Search results for "Statistica"
showing 10 items of 5969 documents
Fractional calculus in solid mechanics: local versus non-local approach
2009
Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by …
Regular and singular pulse and front solutions and possible isochronous behavior in the Extended-Reduced Ostrovsky Equation: Phase-plane, multi-infin…
2016
In this paper we employ three recent analytical approaches to investigate several classes of traveling wave solutions of the so-called extended-reduced Ostrovsky Equation (exROE). A recent extension of phase-plane analysis is first employed to show the existence of breaking kink wave solutions and smooth periodic wave (compacton) solutions. Next, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic orbits of the traveling-wave equations for the exROE equation. These correspond to pulse solutions respectively of the original PDEs. We perform many numerical tests in different parameter regime to pinpoint real saddl…
Looking More Closely at the Rabinovich-Fabrikant System
2016
Recently, we looked more closely into the Rabinovich–Fabrikant system, after a decade of study [Danca & Chen, 2004], discovering some new characteristics such as cycling chaos, transient chaos, chaotic hidden attractors and a new kind of saddle-like attractor. In addition to extensive and accurate numerical analysis, on the assumptive existence of heteroclinic orbits, we provide a few of their approximations.
Stochastic linearization critically re-examined
1997
Abstract The stochastic linearization technique, widely used for the analysis of nonlinear dynamic systems subjected to random excitations, is revisited. It is shown that the standard procedure universally adopted for determining the so-called effective stiffness of the equivalent linear system is erroneous in all previous publications. Two error-free stochastic linearization techniques are elucidated, namely those based on (1) the force linearization and (2) energy linearization.
Quantitative View on the Processes Governing the Upscale Error Growth up to the Planetary Scale Using a Stochastic Convection Scheme
2019
Abstract Two diagnostics based on potential vorticity and the envelope of Rossby waves are used to investigate upscale error growth from a dynamical perspective. The diagnostics are applied to several cases of global, real-case ensemble simulations, in which the only difference between the ensemble members lies in the random seed of the stochastic convection scheme. Based on a tendency equation for the enstrophy error, the relative importance of individual processes to enstrophy-error growth near the tropopause is quantified. After the enstrophy error is saturated on the synoptic scale, the envelope diagnostic is used to investigate error growth up to the planetary scale. The diagnostics re…
Convection and thermodiffusion of colloidal gold tracers by laser light scattering
1999
In a dynamic light scattering experiment, we have investigated the time intensity correlation function and the profile of the transmitted laser beam for organic dispersions of light absorbing colloidal particles containing tiny gold clusters. The correlation functions have been found to show a superposition of an exponential decay, corresponding to Brownian motion of the tracers, and well-defined oscillations. These oscillations are caused by convection due to local heating of the sample by the incident laser beam, which has been confirmed independently via measurements of the local temperature within the sample. It will be shown how the particle convection velocity, which is the order of 1…
Classification of precipitation events with a convective response timescale and their forecasting characteristics
2011
[1] The convective timescale τc, which is mainly determined by the ratio of CAPE and precipitation rate, provides a physically-based measure to distinguish equilibrium and non-equilibrium convection. A statistical analysis of this timescale, based upon observational data from radiosonde ascents, rain gauges, and radar for seven warm seasons in Germany, reveals that the equilibrium and non-equilibrium regimes can be regarded as extremes of a continuous distribution. The two regimes characterize very different interactions between the large-scale flow and convection. The quality of precipitation forecasts from a non-hydrostatic regional weather prediction model with parameterized convection d…
A constructive theory of shape
2021
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of qualitatively similar shapes are constructed giving as input a finite ordered set of characteristic points (landmarks) and the value of a continuous parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the same family are located within the convex hull of the landmarks. The theory is constructive in the sense that it provides a systematic means to build a mathematical model for any shape taken from the physical world. We illustrate this with a va…
R Code for Hausdorff and Simplex Dispersion Orderings in the 2D Case
2010
This paper proposes a software implementation using R of the Hausdorff and simplex dispersion orderings. A copy can be downloaded from http://www.uv.es/~ayala/software/fun-disp.R . The paper provides some examples using the functions exactHausdorff for the Hausdorff dispersion ordering and the function simplex for the simplex dispersion orderings. Some auxiliary functions are commented too.
Perceived Sociability and Social Presence in a Collaborative Serious Game
2013
Collaborative serious games have proven to have the potential to support joint knowledge construction, and there is a growing interest in applying such games to promote high-level learning. However, most of the existing studies have focused on the effects of functional, task-specific support while ignoring the social aspects of collaborative learning. This study is one aim to fill in the knowledge gap in order to understand how learners experience educational games as a means of social interaction and collaboration. The findings indicated that the game environment facilitated and supported players’ socio-emotional processes by eliciting students’ social presence and sociability. This has be…