Partial Decoupling Research Articles

Toroidal normal forms for bifurcations in retarded functional differential equations I: Multiple Hopf and transcritical/multiple Hopf interaction

For finite-dimensional bifurcation problems, it is well known that it is possible to compute normal forms which possess nice symmetry properties. Oftentimes, these symmetries may allow for a partial decoupling of the normal form into a so-called “radial” part and an “angular” part. Analysis of the radial part usually gives an enormous amount of valuable information about the bifurcation and its unfoldings. In this paper, we are interested in the case where such bifurcations occur in retarded functional differential equations, and we revisit the realizability and restrictions problem for the class of radial equations by nonlinear delay-differential equations. Our analysis allows us to recover and considerably generalize recent results by Faria and Magalhães [T. Faria, L.T. Magalhães, Restrictions on the possible flows of scalar retarded functional differential equations in neighborhoods of singularities, J. Dynam. Differential Equations 8 (1996) 35–70] and by Buono and Bélair [P.-L. Buono, J. Bélair, Restrictions and unfolding of double Hopf bifurcation in functional differential equations, J. Differential Equations 189 (2003) 234–266].

Alternative Agricultural Policy Scenarios, Sector Modelling and Indicators: A Sustainability Assessment

ABSTRACT In this article, we assess ecological, economic and social sustainability impacts of four alternative agricultural policy scenarios relevant to the European perspective. The analysed scenarios are: Prolonged Agenda 2000, On-going CAP reform, Integrated rural and environmental policy, and Liberalized Agricultural Trade. An economic agricultural sector model of Finnish agriculture is used in the evaluation of policy impacts up to 2020. Selected indicators representing the three dimensions of sustainability are calculated on the basis of the production variables of the model in each scenario. It is assumed that economic rationality, represented by the sector model, is a driving force directing agricultural production and land use, which, in turn, have a number of ecological, economic and social consequences. Our results show that a partial de-coupling of agricultural support from production and moderate reductions of commodity prices are likely to yield environmental benefits. In addition, there is a clear trade-off between environmental benefits and production volume and intensity. However, full de-coupling and radical price reductions are not likely to bring any additional environmental benefits but will result in a significant down-scaling and regional concentration of remaining agricultural activities. Hence the presented analysis is an interesting platform for discussion for stakeholders when implementing agricultural policy reforms.

Predation cost of rapid growth: behavioural coupling and physiological decoupling

Summary Despite its prominent role in life‐history theory, there is no direct empirical evidence for a behaviourally mediated predation cost of rapid growth. Moreover, we know little about how digestive physiology may also influence the shape of the growth/predation risk trade‐off function. We determined the role of behaviour and digestive physiology in experiments in which damselfly larvae were induced to grow slowly or rapidly by manipulating photoperiod (time stress), and exposure to a fish predator. We showed that larvae under time stress grew more rapidly. Rapid‐growing larvae had a higher foraging activity and a higher growth efficiency. Under predation risk, larvae not only had a lower foraging activity but also a lower growth efficiency. Rapid‐growing larvae (i.e. those under time stress) balanced the growth/predation risk trade‐off differently and took more risk in the presence of a predator, which resulted in a behaviourally mediated higher predation cost compared to slow‐growing larvae. Their higher growth efficiency, however, made this cost smaller compared to a completely behaviourally mediated rapid‐growth strategy. Our results provide the first explicit experimental proof of a behaviourally mediated predation cost of rapid growth. Besides a behavioural coupling of growth and predation risk, resulting in the well‐known trade‐off, we also found a partial decoupling of these two processes by digestive physiology.

A numerical algorithm for some singularly perturbed boundary value problems

A numerical algorithm is proposed to solve singularly perturbed linear two-point value problems. The method starts with a partial decoupling of the system to obtain two independent subsystems, fast and slow components. Each subsystem is then solved separately. A second-order finite difference scheme is used for this purpose. Numerical examples will be presented to show the efficiency of the method.

