Dichotomous Hamiltonians with Unbounded Entries and Solutions of Riccati Equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.Comment: 31 pages, 3 figures; proof of uniqueness of solutions added; to appear in Journal of Evolution Equation

A Model of the Ventral Visual System Based on Temporal Stability and Local Memory

The cerebral cortex is a remarkably homogeneous structure suggesting a rather generic computational machinery. Indeed, under a variety of conditions, functions attributed to specialized areas can be supported by other regions. However, a host of studies have laid out an ever more detailed map of functional cortical areas. This leaves us with the puzzle of whether different cortical areas are intrinsically specialized, or whether they differ mostly by their position in the processing hierarchy and their inputs but apply the same computational principles. Here we show that the computational principle of optimal stability of sensory representations combined with local memory gives rise to a hierarchy of processing stages resembling the ventral visual pathway when it is exposed to continuous natural stimuli. Early processing stages show receptive fields similar to those observed in the primary visual cortex. Subsequent stages are selective for increasingly complex configurations of local features, as observed in higher visual areas. The last stage of the model displays place fields as observed in entorhinal cortex and hippocampus. The results suggest that functionally heterogeneous cortical areas can be generated by only a few computational principles and highlight the importance of the variability of the input signals in forming functional specialization

Understanding the interaction between energetic ions and freestanding graphene towards practical 2D perforation

We report experimentally and theoretically the behavior of freestanding graphene subject to bombardment of energetic ions, investigating the ability of large-scale patterning of freestanding graphene with nanometer sized features by focused ion beam technology. A precise control over the He+ and Ga+ irradiation offered by focused ion beam techniques enables to investigate the interaction of the energetic particles and graphene suspended with no support and allows determining sputter yields of the 2D lattice. We find strong dependency of the 2D sputter yield on the species and kinetic energy of the incident ion beams. Freestanding graphene shows material semi-transparency to He+ at high energies (10-30 keV) allowing the passage of >97% He+ particles without creating destructive lattice vacancy. Large Ga+ ions (5-30 keV), in contrast, collide far more often with the graphene lattice to impart significantly higher sputter yield of ~50%. Binary collision theory applied to monolayer and few-layer graphene can successfully elucidate this collision mechanism, in great agreement with experiments. Raman spectroscopy analysis corroborates the passage of a large fraction of He+ ions across graphene without much damaging the lattice whereas several colliding ions create single vacancy defects. Physical understanding of the interaction between energetic particles and suspended graphene can practically lead to reproducible and efficient pattern generation of unprecedentedly small features on 2D materials by design, manifested by our perforation of sub-5-nm pore arrays. This capability of nanometer scale precision patterning of freestanding 2D lattices shows practical applicability of the focused ion beam technology to 2D material processing for device fabrication and integration.Comment: 31 pages of main text (with 4 figures) plus 4 pages of supporting information (with 2 figures). Original article submitted to a journal for consideration for publicatio

Nonlinear viscoelasticity of metastable complex fluids

Many metastable complex fluids such as colloidal glasses and gels show distinct nonlinear viscoelasticity with increasing oscillatory-strain amplitude; the storage modulus decreases monotonically as the strain amplitude increases whereas the loss modulus has a distinct peak before it decreases at larger strains. We present a qualitative argument to explain this ubiquitous behavior and use mode coupling theory (MCT) to confirm it. We compare theoretical predictions to the measured nonlinear viscoelasticity in a dense hard sphere colloidal suspensions; reasonable agreement is obtained. The argument given here can be used to obtain new information about linear viscoelasticity of metastable complex fluids from nonlinear strain measurements.Comment: 7 pages, 3 figures, accepted for publication in Europhys. Let

Generation of Porous Particle Structures using the Void Expansion Method

The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller "void-particles". Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles' mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure

Do wildflower strips enhance pest control in organic cabbage?

Within this project we assess whether wildflower strips and companion plants increase the control of cabbage pests Plutella xylostella L. (Lepidoptera: Plutellidae), Mamestra brassicae L. (Lepidoptera: Noctuidae) and Pieris rapae L. (Lepidoptera: Pieridae) by (1) naturally occurring parasitoids and predators and (2) mass‐releasedn Trichogramma brassciae (Bezdenko) (Hymenoptera: Trichogrammatidae) parasitoids. Two organic cabbage fields were used for this study: adjacent to each field a wildflower strip was sown and companion plants (Centaurea cyanus L. (Asteraceae)) intermixed within the crop. Within each field ~15,000 M. brassicae eggs were placed out to determine the parasitism rates by mass‐released T. brassicae and to assess the levels of egg predation. Over 1,000 lepidopteran larvae were collected and screened for hymenopteran and tachinid parasitoid DNA using a multiplex PCR assay. Invertebrate generalist predators (n=1,063) were collected for DNA‐based gut content analysis. The wildflower strip had a significant positive effect on M. brassicae egg parasitism rates as rates increased 5‐fold in the vicinity to the strip. Moreover, companion plants enhanced invertebrate predation on M. brassicae eggs. Both, the release of T. brassicae and the use of companion plants, however, did not significantly increase egg parasitism rates. The infestation of plants by caterpillars increased with distance to the wildflower strip and there was a trend of decreasing larval parasitism rates with distance to the strip. Currently the invertebrate predators are being molecularly analysed to assess predation on unparasitized and parasitized lepidopteran pests