Mathematical Handbook for Scientists and Engineers

Lieblein, Julius; Korn, Granino A.; Korn, Theresa M.

doi:10.2307/2003035

Cited by 43 publications

(65 citation statements)

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“…for the scaled ṽm = v m /v c , with f = f /(η 0 v c ) and ηa = η a /η 0 . Only one of its four exact Ferrari's solutions [68] has physical sense and corresponds to v m . It reads [68,69], Furthermore, as noticed in [39], for a > 1/2, the velocity potential may have a maximum for certain values of f and become then bistable for a finite η 0 .…”

Section: A1 Stochastic Simulations and The Spurious Driftmentioning

confidence: 99%

“…Only one of its four exact Ferrari's solutions [68] has physical sense and corresponds to v m . It reads [68,69], Furthermore, as noticed in [39], for a > 1/2, the velocity potential may have a maximum for certain values of f and become then bistable for a finite η 0 . It is reflected by a nonmonotonous behavior of the frictional force η(v)v in figure B1 for two illustrative values of α = 2/3 and α = 1.…”

Section: A1 Stochastic Simulations and The Spurious Driftmentioning

confidence: 99%

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Resonance-like enhancement of forced nonlinear diffusion as a nonequilibrium phase transition

Goychuk

2022

New J. Phys.

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We describe the phenomenon of a resonance-like, giant enhancement of diffusion in a basic model of nonlinear diffusion featured by a nonlinear in velocity friction and the corresponding multiplicative thermal noise. The model is consistent with thermal equilibrium in the absence of driving. Different from previous studies of this phenomenon, where the crucial nonlinearity originates from a periodic external potential while friction is linear, we focus on the case of a constant force driving, whereas the crucial nonlinearity stems from the friction. The basic model of such friction considered interpolates between linear viscous Stokes friction at small velocities and dry Coulomb-like friction at large velocities corresponding to a stress plateau in some nonlinear viscoelastic materials. Recently, a nonequilibrium phase transition to super-diffusion and super-transport was discovered within this basic model. We show that adding a tiny viscous friction part to major nonlinear friction regularizes in part this behavior. Diffusion becomes asymptotically normal. However, the phase transition translates into a giant enhancement of normal diffusion and mobility of particles at the transition point over the intuitively expected large force limit, where the linearization of friction occurs. Such a giant enhancement of diffusion is closely related to the largely enhanced kinetic temperature of the particles at and beyond the critical point. We provide analytical results obtained within an effective mass approximation which nicely agree with stochastic numerics.

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Section: A1 Stochastic Simulations and The Spurious Driftmentioning

confidence: 99%

Section: A1 Stochastic Simulations and The Spurious Driftmentioning

confidence: 99%

Resonance-like enhancement of forced nonlinear diffusion as a nonequilibrium phase transition

Goychuk

2022

New J. Phys.

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“…The parameter θ to be determined is

, where

and

are respectively the adsorption values for some intermediate value of the determining parameter A and the value of adsorption for all pores for the right boundary of the micropore region. Equation (1) was obtained under the assumption that the distribution of the determined parameter θ over the determining parameter A can be represented by the Weibull distribution [ 15 ]:

…”

Section: Methodsmentioning

confidence: 99%

“…Therefore, to solve Equation (33) one can apply the method of steepest descent, also known as the “saddle point” method. Assuming that for the maximum of the integrand, in the vicinity of

, the function

takes a constant value of

, Equation (33) can be rewritten as follows [ 15 ]:

…”

Section: Methodsmentioning

confidence: 99%

Adsorption Hysteresis in Open Slit-like Micropores

Dragan¹,

Кутаров²,

Schieferstein

et al. 2021

Molecules

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Adsorption hysteresis in the low-pressure range is only rarely described in the literature. To optimise, for example, heat storage technologies, a deeper understanding of the low-pressure hysteresis (LPH) process is necessary. Here, two thermodynamically based approaches are further developed for analysing the LPH within the framework of thermodynamically irreversible processes and fractal geometry. With both methods developed, it is possible to obtain the description of the adsorption and desorption branches with high accuracy. Within the framework of the two thermodynamic models of the hysteresis loop, generalised equations are obtained with the control parameter in the form of the degree of irreversibility. This is done by taking the adsorption of water on alumina as an example. It is shown that the fractal dimension of the adsorption process is larger than the fractal dimension of the desorption branch, meaning that the phase state of the adsorbate is more symmetric during the adsorption step than in the desorption process.

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“…where j is the normal frequency function 54 and the standard deviation s = dT rms = h(dT) Using the full range of fluctuations will have an impact on the ability of the PVED bias g to overcome the thermal noise and so select a final chiral sign (see Section 5), but is not as drastic as one might suppose, since the very largest fluctuations, which are those lying beyond three standard deviations, 3s, from the mean, have exponentially vanishing probabilities, and so are extremely rare events, see Fig. 1.…”

Section: Thermal Noise Statisticsmentioning

confidence: 99%