Searcharxiv⌕ Search

arXiv subjects

J. Tothova

Publications and source records attributed to J. Tothova.

15 recordsLinked to original sources
arXiv2017

Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time.

cond-mat.stat-mech↗
arXiv2016

Comment on "Motional Averaging of Nuclear Resonance in a Field Gradient"

In the Letter by Nanette N. Jarenwattananon and Louis-S. Bouchard [PRL 114, 197601 (2015)] an NMR experiment on gases in the presence of a magnetic-field gradient has been considered. As distinct from the traditional description of molecular self-diffusion, the authors calculate the decoherence of the signal taking into account the histories of molecular displacements. For this purpose the generalized Langevin equation (GLE) is applied. We show that the use of this equation is inappropriate. The calculations performed in the Letter are not correct and do not lead to the reported revised expression for line broadening that takes into account the autocorrelation effects in the diffusion process. The surprising temperature behavior of the observed NMR signal is thus not explained. In particular, the linewidth does not follow the power law f ~ T^(-1/2) at high temperatures. We give also Remarks on the Jarenwattananon and Bouchard Reply [Phys. Rev. Lett. 117, 249702 (2016)].

cond-mat.stat-mech↗
arXiv2011

Brownian motion of charged particles driven by correlated noise

Stochastic motion of charged particles in the magnetic field was first studied almost half a century ago in the classical works by Taylor and Kursunoglu in connection with the diffusion of electrons and ions in plasma. In their works the long-time limits of the mean square displacement (MSD) of the particles have been found. Later Furuse on the basis of standard Langevin theory generalized their results for arbitrary times. The currently observed revival of these problems is mainly related to memory effects in the diffusion of particles, which appear when colored random forces act on the particles from their surroundings. In the present work an exact analytical solution of the generalized Langevin equation has been found for the motion of the particle in an external magnetic field when the random force is exponentially correlated in the time. The obtained MSD of the particle motion across the field contains a term proportional to the time, a constant term, and contributions exponentially decaying in the time. The results are more general than the previous results from the literature and are obtained in a considerably simpler way applicable to many other problems of the Brownian motion with memory.

cond-mat.soft↗
arXiv2010

An old efficient approach to anomalous Brownian motion

A number of random processes in various fields of science is described by phenomenological equations containing a stochastic force, the best known example being the Langevin equation (LE) for the Brownian motion (BM) of particles. Long ago Vladimirsky (1942) proposed a simple method for solving such equations. The method, based on the classical Gibbs statistics, consists in converting the stochastic LE into a deterministic one, and is applicable to linear equations with any kind of memory. When the memory effects are taken into account in the description of the BM, the mean square displacement of the particle at long times can exhibit an "anomalous" (different from that in the Einstein theory) time dependence. In the present paper we show how some general properties of such anomalous BM can be easily derived using the Vladimirsky approach. The method can be effectively used in solving many of the problems currently considered in the literature. We apply it to the description of the BM when the memory kernel in the Volterra-type integro-differential LE exponentially decreases with the time. The problem of the hydrodynamic BM of a charged particle in an external magnetic field is also solved.

cond-mat.stat-mech↗
arXiv2007

Rheology of dilute polymer solutions with time-dependent screening of hydrodynamic interactions

The screening of hydrodynamic interactions (HI) essentially affects macroscopic properties of polymeric solutions. This screening depends not only on the polymer concentration but has a dynamic nature. In the present work, a bead-spring theory is developed, in which this phenomenon is described for solutions of nonentangled polymer coils. The equation of motion for the beads of a test polymer is solved together with the Brinkman's equation for the solvent velocity that takes into account the presence of other coils in solution. The time correlation functions for the polymer normal modes are found. A tendency to the screening of HI is demonstrated on the coil diffusion as well as on the relaxation of its internal modes. With the growing concentration of the coils they both show a transition to the exact Rouse behavior. The viscosity of the solution and some other observable quantities are calculated. As the time increaes, the time-dependent quantities change their behavior from the Rouse regime through the Zimm one again to the Rouse dynamics at long times.

cond-mat.soft↗
arXiv2007

Simple derivation of the first cumulant for the Rouse chain

A simple analytic expression for the first cumulant of the dynamic structure factor of a polymer coil in the Rouse model is derived. The obtained formula is exact within the usual assumption of the continuum distribution of beads along the chain. It reflects the contributions to the scattering of light or neutrons from both the internal motion of the polymer and its diffusion, and is valid in the whole region of the wave-vector change at the scattering.

cond-mat.soft↗
arXiv2007

Effects of hydrodynamic noise on the diffusion of polymers in dilute solutions

The Rouse-Zimm equation for the position vectors of beads mapping the polymer is generalized by taking into account the viscous aftereffect and the hydrodynamic noise. For the noise, the random fluctuations of the hydrodynamic tensor of stresses are responsible. The preaveraging of the Oseen tensor for the nonstationary Navier-Stokes equation allowed us to relate the time correlation functions of the Fourier components of the bead position to the correlation functions of the hydrodynamic field created by the noise. The velocity autocorrelation function of the center of inertia of the polymer coil is considered in detail for both the short and long times when it behaves according to the t^(-3/2) law and does not depend on any polymer parameters. The diffusion coefficient of the polymer is close to that from the Zimm theory, with corrections depending on the ratio between the size of the bead and the size of the whole coil.

cond-mat.stat-mech↗
arXiv2007

Addendum to "Monomer motion in single- and double-stranded DNA coils" [arXiv: cond-mat/0509399]

