Some 3d n (4 ≤ n ≤ 7) transition metal compounds exhibit a cooperative transition between a low-spin (LS) and a high-spin (HS) state. This transition is abrupt and occurs with a thermal hysteresis, which confers a memory effect on the system. The intersite interactions and thus the cooperativity are magnified in polymeric compounds such as [Fe(Rtrz) 3 ]A 2 ·nH 2 O in which the Fe 2+ ions are triply bridged by 4-R-substituted-1,2,4-triazole molecules. Moreover, in these compounds, the spin transition is accompanied by a well-pronounced change of color between violet in the LS state and white in the HS state. The transition temperatures of these materials can be fine tuned, using an approach based on the concept of a molecular alloy. In particular, it is possible to design a compound for which room temperature falls in the middle of the thermal hysteresis loop. These materials have many potential applications, for example, as temperature sensors, as active elements of various types of displays, and in information storage and retrieval.

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We propose a vertically-averaged 2D debris flow model based on the non-Newtonian Bingham and Cross rheological formulations. In the Cross model, fluid viscosity changes continuously through the range of shear rates. The 2D model is based on the shallow water equations, where the internal friction losses are implemented using the Cross constitutive relations. The numerical method is based on a four-step, selective lumping, explicit time stepping scheme. We present preliminary tests for one dimensional and two dimensional dam break problems. Model results show very good agreement with experimental data and analytical solutions in one dimensional cases. For the flow early stages, the numerical solution agrees better with the experimental data than with the analytical solution. However, in final stages, the numerical solution predicts that the fluid front advances more rapidly than the analytical solution and measured fluid front. The proposed 2D debris flow model provides very stable results even in the range of very low shear rates, where other discontinuous constitutive relations that use the yield stress may become unstable.

We present a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase of water and fine sediments, and a non-continuum phase of large particles, such as boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method in three dimensions. The fluid phase is governed by the depth-averaged Navier-Stokes equations in two horizontal dimensions and is solved by the Finite Element Method. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in the fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide stable results, even in the range of very low shear rates. The Bingham formulation is better able to simulate the stopping stage of the fluid. The results of the numerical simulations are compared with data from laboratory experiments on a flume-fan model. The results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows that avoid overlapping among particles. An application to simulate a debris flow event that occurred in Northern Venezuela in 1999 shows that the model replicates well the main observed boulder accumulation areas.

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