Two Stable Equilibria of the Atlantic Subpolar Gyre

The cyclonic circulation of the Atlantic subpolar gyre is a key mechanism for North Atlantic climate variability on a wide range of time scales. It is generally accepted that it is driven by both cyclonic winds and buoyancy forcing, yet the individual importance and dynamical interactions of the two contributions remain unclear. The authors propose a simplified four-box model representing the convective basin of the Labrador Sea and its shallow and deep boundary current system, the western subpolar gyre. Convective heat loss drives a baroclinic flow of relatively light water around the dense center. Eddy salt flux from the boundary current to the center increases with a stronger circulation, favors the formation of dense waters, and thereby sustains a strong baroclinic flow, approximately 10%–25% of the total. In contrast, when the baroclinic flow is not active, surface waters may be too fresh to convect, and a buoyancy-driven circulation cannot develop. This situation corresponds to a second stable circulation mode. A hysteresis is found for variations in surface freshwater flux and the salinity of the near-surface boundary current. An analytical solution is presented and analyzed.

Achieving a more realistic assessment of rockfall hazards by coupling three-dimensional process models and field-based tree-ring data

Sound knowledge of the spatial and temporal patterns of rockfalls is fundamental for the management of this very common hazard in mountain environments. Process-based, three-dimensional simulation models are nowadays capable of reproducing the spatial distribution of rockfall occurrences with reasonable accuracy through the simulation of numerous individual trajectories on highly-resolved digital terrain models. At the same time, however, simulation models typically fail to quantify the ‘real’ frequency of rockfalls (in terms of return intervals). The analysis of impact scars on trees, in contrast, yields real rockfall frequencies, but trees may not be present at the location of interest and rare trajectories may not necessarily be captured due to the limited age of forest stands. In this article, we demonstrate that the coupling of modeling with tree-ring techniques may overcome the limitations inherent to both approaches. Based on the analysis of 64 cells (40 m × 40 m) of a rockfall slope located above a 1631-m long road section in the Swiss Alps, we illustrate results from 488 rockfalls detected in 1260 trees. We illustrate that tree impact data cannot only be used (i) to reconstruct the real frequency of rockfalls for individual cells, but that they also serve (ii) the calibration of the rockfall model Rockyfor3D, as well as (iii) the transformation of simulated trajectories into real frequencies. Calibrated simulation results are in good agreement with real rockfall frequencies and exhibit significant differences in rockfall activity between the cells (zones) along the road section. Real frequencies, expressed as rock passages per meter road section, also enable quantification and direct comparison of the hazard potential between the zones. The contribution provides an approach for hazard zoning procedures that complements traditional methods with a quantification of rockfall frequencies in terms of return intervals through a systematic inclusion of impact records in trees.

Conformational analysis of a potent SSTR3-selective somatostatin analogue by NMR in water solution

The three-dimensional structure of a potent SSTR3-selective analogue of somatostatin, cyclo(3-14)H-Cys(3)-Phe(6)-Tyr(7)-D-Agl(8)(N(beta) Me, 2-naphthoyl)-Lys(9)-Thr(10)-Phe(11)-Cys(14)-OH (des-AA(1, 2, 4, 5, 12, 13)[Tyr(7), D-Agl(8)(N(beta) Me, 2-naphthoyl)]-SRIF) (peptide 1) has been determined by (1)H NMR in water and molecular dynamics (MD) simulations. The peptide exists in two conformational isomers differing mainly by the cis/trans isomerization of the side chain in residue 8. The structure of 1 is compared with the consensus structural motifs of other somatostatin analogues that bind predominantly to SSTR1, SSTR2/SSTR5 and SSTR4 receptors, and to the 3D structure of a non-selective SRIF analogue, cyclo(3-14)H-Cys(3)-Phe(6)-Tyr(7)-D-2Nal(8)-Lys(9)-Thr(10)-Phe(11)-Cys(14)-OH (des-AA(1, 2, 4, 5, 12, 13)[Tyr(7), D-2Nal(8)]-SRIF) (peptide 2). The structural determinant factors that could explain selectivity of peptide 1 for SSTR3 receptors are discussed.

On the postnatal development of the striate cortex (V1) in the tree shrew (Tupaia belangeri)

Histological serial sections, three-dimensional reconstructions and morphometry served to study the postnatal development of V1 in tree shrews. The main objectives were to evaluate the expansion of V1, the implications of its growth on the occipital cortex and, vice versa, the effects of the expanding neocortex on the topography of V1. The future V1 was identified on postnatal day 1 by its granular layer IV, covering the superior surface of the occipital cortices including the poles. A subdivision of layer IV, distinctive for the binocular part, was evident in the central region. V1 expanded continuously with age into all directions succeeded by the maturation of layering. The monocular part was recognized from day 15 onward, after the binocular part had reached its medial border. In reference to the retinotopic map of V1, regions emerged in a coherent temporo-spatial sequence delineating the retinal topography in a central to peripheral gradient beginning with the visual streak representation. The growth of V1 was greatest until tree shrews open their eyes, culminated during adolescence, and completed after a subsequent decrease in the young adult. Simultaneous expansion of the neocortex induced a shifting of V1. Translation and elongation of V1 entailed that the occipital cortex covered the superior colliculi along with a downward rotation of the poles. The enlargement of the occipital part of the hemispheres was in addition associated with the formation of a small occipital horn in the lateral ventricles, indicating an incipient 'true' occipital lobe harbouring mainly cortices involved in visual functions.

