Precursor Synthesis and Properties of Nanodispersed Tungsten Carbide and WC:nC Nanocomposites

This work was supported by Act 211 Government of the Russian Federation, agreement No. 02.A03.21.0006

Numerical Modeling of the Internal Temperature in the Mammary Gland

The microwave thermometry method for the diagnosis of breast cancer is based on an analysis of the internal temperature distribution.This paper is devoted to the construction of a mathematical model for increasing the accuracy of measuring the internal temperature of mammary glands, which are regarded as a complex combination of several components, such as fat tissue, muscle tissue, milk lobules, skin, blood flows, tumor tissue. Each of these biocomponents is determined by its own set of physical parameters. Our numerical model is designed to calculate the spatial distributions of the electric microwave field and the temperature inside the biological tissue. We compare the numerical simulations results to the real medical measurements of the internal temperature.Comment: 8 pages, 4 figure

Software for full-color 3D reconstruction of the biological tissues internal structure

A software for processing sets of full-color images of biological tissue histological sections is developed. We used histological sections obtained by the method of high-precision layer-by-layer grinding of frozen biological tissues. The software allows restoring the image of the tissue for an arbitrary cross-section of the tissue sample. Thus, our method is designed to create a full-color 3D reconstruction of the biological tissue structure. The resolution of 3D reconstruction is determined by the quality of the initial histological sections. The newly developed technology available to us provides a resolution of up to 5 - 10 {\mu}m in three dimensions.Comment: 11 pages, 8 figure

Gauge-theoretic invariants for topological insulators: A bridge between Berry, Wess-Zumino, and Fu-Kane-Mele

We establish a connection between two recently-proposed approaches to the understanding of the geometric origin of the Fu-Kane-Mele invariant $\mathrm{FKM} \in \mathbb{Z}_2$, arising in the context of 2-dimensional time-reversal symmetric topological insulators. On the one hand, the $\mathbb{Z}_2$ invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes it is possible to provide an expression for $\mathrm{FKM}$ containing the square root of the Wess-Zumino amplitude for a certain $U(N)$-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above mentioned Wess-Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov-Wiegmann formula for fields $\mathbb{T}^2 \to U(N)$, of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.Comment: 23 pages, 1 figure. To appear in Letters in Mathematical Physic

Exotic Anti-Decuplet of Baryons: Prediction from Chiral Solitons

We predict an exotic Z^+ baryon (having spin 1/2, isospin 0 and strangeness +1) with a relatively low mass of about 1530 MeV and total width of less than 15 MeV. It seems that this region of masses has avoided thorough searches in the past.Comment: Revised version, to appear in Z. fuer Phys. A. The importance of 1/Nc corrections to antidecuplet widths is demonstrated. 21 pages, 1 LaTeX figur

Analytic Continuation of Liouville Theory

Correlation functions in Liouville theory are meromorphic functions of the Liouville momenta, as is shown explicitly by the DOZZ formula for the three-point function on the sphere. In a certain physical region, where a real classical solution exists, the semiclassical limit of the DOZZ formula is known to agree with what one would expect from the action of the classical solution. In this paper, we ask what happens outside of this physical region. Perhaps surprisingly we find that, while in some range of the Liouville momenta the semiclassical limit is associated to complex saddle points, in general Liouville's equations do not have enough complex-valued solutions to account for the semiclassical behavior. For a full picture, we either must include "solutions" of Liouville's equations in which the Liouville field is multivalued (as well as being complex-valued), or else we can reformulate Liouville theory as a Chern-Simons theory in three dimensions, in which the requisite solutions exist in a more conventional sense. We also study the case of "timelike" Liouville theory, where we show that a proposal of Al. B. Zamolodchikov for the exact three-point function on the sphere can be computed by the original Liouville path integral evaluated on a new integration cycle.Comment: 86 pages plus appendices, 9 figures, minor typos fixed, references added, more discussion of the literature adde

Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays

We study transition form factors for radiative and rare semi-leptonic B-meson decays into light pseudoscalar or vector mesons, combining theoretical constraints and phenomenological information from Lattice QCD, light-cone sum rules, and dispersive bounds. We pay particular attention to form factor parameterisations which are based on the so-called series expansion, and study the related systematic uncertainties on a quantitative level. In this context, we also provide the NLO corrections to the correlation function between two flavour-changing tensor currents, which enters the unitarity constraints for the coefficients in the series expansion.Comment: 52 pages; v2: normalization error in (29ff.) corrected, conclusion about relevance of unitarity bounds modified; form factor fits unaffected; references added; v3: discussion on truncation of series expansion added, matches version to be published in JHEP; v4: corrected typos in Tables 5 and

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

Unified framework for generalized and transverse-momentum dependent parton distributions within a 3Q light-cone picture of the nucleon

We present a systematic study of generalized transverse-momentum dependent parton distributions (GTMDs). By taking specific limits or projections, these GTMDs yield various transverse-momentum dependent and generalized parton distributions, thus providing a unified framework to simultaneously model different observables. We present such simultaneous modeling by considering a light-cone wave function overlap representation of the GTMDs. We construct the different quark-quark correlation functions from the 3-quark Fock components within both the light-front constituent quark model as well as within the chiral quark-soliton model. We provide a comparison with available data and make predictions for different observables.Comment: version to appear in JHE

Imaging the Partonic Structure of the Nucleon

We discuss the main properties of different types of parton distribution functions, which provide complementary multidimensional images of the partonic structure of the nucleon. These distributions are the generalized parton distributions, the transverse-momentum dependent parton distributions and the Wigner distributions. They have attracted increasing attention in the last years as they represent new tools to study how the composite structure of the proton results from the underlying quark-gluon dynamics