Coalescence in the 1D Cahn-Hilliard model

We present an approximate analytical solution of the Cahn-Hilliard equation describing the coalescence during a first order phase transition. We have identified all the intermediate profiles, stationary solutions of the noiseless Cahn-Hilliard equation. Using properties of the soliton lattices, periodic solutions of the Ginzburg-Landau equation, we have construct a family of ansatz describing continuously the processus of destabilization and period doubling predicted in Langer's self similar scenario

Interfaces and Grain Boundaries of Lamellar Phases

Interfaces between lamellar and disordered phases, and grain boundaries within lamellar phases, are investigated employing a simple Landau free energy functional. The former are examined using analytic, approximate methods in the weak segregation limit, leading to density profiles which can extend over many wavelengths of the lamellar phase. The latter are studied numerically and exactly. We find a change from smooth chevron configurations typical of small tilt angles to distorted omega configurations at large tilt angles in agreement with experiment.Comment: 9 pages, 6 figures 9 pages, 6 figure

Feedback Loops Between Fields and Underlying Space Curvature: an Augmented Lagrangian Approach

We demonstrate a systematic implementation of coupling between a scalar field and the geometry of the space (curve, surface, etc.) which carries the field. This naturally gives rise to a feedback mechanism between the field and the geometry. We develop a systematic model for the feedback in a general form, inspired by a specific implementation in the context of molecular dynamics (the so-called Rahman-Parrinello molecular dynamics, or RP-MD). We use a generalized Lagrangian that allows for the coupling of the space's metric tensor (the first fundamental form) to the scalar field, and add terms motivated by RP-MD. We present two implementations of the scheme: one in which the metric is only time-dependent [which gives rise to ordinary differential equation (ODE) for its temporal evolution], and one with spatio-temporal dependence [wherein the metric's evolution is governed by a partial differential equation (PDE)]. Numerical results are reported for the (1+1)-dimensional model with a nonlinearity of the sine-Gordon type.Comment: 5 pages, 3 figures, Phys. Rev. E in pres

Offsprings of a point vortex

The distribution engendered by successive splitting of one point vortex are considered. The process of splitting a vortex in three using a reverse three-point vortex collapse course is analysed in great details and shown to be dissipative. A simple process of successive splitting is then defined and the resulting vorticity distribution and vortex populations are analysed

Self-Dual Bending Theory for Vesicles

We present a self-dual bending theory that may enable a better understanding of highly nonlinear global behavior observed in biological vesicles. Adopting this topological approach for spherical vesicles of revolution allows us to describe them as frustrated sine-Gordon kinks. Finally, to illustrate an application of our results, we consider a spherical vesicle globally distorted by two polar latex beads.Comment: 10 pages, 3 figures, LaTeX2e+IOPar

Protein inactivation in mycobacteria by controlled proteolysis and its application to deplete the beta subunit of RNA polymerase

Using a component of the Escherichia coli protein degradation machinery, we have established a system to regulate protein stability in mycobacteria. A protein tag derived from the E. coli SsrA degradation signal did not affect several reporter proteins in wild-type Mycobacterium smegmatis or Mycobacterium tuberculosis. Expression of the adaptor protein SspB, which recognizes this modified tag and helps deliver tagged proteins to the protease ClpXP, strongly decreased the activities and protein levels of different reporters. This inactivation did not occur when the function of ClpX was inhibited. Using this system, we constructed a conditional M. smegmatis knockdown mutant in which addition of anhydrotetracycline (atc) caused depletion of the beta subunit of RNA polymerase, RpoB. The impact of atc on this mutant was dose-dependent. Very low amounts of atc did not prevent growth but increased sensitivity to an antibiotic that inactivates RpoB. Intermediate amounts of RpoB knockdown resulted in bacteriostasis and a more substantial depletion led to a decrease in viability by up to 99%. These studies identify SspB-mediated proteolysis as an efficient approach to conditionally inactivate essential proteins in mycobacteria. They further demonstrate that depletion of RpoB by ∼93% is sufficient to cause death of M. smegmatis