# Anna KirpichnikovaUniversity of Stirling · Department of Computing Science and Mathematics

Anna Kirpichnikova

PhD Mathematics

## About

32

Publications

2,695

Reads

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383

Citations

Citations since 2017

Introduction

I am interested in various applications of mathematical modelling related to the investigation of wave propagation in various multi-component/non-homogeneous/layered structures, including inverse problems, Wave focusing in unknown media, asymptotical methods and numerical analysis of wave propagation, wave propagation in inhomogeneous elasticity, diffraction problems. Also I am working on cardiac modelling of unhealthy cell and game-theoretic approach to MANETs performance improvement.

Additional affiliations

September 2013 - January 2015

April 2010 - July 2013

Education

October 2010 - October 2013

December 2001 - November 2005

September 2000

**Petersburg Department steklov's Mathematical Institute**

Field of study

## Publications

Publications (32)

There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this there is no "gold standard" for model development and assessment in QSP. Moreove...

Abstract: In this contribution we consider the problem of optimal drone positioning for improving the operation of a mobile ad hoc network. We build upon our previous results devoted to the application of game-theoretic methods for computing optimal strategies. One specific problem that arises in this context is that the optimal solution cannot be...

We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic Neumann-to-Dirichlet map $\Lambda$ that corresponds to the physical measurements on the boundary. Using the knowledge of $\Lambd...

We construct shadow creeping waves in the problem of a plane wave diffraction by a smooth axially symmetric prolate body of revolution for both Dirichlet and Neumann boundary conditions. Using Fock's asymptotics as the initial data for the creeping wave amplitude, the theory of residues allows us to present the wave field in the main approximation.

This paper explores the effect that transmission power has on the performance of a Mobile Ad hoc Network (MANET). The goal of this research is to determine if the lifetime of the network can be prolongated by using less energy and thus, resulting in a more energy efficient ‘greener’ architecture. A total of 72 unique simulations are conducted of va...

This paper continues a series of publications on the shortwave diffraction of the plane wave on prolate bodies of revolution with axial symmetry in the Neumann problem. The approach, which is based on the Leontovich–Fock parabolic equation method for the two parameter asymptotic expansion of the solution, is briefly described. Two correction terms...

We describe a novel game-theoretic formulation of the optimal mobile agents’ placement problem which arises in the context of Mobile Ad-hoc Networks (MANETs). This problem is modelled as a sequential multistage game. The definitions of both the Nash equilibrium
and cooperative solution are given. A modification was proposed to ensure the existence...

Poster was prepared for the Science Week 2018

Against a backdrop of global antibiotic resistance and increasing awareness of the importance of the human microbiota, there has been resurgent interest in the potential use of bacteriophages for therapeutic purposes, known as phage therapy. A number of phage therapy phase I and II clinical trials have concluded, and shown phages don't present sign...

In this paper, we describe a novel game-theoretic formulation of the optimal mobile agents placement problem which arises in the context of Mobile Ad-hoc Networks (MANETs). In particular, we consider two classes of multistage games: sequential and simultaneous. For such games, the definitions of the Nash equilibria and the cooperative solution are...

We investigated whether subjective visual complexity (VC) and aesthetic pleasure (AP) of images are reflected in eye movement parameters. Participants (N=26; 13 females) explored greyscale car front images (N=50) while their eye movements were recorded. Following each image exposure (10 sec), image VC and AP were rated on 9-point scales. We found t...

With the help of the asymptotic boundary layer method, the transformation of an elastic SH-polarized surface wave of whispering gallery type (the so-called Love wave) is analyzed in the case where this wave passes many times through a vertical layer between two half-planes, Bibliography: 6 titles.

The SV polarized wave field is investigated in an elastic gradient layer of constant width. A point source is situated on the boundary of the layer. Rigid contact conditions are assumed to be valid on the boundary between the layer and an elastic half-space. It is shown that the interference field in the principal approximation far from the source...

We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider how to focus waves, that is, how to find Neumann boundary values so that at a given time the corresponding wav...

We consider an admissible Riemannian polyhedron with piece-wise smooth boundary. The associated Laplace defines the boundary spectral data as the set of eigenvalues and restrictions to the boundary of the corresponding eigenfunctions. In this paper we prove that the boundary spectral data prescribed on an open subset of the polyhedron boundary dete...

A region that consists of two parts with anisotropic Riemannian metrics is considered. The metric has a jump on the interface.
Asymptotic solutions of the wave equation, reflected and transmitted from the interface, i.e., Gaussian beams (“quasiphotons”),
are constructed. Bibliography: 7 titles.

The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in a layer is investigated. The obstacle is assumed to be an elliptic cylinder whose diameter and focal distance are small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a point source, and its amplitud...

The problem on the diffraction of the electromagnetic plane wave on the impedance interface between two media is investigated. The impedance is assumed to be different from a constant on a segment of the interface, where the impedance is described by piecewise-linear, quadratic, or step functions. Bibliography: 4 titles.

The problem of diffraction of creeping waves by a line of jump of curvature in a three-dimensional acoustic medium is studied. Moreover, a sufficiently ``oblique'' incidence is taken into account. Two cases of the curvature jump on the conjunction line of surfaces are considered: (i) the curvature does not change sign, but changes value, (ii) the s...

We consider the problem of diffraction of a short-wave field by a
cylindrical body with the boundary that consists of a half plane and a
convex-cylindrical surface jointed together along a straight line. The
main feature of the problem under consideration is the jump of curvature
of the boundary on the line. The problems with the Dirichlet, Neumann...

The problem of the diffraction of creeping waves on a point of transition of the convex boundary to the straight boundary of a domain is investigated. It is assumed that at the point of jump of curvature, the tangent to the boundary is continuous and it's derivative has a jump.. It is also assumed that that point of jump is situated in the penumbra...

We consider the diffraction of shortwave radiation by a convex body with the boundary having a jump of curvature. In cross-section the boundary consists of two parts: convex and planar, smoothly joined. A special case of diffraction by the curve with the curvature jump is under consideration: the jump point is situated in the penumbra region. Using...

The problem of diffraction of an electromagnetic plane wave on the impedance interface between two media is investigated. The impedance differs from constant on a segment of the interface, where the impedance is described by piecewise linear, quadratic or step functions

A problem of diffraction of creeping waves on a point of transition of a convex boundary to a convex boundary is investigated. It is assumed that at the point of a jump of curvature, the tangent to the boundary is continuous and its derivative has a jump. An expression for the edge wave is obtained and investigated