Higher Order Analogues of Tracy-Widom Distributions via the Lax Method

We study the distribution of the largest eigenvalue in formal Hermitian one-matrix models at multicriticality, where the spectral density acquires an extra number of k-1 zeros at the edge. The distributions are directly expressed through the norms of orthogonal polynomials on a semi-infinite interval, as an alternative to using Fredholm determinants. They satisfy non-linear recurrence relations which we show form a Lax pair, making contact to the string literature in the early 1990's. The technique of pseudo-differential operators allows us to give compact expressions for the logarithm of the gap probability in terms of the Painleve XXXIV hierarchy. These are the higher order analogues of the Tracy-Widom distribution which has k=1. Using known Backlund transformations we show how to simplify earlier equivalent results that are derived from Fredholm determinant theory, valid for even k in terms of the Painleve II hierarchy.Comment: 24 pages. Improved discussion of Backlund transformations, in addition to other minor improvements in text. Typos corrected. Matches published versio

Resistive damping implementation as a method to improve controllability in stiff ohmic RF-MEMS switches

This paper presents in detail the entire procedure of calculating the bias resistance of an ohmic RF-MEMS switch, controlled under resistive damping (charge drive technique). In case of a very stiff device, like the North Eastern University switch, the actuation control under resistive damping is the only way to achieve controllability. Due to the short switching time as well as the high actuation voltage, it is not practical to apply a tailored control pulse (voltage drive control technique). Implementing a bias resistor of 33 MΩ in series with the voltage source, the impact velocity of the cantilever has been reduced 80 % (13.2 from 65.9 cm/s), eliminating bouncing and high initial impact force during the pull-down phase. However, this results in an affordable cost of switching time increase from 2.38 to 4.34 μs. During the release phase the amplitude of bouncing has also been reduced 34 % (174 from 255 nm), providing significant improvement in both switching operation phases of the switch. © 2013 Springer-Verlag Berlin Heidelberg

Soil rehabilitation in semi-arid Spain: Long-term effect of afforestation and land abandonment on soil quality

In response to the increasing amount of abandoned agricultural land in the European Mediterranean area during the last century, afforestation projects have been conducted as a measure for soil protection and ecosystem restoration. Despite the research on the impact and effectiveness of these projects, the long-term effect on soil quality has hardly been studied. Especially the linkage between soil physical, chemical and hydrological properties is lacking. An intensive fieldwork has been carried out in Murcia, southeastern Spain to study the effects of land abandonment and afforestation on soil quality along a chronosequence and included two afforested areas, planted with Pinus halepensis trees in the early ‘70s and ‘90s. Samples were taken to study changes in soil physical and chemical quality (e.g. Aggregate stability, Corg, N, P, K, Na), Soil Organic Carbon (SOC) stocks and soil hydrological properties, such as infiltration and water retention. A comparison was made between afforestation projects, abandoned agricultural plots of similar age, semi-natural vegetation and cereal crop fields. As the natural vegetation is characterized by a spotted pattern of bare areas and trees, forming so-called “islands of fertility”, both bare and vegetation covered sub-sites were included. Our results indicated that under secondary succession on abandoned fields, soil quality showed a marginal non-linear improvement over the studied period. The afforestation showed a much more pronounced linear increase, resulting in a soil quality comparable to what can be found under semi-natural vegetation. After 40 years afforestation showed to be successful in the restoration of the natural soil hydrological functioning, while the abandoned sites only indicated small changes. For this case study, in semiarid areas, afforesting is the best way forward as it has a clear effect on enhancing soil quality compared to secondary succession on abandoned agricultural fields

The mutual information of a stochastic binary channel: validity of the Replica Symmetry Ansatz

