Exponent Of Frequency Research Articles

Study on the distribution characteristics of TBL fluctuating pressure of a submerged conical-cylindrical structure

The fluctuating pressure within turbulent boundary layers (TBL) has garnered significant attention as a pivotal factor in generating hydrodynamic noise for underwater vehicles. This study employs numerical simulations to investigate the fluctuating pressure of a submerged conical-cylindrical structure, utilizing the Improved Delayed Detached Eddy Simulation (IDDES) method. This research delves into the spatiotemporal distribution characteristics of wall fluctuating pressure across various Reynolds numbers. Notably, the power spectral density (PSD) curve of TBL fluctuating pressure exhibits relative stability at lower frequencies, whereas it undergoes a rapid decline in the high-frequency range, following an inverse proportional trend with the power-law exponent of frequency. Moreover, the dimensionless migration velocity in the parallel mid-body segment is consistent with the TBL over a flat plate, while it is slightly smaller in the outflow segment.

Effects on deep ocean ambient noise caused by typhoon

Sea-surface wind speed has significant impacts on ocean ambient noise at medium and low frequency bands. When a typhoon comes close, sea-surface wind speed increases sharply, which results in the surge of the ambient noise level. By analyzing the sound data collected by a vertical array in deep ocean environment during two typhoon periods, both the wind speed and frequency dependencies of ambient noise are established. Noise field at receivers is calculated via numerical simulations with combination of the source intensity model of wind generated noise and the typhoon generated noise intensity model. Simulated noise intensity is fitted with the experimental data by least square method, through which the exponent of the wind speed and frequency in the source intensity model is determined. Our result indicate that the variations of wind speed caused by typhoon heavily impact on the noise at frequency band higher than 200 Hz. And specifically, the ambient noise intensity is approximately proportional to the 3rd power of the wind speed, where the exponent of frequency is around - 0.85.

The experimental set-valued index of refraction of dielectric and anelastic media

The dielectric parameter, in the generalised Debye form, of all studied substances (Cole and Cole, 1941) contains a rational power of the imaginary frequency which implies that the index of refraction is a multivalued function of the frequency; the same property, concerning the stress strain relation, also applies to anelastic media (Bagley and Torvik, 1983a,b). The multivalued index of refraction implies then that the free modes of dielectric and anelastic media are split into a number of modes which depend on the exponent of the imaginary frequency. In order to estimate if it is possible to observe this splitting, this note computes the parameters appearing in the generalised Debye form of the dielectric parameters of many substances and also the complex anelastic parameter of an anelastic medium. The analysis of the data indicates that, depending on the accuracy of the experimental data, with few exceptions, the splitting is observable.

Temperature dependence of core losses at high frequency for MnZn ferrites

The core losses ( P L ) of MnZn ferrites prepared by a solid-state reaction method were investigated as a function of magnetic induction and frequency ( P L = k B m x f y ). The exponent ( x) of magnetic induction was 2.58 at 1000 kHz and 2.01 at 3000 kHz, and the exponent ( y) of frequency was 2.22 at 30 mT and 2.73 at 10 mT. The core losses ( P L ) were divided into hysteresis loss ( P h ), eddy current loss ( P e ) and residual loss ( P r ). Each loss contribution was discussed to be dependent on temperature. P h decreased monotonically with increasing temperature. P e firstly decreased with increasing temperature, minimized at 100 °C, and then increased. As the temperature increased, the imaginary permeability at MHz was significantly enhanced and the resonance frequency ( f r ) decreased. The increase in P r with increasing temperature should be attributed to the decreasing f r which is due to the resonance in the domain wall caused by high speed rotation of spin inside the domain.

Mechanical stratigraphy and faulting in Cretaceous carbonates

Normal faults measured in exposures of Cretaceous carbonate rocks in Texas provide the basis for fault-strain determination, analysis of fault displacements, and exploring the function of mechanical stratigraphy in influencing fault-size distributions. Layer competence and competence contrast, measured using a Schmidt hammer, allow the analysis of mechanical stratigraphy. Fault frequency and displacement distributions exhibit patterns that correlate to mechanical stratigraphy. In particular, the average competence contrast is related to the exponent (C) of cumulative frequency versus displacement distributions as described by log(cumulative frequency) = (C) log(displacement) + A. This correlation between competence contrast and C values is interpreted to indicate that, at low competence contrast, there are many potential nucleation sites for faults and no mechanisms by which fault displacement can be filtered. In addition, several frequency versus displacement distributions exhibit steep sections, indicating a clustering of fault displacement(s). Clustering of fault displacement(s) is also interpreted as the result of low-competence layers inhibiting the propagation of faults through the layering until a threshold displacement has been reached. This has the effect of creating a cluster of faults with displacements near the threshold displacement value. These patterns are true both for data sets surveyed along a scan line and along a key bed. An appreciation of these effects of mechanical stratigraphy on fault displacement distributions is important when using observed data to infer subseismic fault populations during reservoir evaluation and modeling.

