Modified Kramers formulas for the decay rate in agreement with dynamical modeling

Pavlova, E.; Aktaev, Nurken E.; Gontchar, I. I.

doi:10.1016/j.physa.2012.06.064

Cited by 14 publications

(21 citation statements)

References 38 publications

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“…This effect was discussed earlier for the 1D case (see, e.g. [13,15]). The physical reason is that those particles which overcome the barrier still have a chance to be returned back into the potential well due to fluctuations if they are not absorbed at the border.…”

Section: The Influence Of the Absorptive Bordersupporting

confidence: 57%

“…The rate of thermal decay of a metastable (quasistationary) state in the presence of friction is evaluated for onedimensional motion using the formulas derived by Kramers in Ref. [11] or their modifications [12][13][14][15]. The rates calculated according to those formulas are expected to agree with the long time limit of the escape rate obtained using either the stochastic differential equations (the Langevin equations) or the corresponding partial differential equations (the Fokker-Planck equation or the Smoluchowski equation).…”

Section: Introductionmentioning

confidence: 99%

“…Below this limit is referred to as the Quasistationary Dynamical Rate (QDR) and denoted as D R . The problem of agreement between the approximate analytical rates (Kramers rates, 𝑅 𝐾 ) and D R (which is supposed to be exact within the statistical and numerical errors) was studied in several works [13][14][15][16][17][18] for the case of one degree of freedom (1D). In particular, in [13][14][15][16] the applicability of the Kramers formula for the case of high temperature was studied.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of agreement between the approximate analytical rates (Kramers rates, 𝑅 𝐾 ) and D R (which is supposed to be exact within the statistical and numerical errors) was studied in several works [13][14][15][16][17][18] for the case of one degree of freedom (1D). In particular, in [13][14][15][16] the applicability of the Kramers formula for the case of high temperature was studied. In [12,15] corrections to the Kramers formula were proposed which account for the anharmonicity of the potential.…”

Section: Introductionmentioning

confidence: 99%

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Thermal decay rate of a metastable state with two degrees of freedom: Dynamical modelling versus approximate analytical formula

Gontchar

Chushnyakova

2017

Pramana - J Phys

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Accuracy of the Kramers approximate formula for the thermal decay rate of the metastable state is studied for the twodimensional potential pocket. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. It is shown that the Kramers rate is in agreement with the quasistationary rate within the statistical errors provided the absorptive border is far enough from the potential ridge restricting the metastable state. As the absorptive border (or its part) gets closer to the ridge the Kramers formula underestimate the quasistationary rate. The difference reaches approximately the factor of 2 when the absorptive border coincides with the ridge. Metastable system; quasistationary decay rate; Kramers rate; dynamical modeling PACS numbers: 05.60.-k, 82.20.Pm

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Section: The Influence Of the Absorptive Bordersupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermal decay rate of a metastable state with two degrees of freedom: Dynamical modelling versus approximate analytical formula

Gontchar

Chushnyakova

2017

Pramana - J Phys

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“…The main tool for realization of the principle is Pontryagin's function or as still it is accepted to call, Hamilton function. For record of a Hamiltonian we will use communication, well-known from Hamilton mechanics, with Lagranzhian's L % (Aktaev, 2014;Pavlova, Aktaev, Gontchar, 2012).…”

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confidence: 99%

Forming Numerical Model For Calculating Optimal Tax Rate For Resolving Stakeholders’ Interests

Aktaev¹,

Bannova²

2018

The European Proceedings of Social and Behavioural Sciences

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For a long time by means of taxes, many state issues of redistribution of finance were resolved, and its size defined the standard of living of the citizens residing on a certain territory. By means of taxes, it is possible to increase the standard of living of population, to provide competitiveness of companies within the country. Competitiveness of a company is defined by many factors, such as the level of expenses, including payment of taxes, which is key. For lack of the competition in the domestic market, the tax component does not strongly influence the consumption level, but determines production price.However, when entering the world market or when competing in domestic market with foreign goods, the lowering of the level of expenses is a necessary condition not only for the successful competition, but also for existence of the company as a structural economic unit. However, it is necessary to know the optimal level of tax rate to provide low cost, on the one hand. But, on the other hand, there is a positive dynamics of the state budget. The authors assume that at the optimal level of the tax rate, the value that is the ratio of the company's key indicators is maintained. The dynamics of the company's development is determined by keeping the ratios between the indicators as a constant value. It is assumed that these ratios will serve as an indicator of competitiveness and will determine the company's development strategy in the domestic and foreign markets.

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Langevin Approach to Modeling of Small Levitating Ordered Droplet Clusters

Aktaev¹,

Fedorets²,

Bormashenko

et al. 2018

J. Phys. Chem. Lett.

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A self-assembled cluster of microdroplets levitating over a heated water surface is a fascinating phenomenon with potential applications for microreactors and for chemical and biological analysis of small volumes of liquids. Recently, we suggested a method to synthesize a cluster with an arbitrary number of small monodisperse droplets. However, the interactions, which control the structure of the cluster, are still not well understood. Here we propose a Langevin computational model considering the aerodynamic forces between the droplets and random diffusion-like fluctuations. Characteristic length and time scales and scaling relationships of interactions are discussed. The model shows excellent agreement with experimental observations for a small number of droplets.

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Modified Kramers formulas for the decay rate in agreement with dynamical modeling

Cited by 14 publications

References 38 publications

Thermal decay rate of a metastable state with two degrees of freedom: Dynamical modelling versus approximate analytical formula

Thermal decay rate of a metastable state with two degrees of freedom: Dynamical modelling versus approximate analytical formula

Forming Numerical Model For Calculating Optimal Tax Rate For Resolving Stakeholders’ Interests

Langevin Approach to Modeling of Small Levitating Ordered Droplet Clusters

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