New divisors in the boundary of the instanton moduli space

Let ${\mathcal I}(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on ${\mathbb P}^3$. It is known that ${\mathcal I}(n)$ is an irreducible, nonsingular and affine variety of dimension $8n-3$. Since every rank $2$ instanton bundle on ${\mathbb P}^3$ is stable, we may regard ${\mathcal I}(n)$ as an open subset of the projective Gieseker-Maruyama moduli scheme ${\mathcal M}(n)$ of rank $2$ semistable torsion free sheaves $F$ on ${\mathbb P}^3$ with Chern classes $c_1=c_3=0$ and $c_2=n$, and consider the closure $\overline{{\mathcal I}(n)}$ of ${\mathcal I}(n)$ in ${\mathcal M}(n)$. We construct some of the irreducible components of dimension $8n-4$ of the boundary $\partial{\mathcal I}(n):=\overline{{\mathcal I}(n)}\setminus{\mathcal I}(n)$. These components generically lie in the smooth locus of ${\mathcal M}(n)$ and consist of rank $2$ torsion free instanton sheaves with singularities along rational curves

Collective oscillations in spatially modulated exciton-polariton condensate arrays

We study collective dynamics of interacting centers of exciton-polariton condensation in presence of spatial inhomogeneity, as modeled by diatomic active oscillator lattices. The mode formalism is developed and employed to derive existence and stability criteria of plane wave solutions. It is demonstrated that $k_0=0$ wave number mode with the binary elementary cell on a diatomic lattice possesses superior existence and stability properties. Decreasing net on-site losses (balance of dissipation and pumping) or conservative nonlinearity favors multistability of modes, while increasing frequency mismatch between adjacent oscillators detriments it. On the other hand, spatial inhomogeneity may recover stability of modes at high nonlinearities. Entering the region where all single-mode solutions are unstable we discover subsequent transitions between localized quasiperiodic, chaotic and global chaotic dynamics in the mode space, as nonlinearity increases. Importantly, the last transition evokes the loss of synchronization. These effects may determine lasing dynamics of interacting exciton-polariton condensation centers.Comment: 9 pages, 3 figure

First CRDS-measurements of water vapour continuum in the 940nm absorption band

Measurements of near-infrared water vapour continuum using continuous wave cavity ring down spectroscopy (cw- CRDS) have been performed at around 10611.6 and 10685:2 cm1. The continuum absorption coefficients for N2- broadening have been determined for two temperatures and wavenumbers. These results represent the first near-IR continuum laboratory data determined within the complex spectral environment in the 940nm water vapour band and are in reasonable agreement with simulations using the semiempirical CKD formulation

Space-Time Complexity in Hamiltonian Dynamics

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with ``flights'', trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially close trajectories. The complexity function is similar to the propagator p(t0,x0;t,x) with a replacement of x by the natural lengths s of trajectories, and its introduction does not assume of the space-time independence in the process of evolution of the system. A special stress is done on the choice of variables and the replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider time-algebraic and space-algebraic complexity and some mixed cases. It is shown that for typical cases the entropy function S(epsilon;xi,eta) possesses invariants (alpha,beta) that describe the fractal dimensions of the space-time structures of trajectories. The invariants (alpha,beta) can be linked to the transport properties of the system, from one side, and to the Riemann invariants for simple waves, from the other side. This analog provides a new meaning for the transport exponent mu that can be considered as the speed of a Riemann wave in the log-phase space of the log-space-time variables. Some other applications of new notions are considered and numerical examples are presented.Comment: 27 pages, 6 figure

Irreducible components of the moduli space of rank 2 sheaves of odd determinant on the projective space

We describe new irreducible components of the moduli space of rank $2$ semistable torsion free sheaves on the three-dimensional projective space whose generic point corresponds to non-locally free sheaves whose singular locus is either 0-dimensional or consists of a line plus disjoint points. In particular, we prove that the moduli spaces of semistable sheaves with Chern classes $(c_1,c_2,c_3)=(-1,2n,0)$ and $(c_1,c_2,c_3)=(0,n,0)$ always contain at least one rational irreducible component. As an application, we prove that the number of such components grows as the second Chern class grows, and compute the exact number of irreducible components of the moduli spaces of rank 2 semistable torsion free sheaves with Chern classes $(c_1,c_2,c_3)=(-1,2,m)$ for all possible values for $m$; all components turn out to be rational. Furthermore, we also prove that these moduli spaces are connected, showing that some of sheaves here considered are smoothable

New moduli components of rank 2 bundles on projective space

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to construct a new infinite series of rational moduli components of stable rank two vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank two vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components

Prediction of the Material Composition of the VVER-type Reactor Burned Pellet with Use of Neutron-Physical Codes

The purpose of neutron-physical calculations is typically isotopic composition of the fuel elements. However, in solving materials science problems related to nuclear fuel, researchers are usually interested in elemental composition of the fuel pellets, because the chemical and thermal physic properties are the same for differentisotopes of one chemical element. Nevertheless, for modeling of the elemental composition one should perform calculation of the isotopic composition and carry out the summation over all isotopes of a given chemical element. The development of computational tools allows the use of improved methods and codes, which held the consequent solution of tasks of heat conduction, neutron transport, and kinetics ofnuclides transformation. Thus the calculations take into account the dependence of the thermal conductivity from the changing isotopic composition and fuel burnup. This allows to perform neutron-physical and thermal-physical calculations of the reactor with detailed temperature distribution, taking into account temperature dependence of thermal conductivity and other characteristics. This approach was applied to calculations of the fuel pellet of the VVER type reactor and calculation of its elemental composition. Keywords: materials science, elemental composition, fuel pellet