We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are spanning paths or loops of total negative weight. This kind of percolation problem is fundamentally different from conventional percolation problems, e.g. it does not exhibit transitivity, hence no simple definition of clusters, and several spanning paths/loops might coexist in the percolation regime at the same time. Furthermore, to study this percolation problem numerically, one has to perform a non-trivial transformation of the original graph and apply sophisticated matching algorithms.Using this approach, we study the corresponding percolation transitions on large square, hexagonal and cubic lattices for two types of disorder distributions and determine the critical exponents. The results show that negative-weight percolation is in a different universality class compared to conventional bond/site percolation. On the other hand, negative-weight percolation seems to be related to the ferromagnet/spin-glass transition of random-bond Ising systems, at least in two dimensions.
We study domain walls in 2d Ising spin glasses in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of domain walls, which describes via $<\ell >\simL^{d_f}$ the growth of the average domain-wall length with %% systems size $L\times L$. %% 20.07.07 OM %% Exploring systems up to L=320 we yield $d_f=1.274(2)$ for the case of Gaussian disorder, i.e. a much higher accuracy compared to previous studies. For the case of bimodal disorder, where many equivalent domain walls exist due to the degeneracy of this model, we obtain a true lower bound $d_f=1.095(2)$ and a (lower) estimate $d_f=1.395(3)$ as upper bound. Furthermore, we study the distributions of the domain-wall lengths. Their scaling with system size can be described also only by the exponent $d_f$, i.e. the distributions are monofractal. Finally, we investigate the growth of the domain-wall width with system size (``roughness'') and find a linear behavior.Comment: 8 pages, 8 figures, submitted to Phys. Rev. B; v2: shortened versio
By means of numerical simulations, we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions d=2 through 7, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of system-spanning loops of total negative weight. The resulting negative-weight percolation (NWP) problem is fundamentally different from conventional percolation, as we have seen in previous studies of this model for the two-dimensional case. Here, we characterize the transition for hypercubic systems, where the aim of the present study is to get a grip on the upper critical dimension d u of the NWP problem. For the numerical simulations, we employ a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. We characterize the loops via observables similar to those in percolation theory and perform finite-size scaling analyses, e.g., three-dimensional hypercubic systems with side length up to L=56 sites, in order to estimate the critical properties of the NWP phenomenon. We find our numerical results consistent with an upper critical dimension d u=6 for the NWP problem.
We demonstrate a peculiar mechanism for the formation of bound states of light pulses of substantially different optical frequencies, in which pulses are strongly bound across a vast frequency gap. This is enabled by a propagation constant with two separate regions of anomalous dispersion. The resulting soliton compound exhibits molecule-like binding energy, vibration, and radiation and can be understood as a mutual trapping providing a striking analogy to quantum mechanics. The phenomenon constitutes an intriguing case of two light waves mutually affecting and controlling each other.
Optoacoustic (OA) measurements can not only be used for imaging purposes but as a more general tool to “sense” physical characteristics of biological tissue, such as geometric features and intrinsic optical properties. In order to pave the way for a systematic model-guided analysis of complex objects we devised numerical simulations in accordance with the experimental measurements. We validate our computational approach with experimental results observed for layered polyvinyl alcohol hydrogel samples, using melanin as the absorbing agent. Experimentally, we characterize the acoustic signal observed by a piezoelectric detector in the acoustic far-field in backward mode and we discuss the implication of acoustic diffraction on our measurements. We further attempt an inversion of an OA signal in the far-field approximation.
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