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Alexander Borisenko

Publications and source records attributed to Alexander Borisenko.

13 recordsLinked to original sources
arXiv2023

A discrete Blaschke Theorem for convex polygons in $2$-dimensional space forms

Let $M$ be a $2$-space form. Let $P$ be a convex polygon in $M$. For these polygons, we define (and justify) a curvature $κ_i$ at each vertex $A_i$ of the polygon and and prove the following Blaschke's type theorem: If $P$ is a convex plygon in $M$ with curvature at its vertices $κ_i\ge κ_0 >0$, then the circumradius $R$ of $P$ satisfies $ta_λ(R) \le π/(2κ_0)$ and the equality holds if and only if the polygon is a $2$-covered segment.

math.DG↗
arXiv2021

Coherent effects contribution to a fast gate fidelity in ion quantum computer

Trapped ions are one of the most promising platforms for quantum computing due to the longest qubit coherence times and the highest gate fidelities. However, scaling the number of ions (qubits) in a linear Coulomb crystal is the key difficulty on the way to multi-qubit systems. One of the promising pathways to scale the number of qubits is to implement the pulsed non-adiabatic gates based on the sequence of State Dependent Kicks (SDKs). We have analytically and numerically studied the influence of coherent effects in the SDK sequence and, correspondingly, have deduced the influence of the individual SDK error on the net gate fidelity. We have shown that the coherence effects significantly impact the fidelity of non-adiabatic gates and must be taken into the account. As practical examples, we have developed a numerical model for full simulation of coherence effects using a linear ion microtrap array and a 2D microtrap array. We have also studied the dependency of the gate fidelity on the laser power fluctuations.

physics.atom-ph↗
arXiv2020

Compact transportable 171Yb+ single-ion optical fully automated clock with 4.9E-16 relative instability

The paper describes the results achieved in the development of the compact transportable fully automated optical clock based on a single 171Yb+ ion in a radiofrequency (RF) quadrupole trap. The resulted measurements demonstrated the 4.9E-16 output RF signal relative instability on 1000 s integration time with 298.1 kg weight, 0.921 volume, and 2.766 kW input power consumption of the device. A transformation of the ultrastable optical signal into the RF range was performed via the optical frequency comb with a supercontinuum fiber laser generator. The transformation was conducted without loss of initial stability and accuracy characteristics of the signal.

physics.ins-det↗
arXiv2020

A Simple Algorithm for Scalable Monte Carlo Inference

The methods of statistical physics are widely used for modelling complex networks. Building on the recently proposed Equilibrium Expectation approach, we derive a simple and efficient algorithm for maximum likelihood estimation (MLE) of parameters of exponential family distributions - a family of statistical models, that includes Ising model, Markov Random Field and Exponential Random Graph models. Computational experiments and analysis of empirical data demonstrate that the algorithm increases by orders of magnitude the size of network data amenable to Monte Carlo based inference. We report results suggesting that the applicability of the algorithm may readily be extended to the analysis of large samples of dependent observations commonly found in biology, sociology, astrophysics, and ecology.

stat.CO↗
arXiv2018

Nominal vs. actual supersaturation of solutions

Following the formalism of the Classical Nucleation Theory beyond the dilute solution approximation, this paper considers a difference between the actual solute supersaturation (given by the present-to-saturated solute activity ratio) and the nominal supersaturation (given by the present-to-saturated solute concentration ratio) due to formation of subcritical transient solute clusters, called heterophase fluctuations. Based on their distribution function, we introduce an algebraic equation of supersaturation that couples the nominal supersaturation of a binary metastable solution with its actual supersaturation and a function of the specific interface energy and temperature. The applicability of this approach is validated by comparison to simulation data [E. Clouet et al., Phys. Rev. B \textbf{69}, 064109 (2004)] on nucleation of Al$_{3}$Zr and Al$_{3}$Sc in model binary Al alloys.

physics.chem-ph↗
arXiv2016

Extreme properties of curves with bounded curvature on a sphere

We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for convex curves whose curvatures are bounded from above.

math.DG↗
arXiv2015

Revision of the classical nucleation theory for supersaturated solutions

During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its average bulk value. This feature affects the rates of attachment and detachment of solute atoms at the interface and, therefore, alters the entire nucleation kinetics. Unless quite obvious, this effect has been ignored in the classical nucleation theory. To illustrate the results of this new approach, for the case of homogeneous nucleation, we calculate the total solubility (including the contribution from heterophase fluctuations) and the nucleation rate as functions of two parameters of the model and compare these results to the classical ones. One can conclude that discrepancies with the classical nucleation theory are great in the diffusion-limited regime, when the bulk diffusion mobility of solute atoms is small compared to the interfacial one, while in the opposite interface-limited case they vanish.

physics.chem-ph↗
arXiv2015

Closeness to spheres of hypersurfaces with normal curvature bounded below

For a Riemannian manifold $M^{n+1}$ and a compact domain $Ω\subset M^{n+1}$ bounded by a hypersurface $\partial Ω$ with normal curvature bounded below, estimates are obtained in terms of the distance from $O$ to $\partial Ω$ for the angle between the geodesic line joining a fixed interior point $O$ in $Ω$ to a point on $\partial Ω$ and the outward normal to the surface. Estimates for the width of a spherical shell containing such a hypersurface are also presented.

math.DG↗
arXiv2014

Comparison theorem for support functions of hypersurfaces

For a convex domain $D$ that is enclosed by the hypersurface $\partial D$ of bounded normal curvature, we prove an angle comparison theorem for angles between $\partial D$ and geodesic rays starting from some fixed point in $D$, and the corresponding angles for hypersurfaces of constant normal curvature. Also, we obtain a comparison theorem for support functions of such surfaces. As a corollary, we present a proof of Blaschke's Rolling Theorem.

math.DG↗
arXiv2006

Paramagnetic tunneling state concept of the low-temperature magnetic anomalies of multicomponent insulating glasses

A generalized tunneling model of multicomponent insulating glasses is formulated, considering tunneling states to be paramagnetic centers of the electronic hole type. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of the expression for the nonmonotonic magnetic field dependence of dielectric susceptibility, recently observed in amorphous BaO-Al_2O_3-SiO_2 in sub-Kelvin temperature range.

cond-mat.soft↗
arXiv2005

Paramagnetic tunneling state concept of the magnetic anomalies of amorphous insulators

A generalized tunneling model of insulating glasses is formulated, considering tunneling states to be paramagnetic centers of spin 1/2. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of the expression for the nonmonotonic magnetic field dependence of dielectric constant, recently observed in several glasses in the millikelvin temperature range.

cond-mat.dis-nn↗