AI Article Synopsis
- The study proposes a new method for calculating the transient probability density function (PDF) for nonlinear oscillators influenced by random stimulation, extending previous techniques with an evolutionary exponential-polynomial approach.
- By using weighted residual errors and developing ordinary differential equations, the research allows for the numerical determination of undetermined variables to better model system responses.
- The findings show that this improved method is more effective and efficient than traditional Monte Carlo simulations, particularly capturing asymmetrical PDF solutions and examining the effects of nonlinearity and modulated Gaussian noise on system behavior.
Article Abstract
This study presents an improved solution procedure for determining the transient probability density function (PDF) solutions of the nonlinear oscillators with both odd and even nonlinearity under modulated random stimulation, which is an extension of the exponential-polynomial-closure approach. An evolutionary exponential-polynomial function with time-varying undetermined variables is considered as the transient probabilistic solution. By selecting a set of independent evolutionary base functions spanning a R^{n} space as weight functions, a set of ordinary differential equations can be formulated by integrating the weighted residual error. The undetermined variables can be determined numerically by solving those ordinary differential equations. Three numerical examples illustrate that the improved solution procedure can acquire the transient probabilistic responses of the stochastic dynamic systems effectively and efficiently even in the PDF solution tails when compared with Monte Carlo simulation. Moreover, the results indicate that the PDF solutions of the oscillators are asymmetrical at their nonzero means due to the influence of even nonlinearity. The nonstationary behaviors of the system responses are also investigated along with the behavior of modulated Gaussian white noise.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.108.024209 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Structure and property exploration of two-dimensional, bulk, and cluster lithium sulfide using the IMODE method.
Phys Chem Chem Phys
December 2024
Zhejiang Provincial Key Laboratory of Carbon Materials, College of Chemistry and Materials Engineering, Wenzhou University, Wenzhou 325035, China.
Lithium sulfide (LiS) plays an important role in fields such as energy, environment and semiconductors. Exploration of the microstructure of LiS has significant implications for developing new materials and optimizing related material properties. In this work, the inverse design of materials by the multi-objective differential evolution (IMODE) method combined with density functional theory (DFT) calculations was used to predict the two-dimensional (2D), three-dimensional (3D), and cluster structures of LiS.
View Article and Find Full Text PDFWe present high-order harmonic generation (HHG) in laser-produced aluminium and tin plasmas driven by a two-color field with orthogonal polarization, leading to the generation of both odd and even harmonics. We shape the effective drive field with sub-cycle resolution by controlling the phase between the fundamental wave and its second harmonic. The shape of the drive field influences the electron trajectories of the various harmonics generated in these plasmas.
View Article and Find Full Text PDFTopological Fermiology of gate-tunable Rashba electron gases.
Sci Adv
November 2024
School of Physics and State Key Laboratory of Silicon and Advanced Semiconductor Materials, Zhejiang University, Hangzhou 310027, P. R. China.
By introducing first-order quantum phases as topological invariants, recent symmetry analysis-based theories have reinvigorated magnetic quantum oscillations as a versatile quantum probe for unfolding the Fermi surface topology along with the geometry information, i.e., topo-Fermiology.
View Article and Find Full Text PDFLDOS of electron pair and the role of the Pauli exclusion principle.
J Phys Condens Matter
November 2024
Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-688 Warsaw, Poland.
The local density of states (LDOS) for a pair of non-relativistic electrons, influenced by repulsive Coulomb forces, is expressed in term of one-dimensional integrals over Whittaker functions. The computation of the electron pair's LDOS relies on a two-particle Green's function (GF), a generalization of the one-particle GF applicable to a charged particle in an attractive Coulomb potential. By incorporating electron spins and considering the Pauli exclusion principle, the resulting LDOS consists of two components: one originating from an exchange-even two-particle GF and the other from an exchange-odd two-particle GF.
View Article and Find Full Text PDFChirality and odd mechanics in active columnar phases.
PNAS Nexus
October 2024
Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore, Karnataka 560 012, India.
Chiral active materials display odd dynamical effects in both their elastic and viscous responses. We show that the most symmetric mesophase with 2D odd elasticity in three dimensions is chiral, polar, and columnar, with 2D translational order in the plane perpendicular to the columns and no elastic restoring force for their relative sliding. We derive its hydrodynamic equations from those of a chiral active variant of model H.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!