Non-local dispersal

We consider a model of spatial spread that has applications in both material science and biology. The classical models are based upon partial differential equations, in particular reaction-diffusion equations. Here the dispersal term is given in terms of an integral operator and we restrict ourselves to the scalar case

Phase-field-crystal model for liquid crystals

Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits stable isotropic, nematic, smectic A, columnar, plastic crystalline and orientationally ordered crystalline phases. As far as the dynamics is concerned, the translational density is a conserved order parameter while the orientational ordering is non-conserved. The derived phase-field-crystal model can serve for efficient numerical investigations of various nonequilibrium situations in liquid crystals

Influence of Strain on the Kinetics of Phase Transitions in Solids

We consider a sharp interface kinetic model of phase transitions accompanied by elastic strain, together with its phase-field realization. Quantitative results for the steady-state growth of a new phase in a strip geometry are obtained and different pattern formation processes in this system are investigated

Modeling Elasticity in Crystal Growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to times scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.Comment: 4 pages, 10 figure

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Amplitude equations for systems with long-range interactions

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review

Varicella-Zoster viruses associated with post-herpetic neuralgia induce sodium current density increases in the ND7-23 Nav-1.8 neuroblastoma cell line

Post-herpetic neuralgia (PHN) is the most significant complication of herpes zoster caused by reactivation of latent Varicella-Zoster virus (VZV). We undertook a heterologous infection in vitro study to determine whether PHN-associated VZV isolates induce changes in sodium ion channel currents known to be associated with neuropathic pain. Twenty VZV isolates were studied blind from 11 PHN and 9 non-PHN subjects. Viruses were propagated in the MeWo cell line from which cell-free virus was harvested and applied to the ND7/23-Nav1.8 rat DRG x mouse neuroblastoma hybrid cell line which showed constitutive expression of the exogenous Nav 1.8, and endogenous expression of Nav 1.6 and Nav 1.7 genes all encoding sodium ion channels the dysregulation of which is associated with a range of neuropathic pain syndromes. After 72 hrs all three classes of VZV gene transcripts were detected in the absence of infectious virus. Single cell sodium ion channel recording was performed after 72 hr by voltage-clamping. PHN-associated VZV significantly increased sodium current amplitude in the cell line when compared with non-PHN VZV, wild-type (Dumas) or vaccine VZV strains ((POka, Merck and GSK). These sodium current increases were unaffected by acyclovir pre-treatment but were abolished by exposure to Tetrodotoxin (TTX) which blocks the TTX-sensitive fast Nav 1.6 and Nav 1.7 channels but not the TTX-resistant slow Nav 1.8 channel. PHN-associated VZV sodium current increases were therefore mediated in part by the Nav 1.6 and Nav 1.7 sodium ion channels. An additional observation was a modest increase in message levels of both Nav1.6 and Nav1.7 mRNA but not Nav 1.8 in PHN virally infected cells

Transcriptomal analysis of varicella-zoster virus infection using long oligonucleotide-based microarrays

Varicella-zoster virus (VZV) is a human herpes virus that causes varicella as a primary infection and herpes zoster following reactivation of the virus from a latent state in trigeminal and spinal ganglia. In order to study the global pattern of VZV gene transcription, VZV microarrays using 75-base oligomers to 71 VZV open reading frames (ORFs) were designed and validated. The long-oligonucleotide approach maximizes the stringency of detection and polarity of gene expression. To optimize sensitivity, microarrays were hybridized to target RNA and the extent of hybridization measured using resonance light scattering. Microarray data were normalized to a subset of invariant ranked host-encoded positive-control genes and the data subjected to robust formal statistical analysis. The programme of viral gene expression was determined for VZV (Dumas strain)-infected MeWo cells and SVG cells (an immortalized human astrocyte cell line) 72 h post-infection. Marked quantitative and qualitative differences in the viral transcriptome were observed between the two different cell types using the Dumas laboratory-adapted strain. Oligonucleotide-based VZV arrays have considerable promise as a valuable tool in the analysis of viral gene transcription during both lytic and latent infections, and the observed heterogeneity in the global pattern of viral gene transcription may also have diagnostic potentia

Stability of Solid State Reaction Fronts

We analyze the stability of a planar solid-solid interface at which a chemical reaction occurs. Examples include oxidation, nitridation, or silicide formation. Using a continuum model, including a general formula for the stress-dependence of the reaction rate, we show that stress effects can render a planar interface dynamically unstable with respect to perturbations of intermediate wavelength