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 $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f > 0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.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