Results 1  10
of
12
Turbulent Wind Fields for Gaseous Phenomena
, 1993
"... The realistic depiction of smoke, steam, mist and water reacting to a turbulent field such as wind is an attractive and challenging problem. Its solution requires interlocking models for turbulent fields, gaseous flow, and realistic illumination. We present a model for turbulent wind flow having a d ..."
Abstract

Cited by 135 (11 self)
 Add to MetaCart
(Show Context)
The realistic depiction of smoke, steam, mist and water reacting to a turbulent field such as wind is an attractive and challenging problem. Its solution requires interlocking models for turbulent fields, gaseous flow, and realistic illumination. We present a model for turbulent wind flow having a deterministic component to specify largescale behaviour, and a stochastic component to model turbulent smallscale behaviour. The smallscale component is generated using spacetime Fourier synthesis. Turbulent wind fields can be superposed interactively to create subtle behaviour. An advectiondiffusion model is used to animate particlebased gaseous phenomena embedded in a wind field, and we derive an efficient physicallybased illumination model for rendering the system. Because the number of particles can be quite large, we present a clustering algorithm for efficient animation and rendering. CR Categories and Subject Descriptors: I.3.7 [Com puter Graphics]: ThreeDimensional Graphics...
Generalized Stochastic Subdivision
 ACM Transactions on Graphics
, 1987
"... This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functi ..."
Abstract

Cited by 42 (3 self)
 Add to MetaCart
(Show Context)
This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct highquality random functions, including those with nonfractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism <F11.
A MultipleScale Stochastic Modelling Primitive
"... Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling threedimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements, and by a general lack of user c ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
(Show Context)
Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling threedimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements, and by a general lack of user control. We will present a general stochastic modelling primitive that operates on two or more scales of visual detail, and which offers considerable flexibility and control of the model. At the macroscopic level, the general shape of the model is constrained by an ellipsoidal correlation function that controls the interpolation of usersupplied data values. We use a technique called Kri#in# to perform this interpolation. The microscopic level permits the addition of noise, which allows a user to add interesting visual textural detail and translucency. A wide variety of noisesynthesis techniques can be employed in our model. We shall describe the mathematical structure of our model, and give an attractive rendering implementation that can be embedded in a traditional ray tracer rather than requiring a volume renderer. As an example, we shall apply our approach to the modelling of clouds.
A Cosmic string specific signature on the cosmic microwave background,” Astrophys
 J
, 1994
"... Using an analytical model for the string network we show that the kurtosis of cosmic microwave background (CMB) temperature gradient maps is a good statistic to distinguish between the cosmic string model and inflationary models of structure formation. The difference between the stringy and inflatio ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Using an analytical model for the string network we show that the kurtosis of cosmic microwave background (CMB) temperature gradient maps is a good statistic to distinguish between the cosmic string model and inflationary models of structure formation. The difference between the stringy and inflationary value for the kurtosis is inversely proportional to the angular resolution and to the number of strings per Hubble volume of the strings ’ scaling solution. If strings are indeed responsible for CMB anisotropies then experiments with resolutions of a couple of arcminutes or smaller could determine it using this statistic. 1
A MultiScale Stochastic Model for Computer Graphics
, 1991
"... Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling threedimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements, and by a general lack of user c ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Stochastic modelling has been successfully used in computer graphics to model a wide array of natural phenomena. In modelling threedimensional fuzzy or partially translucent phenomena, however, many approaches are hampered by high memory and computation requirements, and by a general lack of user control. The main contribution of this thesis is the introduction of a general stochastic modelling primitive that operates on two or more scales of visual detail. At the macroscopic level, the general shape of the model is constrained by an ellipsoidal correlation function that controls the interpolation of usersupplied data values. A technique called Kriging is used to perform this interpolation. The microscopic level permits the addition of noise, which allows one to add interesting visual textural detail and translucency. A wide variety of noisesynthesis techniques can be employed in our model. The main advantages of the model over existing ones are low storage requirements and the use o...
unknown title
"... The stochastic finite element analysis of elliptic type partial differential equations are considered. An alternative approach by projecting the solution of the discretized equation into a finite dimensional orthonormal vector basis is investigated. It is shown that the solution can be obtained usi ..."
