First excitations in two- and three-dimensional random-field Ising systems

We present results on the first excited states for the random-field Ising model. These are based on an exact algorithm, with which we study the excitation energies and the excitation sizes for two- and three-dimensional random-field Ising systems with a Gaussian distribution of the random fields. Our algorithm is based on an approach of Frontera and Vives which, in some cases, does not yield the true first excited states. Using the corrected algorithm, we find that the order-disorder phase transition for three dimensions is visible via crossings of the excitations-energy curves for different system sizes, while in two-dimensions these crossings converge to zero disorder. Furthermore, we obtain in three dimensions a fractal dimension of the excitations cluster of d_s=2.42(2). We also provide analytical droplet arguments to understand the behavior of the excitation energies for small and large disorder as well as close to the critical point.Comment: 17 pages, 12 figure

Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks

We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing.Comment: Accepted into Proc. CASC 201

Low-energy excitations in the three-dimensional random-field Ising model

The random-field Ising model (RFIM), one of the basic models for quenched disorder, can be studied numerically with the help of efficient ground-state algorithms. In this study, we extend these algorithm by various methods in order to analyze low-energy excitations for the three-dimensional RFIM with Gaussian distributed disorder that appear in the form of clusters of connected spins. We analyze several properties of these clusters. Our results support the validity of the droplet-model description for the RFIM.Comment: 10 pages, 9 figure

On the critical exponent α of the 5D random-field Ising model

11 pages, 7 figures, final version with minor correctionsInternational audienceWe present a complementary estimation of the critical exponent $\alpha$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $\alpha = 0.12(2)$ is consistent with the estimation coming from the modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at $D = 5$

Early Warning Signals for Critical Transitions: A Generalized Modeling Approach

Critical transitions are sudden, often irreversible, changes that can occur in a large variety of complex systems; signals that warn of critical transitions are therefore highly desirable. We propose a new method for early warning signals that integrates multiple sources of information and data about the system through the framework of a generalized model. We demonstrate our proposed approach through several examples, including a previously published fisheries model. We regard our method as complementary to existing early warning signals, taking an approach of intermediate complexity between model-free approaches and fully parameterized simulations. One potential advantage of our approach is that, under appropriate conditions, it may reduce the amount of time series data required for a robust early warning signal

Revisiting the scaling of the specific heat of the three-dimensional random-field Ising model

We revisit the scaling behavior of the specific heat of the three-dimensional random-field Ising model with a Gaussian distribution of the disorder. Exact ground states of the model are obtained using graph-theoretical algorithms for different strengths = 268 3 spins. By numerically differentiating the bond energy with respect to h, a specific-heat-like quantity is obtained whose maximum is found to converge to a constant in the thermodynamic limit. Compared to a previous study following the same approach, we have studied here much larger system sizes with an increased statistical accuracy. We discuss the relevance of our results under the prism of a modified Rushbrooke inequality for the case of a saturating specific heat. Finally, as a byproduct of our analysis, we provide high-accuracy estimates of the critical field hc = 2.279(7) and the critical exponent of the correlation exponent ν = 1.37(1), in excellent agreement to the most recent computations in the literature

Influence of the PM-Processing Route and Nitrogen Content on the Properties of Ni-Free Austenitic Stainless Steel

Ni-free austenitic steels alloyed with Cr and Mn are an alternative to conventional Ni-containing steels. Nitrogen alloying of these steel grades is beneficial for several reasons such as increased strength and corrosion resistance. Low solubility in liquid and δ-ferrite restricts the maximal N-content that can be achieved via conventional metallurgy. Higher contents can be alloyed by powder-metallurgical (PM) production via gas–solid interaction. The performance of sintered parts is determined by appropriate sintering parameters. Three major PM-processing routes, hot isostatic pressing, supersolidus liquid phase sintering (SLPS), and solid-state sintering, were performed to study the influence of PM-processing route and N-content on densification, fracture, and mechanical properties. Sintering routes are designed with the assistance of thermodynamic calculations, differential thermal analysis, and residual gas analysis. Fracture surfaces were studied by X-ray photoelectron spectroscopy, secondary electron microscopy, and energy dispersive X-ray spectroscopy. Tensile tests and X-ray diffraction were performed to study mechanical properties and austenite stability. This study demonstrates that SLPS process reaches high densification of the high-Mn-containing powder material while the desired N-contents were successfully alloyed via gas–solid interaction. Produced specimens show tensile strengths >1000\ua0MPa combined with strain to fracture of 60\ua0pct and thus overcome the other tested production routes as well as conventional stainless austenitic or martensitic grades