On control of linear spring–mass chains

We consider a finite chain of mass points consecutively linked by linear springs with one of the end points acted upon by an external control force pointing along the chain. Moreover the system is observable by the coordinate of the other end point of the chain. We show that such a system is completely controllable and is completely observable for all choices of the physical parameters.     

Vibrations of a solid sphere or shell of Functionally Graded Materials

We have solved the equation of equilibrium for torsional vibrations of a sphere in which the density and rigidity are functions of the radial distance and co-latitude. Making use of the particular forms of heterogeneity the exact frequency equations are derived. The work is motivated by the recent research activity on functionally graded materials (FGM), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications.     

Optimal timing of a sequence of tasks with general completion costs

Scheduling a sequence of tasks––in the acceptation of finding the execution times––is not a trivial problem when the optimization criterion is irregular as for instance in earliness–tardiness problems. This paper presents an efficient dynamic programming algorithm to solve the problem with general cost functions depending on the end time of the tasks, idle time costs and variable durations also depending on the execution time of the tasks. The algorithm is also valid when the precedence graph is a tree and it can be adapted to determine the possible execution windows for each task not exceeding a maximum fixed cost.     

Dispensing picoliter droplets on substrates using dielectrophoresis

Liquid dielectrophoresis is exploited to initiate rapid, transient flow of aqueous liquids along co-planar electrodes patterned on insulating substrates. The flow induced by the non-uniform electric field leads to a new electrostatic equilibrium. A reduced-order model predicts the transient motion of the rivulet. When the field is removed, capillary instability breaks up the rivulet into regularly spaced droplets. Periodic circular bumps patterned on the structure, when spaced according to the most unstable wavelength based on Rayleigh's inviscid theory for the cylindrical liquid jet, lead to uniformly spaced and sized droplets. A correction factor, based on the dimensionless Ohnesorge number, accounts successfully for the effect of viscosity.     

Control of adiabatic two-phase dielectric fluid flow distribution with EHD conduction pumping

Electrohydrodynamic (EHD) conduction pumping is associated with the heterocharge layers of finite thickness in the vicinity of the electrodes, which are based on the process of dissociation of the neutral electrolytic species and recombination of the generated ions. This paper presents the successful control of dielectric liquid/vapor flow distribution between two parallel branch lines utilizing an EHD conduction pump at a select mass flux level under adiabatic condition.     

Simulation of micro- and nano-scale flows via the lattice Boltzmann method

We use the lattice Boltzmann method (LBM) for analysis of high and moderate Knudsen number phenomena. Simulation results are presented for microscale Couette and Poiseuille flows. The slip velocity, nonlinear pressure drop, and mass flow rate are compared with previous numerical results and/or experimental data. The Knudsen minimum is successfully predicted for the first time within the LBM framework. These results validate the usage of the LBM based commercial, arbitrary geometry code PowerFLOW for simulating nanoscale problems.     

New trends in localization theory

In this article we discuss some recent trends in the research of electron and phonon localization, specially in the field of quasiperiodic potentials. Then, a new scheme to detect and classify localization is developed by studying the band scaling of a related supercrystal made from replicas of the system. For one dimension, this leads to the use of dynamical systems theory to obtain the localization length and the scaling exponents of the wave functions.     

Improved dust capture methods for crushing plant

The use of compressive crushing equipment such as gyratory crushers within minerals processing plants can potentially generate large quantities of dust. Remedies to this problem include the retrofitting of shrouds, enclosures, local exhaust ventilation (LEV) systems and water suppression systems. The single or combined application of these systems must be optimised to ensure they operate efficiently. It is desirable that the future design planning of such facilities include integrated dust suppression and/or removal systems to ensure material delivery rates are maintained and the welfare of the workforce is protected.     

Phase transition and diffusivity in social hierarchies with attractive sites

We study the effects of including a distribution of valuable or attractive sites in a two-dimensional lattice in self-organizing social hierarchies. Agents move aleatorily except in the case where an attractive site is located in their neighborhood. We find that the transition between an egalitarian society at low population density and a hierarchical one at high population density strongly depends on the distribution and percolation of strategic sites. Also, it is shown how agent diffusivity is closely related to the amount of inequality. The proposed model introduces an optimization aspect to the problem of social hierarchies since the system tends to maximize the occupation of attractive sites (wealth per capita). However, when the density of attractive sites is small, the system fails to reach this state, and is trapped in a local minimum, as in a glass or jam transition.