Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model

Co-limitation of marine phytoplankton growth by light and nutrient, both of which are essential for phytoplankton, leads to complex dynamic behavior and a wide array of coherent patterns. The building blocks of this array can be considered to be deep chlorophyll maxima, or DCMs, which are structures localized in a finite depth interior to the water column. From an ecological point of view, DCMs are evocative of a balance between the inflow of light from the water surface and of nutrients from the sediment. From a (linear) bifurcational point of view, they appear through a transcritical bifurcation in which the trivial, no-plankton steady state is destabilized. This article is devoted to the analytic investigation of the weakly nonlinear dynamics of these DCM patterns, and it has two overarching themes. The first of these concerns the fate of the destabilizing stationary DCM mode beyond the center manifold regime. Exploiting the natural singularly perturbed nature of the model, we derive an explicit reduced model of asymptotically high dimension which fully captures these dynamics. Our subsequent and fully detailed study of this model - which involves a subtle asymptotic analysis necessarily transgressing the boundaries of a local center manifold reduction - establishes that a stable DCM pattern indeed appears from a transcritical bifurcation. However, we also deduce that asymptotically close to the original destabilization, the DCM looses its stability in a secondary bifurcation of Hopf type. This is in agreement with indications from numerical simulations available in the literature. Employing the same methods, we also identify a much larger DCM pattern. The development of the method underpinning this work - which, we expect, shall prove useful for a larger class of models - forms the second theme of this article

Meromorphic Solutions to a Differential--Difference Equation Describing Certain Self-Similar Potentials

In this paper we prove the existence of meromorphic solutions to a nonlinear differential difference equation that describe certain self-similar potentials for the Schroedinger operator.Comment: 10 pages, LaTeX, uses additional package

The radiating part of circular sources

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is limited, with the limit fixed by the wavenumber of source multiplied by the source radius (Helmholtz number). The acoustic field is found in terms of the elementary fields generated by a set of line sources whose form is given by Chebyshev polynomials of the second kind, and whose amplitude is found to be given by weighted integrals of the radial source term. The analysis is developed for tonal sources, such as rotors, and, for Helmholtz number less than two, for random disk sources. In this case, the analysis yields the cross-spectrum between two points in the acoustic field. The analysis is applied to the problems of tonal radiation, random source radiation as a model problem for jet noise, and to noise cancellation, as in active control of noise from rotors. It is found that the approach gives an accurate model for the radiation problem and explicitly identifies those parts of a source which radiate.Comment: Submitted to Journal of the Acoustical Society of Americ

Renormalized Vacuum Polarization and Stress Tensor on the Horizon of a Schwarzschild Black Hole Threaded by a Cosmic String

We calculate the renormalized vacuum polarization and stress tensor for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinte straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.Comment: This is an expanded version of a previous submission, we have added the calculation of the stress tensor. 28 pages, 7 figure

Calculations of the Local Density of States for some Simple Systems

A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos for a higher dimensionality out of lower dimensional parts. Some practical and theoretical aspects of this approach are also discussed.Comment: 5 pages, 3 figure

Levy flights from a continuous-time process

The Levy-flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus, this processes is a kind of continuous-time random walks (CTRW), dual to usual Scher-Montroll model, in which $n$ grows sublinearly with t. The models in which Levy-flights emerge due to a temporal subordination let easily discuss the response of a random walker to a weak outer force, which is shown to be nonlinear. On the other hand, the relaxation of en ensemble of such walkers in a harmonic potential follows a simple exponential pattern and leads to a normal Boltzmann distribution. The mixed models, describing normal CTRW in superlinear operational time and Levy-flights under the operational time of subdiffusive CTRW lead to paradoxical diffusive behavior, similar to the one found in transport on polymer chains. The relaxation to the Boltzmann distribution in such models is slow and asymptotically follows a power-law

Type V secretion: mechanism(s) of autotransport through the bacterial outer membrane

Autotransport in Gram-negative bacteria denotes the ability of surface-localized proteins to cross the outer membrane (OM) autonomously. Autotransporters perform this task with the help of a β-barrel transmembrane domain localized in the OM. Different classes of autotransporters have been investigated in detail in recent years; classical monomeric but also trimeric autotransporters comprise many important bacterial virulence factors. So do the two-partner secretion systems, which are a special case as the transported protein resides on a different polypeptide chain than the transporter. Despite the great interest in these proteins, the exact mechanism of the transport process remains elusive. Moreover, different periplasmic and OM factors have been identified that play a role in the translocation, making the term ‘autotransport’ debatable. In this review, we compile the wealth of details known on the mechanism of single autotransporters from different classes and organisms, and put them into a bigger perspective. We also discuss recently discovered or rediscovered classes of autotransporters

The inverse autotransporter intimin exports its passenger domain via a hairpin intermediate

Autotransporter proteins comprise a large family of virulence factors that consist of a-barrel translocation unit and an extracellular effector or passenger domain. The -barrel anchors the protein to the outer membrane of Gram-negative bacteria and facilitates the transport of the passenger domain onto the cell surface. By inserting an epitope tag into the N terminus of the passenger domain of the inverse autotransporter intimin, we generated a mutant defective in autotransport. Using this stalled mutant, we could show that (i) at the time point of stalling, the -barrel appears folded; (ii) the stalled autotransporter is associated with BamA and SurA; (iii) the stalled intimin is decorated with large amounts of SurA; (iv) the stalled autotransporter is not degraded by periplasmic proteases; and (v) inverse autotransporter passenger domains are translocated by a hairpin mechanism. Our results suggest a function for the BAM complex not only in insertion and folding of the -barrel but also for passenger translocation

Correlations in a Generalized Elastic Model: Fractional Langevin Equation Approach

The Generalized Elastic Model (GEM) provides the evolution equation which governs the stochastic motion of several many-body systems in nature, such as polymers, membranes, growing interfaces. On the other hand a probe (\emph{tracer}) particle in these systems performs a fractional Brownian motion due to the spatial interactions with the other system's components. The tracer's anomalous dynamics can be described by a Fractional Langevin Equation (FLE) with a space-time correlated noise. We demonstrate that the description given in terms of GEM coincides with that furnished by the relative FLE, by showing that the correlation functions of the stochastic field obtained within the FLE framework agree to the corresponding quantities calculated from the GEM. Furthermore we show that the Fox $H$-function formalism appears to be very convenient to describe the correlation properties within the FLE approach

Polymer-Chain Adsorption Transition at a Cylindrical Boundary

In a recent letter, a simple method was proposed to generate solvable models that predict the critical properties of statistical systems in hyperspherical geometries. To that end, it was shown how to reduce a random walk in $D$ dimensions to an anisotropic one-dimensional random walk on concentric hyperspheres. Here, I construct such a random walk to model the adsorption-desorption transition of polymer chains growing near an attractive cylindrical boundary such as that of a cell membrane. I find that the fraction of adsorbed monomers on the boundary vanishes exponentially when the adsorption energy decreases towards its critical value. When the adsorption energy rises beyond a certain value above the critical point whose scale is set by the radius of the cell, the adsorption fraction exhibits a crossover to a linear increase characteristic to polymers growing near planar boundaries.Comment: latex, 12 pages, 3 ps-figures, uuencode