Dielectric resonances of ordered passive arrays

The electrical and optical properties of ordered passive arrays, constituted of inductive and capacitive components, are usually deduced from Kirchhoff's rules. Under the assumption of periodic boundary conditions, comparable results may be obtained via an approach employing transfer matrices. In particular, resonances in the dielectric spectrum are demonstrated to occur if all eigenvalues of the transfer matrix of the entire array are unity. The latter condition, which is shown to be equivalent to the habitual definition of a resonance in impedance for an array between electrodes, allows for a convenient and accurate determination of the resonance frequencies, and may thus be used as a tool for the design of materials with a specific dielectric response. For the opposite case of linear arrays in a large network, where periodic boundary condition do not apply, several asymptotic properties are derived. Throughout the article, the derived analytic results are compared to numerical models, based on either Exact Numerical Renormalisation or the spectral method.Comment: 12 pages, 12 figure

Reciprocal regulation of PKA and rac signaling

Activated G protein-coupled receptors (GPCRs) and receptor tyrosine kinases relay extracellular signals through spatial and temporal controlled kinase and GTPase entities. These enzymes are coordinated by multifunctional scaffolding proteins for precise intracellular signal processing. The cAMP-dependent protein kinase A (PKA) is the prime example for compartmentalized signal transmission downstream of distinct GPCRs. A-kinase anchoring proteins tether PKA to specific intracellular sites to ensure precision and directionality of PKA phosphorylation events. Here, we show that the Rho-GTPase Rac contains A-kinase anchoring protein properties and forms a dynamic cellular protein complex with PKA. The formation of this transient core complex depends on binary interactions with PKA subunits, cAMP levels and cellular GTP-loading accounting for bidirectional consequences on PKA and Rac downstream signaling. We show that GTP-Rac stabilizes the inactive PKA holoenzyme. However, β-adrenergic receptor-mediated activation of GTP-Rac–bound PKA routes signals to the Raf-Mek-Erk cascade, which is critically implicated in cell proliferation. We describe a further mechanism of how cAMP enhances nuclear Erk1/2 signaling: It emanates from transphosphorylation of p21-activated kinases in their evolutionary conserved kinase-activation loop through GTP-Rac compartmentalized PKA activities. Sole transphosphorylation of p21-activated kinases is not sufficient to activate Erk1/2. It requires complex formation of both kinases with GTP-Rac1 to unleash cAMP-PKA–boosted activation of Raf-Mek-Erk. Consequently GTP-Rac functions as a dual kinase-tuning scaffold that favors the PKA holoenzyme and contributes to potentiate Erk1/2 signaling. Our findings offer additional mechanistic insights how β-adrenergic receptor-controlled PKA activities enhance GTP-Rac–mediated activation of nuclear Erk1/2 signaling

Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate

The authors present inferences of diapycnal diffusivity from a compilation of over 5200 microstructure profiles. As microstructure observations are sparse, these are supplemented with indirect measurements of mixing obtained from (i) Thorpe-scale overturns from moored profilers, a finescale parameterization applied to (ii) shipboard observations of upper-ocean shear, (iii) strain as measured by profiling floats, and (iv) shear and strain from full-depth lowered acoustic Doppler current profilers (LADCP) and CTD profiles. Vertical profiles of the turbulent dissipation rate are bottom enhanced over rough topography and abrupt, isolated ridges. The geography of depth-integrated dissipation rate shows spatial variability related to internal wave generation, suggesting one direct energy pathway to turbulence. The global-averaged diapycnal diffusivity below 1000-m depth is O(10?4) m2 s?1 and above 1000-m depth is O(10?5) m2 s?1. The compiled microstructure observations sample a wide range of internal wave power inputs and topographic roughness, providing a dataset with which to estimate a representative global-averaged dissipation rate and diffusivity. However, there is strong regional variability in the ratio between local internal wave generation and local dissipation. In some regions, the depth-integrated dissipation rate is comparable to the estimated power input into the local internal wave field. In a few cases, more internal wave power is dissipated than locally generated, suggesting remote internal wave sources. However, at most locations the total power lost through turbulent dissipation is less than the input into the local internal wave field. This suggests dissipation elsewhere, such as continental margins