A comparison of relaxation processes in structurally related van der Waals glass formers: The role of internal degrees of freedom

Depolarized dynamic light scattering (DLS), dielectric relaxation (DS), and deuterium NMR studies of fragile van der Waals glass forming liquids phenylphthalein-dimethylether (PDE) and cresolphthalein-dimethylether (KDE) are presented. In PDE a new dielectric loss process was found, which can be attributed to the 180 degrees flip of the phenyl rings. The previous finding that the distribution of the structural relaxation times measured for PDE and KDE by DS is substantially narrower than that measured by DLS is explained by partial decoupling of the dynamics of the dipole moment from the structural relaxation of the sample. The dynamics of PDE and KDE is compared with the previous studies of two other structurally similar liquids: 1,1'-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC) and 1,1'-bis(p-methoxyphenyl)cyclohexane (BMPC) in order to relate dynamical features with the chemical structure of the material. The evidence for the intramolecular character of the secondary relaxations observed in BMPC and PDE is presented.

Phosphorus burial as a function of paleoproductivity and redox conditions in Arabian Sea sediments

In this study the response of sedimentary phosphorus (P) burial to changes in primary productivity and bottom water oxygen concentrations during the Late Quaternary is investigated, using two sediment cores from the Arabian Sea, one recovered from the continental slope and the other from the deep basin. The average solid-phase P speciation in both cores is similar, authigenic and biogenic (fish debris) apatite make up the bulk of the P inventory (ca. 70%);whereas P adsorbed to iron oxides, organic P, and detrital apatite constitute minor fractions. Postdepositional redistribution has not significantly altered the downcore distribution of total solid-phase P. Phosphorus burial efficiencies are generally lower during periods of increased paleoproductivity. This is caused by (a) partial decoupling of the P export flux, consisting primarily of particulate organic P, and the P burial flux, consisting primarily of biogenic and authigenic apatite; and (b) the lack of increased rates of authigenic CFA formation during periods of higher P deposition. In addition, fluctuations in bottom water oxygen concentrations may have affected P burial in continental slope sediments. The results of this study indicate that higher primary productivity induces more efficient P cycling. On time scales exceeding the oceanic P residence time, this process may induce higher surface water productivity, thus creating a positive feedback loop. In the Arabian Sea, this feedback mechanism may have contributed to changes in sea surface productivity on sub-Milankovitch time scales because P, regenerated on the continental slopes of the Oman and Somalian coastal upwelling zones, is reintroduced into the photic zone relatively fast.

Analysis of the Ni[formula omitted]Fe[formula omitted]/Fe[formula omitted]Mn[formula omitted] exchange bias system with a varying Cu spacer thickness and position for partial decoupling

In order to study the role of the exchange interaction at and near the interface, Ni81Fe19/Fe50Mn50 bilayers have been studied, which have an intervening layer of varying thickness and position in the antiferromagnetic Fe50Mn50 layer. The role of the intervening layer is to generate partial exchange decoupling. As a result, samples were obtained, where in one in-plane direction the position of the intervening layer varies from the interface to the top surface of the Fe50Mn50 layer at a constant intervening layer thickness, and in the other in-plane direction the intervening layer thickness varies. Two-dimensional maps of the resulting exchange bias field and the coercive field were obtained from magneto-optic Kerr effect magnetometry measurements. The role of the position and strength of the partial decoupling within the antiferromagnetic layer on the exchange bias effect and the coercive field is discussed.

