Thermodynamics of three-dimensional Ising-like systems in the higher non-Gaussian approximation: Calculational method and dependence on microscopic parameters

2002 ◽  
Vol 66 (13) ◽  
Author(s):  
I. R. Yukhnovskii ◽  
M. P. Kozlovskii ◽  
I. V. Pylyuk
Keyword(s):  
Gaussian Approximation ◽  
Three Dimensional ◽  
Calculational Method ◽  
Non Gaussian

Critical behavior of a 3D Ising-like system in the higher non-Gaussian approximation: Inclusion of the critical exponent of the correlation function

2014 ◽  
Vol 28 (24) ◽  
pp. 1450160 ◽  
Author(s):  
I. R. Yukhnovskii ◽  
M. P. Kozlovskii ◽  
I. V. Pylyuk
Keyword(s):  
Correlation Function ◽  
Critical Exponent ◽  
Critical Behavior ◽  
Gaussian Approximation ◽  
Three Dimensional ◽  
Universality Class ◽  
Spin Moment ◽  
Collective Variables ◽  
Function Calculation ◽  
Non Gaussian

A microscopic description of the critical behavior of systems belonging to the universality class of the three-dimensional (3D) Ising model is developed within the collective variables (CV) approach. The higher non-Gaussian approximation (the sextic distribution for the modes of spin-moment density oscillations or the ρ6 model) is used. A specific feature of the partition function calculation for an Ising-like system is the inclusion of the correction for the potential averaging. This correction leads to the modified recurrence relations (RR) for the ρ6 model and a nonzero critical exponent of the correlation function η. The RR between the coefficients of the effective sextic distributions are written and analyzed. A technique for determining the small critical exponent η is elaborated in the higher non-Gaussian approximation. It is shown that the renormalized critical exponent of the correlation length has a tendency to a reduction in the case when the exponent η is taken into account.

scholarly journals Free Energy of Three-Dimensional Uniaxial Magnet in the Higher Non-Gaussian Approximation and in the Presence of an External Field

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
M. P. Kozlovskii ◽  
I. V. Pylyuk
Keyword(s):  
Free Energy ◽  
External Field ◽  
Statistical Physics ◽  
Recurrence Relations ◽  
Gaussian Approximation ◽  
Three Dimensional ◽  
Crossover Region ◽  
Effective Measure ◽  
Calculation Technique ◽  
Non Gaussian

A three-dimensional Ising-like system in a homogeneous external field is studied on the basis of the higher non-Gaussian measure density (the model). The presented solutions of recurrence relations for the coefficients of the effective measure densities and the generalized point of exit of the system from the critical regime are used for calculating the free energy of the system at temperatures ( is the phase transition temperature in the absence of an external field). A calculation technique is based on the first principles of statistical physics and is naturally realized without any general assumptions and without any adjustable parameters. The obtained expression for the free energy does not involve series expansions in the scaling variable and is valid near the critical point not only in the regions of the so-called weak and strong external fields, but also in the crossover region between these fields, where power series in the scaling variable are not effective.

Adaptive and augmented nonlinear filters : theory and applications

2018 ◽  
Author(s):  
◽  
Tao Sun
Keyword(s):  
Kalman Filter ◽  
Mean Square Error ◽  
Gaussian Approximation ◽  
Adaptive Strategy ◽  
Nonlinear Filters ◽  
Nonlinear Transformation ◽  
Mean Square ◽  
Gaussian Filters ◽  
Non Gaussian ◽  
Gaussian Estimation

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Nonlinear estimation and filtering have been intensively studied for decades since it has been widely used in engineering and science such as navigation, radar signal processing and target tracking systems. Because the posterior density function is not a Gaussian distribution, then the optimal solution is intractable. The nonlinear/non-Gaussian estimation problem is more challenging than the linear/Gaussian case, which has an optimal closed form solution, i.e. the celebrated Kalman filter. Many nonlinear filters including the extended Kalman filter, the unscented Kalman filter and the Gaussian-approximation filters, have been proposed to address nonlinear/non-Gaussian estimation problems in the past decades. Although the estimate yield by Gaussian-approximation filters such as cubature Kalman filters and Gaussian-Hermite quadrature filters is satisfied in many applications, there are two obvious drawbacks embedded in the use of Gaussian filters. On the one hand, with the increase of the quadrature points, much computational effort is devoted to approximate Gaussian integrals, which is not worthy sometimes. On the other hand, by the use of the update rule, the estimate constrains to be a linear function of the observation. In this dissertation, we aim to address this two shortcoming associated with the conventional nonlinear filters. We propose two nonlinear filters in the dissertation. Based on an adaptive strategy, the first one tries to reduce the computation cost during filtering without sacrificing much accuracy, because when the system is close to be linear, the lower level Gaussian quadrature filter is sufficient to provide accurate estimate. The adaptive strategy is used to evaluate the nonlinearity of the system at current time first and then utilize different quadrature rule for filtering. Another filter aims to modify the conventional update rule, i.e. the linear minimum mean square error (LMMSE) rule, to involve a nonlinear transformation of the observation, which is proven to be an efficient way to exploit more information from the original observation. According to the orthogonal property, we propose a novel approach to construct the nonlinear transformation systematically. The augmented nonlinear filter outperforms Gaussian filters and other conventional augmented filters in terms of the root mean square error and onsistency. Furthermore, we also extend the work to the more general case. The higher order moments can be utilized to construct the nonlinear transformation and in turn, the measurement space can be expand efficiently. Without the Gaussian assumption, the construction of the nonlinear transformation only demand the existence of a finite number of moments. Finally, the simulation results validate and demonstrate the superiority of the adaptive and augmented nonlinear filters.

