Non-zero Variance Research Articles

The multi-stream flows and the dynamics of the cosmic web

A new numerical technique to identify the cosmic web is proposed. It is based on locating multi-stream flows, i.e. the places where the velocity field is multi-valued. The method is local in Eulerian space, simple and computationallyefficient. This technique uses the velocities of particles and thus takes into accountthe dynamical information. This is in contrast with the majority of standard methods that use the coordinates of particles only. Two quantities are computed in every mesh cell: the mean and variance of the velocity field.Ideally in the cells where the velocity is single-valued the variance must be equal to zero exactly, therefore the cells with non-zero variance are identified as multi-stream flows. The technique has been tested in the Zel'dovich approximation and in the N-body simulation of the ΛCDM model. The effect of numerical noise is discussed. The web identified by the new method has been compared withthe web identified by the standard technique using only the particle coordinates.The comparison has shown overall similarity of two webs as expected, however they by no means are identical. For example, the isocontours of the corresponding fieldshave significantly different shapes and some density peaks of similar heights exhibit significant differences in the velocity variance and vice versa.This suggests that the density and velocity variance have a significant degree of independence. The shape of the two-dimensional pdf of density and velocity variance confirms this proposition.Thus, we conclude that the dynamical information probed by this technique introduces an additional dimension into analysis of the web.

On the role of shear in cosmological averaging II: large voids, non-empty voids and a network of different voids

We study the effect of shear on the cosmological backreaction in the context of matching voids and walls together using the exact inhomogeneous Lemaȋtre-Tolman-Bondi solution. Generalizing JCAP 1010 (2010) 021, we allow the size of the voids to be arbitrary and the densities of the voids and walls to vary in the range 0 ⩽ Ωv ⩽ Ωw ⩽ 1. We derive the exact analytic result for the backreaction and consider its series expansion in powers of the ratio of the void size to the horizon size, r0/t0. In addition, we deduce a very simple fitting formula for the backreaction with error less than 1% for voids up to sizes r0≳t0. We also construct an exact solution for a network of voids with different sizes and densities, leading to a non-zero relative variance of the expansion rate between the voids. While the leading order term of the backreaction for a single void-wall pair is of order (r0/t0)2, the relative variance between the different voids in the network is found to be of order (r0/t0)4 and thus very small for voids of the observed size. Furthermore, we show that even for very large voids, the backreaction is suppressed by an order of magnitude relative to the estimate obtained by treating the walls and voids as disjoint Friedmann solutions. Whether the suppression of the backreaction due to the shear is just a consequence of the restrictions of the used exact models, or a generic feature, has to be addressed with more sophisticated solutions.

Effect of surface roughness on magnetohydrodynamic squeeze film characteristics between finite rectangular plates

The effect of surface roughness on the magnetohydrodynamic squeeze film behavior between two rectangular plates is analyzed. A generalized form of surface roughness pattern is considered. A stochastic random variable with non-zero mean, variance and skewness is used to model mathematically the surface roughness of the squeeze film bearings. The modified averaged stochastic Reynolds equation governing the squeeze film pressure is derived. The expressions for the squeeze film pressure, load carrying capacity and squeeze film time are obtained. Numerical computations of the results show that the negatively skewed surface roughness pattern increases the load carrying capacity and squeeze film time. On the contrary the performance of squeeze film suffers due to positively skewed surface roughness pattern. Further the magnetic effect characterized by the Hartmann number improves the performance of the squeeze film lubrication as compared to the classical non-conducting lubricant case.

Evaluation of egg production in layers using random regression models

The objectives of this study were to estimate genetic parameters for egg production over the age trajectory in 3 layer lines, which represent different biotypes for egg production, and to validate the use of breeding values for slope as a measure of persistency to be used in the selection program. Egg production of more than 26,000 layers per line from 6 consecutive generations were analyzed with a random regression model with a within-hatch-nested fifth-order fixed-regression polynomial and linear polynomials for random additive genetic and permanent environmental effects. Daily records were cumulated into biweekly periods. In all lines, a nonzero genetic variance for mean and slope and a positive genetic correlation between mean and slope were estimated. Genetic variance of egg production by 2-wk period was low at the beginning of lay and increased as the birds aged for all 3 lines, which resulted in heritability estimates increasing with age. Breeding values for slope reflected the shape of the egg production curve well and can be used to directly select for persistency of egg production.

