scholarly journals On concentration properties of partially observed chaotic systems

2018 ◽  
Vol 50 (2) ◽  
pp. 440-479
Author(s):  
Daniel Paulin ◽  
Ajay Jasra ◽  
Dan Crisan ◽  
Alexandros Beskos
Keyword(s):  
Standard Deviation ◽  
Dynamical Systems ◽  
Geometric Model ◽  
Three Dimensional ◽  
Lorenz Equations ◽  
Chaotic Dynamical Systems ◽  
Partially Observed ◽  
True Position ◽  
Concentration Properties ◽  
Lorenz 96

AbstractIn this paper we present results on the concentration properties of the smoothing and filtering distributions of some partially observed chaotic dynamical systems. We show that, rather surprisingly, for the geometric model of the Lorenz equations, as well as some other chaotic dynamical systems, the smoothing and filtering distributions do not concentrate around the true position of the signal, as the number of observations tends to ∞. Instead, under various assumptions on the observation noise, we show that the expected value of the diameter of the support of the smoothing and filtering distributions remains lower bounded by a constant multiplied by the standard deviation of the noise, independently of the number of observations. Conversely, under rather general conditions, the diameter of the support of the smoothing and filtering distributions are upper bounded by a constant multiplied by the standard deviation of the noise. To some extent, applications to the three-dimensional Lorenz 63 model and to the Lorenz 96 model of arbitrarily large dimension are considered.

scholarly journals Quantification of Measurement and Model Effects in Monopile Foundation Scour Protection Experiments

2021 ◽  
Vol 9 (6) ◽  
pp. 585
Author(s):  
Minghao Wu ◽  
Leen De Vos ◽  
Carlos Emilio Arboleda Chavez ◽  
Vasiliki Stratigaki ◽  
Maximilian Streicher ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Flow Field ◽  
Three Dimensional ◽  
Small Scale ◽  
Maximum Wave Height ◽  
Chaotic Flow ◽  
The Mean ◽  
Scour Protection ◽  
Damage Number ◽  
Measurement Effects

The present work introduces an analysis of the measurement and model effects that exist in monopile scour protection experiments with repeated small scale tests. The damage erosion is calculated using the three dimensional global damage number S3D and subarea damage number S3D,i. Results show that the standard deviation of the global damage number σ(S3D)=0.257 and is approximately 20% of the mean S3D, and the standard deviation of the subarea damage number σ(S3D,i)=0.42 which can be up to 33% of the mean S3D. The irreproducible maximum wave height, chaotic flow field and non-repeatable armour layer construction are regarded as the main reasons for the occurrence of strong model effects. The measurement effects are limited to σ(S3D)=0.039 and σ(S3D,i)=0.083, which are minor compared to the model effects.

scholarly journals Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Vibration ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 49-63
Author(s):  
Waad Subber ◽  
Sayan Ghosh ◽  
Piyush Pandita ◽  
Yiming Zhang ◽  
Liping Wang
Keyword(s):  
Dynamical Systems ◽  
Computational Cost ◽  
Three Dimensional ◽  
Region Of Interest ◽  
System Response ◽  
Computational Domain ◽  
User Interest ◽  
Numerical Resolution ◽  
Multi Scale ◽  
Operation Conditions

Industrial dynamical systems often exhibit multi-scale responses due to material heterogeneity and complex operation conditions. The smallest length-scale of the systems dynamics controls the numerical resolution required to resolve the embedded physics. In practice however, high numerical resolution is only required in a confined region of the domain where fast dynamics or localized material variability is exhibited, whereas a coarser discretization can be sufficient in the rest majority of the domain. Partitioning the complex dynamical system into smaller easier-to-solve problems based on the localized dynamics and material variability can reduce the overall computational cost. The region of interest can be specified based on the localized features of the solution, user interest, and correlation length of the material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update the prior knowledge of the localized region of interest using measurements of the system response. Once, the region of interest is identified, the localized uncertainty is propagate forward through the computational domain. We demonstrate our framework using numerical experiments on a three-dimensional elastodynamic problem.

A New Geometric Model of Laid-in Weft-Knitted Fabrics

2021 ◽  
pp. 004051752199276
Author(s):  
Ki Wai Fong ◽  
Si Qing Li ◽  
Rong Liu
Keyword(s):  
Cost Estimation ◽  
Geometric Model ◽  
Three Dimensional ◽  
Wearable Electronics ◽  
Material Consumption ◽  
Knitted Fabrics ◽  
Functional Textiles ◽  
Loop Pattern ◽  
Spatial Configurations ◽  
Consumption Prediction