Ac hopping admittance in spinel manganate negative temperature coefficient thermistor electroceramics

In this work, the ac admittance of a thick film nickel manganate spinel negative temperature coefficient thermistor ceramic system containing a glass phase is investigated. The dominating relaxation process is a grain boundary (GB) effect and has been investigated comprehensively. We present double-logarithmic plots of the specific admittance σ′ vs ω and (σ′/σdc) vs ω, and specific impedance z′ vs −z″/ω and [(ρdc/z′)−1] vs ω, in order to characterize GB charge transport. Using the complex admittance notation (σ∗), an unusually low Jonscher exponent of frequency ∼0.007 was obtained and the GB relaxation displayed close to ideal behavior.

Large-Time Behavior of Solutions for the Boltzmann Equation with Hard potentials

We study the quantitative behavior of the solutions of the one-dimensional Boltzmann equation for hard potential models with Grad’s angular cutoff. Our results generalize those of [5] for hard sphere models. The main difference between hard sphere and hard potential models is in the exponent of the collision frequency \(\nu(\xi)\approx (1+|\xi|)^\gamma\). This gives rise to new wave phenomena, particularly the sub-exponential behavior of waves. Unlike the hard sphere models, the spectrum of the Fourier operator \(-i\xi^1\eta+L\) is non-analytic in η for hard potential models. Thus the complex analytic methods for inverting the Fourier transform are not applicable and we need to use the real analytic method in the estimates of the fluidlike waves. We devise a new weighted energy function to account for the sub-exponential behavior of waves.

Analysis of Power Losses in Mn–Zn Ferrites

The power loss of Mn–Zn ferrites has been studied as a function of magnetic flux density and frequency (PL = kBxfy). The exponent (x) of magnetic flux density was 2.94 at 100 kHz and 2.48 at 1 MHz. These results support the switch of power loss mechanism from hysteresis losses at low frequency to residual losses at 1 MHz. In the intermediate frequency range, the eddy current loss was dominant. The power loss linearly increased with an exponent (y≈1.25) at low frequency and deviated from the linearity at higher frequencies, where the exponent of frequency (y) was 2.87 at 100°C and 25 mT. The frequency at which the power loss starts to deviate from the linearity is in good agreement with the onset frequency of the dissipation of magnetic permeabilities. The residual loss is strongly associated with the magnetic resonant process.

岩石の圧縮疲労破壊についてのＣｏｓｔｉｎモデルによる考察

In order to investigate the length of cracks developed by stress corrosion and cyclic fatigue and the time to failure under cyclic loading in compression, the equations proposed by Costin et al. is estimated from the results of creep and fatigue tests for OGINO tuff, KIMACHI sandstone and AKIYOSHI marble. Under the fatigue tests at cyclic frequency of 1 Hz, the ratio of the length of crack due to stress corrosion to the total one increases with increasing upper stress ratio. The length of crack due to cyclic fatigue is proportional to the exponent of cyclic frequency of stress, and the time to failure is affected by it. Also, in case that the length of crack due to stress corrosion occupies the most part of the total crack length, the increase in the time to failure is smaller with decreasing frequency. The time up to failure is longer as the stress amplitude decreases, but below a given ratio of stress amplitude, it is smaller with decreasing the ratio of stress amplitude. Also, the ratio of stress amplitude, at which the time to failure takes a maximum value, and the length of crack due to cyclic fatigue are smaller as the ration of stress amplitude decreases.

Linear systems analysis of cutaneous Type I mechanoreceptors

Linear system transfer functions of Type I mechanoreceptor domes in hairy skin were extracted for study. The system input, defined in units of indentation depth, was a punctate, 85 Hz bandlimited colored noise indenting stimulus. The system output was a dome's afferent AP event stream. After digitally low-pass filtering the AP event stream to prevent aliasing, transfer and coherence function estimates were generated from spectral and cross spectral estimates of the sampled input and output signals. Transfer function magnitudes (receptor sensitivity) beyond 10 Hz could be well fit by a fractional exponent (0.35 +/- 0.10) of frequency, indicating fractional order differentiation. Transfer function phases were near 120 degrees for frequencies less than 10 Hz and decreased progressively beyond 10 Hz. Coherence function estimates were low as a result of inherent nonlinearities, primarily rectification. Single dome results closely matched those reported by French and Kuster [6] for the tactile spine of the cockroach, suggesting that in terms of spectral sensitivity the receptors have similar transduction mechanisms. However, nonlinear systems modeling techniques are required for a more complete system characterization.

Sensory transduction in dorsal cutaneous mechanoreceptors of the frog, Rana pipiens.

