面向色散弹性介质的理性扩展热力学

中文摘要 AI 辅助

我们在理性扩展热力学（RET）框架内建立了一维色散弹性理论，采用局部一阶平衡定律而非高阶空间梯度作为基础描述。补充的机械能定律和Ruggeri-Strumia主场原理确定了可容许的应力、内部通量和产生项。典型的两场层级在显式凸性条件下是对称双曲的，包含非线性弹性和广义应力理论作为主要子系统。对于可逆线性奇异两场类，消除快应力模式可精确得到Love-Rosenau方程，同时给出必要且充分的可实现性条件。非线性弹性应力和非二次高阶场能量与同一RET架构兼容；对于精确的非线性Love-Rosenau约化，我们保留二次高阶场惯性，同时允许非线性弹性应力。约化方程存在行波首次积分。对于主导三次弹性修正，我们在超音速速度窗口中得到精确的参数化光滑孤波脉冲，而截断余弦紧孤子被排除。对双曲母系统的直接模拟显示，在可逆 regime 中脉冲有限时间持续，弱耗散下缓慢衰减。在约化理论中，局部母能量通量与间隙功保持区分。

英文摘要

We develop a one-dimensional theory of dispersive elasticity within Rational Extended Thermodynamics, taking local first-order balance laws rather than higher spatial gradients as the fundamental description. A supplementary mechanical-energy law and the Ruggeri--Strumia main-field principle determine the admissible stress, internal fluxes and production. A canonical two-field hierarchy is symmetric hyperbolic under explicit convexity conditions and contains nonlinear elasticity and a generalized-stress theory as principal subsystems. For the reversible linear singular two-field class, elimination of the fast stress mode yields the Love--Rosenau equation exactly, together with a necessary and sufficient realizability condition. Nonlinear elastic stresses and non-quadratic higher-field energies are compatible with the same RET architecture; for the exact nonlinear Love--Rosenau reduction we retain quadratic higher-field inertia while allowing nonlinear elastic stress. The reduced equation admits a travelling-wave first integral. For the leading cubic elastic correction we obtain an exact parametric smooth solitary pulse in a supersonic velocity window, while the truncated-cosine compacton is excluded. Direct simulations of the hyperbolic parent system show finite-time pulse persistence in the reversible regime and slow decay under weak dissipation. The local parent energy flux is kept distinct from interstitial working in the reduced theory.

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33 pages, 3 figures