Abstract
 Add to MetaCart
(Show Context)
The stochastic finite element analysis of elliptic type partial differential equations are considered. An alternative approach by projecting the solution of the discretized equation into a finite dimensional orthonormal vector basis is investigated. It is shown that the solution can be obtained using a finite series comprising functions of random variables and orthonormal vectors. These functions, called as the spectral functions, can be expressed in terms of the spectral properties of the deterministic coefficient matrices arising due to the discretization of the governing partial differential equation. An explicit relationship between these functions and polynomial chaos functions has been derived. Based on the projection in the orthonormal vector basis, a Galerkin error minimization approach is proposed. The constants appearing in the Galerkin method are solved from a system of linear equations which has the same dimension as the original discretized equation. A hybrid analytical and simulation based computational approach is proposed to obtain the moments and pdf of the solution. The method is illustrated using a stochastic beam problem. The results are compared with the direct Monte Carlo simulation results for different correlation lengths and strengths of randomness.
unknown title
"... If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have poi ..."
Abstract
 Add to MetaCart
If you place a large number of points randomly in the unit square, what is the distribution of the radius of the largest circle containing no points? Of the smallest circle containing 4 points? Why do Brownian sample paths have local maxima but not points of increase, and how nearly do they have points of increase? Given two long strings of letters drawn i.i.d. from a finite alphabet, how long is the longest consecutive (resp. nonconsecutive) substring appearing in both strings? If an imaginary particle performs a simple random walk on the vertices of a highdimensional cube, how long does it take to visit every vertex? If a particle moves under the influence of a potential field and random perturbations of velocity, how long does it take to escape from a deep potential well? If cars on a freeway move with constant speed (random from car to car), what is the longest stretch of empty road you will see during a long journey? If you take a large i.i.d. sample from a 2dimensional rotationallyinvariant distribution, what is the maximum over all halfspaces of the deviation between the empirical and
Bayesian Soil Assessments Combining Prior with Posterior Censored Samples
"... . The geotechnical engineer is often faced with the problem of how to assess the statistical properties of a soil parameter on the basis of a sample measured insitu or in the laboratory with the defect that some values have been replaced by interval bounds because the corresponding soil parameter v ..."
Abstract
 Add to MetaCart
. The geotechnical engineer is often faced with the problem of how to assess the statistical properties of a soil parameter on the basis of a sample measured insitu or in the laboratory with the defect that some values have been replaced by interval bounds because the corresponding soil parameter values have turned out to exceed the capacity of the measuring instrument. Given such a censored sample the problem is to estimate the mean value, variance and certain fractiles of the distribution of the soil parameter as it would be measured by an instrument of unrestricted range. In many situations only a small censored sample is given. To estimate the characteristic value defined as a lower fractile value corresponding to a codified probability value, the geotechnical engineer is thus urged to supplement the information from the measurements at the actual location by considering whatever prior knowledge is available about the soil parameter distribution. The present paper shows how a char...
Climate change, the Hurst phenomenon, and
, 2003
"... Abstract The intensive research of recent years on climate change has led to the strong conclusion that climate has always, throughout the Earth’s history, changed irregularly on all time scales. Climate changes are closely related to the Hurst phenomenon, which has been detected in many long hydroc ..."
Abstract
 Add to MetaCart
Abstract The intensive research of recent years on climate change has led to the strong conclusion that climate has always, throughout the Earth’s history, changed irregularly on all time scales. Climate changes are closely related to the Hurst phenomenon, which has been detected in many long hydroclimatic time series and is stochastically equivalent to a simple scaling behaviour of climate variability over time scale. The climate variability, anthropogenic or natural, increases the uncertainty of the hydrological processes. It is shown that hydrological statistics, the branch of hydrology that deals with uncertainty, in its current state is not consistent with the varying character of climate. Typical statistics used in hydrology such as means, variances, cross and autocorrelations and Hurst coefficients, and the variability thereof, are revisited under the hypothesis of a varying climate following a simple scaling law, and new estimators are studied which, in many cases, differ dramatically from the classical ones. The new statistical framework is applied to realworld examples for typical tasks such as estimation and hypothesis testing where, again, the results depart significantly from those of the classical statistics.