Modelling and characterization of cell collapse in aluminium foams during dynamic loading

Plate-impact experiments have been conducted to investigate the elastic–plastic behaviour of shock wave propagation and pore collapse mechanisms of closed-cell aluminium foams. FE modelling using a meso-scale approach has been carried out with the FE software ABAQUS/Explicit. A micro-computed tomography-based foam geometry has been developed and microstructural changes with time have been investigated to explore the effects of wave propagation. Special attention has been given to the pore collapse mechanism. The effect of velocity variations on deformation has been elucidated with three different impact conditions using the plate-impact method. Free surface velocity (ufs) was measured on the rear of the sample to understand the evolution of the compaction. At low impact velocities, the free-surface velocity increased gradually, whereas an abrupt rise of free-surface velocity was found at an impact velocity of 845 m/s with a copper flyer-plate which correlates with the appearance of shock. A good correlation was found between experimental results and FE predictions

Observational Characterization of the Downward Atmospheric Longwave Radiation at the Surface in the City of São Paulo

This work describes the seasonal and diurnal variations of downward longwave atmospheric irradiance (LW) at the surface in São Paulo, Brazil, using 5-min-averaged values of LW, air temperature, relative humidity, and solar radiation observed continuously and simultaneously from 1997 to 2006 on a micrometeorological platform, located at the top of a 4-story building. An objective procedure, including 2-step filtering and dome emission effect correction, was used to evaluate the quality of the 9-yr-long LW dataset. The comparison between LW values observed and yielded by the Surface Radiation Budget project shows spatial and temporal agreement, indicating that monthly and annual average values of LW observed in one point of São Paulo can be used as representative of the entire metropolitan region of São Paulo. The maximum monthly averaged value of the LW is observed during summer (389 ± 14 W m-2; January), and the minimum is observed during winter (332 ± 12 W m-2; July). The effective emissivity follows the LW and shows a maximum in summer (0.907 ± 0.032; January) and a minimum in winter (0.818 ± 0.029; June). The mean cloud effect, identified objectively by comparing the monthly averaged values of the LW during clear-sky days and all-sky conditions, intensified the monthly average LW by about 32.0 ± 3.5 W m-2 and the atmospheric effective emissivity by about 0.088 ± 0.024. In August, the driest month of the year in São Paulo, the diurnal evolution of the LW shows a minimum (325 ± 11 W m-2) at 0900 LT and a maximum (345 ± 12 W m-2) at 1800 LT, which lags behind (by 4 h) the maximum diurnal variation of the screen temperature. The diurnal evolution of effective emissivity shows a minimum (0.781 ± 0.027) during daytime and a maximum (0.842 ± 0.030) during nighttime. The diurnal evolution of all-sky condition and clear-sky day differences in the effective emissivity remain relatively constant (7% ± 1%), indicating that clouds do not change the emissivity diurnal pattern. The relationship between effective emissivity and screen air temperature and between effective emissivity and water vapor is complex. During the night, when the planetary boundary layer is shallower, the effective emissivity can be estimated by screen parameters. During the day, the relationship between effective emissivity and screen parameters varies from place to place and depends on the planetary boundary layer process. Because the empirical expressions do not contain enough information about the diurnal variation of the vertical stratification of air temperature and moisture in São Paulo, they are likely to fail in reproducing the diurnal variation of the surface emissivity. The most accurate way to estimate the LW for clear-sky conditions in São Paulo is to use an expression derived from a purely empirical approach

Asymptotics of self-similar solutions to coagulation equations with product kernel

We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel $K(\xi,\eta)= (\xi \eta)^{\lambda}$ with $\lambda \in (0,1/2)$. It is known that such self-similar solutions $g(x)$ satisfy that $x^{-1+2\lambda} g(x)$ is bounded above and below as $x \to 0$. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function $h(x)=h_{\lambda} x^{-1+2\lambda} g(x)$ in the limit $\lambda \to 0$. It turns out that $h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)$ as $x \to 0$. As $x$ becomes larger $h$ develops peaks of height $1/\lambda$ that are separated by large regions where $h$ is small. Finally, $h$ converges to zero exponentially fast as $x \to \infty$. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE

Parallel Excluded Volume Tempering for Polymer Melts

We have developed a technique to accelerate the acquisition of effectively uncorrelated configurations for off-lattice models of dense polymer melts which makes use of both parallel tempering and large scale Monte Carlo moves. The method is based upon simulating a set of systems in parallel, each of which has a slightly different repulsive core potential, such that a thermodynamic path from full excluded volume to an ideal gas of random walks is generated. While each system is run with standard stochastic dynamics, resulting in an NVT ensemble, we implement the parallel tempering through stochastic swaps between the configurations of adjacent potentials, and the large scale Monte Carlo moves through attempted pivot and translation moves which reach a realistic acceptance probability as the limit of the ideal gas of random walks is approached. Compared to pure stochastic dynamics, this results in an increased efficiency even for a system of chains as short as $N = 60$ monomers, however at this chain length the large scale Monte Carlo moves were ineffective. For even longer chains the speedup becomes substantial, as observed from preliminary data for $N = 200$

In-Situ Quasistatic Compression and Microstructural Characterization of Aluminium Foams of Different Cell Topology

Quasistatic compression and micro structural characterization of closed cell aluminium foams of different pore size and cell distributions has been carried out. Metallic foams have good potential for lightweight structures for impact and blast mitigation and therefore it is important to find out the optimized foam structure (i.e. cell size, shape, relative density, and distribution) to maximize energy absorption. In this paper, we present results for two different aluminium metal foams of density 0.5 g/cc and 0.7 g/cc respectively that have been tested in quasi-static compression. The influence of cell geometry and cell topology on quasistatic compression behavior has been investigated using computed tomography (micro-CT) analysis. The compression behavior and micro structural characterization will be presented

In-Situ Quasistatic Compression and Microstructural Characterization of Aluminium Foams of Different Cell Topology

Quasistatic compression and micro structural characterization of closed cell aluminium foams of different pore size and cell distributions has been carried out. Metallic foams have good potential for lightweight structures for impact and blast mitigation and therefore it is important to find out the optimized foam structure (i.e. cell size, shape, relative density, and distribution) to maximize energy absorption. In this paper, we present results for two different aluminium metal foams of density 0.5 g/cc and 0.7 g/cc respectively that have been tested in quasi-static compression. The influence of cell geometry and cell topology on quasistatic compression behavior has been investigated using computed tomography (micro-CT) analysis. The compression behavior and micro structural characterization will be presented

Self-similar solutions with fat tails for Smoluchowski's coagulation equation with locally bounded kernels

The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable and the diagonal kernel. In this paper we prove the existence of such self-similar solutions for continuous kernels $K$ that are homogeneous of degree $\gamma \in [0,1)$ and satisfy $K(x,y) \leq C (x^{\gamma} + y^{\gamma})$. More precisely, for any $\rho \in (\gamma,1)$ we establish the existence of a continuous weak self-similar profile with decay $x^{-(1{+}\rho)}$ as $x \to \infty$

Self-similar chain conformations in polymer gels

We use molecular dynamics simulations to study the swelling of randomly end-cross-linked polymer networks in good solvent conditions. We find that the equilibrium degree of swelling saturates at Q_eq = N_e**(3/5) for mean strand lengths N_s exceeding the melt entanglement length N_e. The internal structure of the network strands in the swollen state is characterized by a new exponent nu=0.72. Our findings are in contradiction to de Gennes' c*-theorem, which predicts Q_eq proportional N_s**(4/5) and nu=0.588. We present a simple Flory argument for a self-similar structure of mutually interpenetrating network strands, which yields nu=7/10 and otherwise recovers the classical Flory-Rehner theory. In particular, Q_eq = N_e**(3/5), if N_e is used as effective strand length.Comment: 4 pages, RevTex, 3 Figure