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Chaotic dynamics creates and destroys branched flow

Physical Review E 2025年第1期111卷 014214-014214页

作者： Alexandre Wagemakers Aleksi Hartikainen Alvar Daza Esa Räsänen Miguel A. F. Sanjuán Nonlinear Dynamics Chaos and Complex Systems Group Departamento de Física Universidad Rey Juan Carlos Tulipán s 28933 Móstoles Madrid Spain Computational Physics Laboratory Tampere University 33720 Tampere Finland Department of Physics Harvard University Cambridge Massachusetts 02138 USA

The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently being added to this list. Here, we explore the laws governing the evolution of the branches in periodic potentials. On one hand, we observe that branch formation follows a similar pattern in all nonintegrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, our results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires. Again, the interplay between branched flow and superwires is deeply connected to Hamiltonian chaos. In this work, we explore the relationships between the laws of branched flow and the structures of phase space, providing extensive numerical and theoretical arguments to support our findings.

关键词： Hamiltonians

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Investigation of bright and dark solitons in α,β-Fermi Pasta Ulam lattice

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Chinese physics B 2021年第2期30卷 211-219页

作者： Nkeh Oma Nfor Serge Bruno Yamgoué Francois Marie Moukam Kakmeni Department of Physics Higher Teacher Training College BambiliThe University of BamendaP.O.Box 39Bambili-Cameroon Complex Systems and Theoretical Biology Group Laboratory of Research on Advanced Materials and Nonlinear Science(LaRAMaNS)Department of PhysicsFaculty of ScienceUniversity of BueaP.O.Box 63 Buea-Cameroon

We consider the Hamiltonian ofα,β-Fermi Pasta Ulam lattice and explore the Hamilton-Jacobi formalism to obtain the discrete equation of *** using the continuum limit approximations and incorporating some normalized parameters,the extended Korteweg-de Vries equation is obtained,with solutions that elucidate on the Fermi Pasta Ulam *** further derive the nonlinear Schrodinger amplitude equation from the extended Korteweg-de Vries equation,by exploring the reductive perturbative *** dispersion and nonlinear coefficients of this amplitude equation are functions of theαandβparameters,with theβparameter playing a crucial role in the modulational instability analysis of the ***βgreater than or equal to zero,no modulational instability is observed and only dark solitons are identified in the *** forβless than zero,bright solitons are traced in the lattice for some large values of the *** of numerical simulations of both the Korteweg-de Vries and nonlinear Schr¨odinger amplitude equations with periodic boundary conditions clearly show that the bright solitons conserve their amplitude and shape after collisions.

关键词： Fermi Pasta Ulam paradox bright dark

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Construction of Abundant Solitons in a Coupled nonlinear Pendulum Lattice Through Two Discrete Distinct Techniques

SSRN

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SSRN 2023年

作者： Emmanuel, Fendzi-Donfack Baduidana, Marcial Fernande, Fotsa-Nguaffo Aurélien, Kenfack-Jiotsa Nonlinear Physics and Complex Systems Group Department of Physics The Higher Teacher’s Training College University of Yaoundé I P.O. Box 47 Yaounde Cameroon Pure Physics Laboratory Group of Nonlinear Physics and Complex Systems Department of Physics Faculty of Sciences University of Douala P.O. Box 24157 Douala Cameroon Laboratory of Mechanics Materials and Structures Department of Physics Faculty of Science University of Yaoundé I P.O. Box 812 Yaoundé Cameroon Nonlinear Physics and Complex Systems Group Department of Physics The Higher Teacher’s Training College University of Yaoundé I P.O. Box 47 Yaoundé Cameroon Institute of Wood Technologies University of Yaoundé I P.O. Box 306 Mbalmayo Cameroon

In this paper, we deal with two distinct discrete techniques named the discrete Tanh method and the differential-difference Jacobi elliptic functions sub-ODE method to extract abundant soliton solutions for a coupled nonlinear pendulum chains. According to the two straightforward schemes’, we construct various solutions likewise, kink, anti-kink, bright, dark, singularbright solitary wave, travelling compacton, travelling gray solitonlike, periodic soliton-like haven’t reported on the most recently studied mechanical model. We extract the sought solutions with less approximation (introduction of a discrete wave transformation) and display some graphical representations showing well known, novel shapes discovered in a coupled nonlinear pendulum lattice. The effect of some physical parameters are displayed on the shaped through 2D and 3D graphical simulations. The used methods (tanh, sn, cn, dn Jacobi elliptic functions approaches) previously applied on other physical models (discrete electrical transmission lattices) are presented here in manner to be replicable for exploring more soliton solutions in different nonlinear discrete physical models. © 2023, The Authors. All rights reserved.

