An efficient mixed variational reduced order model formulation for non-linear analyses of elastic shells

The Koiter-Newton method had recently demonstrated a superior performance for non-linear analyses of structures, compared to traditional path-following strategies. The method follows a predictor-corrector scheme to trace the entire equilibrium path. During a predictor step a reduced order model is constructed based on Koiter's asymptotic post-buckling theory which is followed by a Newton iteration in the corrector phase to regain the equilibrium of forces. In this manuscript, we introduce a robust mixed solid-shell formulation to further enhance the efficiency of stability analyses in various aspects. We show that a Hellinger-Reissner variational formulation facilitates the reduced order model construction omitting an expensive evaluation of the inherent fourth order derivatives of the strain energy. We demonstrate that extremely large step sizes with a reasonable out-of-balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path. More importantly, the numerical effort of the corrector phase involving a Newton iteration of the full order model is drastically reduced thus revealing the true strength of the proposed formulation. We study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems

A random laser tailored by directional stimulated emission

A disordered structure embedding an active gain material and able to lase is called random laser (RL). The RL spectrum may appear either like a set of sharp resonances or like a smooth line superimposed to the fluorescence. A recent letter accounts for this duality with the onset of a mode locked regime in which increasing the number of activated modes results in an increased inter mode correlation and a pulse shortening ascribed to a synchronization phenomenon. An extended discussion of our experimental approach together with an original study of the spatial properties of the RL is reported here.Comment: 9 Pages; 16 Figure

Convergent subseries of divergent series

Let X be the set of positive real sequences x= (xn) such that the series ∑ nxn is divergent. For each x∈ X, let Ix be the collection of all A⊆ N such that the subseries ∑ n∈Axn is convergent. Moreover, let A be the set of sequences x∈ X such that lim nxn= 0 and Ix≠ Iy for all sequences y= (yn) ∈ X with lim inf nyn+1/ yn> 0. We show that A is comeager and that contains uncountably many sequences x which generate pairwise nonisomorphic ideals Ix. This answers, in particular, an open question recently posed by M. Filipczak and G. Horbaczewska

Non-locality and collective emission in disordered lasing resonators

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs Works 3.0 Unported license.Random lasing is observed in optically active resonators in the presence of disorder. As the optical cavities involved are open, the modes are coupled, and energy may pour from one state to another provided that they are spatially overlapping. Although the electromagnetic modes are spatially localized, our system may be actively switched to a collective state, presenting a novel form of non-locality revealed by a high degree of spectral correlation between the light emissions collected at distant positions. In a nutshell, light may be stored in a disordered nonlinear structure in different fashions that strongly differ in their spatial properties. This effect is experimentally demonstrated and theoretically explained in titania clusters embedded in a dye, and it provides clear evidence of a transition to a multimodal collective emission involving the entire spatial extent of the disordered system. Our results can be used to develop a novel type of miniaturized, actively controlled all-optical chip. © 2013 CIOMP. All rights reserved.The research leading to these results has received funding from the ERC under the EC’s Seventh Framework Program (FP7/2007–2013) grant agreement n.201766, EU FP7 NoE Nanophotonics4Enery Grant No. 248855; the Spanish MICINN CSD2007-0046 (Nanolight.es); MAT2009-07841 (GLUSFA); and Comunidad de Madrid S2009/MAT2012-31659.Peer Reviewe

Combining Local and Global Direct Derivative-free Optimization for Reinforcement Learning

We consider the problem of optimization in policy space for reinforcement learning. While a plethora of methods have been applied to this problem, only a narrow category of them proved feasible in robotics. We consider the peculiar characteristics of reinforcement learning in robotics, and devise a combination of two algorithms from the literature of derivative-free optimization. The proposed combination is well suited for robotics, as it involves both off-line learning in simulation and on-line learning in the real environment. We demonstrate our approach on a real-world task, where an Autonomous Underwater Vehicle has to survey a target area under potentially unknown environment conditions. We start from a given controller, which can perform the task under foreseeable conditions, and make it adaptive to the actual environment

Condensation in disordered lasers: theory, 3D+1 simulations and experiments

The complex processes underlying the generation of a coherent-like emission from the multiple-scattering of photons and wave-localization in the presence of structural disorder are still mostly un-explored. Here we show that a single nonlinear Schroedinger equation, playing the role of the Schawlow-Townes law for standard lasers, quantitatively reproduces experimental results and three-dimensional time-domain parallel simulations of a colloidal laser system.Comment: 4 pages, 5 figure

Co-transport-induced instability of membrane voltage in tip-growing cells

A salient feature of stationary patterns in tip-growing cells is the key role played by the symports and antiports, membrane proteins that translocate two ionic species at the same time. It is shown that these co-transporters destabilize generically the membrane voltage if the two translocated ions diffuse differently and carry a charge of opposite (same) sign for symports (antiports). Orders of magnitude obtained for the time and lengthscale are in agreement with experiments. A weakly nonlinear analysis characterizes the bifurcation

Planning in answer set programming while learning action costs for mobile robots

For mobile robots to perform complex missions, it may be necessary for them to plan with incomplete information and reason about the indirect effects of their actions. Answer Set Programming (ASP) provides an elegant way of formalizing domains which involve indirect effects of an action and recursively defined fluents. In this paper, we present an approach that uses ASP for robotic task planning, and demonstrate how ASP can be used to generate plans that acquire missing information necessary to achieve the goal. Action costs are also incorporated with planning to produce optimal plans, and we show how these costs can be estimated from experience making planning adaptive. We evaluate our approach using a realistic simulation of an indoor environment where a robot learns to complete its objective in the shortest time