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Anomalous diffusion with under- and overshooting subordination: a competition between the very large jumps in physical and operational times.

Physical review. E, Statistical, nonlinear, and soft matter physics

Stanislavsky A, Weron K.
PMID: 21230450
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Nov;82(5):051120. doi: 10.1103/PhysRevE.82.051120. Epub 2010 Nov 16.

In this paper we present an approach to anomalous diffusion based on subordination of stochastic processes. Application of such a methodology to analysis of the diffusion processes helps better understanding of physical mechanisms underlying the nonexponential relaxation phenomena. In...

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Stanislavsky A, Weron K. Anomalous diffusion with under- and overshooting subordination: a competition between the very large jumps in physical and operational times. Phys Rev E Stat Nonlin Soft Matter Phys. 2010;82(5):051120doi: 10.1103/PhysRevE.82.051120.
Stanislavsky, A., & Weron, K. (2010). Anomalous diffusion with under- and overshooting subordination: a competition between the very large jumps in physical and operational times. Physical review. E, Statistical, nonlinear, and soft matter physics, 82(5), 051120. https://doi.org/10.1103/PhysRevE.82.051120
Stanislavsky, Aleksander, and Weron, Karina. "Anomalous diffusion with under- and overshooting subordination: a competition between the very large jumps in physical and operational times." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 82,5 (2010): 051120. doi: https://doi.org/10.1103/PhysRevE.82.051120
Stanislavsky A, Weron K. Anomalous diffusion with under- and overshooting subordination: a competition between the very large jumps in physical and operational times. Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Nov;82(5):051120. doi: 10.1103/PhysRevE.82.051120. Epub 2010 Nov 16. PMID: 21230450.
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Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics.

Physical review. E, Statistical, nonlinear, and soft matter physics

Trzmiel J, Weron K, Stanislavsky A, Jurlewicz A.
PMID: 21728485
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5):051102. doi: 10.1103/PhysRevE.83.051102. Epub 2011 May 02.

We present dielectric spectroscopy data obtained for gallium-doped Cd(0.99)Mn(0.01)Te:Ga mixed crystals, which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1. We explain this behavior, which cannot be fitted by...

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Trzmiel J, Weron K, Stanislavsky A, et al. Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics. Phys Rev E Stat Nonlin Soft Matter Phys. 2011;83(5):051102doi: 10.1103/PhysRevE.83.051102.
Trzmiel, J., Weron, K., Stanislavsky, A., & Jurlewicz, A. (2011). Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics. Physical review. E, Statistical, nonlinear, and soft matter physics, 83(5), 051102. https://doi.org/10.1103/PhysRevE.83.051102
Trzmiel, Justyna, et al. "Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 83,5 (2011): 051102. doi: https://doi.org/10.1103/PhysRevE.83.051102
Trzmiel J, Weron K, Stanislavsky A, Jurlewicz A. Experimental evidence of the role of compound counting processes in random walk approaches to fractional dynamics. Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5):051102. doi: 10.1103/PhysRevE.83.051102. Epub 2011 May 02. PMID: 21728485.
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Accelerating and retarding anomalous diffusion: A Bernstein function approach.

Physical review. E

Stanislavsky A, Weron A.
PMID: 32575224
Phys Rev E. 2020 May;101(5):052119. doi: 10.1103/PhysRevE.101.052119.

We have discovered here a duality relation between infinitely divisible subordinators which can produce both retarding and accelerating anomalous diffusion in the framework of the special Bernstein function approach. As a consequence, we show that conjugate pairs of Bernstein...

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Stanislavsky A, Weron A. Accelerating and retarding anomalous diffusion: A Bernstein function approach. Phys Rev E. 2020;101(5):052119doi: 10.1103/PhysRevE.101.052119.
Stanislavsky, A., & Weron, A. (2020). Accelerating and retarding anomalous diffusion: A Bernstein function approach. Physical review. E, 101(5), 052119. https://doi.org/10.1103/PhysRevE.101.052119
Stanislavsky, Aleksander, and Weron, Aleksander. "Accelerating and retarding anomalous diffusion: A Bernstein function approach." Physical review. E vol. 101,5 (2020): 052119. doi: https://doi.org/10.1103/PhysRevE.101.052119
Stanislavsky A, Weron A. Accelerating and retarding anomalous diffusion: A Bernstein function approach. Phys Rev E. 2020 May;101(5):052119. doi: 10.1103/PhysRevE.101.052119. PMID: 32575224.
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Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement.

