33 research outputs found
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
Geometric frustration in compositionally modulated ferroelectrics
Geometric frustration is a broad phenomenon that results from an intrinsic
incompatibility between some fundamental interactions and the underlying
lattice geometry1-7. Geometric frustration gives rise to new fundamental
phenomena and is known to yield intriguing effects, such as the formation of
exotic states like spin ice, spin liquids and spin glasses1-7. It has also led
to interesting findings of fractional charge quantization and magnetic
monopoles5,6. Geometric frustration related mechanisms have been proposed to
understand the origins of relaxor behavior in some multiferroics, colossal
magnetocapacitive coupling and unusual and novel mechanisms of high Tc
superconductivity1-5. Although geometric frustration has been particularly well
studied in magnetic systems in the last 20 years or so, its manifestation in
the important class formed by ferroelectric materials (that are compounds
exhibiting electric rather than magnetic dipoles) is basically unknown. Here,
we show, via the use of a first-principles-based technique, that
compositionally graded ferroelectrics possess the characteristic "fingerprints"
associated with geometric frustration. These systems have a highly degenerate
energy surface and exhibit original critical phenomena. They further reveal
exotic orderings with novel stripe phases involving complex spatial
organization. These stripes display spiral states, topological defects and
curvature. Compositionally graded ferroelectrics can thus be considered as the
"missing" link that brings ferroelectrics into the broad category of materials
able to exhibit geometric frustration. Our ab-initio calculations allow a deep
microscopic insight into this novel geometrically frustrated system.Comment: 14 pages, 5 Figures;
http://www.nature.com/nature/journal/v470/n7335/full/nature09752.htm
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
On the angular momentum density of a two-dimensional quantum Heisenberg antiferromagnet
We study Heisenberg spins on an infinite plane. In the continuum limit the Hamiltonian of the system is given by the nonlinear sigma model. Following an approach developed by Mikeska and Affleck, we find that the angular momentum associated with the order parameter presents a classical spin part, associated with the gauge freedom of a trihedra. We show that this gauge held may induce a non-trivial topological term, the Hopf term (or Chern-Simons term), as initially suggested by Dzyaloshinski, Polyakov and Wiegmann