Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

Sound propagation in and radiation from acoustically lined flow ducts: A comparison of experiment and theory

The results of an experimental and theoretical study of many of the fundamental details of sound propagation in hard wall and soft wall annular flow ducts are reported. The theory of sound propagation along such ducts and the theory for determining the complex radiation impedance of higher order modes of an annulus are outlined, and methods for generating acoustic duct modes are developed. The results of a detailed measurement program on propagation in rigid wall annular ducts with and without airflow through the duct are presented. Techniques are described for measuring cut-on frequencies, modal phase speed, and radial and annular mode shapes. The effects of flow velocity on cut-on frequencies and phase speed are measured. Comparisons are made with theoretical predictions for all of the effects studies. The two microphone method of impedance is used to measure the effects of flow on acoustic liners. A numerical study of sound propagation in annular ducts with one or both walls acoustically lined is presented

The 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_BTL kappa_C/R giving rise to an attractive force which tends to contract the tube. We find that kappa_C ~ 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.Comment: 4 pages no figures RevTe

Continuum Derrida Approach to Drift and Diffusivity in Random Media

By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8

Incommensurate phonon anomaly and the nature of charge density waves in cuprates

While charge density wave (CDW) instabilities are ubiquitous to superconducting cuprates, the different ordering wavevectors in various cuprate families have hampered a unified description of the CDW formation mechanism. Here we investigate the temperature dependence of the low energy phonons in the canonical CDW ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$. We discover that the phonon softening wavevector associated with CDW correlations becomes temperature dependent in the high-temperature precursor phase and changes from a wavevector of 0.238 reciprocal space units (r.l.u.) below the ordering transition temperature up to 0.3~r.l.u. at 300~K. This high-temperature behavior shows that "214"-type cuprates can host CDW correlations at a similar wavevector to previously reported CDW correlations in non-"214"-type cuprates such as YBa$_{2}$Cu$_{3}$O$_{6+\delta}$. This indicates that cuprate CDWs may arise from the same underlying instability despite their apparently different low temperature ordering wavevectors.Comment: Accepted in Phys. Rev. X; 9 pages; 5 figures; 3 pages of supplementary materia

The field theory of symmetrical layered electrolytic systems and the thermal Casimir effect

We present a general extension of a field-theoretic approach developed in earlier papers to the calculation of the free energy of symmetrically layered electrolytic systems which is based on the Sine-Gordon field theory for the Coulomb gas. The method is to construct the partition function in terms of the Feynman evolution kernel in the Euclidean time variable associated with the coordinate normal to the surfaces defining the layered structure. The theory is applicable to cylindrical systems and its development is motivated by the possibility that a static van der Waals or thermal Casimir force could provide an attractive force stabilising a dielectric tube formed from a lipid bilayer, an example of which are t-tubules occurring in certain muscle cells. In this context, we apply the theory to the calculation of the thermal Casimir effect for a dielectric tube of radius $R$ and thickness $\delta$ formed from such a membrane in water. In a grand canonical approach we find that the leading contribution to the Casimir energy behaves like $-k_BTL\kappa_C/R$ which gives rise to an attractive force which tends to contract the tube radius. We find that $\kappa_C \sim 0.3$ 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 stabilise such tubes against the bending stress which tend to increase the radius. We briefly discuss the role of lipid membrane reservoir implicit in the approach and whether its nature in biological systems may possibly lead to a stabilising mechanism for such lipid tubes.Comment: 28 pages, 2 figures, LaTe