Focusing and Mode Separation of Elastic Vector Solitons in a 2D Soft Mechanical Metamaterial

International audienceSoft mechanical metamaterials can support a rich set of dynamic responses, which, to date, have received relatively little attention. Here, we report experimental, numerical, and analytical results describing the behavior of an anisotropic two-dimensional flexible mechanical metamaterial when subjected to impact loading. We not only observe the propagation of elastic vector solitons with three components-two translational and one rotational-that are coupled together, but also very rich direction-dependent behaviors such as the formation of sound bullets and the separation of pulses into different solitary modes. Ongoing advances in digital manufacturing technologies are enabling fabrication of systems with an unprecedented level of compositional and structural complexity [1-3]. This remarkable control of geometry has stimulated major advances in the design of mechanical metamaterials-designer matter with unique mechanical properties that are dictated by their engineered structure [4,5]. While initial efforts in the field have focused on systems with unusual linear properties, such as negative Poisson's ratio [6-8], negative stiffness [9,10], and negative thermal expansion [11,12], large deformation and nonlinearities have been recently embraced as a means toward new functionalities, including programmability [13], energy absorption [14], and shape transformation [15]. Moreover, it has been shown that highly deformable mechanical metamaterials can be designed to support the propagation of a variety of nonlinear waves with large displacement amplitudes [16-19], providing a convenient platform to study non-linear wave physics. However, to date the investigation of the nonlinear dynamic response of flexible metamaterials has been limited to one-dimensional (1D) systems. Here, we investigate the nonlinear dynamic response of a 2D flexible mechanical metamaterial comprising a periodic arrangement of squares connected at their vertices by thin ligaments [18,20,21]. Remarkably, our experiments and analyses reveal that several new physical phenomena emerge when subjecting the structure to low-energy impacts. First, our system supports the propagation of elastic vector solitons with three polarization components-two transla-tional and one rotational. Second, we investigate the effect of the anisotropy of the medium on the 2D nature of the soliton and find that such anisotropy plays a crucial role, leading to rich new nonlinear effects. For example, for propagation at 45°from the symmetry axis, a distinct focusing effect is observed. The pulse does not spread along either direction, suggesting that sound bullets may exist in our system. Moreover, we find that for most other propagation angles the wave separates into two distinct solitary modes, each following a principal direction of symmetry. While 2D nonlinear elastic waves have been previously studied in granular media [22-25], the monolithicity and printability of our system allow facile control of the architecture, and hence control of the system's nonlinear dynamic response, providing a powerful platform to explore, visualize, and engineer new wave phenomena. We start by studying experimentally the response of a 2D circular sample with 30 squares along its diameter when excited with an impactor [see Fig. 1(a)]. Our sample is fabricated out of polydimethylsiloxane using direct ink writing, an extrusion-based 3D printing approach [26]

Nonlinear waves at the free surface of flexible mechanical metamaterials

In this letter we investigate the propagation of nonlinear pulses along the free surface of flexible metamaterials based on the rotating squares mechanism. While these metamaterials have previously been shown to support the propagation of elastic vector solitons through their bulk, here we demonstrate that they can also support the stable propagation of nonlinear pulses along their free surface. Further, we show that the stability of these surface pulses is higher when they minimally interact with the linear dispersive surface modes. Finally, we provide guidelines to select geometries that minimize such interactions.Comment: 5 pages, 4 figure

Decoherence induced deformation of the ground state in adiabatic quantum computation

Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties.Comment: 10 pages, 3 figure

Interfibrillar stiffening of echinoderm mutable collagenous tissue demonstrated at the nanoscale

The mutable collagenous tissue (MCT) of echinoderms (e.g., sea cucumbers and starfish) is a remarkable example of a biological material that has the unique attribute, among collagenous tissues, of being able to rapidly change its stiffness and extensibility under neural control. However, the mechanisms of MCT have not been characterized at the nanoscale. Using synchrotron small-angle X-ray diffraction to probe time-dependent changes in fibrillar structure during in situ tensile testing of sea cucumber dermis, we investigate the ultrastructural mechanics of MCT by measuring fibril strain at different chemically induced mechanical states. By measuring a variable interfibrillar stiffness (E(IF)), the mechanism of mutability at the nanoscale can be demonstrated directly. A model of stiffness modulation via enhanced fibrillar recruitment is developed to explain the biophysical mechanisms of MCT. Understanding the mechanisms of MCT quantitatively may have applications in development of new types of mechanically tunable biomaterials

A Measurement of the Interference Structure Function, R_LT, for the 12C(e,e'p) reaction in the Quasielastic Region