Hopf algebras in dynamical systems theory

The theory of exact and of approximate solutions for non-autonomous linear differential equations forms a wide field with strong ties to physics and applied problems. This paper is meant as a stepping stone for an exploration of this long-established theme, through the tinted glasses of a (Hopf and Rota-Baxter) algebraic point of view. By reviewing, reformulating and strengthening known results, we give evidence for the claim that the use of Hopf algebra allows for a refined analysis of differential equations. We revisit the renowned Campbell-Baker-Hausdorff-Dynkin formula by the modern approach involving Lie idempotents. Approximate solutions to differential equations involve, on the one hand, series of iterated integrals solving the corresponding integral equations; on the other hand, exponential solutions. Equating those solutions yields identities among products of iterated Riemann integrals. Now, the Riemann integral satisfies the integration-by-parts rule with the Leibniz rule for derivations as its partner; and skewderivations generalize derivations. Thus we seek an algebraic theory of integration, with the Rota-Baxter relation replacing the classical rule. The methods to deal with noncommutativity are especially highlighted. We find new identities, allowing for an extensive embedding of Dyson-Chen series of time- or path-ordered products (of generalized integration operators); of the corresponding Magnus expansion; and of their relations, into the unified algebraic setting of Rota-Baxter maps and their inverse skewderivations. This picture clarifies the approximate solutions to generalized integral equations corresponding to non-autonomous linear (skew)differential equations.Comment: International Journal of Geometric Methods in Modern Physics, in pres

The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its applications to several physical problem

Vertical Convergence of Turbulent and Double-Diffusive Heat Flux Drives Warming and Erosion of Antarctic Winter Water in Summer

The seasonal warming of Antarctic Winter Water (WW) is a key process that occurs along the path of deep water transformation to intermediate waters. These intermediate waters then enter the upper branch of the circumpolar overturning circulation. Despite its importance, the driving mechanisms that mediate the warming of Antarctic WW remain unknown, and their quantitative evaluation is lacking. Using 38 days of glider measurements of microstructure shear, we characterize the rate of turbulent dissipation and its drivers over a summer season in the northern Weddell Sea. Observed dissipation rates in the surface layer are mainly forced by winds and explained by the stress scaling (r2 = 0.84). However, mixing to the base of the mixed layer during strong wind events is suppressed by vertical stratification from sea ice melt. Between the WW layer and the warm and saline circumpolar deep water, a subsurface layer of enhanced dissipation is maintained by double-diffusive convection (DDC). We develop a WW layer temperature budget and show that a warming trend (0.2°C over 28 days) is driven by a convergence of heat flux through mechanically driven mixing at the base of the mixed layer and DDC at the base of the WW layer. Notably, excluding the contribution from DDC results in an underestimation of WW warming by 23%, highlighting the importance of adequately representing DDC in ocean models. These results further suggest that an increase in storm intensity and frequency during summer could increase the rate of warming of WW with implications for rates of upper-ocean water mass transformation.publishedVersio

Religious Tastes and Styles as Markers of Class Belonging: A Bourdieuian Perspective on Pentecostalism in South America

Studies on the relationship between social class and religion tend to highlight the demographic dimension of class, but neglect its symbolic dimension. By addressing the symbolic dimensions through a Bourdieuian approach, this article contends that religious tastes and styles can be employed as class markers within the sphere of religion. A case study on Argentinean Pentecostalism and in-depth analysis of a lower and middle class church illustrate how symbolic class differences are cultivated in the form of distinctive religious styles. While the lower class church displays a style marked by emotional expressiveness and the search for life improvement through spiritual practices, the middle class church performs a sober and calm style of Pentecostalism. The study highlights the role of styles in the reproduction of class boundaries, while shedding a critical light on the importance of tastes

Storms drive outgassing of CO2 in the subpolar Southern Ocean

The subpolar Southern Ocean is a critical region where CO2 outgassing influences the global mean air-sea CO2 flux (FCO2). However, the processes controlling the outgassing remain elusive. We show, using a multi-glider dataset combining FCO2 and ocean turbulence, that the air-sea gradient of CO2 (∆pCO2) is modulated by synoptic storm-driven ocean variability (20 µatm, 1–10 days) through two processes. Ekman transport explains 60% of the variability, and entrainment drives strong episodic CO2 outgassing events of 2–4 mol m−2 yr−1. Extrapolation across the subpolar Southern Ocean using a process model shows how ocean fronts spatially modulate synoptic variability in ∆pCO2 (6 µatm2 average) and how spatial variations in stratification influence synoptic entrainment of deeper carbon into the mixed layer (3.5 mol m−2 yr−1 average). These results not only constrain aliased-driven uncertainties in FCO2 but also the effects of synoptic variability on slower seasonal or longer ocean physics-carbon dynamics.publishedVersio