10,885 papers in this slice of arXiv.
Artem Alexandrov
We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.
Muchen Dong, Lei Wang
We study two types of mechanisms of state transitions for vector Kuznetsov-Ma breathers (KMBs) in the coupled Fokas-Lenells framework on unequal backgrounds. The amplitude imbalance breaks spectral reflection symmetry and generates richer breather morphologies. In the degenerate sector, KMBs approaching a non-self-conjugate degeneration curve from opposite sides yield different limiting solitons, revealing a discontinuous KMB-to-soliton transition. In the nondegenerate sector, the background plane waves become frequency matched at a special wavenumber, converting the KMB into a single- or two-soliton state. We determine the exact transition threshold and characterize how nearby solutions vary with the parameter. We further investigate special limiting mechanisms arising on the self-conjugate degeneration curve and on the real spectrum at the state-transition wavenumber. Numerical excitation provides further evidence for these results.
R. Ramakrishnan, Samudra Roy, S. Stalin +1
It is known that the generalized coupled nonlinear Schroedinger (GCNLS) equations can be reduced to the basic vector nonlinear Schroedinger models through various symmetry reductions. By using such reductions, soliton solutions of several interesting types can be obtained for the GCNLS system. In this paper, we show how the non-degenerate soliton solutions can be derived using one such reduction and analyze the various special features associated with the resulting soliton solutions. We find that the obtained non-degenerate soliton solutions exhibit breathing behavior, characterized by a breathing frequency. We also show that the vector solitons emerging from the reduction undergo elastic collisions with the standard phase shift, similar to the non-degenerate solitons of other coupled nonlinear Schroedinger models. Further, they undergo interesting energysharing collisions when they interact with the already known bright solitons. These collision scenarios are further confirmed by an appropriate asymptotic analysis. We have also analyzed the stability of the obtained vector solitons and found that they are stable against random perturbations. The results presented here enhance the understanding of the nature and dynamics of non-degenerate vector solitons.
Phillip Nimphius, Nariya Uchida
We studied the wave patterns in non-locally, repulsively coupled oscillators on a 2D lattice. The repulsive coupling is tuned by the phase delay απ and the wave patterns are found in the regime α∈[0.5,1]. We focused on the growth of orientationally correlated domains and found that the average total boundary size ∣B∣ obeys an approximate power law ∣B∣∝t−b for α=0.8 and α=0.9. In contrast, at α=0.7, the dynamics is disrupted by defect-mediated domain formation and domain splitting. The fitting-window dependence of the apparent exponent b, as well as the mean and standard deviation of the wave speed c, decreases with increasing α, which is consistent with the linear stability analysis of the wave solution.
Zhihao Zhang, Yankai Huang, Tiantian Li +2
Modulation instability provides an important framework for understanding rogue wave (RW) formation on continuous backgrounds. However, the formation mechanism and nonlinear spectral structures of RWs in Bose-Einstein condensate (BEC) matter-wave systems with vanishing boundary conditions remain largely unexplored. Here, we employ the nonlinear Fourier transform (NFT), based on the integrable structure of the focusing nonlinear Schrödinger equation and the Zakharov-Shabat scattering problem, to investigate two representative classes of first-order RWs in BEC systems. Through nonlinear spectral analysis and Darboux reconstruction, we demonstrate that both Gaussian-wave-packet-induced extreme localization events and experimentally observed Peregrine solitons are governed by the coherent dynamics of discrete soliton modes encoded in the nonlinear spectrum. For Gaussian initial states, increasing the initial width leads to an increasing number of discrete eigenvalues, resulting in a transition from fundamental solitons and bound states to Christmas-tree-like RW structures. For experimentally observed Peregrine solitons, localized perturbations reshape the discrete spectral configuration and phase evolution, enabling coherent focusing of multiple bound soliton modes. Furthermore, we reveal the spectral mechanism of higher-order RWs and propose an inverse spectral-engineering approach based on discrete-spectrum phase matching. Our results provide a nonlinear spectral perspective for understanding and controlling RW formation in matter-wave systems with vanishing boundary conditions.
Manu Mannattil, Haim Diamant, David Andelman
Elasticity often plays a key role in regulating phase separation in physical systems. Recent experiments have shown that elastic effects can be used to control microphase separation in swollen elastomers. Here, microphase separation arises from a mismatch between the characteristic length scales of elastic and thermodynamic interactions. In this first part of a two-part paper, we show that microphase formation in elastomers can be explained using conventional theories of elasticity through a nonlocal thermodynamic-elastic coupling arising from volume conservation. Our theory reproduces the observed dependence of phase transition temperature and domain size on elastomer stiffness in isotropically swollen elastomers. In the companion paper, we investigate the effects of anisotropic swelling and inhomogeneous elastic moduli.
