On the hierarchy of partially invariant submodels of differential equations

It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. In this framework the complete classification of regular partially invariant solutions of ideal MHD equations is given

Towards nanomedicines of the future: Remote magneto-mechanical actuation of nanomedicines by alternating magnetic fields

The paper describes the concept of magneto-mechanical actuation of single-domain magnetic nanoparticles (MNPs) in super-low and low frequency alternating magnetic fields (AMFs) and its possible use for remote control of nanomedicines and drug delivery systems. The applications of this approach for remote actuation of drug release as well as effects on biomacromolecules, biomembranes, subcellular structures and cells are discussed in comparison to conventional strategies employing magnetic hyperthermia in a radio frequency (RF) AMF. Several quantitative models describing interaction of functionalized MNPs with single macromolecules, lipid membranes, and proteins (e.g. cell membrane receptors, ion channels) are presented. The optimal characteristics of the MNPs and an AMF for effective magneto-mechanical actuation of single molecule responses in biological and bio-inspired systems are discussed. Altogether, the described studies and phenomena offer opportunities for the development of novel therapeutics both alone and in combination with magnetic hyperthermia

Analytical description of stationary ideal MHD flows with constant total pressure

Incompressible stationary flows of ideal plasma are observed. By introduction of curvilinear system of coordinates in which streamlines and magnetic force lines form a family of coordinate surfaces, MHD equations are partially integrated and brought to a certain convenient form. It is demonstrated that the admissible group of Bogoyavlenskij's symmetry transformations performs as a scaling transformation for the curvilinear coordinates. Analytic description of stationary flows with constant total pressure is given. It is shown, that contact magnetic surfaces of such flows are translational surfaces, i.e. are swept out by translating one curve rigidly along another curve. Explicit examples of solutions with constant total pressure possessing a significant functional arbitrariness are given

Electromagnetic Burst Generation during Annihilation of Magnetic Field in Relativistic Laser-Plasma Interaction

We present the results of theoretical studies of formation and evolution of the current sheet in a colliosionless plasma during magnetic reconnection in relativistic limit. Relativistic magnetic reconnection is driven by parallel laser pulses interacting with underdense plasma target. Annihilation of laser created magnetic field of opposite polarity generates strong non-stationary electric field formed in between the region with opposite polarity magnetic field accelerating charged particles within the current sheet. This laser-plasma target configuration is discussed in regard with the laboratory modeling of charged particle acceleration and gamma flash generation in astrophysics. We present the results of 3-dimensional kinetic simulations and theoretical studies on the formation and evolution of the current sheet in a collisionless plasma during magnetic field annihilation in the ultra-relativistic limit. Annihilation of oppositively directed magnetic fields driven by two laser pulses interacting with underdense plasma target is accompanied by an electromagnetic burst generation. The induced strong non-stationary longitudinal electric field accelerates charged particles within the current sheet. Properties of the laser-plasma target configuration are discussed in the context of the laboratory modeling for charged particle acceleration and gamma flash generation in astrophysics