Strain patterns within part of the Willard thrust sheet, Idaho–Utah–Wyoming thrust belt

The Willard thrust sheet, located in northern Utah, USA, contains a 10–15-km-thick sequence of strata that were internally deformed and translated about 50 km ESE. Upper levels of the sheet are relatively little deformed, lower levels have minor folds and cleavage that increase in intensity downward and rotate into parallelism with the thrust, and the basal fault zone contains mylonite and ultracataclasite. Finite strain displays systematic changes with structural position and lithology. Basal levels have strain ratios ( R≈ R XZ ) of 3–5, and angles ( θ) between stretch directions and the thrust of <10° in the profile plane. Diamictite, slate, and greywacke at lower levels have R of 1.5–3 and θ of 10–35°, with overall correlations between increasing R, decreasing θ, and greater mica content. Overlying micaceous quartzite has relatively low strain, with R of 1.3–2 and θ>50°. Principal stretching ( X) directions trend perpendicular to oblique to minor fold axes, which are locally oblique to the overall transport direction, reflecting partial decoupling of internal deformation from thrust slip. Principal axial ratios have R YZ > R XY , but microfabrics indicate only limited extension in the intermediate stretching direction ( Y), corresponding to volume losses of about 10–40%. Strain is factored into components of thrust-perpendicular thinning and thrust-parallel shear that increase downward and in mica-rich layers, minor thrust-parallel shortening to extension, minor longitudinal extension, and minor longitudinal (wrench) shear. These patterns reflect litho-mechanical layering of the thrust sheet, which includes a very weak basal fault zone that formed at elevated fluid pressures, a weak mica-rich lower level with widespread crystal plastic and mass transfer deformation, and a stronger upper part with limited internal deformation.

EVOLUTIONARY DYNAMICS OF COMPLEX BIOMECHANICAL SYSTEMS: AN EXAMPLE USING THE FOUR-BAR MECHANISM

Like many phenotypic traits, biomechanical systems are defined by both an underlying morphology and an emergent functional property. The relationship between these levels may have a profound impact on how selection for functional performance is translated into morphological evolution. In particular, complex mechanical systems are likely to be highly redundant, because many alternative morphologies yield equivalent functions. We suggest that this redundancy weakens the relationship between morphological and functional diversity, and we illustrate this effect using an evolutionary model of the four-bar lever system of labrid fishes. Our results demonstrate that, when traits are complex, the morphological diversity of a clade may only weakly predict its mechanical diversity. Furthermore, parallel or convergent selection on function does not necessarily produce convergence in morphology. Empirical observations suggest that this weak form-function relationship has contributed to the morphological diversity of labrid fishes, as functionally equivalent species may nevertheless possess morphologically distinct jaws. We suggest that partial decoupling of morphology and mechanics due to redundancy is a major factor in morphological diversification.

Sub-Doppler spectroscopy of Rb atoms in a sub-micron vapour cell in the presence of a magnetic field

We report the first use of an extremely thin vapor cell (thickness ~ 400 nm) to study the magnetic-field dependence of laser-induced-fluorescence excitation spectra of alkali atoms. This thin cell allows for sub-Doppler resolution without the complexity of atomic beam or laser cooling techniques. This technique is used to study the laser-induced-fluorescence excitation spectra of Rb in a 50 G magnetic field. At this field strength the electronic angular momentum J and nuclear angular momentum I are only partially decoupled. As a result of the mixing of wavefunctions of different hyperfine states, we observe a nonlinear Zeeman effect for each sublevel, a substantial modification of the transition probabilities between different magnetic sublevels, and the appearance of transitions that are strictly forbidden in the absence of the magnetic field. For the case of right- and left- handed circularly polarized laser excitation, the fluorescence spectra differs qualitatively. Well pronounced magnetic field induced circular dichroism is observed. These observations are explained with a standard approach that describes the partial decoupling of I and J states.

Solvent effects on the photophysics of 3-(benzoxazol-2-yl)-7-(N,N-diethylamino)chromen-2-one.