Alexandre Guillet, Frank Jülicher
Conway's Game of Life shows that simple rules can generate a rich diversity of emerging structures. This cellular automaton has been translated to continuous space by Rafler (2011) in a simulation called SmoothLife. The isotropic rule of this continuous Game of Life generates patterns whose beauty has attracted the attention of a growing community at the intersection of science and computer art. We study a minimal variant of this model, continuous in space and time, that generates cell-like patterns capable of self-replicating, gliding and disappearing. The phenomenology of these unit patterns is reported and related to homogeneous-state bifurcations, symmetry breaking, observed shape instabilities, finite-amplitude morphological changes, and a dilute-to-dense transition associated with cell proliferation. Its mapping onto a large reaction--diffusion system is interpreted in terms of homeostatic concentrations of morphogens, regulated by the nonlinear survival rule and generated through a cell-sourced cascade of auxiliary reactions. Introducing a global conservation law that limits resource availability causes the system to self-organize at this dilute-to-dense transition, which we call the edge of growth. A further exploration of parameter space reveals a variety of phases and the richness of life-like morphologies organized around this edge. Resemblance to biological processes such as division, motility, and death, together with a concise formulation and numerical implementation, makes the continuous Game of Life an appealing model system for investigating the emergence and self-organization of life-like patterns.
Kristian Blom, Uwe Thiele
We derive and analyze a mean-field theory of the chiral Ising model recently introduced by Wang, Pietzonka, and Jülicher in "Edge Currents Shape Condensates in Chiral Active Matter", arXiv:2603.20064. Starting from the master equation for clockwise and counterclockwise rotations of 2x2 spin blocks, we first obtain spatially discrete evolution equations for the spatially resolved average magnetization. On this discrete level, we show that a chiral bias strongly affects phase coarsening: domains coarsen anisotropically, develop nearly rectangular shapes, and eventually display chirality-induced arrested coarsening. Taking the continuum limit of these equations yields an active field theory that has the structure of a relaxational Model-B-type dynamics supplemented by a chiral current that permanently drives the system out of equilibrium. The coarse graining explicitly shows how microscopic rotational bias generates tangential currents localized at interfaces. Using this continuum theory, we perform a linear stability analysis of radially symmetric clusters and identify a chiral fingering instability in which angular perturbations of the interface are amplified and eventually lead to radially asymmetric rotating states or disordered states.
Kazuki Ikeda
We construct quantum Turing patterns in Lindblad lattice dynamics and establish a rigorous theory of their nonlinear order and quantum fluctuations. For an explicit family of completely positive lattice generators with finite-range couplings, the first-moment equations undergo a supercritical instability at a nonzero wave number and admit analytic site- and bond-centered commensurate stripe branches. These branches are locally asymptotically stable in their reflection-fixed period-cell spaces, and projected coherent states exhibit extensive Bragg order on every bounded time interval in the semiclassical limit. We prove O(N−1/2) convergence of microscopic covariances to a nonautonomous Gaussian Lyapunov flow, transferring strict partial-transpose uncertainty violations to sufficiently large N. In the homogeneous Gaussian sector, a single dimensionless ratio controls both the Turing stability determinant and the logarithmic negativity of opposite momenta, relating wavelength selection directly to quantum entanglement. Differential transport shifts the strongest opposite-momentum correlations from the infrared to the selected Turing scale. Numerical continuation and two-dimensional simulations display stripe, spot, and labyrinth morphologies whose Fourier modes and fluctuation spectra concentrate at the same selected wave numbers.
S. Jon Chapman, M. Kavousanakis, E. G. Charalampidis +2
In the present work, we explore the self-focusing and resulting collapse of two-dimensional waveforms involving multiple pulses in a nonlinear Schroedinger equation with a general power-law nonlinearity. We find that a wide range of multi-peaked states bifurcate from the critical threshold of the cubic nonlinearity, thus representing ``bifurcations from infinity'', i.e., the relevant pulses start at infinite distance in the critical limit and draw nearer, as the nonlinearity exponent increases past that threshold. We identify the resulting ``interacting particle system'' as amounting to a force balance between the exponentially interacting tails (modulated by a suitable power law) and a linear phase-induced force. The equilibria emerging from this force balance are found to be in excellent agreement with the identified steady states of the partial differential equation. The spectral stability of multi-peaked configurations is analyzed, leading to the conclusion that all the relevant states are less stable than the single-peak collapsing solution whose stability was analyzed earlier. Indeed, we reveal both symmetry-breaking, as well as motion-inducing destabilizing dynamics, with the former ones among them being dominant and ultimately leading to a single dominant collapse spot. Moreover, we characterize systematically both the real and imaginary eigenvalues of multi-peaked configurations, partitioning them in groups of different sizes, described by powers of the solution's blowup rate G.
