Spectral Density Of Fluctuations Research Articles

Hydrodynamic fluctuations, diffusion and correlation functions in systems of particles adsorbed on solid surfaces

We present the detailed derivation of the equations describing the evolution of the hydrodynamic fluctuations of the coverage of particles adsorbed on homogeneous lattices. Using the method of the non-equilibrium statistical operator, we reduce the balance equation governing the behavior of the individual particles to the diffusion equation. On a macroscopic level, this equation describes the approach to equilibrium of the hydrodynamic coverage fluctuations. We obtain the analytical expressions for the Fickian diffusivity and Onsager phenomenological coefficient. These expressions are derived with account of the lateral interaction between the particles. They are simple functions of the thermodynamic quantities — derivatives of the thermodynamic potential over its arguments. The transport coefficients accurately describe the development of fluctuations in the entire coverage region and in the wide range of lateral interactions. We presented an elementary introduction to the theory of fluctuations in the lattice gas systems. For calculations of the correlation function and spectral density of fluctuations, we use the Langevin approach and the method of moments. The exact coincidence of the analytical expressions for the diffusion coefficients obtained by the two independent calculations is the direct proof of the accuracy of the approach developed in Chumak and Tarasenko (1980).

Advancing frequency locking: Modified FPGA-Guided direct modulation spectroscopy for laser stabilization

In this paper, we propose a cost-effective laser frequency locking scheme based on frequency modulation spectroscopy (FMS) for precision measurements and experiments in various fields. We demonstrate that by digitally modulating the detected signal frequency using a Field-Programmable-Gate-Array (FPGA) driven by a home-built lock-in and a proportional–integral–derivative (PID) control system, our system achieves higher precision, user-friendliness, and versatility. Our system generates a 20 V peak-to-peak amplified voltage to a piezo transducer (PZT), which enables a mode-hop free laser scan of approximately 2 ±0.2 GHz. We directly modulate the detected saturation absorption signal with a sinusoidal waveform, then demodulate it to obtain multiple zero crossing locking points on the D2 transition of Cs at 852.35 nm. We optimized the system for three commonly used atomic transitions and found that researchers can select any of the zero crossing peaks for frequency stabilization depending on their experimental requirements, we locked the laser at the crossover transition. We measured the long-time frequency fluctuation and power spectral density and found that the frequency fluctuation of the laser is much less than the natural line width of the D2 transition of Cs. Our results demonstrate that our laser frequency locking scheme is effective and practical for precision measurements and experiments in various fields.

Fluctuation-dissipation in thermoelectric sensors

Thermoelectric materials exhibit correlated transport of charge and heat. The Johnson-Nyquist noise formula 4k B T R for the spectral density of voltage fluctuations accounts for fluctuations associated solely with Ohmic dissipation. Applying the fluctuation-dissipation theorem, we generalize the Johnson-Nyquist formula for thermoelectrics, finding an enhanced voltage fluctuation spectral density 4k B T R(1 + Z D T) at frequencies below a thermal cut-off frequency f T , where Z D T is the dimensionless thermoelectric device figure of merit. The origin of the enhancement in voltage noise is thermoelectric coupling of temperature fluctuations. We use a wideband , integrated thermoelectric micro-device to experimentally confirm our findings. Measuring the Z D T enhanced voltage noise, we experimentally resolve temperature fluctuations with a root mean square amplitude of at a mean temperature of 295 K. We find that thermoelectric devices can be used for thermometry with sufficient resolution to measure the fundamental temperature fluctuations described by the fluctuation-dissipation theorem.

Experimental investigation of expansion effect on shock wave boundary layer interaction near a compression ramp

The experiment is conducted to investigate the effect of expansion on the shock wave boundary layer interaction near a compression ramp. The small-angle expansion with an angle degree of 5° occurs at different positions in front of the compression ramp. The particle image velocimetry and flow visualization technology show the flow structures, velocity field, and velocity fluctuation near the compression ramp. The mean pressure distribution, pressure fluctuation, and power spectral density are measured by high-frequency response pressure transducers. The experimental results indicate that the expansion before the compression ramp position affects the shock wave boundary layer interaction to induce a large-scale separation. But the velocity fluctuation and pressure fluctuation are attenuated near the large-scale flow separation region. When the expansion occurs closer to the compression ramp, the expansion has a more significant impact on the flow. The fluctuation of velocity and pressure is significantly attenuated, and the wall pressure rise of the separation point is reduced obviously. And the characteristic low-frequency spectrum signal related to the unsteadiness of the shock wave boundary layer interaction is significantly suppressed. In addition, variation of the separation region scale at different compression angle degrees is distinctive with the effect of expansion.