Entropy (Basel, Switzerland)

Stanislavsky A, Weron A.
PMID: 33287082
Entropy (Basel). 2020 Nov 18;22(11). doi: 10.3390/e22111317.

The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit...

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Stanislavsky A, Weron A. Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement. Entropy (Basel). 2020;22(11)doi: 10.3390/e22111317.
Stanislavsky, A., & Weron, A. (2020). Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement. Entropy (Basel, Switzerland), 22(11), . https://doi.org/10.3390/e22111317
Stanislavsky, Aleksander, and Weron, Aleksander. "Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement." Entropy (Basel, Switzerland) vol. 22,11 (2020). doi: https://doi.org/10.3390/e22111317
Stanislavsky A, Weron A. Look at Tempered Subdiffusion in a Conjugate Map: Desire for the Confinement. Entropy (Basel). 2020 Nov 18;22(11). doi: 10.3390/e22111317. PMID: 33287082; PMCID: PMC7712244.
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Anomalous diffusion with transient subordinators: a link to compound relaxation laws.

The Journal of chemical physics

Stanislavsky A, Weron K, Weron A.
PMID: 24511928
J Chem Phys. 2014 Feb 07;140(5):054113. doi: 10.1063/1.4863995.

This paper deals with a problem of transient anomalous diffusion which is currently found to emerge from a wide range of complex processes. The nonscaling behavior of such phenomena reflects changes in time-scaling exponents of the mean-squared displacement through...

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Stanislavsky A, Weron K, Weron A. Anomalous diffusion with transient subordinators: a link to compound relaxation laws. J Chem Phys. 2014;140(5):054113doi: 10.1063/1.4863995.
Stanislavsky, A., Weron, K., & Weron, A. (2014). Anomalous diffusion with transient subordinators: a link to compound relaxation laws. The Journal of chemical physics, 140(5), 054113. https://doi.org/10.1063/1.4863995
Stanislavsky, Aleksander, et al. "Anomalous diffusion with transient subordinators: a link to compound relaxation laws." The Journal of chemical physics vol. 140,5 (2014): 054113. doi: https://doi.org/10.1063/1.4863995
Stanislavsky A, Weron K, Weron A. Anomalous diffusion with transient subordinators: a link to compound relaxation laws. J Chem Phys. 2014 Feb 07;140(5):054113. doi: 10.1063/1.4863995. PMID: 24511928.
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Chaotic and pseudochaotic attractors of perturbed fractional oscillator.

Chaos (Woodbury, N.Y.)

Zaslavsky GM, Stanislavsky AA, Edelman M.
PMID: 16599733
Chaos. 2006 Mar;16(1):013102. doi: 10.1063/1.2126806.

We consider a nonlinear oscillator of the Duffing type with fractional derivative of the order 1

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Zaslavsky GM, Stanislavsky AA, Edelman M. Chaotic and pseudochaotic attractors of perturbed fractional oscillator. Chaos. 2006;16(1):013102doi: 10.1063/1.2126806.
Zaslavsky, G. M., Stanislavsky, A. A., & Edelman, M. (2006). Chaotic and pseudochaotic attractors of perturbed fractional oscillator. Chaos (Woodbury, N.Y.), 16(1), 013102. https://doi.org/10.1063/1.2126806
Zaslavsky, G M, et al. "Chaotic and pseudochaotic attractors of perturbed fractional oscillator." Chaos (Woodbury, N.Y.) vol. 16,1 (2006): 013102. doi: https://doi.org/10.1063/1.2126806
Zaslavsky GM, Stanislavsky AA, Edelman M. Chaotic and pseudochaotic attractors of perturbed fractional oscillator. Chaos. 2006 Mar;16(1):013102. doi: 10.1063/1.2126806. PMID: 16599733.
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Optimal non-Gaussian search with stochastic resetting.

