Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2310.19356

Nonlinear interaction of head$-$on solitary waves in integrable and nonintegrable systems

Shutian Zhang·Shikun Liu·Tengfei Jiao·Min Sun·Decai Huang
View original source ↗Read source document ↗Export metadata ↓

Abstract

This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain (a nonintegrable system) and compares the simulation results with the theoretical results in fluid (an integrable system). Three stages (i.e., pre-in-phase traveling stage, central-collision stage, and post-in-phase traveling stage) are identified to describe the nonlinear interaction processes in the granular chain. The nonlinear scattering effect occurs in the central-collision stage, which decreases the amplitude of incident solitary waves. Compared with the leading-time phase in the incident and separation collision processes, the lagging-time phase in the separation collision process is smaller. This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage. We next find that solitary wave amplitude does not influence the immediate space-phase shift in the granular chain. The space$-$phase shift of the post-in-phase traveling stage is only determined by measurement position rather than wave amplitude. The results are reversed in the fluid. An increase in solitary wave amplitude leads to decreased attachment, detachment and residence times for granular chain and fluid. For the immediate time-phase shift, leading and lagging phenomena appear in the granular chain and the fluid, respectively. These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

Explore related subjects

cond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shutian Zhang, Shikun Liu, Tengfei Jiao, Min Sun, Decai Huang. 2023-10-30. Nonlinear interaction of head$-$on solitary waves in integrable and nonintegrable systems. https://arxiv.org/abs/2310.19356

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

KEEP EXPLORING

Related papers

arXiv2026

Scale dependent chirality in twist-bend liquid crystals

The discovery of new classes of lyotropic and thermotropic liquid crystals (e.g., twist-bend, splay, and ferroelectric phases), together with significant advances in experimental techniques for their investigation, has renewed interest in a number of physical phenomena that have been studied in classical liquid crystals (nematics, cholesterics, and smectics) for more than a century. In this paper, we revisit one such ''old--new'' problem, recently highlighted in the preprint by A. Ashkinazi, H. Chhabra, A. El Moumane, M. M. C. Tortora, and J. P. K. Doye, ''Chirality Transfer in Lyotropic Twist-Bend Nematics,'' arXiv:2508.03544v1 (2025), in which various mechanisms of chirality transfer from the molecular scale to the structural scale were discussed. Here we present a simple theoretical analysis of chirality transfer within a Landau theory describing the phase transition between cholesteric and chiral twist-bend liquid crystals. We demonstrate that the handedness of the heliconical structure is opposite to that of the parent cholesteric phase. This relationship originates from the orthogonality between the cholesteric director and the vector order parameter characterizing the phase.

cond-mat.soft↗
arXiv2026

Why life is hot

The process of evolution by natural selection leads to phenotypes of increasing fitness. For cellular chemical reaction networks, this means optimising a variety of fitness functions such as robustness, precision, or sensitivity to external stimuli. We argue that these diverse goals can be achieved by a versatile, generic mechanism: coupling chemical reaction networks to reservoirs that are strongly out of equilibrium. Using theory and numerics we show that this mechanism of optimisation comes at the price of significant heat dissipation. We compute the heat flux caused by kinetic proofreading in {\it Escherichia coli} and show that it constitutes a significant fraction of the total heat flux experimentally measured in this model organism. We then demonstrate that the degree of optimality achievable saturates, and that Nature appears to operate near saturation despite high energetic costs. We argue that `life is hot' largely because of the need for a versatile mechanism to optimise a variety of fitness functions.

cond-mat.soft↗
arXiv2026

Understanding Structural Representation in Foundation Models for Polymers

From the relative scarcity of training data to the lack of standardized benchmarks, the creation of effective foundation models for polymers faces significant and multi-faceted challenges. At the core, many of these issues are tied directly to the structural representation of polymers. Here, we present a chemical language foundation model built on using a SMILES-based polymer graph representation (CPG) that incorporates polymer architectural features and connectivity that are often missing in other line notations. This foundation model exhibited excellent performance on 30 different polymer property benchmark datasets. Critical evaluation of the developed representation against other variations in control experiments reveals this approach to be a robust method of representing polymers in language-based foundation models. These experiments also reveal a strong invariance of structural representations to small perturbations, with many variations of structural representation exceeding or equaling state-of-the-art (SOTA) performance. Surprisingly, SMILES representations which are chemically or semantically invalid also provided near or SOTA performance in several instances--underscoring an unexamined blind spot in the development of chemistry language models. Examination of error sources and attention maps for the evaluated structural representations corroborate the findings of the control experiments, highlighting the ability of the model to interpolate SMILES sequence space in a manner that is loosely congruent to chemical and architectural space for polymers. Overall, this work highlights the surprising robustness of chemistry language models to structural representation perturbations and identifies the conditions under which CPG representation provides meaningful advantages.

cond-mat.soft↗