The complexity of Free-Flood-It on 2xn boards

We consider the complexity of problems related to the combinatorial game Free-Flood-It, in which players aim to make a coloured graph monochromatic with the minimum possible number of flooding operations. Our main result is that computing the length of an optimal sequence is fixed parameter tractable (with the number of colours present as a parameter) when restricted to rectangular 2xn boards. We also show that, when the number of colours is unbounded, the problem remains NP-hard on such boards. This resolves a question of Clifford, Jalsenius, Montanaro and Sach (2010)

A dam-break flood simulation model in curvilinear coordinates

A dam-break flood model based on a contravariant integral form of the shallow water equations is presented. The numerical integration of the equations of motion is carried out by means of a finite volumefinite difference numerical scheme that involves an exact Riemann solver and which is based on a high-order WENO reconstruction procedure. An original scheme for the simulation of the wet front progress on the dry bed is adopted. The proposed model capacity to correctly simulate the wet front progress velocity is tested by numerically reproducing the dry bed dam-break problem. The model is adopted for the real case study of the Rio Fucino lake-dam collapse and subsequent flood wave propagation, downstream of the Campotosto reservoir (Italy)

Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model

This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment

The cohesive frictional crack model applied to the analysis of the dam-foundation joint

The mechanical behaviour of dam-foundation joints plays a key role in concrete dam engineering since it is the weakest part of the structure and therefore the evolutionary crack process occurring along this joint determines the global load-bearing capacity. The reference volume involved in the above mentioned process is so large that it cannot be tested in a laboratory: structural analysis has to be carried on by numerical modelling. The use of the asymptotic expansions proposed by Karihaloo and Xiao at the tip of a crack with normal cohesion and Coulomb friction can overcome the numerical difficulties that appear in large scale problems when the Newton-Raphson procedure is applied to a set of equilibrium equations based on ordinary shape functions (Standard Finite Element Method). In this way it is possible to analyze problems with friction and crack propagation under the constant load induced by hydro-mechanical coupling. For each position of the fictitious crack tip, the condition K1=K2=0 allows us to obtain the external load level and the tangential stress at the tip. If the joint tangential strength is larger than the value obtained, the solution is acceptable, because the tensile strength is assumed negligible and the condition K1=0 is sufficient to cause the crack growth. Otherwise, the load level obtained can be considered as an overestimation of the critical value and a special form of contact problem has to be solved along the fictitious process zone. For the boundary condition analyzed (ICOLD benchmark on gravity dam model), after an initial increasing phase, the water lag remains almost constant and the maximum value of load carrying capacity is achieved when the water lag reaches its constant valu

Data-driven Flood Emulation: Speeding up Urban Flood Predictions by Deep Convolutional Neural Networks

Computational complexity has been the bottleneck of applying physically-based simulations on large urban areas with high spatial resolution for efficient and systematic flooding analyses and risk assessments. To address this issue of long computational time, this paper proposes that the prediction of maximum water depth rasters can be considered as an image-to-image translation problem where the results are generated from input elevation rasters using the information learned from data rather than by conducting simulations, which can significantly accelerate the prediction process. The proposed approach was implemented by a deep convolutional neural network trained on flood simulation data of 18 designed hyetographs on three selected catchments. Multiple tests with both designed and real rainfall events were performed and the results show that the flood predictions by neural network uses only 0.5 % of time comparing with physically-based approaches, with promising accuracy and ability of generalizations. The proposed neural network can also potentially be applied to different but relevant problems including flood predictions for urban layout planning