The photophysics of 3-(benzoxazol-2-yl)-7-(N,N-diethylamino)chromen-2-one was studied in different solvents and in SDS micelles. This compound presents characteristics which include an S(0)---> S(1) ( pi,pi*) transition with a (1)(n,pi*) perturbative component, due to the electronic coupling between the diethylamino group and the coumarin ring, considerable solvatochromism, dual fluorescence and high fluorescence quantum yields in almost all solvents studied. The electronic structure of the S(1) and S(2) excited states permits vibronic coupling between them, making configurational changes of the S(2) excited state possible, leading to the formation of an S(2)(TICT) state. Analysis of the TCSPC data indicates an equilibrium between the S(2)(TICT) and S(1)(LE) states in favour of the former. In protic solvents, the hydrogen bonding between the solvent and the diethylamino moiety results in the formation of an S(2)(HICT) state, making internal conversion an important deactivation process. Quantum mechanical calculations for the isolated molecule show that the diethylamino group in the S(2)(TICT) state is twisted at least 56 degree from the plane of the coumarin ring, with partial electronic decoupling between -NEt(2) and the coumarin ring. This twisting angle must be positively influenced by solute-solvent interactions. [capital Phi](ST) is found to be small, but not negligible. However, Phi (delta) can be considered negligible, an indication that T(1) is a short-lived state. Based on the experimental data and theoretical calculations, the most probable sequence for the first excited states, including the TICT state, is T(1)(n, pi*) < S(2)(TICT) < S(1)(pi,pi*) approximate S(2) (n,pi*).

EVOLUTIONARY DYNAMICS OF COMPLEX BIOMECHANICAL SYSTEMS: AN EXAMPLE USING THE FOUR-BAR MECHANISM

Like many phenotypic traits, biomechanical systems are defined by both an underlying morphology and an emergent functional property. The relationship between these levels may have a profound impact on how selection for functional performance is translated into morphological evolution. In particular, complex mechanical systems are likely to be highly redundant, because many alternative morphologies yield equivalent functions. We suggest that this redundancy weakens the relationship between morphological and functional diversity, and we illustrate this effect using an evolutionary model of the four-bar lever system of labrid fishes. Our results demonstrate that, when traits are complex, the morphological diversity of a clade may only weakly predict its mechanical diversity. Furthermore, parallel or convergent selection on function does not necessarily produce convergence in morphology. Empirical observations suggest that this weak form-function relationship has contributed to the morphological diversity of labrid fishes, as functionally equivalent species may nevertheless possess morphologically distinct jaws. We suggest that partial decoupling of morphology and mechanics due to redundancy is a major factor in morphological diversification.

Balanced sections and the propagation of décollement: A Jura perspective

The propagation of thrusting is an important problem in tectonics that is usually approached by forward (kinematical) modeling of balanced sections. Although modeling techniques are similar in most foreland fold‐thrust belts, it turns out that in the Jura, there are modeling problems that require modifications of widely used techniques. In particular, attention is called to the role of model constraints that complement the set of observational constraints in order to fully define the model. In the eastern Jura, such model constraints may be inferred from the regional geology, which shows a peculiar noncoaxial relation between thrusts and subsequent folds. This relation implies changes in the direction of translation and the mode of deformation in the course of the propagation of décollement. These changes are conjectured to be the result of a change in partial decoupling between the thin‐skinned fold‐thrust system (nappe) and the obliquely subducted foreland. As a particularly instructive case in point, a cross section through the Weissenstein range is discussed. A two‐step forward (kinematical) model is proposed that uses both local observational constraints as well as model constraints inferred from regional data. As a first step, a fault bend fold is generated in the hanging wall of a thrust of 1500 m shortening. As a second step, this structure is transferred by flexural slip into the actual fold observed at the surface. This requires an additional 1600 m of shortening and leads to folding of the original thrust. Thereafter, the footwall is deformed so as to respect the constraint that this deformation must fit into the space defined by the folded thrust as the upper boundary and the décollement surface as the lower boundary, and that, in addition, should be confined to the area immediately below the fold. In modeling the footwall deformation a mix of balancing methods is used: fault propagation folds for the competent intervals of the stratigraphic column and area balancing for the incompetent ones. Further propagation of décollement into the foreland is made possible by the folding process, which is dominated by a sort of kinking and which is the main contribution to structural elevation and hence to producing a sort of critical taper of the moving thin‐skinned wedge.

