arXiv subjects

Alexander Grigoriev

Publications and source records attributed to Alexander Grigoriev.

33 records · Page 2Linked to original sources

arXiv2015

High Multiplicity Scheduling with Switching Costs for few Products

We study a variant of the single machine capacitated lot-sizing problem with sequence-dependent setup costs and product-dependent inventory costs. We are given a single machine and a set of products associated with a constant demand rate, maximum loading rate and holding costs per time unit. Switching production from one product to another incurs sequencing costs based on the two products. In this work, we show that by considering the high multiplicity setting and switching costs, even trivial cases of the corresponding "normal" counterparts become non-trivial in terms of size and complexity. We present solutions for one and two products.

math.OC↗

arXiv2014

On low treewidth graphs and supertrees

Compatibility of unrooted phylogenetic trees is a well studied problem in phylogenetics. It asks to determine whether for a set of k input trees there exists a larger tree (called a supertree) that contains the topologies of all k input trees. When any such supertree exists we call the instance compatible and otherwise incompatible. It is known that the problem is NP-hard and FPT, although a constructive FPT algorithm is not known. It has been shown that whenever the treewidth of an auxiliary structure known as the display graph is strictly larger than the number of input trees, the instance is incompatible. Here we show that whenever the treewidth of the display graph is at most 2, the instance is compatible. Furthermore, we give a polynomial-time algorithm to construct a supertree in this case. Finally, we demonstrate both compatible and incompatible instances that have display graphs with treewidth 3, highlighting that the treewidth of the display graph is (on its own) not sufficient to determine compatibility.

cs.DM↗

arXiv2013

Nearly Planar Graphs and λ-flat Graphs

A graph G is ξ-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most ξ times. The family of ξ-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative parameterized graph family extending the notion of planarity, the λ-flat graphs, this time defined as powers of plane graphs in regard to a novel notion of distance, the wall-by-wall distance. We show that the two parameterized graph classes are parametrically equivalent.

math.CO↗

arXiv2013

Bidimensionality of Geometric Intersection Graphs

Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection graphs GB where each body of the collection B is represented by a vertex, and two vertices of GB are adjacent if the intersection of the corresponding bodies is non-empty. For such graph classes and under natural restrictions on their maximum degree or subgraph exclusion, we prove that the relation between their treewidth and the maximum size of a grid minor is linear. These combinatorial results vastly extend the applicability of all the meta-algorithmic results of the bidimensionality theory to geometrically defined graph classes.

cs.DM↗

arXiv2010

Spin light in neutrino transition between different mass states

The spin light of neutrino is considered in the process of a neutrino radiative transition between two different mass states in presence of medium. By this study we investigate the influence of background matter on the initial and final neutrino states in the process of massive Dirac neutrino decay due to the non-zero transition magnetic moment. We derive corresponding corrections to the total width of the process over the matter density in most important for applications cases.

hep-ph↗

arXiv2009

Spin light mode of massive neutrino radiative decay in matter

Using the exact solutions for the Dirac neutrino wave function in presence of matter we study the spin light mode in the process of neutrino transition from initial heavier to final lighter state. The spin light is emitted due to the neutrino nonzero transitional magnetic moment.

hep-ph↗

arXiv2008

Dirac and Majorana neutrinos in matter

We consider the matter effects on neutrinos moving in background on the basis of the corresponding quantum wave equations. Both Dirac and Majorana neutrino cases are discussed. The effects for Dirac neutrino reflection and trapping as well as neutrino-antineutrino annihilation and $ν\overlineν$ pair creation in matter at the interface between two media with different densities are considered. The spin light of neutrino in matter is also discussed.

hep-ph↗

arXiv2008

Neutrino energy quantization in rotating medium

Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle moving in the presence of a constant magnetic field. Accordingly, the particle in the rotating matter has circle orbits with energy levels, analogous to the Landau levels in magnetic field. The relevant physical realization of the problem is motion of neutrino inside the rotating neutron star. The feature of such motion to form binding states leads to the prediction of the new mechanism for neutrino trapping. The solution found can be used for detailed description of relativistic and nearly massless neutrino dynamics in neutron stars. Results obtained further develop the "method of exact solutions" in application to particle interactions in presence of dense matter.

hep-ph↗

arXiv2006

Spin light of electron in dense matter

We derive the modified Dirac equation for an electron undergos an influence of the standard model interaction with the nuclear matter. The exact solutions for this equation and the electron energy spectrum in matter are obtained. This establishes a rather powerful method for investigation of different processes that can appear when electrons propagate in background matter. On this basis we study in detail the spin light of electron in nuclear matter, a new type of electromagnetic radiation which can be emitted by an electron moving in dense matter.

