Langevin dual equations for nonlinear multiports

It is shown that the Langevin equations for equilibrium nonlinear multiports comprise a set of dual matrix linear integral transforms, which link a matrix ensemble of noise short-circuit current realizations and that of noise open-circuit voltage realizations; the matrix kernel of each integral transform is entirely determined by linear characteristics of the nonlinear electrical multiport.     

On nonlinear structure of electrical noise generated by slow discharge

Nonlinear structure of electrical noise of slow electrochemical discharge is analyzed within theory of integral random homogeneous fluxes with independent increments. It is shown that the degree of deviation of a flux of elementary acts from the Poissonian flux is defined by the magnitude of the factor of symmetry of slow discharge. An equation that links polyspectra of slow discharge of first, second, and third orders is derived.     

Characterisation of light emitting diodes (LEDs) for application in digital holographic microscopy for inspection of micro and nanostructured surfaces

Partial coherent light sources open up prospects for phase noise reduction in digital holographically reconstructed phase distributions by suppressing multiple reflections in the experimental setup. Thus, light emitting diodes (LEDs) are investigated for application in digital holographic microscopy. First, the spectral properties and the resulting coherence length of an LED are characterised. In addition, an analysis of dispersion effects and their influence on the hologram formation is carried out. The coherence length of LEDs in the range of a few micrometers restricts the maximum interference fringe number in off-axis holography for spatial phase shifting. Thus, the application of temporal phase-shifting-based digital holographic reconstruction techniques is compared to spatial phase-shifting-based methods. It is demonstrated that LEDs are applicable for digital holographic microscopy in connection with both spatial and temporal phase-shifting-based techniques for reduction of noise in comparison to a laser-light-based experimental setup.     

Prediction of noise inside tracked vehicles

In this paper, numerical simulation has been used to predict the noise inside tracked vehicles. To determine the interaction forces between running track system and the chassis hull of a tracked vehicle, a rigid multi-body tracked vehicle mode, which includes the track moving system, was constructed and simulated using ADAMS software. Finite element (FE) and boundary element (BE) models of the chassis hull of a tracked vehicle were created and adopted to perform the vibro-acoustic analysis. Correlation between the FE and BE models and physical measurements proved sufficiently good that the models could be used to predict the interior noise in a tracked vehicle. The structural frequency dynamic response was determined using the software MSC/NASTRAN. The interior noise was predicted using the software SYSNOISE. The predicted noise levels in a tracked vehicle have been found to be in good agreement with physical measurements.     

Temperature effect on tyre-road noise

Tyre-road noise emission decreases when the outdoor temperature increases, with a variation that can exceed −0.1 dB(A)/°C. This effect depends on tyre-road combination, but semi-generic corrections can improve the accuracy of tyre-road noise measurements. In this paper, the variation of pass-by noise level of a passenger car at 90 km/h with temperature is investigated, on seven types of road surfaces, under different temperature conditions. A good correlation between air, road surface and tyre temperature is outlined. A linear relationship between noise level and air temperature variations is observed for bituminous pavements, of about −0.1 dB(A)/°C, but reduced to −0.06 dB(A)/°C for pavements having porosity. No temperature effect is observed on cement concrete pavements. A spectral analysis shows that the temperature effect is highest in low and high frequency range, what can be explained by generating mechanisms rather than propagation.     

Jump Type Cahn-Hilliard Equations with Fractional Noises

The authors explore a class of jump type Cahn-Hilliard equations with fractional noises. The jump component is described by a （pure jump） Lévy space-time white noise. A fixed point scheme is used to investigate the existence of a unique local mild solution under some appropriate assumptions on coefficients.     

On the anomalous flicker noise intensity in high-temperature superconductors

The problem of anomalously high levels of flicker noise observed in the normal state of the high-temperature superconductors is addressed. It is argued that the anomaly is the result of incorrect normalization of the power spectra according to the Hooge formula. A careful analysis of the available experimental data is given, which shows that the scaling of the spectral power with sample size is essentially different from the inverse proportionality. It is demonstrated that the measured spectra obey the law given by the recently proposed quantum theory of fundamental flicker noise.     

A comparison of liquid–liquid porosimetry equations for evaluation of pore size distribution

This paper reviews and numerically tests many of the methods for the determination of pore size distribution of liquid membranes by liquid–liquid porosimetry. The flux through membranes was defined for flow of two immiscible liquids when drops or a liquid jet is formed, as well as the case when the interface is forced out by sufficient pressure. Several methods from literature for the determination of pore size distribution, some variations of these, and one new method are presented with a consistent theoretical basis. Using numerical tests it was found that all methods were very sensitive to measurement noise as low as ±0.1%, and that some form of data smoothing, such as a smoothing spline, was required to obtain a satisfactory distribution. The effects of elastic and permanent membrane compression were tested and a method was proposed to reduce the resulting error. A method based on the ratio of flux liquids with and without a liquid–liquid interface was recommended as it was less sensitive to the effects of compression in some cases and it provides a check when compression is not repeatable.     

Numerical solution of differential equations with colored noise

Using the general theory of numerical integration of stochastic differential equations, a constructive approach to numerical methods for a system with colored noise is proposed. Efficient methods up to the 5/2 strong order and up to the third weak order, including Runge-Kutta and implicit schemes, are presented. The algorithms are tested on the Kubo oscillator.     

Schlesinger Transformations for Linearisable Equations

A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every Itô algebra with a quotient identity has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular, every quantum thermal noise of a finite number of degrees of freedom is the orthogonal sum of a quantum Wiener noise and a quantum Poisson noise as it is stated by the Lévy–Khinchin Theorem in the classical case. Two basic examples of noncommutative Itô finite group algebras are considered.