Physical review. E

Stanislavsky A, Weron A.
PMID: 34412216
Phys Rev E. 2021 Jul;104(1):014125. doi: 10.1103/PhysRevE.104.014125.

In this paper we reveal that each subordinated Brownian process, leading to subdiffusion, under Poissonian resetting has a stationary state with the Laplace distribution. Its location parameter is defined only by the position to which the particle resets, and...

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Stanislavsky A, Weron A. Optimal non-Gaussian search with stochastic resetting. Phys Rev E. 2021;104(1):014125doi: 10.1103/PhysRevE.104.014125.
Stanislavsky, A., & Weron, A. (2021). Optimal non-Gaussian search with stochastic resetting. Physical review. E, 104(1), 014125. https://doi.org/10.1103/PhysRevE.104.014125
Stanislavsky, Aleksander, and Weron, Aleksander. "Optimal non-Gaussian search with stochastic resetting." Physical review. E vol. 104,1 (2021): 014125. doi: https://doi.org/10.1103/PhysRevE.104.014125
Stanislavsky A, Weron A. Optimal non-Gaussian search with stochastic resetting. Phys Rev E. 2021 Jul;104(1):014125. doi: 10.1103/PhysRevE.104.014125. PMID: 34412216.
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Fractional oscillator.

Physical review. E, Statistical, nonlinear, and soft matter physics

Stanislavsky AA.
PMID: 15600586
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Nov;70(5):051103. doi: 10.1103/PhysRevE.70.051103. Epub 2004 Nov 15.

We consider a fractional oscillator which is a generalization of the conventional linear oscillator in the framework of fractional calculus. It is interpreted as an ensemble average of ordinary harmonic oscillators governed by a stochastic time arrow. The intrinsic...

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Stanislavsky AA. Fractional oscillator. Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(5):051103doi: 10.1103/PhysRevE.70.051103.
Stanislavsky, A. A. (2004). Fractional oscillator. Physical review. E, Statistical, nonlinear, and soft matter physics, 70(5), 051103. https://doi.org/10.1103/PhysRevE.70.051103
Stanislavsky, A A. "Fractional oscillator." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 70,5 (2004): 051103. doi: https://doi.org/10.1103/PhysRevE.70.051103
Stanislavsky AA. Fractional oscillator. Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Nov;70(5):051103. doi: 10.1103/PhysRevE.70.051103. Epub 2004 Nov 15. PMID: 15600586.
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Stochastic tools hidden behind the empirical dielectric relaxation laws.

Reports on progress in physics. Physical Society (Great Britain)

Stanislavsky A, Weron K.
PMID: 28155847
Rep Prog Phys. 2017 Mar;80(3):036001. doi: 10.1088/1361-6633/aa5283. Epub 2017 Feb 03.

The paper is devoted to recent advances in stochastic modeling of anomalous kinetic processes observed in dielectric materials which are prominent examples of disordered (complex) systems. Theoretical studies of dynamical properties of 'structures with variations' (Goldenfield and Kadanoff 1999...

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Stanislavsky A, Weron K. Stochastic tools hidden behind the empirical dielectric relaxation laws. Rep Prog Phys. 2017;80(3):036001doi: 10.1088/1361-6633/aa5283.
Stanislavsky, A., & Weron, K. (2017). Stochastic tools hidden behind the empirical dielectric relaxation laws. Reports on progress in physics. Physical Society (Great Britain), 80(3), 036001. https://doi.org/10.1088/1361-6633/aa5283
Stanislavsky, Aleksander, and Weron, Karina. "Stochastic tools hidden behind the empirical dielectric relaxation laws." Reports on progress in physics. Physical Society (Great Britain) vol. 80,3 (2017): 036001. doi: https://doi.org/10.1088/1361-6633/aa5283
Stanislavsky A, Weron K. Stochastic tools hidden behind the empirical dielectric relaxation laws. Rep Prog Phys. 2017 Mar;80(3):036001. doi: 10.1088/1361-6633/aa5283. Epub 2017 Feb 03. PMID: 28155847.
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Fractional dynamics from the ordinary Langevin equation.

