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V. Medvedev

Publications and source records attributed to V. Medvedev.

14 recordsLinked to original sources
arXiv2025

Nonsingular structural stable chaotic 3-flows of attractor-repeller type

We show that any orientable closed 3-manifold $M$ admits structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of a 2-dimensional expanding attractor and finitely many repelling periodic trajectories. For $M=\mathbb{S}^3$, we prove that the set of repelling periodic trajectories can be an arbitrary link provided that this link contains the figure eight knot. When a link consists of a unique repelling periodic trajectory (not necessarily a figure eight knot), we prove that this trajectory cannot be a torus knot. For any closed 3-manifold $M$, we show that there does not admit any structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of a 2-dimensional expanding attractor and a repelling periodic trajectory so that the repelling periodic trajectory is a trivial knot (i.e., it bounds a disk in $M$).

math.DS↗
arXiv2024

On existence of expanding attractors with different dimensions

We prove that $n$-sphere $\mathbb{S}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{S}^n\to\mathbb{S}^n$ with non-orientable expanding attractors of any topological dimension $d\in\{1,\ldots,[\frac{n}{2}]\}$ where $[x]$ is an integer part of $x$. One proves that $n$-torus $\mathbb{T}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{T}^n\to\mathbb{T}^n$ with orientable expanding attractors of any topological dimension $1\leq q\leq n-1$. We also prove that given any closed $n$-manifold $M^n$, $n\geq 2$, and any $d\in\{1,\ldots,[\frac{n}{2}]\}$, there is an axiom A diffeomorphism $f: M^n\to M^n$ with a $d$-dimensional non-orientable expanding attractor. Similar statements hold for axiom A flows.

math.DS↗
arXiv2024

On a classification of axiom A diffeomorphisms with codimension one basic sets and isolated saddles

Let $M^n$, $n\geq 3$, be a closed orientable $n$-manifold and $\mathbb{D}_k(M^n;a,b,c)$ the set of axiom A diffeomorp\-hisms $f: M^n\to M^n$ satisfying the following conditions: (1) $f$ has $k\geq 1$ nontrivial basic sets each is either an orientable codimension one expanding attractor or an orientable codimension one contracting repeller, and other trivial basic sets which are $a$ sinks, $b$ sources, $c$ saddles; (2) the invariant manifolds of isolated saddles are intersected transversally. We classify the diffeomorphisms from $\mathbb{D}_k(M^n;a,b,c)$ up to the global conjugacy on non-wandering sets for the following subsets $\mathbb{S}_k(M^n;a,b,c), \mathbb{P}_k(M^n;0,0,1), \mathbb{M}_k(M^n;0,0,1)$ of $\mathbb{D}_k(M^n;a,b,c)$ where $\mathbb{S}_k(M^n;a,b,c)$ satisfies to the following conditions: ($1_{\mathbb{S}}$) every nontrivial basic set of any $f\in\mathbb{S}_k(M^n;a,b,c)$ is uniquely bunched, and there is at least one nontrivial attractor and at least one nontrivial repeller, i.e. $k\geq 2$; ($2_{\mathbb{S}}$) $c\geq 1$ and all isolated saddles have the same Morse index belonging to $\{1,n-1\}$. The subset $\mathbb{P}_k(M^n;0,0,1)\subset\mathbb{D}_k(M^n;0,0,1)$ satisfies to the following conditions: ($1_{\mathbb{P}}$) any boundary point of $f\in\mathbb{P}_k(M^n;0,0,1)$ is fixed; ($2_{\mathbb{P}}$) a unique isolated saddle has Morse index different from $\{1,n-1\}$. The subset $\mathbb{M}_k(M^n;0,0,1)\subset\mathbb{D}_k(M^n;0,0,1)$ satisfies to the following conditions: ($1_{\mathbb{M}}$) any boundary point of $f\in\mathbb{M}_k(M^n;0,0,1)$ is fixed; ($2_{\mathbb{M}}$) a unique isolated saddle has Morse index belonging to $\{1,n-1\}$. The classification is based on a description of topological structure of supporting manifolds $M^n$.

math.DS↗
arXiv2022

Dynamics of H atoms surface recombination in low-temperature plasma

The dynamics of H atom recombination on materials of interest for a EUV lithographer was studied under a longterm low-pressure H2 plasma exposure. The similarity of the experimental plasma with the typical EUV-induced plasma over the multi-layer mirrors (MLMs) surface of the EUV lithographic machine is demonstrated by means of 2D PIC MC simulation. The measurement of the temporal dynamics of the H atom surface loss probability is chosen for testing the surface modification during the treatment. Time-resolved actinometry of H atoms with Kr as the actinometer gas was used to detect the dynamics of the H-atom loss probability on the surface of Al, Ru, RVS and SiO2. It is demonstrated that significant changes of the materials surface occur only at the very beginning of the treatment and ist due to the surface heating and cleaning effects. After that no changes of the H recombination rate are found, indicating that the surface stays absolutely stable. A special test of the sensitivity of the used method to the state of surface was carried out. Dynamics of the H recombination rate changes with the small O2 addition clearly demonstrated modification of the Al surface due to oxidation with the next removal of the oxygen by the H2 plasma treatment. The rate of oxide removal is shown to be determined by plasma parameters such as the ion energy and flux to the surface.

