The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of incompressibility in the Eulerian variable description by a generalization of Dirac’s constraint method using noncanonical Poisson brackets. Here it is shown how to impose the incompressibility constraint using Dirac’s method in terms of both the canonical Poisson brackets in the Lagrangian variable description and the noncanonical Poisson brackets in the Eulerian description, allowing for the advection of density. Both cases give the dynamics of infinite-dimensional geodesic flow on the group of volume preserving diffeomorphisms and explicit expressions for this dynamics in terms of the constraints and original variables is given. Because Lagrangian and Eulerian conservation laws are not identical, comparison of the various methods is made.

A family of Lorentz invariant scalar functions of the magnetic field is defined in an ideal relativistic plasma. These invariants are advected by the plasma fluid motion and play the role of the potential magnetic field introduced by Hide in (Ann. Geophys., vol. 1, 1983, 59) along the lines of Ertel’s theorem. From these invariants we recover the Cauchy conditions for the magnetic field components in the mapping from Eulerian to Lagrangian variables. In addition, the adopted procedure allows us to formulate, in a Lorentz invariant form, the Alfvén theorem for the conservation of the magnetic flux through a surface comoving with the plasma.

In the single fluid, non-relativistic, ideal magnetohydrodynamic (MHD) plasma description, magnetic field lines play a fundamental role by defining dynamically preserved ‘magnetic connections’ between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D magnetic connection hypersurfaces in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when $\boldsymbol{E}\boldsymbol{\cdot }\boldsymbol{B}=0$.

A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom, the Poincaré map provides a splitting of the phase space into regions where particles have different kinds of motion: periodic, quasi-periodic or chaotic. The boundaries of these regions are transport barriers, i.e. a trajectory cannot cross such boundaries throughout the evolution of the system. Lagrangian coherent structures generalize this method to systems with the most general time dependence, splitting the phase space into regions with different qualitative behaviours. This leads to the definition of finite-time transport barriers, i.e. trajectories cannot cross the barrier for a finite amount of time. This methodology can be used to identify fast recirculating regions in the dynamical system and to characterize the transport between them.

In horses, successful in vitro fertilization procedures are limited by our inability to consistently mature equine oocytes by in vitro methods. Growth hormone (GH) is an important regulator of female reproduction in mammals, playing an important role in ovarian function, follicular growth and steroidogenesis. The objectives of this research were to investigate: the effects of equine growth hormone (eGH) and insulin-like growth factor-I (IGF-I) on the in vitro maturation (IVM) of equine oocytes, and the effects of eGH in addition to estradiol (E2), gonadotropins (FSH and LH) and fetal calf serum (FCS) on IVM. We also evaluated the cytoskeleton organization of equine oocytes after IVM with eGH. Equine oocytes were aspirated from follicles <30 mm in diameter and matured for 30 h at 38.5°C in air with 5% CO2. In experiment 1, selected cumulus–oocyte complexes (COCs) were randomly allocated as follows: (a) control (no additives); (b) 400 ng/ml eGH; (c) 200 ng/ml IGF-I; (d) eGH + IGF-I; and (e) eGH + IGF-I + 200 ng/ml anti-IGF-I. In addition to these treatment groups, we also added 1 μg/ml E2, 5 IU/ml FSH, 10 IU/ml LH and 10% FCS in vitro (experiment 2). Oocytes were stained with markers for microtubules (anti-α-tubulin antibody), microfilaments (AlexaFluor 488 Phalloidin) and chromatin (TO-PRO3-iodide) and assessed via confocal microscopy. No difference was observed when eGH and IGF-I was added into our IVM system. However, following incubation with eGH alone (40%) and eGH, E2, gonadotropins and FCS (36.6%) oocytes were classified as mature v. 17.6% of oocytes in the control group (P < 0.05). Matured equine oocytes showed that a thin network of filaments concentrated within the oocyte cortex and microtubules at the metaphase spindle showed a symmetrical barrel-shaped structure, with chromosomes aligned along its midline. We conclude that the use of E2, gonadotropins and FCS in the presence of eGH increases the number of oocytes reaching oocyte competence.

We review the main results of our previous works, in which we have investigated the development of the Kelvin-Helmholtz (KH) instability in the transitional regime from sub-magnetosonic to super-magnetosonic by varying the solar wind velocity, in conditions typical of those observed at the Earth’s magnetopause flanks. In super-magnetosonic regimes, we show that the vortices produced by the development of the KH instability act as an obstacle in the plasma flow and may generate quasi-perpendicular magnetosonic shock structures extending well outside the region of velocity shear.

Many astrophysical problems, ranging from structure formation in cosmology to dynamics of elliptical galaxies, refer to slow processes of evolution of essentially collisionless self-gravitating systems. To determine the relevant quasi-equilibrium configuration at time t from given initial conditions, such slow evolution is often approximated in terms of adiabatic evolution. Here we focus on the slow process of evolution induced by dynamical friction of a spherical stellar system (the host galaxy) on a minority component of “satellites” (distributed in a spherical shell), to determine to what extent an adiabatic description might be applied.

Ion acceleration by lasers is one of the most important innovations in laser-plasma research in recent years. A mechanism that has gained great attention due to the remarkable properties of the accelerated beam is laser acceleration of protons from the rear surface of solid targets. A striking prediction is that these protons are capable of generating images of micro-structures present on this surface. These images might be useful to measure properties of the accelerated beam. In this article, we address the physics of the generation of images of surface structures imprinted into the target back surface with laser-accelerated protons.

