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Andrey Mironov

Publications and source records attributed to Andrey Mironov.

10 recordsLinked to original sources
arXiv2026

Simultaneous amplification and shaping of excimer lasers using Stimulated Brillouin Scattering in the strongly damped limit

Attaining practical Inertial Fusion Energy (IFE) depends on how efficiently one can couple the driver energy to the nuclear fusion fuel for compression and ignition. While the excimer lasers provide an efficient alternative compared to existing laser technology, it is unclear how the lasers can be harnessed to form a pulse with desired pulse shape and intensity. Stimulated Brillouin Scattering (SBS) provides a path to compressing long, energetic pulses to short intense ones. We consider the equations governing SBS in the Strongly Damped Limit (SDL) and find that it is possible to almost completely specify the final pulse shape by providing an appropriate initial seed pulse. We provide analytic expressions for reverse-engineering the initial seed shape and delineate physical limits concerning the prepulse level.

physics.optics↗
arXiv2026

friends.test: rank-based method for feature selection in interaction matrices

The analysis of the interaction matrix between two distinct sets is essential across diverse fields, from pharmacovigilance to transcriptomics. Not all interactions are equally informative: a marker gene associated with a few specific biological processes is more informative than a highly expressed non-specific gene associated with most observed processes. Identifying these interactions is challenging due to background connections. Furthermore, data heterogeneity across sources precludes universal identification criteria. To address this challenge, we introduce \textsf{friends.test}, a method for identifying specificity by detecting structural breaks in entity interactions. Rank-based representation of the interaction matrix ensures invariance to heterogeneous data and allows for integrating data from diverse sources. To automatically locate the boundary between specific interactions and background activity, we employ model fitting. We demonstrate the applicability of \textsf{friends.test} on the GSE112026 -- transnational data from head and neck cancer. A computationally efficient \textsf{R} implementation is available at https://github.com/favorov/friends.test.

q-bio.QM↗
arXiv2019

Wire billiards, the first steps

Wire billiard is defined by a smooth embedded closed curve of non-vanishing curvature $k$ in $\mathbb{R}^n$ (a wire). For a class of curves, that we call nice wires, the wire billiard map is area preserving twist map of the cylinder. In this paper we are investigating whether the basic features of conventional planar billiards extend to this more general situation. In particular, we extend Lazutkin's KAM result, as well as Mather's converse KAM result, to wire billiards. We address the notion of caustics: for wire billiards, it corresponds to striction curve of the ruled surface spanned by the chords of the invariant curve. If the ruled surface is developable this is a genuine caustic. We found remarkable examples of the wires which are closed orbits of 1-parameter subgroup of $SO(n)$. These wire billiards are totally integrable. Using the theory of interpolating Hamiltonians, we prove that the distribution of impact points of the wire becomes uniform with respect to the measure $k^{2/3} dx$ (where $x$ is the arc length parameter), as the length of the chords tends to zero. Applying this result, we prove that the billiard transformation in an ellipsoid commutes with the reparameterized geodesic flow on a confocal ellipsoid: the speed of the foot point of the line tangent to a geodesic equals $k^{-2/3}$, where $k$ is the curvature of the geodesic in the ambient space. We also discuss perspectives and open problems of this new class of billiards.

math.DS↗
arXiv2017

In search of periodic solutions for a reduction of the Benney chain

We search for smooth periodic solutions for the system of quasi-linear PDEs known as the Lax dispersionless reduction of the Benney moments chain. It is naturally related to the existence of a polynomial in momenta integral for a Classical Hamiltonian system with 1,5 degrees of freedom. For the solution in question it is not known a-priori if the system is elliptic or hyperbolic or of mixed type. We consider two possible regimes for the solution. The first is the case of only one real eigenvalue, where we can completely classify the solutions. The second case of strict Hyperbolicity is really a challenge. We find a remarkable 2 by 2 reduction which is strictly Hyperbolic but violates the condition of genuine non-linearity.

math-ph↗
arXiv2013

Hamiltonian minimal Lagrangian submanifolds in toric varieties

Hamiltonian minimality (H-minimality) for Lagrangian submanifolds is a symplectic analogue of Riemannian minimality. A Lagrangian submanifold is called H-minimal if the variations of its volume along all Hamiltonian vector fields are zero. This notion was introduced in the work of Y.-G. Oh in connection with the celebrated Arnold conjecture on the number of fixed points of a Hamiltonian symplectomorphism. In the previous works the authors defined and studied a family of H-minimal Lagrangian submanifolds in complex space arising from intersections of Hermitian quadrics. Here we extend this construction to define H-minimal submanifolds in toric varieties.

math.DG↗
arXiv2013

Intersections of quadrics, moment-angle manifolds, and Hamiltonian-minimal Lagrangian embeddings

We study the topology of Hamiltonian-minimal Lagrangian submanifolds N in C^m constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the well-known Delzant construction of Hamiltonian toric manifolds. We establish the following topological properties of N: every N embeds as a submanifold in the corresponding moment-angle manifold Z, and every N is the total space of two different fibrations, one over the torus T^{m-n} with fibre a real moment-angle manifold R, and another over a quotient of R by a finite group with fibre a torus. These properties are used to produce new examples of Hamiltonian-minimal Lagrangian submanifolds with quite complicated topology.

math.SG↗
arXiv2013

Cubic and Quartic integrals for geodesic flow on 2-torus via system of Hydrodynamic type

In this paper we deal with the classical question of existence of polynomial in momenta integrals for geodesic flows on the 2-torus. For the quasi-linear system on coefficients of the polynomial integral we consider the region (so called elliptic regions) where there are complex-conjugate eigenvalues. We show that for quartic integrals in the other two eigenvalues are real and genuinely nonlinear. This observation together with the property of the system to be Rich (Semi-Hamiltonian) enables us to classify elliptic regions completely. The case of complex-conjugate eigenvalues for the system corresponding to the integral of degree 3 is done similarly. These results show that if new integrable examples exist they could be found only within the region of Hyperbolicity of the quasi-linear system.

math.DG↗
arXiv2011

New Semi-Hamiltonian hierarchy related to integrable magnetic flows on surfaces

We consider magnetic geodesic flows on the 2-torus. We prove that the question of existence of polynomial in momenta first integrals on one energy level leads to a Semi-Hamiltonian system of quasi-linear equations, i.e. in the hyperbolic regions the system has Riemann invariants and can be written in conservation laws form.

math-ph↗
arXiv2010

Baker-Akhiezer Modules on the Intersections of Shifted Theta Divisors

The restriction, on the spectral variables, of the Baker-Akhiezer (BA) module of a g-dimensional principally polarized abelian variety with the non-singular theta divisor to an intersection of shifted theta divisors is studied. It is shown that the restriction to a k-dimensional variety becomes a free module over the ring of differential operators in $k$ variables. The remaining g-k derivations define evolution equations for generators of the BA-module. As a corollary new examples of commutative ring of partial differential operators with matrix coefficients and their non-trivial evolution equations are obtained.

math.AG↗