 3D Triangles on Dupin Cyclides
2011
This paper considers the conversion of the parametric Bézier surfaces, classically used in CAD-CAM, into patched of a class of non-spherical degree 4 algebraic surfaces called Dupin cyclides, and the definition of 3D triangle with circular edges on Dupin cyclides. Dupin cyclides was discovered by the French mathematician Pierre-Charles Dupin at the beginning of the 19th century. A Dupin cyclide has one parametric equation, two implicit equations, and a set of circular lines of curvature. The authors use the properties of these surfaces to prove that three families of circles (meridian arcs, parallel arcs, and Villarceau circles) can be computed on every Dupin cyclide. A geometric algorithm …
Linear Oscillator with Time-Dependent Frequency
2001
Here is another important example of a path integral calculation, namely the time-dependent oscillator whose Lagrangian is given by $$\displaystyle{ L = \frac{m} {2} \dot{x}^{2} -\frac{m} {2} W(t)x^{2}\;. }$$ (21.1) Since L is quadratic, we again expand around a classical solution so that later on we will be dealing again with the calculation of the following path integral: $$\displaystyle{ \int _{x(t_{i})\,=\,0}^{x(t_{f})\,=\,0}[dx(t)]\text{exp}\left \{ \frac{\text{i}} {\hslash }\,\frac{m} {2} \int _{t_{i}}^{t_{f} }dt\left [\left (\frac{dx} {dt} \right )^{\!2} - W(t)x^{2}\right ]\right \}\;. }$$ (21.2) Using \(x(t_{i}) = 0 = x(t_{f}),\) we can integrate by parts and obtain $$\displaystyle{…
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
2020
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.
The spatial pattern of a forest ecosystem
1998
Abstract Statistical analysis of stands of trees as a whole need suitable methods of spatial statistics. Obviously, trees within a stand affect development and survival of their neighbours. They interact and therefore have to be considered as a system of dependent random variates from an unknown stochastic process. One such statistical model which considers the spatial dependence among trees in a forest and their characteristics is a marked point process. The `points', called events in spatial statistics, are the tree positions and the `marks' are tree characteristics such as crown lengths or tree species. A minimal prerequisite for any serious attempt to model an observed pattern is to tes…
Extension of The Stochastic Differential Calculus To Complex Processes
1996
In structural engineering complex processes arise to predict the first excursion failure, fatigue failure, etc. Indeed to solve these problems the envelope function, which is the modulus of a complex process, is usually introduced. In this paper the statistics of the complex response process related to the envelope statistics of linear systems subjected to parametric stationary normal white noise input are evaluated by using extensively the properties of stochastic differential calculus.
Computation of Yvon-Villarceau circles on Dupin cyclides and construction of circular edge right triangles on tori and Dupin cyclides
2014
Ring Dupin cyclides are non-spherical algebraic surfaces of degree four that can be defined as the image by inversion of a ring torus. They are interesting in geometric modeling because: (1) they have several families of circles embedded on them: parallel, meridian, and Yvon-Villarceau circles, and (2) they are characterized by one parametric equation and two equivalent implicit ones, allowing for better flexibility and easiness of use by adopting one representation or the other, according to the best suitability for a particular application. These facts motivate the construction of circular edge triangles lying on Dupin cyclides and exhibiting the aforementioned properties. Our first contr…
A simple method for the design of hybrid electric power-split cvts: A case study
2018
A brief parametric method for the preliminary design of hybrid electric Power-Split CVTs is performed. The desired torque-speed characteristic is obtained, and general control and optimization criteria are introduced in order to minimize the size of the required electric machines. The optimization is performed by mean of scheme-independent functional parameters, while a specific constructive design is proposed only later, along with possible full electric operations.
A New Simple Computational Method of Simultaneous Constructing and Comparing Confidence Intervals of Shortest Length and Equal Tails for Making Effic…
2021
A confidence interval is a range of values that provides the user with useful information about how accurately a statistic estimates a parameter. In the present paper, a new simple computational method is proposed for simultaneous constructing and comparing confidence intervals of shortest length and equal tails in order to make efficient decisions under parametric uncertainty. This unified computational method provides intervals in several situations that previously required separate analysis using more advanced methods and tables for numerical solutions. In contrast to the Bayesian approach, the proposed approach does not depend on the choice of priors and is a novelty in the theory of st…