"Escargot Effect" and the Chandler Wobble Excitation

L. Zotov; C. Bizouard

doi:10.1088/1742-6596/955/1/012033

Publications

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"Escargot Effect" and the Chandler Wobble Excitation

Journal of Physics: Conference Series. 2018. Vol. 955. No. 1. P. 1–6.

Zotov L., Bizouard C.

We study the Chandler wobble (CW) of the pole from 1846 to 2017 extracted by the Panteleev ltering. The CW has period of 433 days, average amplitude of 0.13 milliarcseconds (mas) which is changing, and phase jump by pi in 1930-th. The CW amplitude strongly (almost to zero) decreases in 1930-th and 2010-th with the phase jump in 1930th. The envelope model contains 83- and 42-years quasi-periodicities. We think the rst one can be represented by the 166-years changes of the envelope, crossing zero in 1930th. We reconstruct Chandler input excitation based on the Euler-Liouville equation. Its amplitude has 20-years variations. We explain this based on simple model and prove, that they appear in consequence of 42-years modulation of CW. The excitation ampli es the amplitude of CW for 20 years then damps it for another 20 years. The analysis of the modulated CW signal in a sliding window demonstrates the specific effect, we called the "escargot effect", when instantaneous "virtual" retrograde component appears in the purely prograde (at long-time interval) signal. Chandler excitation envelope shape is similar to this instantaneous retrograde component, which re ects the changes of ellipticity of the approximation ellipse.

Priority areas: mathematics

Keywords: фильтрация Earth rotation вращение Земли

Bifurcations and Structural Stability of Generic PC-HC Families

Dorovskiy A., / Series arXiv "math". 2026.

In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...

Added: May 14, 2026

On the minimum number of maximal distance-k independent sets in trees

Taletskii D., / Series arXiv "math". 2026.

A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...

Added: May 1, 2026

On Arithmetic Mirror Symmetry for smooth Fano fourfolds

Ovcharenko M., / Series arXiv "math". 2026.

We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...

Added: April 30, 2026

On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization

Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.

We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...

Added: April 18, 2026

On the dimension of the space of static potentials on three-manifolds

Medvedev V., / Series arXiv "math". 2026.

We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...

Added: April 3, 2026

Using predefined vector systems to speed up neural network multimillion class classification

Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.

Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...

Added: April 2, 2026

Влияние выбора стратегии формирования обучающего множества и способа фильтрации на эффективность ИМК, основанного на спектрометрии в ближнем инфракрасном диапазоне

Исаев М. Р., Бобров П. Д., Журнал высшей нервной деятельности им. И.П. Павлова 2022 Т. 72 № 5 С. 728–738

The paper proposes methods for brain–computer interface, based on the hemodynamic activity registration using near–infrared spectroscopy (NIRS) and adapted for using in the movement disorders rehabilitation. Methods include a filtration adapted to the instructions frequency, step by step classification of the rest state and active tasks, as well as training of the interface classifier on ...

Added: March 18, 2026

Chandler Wobble and LOD Anomalyes in 2010–2020s

Zotov L., Sidorenkov N., Bizouard C., , in: Proceedings of the 19th Annual Meeting ofthe Asia Oceania Geosciences Society.: Singapore: World Scientific Publishing Co. Pte. Ltd, 2023. P. 153–155.

In early 2000-s the amplitude of the Chandler wobble (CW) started to decrease and in 2017-2020 reached its historic minima, comparable only with the minima of ~1928 yr. In 2021 the CW appeared again. We demonstrate that the phase of the CW is changing now, as during 1920-1930s. Since 2010 it has changed almost by ...

Added: March 5, 2026

Earth Rotation Variations and the Moon Apsidal-Nodal Effects

Zotov L., Sidorenkov N., Bizouard C., , in: Proceedings of the XV Conference and School (St. Petersburg, Russia, April 22–26). Problems of Geocosmos—2024.: Switzerland: Springer, 2026. P. 289–312.

Earth rotation in recent epoch shows anomalies: its rotation velocity reached decadal maximum in 2024; the Chandler wobble (CW) of the rotation axis disappeared in 2018–2020, then resumed with a phase changed by 180^\circ ◦; the ampli-tude of the Free Core Nutation (FCO) decreased since 2021 as well. We analyzed the CW amplitude modulations since the ...

Added: March 1, 2026

Homogeneous maximizers of the Blaschke-Santalo-type functionals

Kolesnikov A., / Series arXiv "math". 2025.

We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets. We also discuss links to the ...