Intraoperative three-dimensional fluoroscopic cholangiography

Precise intraoperative assessment of the architecture of the biliary tree could reduce lesions to intra- or extrahepatic bile ducts. The aim of this study was to test feasibility of intraoperative three-dimensional imaging during liver resections. Isocentric C-arm fluoroscopy acquires three-dimensional images during a 190 degrees orbital rotation. The bile ducts were displayed three-dimensionally by realtime rotational projections or multiplanar reconstructions. The technique was established ex vivo in a preserved cadaveric human liver. Intraoperative three-dimensional cholangiography was performed in five patients with centrally located liver malignancies. Complete data acquisition in 3 patients depicted precise anatomical details of the architecture of the biliary tree up to third order divisions. Biliary imaging can be improved by the application of real-time intraoperative three-dimensional cholangiography. For the development of computer-aided navigation in hepatobiliary procedures, this technique could be an important prerequisite for defining landmarks of the liver in a three-dimensional space.

Tree species and diversity effects on soil water seepage in a tropical plantation

Plant diversity has been shown to influence the water cycle of forest ecosystems by differences in water consumption and the associated effects on groundwater recharge. However, the effects of biodiversity on soil water fluxes remain poorly understood for native tree species plantations in the tropics. Therefore, we estimated soil water fluxes and assessed the effects of tree species and diversity on these fluxes in an experimental native tree species plantation in Sardinilla (Panama). The study was conducted during the wet season 2008 on plots of monocultures and mixtures of three or six tree species. Rainfall and soil water content were measured and evapotranspiration was estimated with the Penman-Monteith equation. Soil water fluxes were estimated using a simple soil water budget model considering water input, output, and soil water and groundwater storage changes and in addition, were simulated using the physically based one-dimensional water flow model Hydrus-1D. In general, the Hydrus simulation did not reflect the observed pressure heads, in that modeled pressure heads were higher compared to measured ones. On the other hand, the results of the water balance equation (WBE) reproduced observed water use patterns well. In monocultures, the downward fluxes through the 200 cm-depth plane were highest below Hura crepitans (6.13 mm day−1) and lowest below Luehea seemannii (5.18 mm day−1). The average seepage rate in monocultures (±SE) was 5.66 ± 0.18 mm day−1, and therefore, significantly higher than below six-species mixtures (5.49 ± 0.04 mm day−1) according to overyielding analyses. The three-species mixtures had an average seepage rate of 5.63 ± 0.12 mm day−1 and their values did not differ significantly from the average values of the corresponding species in monocultures. Seepage rates were driven by the transpiration of the varying biomass among the plots (r = 0.61, p = 0.017). Thus, a mixture of trees with different growth rates resulted in moderate seepage rates compared to monocultures of either fast growing or slow growing tree species. Our results demonstrate that tree-species specific biomass production and tree diversity are important controls of seepage rates in the Sardinilla plantation during the wet season.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. I. ATMOSPHERIC DYNAMICS VIA THE SHALLOW WATER SYSTEM

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical, and spherical), rotation, magnetic tension, and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag, and magnetic drag), and magnetic tension are included. The global atmospheric structure is largely controlled by a single key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations, and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to develop decisively physical intuition and as a reference point for three-dimensional magnetohydrodynamic simulations of atmospheric circulation.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

The Utilization of Classical Spin Monte Carlo Methods to Simulate the Magnetic Behavior of Extended Three-Dimensional Cubic Networks Incorporating M(II) Ions with an S = 5/2 Ground State Spin

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10−3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH3)4][Mn(N3)] 1, [Mn(CN4)]n 2, and [FeII(bipy)3][MnII2(ox)3] 3, has been carried out. The best fits were those obtained using the following parameters, J = −3.5 cm-1, g = 2.01 (1); J = −8.3 cm-1, g = 1.95 (2); and J = −2.0 cm-1, g = 1.95 (3).

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

The benefits of one-dimensional detectors for high-pressure powder X-ray diffraction

High-pressure powder X-ray diffraction is a fundamental technique for investigating structural responses to externally applied force. Synchrotron sources and two-dimensional detectors are required. In contrast to this conventional setup, high-resolution beamlines equipped with one-dimensional detectors could offer much better resolved peaks but cannot deliver accurate structure factors because they only sample a small portion of the Debye rings, which are usually inhomogeneous and spotty because of the small amount of sample. In this study, a simple method to overcome this problem is presented and successfully applied to solving the structure of an L-serine polymorph from powder data. A comparison of the obtained high-resolution high-pressure data with conventional data shows that this technique, providing up to ten times better angular resolution, can be of advantage for indexing, for lattice parameter refinement, and even for structure refinement and solution in special cases.