We calculate the mutual information (MI) of a two-layered neural network with noiseless, continuous inputs and binary, stochastic outputs under several assumptions on the synaptic efficiencies. The interesting regime corresponds to the limit where the number of both input and output units is large but their ratio is kept fixed at a value $\alpha$. We first present a solution for the MI using the replica technique with a replica symmetric (RS) ansatz. Then we find an exact solution for this quantity valid in a neighborhood of $\alpha = 0$. An analysis of this solution shows that the system must have a phase transition at some finite value of $\alpha$. This transition shows a singularity in the third derivative of the MI. As the RS solution turns out to be infinitely differentiable, it could be regarded as a smooth approximation to the MI. This is checked numerically in the validity domain of the exact solution.Comment: Latex, 29 pages, 2 Encapsulated Post Script figures. To appear in Journal of Physics

Quasiperiodic Patterns in Boundary-Modulated Excitable Waves

We investigate the impact of the domain shape on wave propagation in excitable media. Channelled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration stroboscopically frozen in time. The phenomenon is studied in a model for the photo-sensitive Belousov-Zabotinsky reaction, but we give a theoretical derivation of the spatial return maps prescribing the height and position of the successive fronts that is valid for arbitrary excitable reaction-diffusion systems.Comment: 4 pages (figures included

A metamorphic inorganic framework that can be switched between eight single-crystalline states

The design of highly flexible framework materials requires organic linkers, whereas inorganic materials are more robust but inflexible. Here, by using linkable inorganic rings made up of tungsten oxide (P8W48O184) building blocks, we synthesized an inorganic single crystal material that can undergo at least eight different crystal-to-crystal transformations, with gigantic crystal volume contraction and expansion changes ranging from −2,170 to +1,720 Å3 with no reduction in crystallinity. Not only does this material undergo the largest single crystal-to-single crystal volume transformation thus far reported (to the best of our knowledge), the system also shows conformational flexibility while maintaining robustness over several cycles in the reversible uptake and release of guest molecules switching the crystal between different metamorphic states. This material combines the robustness of inorganic materials with the flexibility of organic frameworks, thereby challenging the notion that flexible materials with robustness are mutually exclusive

Electron cotunneling transport in gold nanocrystal arrays

We describe current-voltage characteristics I(V) of alkyl-ligated gold nanocrystals $\sim 5 nm$ arrays in long screening length limit. Arrays with different alkyl ligand lengths have been prepared to tune the electronic tunnel coupling between the nanocrystals. For long ligands, electronic diffusion occurs through sequential tunneling and follows activated laws, as function of temperature $\sigma \propto e^{-T_0/T}$ and as function of electric field $I \propto e^{-\mathcal{E}_0/\mathcal{E}}$. For better conducting arrays, i.e. with small ligands, the transport properties crossover to the cotunneling regime and follows Efros-Shklovskii laws as function of temperature $\sigma \propto e^{-(T_{ES}/T)^{1/2}}$ and as function of electric field $I \propto e^{-(\mathcal{E}_{ES}/\mathcal{E})^{1/2}}$. The data shows that electronic transport in nanocrystal arrays can be tuned from the sequential tunneling to the cotunneling regime by increasing the tunnel barrier transparency

Entangled random pure states with orthogonal symmetry: exact results

We compute analytically the density $\varrho_{N,M}(\lambda)$ of Schmidt eigenvalues, distributed according to a fixed-trace Wishart-Laguerre measure, and the average R\'enyi entropy $\langle\mathcal{S}_q\rangle$ for reduced density matrices of entangled random pure states with orthogonal symmetry $(\beta=1)$. The results are valid for arbitrary dimensions $N=2k,M$ of the corresponding Hilbert space partitions, and are in excellent agreement with numerical simulations.Comment: 15 pages, 5 figure

Self-control in Sparsely Coded Networks

A complete self-control mechanism is proposed in the dynamics of neural networks through the introduction of a time-dependent threshold, determined in function of both the noise and the pattern activity in the network. Especially for sparsely coded models this mechanism is shown to considerably improve the storage capacity, the basins of attraction and the mutual information content of the network.Comment: 4 pages, 6 Postscript figure

Wave nucleation rate in excitable systems in the low noise limit

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential pair of equations driven by thermal (i.e. white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other non-equilibrium pattern-forming processes