The impact of renormalization on the observable predictions of inflation

We analyze the generation of primordial perturbations in a (single-field) slow-roll inflationary universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a non-zero variance Δ2(k,t). However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize Δ2(k,t). This can be achieved by proper renormalization in an expanding universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the CMB anisotropies is significantly altered.

Hydrodynamic analysis of rough curved pivoted porous slider bearings with couple stress fluid

The purpose of this paper is to study the effect of surface roughness on the performance of curved pivoted porous slider bearings lubricated with couple stress fluid. The modified B–J slip boundary condition is utilised at the porous/fluid film interface to derive the Reynolds type equation for the problem under consideration. To mathematically model the surface roughness due to non-uniform rubbing of bearing surfaces, a stochastic random variable with non-zero mean, variance and skewness is considered. The closed form solution is obtained for the averaged Reynolds equation, and the compact expressions for the mean fluid film pressure mean load carrying capacity, frictional force and the centre of pressure are obtained. The numerical computations of the results show the improved performance due to the couplestresses and the presence of negatively skewed surface roughness. However, the presence of porous facing and positively skewed surface roughness affects the performance of the pivoted porous slider bearing.

Inflation, renormalization, and CMB anisotropies

In single-field, slow-roll inflationary models, scalar and tensorial (Gaussian) perturbations are both characterized by a zero mean and a non-zero variance. In position space, the corresponding variance of those fields diverges in the ultraviolet. The requirement of a finite variance in position space forces its regularization via quantum field renormalization in an expanding universe. This has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales. In particular, we find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio r to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, nt = 0, is now compatible with a non-zero ratio r ≈ 0.12 ± 0.06, which is forbidden by the standard prediction (r = −8nt). Forthcoming observations of the influence of relic gravitational waves on the CMB will offer a non-trivial test of the new predictions.

ON THE PERFORMANCE OF ROUGH INCLINED STEPPED COMPOSITE BEARINGS WITH MICROPOLAR FLUID

In this paper, a theoretical analysis of the effect of surface roughness on the lubrication characteristics of inclined stepped composite bearings with micropolar fluid is examined. A generalized form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The generalized average Reynolds type equation is derived for the rough inclined stepped composite bearings with micropolar fluid. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force. These expressions can be utilized to obtain the performance characteristics of four different types of bearing system viz; rough plane inclined slider, rough composite tapered land bearing, rough stepped bearing and rough composite tapered concave bearing. The numerical computations of the results show that the negatively skewed surface roughness pattern increases fluid film pressure, load carrying capacity and decreases the coefficient of friction whereas adverse effects were found for the positively skewed surface roughness pattern. Further, the rough inclined stepped slider bearing provides the largest load carrying capacity and the least coefficient of friction as compared to the other three geometries under consideration.

Revising the observable consequences of slow-roll inflation

We study the generation of primordial perturbations in a (single-field) slow-roll inflationary universe. In momentum space, these (Gaussian) perturbations are characterized by a zero mean and a non-zero variance $\Delta^2(k, t)$. However, in position space the variance diverges in the ultraviolet. The requirement of a finite variance in position space forces one to regularize $\Delta^2(k, t)$. This can (and should) be achieved by proper renormalization in an expanding universe in a unique way. This affects the predicted scalar and tensorial power spectra (evaluated when the modes acquire classical properties) for wavelengths that today are at observable scales. As a consequence, the imprint of slow-roll inflation on the CMB anisotropies is significantly altered. We find a non-trivial change in the consistency condition that relates the tensor-to-scalar ratio $r$ to the spectral indices. For instance, an exact scale-invariant tensorial power spectrum, $n_t=0$, is now compatible with a non-zero ratio $r\approx 0.12\pm0.06$, which is forbidden by the standard prediction ($r=-8n_t$). The influence of relic gravitational waves on the CMB may soon come within the range of planned measurements, offering a non-trivial test of the new predictions.

