We study a distributed user association algorithm for a heterogeneous wireless network with the objective of maximizing the sum of the utilities (on the received throughput of wireless users). We consider a state dependent wireless network, where the
rate achieved by the users are a function of their user associations as well as the state of the system. We consider three different scenarios depending on the state evolution and the users$text{}$ knowledge of the system state. In this context, we present completely uncoupled user association algorithms for utility maximization where the users$text{}$ association is entirely a function of its past associations and its received throughput. In particular, the user is oblivious to the association of the other users in the network. Using the theory of perturbed Markov chains, we show the optimality of our algorithms under appropriate scenarios.
This paper reports on the frictional properties of smooth rubber substrates sliding against rigid surfaces covered with various densities of colloidal nano-particles (average diameter 77 nm). Friction experiments were carried out using a transparent
Poly(dimethyl siloxane) (PDMS) rubber contacting a silica lens with silica nano-particles sintered onto its surface. Using a previously described methodology (Nguyen textit{et al.}, textit{J. of Adhesion} textbf{87} (2011) 235-250 ), surface shear stress and contact-pressure distribution within the contact were determined from a measurement of the displacement field at the surface of the PDMS elastomer. Addition of silica nano-particles results in a strong, pressure-independent enhancement of the frictional shear stress as compared to the smooth lens. The contribution of viscoelastic losses to these increased frictional properties is analyzed in the light of a numerical model that solves the contact problem between the rubber and the rough surface. An order-of-magnitude agreement is obtained between experimental and theoretical results, the latter showing that the calculation of viscoelastic dissipation within the contact is very sensitive to the details of the topography of the rigid asperities.
Irregular bone remodeling is associated with a number of bone diseases such as osteoporosis and multiple myeloma. Computational and mathematical modeling can aid in therapy and treatment as well as understanding fundamental biology. Different appro
aches to modeling give insight into different aspects of a phenomena so it is useful to have an arsenal of various computational and mathematical models. Here we develop a mathematical representation of bone remodeling that can effectively describe many aspects of the complicated geometries and spatial behavior observed. There is a sharp interface between bone and marrow regions. Also the surface of bone moves in and out, i.e. in the normal direction, due to remodeling. Based on these observations we employ the use of a level-set function to represent the spatial behavior of remodeling. We elaborate on a temporal model for osteoclast and osteoblast population dynamics to determine the change in bone mass which influences how the interface between bone and marrow changes. We exhibit simulations based on our computational model that show the motion of the interface between bone and marrow as a consequence of bone remodeling. The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur emph{in vitro} and emph{in vivo}. By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling. By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as emph{in vitro} and emph{in vivo}. This makes it possible to perform emph{in silica} experiments more closely resembling experimental observations.
We report the magnetic susceptibility, specific heat and dielectric constant on high purity polycrystalline samples of three hexagonal manganites: YMnO_3, LuMnO_3 and ScMnO_3. These materials can exhibit a ferroelectric transition at very high temper
atures (T_{FE} > 700K). At lower temperatures there is magnetic ordering of the frustrated Mn^{3+} spins (S=2) on a triangular Mn lattice (YMnO_3:T_N=71K; LuMnO$_3:T_N=90K and ScMnO_3:T_N=130K). The transition is characterized by a sharp kink in the magnetic susceptibility at T_N below which it continues to increase due to the frustration on the triangular lattice. The specific heat shows one clear continuous phase transition at T_N, which is independent of external magnetic field up to 9T with an entropy content as expected for Mn^{3+} ions. The temperature dependent dielectric constant displays a distinct anomaly at T_N.
