Minimal cubic cones via Clifford algebras

We construct two infinite families of algebraic minimal cones in $R^{n}$. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one correspondence with those of geometrically equivalent Clifford systems. As a byproduct, we prove that for any $n\ge4$, $n\ne 16k+1$, there is at least one minimal cone in $R^{n}$ given by an irreducible homogeneous cubic polynomial. The second family consists of minimal cones in $R^{m^2}$, $m\ge2$, defined by an irreducible homogeneous polynomial of degree $m$. These examples provide particular answers to the questions on algebraic minimal cones posed by Wu-Yi Hsiang in the 1960's.Comment: Final version, corrects typos in Table

Violation of Lorentz Invariance and neutral component of UHECR

The observed clustering of ultra-high energy cosmic rays suggests the existence of a neutral component. The models with violation of Lorentz invariance may explain this component by neutrons becoming stable above some threshold energy E_0. The protons, in turn, may become unstable above some energy E_1>E_0. We calculate the dependence of the threshold energies E_0 and E_1 on the parameters of the model and find E_1/E_0\gsim 1.5. We argue that the characteristic threshold behavior of charged and neutral components may be used as the specific signature of models with violation of Lorentz invariance. The existence of the neutron stability threshold E_0 can be investigated with already existing data.Comment: 14 pages, 2 figure

First-order nonthermal phase transition after preheating

During preheating after inflation, parametric resonance rapidly generates very large fluctuations of scalar fields. In models where the inflaton field $\phi$ oscillates in a double-well potential and interacts with another scalar field $X$, fluctuations of X can keep the \phi to -\phi symmetry temporarily restored. If the coupling of \phi to X is much stronger than the inflaton self-coupling, the subsequent symmetry breaking is a first-order phase transition. We demonstrate the existence of this nonthermal phase transition with lattice simulations of the full nonlinear dynamics of the interacting fields. In particular, we observe nucleation of an expanding bubble.Comment: RevTeX, 4 page

The modern methods of reproduction physiology of horses

The concept of development of horse breeding in Ukraine until 2020 provides for an increase in the number of horses through the intensive use of modern methods of reproduction biotechnology. However, the imperfection of these methods hinders their widespread use in practice. The aim of the work was to draw attention to the most important problems of the physiology of horse reproduction in Ukraine and to show ways to solve them that have already been proposed by domestic and foreign researchers. The development strategy of the physiology of horse reproduction in order to increase its effectiveness should take into account the least studied aspects that were discussed above. The article shows that taking into account the influence of micromycetes, the absolute number of colony forming units of E. coli in semen of stallions; immuno-and cytogenetic features; new methods of sanitary preparation of horses for sperm and insemination; the effect of permissible levels of feed mycotoxins on physiological functions improves the efficiency of equine reproduction physiology methods. However, we first discovered new physiological features of the effect of erythrocyte antigens of blood groups of horses of Ukrainian selection on the indicators of their native sperm. In the presence of ad/bcm and dg/cgm alleles of the blood group D system in stallions, sperm motility is on average less than 5 points; alleles ad/cgm, ad/d, ad/de, ad/dk, bcm/d, bcm/de, bcm/dg, bcm/dk, cegm/cgm, cegm/d, cegm/dg, cegm/dk, cgm/ceg, cgm/cgm, cgm/dg, cgm/dk, de/cgm, de/dk, dg/di, dk/d, dk/de, dk/dk is accompanied by sperm motility from 5 to 7 points; alleles bcm/cgm, dg/dk, de/d, cgm/d, cgm/de sperm motility is observed more than 7 points. The results obtained allowed us to develop for practice ways to increase the efficiency of sperm cryopreservation by immunogenetic parameters. In addition, open physiological correlations can increase the fertility of mares during mating

Reheating and thermalization in a simple scalar model

We consider a simple model for the Universe reheating, which consists of a single self--interacting scalar field in Minkowskian space--time. Making use of the existence of an additional small parameter proportional to the amplitude of the initial spatially homogeneous field oscillations, we show that the behavior of the field can be found reliably. We describe the evolution of the system from the homogeneous oscillations to the moment when thermalization is completed. We compare our results with the Hartree--Fock approximation and argue that some properties found for this model may be the common features of realistic theories.Comment: Some changes in Introduction and Discussion, comparison with the Hartree--Fock results added. 37 pages, 2 postscript figures attache

Evolution of the Order Parameter after Bubble Collisions

If a first-order phase transition is terminated by collisions of new-phase bubbles, there will exist a period of nonequilibrium between the time bubbles collide and the time thermal equilibrium is established. We study the behavior of the order parameter during this phase. We find that large nonthermal fluctuations at this stage tend to restore symmetry, i.e., the order parameter is smaller than its eventual thermal equilibrium value. We comment on possible consequences for electroweak baryogenesis.Comment: 11 page LaTeX file with two figures, fig1.ps and fig2.p

Resonant Production of Topological Defects

We describe a novel phenomenon in which vortices are produced due to resonant oscillations of a scalar field which is driven by a periodically varying temperature T, with T remaining much below the critical temperature $T_c$. Also, in a rapid heating of a localized region to a temperature {\it below} $T_c$, far separated vortex and antivortex can form. We compare our results with recent models of defect production during reheating after inflation. We also discuss possible experimental tests of our predictions of topological defect production {\it without} ever going through a phase transition.Comment: Revtex, 13 pages including 5 postscript figure