We build and solve numerically a phase field model for the growth and detachment of a gas bubble resting on an electrode and being filled with hydrogen produced by water electrolysis. The bubble is surrounded by a viscous liquid, has a prescribed static contact angle and is also subject to gravitational forces. We compute, as a function of the static contact angle, the time at which the bubble detaches from the substrate and what volume it has at that time. We also investigate the dependence of the detachment time on other parameters such as the applied voltage and the hydrogen ion concentration at the fluid bulk.

The evolution of a vortex line following the binormal flow equation (i.e. with a velocity proportional to the local curvature in the direction of the binormal vector) has been postulated as an approximation for the evolution of vortex filaments in both the Euler system for inviscid incompressible fluids and the Gross-Pitaevski equation in superfluids. We address the issue of whether this is a suitable approximation or not and its degree of validity by using rigorous mathematical methods and direct numerical simulations. More specifically, we show that, as the vortex core thickness goes to zero, the vortex core moves (at leading order and for long periods of time) with a velocity proportional to its local curvature and the binormal vector to the curve. The main idea of our analysis lies in a reformulation of the Gross-Pitaevski equation in terms of associated velocity and vorticity fields that resemble the Euler system written in terms of vorticity in its weak form. We also present full numerical simulations aimed to compare Gross-Pitaevski and binormal flow in various physical situations of interest such as the periodic evolution of deformed vortex rings and the reconnection of vortex filaments.

We develop and implement numerically a phase field model for the evolution and detachment of a gas bubble resting on a solid substrate and surrounded by a viscous liquid. The bubble has a static contact angle θ and will be subject to gravitational forces. We compute, as a function of the static contact angle, the critical Bond number, over which bubbles detach from the substrate. Then, we perform similar studies for bubble resting on inclined substrates and bubbles under the action of an external flow. We provide approximate formulas for the critical Bond number under all these circumstances. Our method is also able to resolve the pinch-off of the bubble and the possible appearance of satellites.

In this work we find new null electromagnetic fields that are exact solutions of Maxwell equations in vacuum and generalize the hopfion. The hopfion is an exact solution of Maxwell equations in vacuum in which all the field lines (both electric and magnetic) are topologically equivalent to closed and linked circles, forming a mathematical structure called Hopf fibration. Here we present a generalization to include other field lines topology, such as the Seifert fibration in which the field lines form linked torus knots. Included in this generalization are fields that ergodically fill torus surfaces.

We present the working prototype of a levitation system designed for investigation of flows in cryogenic helium fluids. The current device allows the levitation of a superconducting sphere and has several provisions made for allowing precise control over its motion. We report on progress in the detection and control systems of the prototype and demonstrate how uniform circular motion can be implemented.

We present a method for calculating the stability region of a perfect diamagnet levitated in a magnetic field created by a circular current loop making use of the machine learning techniques. As an application we compute stability regions, points of stable equilibrium and stable oscillatory motions in two chip-based superconducting trap architectures used to levitate superconducting particles. Our procedure is an alternative to a full numerical scheme based on finite element methods which are expensive to implement for optimizing experimental parameters.

We present the calculation of the stability region of a perfect diamagnet levitated in a magnetic field created by a circular current loop. We make use of the machine learning technique of automatic differentiation to illustrate the calculations with the elliptic integrals involved.

In this paper we study the lateral instability in a discharge channel using a continuum model. We observe analogies with the onset of Kelvin-Helmholz instability in fluids. In strong electric fields, lateral long wave length perturbations can grow while small wave length perturbations diminish during the discharge evolution. We perform numerical simulations and carry out asymptotic analysis of the instability. (c) 2021 Elsevier Ltd. All rights reserved.

We present a new mechanical probe to study the properties of superfluid 3He at microkelvin temperatures down to 100 μK. The setup consists of a set of coils for levitating a superconducting sphere and controlling its motion in a wide variety of regimes. In particular, the realisation of motion of a levitating body at a uniform velocity presents both an experimental challenge and a promising direction into the study of the edge states in topological superfluid 3He-B. We include the theoretical study of the device stability and simulations to illustrate the capabilities of the control system.

Seed microbiota is becoming an emergent area of research. Host plant microbial diversity is increasingly well described, yet relatively little is known about the stressors driving plant endomicrobiota at the metaorganism level. The present work examines the role of horizontal and vertical transmission of bacterial microbiota in response to abiotic stress generated by arsenic. Horizontal transmission is achieved by bioaugmentation with the endophyte Rhodococcus rhodochrous, while vertical transmission comes via maternal inheritance from seeds. To achieve this goal, all experiments were conducted with two Jasione species. J. montana is tolerant to arsenic (As), whereas J. sessiliflora, being phylogenetically close to J. montana, was not previously described as As tolerant. The Jasione core bacterial endophytes are composed of genera Pseudomonas, Ralstonia, Undibacterium, Cutibacterium, and Kocuria and family Comamanadaceae across different environmental conditions. All these operational taxonomic units (OTUs) coexisted from seeds to the development of the seedling, independently of As stress, or bioaugmentation treatment and Jasione species. R. rhodochrous colonized efficiently both species, driving the endomicrobiota structure of Jasione with a stronger effect than As stress. Despite the fact that most of the OTUs identified inside Jasione seeds and seedlings belonged to rare microbiota, they represent a large bacterial reservoir offering important physiological and ecological traits to the host. Jasione traits co-regulated with R. rhodochrous, and the associated microbiota improved the host response to As stress. NGS-Illumina tools provided further knowledge about the ecological and functional roles of plant endophytes.

