模式形成与孤子

• 交叉列表
• 替换

查看 最近的 文章

显示 2025年08月07日， 星期四 新的列表

交叉提交 (展示 1 之 1 条目 )

[1] arXiv:2508.04167 (交叉列表自 nlin.CG) [中文pdf, pdf, html, 其他]

标题： 渐近Lenia的滑翔机方程 显示英文标题

标题： The Glider Equation for Asymptotic Lenia

Hiroki Kojima, Ivan Yevenko, Takashi Ikegami

主题： 细胞自动机与格子气体 (nlin.CG) ; 神经与进化计算 (cs.NE) ; 模式形成与孤子 (nlin.PS)

Lenia是康威生命游戏的连续扩展，表现出丰富的模式形成，包括称为滑翔机的自推进结构。 在本文中，我们关注渐近Lenia，这是一种用偏微分方程表述的变体。 通过利用这种数学公式，我们分析推导出滑翔机模式的条件，我们将其称为“滑翔机方程”。 我们证明，通过将此方程作为损失函数，梯度下降方法可以成功发现稳定的滑翔机配置。 这种方法使得能够优化更新规则以找到具有特定属性的新滑翔机，例如更快移动的变体。 我们还推导出一个与速度无关的方程，该方程可表征任何速度的滑翔机，扩展了寻找新图案的搜索空间。 虽然许多优化后的图案导致最终不稳定的各种瞬态滑翔机，但我们的方法能有效识别出通过传统方法难以发现的多样化模式。 最后，我们建立了渐近Lenia与神经场模型之间的联系，突出了连接这些系统的数学关系，并提出了分析连续动力系统中模式形成的新的研究方向。 显示英文摘要

Lenia is a continuous extension of Conway's Game of Life that exhibits rich pattern formations including self-propelling structures called gliders. In this paper, we focus on Asymptotic Lenia, a variant formulated as partial differential equations. By utilizing this mathematical formulation, we analytically derive the conditions for glider patterns, which we term the ``Glider Equation.'' We demonstrate that by using this equation as a loss function, gradient descent methods can successfully discover stable glider configurations. This approach enables the optimization of update rules to find novel gliders with specific properties, such as faster-moving variants. We also derive a velocity-free equation that characterizes gliders of any speed, expanding the search space for novel patterns. While many optimized patterns result in transient gliders that eventually destabilize, our approach effectively identifies diverse pattern formations that would be difficult to discover through traditional methods. Finally, we establish connections between Asymptotic Lenia and neural field models, highlighting mathematical relationships that bridge these systems and suggesting new directions for analyzing pattern formation in continuous dynamical systems.

替换提交 (展示 1 之 1 条目 )

[2] arXiv:2503.00935 (替换) [中文pdf, pdf, html, 其他]

标题： 通过一维量子液滴中的时间晶体频率进行温度测量 显示英文标题

标题： Temperature Measurement via Time Crystal Frequencies in One-Dimensional Quantum Droplets

Saurab Das, Jagnyaseni Jogania, Jayanta Bera, Ajay Nath

主题： 量子气体 (cond-mat.quant-gas) ; 模式形成与孤子 (nlin.PS)

我们提出了一种通过分析一维（1D）量子液滴中生成的时间晶体频率来进行温度测量的方法。 该系统由一个二元玻色-爱因斯坦凝聚物混合物组成，该混合物被限制在一个受驱动的准周期性光晶格（QOL）中，并具有排斥性的立方有效平均场和吸引性的二次超越平均场相互作用。 通过求解一维扩展的格罗斯-皮塔耶夫斯基方程，我们推导出了精确的解析波函数，并在不同的驱动条件下研究了液滴的动力学行为。 具体来说，我们考察了三种情况：(i) 驱动频率恒定但QOL深度线性增加，(ii) QOL深度恒定但驱动频率线性变化，(iii) 驱动频率恒定但QOL深度正弦调制。 快速傅里叶变换分析揭示了谐波密度振荡，证实了时间晶体的形成。 此外，我们建立了一个时间晶体频率与系统温度之间的非平凡相关性，证明时间晶体频率的增加会导致液滴负温度幅度的振荡变化。 最后，数值稳定性分析确认了所获得的解保持鲁棒性，确保了其在实验实现中的可行性。 显示英文摘要

We propose a method for temperature measurement by analyzing the frequency of generated time crystals in one-dimensional (1D) quantum droplets. The system consists of a binary Bose-Einstein condensate mixture confined in a driven quasi-periodic optical lattice (QOL) with repulsive cubic effective mean-field and attractive quadratic beyond-mean-field interactions. By solving the 1D extended Gross-Pitaevskii equation, we derive the exact analytical wavefunction and investigate the droplet dynamics under different driving conditions. Specifically, we examine three cases: (i) constant driving frequency with linearly increasing QOL depth, (ii) constant QOL depth with linearly varying driving frequency, and (iii) constant driving frequency with sinusoidally modulated QOL depth. Fast Fourier Transform analysis reveals harmonic density oscillations, confirming time crystal formation. Additionally, we establish a non-trivial correlation between time crystal frequency and system temperature, demonstrating that an increase in time crystal frequency leads to oscillatory variations in the magnitude of the droplet's negative temperature. Finally, numerical stability analysis confirms that the obtained solutions remain robust, ensuring their feasibility for experimental realization.