hep-ph↗

arXiv2006

Spin light of electron in matter

We further generalize the powerful method, which we have recently developed for description of the background matter influence on neutrinos, for the case of an electron moving in matter. On the basis of the modified Dirac equation for the electron, accounting for the standard model interaction with particles of the background, we predict and investigate in some detail a new mechanism of the electromagnetic radiation that is emitted by moving in matter electron due to its magnetic moment. We have termed this radiation the ``spin light of electron" in matter and predicted that this radiation can have consequences accessible for experimental observations in astrophysical and cosmological settings.

hep-ph↗

arXiv2006

Spin light of neutrino in matter: a new type of electromagnetic radiation

A short review of the properties of the spin light of neutrino ($SLν$) in matter, supplied with some historical notes on the discussed subject, is given. It is shown that consideration of the $SLν$ in matter in hep-ph/0605114 is based on erroneous calculations which ignore the fact that the energy-momentum conservation law can not be violated for this process. An attempt to rename the $SLν$ in matter, undertaken in hep-ph/0606262, is groundless.

hep-ph↗

arXiv2006

Reply to hep-ph/0605114

The claim of preprint hep-ph/0605114 that there is "no neutrino spin light because of photon dispersion in medium" is wrong.

hep-ph↗

arXiv2005

Spin Light of Neutrino in Dense Matter

We develop the quantum theory of the spin light of neutrino ($SLν$) exactly accounting for the effect of background matter. Contrary to the already performed studies of the $SLν$, in this paper we derive explicit and closed expressions for the $SLν$ rate and power and for the emitted photon energy, which are valid for an arbitrary matter density (including very high values). The spatial distribution of the radiation power and the dependence of the emitted photon energy on the direction of radiation are also studied in detail for the first time. We analyze the $SLν$ polarization properties and show that within a wide range of neutrino momenta and matter densities the $SLν$ radiation is circularly polarized. Conditions for effective $SLν$ photon propagation in the electron plasma are discussed. It is also shown that in dense matter the average energy of the emitted photon can reach values in the range from one third of the neutrino momentum up to one half of the neutrino energy in matter. The main features of the studied radiation are summarized, and possibilities for the $SLν$ production during different astrophysical and cosmology processes are discussed.

hep-ph↗

arXiv2005

Generalized Dirac-Pauli equation and spin light of neutrino in magnetized matter

We consider propagation of a massive neutrino in matter within the quantum approach based on the two equations for the neutrino field: the first one is the Dirac-Pauli equation for a massive neutrino in an external magnetic field generalized on the inclusion of effects of the background matter; the second one is the modified Dirac equation derived directly from the neutrino-matter interaction Lagrangian. On the basis of these two equations the quantum theory of a neutrino moving in the background matter is developed (the exact solutions of these equations are found and classified over the neutrino spin states, the corresponding energy spectra are also derived). Using these solutions we study within the quantum approach the spin light of neutrino ($SLν$) in matter with the effect of a longitudinal magnetic field being also incorporated. In particular, the $SLν$ radiation rate and total power are derived. The use of the generalized Dirac-Pauli equation also enables us to consider the $SLν$ in matter polarized under the influence of strong magnetic field.

hep-ph↗

arXiv2004

Spin light of neutrino in gravitational fields

We predict a new mechanism for the spin light of neutrino ($SLν$) that can be emitted by a neutrino moving in gravitational fields. This effect is studied on the basis of the quasiclassical equation for the neutrino spin evolution in a gravitational field. It is shown that the gravitational field of a rotating object, in the weak-field limit, can be considered as an axial vector external field which induces the neutrino spin procession. The corresponding probability of the neutrino spin oscillations in the gravitational field has been derived for the first time. The considered in this paper $SLν$ can be produced in the neutrino spin-flip transitions in gravitational fields. It is shown that the total power of this radiation is proportional to the neutrino gamma factor to the fourth power, and the emitted photon energy, for the case of an ultra relativistic neutrino, could span up to gamma-rays. We investigate the $SLν$ caused by both gravitational and electromagnetic fields, also accounting for effects of arbitrary moving and polarized matter, in various astrophysical environments. In particular, we discuss the $SLν$ emitted by a neutrino moving in the vicinity of a rotating neutron star, black hole surrounded by dense matter, as well as by a neutrino propagating in the relativistic jet from a quasar.

hep-ph↗