关键词： Solitons

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Breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain

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The European Physical Journal B 2022年第5期95卷 1-19页

作者： Ribama, R. Abouem A. Djoufack, Z. I. Nguenang, J. P. Pure Physics Laboratory: Group of Nonlinear physics and Complex systems Department of Physics University of Douala Douala Cameroon Unité de Recherche d’Automatique et Informatique Apliquée (UR-AIA) Fotso Victor University Institute of Technology University of Dschang Bandjoun Cameroon The African Institute for Mathematical Sciences (AIMS) Cape Town South Africa

We study the breather-impurity interactions and modulational instability in a quantum 2D Klein–Gordon chain. By using the second quantification operators, we transform classical Hamiltonian into its quantum version, through Glauber’s coherent state representation in addition to the multiple-scale method, the 2D nonlinear Schrödinger equation (NLSE) is obtained. This NLSE is analytically solved by adopting the Rayleigh–Ritz variational method. Around impurity’s critical mass, we prove the existence of resonant structure. This critical mass is observed when plotting the frequency spectrum under the effect of the impurity mass and harmonic force constants. The effects of impurity mass and the harmonic force constants are found in the amplitude frequency spectra. When the breather interacts with the impurity, the system exhibit different scenario that are: barrier, well, excitation and chaotic all related to the trapping phenomenon. The modulational instability (MI) which helps to confirm the existence of breather is investigated. We have shown that impurity strength increases the instability regions, and the MI growth rate can be dramatically affected by the impurity mass around the critical value.

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Neuromechanical modulation of transmembrane voltage in a model of a nerve

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Physical Review E 2022年第1期105卷 014407-014407页

作者： G. Fongang Achu F. M. Moukam Kakmeni Complex Systems and Theoretical Biology Group (CoSTBiG) and Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS) Department of Physics Faculty of Science University of Buea P.O. Box 63 Buea Cameroon

Despite substantial evidence that mechanical variables play a crucial role in transmembrane voltage regulation, most research efforts focus mostly on the nerve cell's biochemical or electrophysiological activities. We propose an electromechanical model of a nerve in order to advance our understanding of how mechanical forces and thermodynamics also regulate neural electrical activities. We explore the spatiotemporal dynamics of the transmembrane potential using the proposed nonlinear model with a sinusoid as the initial transmembrane potential and periodic boundary conditions. The localized wave from our numerical simulation and transmembrane potentials in nerves are solitary and show the three stages of action potential (depolarization, repolarization, and hyperpolarization), as well as threshold and saturation effects. We show that the mechanical properties of membranes affect the localization of the transmembrane potential. According to simulation data, mechanical pulses of sufficient magnitude can modulate a transmembrane voltage. The current model could be used to describe the dynamics of a transmembrane potential modulated by sound. Mechanical perturbations that modulate an electrical signal have a lot of clinical potential for treating pain and other neurological diseases.

关键词： Action potential propagation Patterns in complex systems

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Lagrangian Homotopy Analysis Method using the Least Action Principle

arXiv

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arXiv 2024年

作者： Beukam, Gervais Nazaire Chendjou Nguenang, Jean Pierre Ruffo, Stefano Trombettoni, Andrea Pure Physics Laboratory Group of Nonlinear Physics and Complex Systems Department of Physics Faculty of Science University of Douala Box 24157 Douala Cameroon SISSA Via Bonomea 265 TriesteI-34136 Italy INFN Sezione di Trieste TriesteI-34151 Italy Istituto dei Sistemi Complessi Consiglio Nazionale delle Ricerche via Madonna del Piano 10 Sesto FiorentinoI-50019 Italy Department of Physics University of Trieste Strada Costiera 11 TriesteI-34151 Italy

The Homotopy Analysis Method (HAM) is a powerful technique which allows to derive approximate solutions of both ordinary and partial differential equations. We propose to use a variational approach based on the Least Action Principle (LAP) in order to improve the efficiency of the HAM when applied to Lagrangian systems. The extremization of the action is achieved by varying the HAM parameter, therefore controlling the accuracy of the approximation. As case studies we consider the harmonic oscillator, the cubic and the quartic anharmonic oscillators, and the Korteweg-de Vries partial differential equation. We compare our results with those obtained using the standard approach, which is based on the residual error square method. We see that our method accelerates the convergence of the HAM parameter to the exact value in the cases in which the exact solution is known. When the exact solution is not analytically known, we find that our method performs better than the standard HAM for the cases we have analyzed. Moreover, our method shows better performance when the order of the approximation is increased and when the nonlinearity of the equations is stronger. © 2024, CC BY.

关键词： Lagrange multipliers

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Negative capacitance effect using a pure imaginary electric mobility controled by an adiabatic parameter in thin film materials based on Drude model

Research Square

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Research Square 2023年

作者： Noupeyi, S.D. Kenfack-Jiotsa, A. Laboratory of Mechanics Materials and Structure Faculty of Sciences University of Yaounde I Yaounde Cameroon Nonlinear Physics and Complex Systems Group The Higher Teacher’s Training College University of Yaounde I Yaounde Cameroon

Existence of a pure imaginary mobility of charge carriers in organic polymers materials, precisely the poly p-phenylene vinylene is explored in this work. Indeed, we propose a new model of dynamic equation of particles able to carry electric charges, we introduce a control parameter of the adiabatic evolution combined with a phase difference between the external perturbation of the material and the position of carrier, leading from then on to the non-use of the complex mobility. This model after transformation allowed us to demonstrate the existence of negative capacitance at low and high frequencies in the poly p-phenylene vinylene. Also thanks to this new model, we were able to obtain results in line with the experimental ones, thus confirming the validity of our model. © 2023, CC BY.

