Shielding of absorbing objects in collisionless flowing plasma

The electrostatic shielding of a charged absorbing object (dust grain) in a flowing collisionless plasma is investigated by using the linearized kinetic equation for plasma ions with a point-sink term accounting for ion absorption on the object. The effect of absorption on the attractive part of the grain potential is investigated. For subthermal ion flows, the attractive part of the grain potential in the direction perpendicular to the ion flow can be significantly reduced or completely destroyed, depending on the absorption rate. For superthermal ion flows, however, the effect of absorption on the grain attraction in the direction perpendicular to the ion flow is shown to be exponentially weak. It is thus argued that, in the limit of superthermal ion flow, the effect of absorption on the grain shielding potential can be safely ignored for typical grain sizes relevant to complex plasmas.Comment: 25 pages, 3 figure

Thermal Duality and Hagedorn Transition from p-adic Strings

We develop the finite temperature theory of p-adic string models. We find that the thermal properties of these non-local field theories can be interpreted either as contributions of standard thermal modes with energies proportional to the temperature, or inverse thermal modes with energies proportional to the inverse of the temperature, leading to a "thermal duality" at leading order (genus one) analogous to the well known T-duality of string theory. The p-adic strings also recover the asymptotic limits (high and low temperature) for arbitrary genus that purely stringy calculations have yielded. We also discuss our findings surrounding the nature of the Hagedorn transition.Comment: 4 pages and 4 figure

Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees

We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization. Using the explicit expression for eigenvalues of such matrices, we compute the spectral density for the Gaussian distribution of matrix elements. We also compute the averaged "survival probability" (SP) having sense of the probability to find a system in the initial state by time $t$. Using the similarity between the averaged SP for locally constant randomized Parisi matrices and the partition function of directed polymers on disordered trees, we show that for times $t>t_{\rm cr}$ (where $t_{\rm cr}$ is some critical time) a "lacunary" structure of the ultrametric space occurs with the probability $1-{\rm const}/t$. This means that the escape from some bounded areas of the ultrametric space of states is locked and the kinetics is confined in these areas for infinitely long time.Comment: 7 pages, 2 figures (the paper is essentially reworked

Dispersion and damping of potential surface waves in a degenerate plasma

Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide range of wavelengths. In the limit of long wavelengths, the wave frequency $\omega$ approaches the cold-plasma limit $\omega=\omega_p/\sqrt{2}$ with $\omega_p$ being the plasma frequency, while at short wavelengths, the wave spectrum asymptotically approaches the spectrum of zero-sound mode propagating along the boundary. It is shown that the surface waves in this system remain weakly damped at all wavelengths (in contrast to strongly damped surface waves in Maxwellian electron plasmas), and the damping rate nonmonotonically depends on the wavelength, with the maximum (yet small) damping occuring for surface waves with wavelength of $\approx5\pi\lambda_{F}$, where $\lambda_{F}$ is the Thomas-Fermi length.Comment: 22 pages, 6 figure

Application of Speckle Dynamics and Raman Light Scattering to Study the Fracture Features of Pipe Steel at High-cycle Fatigue

Despite a long history of research and a large number of publications, currently there are no methods for assessing and calculating the residual life of structural elements with their multi-cycle fatigue that would meet the requirements of engineering practice. In this regard, the role of physical methods to record the features of accumulation of local fatigue damage without stopping the operation or testing of various objects for fatigue increases. In the article two laser methods are used to study the origin of fatigue crack. Earlier, after testing for high-cycle fatigue of polished steel specimen with a Charpy notch, two zones of different sizes with different roughness were found near the notch. The first zone of 50x100 μm was located directly on the top of the notch. It consisted of inhomogeneities up to 10 μm in diameter and about 100 nm in height. In the center of the zone a macro-crack was discovered. The second zone with a diameter of 500-700 microns had a form of a hole (tie) with a depth of about 1 micron. Its center was located at a distance of 250-300 microns from the top of the notch. The aim of the work was to determine the formulation of inhomogeneities in a small zone and the sequence of the two zones’ occurrence. By using Raman microscopy, it is shown that the inhomogeneities are pieces of iron carbide. By the peculiarities of speckle image changes it is shown that the formation of two zones begins almost simultaneously. After the origination of a macro crack with a length of about 100 microns, a new plasticity zone at its top begins to form. Possible formation mechanisms of two zones are discussed. The disadvantages of the speckle method and the direction of further research are considered. © PNRPU.The authors thank I. S. Kamentsev, N.. Drukarenko, I. Tikhonova for help with sample preparation and fatigue testing. The work was carried out on the equipment of centers for collective use " Plastometry" of Institute of Engineering Science of Ural Branch of RAS and " Nanomaterials and Nanotechnology" of Ural Federal University with partial funding RFBR grant № 16-08-01077_a and act 211 of Government of the Russian Federation, agreement No. 02.A03.21.0006

The Epstein-Glaser approach to pQFT: graphs and Hopf algebras

The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudo-unitarity, causality and an associated regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on the operator-valued distributions which are equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well-defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the physical framework, which covers the two recent EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occuring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the EG framework is modeled via a HA which can be seen as the EG-analog of Kreimer's HA.Comment: 52 pages, 5 figure

A representation formula for maps on supermanifolds

In this paper we analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a representation formula for all morphisms from the algebra of functions on an ordinary manifolds to the superalgebra of functions on an open subset of R^{p|q}. We then derive two consequences of this result. The first one is that we can integrate the data associated with a morphism in order to get a (non unique) map defined on an ordinary space (and uniqueness can achieved by restriction to a scheme). The second one is a simple and intuitive recipe to compute pull-back images of a function on a manifold by a map defined on a superspace.Comment: 23 page

Criticality in a Vlasov-Poisson system - a fermionic universality class

A model Vlasov--Poisson system is simulated close the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power--law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality $d=5$ below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead it corresponds to the propagator for the fermionic {\it vector} field and to the {\it upper critical dimensionality} $d_c=2$. This suggests criticality of collisionless Vlasov-Poisson systems as representative of the {\it universality class} of critical phenomena of {\it a fermionic} quantum field description.Comment: 10 pages, 6 figures, Submitted to Phys. Rev.

Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory

We show, that classical Kaluza-Klein theory possesses hidden nematic dynamics. It appears as a consequence of 1+4-decomposition procedure, involving 4D observers 1-form \lambda. After extracting of boundary terms the, so called, "effective matter" part of 5D geometrical action becomes proportional to square of anholonomicity 3-form \lambda\wedge d\lambda. It can be interpreted as twist nematic elastic energy, responsible for elastic reaction of 5D space-time on presence of anholonomic 4D submanifold, defined by \lambda. We derive both 5D covariant and 1+4 forms of 5D nematic equilibrium equations, consider simple examples and discuss some 4D physical aspects of generic 5D nematic topological defects.Comment: Latex-2e, 14 pages, 1 Fig., submitted to GR