Detection of polarized quasi-periodic microstructure emission in millisecond pulsars

Microstructure emission, involving short time scale, often quasi-periodic, intensity fluctuations in subpulse emission, is well known in normal period pulsars. In this letter, we present the first detections of quasi-periodic microstructure emission from millisecond pulsars (MSPs), from Giant Metrewave Radio Telescope (GMRT) observations of two MSPs at 325 and 610 MHz. Similar to the characteristics of microstructure observed in normal period pulsars, we find that these features are often highly polarized, and exhibit quasi-periodic behavior on top of broader subpulse emission, with periods of the order of a few $\mu$s. By measuring their widths and periodicities from single pulse intensity profiles and their autocorrelation functions, we extend the microstructure timescale - rotation period relationship by more than an order of magnitude down to rotation periods $\sim$ 5 ms, and find it to be consistent with the relationship derived earlier for normal pulsars. The similarity of behavior is remarkable, given the significantly different physical properties of MSPs and normal period pulsars, and rules out several previous speculations about the possible different characteristics of microstructure in MSP radio emission. We discuss the possible reasons for the non-detection of these features in previous high time resolution MSP studies along with the physical implications of our results, both in terms of a geometric beam sweeping model and temporal modulation model for micropulse production.Comment: 6 pages, 4 figures, 1 table. Accepted for publication in ApJ Letter

Multiscale modelling and analysis of signalling processes in tissues with non-periodic distribution of cells

In this paper a microscopic model for a signalling process in the left ventricular wall of the heart, comprising a non-periodic brous microstructure, is considered. To derive the macroscopic equations the non-periodic microstructure is approximated by the corresponding locally-periodic microstructure. Then applying the methods of locally-periodic homogenization (the locallyperiodic (l-p) unfolding operator, locally-periodic two-scale (l-t-s) convergence on oscillating surfaces and l-p boundary unfolding operator) we obtain the macroscopic model for a signalling process in the heart tissue

Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures

In this paper we determine, in dimension three, the effective conductivities of non periodic high-contrast two-phase cylindrical composites, placed in a constant magnetic field, without any assumption on the geometry of their cross sections. Our method, in the spirit of the H-convergence of Murat-Tartar, is based on a compactness result and the cylindrical nature of the microstructure. The homogenized laws we obtain extend those of the periodic fibre-reinforcing case of [M. Briane and L. Pater. Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three. J. Math. Anal. Appl., 393 (2) (2012), 563 -589] to the case of periodic and non periodic composites with more general transversal geometries.Comment: 28 page

Wang tiling aided statistical determination of the Representative Volume Element size of random heterogeneous materials

Wang tile based representation of a heterogeneous material facilitates fast synthesis of non-periodic microstructure realizations. In this paper, we apply the tiling approach in numerical homogenization to determine the Representative Volume Element size related to the user-defined significance level and the discrepancy between bounds on the apparent properties. First, the tiling concept is employed to efficiently generate arbitrarily large, statistically consistent realizations of investigated microstructures. Second, benefiting from the regular structure inherent to the tiling concept, the Partition theorem, and statistical sampling, we construct confidence intervals of the apparent properties related to the size of a microstructure specimen. Based on the interval width and the upper and lower bounds on the apparent properties, we adaptively generate additional microstructure realizations in order to arrive at an RVE satisfying the prescribed tolerance. The methodology is illustrated with the homogenization of thermo-mechanical properties of three two-dimensional microstructure models: a microstructure with mono-disperse elliptic inclusions, foam, and sandstone.Comment: 19 pages, 22 figures, post-print versio

Damage as Gamma-limit of microfractures in anti-plane linearized elasticity

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. <br/> According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. <br/> In particular, damage is obtained as limit of periodically distributed microfractures

Homogenization in magnetic-shape-memory polymer composites

Magnetic-shape-memory materials (e.g. specific NiMnGa alloys) react with a large change of shape to the presence of an external magnetic field. As an alternative for the difficult to manifacture single crystal of these alloys we study composite materials in which small magnetic-shape-memory particles are embedded in a polymer matrix. The macroscopic properties of the composite depend strongly on the geometry of the microstructure and on the characteristics of the particles and the polymer. We present a variational model based on micromagnetism and elasticity, and derive via homogenization an effective macroscopic model under the assumption that the microstructure is periodic. We then study numerically the resulting cell problem, and discuss the effect of the microstructure on the macroscopic material behavior. Our results may be used to optimize the shape of the particles and the microstructure.Comment: 17 pages, 4 figure

Crystalline Evolutions in Chessboard-like Microstructures

We describe the macroscopic behavior of evolutions by crystalline curvature of planar sets in a chessboard--like medium, modeled by a periodic forcing term. We show that the underlying microstructure may produce both pinning and confinement effects on the geometric motion.Comment: 17 pages, 10 figures. arXiv admin note: text overlap with arXiv:1707.0334

Auxetic two-dimensional lattice with Poisson's Ratio arbitrarily close to -1

In this paper we propose a new lattice structure having macroscopic Poisson's ratio arbitrarily close to the stability limit -1. We tested experimentally the effective Poisson's ratio of the micro-structured medium; the uniaxial test has been performed on a thermoplastic lattice produced with a 3d printing technology. A theoretical analysis of the effective properties has been performed and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis has been performed on three micro-geometry leading to an isotropic behaviour for the cases of three-fold and six-fold symmetry and to a cubic behaviour for the case of four-fold symmetry.Comment: 26 pages, 12 figures (26 subfigures