Swelling/deswelling of polyacrylamide gels in aqueous NaCl solution: Light scattering and macroscopic swelling study

Swelling kinetics of water-swollen polyacrylamide (PAAm) hydrogels (WSG) was investigated in various concentrations of aqueous NaCl by macroscopic swelling measurements. For lower concentration of NaCl, WSG showed exponential swelling whereas at higher concentration of NaCl it underwent deswelling at short times and exponential swelling at long times. From these studies, collective diffusion coefficient, D, of the polymer network and polymer?Csolvent interaction parameter, ??, were calculated and found to decrease with increase in [NaCl]. Collective diffusion coefficients measured from dynamic light scattering (DLS) and that obtained from macroscopic swelling measurements are found to agree well. Measured ensemble-averaged dynamic structure factor f(q,t) for WSG and salt-swollen gels (SSG) showed an initial decay followed by a plateau at long times and it can be described by harmonically bound Brownian particle (HBBP) model. Enhanced scattering intensity at low scattering angles using static light scattering (SLS) measurements revealed the presence of inhomogeneities in PAAm gels. The reasons for increased scattering intensity of SSG over WSG gel and the linear decrease of D with increase in NaCl concentration are explained.     

Theory of light scattering from a system of interacting Brownian particles

Starting from a N-particle diffusion equation for a system of N interacting spherical Brownian particles, a non-linear transport equation for concentration fluctuations δc(r, t) of the particles is derived. This dynamic equation is transformed into a hierarchy of equations for retarded propagators of increasing numbers of concentration fluctuations. A cluster expansion to lowest order in the average concentration results in a set of two coupled equations. The spectrum of light scattered by the interacting particles is in general not a Lorentzian, due to the non-linear term in the transport equation. For small scattering wave vectors k the width is D(ω)k², where ω is the transferred frequency. It is shown that D(0) = D_e, the effective diffusion coefficient. For a hardcore interaction potential the spectrum is Lorentzian and it is found that D_e = D₀(1 + φ), where D₀ is the diffusion constant for independent particles and φ the volume concentration of Brownian particles.     

Diffusion in a tube consisting of alternating wide and narrow sections

The problem of the diffusion of particles in a tube consisting of identical units, each composed of a wide and narrow section is solved. With an approach based on reducing the problem to a one-dimensional, the statistics of times of particle transition between adjacent sections is determined, which is a detailed characteristic of the diffusion process. An expression for the effective diffusion coefficient D _ef , defining the slow-down of transport due to variations of the tube profile, is derived. It is shown that D _ef behaves monotonically with increasing length of both the narrow and wide sections. The predictions of analytical formulas are in good agreement with the results of computer simulation performed by the Brownian dynamics method.     

Dynamical properties of colloidal systems: III. Collective and self-diffusion of interacting charged particles

The formalism, developed in two earlier papers, for the dynamics of interacting Brownian particles is applied to a system of charged spherical particles in solution. Memory-type transport equations are derived for the propagators of collective and self-diffusion. The memory function for collective diffusion can be related, in the hydrodynamic limit, to the viscosity of the “fluid” of Brownian particles. The memory functions are calculated for a Debye-Hückel system, from an experimentally determined static structure factor S(k), and for an overdamped one-component plasma (OCP). In the two latter cases satisfactory agreement is found with dynamical light scattering results on solutions of polystyrene spheres; in particular, the deviation of the dynamical structure factor from a simple exponential decay can be related to memory effects. With regard to self-diffusion the velocity autocorrelation function, the mean square displacement of one particle and from it the self-diffusion coefficient D_s are calculated. Using S(k) for an actual system, $\text{D}{}_{\mathrm{s}}\text{≈}\text{1}\text{3}\text{D}{}_0$ is obtained, where D₀ is the free diffusion constant. The calculations on the basis of the overdamped OCP-model show that the dynamical properties of the experimentally investigated systems of charged polystyrene spheres can be described by this model for a wide range of scattering angles.     

Effective diffusivity of solute in multiphase materials with segregation

The effective diffusion coefficient D_eff for solute in a multiphase microstructure in which solute segregation can occur is related to D_eff for an isomorphic microstructure in which no segregation occurs. This permits analytical expressions (approximations, bounds, etc.) and methods of numerical calculation for D_eff that neglect solute segregation to be applied to systems that exhibit segregation. As an example, exact results are obtained for solute diffusion and segregation to grain boundaries in an idealized polycrystalline microstructure.     

