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In this paper, we derive geometric and analytic properties of invariant sets, including orbit closures, of a large class of piecewise-affine maps
. We assume that (i)
consists of finitely many affine maps defined on a Borel measurable partition of
, (ii) there is a lattice
that contains all of the mutual differences of the translation vectors of these affine maps, and (iii) all of the affine maps have the same linear part that is an automorphism of
. We prove that finite-volume invariant sets of such piecewise-affine maps always consist of translational tiles relative to this lattice, up to some multiplicity. When the partition is Jordan measurable, we show that closures of bounded orbits of
are invariant and yield Jordan measurable tiles, again up to some multiplicity. In the latter case, we show that compact
-invariant sets also consist of Jordan measurable tiles. We then utilize these results to quantify the rate of convergence of ergodic averages for
in the case of bounded single tiles.
Prenatal adversity shapes child neurodevelopment and risk for later mental health problems. The quality of the early care environment can buffer some of the negative effects of prenatal adversity on child development. Retrospective studies, in adult samples, highlight epigenetic modifications as sentinel markers of the quality of the early care environment; however, comparable data from pediatric cohorts are lacking. Participants were drawn from the Maternal Adversity Vulnerability and Neurodevelopment (MAVAN) study, a longitudinal cohort with measures of infant attachment, infant development, and child mental health. Children provided buccal epithelial samples (mean age = 6.99, SD = 1.33 years, n = 226), which were used for analyses of genome-wide DNA methylation and genetic variation. We used a series of linear models to describe the association between infant attachment and (a) measures of child outcome and (b) DNA methylation across the genome. Paired genetic data was used to determine the genetic contribution to DNA methylation at attachment-associated sites. Infant attachment style was associated with infant cognitive development (Mental Development Index) and behavior (Behavior Rating Scale) assessed with the Bayley Scales of Infant Development at 36 months. Infant attachment style moderated the effects of prenatal adversity on Behavior Rating Scale scores at 36 months. Infant attachment was also significantly associated with a principal component that accounted for 11.9% of the variation in genome-wide DNA methylation. These effects were most apparent when comparing children with a secure versus a disorganized attachment style and most pronounced in females. The availability of paired genetic data revealed that DNA methylation at approximately half of all infant attachment-associated sites was best explained by considering both infant attachment and child genetic variation. This study provides further evidence that infant attachment can buffer some of the negative effects of early adversity on measures of infant behavior. We also highlight the interplay between infant attachment and child genotype in shaping variation in DNA methylation. Such findings provide preliminary evidence for a molecular signature of infant attachment and may help inform attachment-focused early intervention programs.
Thin film couple of NiFe/FeMn has been used in the magnetoresistive read head design in the magnetic recording industry. The strong magnetic coupling between FeMn and NiFe is of most importance in providing the stability of the MR head. FeMn has been shown to grow epitaxially on NiFe surface and form a metastable fcc structure. The existence of this fcc structure is believed to be the source of the magnetic coupling. It has also been shown that the grain to grain epitaxy exists in this polycrystalline thin film couple, however with only indirect evidence such as Moiré fringes across the interface boundary. To further study this pseudomorphic growth phenomenon, a specially prepared large grain FeMn/NiFe thin film couple was used. Lattice imaging of the interfacial structure was obtained by high resolution cross-section transmission electron microscopy. The plan-view TEM imaging and electron dilfraction patterns also show clear evidence of the grain to grain epitaxy in almost all the grains. The epitaxial strain associated with each coupled grain was also evidenced by the isolated strain contours within each grain. Detailed interfacial structure analysis will be given to elucidate the mechanism(s) by which the interfacial strain is accommodated.
This paper presents a thermoviscoelastic model for shape memory polymers (SMPs). The model has been developed base on the hypothesis that structural and stress relaxation are the primary shape memory mechanisms of crosslinked, glassy SMP, and that consideration of these mechanisms is essential for predicting the time-dependence of the shape memory response. Comparisons with experiments show that the model can reproduce the rate-dependent strain-temperature and stress-strain response of a crossslinked, glassy SMP. The model also captures many important features of the temperature and time dependence of the free strain recovery and constrained stress recovery response.
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