In our work [J. Tothova et al., cond-mat/0509399] the first observation of the kinetics of individual polymer monomers using the fluorescence correlation technique [R. Shusterman et al., Phys. Rev. Lett. 92, 048303 (2004)] has been interpreted within the joint Rouse-Zimm theory. Optimizing the theory to the experimental data the phenomenological parameters for the statistical-mechanical description of the universal behavior of double- and single-stranded DNA and the dominant types of their dynamics have been determined. Recently, these data have been corrected [R. Shusterman et al., Phys. Rev. Lett. 98, 029901 (2007)]. In this Addendum the fits of the theory to the new data are presented. The main conclusions of our preceding work remain unchanged. Moreover, the new data allow a significantly better agreement with the theory than the previous ones.

cond-mat.soft↗
arXiv2005

The Rouse-Zimm-Brinkman theory of the dynamics of polymers in dilute solutions

We propose a theory of the dynamics of polymers in dilute solution, in which the popular Zimm and Rouse models are limiting cases of infinitely large and small draining parameter. The equation of motion for the polymer segments beads) is solved together with Brinkman's equation for the solvent velocity that takes into account the presence of other polymer coils in the solution. The equation for the polymer normal modes is obtained and the relevant time correlation functions are found. A tendency to the time-dependent hydrodynamic screening is demonstrated on the diffusion of the polymers as well as on the relaxation of their internal modes. With the growing concentration of the coils in solution they both show a transition to the (exactly) Rouse behavior. The shear viscosity of the solution, the Huggins coefficient and other quantities are calculated and shown to be notably different from the known results.

cond-mat.soft↗
arXiv2005

Monomer motion in single- and double-stranded DNA coils

The dynamics of flexible polymers in dilute solution is usually described in terms of the pure Rouse or Zimm bead-spring models assuming continuous distribution of the internal relaxation modes. We show that this approach may lead to misleading interpretation of experimental data. The more correct description should come from the joint Rouse-Zimm (RZ) theory that contains the Rouse and Zimm models as limiting cases. The internal modes are discrete with respect to the mode number, and the type of the bead motion changes in the time from the Rouse to Zimm behavior. We demonstrate this interpreting the recent first observation of the kinetics of individual polymer monomers using the fluorescence correlation technique [R. Shusterman et al., Phys. Rev. Lett. 92, 048303 (2004)]. Optimizing the RZ theory to the data on double- and single-stranded DNA coils (dsDNA and ssDNA) the parameters for the statistical-mechanical description of the behavior of these polymers have been determined. The calculations indicate that dsDNA follows mainly the classical Zimm-type kinetics rather than the Rouse one as it was originally proposed. Single-stranded DNA also behaves predominantly as the Zimm polymer. For dsDNA the Kuhn length agrees with the commonly accepted value in the literature while in the case of ssDNA it takes a value much larger than it is usually cited in the literature.

cond-mat.soft↗
arXiv2005

The dynamics of polymers in solution with hydrodynamic memory

The theory of the dynamics of polymers in solution is developed coming from the hydrodynamic theory of the Brownian motion (BM) and the Rouse-Zimm (RZ) model. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the previous RZ models based on the Einstein theory of BM. The MSD of the polymer coil is at short times proportional to t^2 (instead of t). At long times it contains additional (to the Einstein term) contributions, the leading of which is ~ t^{1/2}. The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. This is displayed in the tails of their correlation functions, the longest-lived being ~ t^{-3/2} in the Rouse limit and t^{-5/2} in the Zimm case when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular a slower diffusion of the coil, should be observable in dynamic scattering experiments. The dynamic structure factor and the first cumulant of the polymer coil are calculated. The theory is extended to the situation when the dynamics of the studied polymer is influenced by the presence of other polymers in dilute solution.

cond-mat.soft↗
arXiv2004

On two direct methods for measurement of interfacial tension at microdroplet surfaces

In the presence of surfactants, the interfacial tension (IFT) of microscopic droplets differs significantly from IFT of macroscopic drops for the same surfactant solutions. As a result, IFT between two immiscible liquids can strongly depend on the experimental design. In the present work a simple theoretical description of two possible techniques for measurement of IFT at microdroplet surfaces is proposed: the spinning drop and the micropipette methods. We take into account that for microdroplets the IFT can be not the unique parameter determining the surface elastic energy. The previous interpretation of the experiments is generalized within the Helfrich's concept of interfacial elasticity. Simple equations are obtained that could be used to test the Helfrich's theory and in the direct determination, in addition to IFT, of such characteristics of the interface as the bending rigidity and spontaneous curvature.

cond-mat.soft↗
arXiv2004

On the (hydrodynamic) memory in the theory of Brownian motion

The aim of this paper is to remember and review several exceptional investigations on the theory of the Brownian motion. Although in these works the first correct hydrodynamic theories of the translational and rotational Brownian motion have been created, they remained unknown or very little known to the physical community and long time after the appearance of the original papers their main results were rediscovered by other authors. The reviewed works are highly interesting not only historically but from the methodical point of view as well.

cond-mat.stat-mech↗
arXiv2004

Long-time dynamics of Rouse-Zimm polymers in dilute solutions with hydrodynamic memory

The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times \~ t^2 (instead of ~ t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is ~ t^(1/2). The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest-lived being ~ t^(-3/2) in the Rouse limit and t^(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments.

cond-mat.soft↗