How Stickiness Can Speed Up Diffusion in Confined Systems.

The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian tracers. Here, using a general adsorption desorption model with surface diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion. In particular, we show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk. Even more remarkably, this enhancement effect occurs when the effective diffusion constant, when restricted to surfaces only, is lower than the effective diffusivity with purely reflecting boundaries. We give analytical formulas for this intriguing effect in periodic arrays of spheres as well as undulating microchannels. Our results are confirmed by numerical calculations and Monte Carlo simulations.

Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks.

We revisit the classic problem of the effective diffusion constant of a Brownian particle in a square lattice of reflecting impenetrable hard disks. This diffusion constant is also related to the effective conductivity of non-conducting and infinitely conductive disks in the same geometry. We show how a recently derived Green's function for the periodic lattice can be exploited to derive a series expansion of the diffusion constant in terms of the disk's volume fraction φ. Second, we propose a variant of the Fick-Jacobs approximation to study the large volume fraction limit. This combination of analytical results is shown to describe the behavior of the diffusion constant for all volume fractions.

Dispersion in two-dimensional periodic channels with discontinuous profiles.

The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose cross section presents singular points, such as abrupt changes of radius or the presence of thin walls, with openings, delimiting periodic compartments composing the channel. Dispersion in such systems is analyzed using the Fick-Jacobs (FJ) approximation. This approximation assumes a much faster equilibration in the lateral than in the axial direction, along which the dispersion is measured. If the characteristic width a of the channel is much smaller than the period L of the channel, i.e., ε = a/L is small, this assumption is clearly valid for Brownian particles. For discontinuous channels, the FJ approximation is only valid at the lowest order in ε and provides a rough, though on occasions rather accurate, estimate of the effective diffusivity. Here we provide formulas for the effective diffusivity in discontinuous channels that are asymptotically exact at the next-to-leading order in ε. Each discontinuity leads to a reduction of the effective diffusivity. We show that our theory is consistent with the picture of effective trapping rates associated with each discontinuity, for which our theory provides explicit and asymptotically exact formulas. Our analytical predictions are confirmed by numerical analysis. Our results provide a precise quantification of the kinetic entropic barriers associated with profile singularities.

Prevalence and predictors of thyroid functional abnormalities in newly diagnosed AL amyloidosis.

BACKGROUND: Data on the effect of systemic immunoglobulin light chain amyloidosis (AL amyloidosis) on thyroid function are limited. OBJECTIVE: To assess the prevalence of hypothyroidism in AL amyloidosis patients and determine its predictors. METHODS: 1142 newly diagnosed AL amyloidosis patients were grouped based on the thyroid-stimulating hormone (TSH) measurement at diagnosis: hypothyroid group (TSH above upper normal reference; >5 mIU L-1 ; n = 217, 19% of study participants) and euthyroid group (n = 925, 81%). Predictors for hypothyroidism were assessed in a binary multivariate model. Survival between groups was compared using the log-rank test and a multivariate analysis. RESULTS: Patients with hypothyroidism were older, more likely to present with renal and hepatic involvement and had a higher light chain burden compared to patients in the euthyroid group. Higher proteinuria in patients with renal involvement and lower albumin in patients with hepatic involvement were associated with hypothyroidism. In a binary logistic regression model, age ≥65 years, female sex, renal involvement, hepatic involvement, kappa light chain restriction and amiodarone use were independently associated with hypothyroidism. Ninety-three per cent of patients in the hypothyroid group with free thyroxine measurement had normal values, consistent with subclinical hypothyroidism. Patients in the hypothyroid group had a shorter survival compared to patients in the euthyroid group (4-year survival 36% vs 43%; P = 0.008), a difference that was maintained in a multivariate analysis. CONCLUSION: A significant proportion of patients with AL amyloidosis present with hypothyroidism, predominantly subclinical, which carries a survival disadvantage. Routine assessment of TSH in these patients is warranted.

Universal time-dependent dispersion properties for diffusion in a one-dimensional critically tilted potential.

We consider the time-dependent dispersion properties of overdamped tracer particles diffusing in a one-dimensional periodic potential under the influence of an additional constant tilting force F. The system is studied in the region where the force is close to the critical value F_{c} at which the barriers separating neighboring potential wells disappear. We show that, when F crosses the critical value, the shape of the mean-square displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate-time scales with an effective diffusion coefficient which is much larger than the late-time diffusion coefficient for F>F_{c}, whereas for F

Force-Induced Dispersion in Heterogeneous Media.

