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1
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Hydrodynamic Memory in the Motion of Charged Brownian Particles across the Magnetic Field

100%
Tóthová J., Lisý V.
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issue 5
1051-1053
EN
An exact solution of the Langevin equation is given for a charged Brownian particle driven in an incompressible fluid by the magnetic field, taking into account the hydrodynamic aftereffect. The stochastic integro-differential Langevin equation is converted to a deterministic equation for the particle mean square displacement. We have found the mean square displacement and other time correlation functions describing the particle motion. For the motion along the field the known results from the theory of the hydrodynamic motion of a free Brownian particle are recovered. The correlation functions across the field contain at long times the familiar Einstein terms and additional algebraic tails. The longest-lived tail in the mean square displacement is proportional to t^{1/2}. At short times the motion is ballistic and independent of the magnetic field.
2
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Effect of Magnetic Field on the Fluctuations of Charged Oscillators in Viscoelastic Fluids

100%
Lisý V., Tóthová J.
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vol. 126
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issue 1
413-414
EN
In the present work the generalized Langevin equation is solved for the motion of a charged Brownian oscillator in a magnetic field, when the thermal random force is exponentially correlated in the time. This model is consistent with the assumption that the medium has weakly viscoelastic properties. The velocity autocorrelation function, time-dependent diffusion coefficient and mean square displacement of the particle have been calculated. Our solutions generalize the previous results from the literature and are obtained in a way applicable to other problems of the Brownian motion with memory.
3
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Research of Particle Transport with External Driving Force and Entropy Barrier

100%
Li S., Zhang Z., Chen D.
Acta Physica Polonica A
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2016
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vol. 129
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issue 6
1105-1108
EN
Transport of Brownian particle moving along a three-dimensional throat-like channel is investigated in the presence of an external constant force. The solution of the Fick-Jacobs equation in the situation is solved, and the probability current density and particle current describing the motion of particle are obtained. It is found that entropy barrier and external force can reverse the direction of particle current. The motion of Brownian particle can be tuned by the entropy barrier and the external force.
4
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Mobility of Hematite Submicron Particles in Water Solutions of Sugar

100%
Fornal P., Stanek J.
Acta Physica Polonica A
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2008
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vol. 114
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issue 6
1667-1673
EN
The mobility of the 100 nm Fe_2O_3 particles in dense water solutions of sugar (sucrose) was determined from the analysis of the resonance absorption line shape of the Mössbauer spectra recorded in the -5°C to 40°C temperature range for different sugar concentrations. The discrepancy between the experimental data and the prediction of the classical theory of Brownian movement are interpreted in the term of the short observation time and the interaction between the solid particles in fluids, which extends in water up to 300 nm. The sedimentation process in the studied colloids was observed.
5
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Order-Disorder Transition in 2D Conserved Spin System with Cooperative Dynamics

100%
Hałagan K., Polanowski P.
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EN
In this work Monte Carlo simulations with usage of dynamic lattice liquid model are presented, instead of the widely used direct exchange or vacancy dynamics, to investigate the dynamics of phase separation phenomenon in spin conserved system with all lattice sites occupied. The dynamic behaviour of domain growth and particle diffusion is discussed for the modified conserved order parameter Ising model. The dynamic lattice liquid model dynamics enables non-locally correlated relaxation dynamics and allows to simulate dense systems in absence of vacancies and parallel treatment of all spins. This approach involves cooperative movement of system elements enabling observation of the order-disorder phase transition in a system with highly correlated motions. Simulations were performed on 2D triangular lattice for several investigated temperatures. Presented results include temporal evolution of domain morphology and diffusion of system elements.
6
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Kinetic Theory of the Langevin Saturation in Dilute Solution of Dipolar Symmetric-Top Molecules in Spherical Solvents

100%
Alexiewicz W., Grygiel K.
Acta Physica Polonica A
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2008
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vol. 114
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issue 4
667-686
EN
Assuming the low molecular reorientation approximation, the formulae for the third-order electric polarization induced in liquids composed of rigid noninteracting dipolar, symmetric-top molecules in spherical solvents were derived. Our medium is acted on by a strong external dc bias electric field superimposed on a weak ac electric field, and the classical Smoluchowski-Debye equation for rotational diffusion of the symmetric-top molecules is applied. In order to highlight the influence of the anisotropy of rotational diffusion tensor components and the orientation of permanent dipole moment of the molecule on the complex linear and nonlinear electric susceptibilities, we present three-dimensional plots of the linear and nonlinear dispersion and absorption spectra, for different values of the frequency of ac electric field.
7
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Cole-Cole Plots for Linear and Nonlinear Dielectric Relaxation in Solutions of Rigid Highly Dipolar Symmetric-Top Molecules in Spherical Solvents

