39 papers
This paper reviews deterministic and stochastic network-level models to explain how Arrhenius-like temperature dependencies in individual biochemical reactions transform into complex emergent system behaviors, such as non-Arrhenius scaling and thermal limits, thereby bridging empirical temperature response curves with the molecular organization of biological systems.
This paper constructs modular families of quantum-integrable elliptic long-range spin chains with q-deformed interactions by freezing spin-Ruijsenaars systems at classical equilibrium configurations, thereby providing a unified framework that interpolates between nearest-neighbour and long-range models while encompassing various known integrable chains and their deformations.
This paper revisits quadratic Bureau-Guillot systems containing first and second Painlevé transcendent coefficients, utilizing Okamoto's geometric approach and iterative polynomial regularisation to establish their birational equivalence, resolve the Painlevé equivalence problem for non-rational meromorphic coefficients, and identify a Hamiltonian formulation for one of the systems.
This paper provides an informal introduction to the integrable systems approach to the Schottky problem, detailing how Jacobian theta functions yield solutions to the KP equation and culminating in Krichever's proof of Welters' trisecant conjecture for the most degenerate flex line case.
This paper introduces a deformation-based framework for static billiards that utilizes the Jacobian determinant in noncanonical angular coordinates to reveal structured local phase-space expansion and contraction, demonstrating how these local variations globally balance to preserve area and correlate with invariant manifolds and periodic orbits.
This paper demonstrates through both numerical simulations and physical experiments that two coupled identical chaotic Lorenz oscillators exhibit simultaneous deterministic coherence and anti-coherence resonances in their respective state variables when the coupling strength is below the threshold for complete synchronization, a regime characterized by hyperchaotic dynamics and on-off intermittency.
This paper presents an energetics-based mathematical model for the diffusiophoretic motion of a deformable droplet on a liquid surface, deriving time-evolution equations for translation and elliptic deformation to identify three stable states and analyze the transitions between them.
This thesis investigates the dynamics and interactions of solitons (kinks, oscillons, vortices, and sphalerons) in one- and two-dimensional models by employing effective collective coordinate models to introduce radiation modes, generalize moduli space metrics with vibrational degrees of freedom, identify semi-BPS sphalerons, and propose a dynamic stabilization mechanism driven by internal modes.
This paper numerically investigates how external magnetic fields influence the long-range transport of large polarons (solitons) in discrete quasi-one-dimensional systems, demonstrating that the effect depends on both field strength and specific system parameters that define soliton properties, while also examining polarons generated by donor complexes.
This paper reports the deterministic experimental realization of breathing magnetic multi-solitons in a two-component Bose gas and demonstrates their controlled fission into fundamental constituents via a localized perturbation, effectively serving as an experimental analog of the inverse scattering transform.
GradNet introduces a gradient-based, AI-enabled framework that inverts traditional network science by treating topology as a continuously differentiable object to optimize arbitrary dynamical objectives under constraints, thereby demonstrating that canonical network features emerge spontaneously from constrained optimization rather than explicit design.
This paper demonstrates that while the self-similar photon ring structure of a Kerr black hole persists in phase space without exhibiting chaos, deforming the spacetime away from the Kerr geometry induces chaotic dynamics near resonant bound orbits, resulting in a fractal phase-space structure encoded in the first-return map.
This paper reveals a layered organization in the Kuramoto-Sivashinsky equation's state space where multiple invariant sets, including chaotic attractors and periodic orbits, coexist and are selected by initial energy levels, a phenomenon linked to continuous spatial translational symmetry.
Using the Whitham modulation method, this paper demonstrates that in conservative nonlinear Klein-Gordon systems, instability fronts propagate at the maximal group velocity as the solution evolves into a self-similar regime at asymptotically large times.
This paper reviews and contrasts the long-time behavior of initial-boundary value problems for systems admitting Lax Pair formulations, illustrating cases where integrability ensures regular asymptotic behavior alongside instances where irregular, fractal-like chaos emerges, while connecting these findings to perturbed Lax Pair theory on the real line.
This paper utilizes numerical simulations of chaotic intermittency dynamics in a finite 3D Z(3) spin lattice to reveal a complex phase behavior characterized by a second-order transition with hysteresis and resonances, a hybrid universality class combining mean-field and 3D Ising features, and a weak first-order transition via a tricritical crossover.
This paper constructs a novel family of exact cnoidal waves and dark solitons for the focusing and defocusing Ablowitz-Ladik equations, characterized by a "swinging" phase with nonlinear dependence on time and site number, derived via a two-point map that enables arbitrary lattice positioning and establishes explicit velocity quantization rules for waves on closed loops.
This paper extends semi-classical instanton analysis to a symmetric quartic potential with four degenerate minima, deriving energy splittings and Rabi oscillations for distinct tunneling pathways that show excellent agreement with numerical results while revealing a critical coupling regime where the discrete symmetry melts into a continuous symmetry.
The paper introduces Panda, a pretrained foundation model for chaotic dynamics that, despite being trained exclusively on synthetic low-dimensional ordinary differential equations, demonstrates emergent zero-shot forecasting capabilities for unseen chaotic systems, real-world experimental data, and even partial differential equations.
This paper analyzes a one-dimensional model of a self-propelled camphor disk perturbed by a second localized source, demonstrating through both numerical simulations and analytical solutions that the rotor's velocity exhibits a pronounced asymmetry depending on whether it approaches or recedes from the perturbation.