Papers

Multi-phonon resonance conditions underpin kinetic theories of phonon transport and lattice thermalization. We show that exact resonance matching, nonzero interaction coefficients, and network connectivity do not guarantee persistent energy diffusion. Symmetry-enforced balance relations drive exact-resonant collision currents to nonthermal zero-flux states, producing kinetic arrest from individual resonant sets to connected networks. Complete energy spreading is sustained by quasi-resonances. The thermodynamic and weak-nonlinearity limits do not commute: the leading kinetic behavior is recovered in the former, whereas at fixed finite size the thermalization time diverges through higher-order crossovers as the nonlinearity vanishes. Exact-resonance existence and connectivity are therefore kinematic, not sufficient dynamical, criteria for phonon energy diffusion.

A solution procedure is formulated and solved for treating the nonlinear Dissipation Inequality as a constraint equation within continuum mechanics, and allowing for incomplete knowledge of constitutive behavior. The scheme is demonstrated in the context of the rate-dependent, elastoplastic response of a bar, resulting in a nonlinear problem of constrained optimization. Both closed form and computational results are developed. The computational solutions utilize a sequence of convex optimization problems, and are shown to be accurate. In the example considered, the approach is shown to automatically correct an (intentionally) faulty constitutive specification, resulting in the solution to be in accord with the fundamental postulates of continuum mechanics.

Temporal interfaces enable wave manipulation through broken time-translation symmetry, but conventional formulations generally assume that spatial-translation symmetry is preserved across the interface. Here we consider temporal interfaces between periodic media with mismatched spatial symmetries. It is discovered that the reciprocal-lattice vectors of the pre- and post-switching media enter a generalized quasi-momentum-matching condition, giving rise to reciprocal-lattice-assisted wave-vector conversion. We then develop a multichannel temporal-scattering theory and validate it in one- and two-dimensional elastic lattices. A single incident Bloch mode can thereby excite multiple post-interface Bloch modes with distinct wave vectors and frequencies, a response inaccessible at conventional temporal interfaces. These results establish symmetry mismatch as a new degree of freedom for simultaneous control of wave vector and frequency in time-modulated periodic media.

Generalised continuum theories couple the macroscopic deformation and the micro-/meso-scopic deformation of an underlying micro-structure. They can account for internal length-scale effects and higher-order mechanical loadings absent from classical Cauchy elasticity and has shown its efficiency in modelling metamaterials. This has led to a proliferation of higher-grade and higher-order models (e.g. strain-gradient, micromorphic, micro-polar) whose underlying kinematic reduction strategies, in particular to reduce the number of material parameters, are rarely identifiable from the free energy alone. It leaves two open issues: the lack of a systematic criterion for selecting an appropriate model, and a persistent ambiguity regarding the physical status of the local frames (”directors of matter”) used in their kinematic description. Are they physical quantities describing the change of state of the given micro-structure or arbitrary kinematic descriptors of its deformation\,? This work addresses both questions through a gauge-theoretic formulation of generalised continua in finite strains. While relying on tools and modelling choices consistent with the existing geometric literature on continuum mechanics, the present approach departs from it in its objectives, aiming at a unifying classification of available mechanical models rather than the description of a specific microstructural phenomenon such as defects. In this work, generalised configurations are defined as moving frames over classical configurations, and invariance with respect to the reference generalised configuration is shown to be a necessary and sufficient condition for a gauge invariance, recovering the micromorphic theory as the general-purpose theory of the deformation of arbitrary directors of matter. A systematic classification of first-order generalised media follows from structural group reduction, while strain-gradient continua are recovered through convected frames, and finally constrained media (e.g. couple-stress) are addressed.

Dissipative equations admit distinct variational descriptions in the Bateman and Caldirola–Kanai (CK) formalisms. The classical correspondence between them is extended to a homogeneous canonical scalar field on a prescribed spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) background, where the expansion produces the time-dependent damping coefficient $3H(t)$. A multiplier action yields the Klein–Gordon equation and a complementary anti-damped equation containing the term $-3\dot{H}(t)\chi$. A first-order Bateman Lagrangian derived from the same multiplier action reproduces this physical–auxiliary pair for a general potential. Specializing to a free massive field gives the Bateman and doubled CK Lagrangians and Hamiltonians used in the canonical comparison. The factors $a^{3}(t)$ and $a^{-3}(t)$ generate the damped and anti-damped CK sectors, respectively. An explicit time-dependent canonical transformation, generated by a function linear in the Bateman momenta, maps the complete doubled CK system to the Bateman system. For this point transformation, the terms proportional to $\dot{H}(t)$ are required for Hamiltonian equivalence. In rotated variables, the Bateman scalar-field Hamiltonian takes the difference form $H_{B,\mathrm{SF}} = E_{u} - E_{v}$. It is conserved for constant $H$ and generally varies with time otherwise. For the power-law background $a(t) \propto t^{p}$, however, a correlated family at $p = 2/3$ has conserved $H_{B,\mathrm{SF}}$ despite the time dependence of $H(t)$. These results concern classical homogeneous fields on a prescribed FLRW background and exclude the gravitational phase space.