Angle-of-arrival variance’s dependence on the aperture size for indoor convective turbulence

We analyze the angle-of-arrival variance of an expanded and collimated laser beam once it has traveled through an indoor convective turbulence. A continuous position detector is set at the focus of a lens collecting the laser beam. The effect of the different turbulent scales, between the inner and the outer scales, is studied by changing the diameter of a circular pupil before the collector lens. The experimental optical setup follows the design introduced by Masciadri and Vernin [Appl. Opt., 36(6) (1997) 1320]. Tilt data measurements are studied using the fractional Brownian motion model for the turbulent wave-front phase introduced in a previous paper [Pérez et al., J. Opt. Soc. Am. A 21(10) (2004) 1962]. The Hurst exponents associated to different strengths of turbulence are obtained from the here proposed D^2H−2 dependence.     

Effect of thermal inhomogeneity on the performance of a Brownian heat engine

We explore the effect of thermal inhomogeneity on the performance of a Brownian heat engine by considering exactly solvable models. We first consider a Brownian heat engine which is modeled as a Brownian particle in a ratchet potential moving through a highly viscous medium driven by the thermal kick it receives from a linearly decreasing background temperature. We show that even though the energy transfer due to kinetic energy is neglected, Carnot efficiency cannot be achieved at quasistatic limit. At quasistatic limit, the efficiency for such a Brownian heat engine approaches the efficiency of endoreversible engine η = 1 ? √T _c /T _h [F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)]. Moreover, the dependence of the current, the efficiency and the coefficient of performance of the refrigerator on the model parameters is also explored via Brownian dynamic simulations and analytically. We show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature [M. Asfaw, M. Bekele, Eur. Phys. J. B 38, 457 (2004), M. Asfaw, M. Bekele, Physica A 384, 346 (2007)]. Furthermore, for a Brownian heat engine driven by a piecewise constant temperature, we show that systematic removal of the inhomogeneous medium leads to a homogeneous medium with a uniform temperature where the effect of temperature inhomogeneity is replaced by an effective load.     

On the integrability of the SU(N) Hubbard model

We exhibit explicitly the intertwiner operator for the monodromy matrices of the SU(N) Hubbard model recently proposed by Maassarani [Phys. Lett. A 239 (1998) 187]. This produces a new family of non-additive R-matrices and generalizes an earlier result by Shastry [Phys. Rev. Lett. 56 (1986) 2453; J. Stat. Phys. 30 (1988) 57].     

Characterisation of a three-dimensional Brownian motor in optical lattices

We present here a detailed study of the behaviour of a three dimensional Brownian motor based on cold atoms in a double optical lattice [P. Sj?lund et al., Phys. Rev. Lett. 96, 190602 (2006)]. This includes both experiments and numerical simulations of a Brownian particle. The potentials used are spatially and temporally symmetric, but combined spatiotemporal symmetry is broken by phase shifts and asymmetric transfer rates between potentials. The diffusion of atoms in the optical lattices is rectified and controlled both in direction and speed along three dimensions. We explore a large range of experimental parameters, where irradiances and detunings of the optical lattice lights are varied within the dissipative regime. Induced drift velocities in the order of one atomic recoil velocity have been achieved.     

Classical oscillator with position-dependent mass in a complex domain

We study complexified Harmonic Oscillator with a position-dependent mass, termed as Complex Exotic Oscillator (CEO). The complexification induces a gauge invariance [A.V. Smilga, J. Phys. A 41 (2008) 244026, arXiv:0706.4064; A. Mostafazadeh, J. Math. Phys. 43 (2002) 205; A. Mostafazadeh, J. Math. Phys. 43 (2002) 2814; A. Mostafazadeh, J. Math. Phys. 43 (2002) 3944]. The role of PT-symmetry is discussed from the perspective of classical trajectories of CEO for real energy. Some trajectories of CEO are similar to those for the particle in a quartic potential in the complex domain [C.M. Bender, S. Boettcher, P.N. Meisinger, J. Math. Phys. 40 (1999) 2201; C.M. Bender, D.D. Holm, D. Hook, J. Phys. A 40 (2007) F793, arXiv:0705.3893].     

Simulation study of lateral diffusion in lipid-sterol bilayer mixtures

We employ off-lattice Monte Carlo simulations to study lateral diffusion in lipid-sterol bilayers using a two-dimensional model system which has been designed to simulate the experimental phase diagrams of both lipid-cholesterol and lipid-lanosterol systems. We focus on the effects of varying sterol concentration and temperature on the tracer diffusion coefficient, D, which characterizes the lateral motion of single tagged lipids in a bilayer. Generally, we find that increasing the cholesterol concentration suppresses D due to an increased conformational ordering of lipid chains. We argue that this effect competes with an increase in the average free area per lipid, which favours an increase in D. At temperatures close to the main transition temperature, the competition between the two effects leads to intriguing behavior of D. Overall, the model results are in excellent qualitative agreement with available experimental results for lipid-cholesterol mixtures. Additional studies of a model lipid-lanosterol system, for which experimental diffusion results are not available, predict that the presence of lanosterol has a smaller effect than cholesterol on reducing D relative to the pure lipid system. We conclude that the molecular model employed contains the essential features required to describe many of the qualitative features of the lateral diffusion behavior in lipid-sterol systems. Received 24 November 2000 and Received in final form 30 April 2001     