Two-Layer Models of Abyssal Equator-Crossing Flow

The role of baroclinicity in the dynamics of abyssal equator-crossing flows is examined by studying two-layer models of the flow valid in the equatorial region. Three new analytical models are derived from two-layer shallow-water theory. One of these models (Equatorial Model I, or EMI) reduces to the Swaters and Flierl coupled model in the midlatitude limit. In the equatorial limit, the lower-layer dynamics of EMI are that of the complete shallow-water equations, and the upper-layer dynamics are built upon quasigeostrophic potential vorticity conservation with a balance equation to relate the streamfunction and pressure. Simple numerical simulations are performed using this model to investigate its behavior in certain idealized situations, including equatorcrossing lenses and currents. In the midlatitudes, the dynamics of EMI are characterized by strong baroclinic interactions between the layers, while near the equator all three models exhibit a partial decoupling of the layers. This motivates the use of a one-layer reduced-gravity model to simulate abyssal dynamics in the immediate vicinity of the equator. Such simulations are reported elsewhere. A uniformly valid metamodel is derived that contains all of the necessary terms so that it may reduce, in the appropriate parameter limit, to any of the three models derived here.

Mechanical (de-)coupling of the lithosphere in the Valencia Trough (NW Mediterranean): what does it mean?

We study the mechanics of lithospheric decoupling in continental extensional basins in relation to the distribution of (non-)competent mechanical layers within the lithosphere and the position of the isostatic compensation level. We specifically address the different modes of deformation taking place in crustal levels according to a self-consistent formulation of the concept of mechanical decoupling. Subsequently, we investigate the style of lithospheric decoupling in the Valencia Trough (NW Mediterranean), a prime example of a young continental rift basin. During its evolution, the lower crust (or at least part of it) acted as a weak, non-competent layer that eventually flowed laterally to accommodate deformation in the subcrustal lithosphere and overlying crust, which became mechanically decoupled. We use a numerical model to discern whether these two layers deformed fully independently (vertical decoupling), or maintaining a mechanical link (horizontal and partial decoupling). Results of our study, constrained by a high-quality database, exclude fully decoupled mode and favor isostatic compensation level in the asthenosphere. Interpretation of our results in light of geological and geophysical data suggests that the present Valencia Trough is best described by partial lithospheric decoupling.

Evolution of orogenic wedges and continental plateaux: insights from crustal thermal-mechanical models overlying subducting mantle lithosphere

The links between an early phase of orogenesis, when orogens are commonly wedge shaped, and a later phase, with a plateau geometry, are investigated using coupled thermal–mechanical models with uniform velocity subduction boundary conditions applied to the base of the crust, and simple frictional–plastic and viscous rheologies. Models in which rheological properties do not change with depth or temperature are characterized by growth of back-to-back wedges above the subduction zone. Wedge taper is inversely dependent on the Ramberg number (Rm; gravity stress/basal traction); increasing convergence velocity or crustal strength produces narrower and thicker wedges. Models that are characterized by a decrease in crustal viscosity from ηc to ηb with depth or temperature, leading to partial or full basal decoupling of the crust from the mantle, display more complex behaviour. For models with a moderate viscosity ratio, ηb/ηc∼ 10−1, the crustal wedges have dual tapers with a lower taper in the central region and a higher taper at the edges of the deformed crust. A reduction in the viscosity ratio (ηb/ηc∼ 10−2) is sufficient to cause a transition of the central wedge region to a plateau. This transition depends on the basal traction, therefore the thickness of the weak basal layer also affects the transition. Further reduction of the viscosity ratio (ηb/ηc∼ 10−4) leads to full basal decoupling and the development of plateaux in all cases considered. In most models, the plateaux grow laterally at constant thickness between characteristic edge peaks associated with the transitions from coupled to decoupled lower crust. Where the crust is fully decoupled, large-scale model geometries for both depth- and temperature-dependent rheologies are similar with gravity-driven flow concentrated in the low-viscosity region. However, strong lateral temperature gradients within these models, controlled by the interaction of horizontal and vertical thermal advection, diffusion and heterogeneous thickening of the radioactive crustal layer, lead to differences in the velocity and deformation fields between the two cases, particularly at the plateau margins. The results suggest that simple depth-dependent viscosity models may be reasonable approximations for describing the large-scale geometry of fully developed plateaux, but that they are not appropriate for describing the internal features of large orogenic systems or the transition from wedge to plateau geometry.