Low-Frequency Noise Investigation of 1.09 μm GaAsBi Laser Diodes.

GaAsBi is a suitable and very attractive material system to be used as an active layer in laser diodes (LDs). To understand the performance and the reliability of such devices and also for further laser diode improvements, the origin of noise sources should be clarified. A detailed study of near-infrared 1.09 μm wavelength GaAsBi type-I laser diodes using the low-frequency noise spectroscopy in a temperature range of (180–300) K is presented. Different types of voltage fluctuation spectral density dependencies on the forward current far below the lasing threshold have been observed. According to this, investigated samples have been classified into two groups and two equivalent noise circuits with the corresponding voltage noise sources are presented. Calculations on the voltage spectral density of the electrical noise and current-voltage characteristic approximations have been performed and the results are consistent with the experimental data. The analysis showed that one group of LDs is characterized by 1/fα-type electrical fluctuations with one steep electrical bump in the electrical noise dependence on forward current, and the origin of these fluctuations is the surface leakage channel. The LDs of the other group have two bumps in the electrical noise dependence on current where the first bump is determined by overall LD defectiveness and the second bump by Bi-related defects in the active area of LD with characteristic Lorentzian-type fluctuations having the activation energy of (0.16–0.18) eV.

Vibrational damping effects on electronic energy relaxation in molecular aggregates

Representation of molecular vibrational degrees of freedom by independent harmonic oscillators, when describing electronic spectra or electronic excitation energy transport, raises unfavourable effects as vibrational energy relaxation becomes inaccessible. A standard theoretical description is extended in this paper by including both electronic-phonon and vibrational-phonon couplings. Using this approach we have simulated a model pigment-protein system and have shown that intermode coupling leads to the quenching of pigment vibrational modes, and to the redistribution of fluctuation spectral density with respect to the electronic excitations. Moreover, new energy relaxation pathways, opened by the vibrational-phonon interaction, allow to reach the electronic excited state equilibrium quicker in the naturally occurring water soluble chlorophyll binding protein (WSCP) aggregate, demonstrating the significance that the damping of molecular vibrations has for the rate of the intramolecular energy relaxation process.

Flicker Noise in a Locally Nonequilibrium Medium

A model implying that particles of a medium are subjected to external forces with a flicker noise spectrum has been proposed to describe fluctuations in locally nonequilibrium physical media. The Langevin equation with additional integral terms describing the action of the locally nonequilibrium medium has been derived. The spectral density of fluctuations of an electric current flowing in the locally nonequilibrium medium has been calculated. It has been found that this density in the low-frequency spectral range is flicker noise.

Properties of the surface generation-recombination noise in 1.94 µm GaSb-based laser diodes

A detail investigation of generation-recombination (g-r) noise in 1.94 µm GaSb-based type-I ridge waveguide laser diodes (LDs) has been performed in a temperature range (230–295) K. Lorentzian-type noise spectra have been observed in the current range below the threshold at the forward and reverse biases of the LDs with the same characteristic time (3.7 μs) and activation energy (≈0.37 eV) of charge carriers transitions associated with the g-r processes. An equivalent electrical circuit possessing the voltage noise source is presented, which allows the description of both the current-voltage characteristic and the voltage fluctuation spectral density of the laser diode. Results indicate that the origin of the g-r noise in the investigated samples is the surface recombination caused by the surface leakage current channel between n+GaSb and p+GaSb contacts, which is practically independent from the applied bias polarity.

Elastic instabilities during the flow of hydrolyzed polyacrylamide solution in porous media: effect of pore-shape and salt.

We experimentally investigate the flow of hydrolyzed polyacrylamide (HPAM) solution with and without salt in model porous media at high Weissenberg numbers (Wi > 1.0). The effect of pore shapes on the flow pattern and pressure drop is explored by using periodic arrays of circular and square pillars in aligned and staggered layouts. In the apparent shear-thinning regime, we observe stationary dead zones upstream of the pillars. In addition, we confirm that the size of stationary dead zones correlates with the level of shear-thinning, by varying the amount of salt in HPAM solution. At higher shear rates (or Wi), these dead zones are periodically washed away. We present the mechanism of this elastic instability and characterize it based on the pressure drop fluctuation spectral density.