The coincidence cross-section and the interference structure function, R_LT, were measured for the 12C(e,e'p) 11B reaction at quasielastic kinematics and central momentum transfer of q=400 MeV/c. The measurement was at an opening angle of theta_pq=11 degrees, covering a range in missing energy of E_m = 0 to 65 MeV. The R_LT structure function is found to be consistent with zero for E_m > 50 MeV, confirming an earlier study which indicated that R_L vanishes in this region. The integrated strengths of the p- and s-shell are compared with a Distorted Wave Impulse Approximation calculation. The s-shell strength and shape are compared with a Hartree Fock-Random Phase Approximation calculation. The DWIA calculation overestimates the cross sections for p- and s-shell proton knockout as expected, but surprisingly agrees with the extracted R_LT value for both shells. The HF-RPA calculation describes the data more consistently, which may be due to the inclusion of 2-body currents in this calculation.Comment: 8 Pages LaTex, 5 postscript figures. Submitted to Phys. Rev.

Zheng Banqiao’s Nande hutu

In 1751, Zheng Banqiao wrote his famous calligraphy Nande hutu (难得糊涂; “It’s difficult to be muddled”). Inquiries into the calligraphy reveal different dimensions of the saying. Its most popular interpretation can be found in self-improvement books on “the art of being muddled” (hutuxue). What academic, official, and popular discourses on the saying have in common is their dialectical reasoning and frequent references to other popular related sayings, to quotes from the ancient classics, and to ancient heroes and historical figures. This issue will explore a few interpretations of the saying. Some prove to be critical with regard to the application of its underlying wisdom, while others focus on its philosophical (Confucian, Daoist, Buddhist), psychological, and/or sociocultural dimension. This issue will also shed light on its pragmatic interpretation as a popular strategy to navigate more positively through life

Galaxy Zoo: the dependence of morphology and colour on environment

We analyse the relationships between galaxy morphology, colour, environment and stellar mass using data for over 100,000 objects from Galaxy Zoo, the largest sample of visually classified morphologies yet compiled. We conclusively show that colour and morphology fractions are very different functions of environment. Both are sensitive to stellar mass; however, at fixed stellar mass, while colour is also highly sensitive to environment, morphology displays much weaker environmental trends. Only a small part of both relations can be attributed to variation in the stellar mass function with environment. Galaxies with high stellar masses are mostly red, in all environments and irrespective of their morphology. Low stellar-mass galaxies are mostly blue in low-density environments, but mostly red in high-density environments, again irrespective of their morphology. The colour-density relation is primarily driven by variations in colour fractions at fixed morphology, in particular the fraction of spiral galaxies that have red colours, and especially at low stellar masses. We demonstrate that our red spirals primarily include galaxies with true spiral morphology. We clearly show there is an environmental dependence for colour beyond that for morphology. Before using the Galaxy Zoo morphologies to produce the above results, we first quantify a luminosity-, size- and redshift-dependent classification bias that affects this dataset, and probably most other studies of galaxy population morphology. A correction for this bias is derived and applied to produce a sample of galaxies with reliable morphological type likelihoods, on which we base our analysis.Comment: 25 pages, 20 figures (+ 6 pages, 11 figures in appendices); moderately revised following referee's comments; accepted by MNRA

Hybrid suspension/solution precursor plasma spraying of a complex Ba(Mg1/3Ta2/3)O3 perovskite: Effects of processing parameters and precursor chemistry on phase formation and decomposition

Abstract: Ba(Mg1/3Ta2/3)O3 (BMT) has a high melting point and is envisioned as a thermal barrier coating material. In this study, a hybrid suspension/solution precursor plasma spray process with a radio frequency thermal plasma torch is designed to deposit BMT nanostructured coatings. Six combinations of chemical reagents are investigated as coating precursors: one BMT powder suspension and five Ta2O5 suspensions in nitrate- or acetate-based solutions. X-ray photoelectron spectroscopy is used to evaluate the element evaporation during plasma spraying, while a thermogravimetric/differential thermal analysis is applied to investigate the BMT formation. Parameters such as precursor chemistry, plasma power, spraying distance and substrate preheating are studied with regard to the coating phase structure. Twice the Mg stoichiometric amount with a power of 50 kW shows the best results when using nanocrystallized Ta2O5 as a tantalum precursor. When choosing nitrates as Ba and Mg precursors, crystallized BMT is obtained at lower plasma power (45 kW) when compared to acetates (50 kW). BaTa2O6, Ba3Ta5O15, Ba4Ta2O9, Mg4Ta2O9 are the main secondary phases observed during the BMT coatings deposition. Because of the complicated acetate decomposition process, the coating deposition rate from nitrate precursors is 1.56 times higher than that from acetate precursors