Sensory transduction was studied in dorsal skin mechanoreceptors of the frog, Rana pipiens. The skin was clamped and stretched before being stimulated with the tip of a glass rod mounted on a servo-controlled loudspeaker. Afferent activity was recorded extracellularly from a dorsal cutaneous nerve. Three groups of sensory units could be identified by the size of their recorded action potentials and their response to mechanical stimuli. Action potential amplitudes for the three groups were: less than 50 microV (group I), 50-250 microV (group II) and greater than 300 microV (group III). Group II were selected for further study because of their amplitude and their resistance to fatigue. Three types of mechanical stimuli were used to examine the dynamic properties of group II receptors, steps, sinusoids, and band-limited random displacement. In each case the responses could be well fitted by a power-law model with a fractional exponent of time or frequency. Random stimulation of a large number of group II receptors showed considerable variability in their sensitivity and in their dynamic behavior, as measured by the fractional exponent of frequency. However, the distributions of these two parameters were both unimodal and strongly clustered around the modes, suggesting that the recordings were from a single class of receptors. Varying the temperature of the receptors had little effect on their sensitivity or dynamic properties. This is in contrast to findings on other mechanoreceptors. Doubling the potassium concentration in the bathing solution affected the dynamic properties of the receptors within 5 min but several distinct patterns of change in dynamic behavior were seen.(ABSTRACT TRUNCATED AT 250 WORDS)

Sensory transduction in a locust multipolar joint receptor: The dynamic behaviour under a variety of stimulus conditions

1. The dynamic behaviour of a multipolar mechanoreceptor in the locust femoro-tibial joint has been studied by linear systems analysis using both sinusoidal and pseudo-random mechanical stimuli. Experiments were performed at different mean positions of the joint and with a range of stimulating signal strengths. 2. The joint sensilla respond to increasing joint extension with increasing tonic firing of action potentials. Movements of the joint position produce modulation of the firing rate around the mean level which allows faithful reproduction of the input signal in the probability of action potential occurrence. However, at frequencies of about 1 Hz and above the response increasingly phase-locks to a repetitive signal. 3. For sinusoidal stimuli up to 1 Hz and for random stimuli up to 10 Hz the dynamic behaviour can be very well characterized as fractional differentiation. In the frequency domain this corresponds to a frequency response function which can be represented by the gain at a frequency of 1 radian/s and a fractional exponent of frequency. 4. The dynamic behaviour of these sensilla is discussed in terms of models of transduction for cuticular and multipolar sensilla.

The effects of temperature on mechanotransduction in the cockroach tactile spine

1. The dynamic behaviour of the cockroach femoral tactile spine can be characterised as fractional differentiation. In the frequency domain this corresponds to a frequency response function which can be completely represented by two parameters: the gain at a frequency of 1 radian/s and an exponent of frequency. 2. Frequency response functions for mechanotransduction in the tactile spine have been measured at temperatures in the range of 10–40 °C. Sensory transduction fails at temperatures a few degrees Celsius outside this range. 3. The effect of temperature upon sensory transduction is to multiply the entire response by a constant factor, independent of frequency, at each temperature. The multiplication factor increases with warming up to about 35 °C and then decreases rapidly. The data up to 35 °C is well fitted by an Arrhenius relationship with an activation energy of 18.6 kcal/ mole. 4. Changing the temperature has no effect upon the exponent of frequency which stays constant at approximately 0.5, corresponding to a system which performs semi-differentiation. 5. The possible sites of temperature sensitivity and sensory transduction in these mechanoreceptors are discussed. Possible origins of the semi-differentiation behaviour are reviewed and a visco-elastic travelling wave model of the tubular body is suggested. Comparisons are drawn throughout to the behaviour of Pacinian corpuscles, muscle spindle primary afferents and other cuticular mechanoreceptors.

Sensory transduction in an insect mechanoreceptor: extended bandwidth measurements and sensitivity to simulus strenght

The dynamic properties of sensory transduction in an insect mechanoreceptor, the femoral tactile spine of the cockroach, Periplaneta americana, have been studied by measurement of the frequency response function between randomly varying movement of the tactile spine and afferent action potentials from the sensory neuron which innervates it. The frequency response function of the mechanoreceptor has been characterized over a frequency range which is more than ten times larger than has previously been used for this preparation. Also the effects of varying the amplitude of the stimulating signal have been studied by the use of a range of input signal strengths from about 0.5 to 10 μm R.M.S. displacement. The measured frequency response functions can all be well fitted by a theoretical relationship which is a fractional exponent of complex frequency, provided that the time delay caused by conduction of the action potentials from the sensory dendrite to the recording electrodes is taken into account. Under small signal conditions the exponent of complex frequency is close to 0.5 but with larger displacements its value decreases to about half this value. The overall sensitivity of the receptor, as measured by the gain of the frequency response function at a natural frequency of 1 radian/s, is not significantly altered by changes in the input movement amplitude, so that the receptor behaves linearly in this respect. However, the mean rate of action potential occurrence is not linearly related to input movement amplitude. These results are discussed in terms of current theories of sensory transduction and the possible role of tubular bodies in the dynamic behaviour of insect cuticular mechanoreceptors.