Friedmann inflation in Horava–Lifshitz gravity with a scalar field

We study Friedmann inflation in general Horava–Lifshitz (HL) gravity with detailed and nondetailed and also without the projectability conditions. Accordingly, we derive the modifications in the Friedmann equations due to single scalar field potentials describing power-law and minimal-supersymmetrically extended inflation. By implementing four types of the equations-of-state characterizing the cosmic background geometry, the dependence of the tensorial and spectral density fluctuations and their ratio on the inflation field is determined. The latter characterizes the time evolution of the inflation field relative to the Hubble parameter. Furthermore, the ratio of tensorial-to-spectral density fluctuations is calculated in dependence on the spectral index. The resulting slow-roll parameters apparently differ from the ones deduced from the standard General Relativity (Friedmann gravity). We also observe that the tensorial-to-spectral density fluctuations continuously decrease when moving from nondetailed HL gravity, to Friedmann gravity, to HL gravity without the projectability, and to detailed HL gravity. This regular pattern is valid for three types of cosmic equations-of-state and different inflation potential models. The results fit well with the recent Planck observations.

Randomness and Earth’s Climate Variability

Paleo-Sciences including palaeoclimatology and palaeoecology have accumulated numerous records related to climatic changes. The researchers have usually tried to identify periodic and quasi-periodic processes in these paleoscientific records. In this paper, we show that this analysis is incomplete. As follows from our results, random processes, namely processes with a single-time-constant [Formula: see text] (noise with a Lorentzian noise spectrum), play a very important and, perhaps, a decisive role in numerous natural phenomena. For several of very important natural phenomena the characteristic time constants [Formula: see text] are very similar and equal to [Formula: see text] years. However, this value of [Formula: see text] is not universal. For example, the spectral density fluctuations of the atmospheric radiocarbon [Formula: see text]C are characterized by a Lorentzian with [Formula: see text] years. The frequency dependence of spectral density fluctuations for benthic [Formula: see text]O records contains two Lorentzians with [Formula: see text] years and [Formula: see text] years.

Effect of Dynamic SGS Model in a Kerosene-LOx Swirl Injector under Supercritical Condition

In this study, numerical simulations are carried out to investigate the dynamic SGS model effects in a Kerosene-LOx coaxial swirl injector under high pressure conditions. The turbulent model is based on large-eddy simulation (LES) with real-fluid transport and thermodynamics. To assess the effect of the dynamic subgrid-scale (SGS) model, the dynamic SGS model is compared with that of the algebraic SGS model. In a swirl injector under supercritical pressure, the characteristics of temporal pressure fluctuation and power spectral density (PSD) present comparable discrepancies dependant on the SGS models, which affect the mixing characteristics. Mixing efficiency and the probability density (PDF) function are conducted for a statistical description of the turbulent flow fields according to the SGS models. The back-scattering of turbulent kinetic energy is estimated in terms of the film thickness of the swirl injector.

Channel-noise-induced critical slowing in the subthreshold Hodgkin-Huxley neuron.

The dynamics of a spiking neuron approaching threshold is investigated in the framework of Markov-chain models describing the random state-transitions of the underlying ion-channel proteins. We characterize subthreshold channel-noise-induced transmembrane potential fluctuations in both type-I (integrator) and type-II (resonator) parametrizations of the classic conductance-based Hodgkin-Huxley equations. As each neuron approaches spiking threshold from below, numerical simulations of stochastic trajectories demonstrate pronounced growth in amplitude simultaneous with decay in frequency of membrane voltage fluctuations induced by ion-channel state transitions. To explore this progression of fluctuation statistics, we approximate the exact Markov treatment with a 12-variable channel-based stochastic differential equation (SDE) and its Ornstein-Uhlenbeck (OU) linearization and show excellent agreement between Markov and SDE numerical simulations. Predictions of the OU theory with respect to membrane potential fluctuation variance, autocorrelation, correlation time, and spectral density are also in agreement and illustrate the close connection between the eigenvalue structure of the associated deterministic bifurcations and the observed behavior of the noisy Markov traces on close approach to threshold for both integrator and resonator point-neuron varieties.

Displacement of the electron cyclotron resonance heating region and time evolution of the characteristics of short-wavelength turbulence in the 3D magnetic configuration of the L-2M stellarator

Reflection of the heating extraordinary microwave incident obliquely onto the surface of the electron cyclotron resonance (ECR) at the second harmonic of the electron gyrofrequency in the 3D magnetic configuration of the L-2M stellarator was studied experimentally. The plasma was heated using two gyrotrons with a total power of 600–700 kW, the specific heating power being 2.4–2.8 MW/m3. The displacement of the ECR region in the course of heating was monitored by measuring the phase of the reflected extraordinary wave. It is found that the growth of the plasma density is accompanied by the displacement of the ECR heating region from the center of the plasma column toward its periphery. The coefficient of reflection of the heating microwave beam from the ECR region was measured. The spectra of short-wavelength (k s ≈ 30 cm−1) plasma density fluctuations were explored by analyzing backscattered microwave radiation. A tenfold increase in the energy of short-wavelength density fluctuations and the growth of the spectral density of fluctuations in the frequency range of 0.3–1.5 MHz were observed.

