Manuel Arrayás

How Do Sinking Phytoplankton Species Manage to Persist

Phytoplankton require light for photosynthesis. Yet, most phytoplankton species are heavier than water and therefore sink. How can these sinking species persist? Somehow, the answer should lie in the turbulent motion that redisperses sinking phytoplankton over the vertical water column. Here, we show, using a reaction‐advection‐diffusion equation of light‐limited phytoplankton, that there is a turbulence window sustaining sinking phytoplankton species in deep waters. If turbulent diffusion is too high, phytoplankton are mixed to great depths, and the depth‐averaged light conditions are too low to allow net positive population growth. Conversely, if turbulent diffusion is too low, sinking phytoplankton populations end up at the ocean floor and succumb in the dark. At intermediate levels of turbulent diffusion, however, phytoplankton populations can outgrow both mixing rates and sinking rates. In this way, the reproducing population as a whole can maintain a position in the well‐lit zone near the top of the water column, even if all individuals within the population have a tendency to sink. This theory unites earlier classic results by Sverdrup and Riley as well as our own recent findings and provides a new conceptual framework for the understanding of phytoplankton dynamics under the influence of mixing processes.

Stability of negative ionization fronts: Regularization by electric screening?

We recently have proposed that a reduced interfacial model for streamer propagation is able to explain spontaneous branching. Such models require regularization. In the present paper we investigate how transversal Fourier modes of a planar ionization front are regularized by the electric screening length. For a fixed value of the electric field ahead of the front we calculate the dispersion relation numerically. These results guide the derivation of analytical asymptotes for arbitrary fields: for small wave-vector k, the growth rate s(k) grows linearly with k, for large k, it saturates at some positive plateau value. We give a physical interpretation of these results.

Mechanism of branching in negative ionization fronts

When a strong electric field is applied to nonconducting matter, narrow channels of plasma called streamers may form. Branchlike patterns of streamers have been observed in anode directed discharges. We explain a mechanism for branching as the result of a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. The dispersion relation for transversal perturbation of a planar negative front is obtained analytically when the ratio D between the electron diffusion coefficient and the intensity of the externally imposed electric field is small. We estimate the spacing lambda between streamers and deduce a scaling law lambda approximately D(1/3).

Exchange of helicity in a knotted electromagnetic field

There are solutions of Maxwell equations in vacuum in which the magnetic and the electric lines have a nontrivial topology. This behaviour has physical consequences since it is related to classical expressions indicating aspects of the photon content of the electromagnetic field. In this work we present for the first time an exact solution of Maxwell equations in vacuum, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field. We calculate the temporal evolution of the magnetic and electric helicities, and explain the exchange of helicity making use of the Chern-Simon form. We also have found and explained that, as time goes to infinity, both helicities reach the same value and the exchange between the magnetic and electric part of the field stops. c

A class of non-null toroidal electromagnetic fields and its relation to the model of electromagnetic knots

An electromagnetic knot is an electromagnetic field in vacuum in which the magnetic lines and the electric lines coincide with the level curves of a pair of complex scalar fields ϕ and θ (see equations (A.1), (A.2)). When electromagnetism is expressed in terms of electromagnetic knots, it includes mechanisms for the topological quantization of the electromagnetic helicity, the electric charge, the electromagnetic energy inside a cavity and the magnetic flux through a superconducting ring. In the case of electromagnetic helicity, its topological quantization depends on the linking number of the field lines, both electric and magnetic. Consequently, to find solutions of the electromagnetic knot equations with nontrivial topology of the field lines has important physical consequences. We study a new class of solutions of Maxwellʼs equations in vacuum Arrayas and Trueba (2011 arXiv:1106.1122) obtained from complex scalar fields that can be interpreted as maps , in which the topology of the field lines is that of the whole torus-knot set. Thus this class of solutions is built as electromagnetic knots at initial time. We study some properties of those fields and consider if detection based on the energy and momentum observables is possible.

Motion of charged particles in a knotted electromagnetic field

In this paper we consider the classical relativistic motion of charged particles in a knotted electromagnetic field. After reviewing how to construct electromagnetic knots from maps between the three-sphere and the two-sphere, we introduce a mean quadratic radius of the energy density distribution in order to study some properties of this field. We study the classical relativistic motion of electrons in the electromagnetic field of the Hopf map, and compute their trajectories. It is observed that these electrons initially at rest are strongly accelerated by the electromagnetic force, becoming ultrarelativistic in a period of time that depends on the knot energy and size.

Photoionization effects in ionization fronts

In this paper we study the effects of photoionization processes on the propagation of both negative and positive ionization fronts in streamer discharge. We show that negative fronts accelerate in the presence of photoionization events. The appearance and propagation of positive ionization fronts travelling with constant velocity is explained as the result of the combined effects of photoionization and electron diffusion. The photoionization range plays an important role in the selection of the velocity of the ionization front as we show in this work.

Ionization fronts in negative corona discharges

We use a hydrodynamic minimal streamer model to study negative corona discharge. By reformulating the model in terms of a quantity called a shielding factor, we deduce laws for the evolution in time of both the radius and intensity of the ionization fronts. We also compute the evolution of the front thickness under the conditions for which it diffuses due to the geometry of the problem and show its self-similar character.

Fingering from Ionization Fronts in Plasmas

In this paper we describe the formation of fingers from ionization fronts for a hydrodynamic plasma model. The fingers result from a balance between the destabilizing effect of impact ionization and the stabilizing effect of electron diffusion on ionization fronts. We show that electron diffusion acts as an effective surface tension on moving fronts and we estimate analytically the size of the fingers and its dependence on both the electric field and electron diffusion coefficient. We perform direct numerical simulation of the model and compute finger-like traveling waves analogous to structures such as Saffman–Taylor fingers and Ivantsov paraboloid in the context of Hele–Shaw and Stefan problems, respectively.

Power laws and self-similar behaviour in negative ionization fronts

We study anode-directed ionization fronts in curved geometries. An electric shielding factor determines the behaviour of the electric field and the charged particle densities. From a minimal streamer model, a Burgers type equation which governs the dynamics of the electric shielding factor is obtained when electron diffusion is neglected. A Lagrangian formulation is then derived to analyse the ionization fronts. Power laws for the velocity and the amplitude of streamer fronts are found numerically and calculated analytically by using the shielding factor formulation. The phenomenon of geometrical diffusion is explained and clarified, and a universal self-similar asymptotic behaviour is derived.