Field Emission to control nanometer tip-medium distances in probe storage

In this work, we present a novel concept for high resolution proximity sending based on field emission and provide more insight in the vacuum conditions and electronics needed for stable operation

Statistics of Avalanches with Relaxation, and Barkhausen Noise: A Solvable Model

We study a generalization of the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model of a particle in a Brownian force landscape, including retardation effects. We show that under monotonous driving the particle moves forward at all times, as it does in absence of retardation (Middleton's theorem). This remarkable property allows us to develop an analytical treatment. The model with an exponentially decaying memory kernel is realized in Barkhausen experiments with eddy-current relaxation, and has previously been shown numerically to account for the experimentally observed asymmetry of Barkhausen-pulse shapes. We elucidate another qualitatively new feature: the breakup of each avalanche of the standard ABBM model into a cluster of sub-avalanches, sharply delimited for slow relaxation under quasi-static driving. These conditions are typical for earthquake dynamics. With relaxation and aftershock clustering, the present model includes important ingredients for an effective description of earthquakes. We analyze quantitatively the limits of slow and fast relaxation for stationary driving with velocity v>0. The v-dependent power-law exponent for small velocities, and the critical driving velocity at which the particle velocity never vanishes, are modified. We also analyze non-stationary avalanches following a step in the driving magnetic field. Analytically, we obtain the mean avalanche shape at fixed size, the duration distribution of the first sub-avalanche, and the time dependence of the mean velocity. We propose to study these observables in experiments, allowing to directly measure the shape of the memory kernel, and to trace eddy current relaxation in Barkhausen noise.Comment: 39 pages, 26 figure

Avalanche shape and exponents beyond mean-field theory

Elastic systems, such as magnetic domain walls, density waves, contact lines, and cracks, are all pinned by substrate disorder. When driven, they move via successive jumps called avalanches, with power law distributions of size, duration and velocity. Their exponents, and the shape of an avalanche, defined as its mean velocity as function of time, have recently been studied. They are known approximatively from experiments and simulations, and were predicted from mean-field models, such as the Brownian force model (BFM), where each point of the elastic interface sees a force field which itself is a random walk. As we showed in EPL 97 (2012) 46004, the BFM is the starting point for an $\epsilon = d_{\rm c}-d$ expansion around the upper critical dimension, with $d_{\rm c}=4$ for short-ranged elasticity, and $d_{\rm c}=2$ for long-ranged elasticity. Here we calculate analytically the ${\cal O}(\epsilon)$, i.e. 1-loop, correction to the avalanche shape at fixed duration $T$, for both types of elasticity. The exact expression is well approximated by \left_T\simeq [ Tx(1-x)]^{\gamma-1} \exp\left( {\cal A}\left[\frac12-x\right]\right), $0<x<1$. The asymmetry ${\cal A}\approx - 0.336 (1-d/d_{\rm c})$ is negative for $d$ close to $d_{\rm c}$, skewing the avalanche towards its end, as observed in numerical simulations in $d=2$ and $3$. The exponent $\gamma=(d+\zeta)/z$ is given by the two independent exponents at depinning, the roughness $\zeta$ and the dynamical exponent $z$. We propose a general procedure to predict other avalanche exponents in terms of $\zeta$ and $z$. We finally introduce and calculate the shape at fixed avalanche size, not yet measured in experiments or simulations.Comment: 6 pages, 2 figure

Tuning Poly(Isopropyl Glycidyl Ether-\u3cem\u3eblock\u3c/em\u3e-Polyethylene Glycol-\u3cem\u3eblock\u3c/em\u3e-Isopropyl Glycidyl Ether) Poly(iPrGE-PEG-iPrGE) Triblock Hydrogels for Use in 3D Printing

