Asymptotic network models of subwavelength metamaterials formed by closely packed photonic and phononic crystals

We demonstrate that photonic and phononic crystals consisting of closely spaced inclusions constitute a versatile class of subwavelength metamaterials. Intuitively, the voids and narrow gaps that characterise the crystal form an interconnected network of Helmholtz-like resonators. We use this intuition to argue that these continuous photonic (phononic) crystals are in fact asymptotically equivalent, at low frequencies, to discrete capacitor-inductor (mass-spring) networks whose lumped parameters we derive explicitly. The crystals are tantamount to metamaterials as their entire acoustic branch, or branches when the discrete analogue is polyatomic, is squeezed into a subwavelength regime where the ratio of wavelength to period scales like the ratio of period to gap width raised to the power 1/4; at yet larger wavelengths we accordingly find a comparably large effective refractive index. The fully analytical dispersion relations predicted by the discrete models yield dispersion curves that agree with those from finite-element simulations of the continuous crystals. The insight gained from the network approach is used to show that, surprisingly, the continuum created by a closely packed hexagonal lattice of cylinders is represented by a discrete honeycomb lattice. The analogy is utilised to show that the hexagonal continuum lattice has a Dirac-point degeneracy that is lifted in a controlled manner by specifying the area of a symmetry-breaking defect

Green's function probe of a static granular piling

We present an experiment which aim is to investigate the mechanical properties of a static granular assembly. The piling is an horizontal 3D granular layer confined in a box, we apply a localized extra force at the surface and the spatial distribution of stresses at the bottom is obtained (the mechanical Green's function). For different types of granular media, we observe a linear pressure response which profile shows one peak centered at the vertical of the point of application. The peak's width increases linearly when increasing the depth. This green function seems to be in -at least- qualitative agreement with predictions of elastic theory.Comment: 9 pages, 3 .eps figures, submitted to PR

Stresses in silos: Comparison between theoretical models and new experiments

We present precise and reproducible mean pressure measurements at the bottom of a cylindrical granular column. If a constant overload is added, the pressure is linear in overload and nonmonotonic in the column height. The results are {\em quantitatively} consistent with a local, linear relation between stress components, as was recently proposed by some of us. They contradict the simplest classical (Janssen) approximation, and may pose a rather severe test of competing models.Comment: 4 pages, 2 figures, final version to appear in Phys. Rev. Let

Morphology of two dimensional fracture surface

We consider the morphology of two dimensional cracks observed in experimental results obtained from paper samples and compare these results with the numerical simulations of the random fuse model (RFM). We demonstrate that the data obey multiscaling at small scales but cross over to self-affine scaling at larger scales. Next, we show that the roughness exponent of the random fuse model is recovered by a simpler model that produces a connected crack, while a directed crack yields a different result, close to a random walk. We discuss the multiscaling behavior of all these models.Comment: slightly revise

Fluctuation of the Top Location and Avalanches in the Formation Process of a Sandpile

We investigate the formation processes of a sandpile using numerical simulation. We find a new relation between the fluctuation of the motion of the top and the surface state of a sandpile. The top moves frequently as particles are fed one by one every time interval T. The time series of the top location has the power spectrum which obeys a power law, S(f)~f^{\alpha}, and its exponent \alpha depends on T and the system size w. The surface state is characterized by two time scales; the lifetime of an avalanche, T_{a}, and the time required to cause an avalanche, T_{s}. The surface state is fluid-like when T_{a}~T_{s}, and it is solid-like when T_{a}<<T_{s}. Our numerical results show that \alpha is a function of T_{s}/T_{a}.Comment: 15 pages, 13 figure

Footprints in Sand: The Response of a Granular Material to Local Perturbations

We experimentally determine ensemble-averaged responses of granular packings to point forces, and we compare these results to recent models for force propagation in a granular material. We used 2D granular arrays consisting of photoelastic particles: either disks or pentagons, thus spanning the range from ordered to disordered packings. A key finding is that spatial ordering of the particles is a key factor in the force response. Ordered packings have a propagative component that does not occur in disordered packings.Comment: 5 pages, 4 eps figures, Phys. Rev. Lett. 87, 035506 (2001