The effect of a constant applied external force, induced for instance by an electric or gravitational field, on the dispersion of Brownian particles in periodic media with spatially varying diffusivity, and thus mobility, is studied. We show that external forces can greatly enhance dispersion in the direction of the applied force and also modify, to a lesser extent and in some cases nonmonotonically, dispersion perpendicular to the applied force. Our results thus open up the intriguing possibility of modulating the dispersive properties of heterogeneous media by using externally applied force fields. These results are obtained via a Kubo formula that can be applied to any periodic advection diffusion system in any spatial dimension.

Kubo formulas for dispersion in heterogeneous periodic nonequilibrium systems.

We consider the dispersion properties of tracer particles moving in nonequilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drifts, eventually with the presence of obstacles. We derive a Kubo-like formula for the time-dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite-time corrections to these transport coefficients. In one dimension, we give a closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary nonequilibrium periodic advection-diffusion systems.

Drag forces on inclusions in classical fields with dissipative dynamics.

We study the drag force on uniformly moving inclusions which interact linearly with dynamical free field theories commonly used to study soft condensed matter systems. Drag forces are shown to be nonlinear functions of the inclusion velocity and depend strongly on the field dynamics. The general results obtained can be used to explain drag forces in Ising systems and also predict the existence of drag forces on proteins in membranes due to couplings to various physical parameters of the membrane such as composition, phase and height fluctuations.

Path integrals for stiff polymers applied to membrane physics.

Path integrals similar to those describing stiff polymers arise in the Helfrich model for membranes. We show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in a bulk membrane. The fluctuation induced contribution to the line tension between the stripe and the bulk phase is computed. Also the effective interaction between the interfaces of the two phases can be computed. Explicit forms are given for this Casmir-like interaction in the tensionless case where the two phases have differing bending rigidities.

Membrane perturbation by an external electric field: a mechanism to permit molecular uptake.

Electropermeabilisation is a well established physical method, based on the application of electric pulses, which induces the transient permeabilisation of the cell membrane. External molecules, otherwise nonpermeant, can enter the cell. Electropermeabilisation is now in use for the delivery of a large variety of molecules, as drugs and nucleic acids. Therefore, the method has great potential in the fields of cancer treatment and gene therapy. However many open questions about the underlying physical mechanisms involved remain to be answered or fully elucidated. In particular, the induced changes by the effects of the applied field on the membrane structure are still far from being fully understood. The present review focuses on questions related to the current theories, i.e. the basic physical processes responsible for the electropermeabilisation of lipid membranes. It also addresses recent findings using molecular dynamics simulations as well as experimental studies of the effect of the field on membrane components.

Fluctuation-induced interactions between domains in membranes.

We study a model lipid bilayer composed of a mixture of two incompatible lipid types which have a natural tendency to segregate in the absence of membrane fluctuations. The membrane is mechanically characterized by a local bending rigidity kappa(phi) which varies with the average local lipid composition phi. We show, in the case where kappa varies weakly with phi, that the effective interaction between lipids of the same type either can be everywhere attractive or can have a repulsive component at intermediate distances greater than the typical lipid size. When this interaction has a repulsive component, it can prevent macrophase separation and lead to separation in mesophases with a finite domain size. This effect could be relevant to certain experimental and numerical observations of mesoscopic domains in such systems.

Renormalization of membrane rigidity by long-range interactions.

We consider the renormalization of the bending and Gaussian rigidity of model membranes induced by long-range interactions between the components making up the membrane. In particular we analyze the effect of a finite membrane thickness on the renormalization of the bending and Gaussian rigidity by long-range interactions. Particular attention is paid to the case where the interactions are of a van der Waals type.

Thermal Casimir effect in lipid bilayer tubules.

We calculate the thermal Casimir effect for a dielectric tube of radius R and thickness delta formed from a membrane in water. The method uses a field-theoretic approach in the grand canonical ensemble. The leading contribution to the Casimir free energy behaves as -k(B)TLkappa(c)/R giving rise to an attractive force which tends to contract the tube. We find that kappa(c) approximately 0.3 for the case of typical lipid membrane t tubules. We conclude that except in the case of a very soft membrane this force is insufficient to stabilize such tubes against the bending stress which tends to increase the radius.

Resummed two-loop calculation of the disjoining pressure of a symmetric electrolyte soap film.