J. Hareesh, Sitabhra Sinha
Despite the variability in gene regulation and environmental conditions, development of an organism occurs through a sequence of highly coordinated patterning processes. Cells integrate different signals to accurately infer their position in order to adopt an appropriate identity. Using a model of epigenetic landscape originally proposed by Waddington to describe cell-fate determination, we establish the critical role played by juxtacrine signaling between cells in determining tissue patterns. Subsequently we systematically coarse-grain the model at the tissue scale to map its patterning to transition between states in a binary spin model having a free energy landscape. We show that such landscapes serve as a powerful unifying framework for describing development of biological systems across distinct spatio-temporal scales.
Su Yang, Wenrong Sun
In this paper, we study an analog of the scalar two-dimensional Fermi-Pasta-Ulam (FPU) lattice. In particular, a variety of dispersive wave structures and localized patterns are numerically identified in the numerical simulations of the FPU lattice, but, to the best of our knowledge, all of these particular wave structures do not admit analytical closed-form expressions. In order to resolve this issue, we perform a dimensional reduction and accordingly derive a modified KdV equation. Based on this reduction, we first take advantage of some of its exact localized solutions to model the associated wave patterns in the FPU lattice. In addition, we explore the two-dimensional generalization of the Riemann problems for the FPU lattice and the corresponding modified KdV reduction, whose evolution dynamics lead to the formation of multiple composite dispersive structures. Moreover, we propose and rigorously derive the KPII limit of the FPU lattice and investigate their associated wedge problems. Finally, all these relevant numerical dynamics are compared to examine the performance of these quasi-continuum long-wave asymptotic limits.
Z. Drogosz, E. I. Sfakianakis, K. Slawinska +1
We show that the inclusion of a dimension-six operator in the Higgs potential has a dramatic impact on the stability of oscillons in the SU(2) bosonic sector of the Standard Model, extending their lifetime by orders of magnitude. This happens for the physical value of the ratio between the Higgs and W boson masses, mH/mW=1.556 and for the dimension-six operator O6=(Φ†Φ)3 whose coupling constant is below the current upper bound.
Chandroth P. Jisha, Stefan Nolte, Alessandro Alberucci
We discuss how to generalize the Ehrenfest theorem for the computation of the width of nonlinear waves obeying the nonlinear Schrodinger equation. To do that, we model the nonlinear potential as a quantum harmonic oscillator (QHO) whose strength depends on the power and on the wavefunction width. We apply the model to different types of nonlinear responses, eventually comparing the results with numerical simulations. Our model has the advantage of explaining the main properties of nonlinear confined waves, such as stability and breathing, in a relatively simple and intuitive manner.
Taohua Luo, Zhenya Yan, Guoqiang Zhang
In this paper, we investigate the long-time asymptotics for the solution of the Cauchy problem of the defocusing Hirota equation on a finite-genus algebro-geometric background in the whole (x,t)-half-plane, whose method is mainly based on a Riemann-Hilbert (RH) formulation and Deift-Zhou nonlinear steepest descent method. The critical values of the phase function in the associated RH problem divide the space-time plane into four regions, in which the leading-order term is given by a phase-shifted finite-genus algebro-geometric solution. The subleading behavior depends on the region: the correction is of order t−1/3 and is governed by a Painlevé-XXXIV model RH problem in the transition regions; the leading radiation is of order t−1/2 in the Zakharov--Manakov region; and the error is O(t−1) in the fast-decay region. These results can also be extended to other higher-order members of the AKNS hierarchy.
Martin Biehl, Nathaniel Virgo
Chemistry describes aspects of the universe in terms of molecules and their reactions. In this exploratory work we present a way to describe aspects of any dynamical system in similar terms. To describe a dynamical system in this way three decisions have to be made. The first is how many different "places" there are at which molecules or chemical species can occur; the second is how to determine the species present (or not) at each place; and the third is the set of transitions and reactions that can occur between the species in the various places. For these choices to be compatible with the state update of the dynamical system each state must be able to determine transitions that take the currently occurring molecules to those occurring in the updated state. We also propose an additional requirement that there is always a unique way to choose the least amount of transitions occurring during state updates. We discuss gliders in the game of life cellular and argue that when following their definition of according to Randall Beer they satisfy the additional criterion as well. We also point out some issues with the approach.
