Dynamics and Steady States in excitable mobile agent systems

We study the spreading of excitations in 2D systems of mobile agents where the excitation is transmitted when a quiescent agent keeps contact with an excited one during a non-vanishing time. We show that the steady states strongly depend on the spatial agent dynamics. Moreover, the coupling between exposition time ($\omega$) and agent-agent contact rate (CR) becomes crucial to understand the excitation dynamics, which exhibits three regimes with CR: no excitation for low CR, an excited regime in which the number of quiescent agents (S) is inversely proportional to CR, and for high CR, a novel third regime, model dependent, here S scales with an exponent $\xi -1$, with $\xi$ being the scaling exponent of $\omega$ with CR

An Inverse Scattering Transform for the Lattice Potential KdV Equation

The lattice potential Korteweg-de Vries equation (LKdV) is a partial difference equation in two independent variables, which possesses many properties that are analogous to those of the celebrated Korteweg-de Vries equation. These include discrete soliton solutions, Backlund transformations and an associated linear problem, called a Lax pair, for which it provides the compatibility condition. In this paper, we solve the initial value problem for the LKdV equation through a discrete implementation of the inverse scattering transform method applied to the Lax pair. The initial value used for the LKdV equation is assumed to be real and decaying to zero as the absolute value of the discrete spatial variable approaches large values. An interesting feature of our approach is the solution of a discrete Gel'fand-Levitan equation. Moreover, we provide a complete characterization of reflectionless potentials and show that this leads to the Cauchy matrix form of N-soliton solutions

Multidimensional Inverse Scattering of Integrable Lattice Equations

We present a discrete inverse scattering transform for all ABS equations excluding Q4. The nonlinear partial difference equations presented in the ABS hierarchy represent a comprehensive class of scalar affine-linear lattice equations which possess the multidimensional consistency property. Due to this property it is natural to consider these equations living in an N-dimensional lattice, where the solutions depend on N distinct independent variables and associated parameters. The direct scattering procedure, which is one-dimensional, is carried out along a staircase within this multidimensional lattice. The solutions obtained are dependent on all N lattice variables and parameters. We further show that the soliton solutions derived from the Cauchy matrix approach are exactly the solutions obtained from reflectionless potentials, and we give a short discussion on inverse scattering solutions of some previously known lattice equations, such as the lattice KdV equation.Comment: 18 page

Localization of a Breathing Crack Using Super-Harmonic Signals due to System Nonlinearity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76712/1/AIAA-38947-457.pd

On the Floquet Theory of Delay Differential Equations

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincar'e Lindstedt and the Shohat expansions which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions

Hare: a file system for non-cache-coherent multicores

Hare is a new file system that provides a POSIX-like interface on multicore processors without cache coherence. Hare allows applications on different cores to share files, directories, and file descriptors. The challenge in designing Hare is to support the shared abstractions faithfully enough to run applications that run on traditional shared-memory operating systems, with few modifications, and to do so while scaling with an increasing number of cores. To achieve this goal, Hare must support features (such as shared file descriptors) that traditional network file systems don't support, as well as implement them in a way that scales (e.g., shard a directory across servers to allow concurrent operations in that directory). Hare achieves this goal through a combination of new protocols (including a 3-phase commit protocol to implement directory operations correctly and scalably) and leveraging properties of non-cache-coherent multiprocessors (e.g., atomic low-latency message delivery and shared DRAM). An evaluation on a 40-core machine demonstrates that Hare can run many challenging Linux applications (including a mail server and a Linux kernel build) with minimal or no modifications. The results also show these applications achieve good scalability on Hare, and that Hare's techniques are important to achieving scalability.Quanta Computer (Firm

Effects of White Leds on Growth and Phytonutrients of Outredgeous Romaine Lettuce When Supplemented with Various Monochromatic Wavelengths

Growing plants in space will be an essential part of sustaining astronauts during long-range missions. To drive photosynthesis, light-emitting diodes (LEDs) are becoming superior because of their efficiency, longevity, small size, safety, and wavelength versatility. Isolating the effects of certain wavelengths on plant growth when combined with white light is attracting attention. To optimize crop production/quality in space, this study has aimed to configure novel light recipes for the Advanced Plant Habitat currently aboard the International Space Station (ISS). By using white light as a background to maintain normal growth, the addition of monochromatic wavelengths provides a clearer understanding of how each part of the visible spectrum affects plant growth. By growing Outredgeous lettuce under six treatments of White (W) LEDs, W + blue (B), W+ green (G), W + red (R), W + far red (FR), and RGB + FR LEDs with ratios similar to natural sunlight, this investigation has assessed differences in biomass, morphology, chlorophyll, and the synthesis of key phytonutrients. The potential for Outredgeous to produce anthocyanin, lutein, potassium, magnesium, and iron is paramount to maintaining astronaut health. The crop responses to each treatment have been evaluated and the optimal LED combination for both plant yield and nutrient content will be presented

Multi-barrier resonant tunneling for the one-dimensional nonlinear Schr\"odinger Equation

For the stationary one-dimensional nonlinear Schr\"odinger equation (or Gross-Pitaevskii equation) nonlinear resonant transmission through a finite number of equidistant identical barriers is studied using a (semi-) analytical approach. In addition to the occurrence of bistable transmission peaks known from nonlinear resonant transmission through a single quantum well (respectively a double barrier) complicated (looped) structures are observed in the transmission coefficient which can be identified as the result of symmetry breaking similar to the emergence of self-trapping states in double well potentials. Furthermore it is shown that these results are well reproduced by a nonlinear oscillator model based on a small number of resonance eigenfunctions of the corresponding linear system.Comment: 22 pages, 11 figure