Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0409282

Reconstruction of stochastic nonlinear dynamical models from trajectory measurements

V. N. Smelyanskiy·D. G. Luchinsky·D. A. Timucin·A. Bandrivskyy
View original source ↗Read source document ↗Export metadata ↓

Abstract

A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. The strengths of the algorithm are illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. The efficiency and accuracy of the algorithm are further demonstrated by inferring a model for a system of five globally- and locally-coupled noisy oscillators.

Explore related subjects

cond-mat.othermath.OCphysics.data-an

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

V. N. Smelyanskiy, D. G. Luchinsky, D. A. Timucin, A. Bandrivskyy. 2005-03-02. Reconstruction of stochastic nonlinear dynamical models from trajectory measurements. https://doi.org/10.1103/physreve.72.026202

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Nanoscale Inclined Four-electrode Ion Traps: Finite-Element Modelling, Floquet Stability, and Surface-Potential Response

Developing miniaturised trapped-ion systems requires electrode architectures that provide controlled radio-frequency (RF) confinement while accounting for nanoscale features and surface-induced perturbations. Here, we present a finite-element investigation of an inclined four-blade RF ion-trap architecture for 171Yb+, combining pseudopotential characterisation, matrix Mathieu analysis, Floquet stability assessment, and localised surface-potential modelling. The architecture incorporates exposed electrode-face features of approximately 99-150 nm within an opposing-electrode separation of 20 um. At an electrode inclination of 6 degrees, an RF amplitude of 150 V, and a drive frequency of 15 MHz, the calculated pseudopotential exhibits directional in-plane barriers of 3.430 and 3.389 meV along the principal diagonal paths. The full RF-potential Hessian, including off-diagonal coupling terms, is used to construct the matrix Mathieu equation. Numerical propagation over one RF period identifies two dominant motional branches with secular-frequency estimates of 1.8137 and 1.8181 MHz. A third, predominantly axial branch exhibits a nominal frequency near 7.90 kHz, although its quantitative resolution is limited by the residual Hessian trace and phase-return drift. Additionally, a four-source electrostatic model is developed to investigate the effects of localised surface potentials on modal electric-field responses. Parametric analysis reveals correlation-dependent suppression and enhancement of normalised response coefficients, with multipliers ranging from approximately 0.5 to 1.5. This study establishes a computational framework for investigating nanoscale inclined blade-electrode architectures, their motional characteristics, and surface-potential responses, while highlighting numerical convergence requirements for reliable three-dimensional trap characterisation.

cond-mat.other↗
arXiv2026

Chiral-vibration-induced magnetism and circular dichroism in organic molecules

We investigate the vibrational inverse Faraday effect and transient vibrational circular dichroism in benzene, coronene, and methane at the single-molecule level. We combine density-functional tight-binding calculations with damped normal-mode dynamics. Circularly polarized light excites suitable degenerate infrared-active modes, driving chiral nuclear motion that produces effective magnetic moments. Reversing the pump helicity reverses the vibrational chirality and the sign of the transient dichroic response. These results support a writing-readout scheme in which circularly polarized pumping prepares a chiral vibrational state and transient vibrational circular dichroism probes its handedness. We further examine how molecular symmetry shapes the light-induced chiral response across the three molecular systems. This work provides a valuable platform for exploring all-optical control of magnetism and chiroptical probing at the molecular scale.

cond-mat.other↗
arXiv2026

A Construction Framework for Three-Dimensional Topological Magnetic Textures

Three-dimensional magnetic systems offer diverse possibilities for constructing complex topological textures from simpler magnetic configurations. Here, we present different routes for constructing complex three-dimensional magnetic textures from simpler parent configurations and discuss their impact on the topology of the resulting structures. We identify four construction principles: (i) adding transverse modulations, (ii) adding structures, (iii) entangling textures (e.g. braiding, or twisting), and (iv) introducing singularities. Using the skyrmion tube as an explicit parent configuration, we show how these principles give rise to several known three-dimensional magnetic textures. We then apply the same principles to predict novel textures derived from a meron tube, which are confirmed by micromagnetic simulations to be metastable in chiral magnets. Our results establish general principles for the systematic construction and discovery of complex three-dimensional magnetic textures.

cond-mat.other↗