Additive manufacturing, otherwise known as 3D printing, is an emerging technology with wide applications. The goal of this work is to study hydrogels comprised of the poly(isopropyl glycidyl ether-block-polyethylene glycol-block-isopropyl glycidyl ether) triblock copolymer, poly(iPrGE-PEG-iPrGE), for 3D printing. The hydrogel blends contain poly(iPrGE-PEG-iPrGE) along with varying concentrations of 2.5k PEG, 4k PEG, 8k PEG, 18.5k PEG or 2.5k iPrGE homopolymers. The effectiveness of the blends was measured by comparing the gel point, storage modulus, equilibrium modulus, and yield stress of the hydrogels. The average gel point for the samples ranged from 7.03-12.78 °C and the hydrogels were thermoreversible. The concentration of the triblock was the biggest contributor for differences in the gel point. All of the hydrogels exhibited non-Newtonian shear-thinning properties as well as the ability to recover strength following a period of high strain. The 1 and 5% iPrGE hydrogel blends were the strongest hydrogels, based on the equilibrium modulus and yield stress at room temperature. However, due to interactions in the hydrophobic domain, iPrGE hydrogels had the smallest temperature range and exhibited syneresis at lower temperatures compared to other hydrogel blends. Triblock hydrogels were successfully created and tuned to different levels of strength through the addition of homopolymer

High-precision simulation of the height distribution for the KPZ equation

The one-point distribution of the height for the continuum Kardar-Parisi-Zhang (KPZ) equation is determined numerically using the mapping to the directed polymer in a random potential at high temperature. Using an importance sampling approach, the distribution is obtained over a large range of values, down to a probability density as small as 10^{-1000} in the tails. Both short and long times are investigated and compared with recent analytical predictions for the large-deviation forms of the probability of rare fluctuations. At short times the agreement with the analytical expression is spectacular. We observe that the far left and right tails, with exponents 5/2 and 3/2 respectively, are preserved until large time. We present some evidence for the predicted non-trivial crossover in the left tail from the 5/2 tail exponent to the cubic tail of Tracy-Widom, although the details of the full scaling form remains beyond reach.Comment: 6 pages, 5 figure

JSBML: a flexible Java library for working with SBML

The specifications of the Systems Biology Markup Language (SBML) define standards for storing and exchanging computer models of biological processes in text files. In order to perform model simulations, graphical visualizations and other software manipulations, an in-memory representation of SBML is required. We developed JSBML for this purpose. In contrast to prior implementations of SBML APIs, JSBML has been designed from the ground up for the Java™ programming language, and can therefore be used on all platforms supported by a Java Runtime Environment. This offers important benefits for Java users, including the ability to distribute software as Java Web Start applications. JSBML supports all SBML Levels and Versions through Level 3 Version 1, and we have strived to maintain the highest possible degree of compatibility with the popular library libSBML. JSBML also supports modules that can facilitate the development of plugins for end user applications, as well as ease migration from a libSBML-based backend

Asmptotically Plane Wave Spacetimes

In this thesis we study aspects of plane wave spacetimes in the hope of shedding light of the nature of holography for plane waves. In particular, we would like to understand better the space of asymptotically plane wave solutions. We first review the necessary background on plane waves, variational principles for gravity and black holes in higher dimensions. We then propose a definition of asymptotically plane wave spacetimes in vacuum gravity in terms of the asymptotic fall-off of the metric and discuss the relation to previously constructed exact solutions. We construct a well-behaved action principle for such spacetimes, using the formalism developed by Mann and Marolf. We show that the action is finite on-shell and that the variational principle is well-defined for solutions of vacuum gravity satisfying our asymptotically plane wave fall-off conditions. Next we investigate the construction of black holes and black strings in vacuum plane wave spacetimes using the method of matched asymptotic expansions. We find solutions of the linearised equations of motion in the asymptotic region for a general source on a plane wave background. We observe that these solutions have some unusual propeties and do not satisfy our previously defined conditions for being asymptotically plane wave. Hence, the space of asymptotically plane solutions is restricted. We consider the solution in the near horizon region, treating the plane wave as a perturbation of a black object, and find that there is a regular black string solution. We find that no regular black hole solution exists, which is a counter-example to the conjecture of Emparan et. al. We end with a discussion of our results and suggest possible directions for future work