100%
Alexiewicz W., Grygiel K.
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EN
The graphical analysis of the influence of the rotational diffusion tensor anisotropy and the orientation of the permanent dipole moment on the linear and nonlinear dielectric relaxation is shown. The solution of Smoluchowski-Debye rotational diffusion equation for rigid, and noninteracting polar, symmetric-top molecules, in the "weak molecular reorientation approximation", was used. In order to highlight the influence of the symmetric shape of molecule, in comparison with classical, spherical-top Smoluchowski rotational diffusion, we present sets of Argand-type plots and three-dimensional Cole-Cole diagrams for linear and nonlinear electric susceptibilities. The results indicate that, in describing the nonlinear dielectric relaxation, the simplest spherical-top rotational diffusion model may be a sufficient approximation in some special cases only.
8
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Student's t-Distribution versus Zeldovich-Kompaneets Solution of Diffusion Problem

100%
Wojnar R.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-133-B-136
EN
Student's t-distribution is compared to a solution of superdiffusion equation. This t-distribution is a continuous probability distribution that arises in the problem of estimating the mean of a normally distributed population when the sample size is small. Formally it can written in the form similar to the Gaussian distribution, in which, however, instead of usual exponential function, the so called K-exponential - a form of binomial distribution - appears. Similar binomial form has the Zeldovich-Kompaneets solution of nonlinear diffusion-like problems. A superdiffusion process, similar to a Zeldovich-Kompaneets heat conduction process, is defined by a nonlinear diffusion equation in which the diffusion coefficient takes the form $D=a(t)(1/f)^n$, where a=a(t) is an external time modulation, n is a positive constant, and f=f(x,t) is a solution to the nonlinear diffusion equation. It is also shown that a Zeldovich-Kompaneets solution still satisfies the superdiffusion equation if a=a(t) is replaced by the mean value of a. A solution to the superdiffusion equation is given. This may be useful in description of social, financial, and biological processes. In particular, the solution possesses a fat tail character that is similar to probability distributions observed at stock markets. The limitation of the analogy with the Student distribution is also indicated.
9
Content available remote

Brownian Movement of Inorganic Nanoparticles in Sediments

88%
Fornal P., Stanek J.
Acta Physica Polonica A
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2011
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vol. 119
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issue 1
12-14
EN
The 100 nm particles of Fe_{2}O_{3} and metallic Fe sedimented jointly with Al_{2}O_{3} powder from their suspension in oleic acid exhibit distinguished mobility which depends on the concentration of aluminum oxide. This observation is interpreted as the result of the interparticle Fe-Fe magnetic interactions which lead to the formation of the rigid network of magnetic metallic iron nanoparticles.
10
Content available remote

Use of Quantum Mechanical Methods to Obtain a Bohm-Type Coefficient of Diffusion. Part II

75%
Jiménez-Domínguez H.
Acta Physica Polonica A
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2011
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vol. 119
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issue 6
798-802
EN
The research reported in an article previously published in this journal is pursued here further on. A staircase profile of the graphical representation of the absolute value of the expression for Bohm-type diffusion in two dimensions is analyzed allowing the suggestion that its shape could be related to the well-known structure of levels of the quantized square of the guiding center radius vector and that this structure could be responsible for the appearance of the successive steps in such a profile. When these considerations are taken into account, the expression for Bohm-type diffusion in two dimensions is normalized according to the formula for the quantized square of the guiding center radius vector and a diffusion coefficient whose value is 4/π times the Bohm diffusion coefficient is obtained for large values of the independent variable.
11
Content available remote

Subdiffusion with External Time Modulation

75%
Wojnar R.
Acta Physica Polonica A
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2008
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vol. 114
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issue 3
607-611
EN
A subdiffusion process, similar to a Zeldovich-Kompaneets heat conduction process, is defined by a nonlinear diffusion equation in which the diffusion coefficient takes the form D=a(t)f^n, where a=a(t) is an external time modulation, n is a positive constant, and f=f(x, t) is a solution to the nonlinear diffusive equation. It is shown that a Zeldovich-Kompaneets solution satisfies the subdiffusion equation if a=a(t) is replaced by the mean value of a. Also, a solution to the subdiffusion equation is constructed that may be useful in description of biological, social, and financial processes.
12
Content available remote

Rayleigh's Distribution, Wigner's Surmise and Equation of the Diffusion

75%
Wojnar R.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
624-628
EN
After summaries on Rayleigh's distribution and Wigner's surmise, the time evolution of Rayleigh-Wigner's statistics is studied and a suitable diffusion type equation is proposed. Also the variance and kurtosis of time evolution of Rayleigh's distribution are calculated. Obtained results may be useful in description of physical, social and biological processes.
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