A Study Of Magnetic Fluid Based Squeeze Film Between Porous Rough Elliptical Plates

Efforts have been made to study and analyze the effect of surface roughness on the performance of magnetic fluid based squeeze film between porous elliptic plates. The transverse roughness of the bearing surface is characterized by a stochastic random variable with non-zero mean, variance and skewness. The associated Reynolds’ equation is solved with appropriate boundary conditions to obtain the pressure distribution leading to the calculation of load carrying capacity. It is observed that the load carrying capacity increases with respect to the magnetization parameter. This increase assumes significance especially when aspect ratio gets increased. However, it is noticed that more or less the bearing suffers owing to transverse surface roughness. Further, it isseen that negatively skewed roughness enhances the performance of thebearing system for suitable choices of variance. The performance of thebearing system records a significant improvement with the increasing values of the aspect ratio when negative variance occurs. Besides, the response time almost follows the trends of load carrying capacity. A close glance at the graphs reveals that the bearing system may register a considerably enhanced performance by choosing a suitable combination of magnetization parameter and the aspect ratio in the case of negatively skewed roughness.Key words: Magnetic fluid, Reynolds’ equation, Transverse roughness, Squeeze film, Load carrying capacity.

Water waves over a random bottom

This paper gives a new derivation and an analysis of long-wave model equations for the dynamics of the free surface of a body of water which has random bathymetry. This is a problem of hydrodynamical significance to coastal regions and to global-scale propagation of tsunamis, for which there may be imperfect knowledge of the detailed topography of the bottom. The surface motion is assumed to be in a long-wavelength dynamical regime, while the bottom of the fluid region is given by a stationary random process whose realizations vary over short length scales and are decorrelated on the longer principal length scale of the surface waves. Our basic conclusions are that coherent solutions propagating over a random bottom maintain basic properties of their structure over long distances, but however, the effect of the random bottom introduces uncertainty in the location of the solution profile and modifies the amplitude by random factors. It also gives rise to a random scattered component of the solution, but this does not result in the dispersion of the principal component of the solution, at least over length and time scales considered in this regime. We illustrate these results with numerical simulations.The mathematical question is one of homogenization theory in the long-wave scaling regime, for which our work is a reappraisal of the paper of Rosales & Papanicolaou (Stud. Appl. Math., vol. 68, 1983, pp. 89–102). In particular, we derive appropriate Boussinesq and Korteweg–deVries type equations with random coefficients which describe the free-surface evolution in this regime. The derivation is performed from the point of view of perturbation theory for Hamiltonian partial differential equations with a small parameter, with a subsequent analysis of the random effects in the resulting solutions. In the analysis, we highlight the distinction between the effective equations for a fixed typical realization, for which there are coherent solitary-wave solutions, and their ensemble average, which may exhibit diffusive effects. Our results extend the prior analysis to the case of non-zero variance σ2β > 0, and furthermore the analysis identifies the canonical limit random process as a white noise with covariance σβ2δ(X − X′) and quantifies the variations in phase and amplitude of the principal and scattered components of solutions. We find that the random topography can give rise to an additional linear term in the KdV limit equations, which depends upon a skew property of the random process and whose sign affects the stability of solutions. Finally we generalize this analysis to the case in which the bottom has large-scale deterministic variations on which are superposed random fluctuations with slowly varying statistical properties.

Accurate tests and intervals based on nonlinear cusum statistics

Suppose that we are monitoring incoming observations for a change in mean via a cusum test statistic. The usual nonparametric methods give first and second order approximations for the one- and two-sided cases. Withers and Nadarajah [2009. Accurate tests and intervals based on linear cusum statistics. Statistics and Probability Letters 79, 689–697] showed how to improve the order of these approximations for linear statistics. Here, an extension is provided for nonlinear statistics with non-zero asymptotic variances. This involves development of two calculi analogous to that of von Mises.

