712 research outputs found
Controlled release of free-falling test models
Releasing device, powered by a drill motor through an adjustable speed reducer, has a spinning release head with three retractable spring-loaded fingers. The fingers are retracted by manual triggering of a cable at the motor end of the unit
Finite to infinite steady state solutions, bifurcations of an integro-differential equation
We consider a bistable integral equation which governs the stationary
solutions of a convolution model of solid--solid phase transitions on a circle.
We study the bifurcations of the set of the stationary solutions as the
diffusion coefficient is varied to examine the transition from an infinite
number of steady states to three for the continuum limit of the
semi--discretised system. We show how the symmetry of the problem is
responsible for the generation and stabilisation of equilibria and comment on
the puzzling connection between continuity and stability that exists in this
problem
Drift- or Fluctuation-Induced Ordering and Self-Organization in Driven Many-Particle Systems
According to empirical observations, some pattern formation phenomena in
driven many-particle systems are more pronounced in the presence of a certain
noise level. We investigate this phenomenon of fluctuation-driven ordering with
a cellular automaton model of interactive motion in space and find an optimal
noise strength, while order breaks down at high(er) fluctuation levels.
Additionally, we discuss the phenomenon of noise- and drift-induced
self-organization in systems that would show disorder in the absence of
fluctuations. In the future, related studies may have applications to the
control of many-particle systems such as the efficient separation of particles.
The rather general formulation of our model in the spirit of game theory may
allow to shed some light on several different kinds of noise-induced ordering
phenomena observed in physical, chemical, biological, and socio-economic
systems (e.g., attractive and repulsive agglomeration, or segregation).Comment: For related work see http://www.helbing.or
Analytical Investigation of Innovation Dynamics Considering Stochasticity in the Evaluation of Fitness
We investigate a selection-mutation model for the dynamics of technological
innovation,a special case of reaction-diffusion equations. Although mutations
are assumed to increase the variety of technologies, not their average success
("fitness"), they are an essential prerequisite for innovation. Together with a
selection of above-average technologies due to imitation behavior, they are the
"driving force" for the continuous increase in fitness. We will give analytical
solutions for the probability distribution of technologies for special cases
and in the limit of large times.
The selection dynamics is modelled by a "proportional imitation" of better
technologies. However, the assessment of a technology's fitness may be
imperfect and, therefore, vary stochastically. We will derive conditions, under
which wrong assessment of fitness can accelerate the innovation dynamics, as it
has been found in some surprising numerical investigations.Comment: For related work see http://www.helbing.or
Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns
Domain walls in equilibrium phase transitions propagate in a preferred
direction so as to minimize the free energy of the system. As a result, initial
spatio-temporal patterns ultimately decay toward uniform states. The absence of
a variational principle far from equilibrium allows the coexistence of domain
walls propagating in any direction. As a consequence, *persistent* patterns may
emerge. We study this mechanism of pattern formation using a non-variational
extension of Landau's model for second order phase transitions. PACS numbers:
05.70.Fh, 42.65.Pc, 47.20.Ky, 82.20MjComment: 12 pages LaTeX, 5 postscript figures To appear in Phys. Rev.
Kink Arrays and Solitary Structures in Optically Biased Phase Transition
An interphase boundary may be immobilized due to nonlinear diffractional
interactions in a feedback optical device. This effect reminds of the Turing
mechanism, with the optical field playing the role of a diffusive inhibitor.
Two examples of pattern formation are considered in detail: arrays of kinks in
1d, and solitary spots in 2d. In both cases, a large number of equilibrium
solutions is possible due to the oscillatory character of diffractional
interaction.Comment: RevTeX 13 pages, 3 PS-figure
Scanning micro-Hall probe mapping of magnetic flux distributions and current densities in YBa2Cu3O7 thin films
Mapping of the magnetic flux density B(sub z) (perpendicular to the film plane) for a YBa2Cu3O7 thin-film sample was carried out using a scanning micro-Hall probe. The sheet magnetization and sheet current densities were calculated from the B(sub z) distributions. From the known sheet magnetization, the tangential (B(sub x,y)) and normal components of the flux density B were calculated in the vicinity of the film. It was found that the sheet current density was mostly determined by 2B(sub x,y)/d, where d is the film thickness. The evolution of flux penetration as a function of applied field will be shown
Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation
Cellular differentiation in a developping organism is studied via a discrete
bistable reaction-diffusion model. A system of undifferentiated cells is
allowed to receive an inductive signal emenating from its environment.
Depending on the form of the nonlinear reaction kinetics, this signal can
trigger a series of bifurcations in the system. Differentiation starts at the
surface where the signal is received, and cells change type up to a given
distance, or under other conditions, the differentiation process propagates
through the whole domain. When the signal diminishes hysteresis is observed
The Speed of Fronts of the Reaction Diffusion Equation
We study the speed of propagation of fronts for the scalar reaction-diffusion
equation \, with . We give a new integral
variational principle for the speed of the fronts joining the state to
. No assumptions are made on the reaction term other than those
needed to guarantee the existence of the front. Therefore our results apply to
the classical case in , to the bistable case and to cases in
which has more than one internal zero in .Comment: 7 pages Revtex, 1 figure not include
Deviations from the local field approximation in negative streamer heads
Negative streamer ionization fronts in nitrogen under normal conditions are
investigated both in a particle model and in a fluid model in local field
approximation. The parameter functions for the fluid model are derived from
swarm experiments in the particle model. The front structure on the inner scale
is investigated in a 1D setting, allowing reasonable run-time and memory
consumption and high numerical accuracy without introducing super-particles. If
the reduced electric field immediately before the front is >= 50kV/(cm bar),
solutions of fluid and particle model agree very well. If the field increases
up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in
particular, the ionization level behind the front becomes up to 60% higher in
the particle model while the velocity is rather insensitive. Particle and fluid
model deviate because electrons with high energies do not yet fully run away
from the front, but are somewhat ahead. This leads to increasing ionization
rates in the particle model at the very tip of the front. The energy overshoot
of electrons in the leading edge of the front actually agrees quantitatively
with the energy overshoot in the leading edge of an electron swarm or avalanche
in the same electric field.Comment: The paper has 17 pages, including 15 figures and 3 table
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