Fluctuation and Noise Letters

Explicit formulae for correlation functions and fluctuation spectra of the irreducible three-state Markov processes are presented. The necessary and sufficient conditions of existing nonmonotonic fluctuation spectra on [0, +∞) with respect to real functions are given, which reveals that the nonequilibrium flux must be strong enough to produce a peak in the fluctuation spectrum and the monotonicity of fluctuation spectra is related to the time scales of Markov processes.

The Boltzmann equation with electron-electron (e − e) interactions has been reduced to a Fokker-Planck equation (e − e FP) in a previuos paper. In steady-state conditions, its solution q₀(v) (where v is the electron speed) depends on the square of the acceleration a = eE/m. If we introduce the nonrenormalized zero-point field (ZPF) of QED, i.e., the one considered in stochastic electrodynamics, so that , then q₀(v) becomes similar to the Fermi-Dirac equation, and the two collision frequencies ν₁(v) and ν₂(v) appearing in the e − e FP become both proportional to 1/v in a small δv interval. The condition ν₁(v) ∝ ν₂(v) ∝ 1/v is at the threshold of the runaways. In the same δv range, the time-dependent solution q₀(v,τ) of the e − e FP decays no longer exponentially but according to a power law ∝ τ^{− ɛ} where 0.004 < ɛ < 0.006, until τ → ∞. That extremely long memory of a fluctuation implies the same dependence τ ^{− ɛ} for the conductance correlation function, hence a corresponding power-spectral noise S(f) ∝ f^ɛ−1 where f is the frequency. That behaviour is maintained even for a small sample because the back diffusion velocity of the electrons in the effective range δv, where they are in runaway conditions, is much larger than the drift velocity.

Detecting community structure in real-world networks is a challenging problem. Recently, it has been shown that the resolution of methods based on optimizing a modularity measure or a corresponding energy is limited; communities with sizes below some threshold remain unresolved. One possibility to go around this problem is to vary the threshold by using a tuning parameter, and investigate the community structure at variable resolutions. Here, we analyze the resolution limit and multiresolution behavior for two different methods: a q-state Potts method proposed by Reichard and Bornholdt, and a recent multiresolution method by Arenas, Fernández, and Gómez. These methods are studied analytically, and applied to three test networks using simulated annealing.

We argue that when individuals enunciate sounds which are perceived to be the same, the sounds have the commonalty that their spectra can be transformed into a new domain which results in identical spectra except for a speaker dependent translation factor. We call the transformation function the speech scale. The speech scale is experimentally obtained. In this paper we explore the mathematical issues involved and obtain various criteria for when a transformation to a new domain results in a speaker independent transform.

The influence of time-delayed feedback on the dynamics of a net of oscillatory FitzHugh-Nagumo elements is investigated. We show that the global oscillation of the net can be suppressed (amplitude death) via time-delayed feedback for properly chosen delay time and feedback strength. The result of a linear stability analysis fits very well to the simulations. In the amplitude death regime, weak additive noise can induce excitation waves (noise-induced pattern formation), a fingerprint of excitable network dynamics.

In this paper we demonstrate that by exploiting the non linear characteristic of low noise PN junction diodes, a very low noise, high stability voltage reference can be obtained starting from a conventional solid state series voltage reference. In order to obtain such a result, a series connection of N identical diodes is supplied in the forward region of the I-V characteristic by means of a proper resistance. While the DC voltage drop across the diodes can be a large fraction of the voltage supplied by the reference, the noise introduced by the reference itself is reduced by a much larger factor because of the low value of the small signal equivalent resistance of the diodes. In its simplest implementation, such a voltage source would suffer from a relatively high temperature dependence of the supplied voltages because of the intrinsic properties of PN junctions. However, by resorting to a proper temperature control circuit, high stability can be obtained. As an example, by employing an AD586 voltage reference and with N = 4, a 2.560 V reference has been obtained with a stability over temperature better that 50 μV/°C and a voltage noise as low as 2 × 10⁻¹⁵, 6 × 10⁻¹⁷ and 1.5 × 10⁻¹⁷V²/Hz at 100 mHz, 1 Hz and for frequencies larger than 10 Hz, respectively.

Spatial and temporal fluctuations of the electric polarization were imaged in polymer thin films near the glass transition using electric force microscopy. Below the glass transition the fluctuations are quasi-static and spatial fluctuations were found to quantitatively agree with predictions for thermal fluctuations. Temporal fluctuations appear near the glass transition. Images of the space-time nanoscale dynamics near the glass transition are produced and analyzed. Local, complex dielectric susceptibility was also studied, and shows that dynamics on the free-surface are faster relative to the bulk.

Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long-range correlations in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short-range correlations in non stationary and stationary systems. Applying DFA to AR processes can help understanding the non-uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short-range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of an interaction between distant terms with characteristic time constant in the series, in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will significantly decrease the range of interaction, only. This analysis demonstrate the possibility to identify an AR(1) model in an unknown DFA plot or to distinguish between AR(1) and AR(2) models.

This paper presents a new on-line technique for denoising impulsive vibration signals in noisy environments using Wavelet Packets. The proposed algorithm is based on localizing the frequency subbands of the resonances embedded in impulsive vibration signals. The performance of the algorithm is evaluated in denoising real vibration signals measured from faulty bearings. The results compared to the theoretical values and those obtained by the HFD algorithm show the effectiveness of the proposed algorithm while the computational cost reduces to half.

Scaling regularities associated with additive noise are examined in a model of the pitch-fork bifurcation map with multiplicative quasiperiodic driving (Grebogi et al., Physica D13, 261) with the golden-mean frequency ratio at the birth of a strange nonchaotic attractor (SNA). This case of the onset of SNA termed as the blowout bifurcation route was discussed in the context of realistic systems governed by non-autonomous differential equations (Yalçynkaya and Lai, Phys. Rev. Lett., 77, 5039). Our method taking into the account of noise is based on renormalization group (RG) analysis of the birth of SNA (Kuznetsov et al., Phys. Rev. E51, 1629) with application of an appropriate generalization of the approach of Crutchfield et al. (Phys. Rev. Lett., 46, 933) and Shraiman et al. (Phys. Rev. Lett., 46, 935) originally developed for the period doubling transition to chaos. A constant γ=7.4246 is evaluated that determines the scaling law regarding the intensity of noise: A decrease of the noise amplitude by this factor allows resolving one more level of the fractal-like structure associated with the characteristic time scale which is increased by a factor of . Numeric results demonstrating evidence of the expected regularities are presented, e.g. portraits of the noisy attractors in different scales.

We study the statistical properties of community dynamics in large social networks, where the evolving communities are obtained from subsequent snapshots of the modular structure. Such cohesive groups of people can grow by recruiting new members, or contract by loosing members; two (or more) groups may merge into a single community, while a large enough social group can split into several smaller ones; new communities are born and old ones may disappear. We find significant difference between the behavior of smaller collaborative or friendship circles and larger communities, eg. institutions. Social groups containing only a few members persist longer on average when the fluctuations of the members is small. In contrast, we find that the condition for stability for large communities is continuous changes in their membership, allowing for the possibility that after some time practically all members are exchanged.

Analytical expressions for the PM noise in FET oscillators are derived in terms of the FET equivalent circuit elements and the passive circuitry. Efficient methods to reduce the PM noise in fundamental and in harmonic modes are suggested and implemented. The effects of the different FET equivalent circuit parameters on large-signal, small-signal, and noise behavior of FET oscillators are investigated. Finally, the effects of harmonic signal on the output noise power and on the phase noise at both fundamental and harmonic frequencies are determined.

Based on Boltzmann transport equation, the drift-diffusion, hydrodynamic, and Monte-Carlo physical simulators are accurately developed. For each simulator, the model equations are self-consistently solved with Poisson equation, and with Schrödinger equation when quantization effects take place, in one and two-dimensions to characterize the operation and optimize the structure of mm-wave devices. The effects of the device dimensions, biasing conditions, and operating frequencies on the accuracy of results obtained from the simulators are thoroughly investigated. Based on physical understanding of the models, the simulation results are analyzed to fully determine the limits at which a certain device simulator can be accurately and efficiently used to characterize the noise behavior of mm-wave devices.

In this work, the fluctuations in the spectrum level of shallow water ambient noise is analyzed for 3 different sea states. The shallow water ambient noise data were collected of Bay of Bengal using an omni directional hydrophone and a portable data acquisition system.100 sets of data were collected and organized according to the three different sea states using Beaufort scale. Fluctuations in noise spectrum level at different sea states were studied by dividing the spectral bandwidth of 12 kHz into low, mid and high frequency bands. Mean noise spectrum level for each sea state was calculated and the result shows the noise spectrum level increases with the sea state. Further it was found that the noise level was higher in lower frequency band and decreases in the higher frequency band. Also the correlation between the noise level and sea state was higher in the low frequency band and tend to decrease in the mid frequency band and there was no correlation in the higher frequency bands. The higher noise levels were associated with lower frequencies of the bandwidth whereas it is less in higher frequencies. The fluctuations were found to be higher in the lower frequency band than the mid and higher frequency band. In this paper the data collection, data processing and noise spectrum analysis are presented in detail. As the fluctuations in power spectrum level of the ambient noise is one of the primary factor which decides the signal to noise ratio of most of the acoustic instruments, these results seems to be significant.

