Biomedical subjects
Publications and source records attributed to R R Horgan.
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.
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.
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.
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.
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.
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.
We present a self-consistent determination of the screening mass for chromomagnetic fields in QCD within the framework of dimensional reduction. The three-dimensional Chern-Simons density is used as a mass term for a self-consistent perturbative calculation that yields a value of m approximately 1.604(g(2)N/2pi)T for the magnetic screening mass.
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.
The advection of a passive scalar by a quenched (frozen) incompressible velocity field is studied by extensive high precision numerical simulation and various approximation schemes. We show that second-order self-consistent perturbation theory, in the absence of helicity, perfectly predicts the effective diffusivity of a tracer particle in such a field. In the presence of helicity in the flow, simulations reveal an unexpectedly strong enhancement of the effective diffusivity which is highly nonperturbative and most visible when the bare molecular diffusivity of the particle is small. We develop and analyze a series of approximation schemes which indicate that this enhancement of the diffusivity is due to a second order effect, whereby the helical component of the field, which does not directly renormalize the effective diffusivity, enhances the strength of the nonhelical part of the flow, which in turn renormalizes the molecular diffusivity. We show that this renormalization is most important at a low bare molecular diffusivity, in agreement with numerical simulations.