Added: February 13, 2026

Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection

Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.

Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...

Added: January 15, 2026

On finding formal power-logarithmic expansions of solutions to q-difference equations

Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.

An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...

Added: December 25, 2025

Ideal of the variety of flexes of plane cubics

Popov V., / Series arXiv "math". 2025. No. 2502.01539.

We prove that the variety of flexes of algebraic curves of degree 3 in the projective plane is an ideal theoretic complete intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...

Added: December 16, 2025

Фильтр Калмана с полосовой частотной фильтрацией для выделения Чандлеровского колебания полюса.

Zotov L., Логинов А. В., Ольховский А. А. et al., В кн.: ВОПРОСЫ ТЕОРИИ И ПРАКТИКИ ГЕОЛОГИЧЕСКОЙ ИНТЕРПРЕТАЦИИ ГРАВИТАЦИОННЫХ, МАГНИТНЫХ И ЭЛЕКТРИЧЕСКИХ ПОЛЕЙ 51-я сессия Международного семинара им. Д.Г. Успенского - В.Н. Страхова. Москва, 2025.: Пермский государственный университет, 2025.

One of the major components of the Earth’s polar motion is Chandler wobble with 433-day period. To extract it from observations narrow-band filtering is required. We have developed method which joins Kalman filtering and band-pass filtering in direct time with the phase correction in reversed time. By using Euler-Liouville equation generating resonant CW as a ...

Added: December 10, 2025

Random walks on rank one symmetric spaces of noncompact type

Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.

We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes the real hyperbolic space Hn. Our approach introduces ...

Added: December 5, 2025

Cascades of Lorenz attractors in the Shimizu-Morioka model

Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.

The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...

Added: December 4, 2025

Асимптотический вариант метода параметрикс для цепей Маркова, сходящихся к диффузиям

Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.

В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...

Added: December 3, 2025

Изменения государственной политики и практик фильтрации военнослужащих Красной армии, вернувшихся из плена. 1939–1946 гг.

Latyshev A., В кн.: Государственное управление в СССР в годы Второй мировой войны. Фронт и тыл: Материалы XVII Международной научной конференции. Екатеринбург, 19–22 июня 2025 г.: М.: Издательство "Политическая энциклопедия", 2025. С. 490–498.

The article analyzes the institutional, organizational, and ideological aspects of the state's work with returning military personnel after the battles with Japan at Khalkhin Gol, the war with Finland, during and after the Great Patriotic War. The priorities of the state and state security agencies, the logic of the latter's work, are being clarified. The ...

Added: December 2, 2025

Stabilization of direct images for curves

Bogomolov F. A., Schrandt S., / Series arXiv "math". 2025.

We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree. ...

Added: December 1, 2025

Upper Bounds on the Torsion Index of Half-Spin Groups

Deviatov R., Baek S., / Series arXiv "math". 2025.

The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for the torsion index of half-spin groups, the only remaining case in the calculation of ...

Added: December 1, 2025

Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset

Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.

Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...

Added: December 1, 2025

Birational transformations of threefold Q-conic bundles

Prokhorov Y., / Series arXiv "math". 2025.

A $\mathbf{Q}$-conic bundle is a contraction $f: X\to Z$ of a three-dimensional algebraic variety $X$ to a surface~$Z$ such that the variety~$X$ has only terminal $\mathbf{Q}$-factorial singularities, the anticanonical divisor $-K_X$ is~$f$-ample, and $\uprho(X/Z)=1$. We provide an algorithm to transform a $\mathbf{Q}$-conic bundle to its standard form. ...

Added: December 1, 2025

Birational geometry of hyperkahler manifolds and the Hu-Yau conjecture

Amerik E., Verbitsky M., Soldatenkov A., / Series arXiv "math". 2025.

Wierzba and Wisniewski proved that in dimension 4, every bimeromorphic map of hyperkahler manifolds is represented as a composition of Mukai flops. Hu and Yau conjectured that this result can be generalized to arbitrary dimension. They defined ``Mukai's elementary transformation'' as the blow-up of a subvariety ruled by complex projective spaces, composed with the contraction ...

Added: December 1, 2025

Two Types of Filtrations for wK4 and Its Relatives

Kudinov A., Shapirovsky I., Studia Logica 2025 P. 1–25

We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For m > 0, let Lm be the logic defined by axiom ♦^{m+1}p → ♦p ∨ p. We construct quotient filtrations for the logics Lm, which implies that these logics and their tense counterparts have the finite model property. Then, we construct selective filtrations ...

Added: October 14, 2025