In this work, different standard and non-standard continualization methods are applied to an anisotropic membrane lattice obtain non-classical continuum models, capable of accurately capturing its dynamic behaviour. Their performance is evaluated by comparing the discrete models through their dispersion relations, as well natural frequencies for fixed-edge configuration. Moreover, occurrence ce...

A random graph order, also known as a transitive percolation process, is defined by taking a random graph on the vertex set {0, . . . , n− 1}, and putting i below j if there is a path i = i1 · · · ik = j in the graph with i1 < · · · < ik. In [15], Rideout and Sorkin provide computational evidence that suitably normalised sequences of random graph orders have a “continuum limit”. We confirm that...

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We investigate (2+1)-d Hamiltonian lattice gauge theory using a class of Hamiltonians having exactly known vacuum states. These theories are shown to have a wide range of possible classical continuum limits which differ from that of the standard Kogut-Susskind Hamiltonian. This conclusion is at variance with some previously published results. We examine the quantum continuum behavior of these t...

The classical approach to linking lattice dynamics properties to continuum equations of motion, the “method of long waves,” is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the first part of the article, the derivation is made within the harmonic approximation for the perfect lattice response. Higher order terms are included in the...

A redesigned starting point for covariant φn, n ≥ 4, models is suggested that takes the form of an alternative lattice action and which may have the virtue of leading to a nontrivial quantum field theory in the continuum limit. The lack of conventional scattering for such theories is understood through an interchange of limits. Despite being perturbatively nonrenormalizable, the quantum theory ...

The scattering of guided waves through a complex structure is great importance in predicting vibration energy transmission and reflection across structures. Multi-scale models based on generalized continuum theory have been developed recently to investigate the behavior media frame mechanics. In this study, second strain gradient are employed together with matrix method study wave non-classical...

Twisted Eguchi-Kawai reduced chiral models are shown to be formally equivalent a U(1) non-commutative parent theory. The non-commutative theory describes the vacuum dynamics of the non-commutative charged tachyonic field of a brane system. To make contact with the continuum non-commutative theory, a double scaling large N limit for the reduced model is required. We show a possible limiting proc...

A number of years ago, Widom and Rowlinson proposed a continuum model of interacting spherical particles and provided compelling evidence that this model has a phase transition. A rigorous proof of the existence of a two-phase regime in this model emerged shortly thereafter and recently, this phase transition has been understood in geometric terms—as a percolation phenomenon. Nevertheless, prog...