Efficient stress relief in GaN heteroepitaxy on Si(1 1 1) using low-temperature AlN interlayers

Low-temperature (LT) AlN interlayers can be applied to reduce the tensile stress and cracks in thick GaN layers on Si. Here, we present an X-ray diffractometry study revealing the influence of metalorganic chemical vapor phase deposition parameters on stress relaxation by these interlayers. The degree of stress relaxation is observed to strongly depend on interlayer deposition temperature. At low temperatures, LT-AlN grows incoherently on GaN, which leads to a temperature-dependent partial decoupling of stress and also to a decoupling of the GaN layers separated by the interlayers. We further observe a Ga incorporation into the LT-AlN interlayers dependent on growth temperature and Al-content of AlGaN layers grown on top of LT-AlN layers. By introducing LT-AlN interlayers a GaN X-ray diffractometry rocking curve FWHM of the (0 0 0 2) reflection of 400 arcsec for 3 μm thick crack-free layers is achieved.

Visual Servoing from Lines

In this paper, we present a new approach to visual servoing using lines. It is based on a theoretical and geometrical study of the main line representations, which allows us to define a new representation, the so-called binormalized Plücker coordinates. These are particularly well suited for visual servoing. Indeed, they allow the definition of an image line alignment concept. Moreover, the control law which realizes such an alignment has several properties: partial decoupling between rotation and translation, analytical inversion of the motion equations and global asymptotic stability conditions. This control law was validated both in simulation and experimentally in the specific case of an orthogonal trihedron.

A version of the Swendsen–Wang algorithm for restoration of images degraded by Poisson noise

An algorithm for restoration of images degraded by Poisson noise is proposed. The algorithm belongs to the family of Markov chain Monte Carlo methods with auxiliary variables. We explicitly use the fact that medical images consist of finitely many, often relatively few, grey-levels. The continuous scale of grey-levels is discretized in an adaptive way, so that a straightforward application of the Swendsen–Wang (Phys. Rev. Lett. 58 (1987) 86) algorithm becomes possible. Partial decoupling method due to Higdon (J. Am. Statist. Assoc. 93 (1998) 442, 585) is also incorporated into the algorithm. Simulation results suggest that the algorithm is reliable and efficient.

Sedimentary pyrite formation in the Arabian Sea

In this study, pyrite formation in relation to environmental conditions was investigated in sediment records from the northern Arabian Sea. Considering the low bottom-water oxygen concentrations in the oxygen minimum zone (OMZ) and the high rates of primary productivity on the Oman and Pakistan Margins, sedimentary pyritic S concentrations are unexpectedly low (on average 0.4 wt%) compared to organic contents. Sediments located deeper than the OMZ exhibit a good correlation between organic carbon and reduced sulphur. Conversely, the C versus S distribution for OMZ sediments indicates a partial decoupling between organic carbon accumulation and pyrite formation. Early post-depositional sulphidisation resulted in the diagenetic sulphur enrichment of organic-poor intervals. This is evidenced by the presence of pyrite enrichments located below organic-rich intervals. Pyrite formation in the sediments within the Arabian Sea OMZ was limited by the availability of reactive iron oxides. This was caused by the low oxygen concentrations of the OMZ, which resulted in the reduction of iron oxides in the water column or at the sediment–water interface. However, on the basis of the relatively high sedimentary C/S ratios and the presence of bioturbation it is clear that no euxinic conditions developed in the OMZ in the Arabian sea during the last 120 kyr.