Kinematic Basis of Emergent Energetics of Complex Dynamics

Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function $\varphi(x)$ emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the $\nabla\varphi$ and its orthogonal field $\gamma(x)\perp\nabla\varphi$, a general vector field $b(x)$ can be decomposed into $-D(x)\nabla\varphi+\gamma$, where $\nabla\cdot\big(\omega(x)\gamma(x)\big)=$ $-\nabla\omega D(x)\nabla\varphi$. The matrix $D(x)$ and scalar $\omega(x)$, two additional characteristics to the $b(x)$ alone, represent the local geometry and density of states intrinsic to the statistical motion in the state space at $x$. $\varphi(x)$ and $\omega(x)$ are interpreted as the emergent energy and degeneracy of the motion, with an energy balance equation $d\varphi(x(t))/dt=\gamma D^{-1}\gamma-bD^{-1}b$, reflecting the geometrical $\|D\nabla\varphi\|^2+\|\gamma\|^2=\|b\|^2$. The partition function employed in statistical mechanics and J. W. Gibbs' method of ensemble change naturally arise; a fluctuation-dissipation theorem is established via the two leading-order asymptotics of entropy production as $\epsilon\to 0$. The present theory provides a mathematical basis for P. W. Anderson's emergent behavior in the hierarchical structure of complexity science.Comment: 7 page

A Concentric-based Sleep Scheduling Scheme for Wireless Sensor Networks

[[abstract]]In Wireless Sensor Networks (WSNs), how to extend the lifetime is an important issue. Our research uses Sleeping Scheduling scheme which divides the network into many concentric layers and rotates sensors in different odd and even layers to sleep. By our scheme, we can balance the power consumption among all sensors and reduce power and transmission load of sensors near sink. Our research use Transmit Power Control (TPC) technique to control topology and divide concentric layers, and use the topology to transmit packets to sink. Finally, the performance of our scheme is better than other Sleeping Scheduling schemes in the simulations.[[sponsorship]]Tamkang University[[incitationindex]]EI[[conferencetype]]åé[[conferencetkucampus]]å°åæ ¡å[[conferencedate]]20150902~20150903[[booktype]]é»å­ç[[iscallforpapers]]Y[[conferencelocation]]Taipei, Taiwa