Jamming and Fluctuations in Granular Drag

We investigate the dynamic evolution of jamming in granular media through fluctuations in the granular drag force. The successive collapse and formation of jammed states give a stick-slip nature to the fluctuations which is independent of the contact surface between the grains and the dragged object -- thus implying that the stress-induced collapse is nucleated in the bulk of the granular sample. We also find that while the fluctuations are periodic at small depths, they become "stepped" at large depths, a transition which we interpret as a consequence of the long-range nature of the force chains.Comment: 7 pages, 4 figures, RevTe

Modeling and Flowsheet Design of an Am Separation Process Using TODGA and H₄TPAEN

Recycling americium from spent fuels is an important consideration for the future nuclear fuel cycle, as americium is the main contributor to the long-term radiotoxicity and heat power of the final waste, after separation of uranium and plutonium using the PUREX process. The separation of americium alone from a PUREX raffinate can be achieved by co-extracting lanthanide (Ln(III)) and actinide (An(III)) cations into an organic phase containing the diglycolamide extractant TODGA, and then stripping Am(III) with selectivity towards Cm(III) and lanthanides. The water soluble ligand H4TPAEN was tested to selectively strip Am from a loaded organic phase. Based on experimental data obtained by Jülich, NNL and CEA laboratories since 2013, a phenomenological model has been developed to simulate the behavior of americium, curium and lanthanides during their extraction by TODGA and their complexation by H4TPAEN (complex stoichiometry, extraction and complexation constants, kinetics). The model was gradually implemented in the PAREX code and helped to narrow down the best operating conditions. Thus, the following modifications of initial operating conditions were proposed: • An increase in the concentration of TPAEN as much as the solubility limit allows. • An improvement of the lanthanide scrubbing from the americium flow by adding nitrates to the aqueous phase. A qualification of the model was begun by comparing on the one hand constants determined with the model to those measured experimentally, and on the other hand, simulation results and experimental data on new independent batch experiments. A first sensitivity analysis identified which parameter has the most dominant effect on the process. A flowsheet was proposed for a spiked test in centrifugal contactors performed with a simulated PUREX raffinate with trace amounts of Am and Cm. If the feasibility of the process is confirmed, the results of this test will be used to consolidate the model and to design a flowsheet for a test on a genuine PUREX raffinate. This work is the result of collaborations in the framework of the SACSESS European Project

Modeling and Flowsheet Design of an Am Separation Process Using TODGA and H₄TPAEN

Recycling americium from spent fuels is an important consideration for the future nuclear fuel cycle, as americium is the main contributor to the long-term radiotoxicity and heat power of the final waste, after separation of uranium and plutonium using the PUREX process. The separation of americium alone from a PUREX raffinate can be achieved by co-extracting lanthanide (Ln(III)) and actinide (An(III)) cations into an organic phase containing the diglycolamide extractant TODGA, and then stripping Am(III) with selectivity towards Cm(III) and lanthanides. The water soluble ligand H4TPAEN was tested to selectively strip Am from a loaded organic phase. Based on experimental data obtained by Jülich, NNL and CEA laboratories since 2013, a phenomenological model has been developed to simulate the behavior of americium, curium and lanthanides during their extraction by TODGA and their complexation by H4TPAEN (complex stoichiometry, extraction and complexation constants, kinetics). The model was gradually implemented in the PAREX code and helped to narrow down the best operating conditions. Thus, the following modifications of initial operating conditions were proposed: • An increase in the concentration of TPAEN as much as the solubility limit allows. • An improvement of the lanthanide scrubbing from the americium flow by adding nitrates to the aqueous phase. A qualification of the model was begun by comparing on the one hand constants determined with the model to those measured experimentally, and on the other hand, simulation results and experimental data on new independent batch experiments. A first sensitivity analysis identified which parameter has the most dominant effect on the process. A flowsheet was proposed for a spiked test in centrifugal contactors performed with a simulated PUREX raffinate with trace amounts of Am and Cm. If the feasibility of the process is confirmed, the results of this test will be used to consolidate the model and to design a flowsheet for a test on a genuine PUREX raffinate. This work is the result of collaborations in the framework of the SACSESS European Project