arXiv subjects

A. Levin

Publications and source records attributed to A. Levin.

At least 19 recordsLinked to original sources

arXiv2025

Deformable Linear Object Surface Placement Using Elastica Planning and Local Shape Control

Manipulation of deformable linear objects (DLOs) in constrained environments is a challenging task. This paper describes a two-layered approach for placing DLOs on a flat surface using a single robot hand. The high-level layer is a novel DLO surface placement method based on Euler's elastica solutions. During this process one DLO endpoint is manipulated by the robot gripper while a variable interior point of the DLO serves as the start point of the portion aligned with the placement surface. The low-level layer forms a pipeline controller. The controller estimates the DLO current shape using a Residual Neural Network (ResNet) and uses low-level feedback to ensure task execution in the presence of modeling and placement errors. The resulting DLO placement approach can recover from states where the high-level manipulation planner has failed as required by practical robot manipulation systems. The DLO placement approach is demonstrated with simulations and experiments that use silicon mock-up objects prepared for fresh food applications.

cs.RO↗

arXiv2025

Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation

We describe deformations of the classical principle chiral model and 1+1 Gaudin model related to ${\rm GL}_N$ Lie group. The deformations are generated by $R$-matrices satisfying the associative Yang-Baxter equation. Using the coefficients of the expansion for these $R$-matrices we derive equations of motion based on a certain ansatz for $U$-$V$ pair satisfying the Zakharov-Shabat equation. Another deformation comes from the twist function, which we identify with the cocentral charge in the affine Higgs bundle underlying the Hitchin approach to 2d integrable models.

math-ph↗

arXiv2024

Modular Arrangements

The modular curves serve as excellent objects for testing conjectures in arithmetic geometry. They possess a natural geometric definition in contrast with rather nontrivial structure. On the other hand, they are well-studied from the perspective of number theory. Furthermore, there is a well-developed and powerful analytic technique available. We will use the square of the modular curve as the experimental object to investigate the arithmetic properties of the periods of mixed Hodge structures. There is an additional reason for this study: this square is naturally associated with a family of (Hecke) curves. These curves form components of the Neron-Severi locus, allowing for the interpretation of the square of the moduli curve as the moduli space of split (i.e., the product of two elliptic curves) abelian surfaces.

math.AG↗

arXiv2022

Quality Control of Mass-Produced GEM Detectors for the CMS GE1/1 Muon Upgrade

The series of upgrades to the Large Hadron Collider, culminating in the High Luminosity Large Hadron Collider, will enable a significant expansion of the physics program of the CMS experiment. However, the accelerator upgrades will also make the experimental conditions more challenging, with implications for detector operations, triggering, and data analysis. The luminosity of the proton-proton collisions is expected to exceed $2-3\times10^{34}$~cm$^{-2}$s$^{-1}$ for Run 3 (starting in 2022), and it will be at least $5\times10^{34}$~cm$^{-2}$s$^{-1}$ when the High Luminosity Large Hadron Collider is completed for Run 4. These conditions will affect muon triggering, identification, and measurement, which are critical capabilities of the experiment. To address these challenges, additional muon detectors are being installed in the CMS endcaps, based on Gas Electron Multiplier technology. For this purpose, 161 large triple-Gas Electron Multiplier detectors have been constructed and tested. Installation of these devices began in 2019 with the GE1/1 station and will be followed by two additional stations, GE2/1 and ME0, to be installed in 2023 and 2026, respectively. The assembly and quality control of the GE1/1 detectors were distributed across several production sites around the world. We motivate and discuss the quality control procedures that were developed to standardize the performance of the detectors, and we present the final results of the production. Out of 161 detectors produced, 156 detectors passed all tests, and 144 detectors are now installed in the CMS experiment. The various visual inspections, gas tightness tests, intrinsic noise rate characterizations, and effective gas gain and response uniformity tests allowed the project to achieve this high success rate.

physics.ins-det↗

arXiv2022

2d Integrable systems, 4d Chern-Simons theory and Affine Higgs bundles

In this short review we compare constructions of 2d integrable models by means of two gauge field theories. The first one is the 4d Chern-Simons (4d-CS) theory proposed by Costello and Yamazaki. The second one is the 2d generalization of the Hitchin integrable systems constructed by means the Affine Higgs bundles (AHB). We illustrate this approach by considering 1+1 field versions of elliptic integrable systems including the Calogero-Moser field theory, the Landau-Lifshitz model and the field theory generalization of the elliptic Gaudin model.

hep-th↗

arXiv2021

Performance of a Triple-GEM Demonstrator in $pp$ Collisions at the CMS Detector

After the Phase-2 high-luminosity upgrade to the Large Hadron Collider (LHC), the collision rate and therefore the background rate will significantly increase, particularly in the high $\eta$ region. To improve both the tracking and triggering of muons, the Compact Muon Solenoid (CMS) Collaboration plans to install triple-layer Gas Electron Multiplier (GEM) detectors in the CMS muon endcaps. Demonstrator GEM detectors were installed in CMS during 2017 to gain operational experience and perform a preliminary investigation of detector performance. We present the results of triple-GEM detector performance studies performed in situ during normal CMS and LHC operations in 2018. The distribution of cluster size and the efficiency to reconstruct high $p_T$ muons in proton--proton collisions are presented as well as the measurement of the environmental background rate to produce hits in the GEM detector.