Physical review. E, Statistical, nonlinear, and soft matter physics

Stanislavsky AA.
PMID: 12636657
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2):021111. doi: 10.1103/PhysRevE.67.021111. Epub 2003 Feb 27.

We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing. The...

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Stanislavsky AA. Fractional dynamics from the ordinary Langevin equation. Phys Rev E Stat Nonlin Soft Matter Phys. 2003;67(2):021111doi: 10.1103/PhysRevE.67.021111.
Stanislavsky, A. A. (2003). Fractional dynamics from the ordinary Langevin equation. Physical review. E, Statistical, nonlinear, and soft matter physics, 67(2), 021111. https://doi.org/10.1103/PhysRevE.67.021111
Stanislavsky, A A. "Fractional dynamics from the ordinary Langevin equation." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 67,2 (2003): 021111. doi: https://doi.org/10.1103/PhysRevE.67.021111
Stanislavsky AA. Fractional dynamics from the ordinary Langevin equation. Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2):021111. doi: 10.1103/PhysRevE.67.021111. Epub 2003 Feb 27. PMID: 12636657.
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Transient anomalous diffusion with Prabhakar-type memory.

The Journal of chemical physics

Stanislavsky A, Weron A.
PMID: 30068155
J Chem Phys. 2018 Jul 28;149(4):044107. doi: 10.1063/1.5042075.

In this paper, we derive the general properties of anomalous diffusion and non-exponential relaxation from the Fokker-Planck equation with the memory function related to the Prabhakar integral operator. The operator is a generalization of the Riemann-Liouville fractional integral and...

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Stanislavsky A, Weron A. Transient anomalous diffusion with Prabhakar-type memory. J Chem Phys. 2018;149(4):044107doi: 10.1063/1.5042075.
Stanislavsky, A., & Weron, A. (2018). Transient anomalous diffusion with Prabhakar-type memory. The Journal of chemical physics, 149(4), 044107. https://doi.org/10.1063/1.5042075
Stanislavsky, Aleksander, and Weron, Aleksander. "Transient anomalous diffusion with Prabhakar-type memory." The Journal of chemical physics vol. 149,4 (2018): 044107. doi: https://doi.org/10.1063/1.5042075
Stanislavsky A, Weron A. Transient anomalous diffusion with Prabhakar-type memory. J Chem Phys. 2018 Jul 28;149(4):044107. doi: 10.1063/1.5042075. PMID: 30068155.
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Diffusion and relaxation controlled by tempered alpha-stable processes.

Physical review. E, Statistical, nonlinear, and soft matter physics

Stanislavsky A, Weron K, Weron A.
PMID: 19113094
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Nov;78(5):051106. doi: 10.1103/PhysRevE.78.051106. Epub 2008 Nov 11.

We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered alpha-stable processes. The tempering results in the existence of all moments of operational time. The subordination by the inverse tempered alpha-stable process provides diffusion...

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Stanislavsky A, Weron K, Weron A. Diffusion and relaxation controlled by tempered alpha-stable processes. Phys Rev E Stat Nonlin Soft Matter Phys. 2008;78(5):051106doi: 10.1103/PhysRevE.78.051106.
Stanislavsky, A., Weron, K., & Weron, A. (2008). Diffusion and relaxation controlled by tempered alpha-stable processes. Physical review. E, Statistical, nonlinear, and soft matter physics, 78(5), 051106. https://doi.org/10.1103/PhysRevE.78.051106
Stanislavsky, Aleksander, et al. "Diffusion and relaxation controlled by tempered alpha-stable processes." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 78,5 (2008): 051106. doi: https://doi.org/10.1103/PhysRevE.78.051106
Stanislavsky A, Weron K, Weron A. Diffusion and relaxation controlled by tempered alpha-stable processes. Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Nov;78(5):051106. doi: 10.1103/PhysRevE.78.051106. Epub 2008 Nov 11. PMID: 19113094.
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Showing 1 to 12 of 15 entries