Catastrophic Phase Transitions and Early Warnings in a Spatial Ecological Model

Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts are fundamental for designing management protocols for ecosystems. Here we study the spatial version of a popular ecological model, involving a logistically growing single species subject to exploitation, which is known to exhibit ASS. Spatial heterogeneity is introduced by a carrying capacity parameter varying from cell to cell in a regular lattice. Transport of biomass among cells is included in the form of diffusion. We investigate whether different quantities from statistical mechanics -like the variance, the two-point correlation function and the patchiness- may serve as early warnings of catastrophic phase transitions between the ASS. In particular, we find that the patch-size distribution follows a power law when the system is close to the catastrophic transition. We also provide links between spatial and temporal indicators and analyze how the interplay between diffusion and spatial heterogeneity may affect the earliness of each of the observables. We find that possible remedial procedures, which can be followed after these early signals, are more effective as the diffusion becomes lower. Finally, we comment on similarities and differences between these catastrophic shifts and paradigmatic thermodynamic phase transitions like the liquid-vapour change of state for a fluid like water

Dynamic noise, chaos and parameter estimation in population biology

We revisit the parameter estimation framework for population biological dynamical systems, and apply it to calibrate various models in epidemiology with empirical time series, namely influenza and dengue fever. When it comes to more complex models such as multi-strain dynamics to describe the virus–host interaction in dengue fever, even the most recently developed parameter estimation techniques, such as maximum likelihood iterated filtering, reach their computational limits. However, the first results of parameter estimation with data on dengue fever from Thailand indicate a subtle interplay between stochasticity and the deterministic skeleton. The deterministic system on its own already displays complex dynamics up to deterministic chaos and coexistence of multiple attractors

Response of the Brazilian gravitational wave detector to signals from a black hole ringdown

It is assumed that a black hole can be disturbed in such a way that a ringdown gravitational wave would be generated. This ringdown waveform is well understood and is modelled as an exponentially damped sinusoid. In this work we use this kind of waveform to study the performance of the SCHENBERG gravitational wave detector. This first realistic simulation will help us to develop strategies for the signal analysis of this Brazilian detector. We calculated the signal-to-noise ratio as a function of frequency for the simulated signals and obtained results that show that SCHENBERG is expected to be sensitive enough to detect this kind of signal up to a distance of $\sim 20\mathrm{kpc}$.Comment: 5 pages, 4 figures, Amaldi 5 Conference Proceedings contribution. Submitted to Class. Quantum Gra

New order parameters in the Potts model on a Cayley tree

For the $q-$state Potts model new order parameters projecting on a group of spins instead of a single spin are introduced. On a Cayley tree this allows the physical interpretation of the Potts model at noninteger values q of the number of states. The model can be solved recursively. This recursion exhibits chaotic behaviour changing qualitatively at critical values of $q_0$ . Using an additional order parameter belonging to a group of zero extrapolated size the additional ordering is related to a percolation problem. This percolation distinguishes different phases and explains the critical indices of percolation class occuring at the Peierls temperature.Comment: 16 pages TeX, 5 figures PostScrip

Afforestation of savannas: an impending ecological disaster.

Made available in DSpace on 2018-08-04T00:53:27Z (GMT). No. of bitstreams: 1 1s2.0S1679007316300779main.pdf: 2087352 bytes, checksum: f7e5fc4f6f8dbc44cbc3b894fadca5f3 (MD5) Previous issue date: 2017-02-06bitstream/item/180899/1/1-s2.0-S1679007316300779-main.pd

Second Order Dissipative Fluid Dynamics for Ultra-Relativistic Nuclear Collisions

The M\"uller-Israel-Stewart second order theory of relativistic imperfect fluids based on Grad's moment method is used to study the expansion of hot matter produced in ultra-relativistic heavy ion collisions. The temperature evolution is investigated in the framework of the Bjorken boost-invariant scaling limit. The results of these second-order theories are compared to those of first-order theories due to Eckart and to Landau and Lifshitz and those of zeroth order (perfect fluid) due to Euler.Comment: 5 pages, 4 figures, size of y-axis tick marks for Figs. 3 and 4 fixe

The GHZ/W-calculus contains rational arithmetic

Graphical calculi for representing interacting quantum systems serve a number of purposes: compositionally, intuitive graphical reasoning, and a logical underpinning for automation. The power of these calculi stems from the fact that they embody generalized symmetries of the structure of quantum operations, which, for example, stretch well beyond the Choi-Jamiolkowski isomorphism. One such calculus takes the GHZ and W states as its basic generators. Here we show that this language allows one to encode standard rational calculus, with the GHZ state as multiplication, the W state as addition, the Pauli X gate as multiplicative inversion, and the Pauli Z gate as additive inversion.Comment: In Proceedings HPC 2010, arXiv:1103.226