Klaus Regenauer-Lieb, Francois Nicot, Amir Saker
This three-part series establishes a parameter-free, topological classification of multi-field instability in granular continua, extending Maxwell's rigidity count to dynamic, non-equilibrium processes. Part 1 (Foundations): a discrete Volumetric-Mechanical-Configurational (VMC) contact formulation maps contact-scale topology to macroscopic multiphysics coupling. A Parity Theorem, det(L)=(−1)Ndet(L), forces a structural null-mode for every odd channel count N, creating "Gateway" layers of broken time-reversal symmetry; once the basis-invariant Gateway number Ginv≥1, gyroscopic pumping drives non-modal transient amplification along the null direction. Part 2 (analytical, 1-D spin chains): the minimal Gateway is the N=3 VMC contact, whose skew block L∈so(3) carries a persistent zero eigenvalue and an unresisted configurational drift that operates even without friction. In an acyclic chain (first Betti number β1=0) this isolates dilatancy; closed-form solutions give secular drift for N=3 and harmonic confinement for N=4. Part 3 (numerical upscaling): quad-precision integration of tridiagonal skew-symmetric Onsager chains (N=3 to 50) confirms the contrast between odd-N secular drift and even-N confinement on invariant tori, with even-chain frequencies scaling as ∣λmineven∣∼γπ/N. VMC channels map to measurable DEM observables, enabling parameter-free evaluation of G and four falsifiable oedometer protocols.
Priyanka D. Bhoyar, Prashant M. Gade
We investigate deterministic coarsening dynamics in a spatially extended bistable gene toggle model with diffusive coupling. Unlike classical curvature-driven coarsening, where domain walls move continuously and annihilate gradually, the present system exhibits a qualitatively different mechanism. The domain walls remain pinned for long intervals and disappear abruptly through collective cascade events. The density of domain walls decays approximately as ρ(t)∼t−δ, but the coarsening exhibits clear log-periodic oscillations superimposed on the power-law behavior. For all values of the promoter strength α considered, the measured exponent satisfies δ<0.5, indicating a systematic deviation from the classical Allen--Cahn prediction δ=1/2 for curvature-driven coarsening. We show that log-periodic oscillations are not controlled by the density of domain walls, but by the domains that disappear in each cascade. The average size of disappearing domains grows roughly linearly with cascade index, producing a constant geometric spacing of cascade times, consistent with discrete scale invariance.
Hanqi Dong, Boris A. Malomed, Zhiwei Men
We address the existence, stability, and propagation dynamics of multipole solitons and vortex clusters in cubicquintic media subject to a harmonic trapping potential.We found that vortex clusters comprising N off centered vortices with alternating topological charges m equal to +(-)1, evenly distributed on a ring, can bifurcate from a multipole soliton for N less than or equal to 4 and from a second-order ring soliton for N greater than 4. Rigorous linear stability analysis, corroborated by direct numerical simulations, shows that upper branch vortex clusters with N equal to 2 and 4 remain stable over a wide range of the propagation constant. Thus, we reveal the formation mechanism of vortex clusters.
Francis F. Franco, Gabriel de T. Paula, Roman Chertovskih +2
The impact of an externally imposed magnetic field on numerical simulations of two-dimensional Rayleigh-Bénard convection (RBC) is investigated. Initially, the RBC model is examined in the absence of a magnetic field to establish a baseline. Then, a background magnetic field is introduced, and its influence on the transition to chaos is explored. For the purely hydrodynamic case and a range of the reduced Rayleigh number, the system exhibits traveling rolls which, after an attractor-merging crisis, give way to chaotic traveling rolls. Upon imposing a background magnetic field, there is a notable increase in the occurrence of traveling roll dynamics. Furthermore, the presence of the magnetic field favors the splitting/breaking of convective rolls, indicating a possible mechanism for transition to two-dimensional turbulence, with the structure of the convection cell being disrupted. A detailed analysis of the velocity field reveals that the collision between a saddle point and the center of a convective roll restores the system's original topology, with two symmetric kinetic vortices. During this collision, a magnetic vortex splits in two as a result of a magnetic reconnection. This behavior occurs intermittently in time.