Analysis of squeeze film performance between rough porous infinitely long parallel plates with porous matrix of non-uniform thickness under presence of magnetic fluid lubricant

The performance of a magnetic fluid based squeeze film between infinitely long porous rough parallel plates with porous matrix of non-uniform thickness has been investigated. The bearing surfaces are considered to be transversely rough. The stochastic film thickness characterising the random roughness is assumed to be asymmetric with non-zero mean and variance. A magnetic fluid is used as a lubricant and the external magnetic field is oblique to the lower plate. With usual assumptions of hydrodynamic lubrication the associated Reynolds' equation is solved with suitable boundary conditions. Then expressions for pressure distribution, load carrying capacity and response time are obtained. It is observed that the load carrying capacity increases nominally due to magnetic fluid lubricant resulting in improved performance. But it is also seen that the composite roughness of the bearing surfaces introduces an adverse effect which gets more compounded due to the thickness ratio. However, the negative effect can be compensated to certain extent by the magnetic fluid lubricant in the case of negatively skewed roughness. This compensation further enhances when negative variance is involved. This study tends to suggest that the thickness ratio may play a crucial role for a better performance of the magnetic fluid based bearing system besides providing an additional degree of freedom.

Time-averaged properties of unstable periodic orbits and chaotic orbits in ordinary differential equation systems

It has recently been found in some dynamical systems in fluid dynamics that only a few unstable periodic orbits (UPOs) with low periods can give good approximations to the mean properties of turbulent (chaotic) solutions. By employing three chaotic systems described by ordinary differential equations, we compare time-averaged properties of a set of UPOs and those of a set of segments of chaotic orbits. For every chaotic system we study, the distributions of a time average of a dynamical variable along UPOs with lower and higher periods are similar to each other and the variance of the distribution is small, in contrast with that along chaotic segments. The distribution seems to converge to some limiting distribution with nonzero variance as the period of the UPO increases, although that along chaotic orbits inclines to converge to a delta -like distribution. These properties seem to lie in the background of why only a few UPOs with low periods can give good mean statistical properties in dynamical systems in fluid dynamics.

Stability of random brain networks with excitatory and inhibitory connections

Stability of randomly connected networks of neural populations with randomly distributed excitatory and inhibitory connections is investigated using a simplified physiologically-based model of brain electrical activity. Connections within a random network are randomly assigned to be excitatory or inhibitory, and the strengths of excitatory and inhibitory connections have two distinct distributions. Stability is shown to depend on the size of the network, the connection probability, and the mean and variance of the network's distribution of connection strengths, thus constraining these quantities. Networks with a nonzero variance for their excitatory and inhibitory strengths are less likely to be stable than networks with zero variance. The effect of changes in overall network activity on an individual population is also investigated. The maximum excitatory and inhibitory inputs into a population are constrained by stability and occur when the magnitudes of the mean excitatory and inhibitory connection strengths are equal and the proportion of connections that are inhibitory has a fixed value less than 0.5 . Results consistent with experimentally determined brain networks.

Behaviour of hydromagnetic squeeze films between two conducting rough porous circular plates

In this paper, the problem of squeeze films between electrically conducting rough porous surfaces and electrically conducting lubricant in the presence of transverse magnetic field is investigated for circular shape of the bearing surfaces. The bearing surfaces are assumed to be transversely rough. The roughness of the bearing surface is modelled by a stochastic random variable with non-zero mean, variance, and skewness. The associated Reynolds equation is stochastically averaged with respect to the random roughness parameter. Then, it is solved with appropriate boundary conditions to get the pressure distribution, which is further used to obtain the load carrying capacity leading to the calculation of response time. The results are presented graphically. It is noticed that the bearing suffers on account of transverse surface roughness in general. However, the situation can be retrieved up to a certain extent in the case of negatively skewed roughness especially, when negative variance occurs by suitable choice of plate conductivities. In addition, it is observed that the bearing with magnetic field can support a load even when there is no flow.

