Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Dynamic in situ optical and magneto-optical monitoring of the growth of Co-Pd multilayers

In situ ellipsometry and Kerr polarimetry have been used to follow the continuous evolution of the optical and magneto- optical properties of multiple layers of Co and Pd during their growth. Films were sputter deposited onto a Pd buffer layer on glass substrates up to a maximum of N = 10 bi-layer periods according to the scheme glass/Pd(10)Ar x (0.3Co/3Pd) (nm). Magnetic hysteresis measurements taken during the deposition consistently showed strong perpendicular anisotropy at all stages of film growth following the deposition of a single monolayer of Co. Magneto-optic signals associated with the normal-incidence polar Kerr effect indicated strong polarization of Pd atoms at both Co-Pd and Pd-Co interfaces and that the magnitude of the complex magneto-optic Voigt parameter and the magnetic moment of the Pd decrease exponentially with distance from the interface with a decay constant of 1.1 nm(- 1). Theoretical simulations have provided an understanding of the observations and allow the determination of the ultrathin- film values of the elements of the skew-symmetric permittivity tensor that describe the optical and magneto-optical properties for both CO and Pd. Detailed structure in the observed Kerr ellipticity shows distinct Pd-thickness-dependent oscillations with a spatial period of about 1.6 nm that are believed to be associated with quantum well levels in the growing Pd layer.

Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Abnormal integrity of association fiber tracts in amnestic mild cognitive impairment.

The association fiber tracts integrity of the inter-hemispheric and within-hemispheric communication was poor understood in amnestic type mild cognitive impairment (aMCI) patients by diffusion tensor imaging (DTI). A region of interest-based DTI approach was applied to explore fiber tract differences between 22 aMCI patients and 22 well-matched normal aging. Correlations were also sought between fractional anisotropy (FA) values and the cognitive performance scores in the aMCI patients. Extensive impairment of association fiber tracts integrity was observed in aMCI patients, including bilateral inferior fronto-occipital fascicles, the genu of corpus callosum, bilateral cingulate bundles and bilateral superior longitudinal fascicles II (SLE II) subcomponent. In addition, the FA value of right SLE II was significantly negatively correlated to the performance of Trail Making Test A and B, whilst the values of right posterior cingulate bundle was significantly positive correlation with MMSE score. As aMCI is a putative prodromal syndrome to Alzheimer's disease (AD), this study suggested that investigation of association fiber tracts between remote cortexes may yield important new data to predict whether a patient will eventually develop AD.

The maximal C*-algebra of quotients as an operator bimodule

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product of A with itself labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved.

Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Propagation regimes for an electromagnetic beam in magnetized plasma

The propagation of a Gaussian electromagnetic beam along the direction of magnetic field in a plasma is investigated. The extraordinary (E-x+iE(y)) mode is explicitly considered in the analysis, although the results for the ordinary mode can be obtained upon replacing the electron cyclotron frequency omega(c) by -omega(c). The propagating beam electric field is coupled to the surrounding plasma via the dielectric tensor, taking into account the existence of a stationary magnetic field. Both collisionless and collisional cases are considered, separately. Adopting an established methodological framework for beam propagation in unmagnetized plasmas, we extend to magnetized plasmas by considering the beam profile for points below the critical curve in the beam-power versus beam-width plane, and by employing a relationship among electron concentration and electron temperature, provided by kinetic theory (rather than phenomenology). It is shown that, for points lying above the critical curve in the beam-power versus beam-width plane, the beam experiences oscillatory convergence (self-focusing), while for points between the critical curve and divider curve, the beam undergoes oscillatory divergence and for points on and below the divider curve the beam suffers a steady divergence. For typical values of parameters, numerical results are presented and discussed. (C) 2008 American Institute of Physics.

Optical Nonlocalities and Additional Waves in Epsilon-Near-Zero Metamaterials

We analyze the optical properties of plasmonic nanorod metamaterials in the epsilon-near-zero regime and show, both theoretically and experimentally, that the performance of these composites is strongly affected by nonlocal response of the effective permittivity tensor. We provide the evidence of interference between main and additional waves propagating in the room-temperature nanorod metamaterials and develop an analytical description of this phenomenon. Additional waves are present in the majority of low-loss epsilon-near-zero structures and should be explicitly considered when designing applications of epsilon-near-zero composites, as they represent a separate communication channel.

Phonons, Instabilities and Origin of Polarization in KDP Crystals

The -phonons of KH2PO4 (KDP) and its deuterated analog DKDP are studied via first-principles linear response calculations. The paraelectric phase shows two instabilities. One for a z-polarized mode, which leads to the spontaneous polarization Ps of the ferroelectric phase. The other corresponds to a two-fold degenerate xy-polarized mode. Other phonons are analyzed, which couple to the ferroelectric one at large amplitudes and are relevant for the ferroelectric transition. We show that Ps is mainly of electronic nature, since it arises mostly from an off-diagonal component of the Born effective charge tensor of H, with minor contribution from P atoms displacements.

