Global Solutions for Incompressible Viscoelastic Fluids

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial data. The results hold in both two and three dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy problem for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial dat

On 2D Viscoelasticity with Small Strain

An exact two-dimensional rotation-strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under the smallness assumptions only on the size of initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.Comment: Different contributions of strain and rotation of the deformation are studied for viscoelastic fluids of Oldroyd-B type in 2

Proactive Highly Ambulatory Sensor Routing (PHASeR) protocol for mobile wireless sensor networks

This paper presents a novel multihop routing protocol for mobile wireless sensor networks called PHASeR (Proactive Highly Ambulatory Sensor Routing). The proposed protocol uses a simple hop-count metric to enable the dynamic and robust routing of data towards the sink in mobile environments. It is motivated by the application of radiation mapping by unmanned vehicles, which requires the reliable and timely delivery of regular measurements to the sink. PHASeR maintains a gradient metric in mobile environments by using a global TDMA MAC layer. It also uses the technique of blind forwarding to pass messages through the network in a multipath manner. PHASeR is analysed mathematically based on packet delivery ratio, average packet delay, throughput and overhead. It is then simulated with varying mobility, scalability and traffic loads. The protocol gives good results over all measures, which suggests that it may also be suitable for a wider array of emerging applications

Low-temperature anomalous specific heat without tunneling modes: a simulation for a-Si with voids

Using empirical potential molecular dynamics we compute dynamical matrix eigenvalues and eigenvectors for a 4096 atom model of amorphous silicon and a set of models with voids of different size based on it. This information is then employed to study the localization properties of the low-energy vibrational states, calculate the specific heat C(T) and examine the low-temperature properties of our models usually attributed to the presence of tunneling states in amorphous silicon. The results of our calculations for C(T) and "excess specific heat bulge" in the C(T)/T^3 vs. T graph for voidless a-Si appear to be in good agreement with experiment; moreover our investigation shows that the presence of localized low-energy excitations in the vibrational spectrum of our models with voids strongly manifests itself as a sharp peak in C(T)/T^3 dependence at T < 3K. To our knowledge this is the first numerical simulation that provides adequate agreement with experiment for the very low-temperature properties of specific heat in disordered systems within the limits of harmonic approximation.Comment: 5 pages with 2 ps figures, submitted to PR

Analytical characterization of damping in gear teeth dynamics under hydrodynamic conditions

Using an analytical method, we characterize damping and stiffness in lightly loaded, lubricated gear pairs at different operating speeds and lubricant temperatures. This is accomplished by employing a trace method to approximate and model the hysteresis loop of the lubricant reaction, thus recording the energy transformation mechanism during the gear teeth oscillatory motion. The method can be expanded for use in a variety of problems where hydrodynamic vibro-impacts lead to energy dissipation

Tailoring strongly nonlinear negative stiffness

Negative, nonlinear stiffness elements have been recently designed as configurations of pairs or groups of linear springs. We propose a new design of such a system by using a single linear spring with its moving end rolling on a path described by an equation of varying complexity. We examine the effect that the selection of the path has on the size of the deflection regime where negative stiffness is achieved. The stability properties of the equilibrium positions of the system are also investigated, highlighting the influence that the complexity of the path equation brings. The latter naturally affects the characteristics of the forcing functions around these positions. It is demonstrated that the properties of the system can be tailored according to the nature of the equation used and we show how essentially nonlinear negative stiffness elements, (i.e., with no linear parts) can be designed. These results provide a useful standpoint for designers of such systems, who wish to achieve the desired properties in reduced space, which is a common requirement in modern applications

Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure

Wavy stripes and squares in zero P number convection

A simple model to explain numerically observed behaviour of chaotically varying stripes and square patterns in zero Prandtl number convection in Boussinesq fluid is presented. The nonlinear interaction of mutually perpendicular sets of wavy rolls, via higher mode, may lead to a competition between the two sets of wavy rolls. The appearance of square patterns is due to the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late

Integration of molecular biology tools for identifying promoters and genes abundantly expressed in flowers of Oncidium Gower Ramsey

<p>Abstract</p> <p>Background</p> <p>Orchids comprise one of the largest families of flowering plants and generate commercially important flowers. However, model plants, such as <it>Arabidopsis thaliana </it>do not contain all plant genes, and agronomic and horticulturally important genera and species must be individually studied.</p> <p>Results</p> <p>Several molecular biology tools were used to isolate flower-specific gene promoters from <it>Oncidium </it>'Gower Ramsey' (<it>Onc</it>. GR). A cDNA library of reproductive tissues was used to construct a microarray in order to compare gene expression in flowers and leaves. Five genes were highly expressed in flower tissues, and the subcellular locations of the corresponding proteins were identified using lip transient transformation with fluorescent protein-fusion constructs. BAC clones of the 5 genes, together with 7 previously published flower- and reproductive growth-specific genes in <it>Onc</it>. GR, were identified for cloning of their promoter regions. Interestingly, 3 of the 5 novel flower-abundant genes were putative trypsin inhibitor (<it>TI</it>) genes (<it>OnTI1</it>, <it>OnTI2 </it>and <it>OnTI3</it>), which were tandemly duplicated in the same BAC clone. Their promoters were identified using transient GUS reporter gene transformation and stable <it>A. thaliana </it>transformation analyses.</p> <p>Conclusions</p> <p>By combining cDNA microarray, BAC library, and bombardment assay techniques, we successfully identified flower-directed orchid genes and promoters.</p

Differential scanning calorimetry (DSC) and thermodynamic prediction of liquid fraction vs temperature for two high-performance alloys for semi-solid processing (Al-Si-Cu-Mg (319s) and Al-Cu-Ag (201))

There is a need to extend the application of semi-solid processing (SSP) to higher performance alloys such as 319s (Al-Si-Cu-Mg) and 201 (Al-Cu-Ag). The melting of these two alloys was investigated using differential scanning calorimetry (DSC) and thermodynamic prediction. The alloys had been processed by magneto-hydrodynamic (MHD) stirring before receipt to produce a microstructure suitable for SSP. The DSC results for the as-received MHD material were compared with those for material which has been taken through a complete DSC cycle and then reheated for a second DSC run. The effects of microsegregation were then analyzed. A higher liquid fraction for a particular temperature is found in the second DSC run than the first. Microstructural observations suggest this is because the intermetallics which form during the first cooling cycle tend to co-located. Quaternary and ternary reactions then occur during the second DSC heat and the co-location leads to enhanced peaks. The calculated liquid fraction is lower with 10 K/min DSC heating rate comparing with 3 K/min at a given temperature. The DSC scan rate must therefore be carefully considered if it is to be used to identify temperature parameters or the suitability of alloys for SSP. In addition, the starting material for DSC must represent the starting material for the SSP. With thermodynamic prediction, the equilibrium condition will provide better guidance for the thixoforming of MHD stirred starting material than the Scheil condition. The Scheil mode approximates more closely with a strongly microsegregated state