Electroelasticity of dielectric elastomers based on molecular chain statistics

2018 ◽  
Vol 24 (3) ◽  
pp. 862-873 ◽  
Author(s):  
Mikhail Itskov ◽  
Vu Ngoc Khiêm ◽  
Sugeng Waluyo
Keyword(s):  
Constitutive Model ◽  
Polymer Chain ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Polymer Chains ◽  
Molecular Chain ◽  
Dielectric Elastomers ◽  
Finite Extensibility ◽  
Single Polymer Chain ◽  
Non Gaussian

The mechanical response of dielectric elastomers can be influenced or even controlled by an imposed electric field. It can, for example, cause mechanical stress or strain without any applied load; this phenomenon is referred to as electrostriction. There are many purely phenomenological hyperelastic models describing this electroactive response of dielectric elastomers. In this contribution, we propose an electromechanical constitutive model based on molecular chain statistics. The model considers polarization of single polymer chain segments and takes into account their directional distribution. The latter results from non-Gaussian chain statistics, taking finite extensibility of polymer chains into account. The resulting (one-dimensional) electric potential of a single polymer chain is further generalized to the (three-dimensional) network potential. To this end, we apply directional averaging on the basis of numerical integration over a unit sphere. In a special case of the eight-direction (Arruda–Boyce) model, directional averaging is obtained analytically. This results in an invariant-based electroelastic constitutive model of dielectric elastomers. The model includes a small number of physically interpretable material constants and demonstrates good agreement with experimental data, with respect to the electroactive response and electrostriction of dielectric elastomers.

scholarly journals Extended Particle-Aided Unscented Kalman Filter Based on Self-Driving Car Localization

2020 ◽  
Vol 10 (15) ◽  
pp. 5045 ◽  
Author(s):  
Ming Lin ◽  
Byeongwoo Kim
Keyword(s):  
Kalman Filter ◽  
Real World ◽  
Gaussian Noise ◽  
Unscented Kalman Filter ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Localization Problem ◽  
Simulation Results ◽  
Non Gaussian ◽  
Self Driving Cars

The location of the vehicle is a basic parameter for self-driving cars. The key problem of localization is the noise of the sensors. In previous research, we proposed a particle-aided unscented Kalman filter (PAUKF) to handle the localization problem in non-Gaussian noise environments. However, the previous basic PAUKF only considers the infrastructures in two dimensions (2D). This previous PAUKF 2D limitation rendered it inoperable in the real world, which is full of three-dimensional (3D) features. In this paper, we have extended the previous basic PAUKF’s particle weighting process based on the multivariable normal distribution for handling 3D features. The extended PAUKF also raises the feasibility of fusing multisource perception data into the PAUKF framework. The simulation results show that the extended PAUKF has better real-world applicability than the previous basic PAUKF.

The spatial structure and statistical properties of homogeneous turbulence

1991 ◽  
Vol 225 ◽  
pp. 1-20 ◽  
Author(s):  
A. Vincent ◽  
M. Meneguzzi
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Velocity Structure ◽  
Three Dimensional ◽  
Inertial Subrange ◽  
Integral Scale ◽  
Turbulent Field ◽  
Velocity Derivative ◽  
Non Gaussian

A direct numerical simulation at resolution 2403 is used to obtain a statistically stationary three-dimensional homogeneous and isotropic turbulent field at a Reynolds number around 1000 (Rλ ≈ 150). The energy spectrum displays an inertial subrange. The velocity derivative distribution, known to be strongly non-Gaussian, is found to be close to, but not, exponential. The nth-order moments of this distribution, as well as the velocity structure functions, do not scale with n as predicted by intermittency models. Visualization of the flow confirms the previous finding that the strongest vorticity is organized in very elongated thin tubes. The width of these tubes is of the order of a few dissipation scales, while their length can reach the integral scale of the flow.

RECOVERY OF NONRIGID STRUCTURES FROM 2D OBSERVATIONS

2008 ◽  
Vol 22 (02) ◽  
pp. 279-294 ◽  
Author(s):  
HUIYU ZHOU ◽  
XUELONG LI ◽  
TANGWEI LIU ◽  
FAQUAN LIN ◽  
YUSHENG PANG ◽  
...  
Keyword(s):  
3D Structure ◽  
Three Dimensional ◽  
Image Sequences ◽  
Nonrigid Motion ◽  
Feature Points ◽  
Variance Estimator ◽  
Deformable Structure ◽  
Non Gaussian ◽  
2D Data ◽  
Rigid Component

We present a new method for simultaneously determining three-dimensional (3D) motion and structure of a nonrigid object from its uncalibrated two-dimensional (2D) data with Gaussian or non-Gaussian distributions. A nonrigid motion can be treated as a combination of a rigid component and a nonrigid deformation. To reduce the high dimensionality of the deformable structure or shape, we estimate the probability distribution function (PDF) of the structure through random sampling, integrating an established probabilistic model. The fitting between the observations and the estimated 3D structure will be evaluated using the pooled variance estimator. The recovered structure is only available when the 2D feature points have been properly corresponded over two image frames. Applications of the proposed method to both synthetic and real image sequences are demonstrated with promising results.

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