Memory-Controlled Diffusion

Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and non-local spatial-temporal memory effects. The realization of the memory kernels are restricted due the conservation of the basic quantity $p$. A general criteria is given for the existence of stationary solutions. In case the memory kernel depends on $p$ polynomially the transport is prevented. Owing to the delay effects a finite amount of particles remains localized and the further transport is terminated. For diffusion with non-linear memory effects we find an exact solution in the long-time limit. Although the mean square displacement shows diffusive behavior, higher order cumulants exhibits differences to diffusion and they depend on the memory strength

Sensitivity-analysis method for inverse simulation application

An important criticism of traditional methods of inverse simulation that are based on the Newton–Raphson algorithm is that they suffer from numerical problems. In this paper these problems are discussed and a new method based on sensitivity-analysis theory is developed and evaluated. The Jacobian matrix may be calculated by solving a sensitivity equation and this has advantages over the approximation methods that are usually applied when the derivatives of output variables with respect to inputs cannot be found analytically. The methodology also overcomes problems of input-output redundancy that arise in the traditional approaches to inverse simulation. The sensitivity- analysis approach makes full use of information within the time interval over which key quantities are compared, such as the difference between calculated values and the given ideal maneuver after each integration step. Applications to nonlinear HS125 aircraft and Lynx helicopter models show that, for this sensitivity-analysis method, more stable and accurate results are obtained than from use of the traditional Newton–Raphson approach

The bar PANDA focussing-lightguide disc DIRC

bar PANDA will be a fixed target experiment internal to the HESR antiproton storage ring at the future FAIR complex. The ANDA detector requires excellent particle-identification capabilities in order to achieve its scientific potential. Cherenkov counters employing the DIRC principle were chosen as PID detectors for the Target Spectrometer. The proposed Focussing-Lightguide Disc DIRC will cover the forward part of the Target Spectrometer acceptance in the angular range between 5° and 22°. Its design includes a novel approach to mitigate dispersion effects in the solid radiator of a DIRC counter using optical elements. The dispersion correction will enable the Focussing-Lightguide Disc DIRC to provide pion-kaon identification for momenta well above 3.5 GeV/c

Thermodynamics of Chemical Waves

Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a rigorous thermodynamic theory of reaction-diffusion systems to characterize chemical waves. Our main result is the definition of the proper thermodynamic potential of the local dynamics as a nonequilibrium free energy density and establishing its balance equation. This enables us to identify the dynamics of the free energy, of the dissipation, and of the work spent to sustain the wave propagation. Two prototypical classes of chemical waves are examined. From a thermodynamic perspective, the first is sustained by relaxation towards equilibrium and the second by nonconservative forces generated by chemostats. We analytically study step-like waves, called wavefronts, using the Fisher-Kolmogorov equation as representative of the first class and oscillating waves in the Brusselator model as representative of the second. Given the fundamental role of chemical waves as message carriers in biosystems, our thermodynamic theory constitutes an important step toward an understanding of information transfers and processing in biology.Comment: 12 pages, 2 figure

Natural resources inventory and monitoring in Oregon with ERTS imagery

Multidiscipline team interpretation of ERTS satellite and highflight imagery is providing resource and land use information needed for land use planning in Oregon. A coordinated inventory of geology, soil-landscapes, forest and range vegetation, and land use for Crook County, illustrates the value of this approach for broad area and state planning. Other applications include mapping fault zones, inventory of forest clearcut areas, location of forest insect damage, and monitoring irrigation development. Computer classification is being developed for use in conjunction with visual interpretation

Emergent singular solutions of non-local density-magnetization equations in one dimension

We investigate the emergence of singular solutions in a non-local model for a magnetic system. We study a modified Gilbert-type equation for the magnetization vector and find that the evolution depends strongly on the length scales of the non-local effects. We pass to a coupled density-magnetization model and perform a linear stability analysis, noting the effect of the length scales of non-locality on the system's stability properties. We carry out numerical simulations of the coupled system and find that singular solutions emerge from smooth initial data. The singular solutions represent a collection of interacting particles (clumpons). By restricting ourselves to the two-clumpon case, we are reduced to a two-dimensional dynamical system that is readily analyzed, and thus we classify the different clumpon interactions possible.Comment: 19 pages, 13 figures. Submitted to Phys. Rev.

The Accretion of Lyman Alplha Clouds onto Gas-Rech Protogalaxies; A Scenario for the Formation of Globular Star Clusters

A satisfactory theory for the formation of globular star clusters (GCs) has long been elusive, perhaps because their true progenitors had not yet been guessed. In this paper I propose a causal relationship between the strongly decreasing densities of Lyman alpha (LyA) clouds at high redshift and the formation of GCs - namely that GCs were created by the accretion of LyA clouds onto protogalaxies. I describe a scenario which involves an inherently stable and orderly cycling of compression and cooling in the central cores of clouds during the extended period of dissipation in the outer regins of gas-rich proto galaxies, culminating in a burst of efficient star formation. I demonstrate that the comoving density of GCs is comparable to that of LyA clouds at high redshift, that the energetic requirements for compression to core GC densities can be met, and that the time-scale for cooling is within obvious limits imposed by dynamical stability. This dissipative process requires there to be a large column of dissipated gas about the attractor in order to form GCs. In addition, the energy requirements for compression requires attractor masses greater than that capable of sustaining circular velocities of ~40 km/s. If this scenario is supported by numerical simulations, then by implication, the GCs were formed at modest redshifts of z~1-3. This knowledge could help to break the degeneracy between lookback time and redshift. The model is consistent with a picture of hierarchical galaxy growth over time scales of many billions of years.Comment: 7 pages. Accepted, 10 June 1999 Astrophysical Journa

A modified Oster-Murray-Harris mechanical model of morphogenesis

There are two main modeling paradigms for biological pattern formation in developmental biology: chemical prepattern models and cell aggregation models. This paper focuses on an example of a cell aggregation model, the mechanical model developed by Oster, Murray, and Harris [Development, 78 (1983), pp. 83--125]. We revisit the Oster--Murray--Harris model and find that, due to the infinitesimal displacement assumption made in the original version of this model, there is a restriction on the types of boundary conditions that can be prescribed. We derive a modified form of the model which relaxes the infinitesimal displacement assumption. We analyze the dynamics of this model using linear and multiscale nonlinear analysis and show that it has the same linear behavior as the original Oster--Murray--Harris model. Nonlinear analysis, however, predicts that the modified model will allow for a wider range of parameters where the solution evolves to a bounded steady state. The results from both analyses are verified through numerical simulations of the full nonlinear model in one and two dimensions. The increased range of boundary conditions that are well-posed, as well as a wider range of parameters that yield bounded steady states, renders the modified model more applicable to, and more robust for, comparisons with experiments