physics.ins-det↗

arXiv2021

Modeling the triple-GEM detector response to background particles for the CMS Experiment

An estimate of environmental background hit rate on triple-GEM chambers is performed using Monte Carlo (MC) simulation and compared to data taken by test chambers installed in the CMS experiment (GE1/1) during Run-2 at the Large Hadron Collider (LHC). The hit rate is measured using data collected with proton-proton collisions at 13 TeV and a luminosity of 1.5$\times10^{34}$ cm$^{-2}$ s$^{-1}$. The simulation framework uses a combination of the FLUKA and Geant4 packages to obtain the hit rate. FLUKA provides the radiation environment around the GE1/1 chambers, which is comprised of the particle flux with momentum direction and energy spectra ranging from $10^{-11}$ to $10^{4}$ MeV for neutrons, $10^{-3}$ to $10^{4}$ MeV for $\gamma$'s, $10^{-2}$ to $10^{4}$ MeV for $e^{\pm}$, and $10^{-1}$ to $10^{4}$ MeV for charged hadrons. Geant4 provides an estimate of detector response (sensitivity) based on an accurate description of detector geometry, material composition and interaction of particles with the various detector layers. The MC simulated hit rate is estimated as a function of the perpendicular distance from the beam line and agrees with data within the assigned uncertainties of 10-14.5%. This simulation framework can be used to obtain a reliable estimate of background rates expected at the High Luminosity LHC.

physics.ins-det↗

arXiv2020

Interstrip Capacitances of the Readout Board used in Large Triple-GEM Detectors for the CMS Muon Upgrade

We present analytical calculations, Finite Element Analysis modeling, and physical measurements of the interstrip capacitances for different potential strip geometries and dimensions of the readout boards for the GE2/1 triple-Gas Electron Multiplier detector in the CMS muon system upgrade. The main goal of the study is to find configurations that minimize the interstrip capacitances and consequently maximize the signal-to-noise ratio for the detector. We find agreement at the 1.5--4.8% level between the two methods of calculations and on the average at the 17% level between calculations and measurements. A configuration with halved strip lengths and doubled strip widths results in a measured 27--29% reduction over the original configuration while leaving the total number of strips unchanged. We have now adopted this design modification for all eight module types of the GE2/1 detector and will produce the final detector with this new strip design.

physics.ins-det↗

arXiv2019

Odd supersymmetrization of elliptic R-matrices

We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical and quantum elliptic $R$-matrices. They are shown to satisfy the classical Yang-Baxter equation and the associative Yang-Baxter equation. The quantum Yang-Baxter is discussed as well. It acquires additional term in the case of supersymmetric $R$-matrices.

math-ph↗

arXiv2019

Odd supersymmetric Kronecker elliptic function and Yang-Baxter equations

We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application we construct an odd supersymmetric extensions of the elliptic $R$-matrices, which satisfy the classical and the associative Yang-Baxter equations.

math-ph↗

arXiv2018

Thermopower of a Two-Dimensional Semimetal in a HgTe Quantum Well

The thermopower in a two-dimensional semimetal existing in HgTe quantum wells 18-21 nm thick has been studied experimentally and theoretically for the first time. It has been found theoretically and experimentally that the thermopower has two components - diffusion and phonon drag and that the second component is several times larger than the first. It has been concluded that the electron-hole scattering plays an important role in both mechanisms of the thermopower.

cond-mat.mes-hall↗

arXiv2017

Quasi-compact Higgs bundles and Calogero-Sutherland systems with two types spins

We define the quasi-compact Higgs $G^{\mathbb C}$-bundles over singular curves introduced in our previous paper for the Lie group SL($N$). The quasi-compact structure means that the automorphism groups of the bundles are reduced to the maximal compact subgroups of $G^{\mathbb C}$ at marked points of the curves. We demonstrate that in particular cases this construction leads to the classical integrable systems of Hitchin type. The examples of the systems are analogues of the classical Calogero-Sutherland systems related to a simple complex Lie group $G^{\mathbb C}$ with two types of interacting spin variables. These type models were introduced previously by Feher and Pusztai. We construct the Lax operators of the systems as the Higgs fields defined over a singular rational curve. We also construct hierarchy of independent integrals of motion. Then we pass to a fixed point set of real involution related to one of the complex structures on the moduli space of the Higgs bundles. We prove that the number of independent integrals of motion is equal to the half of dimension of the fixed point set. The latter is a phase space of a real completely integrable system. We construct the classical $r$-matrix depending on the spectral parameter on a real singular curve, and in this way prove the complete integrability of the system. We present three equivalent descriptions of the system and establish their equivalence.

