95 research outputs found
Flat Spacetime Vacuum in Loop Quantum Gravity
We construct a state in the loop quantum gravity theory with zero
cosmological constant, which should correspond to the flat spacetime vacuum
solution. This is done by defining the loop transform coefficients of a flat
connection wavefunction in the holomorphic representation which satisfies all
the constraints of quantum General Relativity and it is peaked around the flat
space triads. The loop transform coefficients are defined as spin foam state
sum invariants of the spin networks embedded in the spatial manifold for the
SU(2) quantum group. We also obtain an expression for the vacuum wavefunction
in the triad represntation, by defining the corresponding spin networks
functional integrals as SU(2) quantum group state sums.Comment: 20 pages, 6 figure
Harmonic forcing of an extended oscillatory system: Homogeneous and periodic solutions
In this paper we study the effect of external harmonic forcing on a
one-dimensional oscillatory system described by the complex Ginzburg-Landau
equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous
state with no spatial structure is observed. The state becomes unstable to a
spatially periodic ``stripe'' state via a supercritical bifurcation as the
forcing amplitude decreases. An approximate phase equation is derived, and an
analytic solution for the stripe state is obtained, through which the
asymmetric behavior of the stability border of the state is explained. The
phase equation, in particular the analytic solution, is found to be very useful
in understanding the stability borders of the homogeneous and stripe states of
the forced CGLE.Comment: 6 pages, 4 figures, 2 column revtex format, to be published in Phys.
Rev.
Creation and Reproduction of Model Cells with Semipermeable Membrane
A high activity of reactions can be confined in a model cell with a
semipermeable membrane in the Schl\"ogl model. It is interpreted as a model of
primitive metabolism in a cell. We study two generalized models to understand
the creation of primitive cell systems conceptually from the view point of the
nonlinear-nonequilibrium physics. In the first model, a single-cell system with
a highly active state confined by a semipermeable membrane is spontaneously
created from an inactive homogeneous state by a stochastic jump process. In the
second model, many cell structures are reproduced from a single cell, and a
multicellular system is created.Comment: 11 pages, 7 figure
Reaction-Diffusion System in a Vesicle with Semi-Permeable Membrane
We study the Schloegl model in a vesicle with semi-permeable membrane. The
diffusion constant takes a smaller value in the membrane region, which prevents
the outflow of self-catalytic product. A nonequilibrium state is stably
maintained inside of the vesicle. Nutrients are absorbed and waste materials
are exhausted through the membrane by diffusion. It is interpreted as a model
of primitive metabolism in a cell.Comment: 8 pages, 6 figure
Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model
Spatio-temporal bifurcations and complex dynamics in globally coupled
intrinsically bistable electrochemical systems with an S-shaped current-voltage
characteristic under galvanostatic control are studied theoretically on a
one-dimensional domain. The results are compared with the dynamics and the
bifurcation scenarios occurring in a closely related model which describes
pattern formation in semiconductors. Under galvanostatic control both systems
are unstable with respect to the formation of stationary large amplitude
current domains. The current domains as well as the homogeneous steady state
exhibit oscillatory instabilities for slow dynamics of the potential drop
across the double layer, or across the semiconductor device, respectively. The
interplay of the different instabilities leads to complex spatio-temporal
behavior. We find breathing current domains and chaotic spatio-temporal
dynamics in the electrochemical system. Comparing these findings with the
results obtained earlier for the semiconductor system, we outline bifurcation
scenarios leading to complex dynamics in globally coupled bistable systems with
subcritical spatial bifurcations.Comment: 13 pages, 11 figures, 70 references, RevTex4 accepted by PRE
http://pre.aps.or
Pentanary cross-diffusion in water-in-oil microemulsions loaded with two components of the belousov-zhabotinsky reaction
We measure cross-diffusion coefficients in a five-component system, an aerosol OT (AOT) water-in-oil microemulsion loaded with two constituents of the Belousov-Zhabotinsky (BZ) reaction (H2O/AOT/BZ1/BZ2/octane). The species BZ1 is either NaBr, an inhibitor of the BZ reaction, or ferroin, a catalyst for the reaction. As species BZ2, we choose Br2, an intermediate in the reaction. The cross-diffusion coefficients between BZ1 and BZ2 are found to be negative, which can be understood in terms of complexation between these species. Using a four-variable model for the BZ reaction, we find that the cross-diffusion coefficients measured here can lead to a noticeable shift in the onset of Turing instability in the BZ-AOT system
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