Quantum mechanics and relativity in the continuum imply the well known spin-statistics connection. However for particles hopping on a lattice, there is no such constraint. If a lattice model yields a relativistic field theory in a continuum limit, this constraint must ”emerge” for physical excitations. We discuss a few models where a spin-less fermion hopping on a lattice gives excitations whic...

In this paper, three dimensional (3D) static and dynamic analysis of thick plates based on the Meshless Local Petrov-Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

Adler’s lattice equation has acquired the status of a master equation among 2D discrete integrable systems. In this paper we derive what we believe are the first explicit solutions of this equation. In particular it turns out necessary to establish a non-trivial seed solution from which soliton solutions can subsequently be constructed using the Bäcklund transformation. As a corollary we find t...

For a class of systems obeying Euler's equation of motion the existence of a quantity to be named "proper mechanical energy" (PME) is shown which, together with internal energy, results in a quantity to be named "proper energy" (PE), which is conserved under conditions of time-dependent potentials. The appertaining formal structure for the continuum mechanics of such systems is the counterpart ...

In this paper, we construct Grammian-like quasideterminant solutions of a non-Abelian Hirota–Miwa equation. Through continuum limits of this non-Abelian Hirota–Miwa equation and its quasideterminant solutions, we construct a cascade of noncommutative differential-difference equations ending with the non-commutative KP equation. For each of these systems, the quasideterminant solutions are const...

A eld computer is a (spatial) continuum-limit neural net (MacLennan 1987). We investigate eld computers whose temporal dynamics is also continuum-limit, being governed by an integro-diierential equation. We prove that even when they are purely linear, such systems are computationally universal. The \trick" used to get such universal (and therefore in general nonlinear) behavior is quite similar...

The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the...

This research discusses how to make 3DCG animations of flowers, wings, and cloths etc. which are modeled by continuum surfaces. The Newtonian dynamics equation of the surface deformation is derived from the potential functions ( the energy functions ) of the surfaces based on the variational principle of the continuum mechanics. The Newtonian dynamics equation of the surface deformation is ob...

The Casimir attraction can significantly interfere the physical response of nanoactuators. The intensity of the Casimir force depends on the geometries of interacting bodies. The present paper is dedicated to model the influence of the Casimir attraction on the electrostatic stability of nanoactuators made of cylindrical conductive nanowire/nanotube. An asymptotic solution, based on path-integr...