Vibration of an elastic tensegrity structure

The dynamic behavior of a simple elastic tensegrity structure is examined, in order to validate observations that the natural damping of the elastic elements in such a structure is poorly mobilized, due to the natural flexibility of the equilibrium position of the structure. It is confirmed, analytically and numerically, that the energy decay of such a system is slower than that of a linearly-damped system.     

Nonlinear response theory for inhomogeneous systems in various ensembles

Nonlinear equations governing the relaxation of some macroscopic quantities, a(r,t) are derived using Kubo's response theory, in isolated inhomogeneous systems. The resulting equations contain microcanonical time correlation functions. It is shown how to express these in terms of arbitrary ensemble correlation functions and correction arising from their infinite time behaviour are discussed. In addition it is shown that the concept of local equilibrium must be modified somewhat.     

Mode coupling theory of hydrodynamics and steady state systems

We construct a formal mode coupling theory for hydrodynamic systems which includes contributions from all powers of the hydrodynamic variables. This theory is applied to nonequilibrium steady state systems. A generalization of the local equilibrium distribution is used to describe the nonequilibrium state. This distribution independently constrains all moments of the hydrodynamic variables. The infinite hierarchy of equations for the moments of the hydrodynamic variables is truncated using an inverse system size expansion. Explicit results are obtained for the time correlation functions of fluids with a linear temperature gradient or a linear shear. These results agree with previous studies of these steady states.     

Transport in two dimensions. II the thermal conductivity coefficient

The study of generalized transport coefficients in two dimensions is continued. In this article, the thermal conductivity coefficient is examined. The Mori formalism is used and the set of variables consists of all finite multilinear products of two collective conserved variables, the energy density and the momentum density. The tensorial symmetry of Euler and dissipative matrix elements is taken into account explicitly. Two simultaneous non-linear integral equations are obtained, the asymptotic solution for which behave in the same manner as the self-diffusion coefficient studied in an earlier paper. However, the coefficient is dependent upon the intermolecular potential. The heat current auto-correlation function decays asymptotically as $\text{[t}\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{t]}{}^{\mathrm{?1}}$. The asymptotic form for the shear viscosity coefficient is examined briefly and found to be independent of the intermolecular potential. A better approximation for the coefficient of the asymptotic form of the self-diffusion coefficient is presented.