physics.plasm-ph↗
arXiv2019

On 2-dimensional expanding attractors of A-flows

We prove that given any closed $n$-manifold $M^n$, $n\geq 4$, there is an A-flow $f^t$ on $M^n$ such that the non-wandering set $NW(f^t)$ consists of 2-dimensional expanding attractor (the both, orientable and non-orientable) and trivial basic sets. For 3-manifolds, we prove that given any closed 3-manifold $M^3$, there is an A-flow $f^t$ on $M^3$ such that the non-wandering set $NW(f^t)$ consists of a non-orientable 2-dimensional expanding attractor and trivial basic sets. Moreover, there is a nonsingular A-flow $f^t$ on a 3-sphere such that the non-wandering set $NW(f^t)$ consists of an orientable 2-dimensional expanding attractor and trivial basic sets (isolated periodic trajectories).

math.DS↗
arXiv2018

On conjugacy of Smale homeomorphisms

Given closed topological $n$-manifold $M^n$, $n\geq 2$, one introduces the classes of Smale regular $SRH(M^n)$ and Smale semi-regular $SsRH(M^n)$ homeomorphisms of $M^n$ with $SRH(M^n)\subset~SsRH(M^n)$. The class $SRH(M^n)$ contains all Morse-Smale diffeomorphisms, while $SsRH(M^n)$ contains A-diffeomorphisms with trivial and some nontrivial basic sets provided $M^n$ admits a smooth structure. We select invariant sets that determine dynamics of Smale homeomorphisms. This allows us to get necessary and sufficient conditions of conjugacy for $SRH(M^n)$ and $SsRH(M^n)$. We deduce applications for some Morse-Smale diffeomorphisms and A-diffeomorphisms with codimension one expanding attractors.

math.DS↗
arXiv2014

Characterization of carbon contamination under ion and hot atom bombardment in a tin-plasma extreme ultraviolet light source

Molecular contamination of a grazing incidence collector for extreme ultraviolet (EUV) lithography was experimentally studied. A carbon film was found to have grown under irradiation from a pulsed tin plasma discharge. Our studies show that the film is chemically inert and has characteristics that are typical for a hydrogenated amorphous carbon film. It was experimentally observed that the film consists of carbon (~70 at. %), oxygen (~20 at. %) and hydrogen (bound to oxygen and carbon), along with a few at. % of tin. Most of the oxygen and hydrogen are most likely present as OH groups, chemically bound to carbon, indicating an important role for adsorbed water during the film formation process. It was observed that the film is predominantly sp3 hybridized carbon, as is typical for diamond-like carbon. The Raman spectra of the film, under 514 and 264 nm excitation, are typical for hydrogenated diamond-like carbon. Additionally, the lower etch rate and higher energy threshold in chemical ion sputtering in H2 plasma, compared to magnetron-sputtered carbon films, suggests that the film exhibits diamond-like carbon properties.

cond-mat.mtrl-sci↗
arXiv2003

Single-Spin Asymmetry in Inclusive $π^0$ Production Measured at the Protvino 70 GeV Accelerator

Single Spin Asymmetries (SSA) $A_N$ measured in the two reactions at the Protvino 70 GeV accelerator are presented. $A_N$ in the reaction $p+p(pol)->π^0+X$ in the central region is close to zero within the error bars. SSA in the reaction $π^- +p(pol)->π^0+X$ in the polarized target fragmentation region is equal to $(-15 \pm 4)%$ at $|x_F|>0.4$. There is an indication that the asymmetry arises at the same pion energy in the center of mass system.

hep-ex↗
arXiv2003

Recent Results from Protvino Polarized Experiment Proza-M

Single Spin Asymmetry $A_N$ (SSA) was measured at the Protvino 70 GeV accelerator. Asymmetry in the reaction $\ppdup$ is close to zero within error bars at small $|\xf|$ and $p_T<1.5$ GeV/c. SSA in the reaction $\pimp$ at polarized target fragmentation region equals to $(-13.8 \pm 3.8)%$ at $|x_f|>0.4$. There is an indication that the asymmetry begins to rise up at the same centre of mass system pion energy.

hep-ex↗
arXiv2001

Dynamics of adsorbed islands with nanoscale resolution

Surface catalytic processes produce, under certain conditions, small clusters of adsorbed atoms or groups, called {\em islands} which, after they have been formed, move as individual entities. Here we consider the catalytic reduction of NO with hydrogen on platinum. (i) Using video field ion microscopy, we observe the dynamic motion of small hydroxyl islands on the Pt(001) plane; despite changes in their morphology, the islands dimensions are confined to values corresponding to 10 to 30 Pt atoms suggesting cooperative effects to be in operation. (ii) We construct an automaton (or lattice Monte-Carlo) model on the basis of a set of elementary processes governing the microscopic dynamics. The agreement between the simulation results and the experimental observations suggests a possible mechanism for the formation and dynamics of hydroxyl islands.

cond-mat↗