Quotients, exactness, and nuclearity in the operator system category

We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.

Slower postnatal growth is associated with delayed cerebral cortical maturation in preterm newborns

Slower postnatal growth is an important predictor of adverse neurodevelopmental outcomes in infants born preterm. However, the relationship between postnatal growth and cortical development remains largely unknown. Therefore, we examined the association between neonatal growth and diffusion tensor imaging measures of microstructural cortical development in infants born very preterm. Participants were 95 neonates born between 24 and 32 weeks gestational age studied twice with diffusion tensor imaging: scan 1 at a median of 32.1 weeks (interquartile range, 30.4 to 33.6) and scan 2 at a median of 40.3 weeks (interquartile range, 38.7 to 42.7). Fractional anisotropy and eigenvalues were recorded from 15 anatomically defined cortical regions. Weight, head circumference, and length were recorded at birth and at the time of each scan. Growth between scans was examined in relation to diffusion tensor imaging measures at scans 1 and 2, accounting for gestational age, birth weight, sex, postmenstrual age, known brain injury (white matter injury, intraventricular hemorrhage, and cerebellar hemorrhage), and neonatal illness (patent ductus arteriosus, days intubated, infection, and necrotizing enterocolitis). Impaired weight, length, and head growth were associated with delayed microstructural development of the cortical gray matter (fractional anisotropy: P <0.001), but not white matter (fractional anisotropy: P = 0.529), after accounting for prenatal growth, neonatal illness, and brain injury. Avoiding growth impairment during neonatal care may allow cortical development to proceed optimally and, ultimately, may provide an opportunity to reduce neurological disabilities related to preterm birth.

Score for neonatal acute physiology-II and neonatal pain predict corticospinal tract development in premature newborns

Premature infants are at risk for adverse motor outcomes, including cerebral palsy and developmental coordination disorder. The purpose of this study was to examine the relationship of antenatal, perinatal, and postnatal risk factors for abnormal development of the corticospinal tract, the major voluntary motor pathway, during the neonatal period. In a prospective cohort study, 126 premature neonates (24-32 weeks' gestational age) underwent serial brain imaging near birth and at term-equivalent age. With diffusion tensor tractography, mean diffusivity and fractional anisotropy of the corticospinal tract were measured to reflect microstructural development. Generalized estimating equation models examined associations of risk factors on corticospinal tract development. The perinatal risk factor of greater early illness severity (as measured by the Score for Neonatal Acute Physiology-II [SNAP-II]) was associated with a slower rise in fractional anisotropy of the corticospinal tract (P = 0.02), even after correcting for gestational age at birth and postnatal risk factors (P = 0.009). Consistent with previous findings, neonatal pain adjusted for morphine and postnatal infection were also associated with a slower rise in fractional anisotropy of the corticospinal tract (P = 0.03 and 0.02, respectively). Lessening illness severity in the first hours of life might offer potential to improve motor pathway development in premature newborns.

Procedural pain and brain development in premature newborns

Objective: Preterm infants are exposed to multiple painful procedures in the neonatal intensive care unit (NICU) during a period of rapid brain development. Our aim was to examine relationships between procedural pain in the NICU and early brain development in very preterm infants.

Methods: Infants born very preterm (N ¼ 86; 24–32 weeks gestational age) were followed prospectively from birth, and studied with magnetic resonance imaging, 3-dimensional magnetic resonance spectroscopic imaging, and diffusion tensor imaging: scan 1 early in life (median, 32.1 weeks) and scan 2 at term-equivalent age (median, 40 weeks). We calculated N-acetylaspartate to choline ratios (NAA/choline), lactate to choline ratios, average diffusivity, and white matter fractional anisotropy (FA) from up to 7 white and 4 subcortical gray matter regions of interest. Procedural pain was quantified as the number of skin-breaking events from birth to term or scan 2. Data were
analyzed using generalized estimating equation modeling adjusting for clinical confounders such as illness severity, morphine exposure, brain injury, and surgery.

Results: After comprehensively adjusting for multiple clinical factors, greater neonatal procedural pain was associated with reduced white matter FA (b ¼ 0.0002, p ¼ 0.028) and reduced subcortical gray matter NAA/choline (b ¼ 0.0006, p ¼ 0.004). Reduced FA was predicted by early pain (before scan 1), whereas lower NAA/choline was predicted by pain exposure throughout the neonatal course, suggesting a primary and early effect on subcortical structures with secondary white matter changes.

Interpretation: Early procedural pain in very preterm infants may contribute to impaired brain development.

Tractography-based quantitation of corticospinal tract development in premature newborns

To evaluate the impact of early brain injury and neonatal illness on corticospinal tract (CST) development in premature newborns serially studied with diffusion tensor tractography.