Effect of electron-cyclotron resonance heating conditions on the local parameters of short-wavelength plasma turbulence in the L-2M stellarator

Changes in the energy spectra of short-wavelength (ks ≈ 35 cm−1) plasma density fluctuations in the local region of the plasma column (r/a = 0.5–0.6) of the L-2M stellarator were studied by the method of collective scattering of 150-GHz radiation. The plasma was heated at the second harmonic of the electron gyrofrequency, the microwave heating power being in the range of 90–170 kW. A sector limiter was introduced in the peripheral plasma (r/a ≥ 0.8), and the Shafranov shift of the magnetic axis was varied by varying the vertical magnetic field. The results of measurements were averaged over 9–16 discharges. It is found that an increase in the heating power and/or the introduction of the sector limiter in the plasma lead to an increase in the energy of density fluctuations, which correlates with a decrease in the plasma energy lifetime. In the spectra of fluctuations, a broad spectral band in the range of 3–50 kHz was observed in which the spectral density was one order of magnitude higher than in the rest of the spectrum. Analysis of the Fourier spectra showed that the introduction of the sector limiter in the plasma resulted in an increase in both the spectral density of fluctuations in the range of 3–50 kHz and the fraction of quasi-coherent structures in turbulent density fluctuations.

Holographic tissue dynamics spectroscopy

Tissue dynamics spectroscopy uses digital holography as a coherence gate to extract depth-resolved quasi-elastic dynamic light scattering from inside multicellular tumor spheroids. The temporal speckle contrast provides endogenous dynamical images of proliferating and hypoxic or necrotic tissues. Fluctuation spectroscopy similar to diffusing wave spectroscopy is performed on the dynamic speckle to generate tissue-response spectrograms that track time-resolved changes in intracellular motility in response to environmental perturbations. The spectrograms consist of several frequency bands that range from 0.005 to 5 Hz. The fluctuation spectral density and temporal autocorrelations show the signature of constrained anomalous diffusion, but with large fluctuation amplitudes caused by active processes far from equilibrium. Differences in the tissue-response spectrograms between the proliferating outer shell and the hypoxic inner core differentiate normal from starved conditions. The differential spectrograms provide an initial library of tissue-response signatures to environmental conditions of temperature, osmolarity, pH, and serum growth factors.

Predictions of Taylor's power law, density dependence and pink noise from a neutrally modeled time series

There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed ‘pink noise’: a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.

Spectral density of fluctuations in fractional bistable Klein-Kramers systems

We investigate the stationary spectral density of fractional bistable Klein-Kramers systems. First, we deduce a dissipation-fluctuation relation between the stationary spectral density at thermal equilibrium and the linear response of the system to an applied perturbation. Second, we describe how to obtain the linear dynamic susceptibility from the method of moments, and thus we derive the fluctuating spectral density from the dissipation-fluctuation relation. Finally, we exhibit the structure of this fluctuating spectral distribution and explore the effect of the subdiffusion on it. Compared with the standard bistable Klein-Kramers systems, our observation on the spectral distribution in fractional systems reveals that the subdiffusion weakens the oscillatory components of the intrawell oscillation and the above-barrier motion. This phenomenon should reflect a fact that the particles tend to stand still in separate wells in subdiffusive processes.

On characterization of reversible Markov processes by monotonicity of the fluctuation spectral density

For the system driven by a stationary Markov process {ξt:t∊R+}, if it is in nonequilibrium steady state (i.e., irreversible), then there exists a function φ such that the fluctuation spectrum (or say: power spectrum density) of {φ(ξt)} is nonmonotonic in [0,+∞) under mild conditions, which means that there exist nonzero spectrum peaks of the fluctuation spectrum. For the system driven by a Markov chain with discrete time {ξt:t∊Z+}, even if it is in equilibrium state (i.e., reversible), one cannot distinguish the equilibrium and nonequilibrium steady state in terms of the monotonicity of the fluctuation spectrum any more.

Effect of stress on variability of systemic hemodynamics in rats of various genetic strains.

Power spectral density of heart rate fluctuations in the range of 0.02-5.00 Hz in August rats was lower than in Wistar rats. Changes in mean blood pressure and heart rate during stress (15-min immobilization) were similar in animals of both strains. As differentiated from Wistar rats, power spectral density of fluctuations in August rats considerably decreased after stress. August rats were characterized by low spectral power at rest and high resistance to the arrhythmogenic effect of 10-min acute myocardial ischemia.