In this paper we consider the calculation of the disjoining pressure of a symmetric electrolytic soap film correct to two loops in perturbation theory. We show that the disjoining pressure is finite when the loop expansion is resummed using a cumulant expansion and requires no short distance cutoff in order to give a finite result. The loop expansion is resummed in terms of an expansion in g= lB / lD where lD is the Debye length and lB is the Bjerrum length. We show that there there is a nonanalytic contribution of order g ln(g). We also show that the two-loop correction is greater than the one-loop term at large film thicknesses suggesting a nonperturbative correction to the one-loop result in this limit.

Self-diffusion in a system of interacting Langevin particles.

The behavior of the self-diffusion constant of Langevin particles interacting via a pairwise interaction is considered. The diffusion constant is calculated approximately within a perturbation theory in the potential strength about the bare diffusion constant. It is shown how this expansion leads to a systematic double expansion in the inverse temperature beta and the particle density rho. The one-loop diagrams in this expansion can be summed exactly and we show that this result is exact in the limit of small beta and rhobeta constants. The one-loop result can also be resummed using a semiphenomenological renormalization group method which has proved useful in the study of diffusion in random media. In certain cases the renormalization group calculation predicts the existence of a diverging relaxation time signaled by the vanishing of the diffusion constant, possible forms of divergence coming from this approximation are discussed. Finally, at a more quantitative level, the results are compared with numerical simulations, in two dimensions, of particles interacting via a soft potential recently used to model the interaction between coiled polymers.

Field theoretic calculation of the surface tension for a model electrolyte system.

We carry out the calculation of the surface tension for a model electrolyte to first order in a cumulant expansion about a free-field theory equivalent to the Debye-Hückel approximation. In contrast with previous calculations, the surface tension is calculated directly without recourse to integrating thermodynamic relations. The system considered is a monovalent electrolyte with a region at the interface, of width h, from which the ionic species are excluded. In the case where the external dielectric constant epsilon(0) is smaller than the electrolyte solution's dielectric constant epsilon we show that the calculation at this order can be fully regularized. In the case where h is taken to be zero the Onsager-Samaras limiting law for the excess surface tension of dilute electrolyte solutions is recovered, with corrections coming from a nonzero value of epsilon(0) /epsilon.

Weak nonlinear surface-charging effects in electrolytic films.

A simple model of soap films with nonionic surfactants stabilized by added electrolyte is studied. The model exhibits charge regularization due to the incorporation of a physical mechanism responsible for the formation of a surface charge. We use a Gaussian field theory in the film but the full nonlinear surface terms which are then treated at a one-loop level by calculating the mean-field Poisson-Boltzmann solution and then the fluctuations about this solution. We carefully analyze the renormalization of the theory and apply it to a triple-layer model for a thin film with Stern layer of thickness h. For this model we give expressions for the surface charge sigma(L) and the disjoining pressure P(d)(L) and show their dependence on the parameters. The influence of image charges naturally arises in the formalism, and we show that predictions depend strongly on h because of their effects. In particular, we show that the surface charge vanishes as the film thickness L-->0. The fluctuation terms in this class of theories contribute a Casimir-like attraction across the film. Although this attraction is well known to be negligible compared with the mean-field component for model electrolytic films with no surface-charge regulation, in the model studied here these fluctuations also affect the surface-charge regulation leading to a fluctuation component in the disjoining pressure which has the same behavior as the mean-field component even for large film thickness.

Role of the interaction matrix in mean-field spin glass models.

Mean-field models of two-spin Ising spin glasses with interaction matrices taken from ensembles that are invariant under O(N) transformations are studied. A general study shows that the nature of the spin glass transition can be deduced from the eigenvalue spectrum of the interaction matrix. A simple replica approach is derived to carry out the average over the O(N) disorder. The analytic results are confirmed by the extensive Monte Carlo simulations for large system sizes and by the exact enumeration for small system sizes.

Field theoretic derivation of the contact value theorem in planar geometries and its modification by the Casimir effect.

The contact value theorem for Coulomb gases in planar or filmlike geometries is derived using a Hamiltonian field theoretic representation of the system. The case where the film is enclosed by a material of different dielectric constant to that of the film is shown to contain an additional Casimir-like term which is generated by fluctuations of the electric potential about its mean-field value.

Electrostatic fluctuations in soap films.

A field theory to describe electrostatic interactions in soap films, described by electric multilayers with a generalized thermodynamic surface-charging mechanism, is studied. In the limit where the electrostatic interactions are weak, this theory is exactly soluble. The theory incorporates in a consistent way, the surface-charging mechanism and the fluctuations in the electrostatic field that correspond to the zero-frequency component of the van der Waals force. It is shown that these terms lead to a Casimir-like attraction that can be sufficiently large to explain the transition between the common black film to a Newton black film.