Lotka--Volterra Type Equations and their Explicit Integration

In the present note we give an explicit integration of some two--dimensionalised Lotka--Volterra type equations associated with simple Lie algebras, other than the familiar $A_n$ case, possessing a representation without branching. This allows us, in particular, to treat the first fundamental representations of $A_r$, $B_r$, $C_r$, and $G_2$ on the same footing.Comment: 3 pages LATEX fil

Novel kinetic consistent mhd algorithm for high performance computing

The impressive progress of the kinetic schemes in the solution of gas dy- namics problems and the development of effective parallel algorithms for modern high performance parallel computing systems led to the development of advanced methods for the solution of the magnetohydrodynamics problem in the important area of plasma physics. The novel feature of the method is the formulation of the complex Boltzmann- like distribution function of kinetic method with the implementation of electromagnetic interaction terms. The numerical method is based on the explicit schemes. Due to logical simplicity and its efficiency, the algorithm is easily adapted to modern high performance parallel computer systems including hybrid computing systems with graphic processors

Statistical distribution function of charged particles in magnetic field

The statistical distribution function introduced by Boltzmann and his ki- netic equation are the fundamental basis of the kinetic theory of gases and of the basic methods of solution of problems in the gas dynamics. At present time one of the areas of high interest in modern physics is the plasma in fusion processes and astrophysics which requires an extension of the kinetic processes to charged particles, in particular regard- ing the electromagnetic interactions. We propose a unified distribution function which includes the electromagnetic interactions for charged particles and is suitable for the solu- tion of problems of charged particle dynamics with Boltzmann type equations and kinetic consistent magneto gas dynamic equations

Novel kinetic consistent algorithm for the modeling of incompressible conducting flows

In this study we aim at demonstrating that kinetic consistent magneto gas dynamic algorithms are a valid for the computation of the dynamics of incompressible conductive flows. We obtain numerical solutions for the test problems, namely the laminar flow inside a wall-driven cavity and a magnetic driven pump. We show that kinetic consistent algorithms have a high stability in the solution of convection-dominated flows, due to a correct physical modeling of the fluid viscosity and to the possibility of tuning appropriate regularization terms on the basis of the physical properties of the fluid. We show that the kinetic consistent approach offers a stable basis for a correct physical description of the shear viscosity, thermal conduction and electric resistivity effects in incompressible magneto hydrodynamics flows

Ultra-relativistic electrostatic Bernstein waves

A new general form of the dispersion relation for electrostatic Bernstein waves in ultra-relativistic pair plasmas, characterized by a−1 = kBT/(mec2)  1, is derived in this paper. The parameter Sp = aΩ0/ωp, where Ω0 is the rest cyclotron frequency for electrons or positrons and ωp is the electron (or positron) plasma frequency, plays a crucial role in characterizing these waves. In particular, Sp has a restricted range for permitted wave solutions; this range is effectively unlimited for classical plasmas, but is significant for the ultra-relativistic case. The characterization of these waves is applied in particular to the presence of such plasmas in pulsar atmospheres

Novel kinetic consistent 3d mhd algorithm for high performance parallel computing systems

The impressive progress of the kinetic consistent schemes in the solution of the gas dynamics problems and the development of the effective parallel algorithms for the modern high performance parallel computing systems lead to the development of advanced methods for the solution of the magnetohydrodynamics problems for plasma physics. The novel feature of the method is the formulation of the complex Boltzmann-like distribution function of the kinetic method with the implementation of the electromagnetic interaction term. The numerical method is based on the explicit schemes, due to the logical simplicity and high efficiency of the algorithm and the easy adaptation to the modern high performance parallel computing systems

Topological gravity on plumbed V-cobordisms

An ensemble of cosmological models based on generalized BF-theory is constructed where the role of vacuum (zero-level) coupling constants is played by topologically invariant rational intersection forms (cosmological-constant matrices) of 4-dimensional plumbed V-cobordisms which are interpreted as Euclidean spacetime regions. For these regions describing topology changes, the rational and integer intersection matrices are calculated. A relation is found between the hierarchy of certain elements of these matrices and the hierarchy of coupling constants of the universal (low-energy) interactions. PACS numbers: 0420G, 0240, 0460Comment: 29 page

WW--geometry of the Toda systems associated with non-exceptional simple Lie algebras

The present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Pl\"ucker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding K\"ahler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with appropriate choices of $N$. In addition, these W-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Pl\"ucker embedding. These conditions are automatically fulfiled when Toda equations hold.Comment: 30 pages, no figur

The Digital Silicon Photomultiplier

The Silicon Photomultipliers (SiPMs) are the new step in the development of the modern detection structures in the area of low photon flux detection with a unique capability of detection up to the single photons. The Silicon Photomultiplier intrinsically represents a digital signal source on the elementary cell level. The materials and technology of SiPMs are consistent with the modern electronics technology. We present the realization and implementation of a fully digital Silicon Photomultiplier Imager with an enclosed readout and processing on the basis of modern 3D technology

A novel method for magnetohydrodynamic simulations and its first applications in astrophysics and cosmology on high performance computational systems

Magnetic fields are one of the most important phenomena in science and engineering, as they are present on almost every scale in nature, ranging from atomic magnetic moments to the intergalactic space, and are used in applications ranging from Magnetic Resonance Imaging to nuclear fusion. In this work we first present a novel powerful method for high performance magnetohydrodynamic (MHD) calculations which is based on kinetic schemes. In particular, using it, it is possible to derive the MHD equations directly from the Boltzmann Equation without the necessity of an ad hoc introduction of terms related to electromagnetic interactions. With that at hand, we were then able to apply the method to one of the most important problems in present day astrophysics and cosmology, namely to the question of the origin and time evolution of Intergalactic Magnetic Fields. As for their origin, there are mainly two scenarios discussed in the literature – on the one hand the cosmological one, where the magnetic field is produced by some process in the very early Universe, and on the other hand the cosmological one, where a seed of the magnetic field is created during structure formation and then amplified by some dynamo effect. Here, we show first results of the aforementioned application of our method – on the one hand, concerning the astrophysical scenario, the simulation of galactic winds, i.e. the ejection of matter from galaxies which might also carry magnetic energy, and on the other hand, for the cosmological scenario, the time evolution of primordial magnetic fields and their possible imprints on the Cosmic Microwave Background (CMB)