Laser Wake Field Acceleration of relativistic electron bunches is a promising method to produce a large amount of energetic particles with table top equipment. One of the possible methods to inject particles in the appropriate acceleration phase of the wake behind the pulse takes advantage of the partial longitudinal breaking of the wake crests across a density downramp. In this paper results of 2.5D PIC simulations, showing the production of an electron bunch with reduced energy spread, are reported. Also, a possible method to produce the required plasma density transition by laser explosion of a suitable couple of thin foils is discussed.

Energetic ion beams are produced during the interaction of ultrahigh-intensity, short laser pulses with plasmas. These laser-produced ion beams have important applications ranging from the fast ignition of thermonuclear targets to proton imaging, deep proton lithography, medical physics, and injectors for conventional accelerators. Although the basic physical mechanisms of ion beam generation in the plasma produced by the laser pulse interaction with the target are common to all these applications, each application requires a specific optimization of the ion beam properties, that is, an appropriate choice of the target design and of the laser pulse intensity, shape, and duration.

Low-frequency, relativistic, subcycle solitary waves are found in two-dimensional and three-dimensional particle-in-cell (PIC) numerical simulations, as a result of the interaction of ultrashort, high-intensity laser pulses with plasmas. Moreover, nondrifting, subcycle relativistic electromagnetic solitons have been obtained as solutions of the hydrodynamic equations for an electron–ion warm plasma, by assuming the quasi-neutrality character of the plasma response. In addition, the formation of long-living macroscopic soliton-like structures has been experimentally observed by means of the proton imaging diagnostics. Several common features result from these investigations, as, for example, the quasi-neutral plasma response to the soliton radiation, in the long-term evolution of the system, which leads to the almost complete expulsion of the plasma from the region where the electromagnetic radiation is concentrated, even at subrelativistic field intensity. The results of the theoretical investigations are reviewed with special attention to these similarities.

By analytical modeling and numerical simulation, we show that surface modes in moderately overdense plasmas may be excited parametrically by an intense, ultrashort laser pulse. This process has a feedback effect on fast electron generation and may seed a fast distortion of plasma “moving mirrors.”

Clusters represent a new class of laser pulse targets which show both the properties of underdense and of overdense plasmas. We present analytical and numerical results (based on 2D- and 3D-PIC simulations) of the Coulomb explosion of the ion cloud that is formed when a cluster is irradiated by a high-intensity laser pulse. For laser pulse intensities in the range of 1021−1022 W/cm2, the laser light can rip electrons from atoms almost instantaneously and can create a cloud made of an electrically nonneutral plasma. Ions can then be accelerated up to high energy during the Coulomb explosion of the cloud.

2D, low-frequency, relativistic solitary waves have been found recently in 2D. Particle-in-cell simulations of ultraintense laser pulses propagating in underdense plasmas, in regimes where the laser pulse undergoes energy depletion and downshifting of its frequency. These slowly propagating, spatially localized, electromagnetic structures represent an important channel of energy conversion from the laser pulse to the plasma. Pulse energy can also be converted into fast propagating structures, associated with collimated beams of ultrarelativistic electrons. Lienard–Wiechert magnetic field structures have been observed in PIC simulations to move together with focalized ultrarelativistic electron beams in the plasma.

We discuss the nonlinear evolution of the Weibel instability of two counter-streaming electron beams in the relativistic and non-relativistic regimes in the framework of a two-fluid description. We show the presence of two singularities per wavelength, responsible for the formation of very large density spikes. In the case of non-symmetric beams, we observe the compressive wave-break of the fast electron population, and the generation of a dipolar magnetic field associated with a central fast thin current and two larger slow return currents. This structure is very similar to those observed in PIC simulations of laser-plasma interactions.

Nonlinear structures in the formof coherent tripolar vortices, associated with shear-Alfvén perturbations in the presence of both magnetic and velocity shears, are studied analytically.

Hamiltonian vortices and reconnection in magnetized plasmas are investigated analytically and numerically using a two-fluid model. The equations are written in the Lagrangian form of three fields that are advected with different velocities. This system can be considered as a generalization and extension of the two-dimensional Euler equation for an ordinary fluid. It is pointed out that these equations allow solutions in the form of singular current-vortex filaments, drift-Alfvén vortices and magnetic islands, and admit collisionless magnetic reconnection where magnetic flux is converted into electron momentum and ion vorticity.

The proliferative characteristics of human acute leukaemia cells are reported and the relationships between the proliferative alterations and differentiation defect of these cells discussed. The proliferative activity of acute leukaemia cells was also studied in relation to cytostatic treatment.

Emphasis is laid on the fact that in all cases of acute leukaemia the characteristic blast cells of the disease do not constitute a homogenous cell population but can be divided into various sub-classes with different kinetic and proliferative characteristics. It is also pointed out that all cytostatic treatment acts on the most actively proliferating classes and only indirectly on the non-proliferating classes.

Finally, the need for more detailed study of DNA synthesis at chromosome and sub-chromosome level for the purpose of more fully understanding the response of leukaemic cells to the various chemiotherapies is underlined.