An atomistic approach to the dielectric modes of BaTiO3 and SrTiO3

Recently, a clear long-sought Debye mode (D) in barium titanate (BT) was identified [J. Hlinka, T. Ostapchuk, D. Nuzhnyy, J. Petzelt, P. Kuzel, C. Kadlec, P. Vanek, I. Ponomareva, L. Bellaiche, Phys. Rev. Lett. 101 (2008) 167402] and this mode was shown to originate from the polar coordinate that also generates the so-called Slater mode (S). The inter-relations between the D mode and the normal A1-type phonon modes were studied by those authors using a four-mode phenomenological model. The present work is to offer an atomistic support of their work and to better illustrate the nature of and the couplings between these modes. In addition, we extend the as-obtained insights to the investigation of the nature of the low frequency Raman peaks that were found in ¹⁸O-substituted strontium titanate (ST) many years ago [M. Itoh, R. Wang, Y. Inaguma, T. Yamaguchi, Y.-J. Shan, T. Nakamura, Phys. Rev. Lett. 82 (1999) 3540]. Thus, our work provides important information on the connections between the lattice dynamics of BT and ST.     

Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks) are observed for any N and for low values of the external amplitude F. The coexistence of left and right running states enhances the power α from the time dependence of the mean square displacement (MSD). It is shown that α is twice the average of the power of the separated left and right MSDs. Normal random walks are obtained by increasing F. We show that the maximal mobility of particles along the periodic structure occurs just before superdiffusive motion disappears and Levy walks are transformed into normal random walks.     

Diffusion of electrons scattered by short-range impurities in a quantizing magnetic field

Formulas for transverse diffusion and conductivity in a semiconductor are obtained for electrons scattered by neutral impurities in a quantizing magnetic field. The formulas are valid for an impurity potential of arbitrary depth. Based on Kubo’s theory [1], calculations are performed using electron wavefunctions of the problem of single-impurity scattering in a magnetic field [2]. The poles of the scattering amplitude correctly determine electron eigenstates and magnetic impurity states. As a result, an exact expression is found for the dependence of transverse diffusion coefficient D _⊥ on longitudinal electron energy ? due to scattering by short-range (neutral) impurities. The behavior of D _⊥(?) is examined over an interval of magnetic field strength for several values of impurity potential depth. The experimental observability of diffusion and conductivity using IR lasers is discussed.     

Ionic contribution to Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions

A theoretical treatment is performed of the mechanism (suggested in N. F. Bunkin andA. V. Lobeev, Z. Phys. Chem. 214, 269 (2000)) of ionic effect on the Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions. The mechanism consists essentially in that the fluctuation electric field caused by Brownian motion of ions dissolved in a liquid leads, because of the Kerr polarization effect, to fluctuations of optical anisotropy of the scattering medium. The spectral characteristics of the Rayleigh line wing are obtained using the fluctuation-dissipative theorem as applied to equilibrium thermal electromagnetic field. Expressions are derived for the integral intensity and spectral width (Δν) of the Rayleigh line wing in terms of parameters of liquid solution such as the temperature T, the viscosity η, the concentration of dissolved ions n _i, and the coefficient of their diffusion D _i. It is demonstrated that Δν ∝ exp(?W/2T), where W is the activation energy of ion mobility b _i = D_i/T. The possible region of validity of developed theoretical concepts as applied to the experimental data for the Rayleigh line wing in electrolytic solutions is discussed.     

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter N _b, thermophoresis parameter N _t, radiation parameter N _r, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.     

Mean first passage time of active Brownian particle in one dimension

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free active Brownian particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r* for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.     

Many-body effects in the binding energies of image states at surfaces

A study of the influence of many-body effects on binding energies and effective masses of image potential induced surface states is presented. The binding energies calculated using experimentally measured ε(ω) response functions show a dependence on the electron density different from that obtained using a plasmon model, and are in agreement with recent experimental data of diesen et al. [Phys. Rev. B33 (1986) 5241]. The effects of plasmon dispersion and single particle excitations on binding energies are evaluated with a simple model, and it is shown that they result in a strong cancellation in the range of r_s values where most experimental data have been obtained (r_s ≈ 3), if realistic values of the surface plasmon dispersion relation are used. Corrections to the effective masses due to many-body effects are shown to be of the order of 1%.