An experimental evolution system with a wood-rotting microbial consortium (BOS08) has demonstrated the acquisition of a new ability to exploit a previously untapped carbon source, such as the recalcitrant carbamazepine (CBZ). The improved extraction method has provided an accurate CBZ depletion rate from BOS08 of $$2.14 \pm 0.42 \times 10^{-3}\;\text{ h }^{-1}$$ . The consortium did not use cometabolism to process CBZ and the intermediate metabolite produced 10,11-dihydroxycarbamazepine was not pharmacologically active and toxic. The bacteria identification by massive sequencing (Illumina) confirmed the dominance of Proteobacteria Phylum such as genera Cupriavidus sp., Sphingomonas sp., Delftia sp., Acinetobacter sp. and Methylobacterium sp. coexisting through all biodegradation process. Based on biological principles, we model the consortium-CBZ kinetics with a set of nonlinear ordinary differential equations with logistic growth type terms. The use of experimental data combined with logistic growth models allow us to test new functional features acquired by the consortium.

In this paper we study the lateral instability of streamer discharges using a continuum discharge model. We observe similarities to Kelvin-Helmholz instability in fluids. In strong electric fields, lateral long wave length perturbations can grow while small wave length perturbations diminish during the discharge evolution. We perform numerical simulations and carry out asymptotic analysis of the instability. Our results could explain the growth observed in experimental discharges.

The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in a vacuum with non-trivial topology of the field lines and special properties. The program followed in this work allows us to present the main ideas and the explicit calculations at undergraduate level, so they are not obscured by a more involved formulation. We make use of the helicity basis for calculating the electromagnetic helicity and the photon content of the fields.

The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted solutions with the properties of being null. The new fields are obtained by a homothetic transformation (dilatation) and a rotation of the hopfion, and we study the constraints that the transformations must fulfill in order to generate valid electromagnetic fields propagating in a vacuum. We make use of the Bateman construction and calculate the four-potentials and the electromagnetic helicities. It is observed that the topology of the field lines does not seem to be conserved as it is for the hopfion.

This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current observational astronomy. Our approach is formulated as a classical Einstein-vector-scalar-Maxwell-fluid field theory on a spacetime with three-sphere spatial sections. Analytic cosmological solutions are found using local charts familiar from standard LFRW cosmological models. These solutions can be used to describe different types of evolution for the metric scale factor, the Hubble, jerk and de-acceleration functions, the scalar spacetime curvature and the Kretschmann invariant. The cosmological sector of the theory accommodates a particular single big-bang scenario followed by an eternal exponential acceleration of the scale factor. Such a solution does not require an externally prescribed fluid equation of state and leads to a number of new predictions including a current value of the "jerk" parameter, "Hopfian-like" source-free Maxwell field configurations with magnetic helicity and distributional "bi-polar" solutions exhibiting a new charge conjugation symmetry. An approximate scheme for field perturbations about this particular cosmology is explored and its consequences for a thermalisation process and a thermal history are derived, leading to a prediction of the time interval between the big-bang and the decoupling era. Finally it is shown that field couplings exist where both vector and scalar localised linearised perturbations exhibit dispersive wave-packet behaviours. The scalar perturbation may also give rise to Yukawa solutions associated with a massive Klein-Gordon particle. It is argued that the vector and scalar fields may offer candidates for "dark-energy" and "dark-matter" respectively.

In this work, we study the influence of orbital viscosity on the evolution of the order-parameter and texture in the B phase of superfluid 3 He near a moving boundary. From the redistribution of thermal quasiparticles within the texture, we develop a model which confers a substantial effective mass on the interface, and provides a new mechanism for friction as the boundary moves. We have tested the model against existing data for the motion of an A-B interface whose motion was controlled by a magnetic field. The model allows us to make predictions for the behaviour in experimental situations which involve texture rearrangement arising from motion of the B-phase boundary.

We report on nanomechanical resonators with very high-quality factors operated as mechanical probes in liquid helium \(^4\mathrm{He}\), with special attention to the superfluid regime down to millikelvin temperatures. Such resonators have been used to map out the full range of damping mechanisms in the liquid on the nanometer scale from \(10\,\mathrm{mK}\) up to \(\sim3\,\mathrm{K}\). The high sensitivity of these doubly-clamped beams to thermal excitations in the superfluid \(^4\mathrm{He}\) makes it possible to drive them using the momentum transfer from phonons generated by a nearby heater. This so-called \textit{phonon wind} is an inverse thermomechanical effect that until now has never been demonstrated, and provides the possibility to perform a new type of optomechanical experiments in quantum fluids.

We calculate analytically the spin-orbital decomposition of the angular momentum using completely nonparaxial fields that have a certain degree of linkage of electric and magnetic lines. The split of the angular momentum into spin-orbital components is worked out for non-null knotted electromagnetic fields. The relation between magnetic and electric helicities and spin-orbital decomposition of the angular momentum is considered. We demonstrate that even if the total angular momentum and the values of the spin and orbital momentum are the same, the behavior of the local angular momentum density is rather different. By taking cases with constant and non-constant electric and magnetic helicities, we show that the total angular momentum density presents different characteristics during time evolution.

Intense electromagnetic pulses interacting with a plasma can create a wake of plasma oscillations. Electrons trapped in such oscillations can be accelerated under certain conditions to very high energies. We study the optimal conditions for the wakefield acceleration to produce MeV electrons in planetary plasmas under collisionless conditions. The conditions for the optimal plasma densities can be found in the Earth atmosphere at higher altitudes than 10-15 km, which are the altitudes where lightning leaders can take place.