math-ph↗

arXiv2017

Calogero-Sutherland system with two types interacting spins

We consider the classical Calogero-Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero-Sutherland system, when one of the spin variables vanishes. We describe the model in the Hitchin approach and prove complete integrability of the system by constructing the Lax pair and the classical $r$-matrix with the spectral parameter on a singular curve.

math-ph↗

arXiv2016

Noncommutative extensions of elliptic integrable Euler-Arnold tops and Painleve VI equation

In this paper we suggest generalizations of elliptic integrable tops to matrix-valued variables. Our consideration is based on $R$-matrix description which provides Lax pairs in terms of quantum and classical $R$-matrices. First, we prove that for relativistic (and non-relativistic) tops such Lax pairs with spectral parameter follow from the associative Yang-Baxter equation and its degenerations. Then we proceed to matrix extensions of the models and find out that some additional constraints are required for their construction. We describe a matrix version of ${\mathbb Z}_2$ reduced elliptic top and verify that the latter constraints are fulfilled in this case. The construction of matrix extensions is naturally generalized to the monodromy preserving equation. In this way we get matrix extensions of the Painlev\'e VI equation and its multidimensional analogues written in the form of non-autonomous elliptic tops. Finally, it is mentioned that the matrix valued variables can be replaced by elements of noncommutative associative algebra. In the end of the paper we also describe special elliptic Gaudin models which can be considered as matrix extensions of the (${\mathbb Z}_2$ reduced) elliptic top.

math-ph↗

arXiv2015

Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations

We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by an arbitrary finite order automorphisms of the underlying Lie algebras. In this way we obtain the spin generalization of the twisted D'Hoker- Phong and Bordner-Corrigan-Sasaki-Takasaki systems. As by product, we construct the corresponding twisted classical dynamical r-matrices and Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms of the Lie algebras.

math-ph↗

arXiv2015

Yang-Baxter equations with two Planck constants

We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled ${\rm GL}(N)$ Sklyanin elliptic algebras. Then we proceed to a natural generalization of the Baxter-Belavin quantum $R$-matrix to the case ${\rm Mat}(N,\mathbb C)^{\otimes 2}\otimes {\rm Mat}(M,\mathbb C)^{\otimes 2}$. It can be viewed as symmetric form of ${\rm GL}(NM)$ $R$-matrix in the sense that the Planck constant and the spectral parameter enter (almost) symmetrically. Such type (symmetric) $R$-matrices are also shown to satisfy the Yang-Baxter like quadratic and cubic equations.

math-ph↗

arXiv2015

Quantum Baxter-Belavin R-matrices and multidimensional Lax pairs for Painleve VI

The quantum elliptic $R$-matrices of Baxter-Belavin type satisfy the associative Yang-Baxter equation in ${\rm Mat}(N,\mathbb C)^{\otimes 3}$. The latter can be considered as noncommutative analogue of the Fay identity for the scalar Kronecker function. In this paper we extend the list of $R$-matrix valued analogues of elliptic function identities. In particular, we propose counterparts of the Fay identities in ${\rm Mat}(N,\mathbb C)^{\otimes 2}$. As an application we construct $R$-matrix valued $2N^2\times 2N^2$ Lax pairs for the Painlev\'e VI equation (in elliptic form) with four free constants using ${\mathbb Z}_N\times {\mathbb Z}_N$ elliptic $R$-matrix. More precisely, the four free constants case appears for an odd $N$ while even $N$'s correspond to a single constant.

math-ph↗

arXiv2014

Planck Constant as Spectral Parameter in Integrable Systems and KZB Equations

We construct special rational ${\rm gl}_N$ Knizhnik-Zamolodchikov-Bernard (KZB) equations with $\tilde N$ punctures by deformation of the corresponding quantum ${\rm gl}_N$ rational $R$-matrix. They have two parameters. The limit of the first one brings the model to the ordinary rational KZ equation. Another one is $\tau$. At the level of classical mechanics the deformation parameter $\tau$ allows to extend the previously obtained modified Gaudin models to the modified Schlesinger systems. Next, we notice that the identities underlying generic (elliptic) KZB equations follow from some additional relations for the properly normalized $R$-matrices. The relations are noncommutative analogues of identities for (scalar) elliptic functions. The simplest one is the unitarity condition. The quadratic (in $R$ matrices) relations are generated by noncommutative Fay identities. In particular, one can derive the quantum Yang-Baxter equations from the Fay identities. The cubic relations provide identities for the KZB equations as well as quadratic relations for the classical $r$-matrices which can be halves of the classical Yang-Baxter equation. At last we discuss the $R$-matrix valued linear problems which provide ${\rm gl}_{\tilde N}$ Calogero-Moser (CM) models and Painleve equations via the above mentioned identities. The role of the spectral parameter plays the Planck constant of the quantum $R$-matrix. When the quantum ${\rm gl}_N$ $R$-matrix is scalar ($N=1$) the linear problem reproduces the Krichever's ansatz for the Lax matrices with spectral parameter for the ${\rm gl}_{\tilde N}$ CM models. The linear problems for the quantum CM models generalize the KZ equations in the same way as the Lax pairs with spectral parameter generalize those without it.

hep-th↗