Inlay yarn and laid-in structures are important technical knitting elements that have been increasingly applied in the structural design of functional textiles in industrial, medical, and wearable electronics fields. However, there is no currently established geometric model to numerically analyze their spatial morphologies and structural properties. This study presents a new geometric model and numerical analysis approach to characterize spatial configurations of inlay yarn and ground yarn in a three-dimensional scenario for laid-in weft-knitted fabrics. Loop lengths of the inlay and ground yarn materials were calculated and analyzed under different contact and deformation conditions to estimate material consumption in this complex interlooping layout. Series of laid-in weft-knitted fabrics made of different combinations of ground and inlay yarns were fabricated with the 1 × 1 laid-in loop pattern and tested for the model validation. The comparisons between the experimental and calculated results indicated that the newly developed geometric model favorably agreed with the experimental measurements regarding the ground loop lengths and inlay loop lengths applied in the laid-in weft-knitted structures. The results indicated the applicability of the developed geometric model of laid-in weft-knitted fabrics with similar structural patterns in practical use. The output of this study provides a theoretical and practical reference for structural and physical properties analysis, material consumption prediction, even cost estimation of laid-in weft-knitted fabrics.

scholarly journals Forest Height Estimation Based on P-Band Pol-InSAR Modeling and Multi-Baseline Inversion

2020 ◽  
Vol 12 (8) ◽  
pp. 1319
Author(s):  
Xiaofan Sun ◽  
Bingnan Wang ◽  
Maosheng Xiang ◽  
Liangjiang Zhou ◽  
Shuai Jiang
Keyword(s):  
Standard Deviation ◽  
Vertical Structure ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Solution Space ◽  
Model Complexity ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Model Inversion ◽  
Forest Height

The Gaussian vertical backscatter (GVB) model has a pivotal role in describing the forest vertical structure more accurately, which is reflected by P-band polarimetric interferometric synthetic aperture radar (Pol-InSAR) with strong penetrability. The model uses a three-dimensional parameter space (forest height, Gaussian mean representing the strongest backscattered power elevation, and the corresponding standard deviation) to interpret the forest vertical structure. This paper establishes a two-dimensional GVB model by simplifying the three-dimensional one. Specifically, the two-dimensional GVB model includes the following three cases: the Gaussian mean is located at the bottom of the canopy, the Gaussian mean is located at the top of the canopy, as well as a constant volume profile. In the first two cases, only the forest height and the Gaussian standard deviation are variable. The above approximation operation generates a two-dimensional volume only coherence solution space on the complex plane. Based on the established two-dimensional GVB model, the three-baseline inversion is achieved without the null ground-to-volume ratio assumption. The proposed method improves the performance by 18.62% compared to the three-baseline Random Volume over Ground (RVoG) model inversion. In particular, in the area where the radar incidence angle is less than 0.6 rad, the proposed method improves the inversion accuracy by 34.71%. It suggests that the two-dimensional GVB model reduces the GVB model complexity while maintaining a strong description ability.

scholarly journals Simulation and Analysis of Floodlighting Based on 3D Computer Graphics

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1042
Author(s):  
Rafał Krupiński
Keyword(s):  
Computer Graphics ◽  
External Surface ◽  
Geometric Model ◽  
Three Dimensional ◽  
Fold Increase ◽  
Luminance Level ◽  
Object Model ◽  
Geometric Mesh ◽  
Average Luminance ◽  
To Receive

The paper presents the opportunities to apply computer graphics in an object floodlighting design process and in an analysis of object illumination. The course of object floodlighting design has been defined based on a virtual three-dimensional geometric model. The problems related to carrying out the analysis of lighting, calculating the average illuminance, luminance levels and determining the illuminated object surface area are also described. These parameters are directly tied with the calculations of the Floodlighting Utilisation Factor, and therefore, with the energy efficiency of the design as well as the aspects of light pollution of the natural environment. The paper shows how high an impact of the geometric model of the object has on the accuracy of photometric calculations. Very often the model contains the components that should not be taken into account in the photometric calculations. The research on what influence the purity of the geometric mesh of the illuminated object has on the obtained results is presented. It shows that the errors can be significant, but it is possible to optimise the 3D object model appropriately in order to receive the precise results. For the example object presented in this paper, removing the planes that do not constitute its external surface has caused a two-fold increase in the average illuminance and average luminance. This is dangerous because a designer who wants to achieve a specific average luminance level in their design without optimizing the model will obtain the luminance values that will actually be much higher.

Pseudorandom Number Generators Based on Chaotic Dynamical Systems

2001 ◽  
Vol 08 (02) ◽  
pp. 137-146 ◽  
Author(s):  
Janusz Szczepański ◽  
Zbigniew Kotulski
Keyword(s):  
Dynamical Systems ◽  
Communication Systems ◽  
Initial Conditions ◽  
Pseudorandom Number ◽  
New Approach ◽  
Chaotic Dynamical Systems ◽  
Pseudorandom Number Generators ◽  
Transmission Of Information ◽  
Extreme Sensitivity ◽  
Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

Development of mixing and isotropy in inviscid homogeneous turbulence

1982 ◽  
Vol 120 ◽  
pp. 155-183 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Dynamical Systems ◽  
Lower Order ◽  
Stokes System ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Fourier Space ◽  
Kolmogorov Entropy ◽  
Navier Stokes Equations ◽  
Constant Energy

We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic corre- lation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical charac- terization of positive Kolmogorov entropy (K-system).

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