24 research outputs found
Liesegang patterns: Effect of dissociation of the invading electrolyte
The effect of dissociation of the invading electrolyte on the formation of
Liesegang bands is investigated. We find, using organic compounds with known
dissociation constants, that the spacing coefficient, 1+p, that characterizes
the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing
dissociation constant, K_d. Theoretical arguments are developed to explain
these experimental findings and to calculate explicitly the K_d dependence of
1+p.Comment: RevTex, 8 pages, 3 eps figure
Variational study of the Holstein polaron
The paper deals with the ground and the first excited state of the polaron in
the one dimensional Holstein model. Various variational methods are used to
investigate both the weak coupling and strong coupling case, as well as the
crossover regime between them. Two of the methods, which are presented here for
the first time, introduce interesting elements to the understanding of the
nature of the polaron. Reliable numerical evidence is found that, in the strong
coupling regime, the ground and the first excited state of the self-trapped
polaron are well described within the adiabatic limit. The lattice vibration
modes associated with the self-trapped polarons are analyzed in detail, and the
frequency softening of the vibration mode at the central site of the small
polaron is estimated. It is shown that the first excited state of the system in
the strong coupling regime corresponds to the excitation of the soft phonon
mode within the polaron. In the crossover regime, the ground and the first
excited state of the system can be approximated by the anticrossing of the
self-trapped and the delocalized polaron state. In this way, the connection
between the behavior of the ground and the first excited state is qualitatively
explained.Comment: 11 pages, 4 figures, PRB 65, 14430
The Origins of Concentric Demyelination: Self-Organization in the Human Brain
Baló's concentric sclerosis is a rare atypical form of multiple sclerosis characterized by striking concentric demyelination patterns. We propose a robust mathematical model for Baló's sclerosis, sharing common molecular and cellular mechanisms with multiple sclerosis. A reconsideration of the analogies between Baló's sclerosis and the Liesegang periodic precipitation phenomenon led us to propose a chemotactic cellular model for this disease. Rings of demyelination appear as a result of self-organization processes, and closely mimic Baló lesions. According to our results, homogeneous and concentric demyelinations may be two different macroscopic outcomes of a single fundamental immune disorder. Furthermore, in chemotactic models, cellular aggressivity appears to play a central role in pattern formation
Konstruktive Entwicklung korrekter Software mit flexibler Rechnerstuetzung Schlussbericht
SIGLEAvailable from TIB Hannover: D.Dt.F.QN1(12,47) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekBundesministerium fuer Forschung und Technologie (BMFT), Bonn (Germany)DEGerman
Ostwald ripening of faceted two-dimensional islands
We study Ostwald ripening of two-dimensional adatom and advacancy islands on
a crystal surface by means of kinetic Monte Carlo simulations. At large bond
energies the islands are square-shaped, which qualitatively changes the
coarsening kinetics. The Gibbs--Thomson chemical potential is violated: the
coarsening proceeds through a sequence of `magic' sizes corresponding to square
or rectangular islands. The coarsening becomes attachment-limited, but Wagner's
asymptotic law is reached after a very long transient time. The unusual
coarsening kinetics obtained in Monte Carlo simulations are well described by
the Becker--D\"oring equations of nucleation kinetics. These equations can be
applied to a wide range of coarsening problems
Independence of Primary and Secondary Structures in Periodic Precipitation Patterns
Microscopic periodic precipitation patterns featuring both-primary, and secondary bands form in thin gel films. The initial conditions for the precipitation process, are defined, by wet stamping and are chosen such that the primary and secondary structures are not necessarily collinear; the fact that these structures propagate in different directions suggests that they form independently of one another. This hypothesis is further, supported by a theoretical model in which two different intermediate species mediate band formation