Surface roughness effects on the static and dynamic behaviour of squeeze film lubrication of short journal bearings with micropolar fluids

The theoretical study of the effect of surface roughness on the squeeze film lubrication of short journal bearings with no journal rotation under fluctuating loads with micropolar fluids is made. A more general form of surface roughness is mathematically modelled by a stochastic random variable with non-zero mean, variance, and skewness. The generalized average Reynolds type equation is derived for the squeeze film lubrication of rough journal bearings with micropolar fluids as lubricant. The closed form expressions for the bearing characteristics are obtained. The cases of a constant applied load and an alternating applied load are analysed. Under a cyclic load the micropolar fluids provide a reduction in the journal centre velocity. Further, it is observed that, the presence of microstructure additives and the negatively skewed surface roughness on the bearing surface increases the load carrying capacity and decreases the journal centre velocity.

Analytical Model of the DC Actuation of Electrostatic MEMS Devices With Distributed Dielectric Charging and Nonplanar Electrodes

This paper gives a new insight into the problem of the irreversible stiction of RF microelectromechanical systems (MEMS) attributed to the dielectric charging. We present a model for the electrostatic actuation of MEMS devices taking into account the nonuniform distributions of the air gap and the charges in the dielectric layer. The major result of our study is the impossibility to invoke the sole uniform dielectric charging phenomenon to explain the irreversible stiction of electrostatic MEMS devices. In the absence of other forces, a nonzero variance of the charge distribution is required to explain the stiction of the device. Considering only uniform residual charge densities, previous reported works could only account for a drift of the actuation characteristics as a whole. In case of a uniform air-gap distribution, our analytical model can already account for an increase of the up-capacitance, a shift of the - , its narrowing, and the stiction by a closure of the pull-out window. We further show that the combined nonuniformities of air gaps and charges break the symmetry of the actuation characteristics. The asymmetry can be such that one of the pull-in points disappears, which is replaced by a continuous tuning range while the other pull-in point still exists.

Combined effects of surface roughness and couple stresses on static and dynamic behaviour of squeeze film lubrication of porous journal bearings

The combined effects of surface roughness and the couple stresses on the static and dynamic characteristics of squeeze film lubrication in porous journal bearings with no journal rotation are theoretically studied. The Stokes couple stress fluid model is considered to model the lubricants with additives. The surface roughness on the porous journal bearing is mathematically modelled by a random variable with non-zero mean, variance and skewness. The generalised stochastic Reynolds type equation is derived for the problem under consideration. The applied load is considered as a sinusoidal function of time to simulate the bearings operating under cyclic loads. The closed form expressions for the bearing characteristics are obtained for the short porous journal bearings. It is observed that the negatively skewed surface roughness and couple stresses improve the performance of the porous journal bearings as compared to the smooth journal bearings with Newtonian lubricants. However, the presence of positively skewed surface roughness on the bearing surface affects its performance.

Incorporation of Inter‐individual Heterogeneity into the Multistage Carcinogenesis Model: Approach to the Analysis of Cancer Incidence Data

We investigate a multistage carcinogenesis frailty model to incorporate inter-individual heterogeneity into carcinogenic response. Attention is focused on inference concerning the effects of different sources of population heterogeneity on cancer rates. The authors consider unobserved variability arising from either carcinogen exposure or background characteristics. Gamma and Inverse-Gaussian distributions are selected for frailty models, and the baseline hazard function is the generalized Armitage-Doll model (i.e. non-frailty model) in which exposure effects shift the age scale instead of acting multiplicatively on cancer rates. For illustration, we apply the method to solid cancer data from a cohort of atomic bomb survivors to examine some features of proposed models. The results show that the Gamma frailty model for the heterogeneity of baseline rates provides the best goodness-of-fit of the model and a non-zero frailty variance. Parameter estimates are, for the most part, comparable between the Gamma and Inverse-Gaussian frailty models. In a heterogeneous population the exposure effects on young adulthood cancer rates might be underestimated for the non-frailty model. Meaningful information regarding each source of heterogeneity has been provided by the proposed method. Therefore, the multistage carcinogenesis frailty model approach is useful for analyses of epidemiological cancer data to assess population heterogeneity and heterogeneity-influenced exposure effects.