关键词： Capacitance

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Influence of next-nearest neighbor interactions on the dynamics of discrete energy transport within neuronal microtubules

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Chaos, Solitons and Fractals 2025年 198卷

作者： Abouem A Ribama, R. Youssoufa, M. Ondoua, R.Y. Djoufack, Z.I. Nguenang, J.P. Pure Physics Laboratory: Group of Nonlinear physics and Complex systems Department of Physics University of Douala P.O. Box 24157 Douala Cameroon Laboratory of Biophysics Department of Physics Faculty of Science University of Yaoundé I P.O. Box 812 Yaoundé Cameroon African Centre for Advanced Studies P.O. Box 4477 Yaoundé Cameroon Fotso Victor University Institute of Technology P.O. Box 134 Bandjoun University of Dschang Cameroon 6 Melrose Road Muizenberg Cape Town7945 South Africa

In this study, we investigate the influence of next-nearest neighbor interactions or homodimer coupling on the dynamics of quantum breathers in neuronal microtubules (nMTs) using both analytical and numerical methods. From the classical model describing the dynamics of the microtubule using a Hamiltonian, we formulated its quantum equivalent through Bose operators. By employing Ehrenfest's theorem and Glauber's method of coherent states, we showed that nMT dynamics can be described by the discrete nonlinear Schrödinger equation (DNLSE). The analysis of modulational instability (MI) allowed us to define localization zones for breathers, revealing the impact of the second coupling term and well width on system's behavior. We conducted numerical simulations to examine three scenarios based on homodimer and heterodimer coupling values in relation to breather propagation. We found that homodimer coupling enhances the temporal distribution of energy and extends breather localization towards the central site. Additionally, we observed that energy within nMTs is quantized with a linear profile, influenced by homodimer coupling. The interaction between two breathers indicated that this coupling also affects energy exchanges, impacting the collective dynamics of microtubules and potentially stabilizing or destabilizing configurations, thereby influencing neuronal responses. These findings enhance the understanding of energy transfer in biological systems such as the nervous system, which is responsible for coordinating actions and rapid communication within the body. This system, also known as the neuronal system, utilizes synapses to transmit signals. In this process, neurons release chemical neurotransmitters that can influence the activity of receiving cells. © 2025 Elsevier Ltd

关键词： nonlinear equations

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Experimental demonstration of topological bounds in quantum metrology

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National Science Review 2024年第10期11卷 254-262页

作者： Min Yu Xiangbei Li Yaoming Chu Bruno Mera F.Nur ünal Pengcheng Yang Yu Liu Nathan Goldman Jianming Cai School of Physics Hubei Key Laboratory of Gravitation and Quantum Physics Institute for Quantum Science and Engineering Huazhong University of Science and Technology International Joint Laboratory on Quantum Sensing and Quantum Metrology Huazhong University of Science and Technology Advanced Institute for Materials Research (WPI-AIMR) Tohoku University TCM Group Cavendish Laboratory University of Cambridge Institut für Theoretische Physik and IQST Universit?t Ulm Center for Nonlinear Phenomena and Complex Systems Université Libre de Bruxelles Laboratoire Kastler Brossel Collège de France Shanghai Key Laboratory of Magnetic Resonance East China Normal University

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of band structures can dictate strict lower bounds on metrological properties, hence establishing a strong connection between topology and quantum metrology. In this work,we provide a first experimental verification of such topological bounds, by performing optimal quantum multi-parameter estimation and achieving the best possible measurement precision. By emulating the band structure of a Chern insulator, we experimentally determine the metrological potential across a topological phase transition, and demonstrate strong enhancement in the topologically non-trivial regime. Our work opens the door to metrological applications empowered by topology, with potential implications for quantum many-body systems.

关键词： quantum metrology multi-parameter estimation topological bounds Berry curvature Chern number topological phase transition

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Chaotic dynamics creates and destroys branched flow

arXiv

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arXiv 2024年

作者： Wagemakers, Alexandre Hartikainen, Aleksi Daza, Alvar Räsänen, Esa Sanjuán, Miguel A.F. Nonlinear Dynamics Chaos and Complex Systems Group Departamento de Física Universidad Rey Juan Carlos Tulipán s/n Madrid Móstoles28933 Spain Computational Physics Laboratory Tampere University Tampere33720 Finland Department of Physics Harvard University CambridgeMA02138 United States

The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently being added to this list. Here, we explore the laws governing the evolution of the branches in periodic potentials. On one hand, we observe that branch formation follows a similar pattern in all non-integrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, our results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires. Again, the interplay between branched flow and superwires is deeply connected to Hamiltonian chaos. In this work, we explore the relationships between the laws of branched flow and the structures of phase space, providing extensive numerical and theoretical arguments to support our findings. © 2024, CC BY-SA.

关键词： Chaotic systems

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