New aspects in 1/&lt;i&gt;f&lt;/i&gt; noise studies

Bochkov, G. N.; Kuzovlev, Yu. E.

doi:10.3367/ufnr.0141.198309d.0151

Cited by 39 publications

(18 citation statements)

References 8 publications

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“…Some possible losses already were characterized in [8] (and principally even much earlier in [9,14]) and in part filled up in [8] as well as preprints 4 (it may be useful also to see some of my recent works 6 ). Therefore here we confine ourselves (continuing 5-th paragraph of Introduction) by remark that cutting of the (s + 1)-particle correlation means cutting of s-th and higher statistical moments of fluctuations in relative frequency of TM's collisions with gas molecules (in other words, fluctuations in diffusivity of TM [9]).…”

Section: Discussion and Resumementioning

confidence: 99%

A lemma about molecular chaos

Kuzovlev

2009

Preprint

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Section: Discussion and Resumementioning

confidence: 99%

A lemma about molecular chaos

Kuzovlev

2009

Preprint

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“…As the Brownian motion of ions is very poorly connected with fluctuations of their numbers, a disappearance of sone particles and the creation of others does not change the essence of the process analyzed. An arbitrarily large number of charge can be transferred by any path through the given section inside a conductor [16,17]. This process is a stationary, Gaussian and Markovian, process.…”

Section: Basic Equationmentioning

confidence: 99%

New mechanism of solution of the k B T-problem in magnetobiology

Kanokov¹,

Schmelzer²,

Nasirov³

2010

Open Physics

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Abstract:The effects of ultralow-frequency or static magnetic and electric fields on biological processes is of huge interest for researchers due to the resonant change of the intensity of biochemical reactions, despite the energy in such fields being small in comparison with the characteristic energy B T of the chemical reactions.In the present work, a simplified model to study the effects of weak static magnetic fields on fluctuations of the random ionic currents in blood is presented with a view to solving the B T problem in magnetobiology. An analytic expression for the kinetic energy of the molecules dissolved in certain liquid media is obtained. The values of the magnetic field leading to resonant effects in capillaries are then estimated. The numerical estimates show that the resonant values of the energy of molecules in capillaries and the aorta are different. These estimates prove that under identical conditions, a molecule in the aorta gets 10 −9 times less energy than the molecules in blood capillaries. Therefore, the capillaries are very sensitive to the resonant effect. As the magnetic field approaches the resonant value, the average energy of a molecule localized in a capillary is increased by several orders of magnitude as compared to its thermal energy. This amount of energy is sufficient to cause deterioration of certain chemical bonds.

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“…(29) it follows that fluctuations of the plane surface velocity ( ) V t in the viscous liquid represent flicker noise [6], which at low frequencies is inversely proportional to the frequency. Figure 4 shows the dependences of the spectral density ( ) V G ω calculated by Eqs.…”

Section: ( )mentioning

confidence: 99%

“…We note also that the processes proceeding in physical and technical systems are often non-Markovian ones [3][4][5]. In particular, the flicker noise observed in various physical processes can serve as an example of a non-Markovian process [6]. Various physical fluctuations of the kinetic coefficients observed experimentally (for example, fluctuations of the electrical conductivity) have the spectral density characteristic typical of the flicker noise.…”

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Application of integral transforms to a description of the Brownian motion by a non-Markovian random process

Morozov

Skripkin

2009

Russ Phys J

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The one-dimensional Brownian motion and the Brownian motion of a spherical particle in an infinite medium are described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. A harmonic oscillator in a viscous medium is also considered within the framework of the examined model. It is demonstrated that for rheological models, random dynamic processes are also non-Markovian in character.Application of the theory of Markovian processes to a description of the Brownian motion in actual physical media is approximate, because it ignores the special features of the interaction of the Brownian particles with particles of the medium [1, 2]. We note also that the processes proceeding in physical and technical systems are often non-Markovian ones [3][4][5]. In particular, the flicker noise observed in various physical processes can serve as an example of a non-Markovian process [6]. Various physical fluctuations of the kinetic coefficients observed experimentally (for example, fluctuations of the electrical conductivity) have the spectral density characteristic typical of the flicker noise. The flicker noise is the main type of noise limiting the sensitivity of electronic devices at low frequencies [7]. Actual radio engineering signals with amplitude and phase modulation by a combination of deterministic and random processes also belong to the non-Markovian process [5].We note also that when a Markovian random process acts on a dynamic system, its response represents a non-Markovian random process. The sum of two Markovian processes is a non-Markovian process. The processes observed after integration of a Markovian process or finding of a sliding average of the process with independent values are also non-Markovian ones [4]. In particular, the coordinate of the Brownian particle calculated as an integral of its velocity is not always described by the model of a random Markovian process. The Wiener approximation is correct for the Brownian particles only for sufficiently long time intervals much longer than the particle relaxation time.The above-indicated reasons demonstrate that we practically always use non-Markovian random processes to describe and to analyze actual physical processes and technical devices, and models of the Markovian process can be considered only as a first approximation. BROWNIAN MOTION AS A MARKOVIAN PROCESSTo describe the Brownian motion, the approach based on the application of the stochastic Langevin equation is conventionally used [1,8]. This approach allows the researchers to take advantage of the well-developed theory of stochastic differential systems [9, 10] which determines all necessary statistical characteristics of the velocity fluctuations of the Brownian particle motion.

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New aspects in 1/<i>f</i> noise studies

Cited by 39 publications

References 8 publications

A lemma about molecular chaos

A lemma about molecular chaos

New mechanism of solution of the k B T-problem in magnetobiology

Application of integral transforms to a description of the Brownian motion by a non-Markovian random process

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