Search results for "PROBABILITY"

A method for the probabilistic analysis of nonlinear systems

1995

Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…

Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method

2011

In this paper the response in terms of probability density function of nonlinear systems under combined normal and Poisson white noise is considered. The problem is handled via a Path Integral Solution (PIS) that may be considered as a step-by-step solution technique in terms of probability density function. A nonlinear system under normal white noise, Poissonian white noise and under the superposition of normal and Poisson white noise is performed through PIS. The spectral counterpart of the PIS, ruling the evolution of the characteristic functions is also derived. It is shown that at the limit when the time step becomes an infinitesimal quantity an equation ruling the evolution of the pro…

Critical point and coexistence curve properties of the Lennard-Jones fluid: A finite-size scaling study

1995

Monte Carlo simulations within the grand canonical ensemble are used to explore the liquid-vapour coexistence curve and critical point properties of the Lennard-Jones fluid. Attention is focused on the joint distribution of density and energy fluctuations at coexistence. In the vicinity of the critical point, this distribution is analysed using mixed-field finite-size scaling techniques aided by histogram reweighting methods. The analysis yields highly accurate estimates of the critical point parameters, as well as exposing the size and character of corrections to scaling. In the sub-critical coexistence region the density distribution is obtained by combining multicanonical simulations wit…

Levy flights in confining environments: Random paths and their statistics

2013

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental inhomogeneities), the pertinent random motion asymptotically sets down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) $\rho_*(x) \sim \exp [-\Phi (x)]$. Since there is no Langevin representation of the dynamics in question, our main goal here is to establish the appropriate path-wise description of the underlying jump-type process and next infer the $\rho (x,t)$ dynamics directly from the random paths statistics. A pr…

Revised Atomistic Models of the Crystal Structure of C–S–H with high C/S Ratio

2016

Abstract The atomic structure of calcium-silicate-hydrate (C1.67–S–H x ) has been studied. Atomistic C–S–H models suggested in our previous study have been revised in order to perform a direct comparison of energetic stability of the different structures. An extensive set of periodic structures of C–S–H with variation of water content was created, and then optimized using molecular dynamics with reactive force field ReaxFF and quantum chemical semiempirical method PM6. All models show organization of water molecules inside the structure of C–S–H. The new geometries of C–S–H, reported in this paper, show lower relative energy with respect to the geometries from the original definition of C–S…

Use of response factorial design for process optimization of basic dye adsorption onto activated carbon derived from Persea species

2017

Abstract Full factorial design is a powerful and efficient mathematical approach widely applied in the optimization of response. The important parameters which affect the removal efficiency of methylene blue such temperature, initial pH of the solution, concentration and adsorbent dosage were optimized. They coded as A, B, C and D, consecutively, and were investigated at two levels (+ 1 and − 1). A linear mathematical model representing the influence of the different variables and their interactions was obtained. Main effect, Normal probability plot of residuals, analysis of variance (ANOVA), surface plots, and contour plots were used to study the effects and interaction effects between ope…

An MO study of neutral C8 high-symmetry clusters

1997

Abstract Highly symmetric octacarbon clusters, i.e. a cube (O h ), a twisted cube (T d ), a tricyclic cage (C 3v ) and a planar (D 4h ) structure, were fully optimized at the HF, B3LYP and MP2(Full) levels of theory. These stationary points were shown to be local minima on the potential energy surface by frequency calculations. The stability of these clusters compared to the cyclic planar (C 4h ) ground state was found to be strongly dependent on the level of theory. MP2(Full) calculations suggest that cubic C 8 is a local minimum, its energy being 273 kJ/mol higher than the ground state. Structural parameters and fundamental vibrations are presented.

Van't Hoff's stability rule

1931

Prevalence, correlates, and predictors of depersonalization experiences in the German general population.

2009

The survey aimed to investigate the prevalence of depersonalization (DP) experiences, its sociodemographic characteristics and its associations with medical conditions, illness behavior, and potential etiologic factors. A representative face-to-face household survey was conducted. The sample consists of n = 1,287 participants aged 14 to 90 years. Sociodemographic variables, medical conditions, current mental disorders, health care utilization, and childhood adversities were assessed. A total of 1.9% participants scored in the range of clinically significant DP (DP-C) and 9.7% reported at least some impairment through DP (DP-I). DP-C/DP-I were strongly associated with depression and anxiety.…

Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion …

2013

A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for th…