Often the 1/f noise in MOSFETs is stated to be an ensemble of many RTS with different time constants. The majority of literature on 1/f noise is overlooking the contribution due to mobility fluctuations that are uncorrelated with number fluctuations. Here, we demonstrate that the so-called proofs for ΔN can also be obtained from the empirical relation. The following misunderstandings and controversial topics on the surface and bulk contributions to the low-frequency noise will be addressed: 1) 1/f and RTS noise can have different physical origins. An analysis in time domain shows that the low-frequency noise with RTS is nothing else than a superposition of a two level noise with a Lorentzian spectrum and a Gaussian noise with a pure 1/f spectrum and different bias dependency. 2) It is very unlikely that in a spectrum consisting of one strong two level RTS and a pure 1/f noise, the 1/f noise is a superposition of many RTS with different time constants. 3) The spreading in WLS_I /I² below a critical WL is not a proof for the ΔN origin. 4) The typical shape in the double log plot from sub threshold to strong inversion of S_I/I² versus I, is also not a proof for the ΔN origin.

Bistatic synthetic aperture radar (SAR) operates with distinct transmit and receive antennas that are mounted on separate platforms. Such a spatial separation has several operational advantages, which will increase the capability, reliability and flexibility of future SAR missions. However, this configuration results that there is no cancelation of low frequency oscillator noise as in the monostatic cases. As a consequence, high accurate time synchronization or clock timing jitter compensation must be provided. Literature search reveals little time synchronization work for bistatic SAR has been reported. As such, the use of a new range alignment algorithm to quantify and compensate clock timing jitter is proposed. The impact of clock timing jitter on bistatic SAR is analyzed, and the performance of the proposed algorithm is evaluated. Simulation results show that successful clock timing jitter compensation for bistatic SAR is achieved by using the proposed algorithm.

The occurrence of wide peaks in the frequency range spanning fifteen decades from mHz to above THz was reported in the power spectra of many natural systems. Mostly, these spectral peaks appear superimposed to the 1/f noise. Actually, two different types of spectral peaks were picked out: a first type characterized by wide peaks and high 1/f slope of the overall spectral behavior, the second one by narrow peaks spanning less than one frequency decade and low slopes. Here we highlight the role of correlation among avalanches as the main source of the wide noise peaks observed. The present theory is based on first principle statistics of elementary events clustered in time-amplitude correlated avalanches. A spectral power master equation suitable to explain peaked noise spectra arising from avalanche correlations is achieved analytically. Excellent agreement with our experiments in superconductors and many other observations in biological and natural systems are reported. Our statistical model shows that avalanche correlation gives wide peaks in the power spectrum superimposed to the 1/f behavior with high slope, a typical signature of avalanche processes.

Optical and electrical noises and correlation factor between optical and electrical fluctuations of nitride-based light emitting diodes (LEDs) have been investigated under forward bias. Their electrical, optical and noise characteristics were compared with ones of LEDs of other materials. LED noise characteristic changes during aging have been measured, too. It is found that optical and electrical noise spectra under forward bias for more reliable LEDs distinguish by lower l/f type fluctuations and Lorentzian type noise at higher frequencies. LEDs with intensive 1/f noise demonstrate shorter lifetime. It is shown that reason of LED degradation is related with defects presence in device structure. These defects can be formed during device fabrication or appear during operation. An analysis of LED current-voltage and electrical noise characteristics under forward and reverse bias has shown that LEDs with intensive 1/f electrical noise, large reverse current (low reverse breakdown voltage) and larger terminal voltage under forward bias distinguish by short lifetime.

A detailed study of photosensitivity and noise characteristics of ultrafast InGaAsP/InP avalanche photodiodes (APDs) with separate absorption, grading, charge and multiplication regions was carried out. Carrier multiplication and noise factors were evaluated. Noise origin in investigated APDs is 1/f, generation-recombination and shot noises. Different quality samples have been investigated and it is shown that noise characteristics well reflect APD quality problems. It is shown that low-frequency noise and excess shot noise characteristics are very sensitive to the APD quality problems and clear up physical processes in device structure. Noise characteristic analyses can be used for the APD quality problems revealing and optimal design development.