A paradigmatic minimal system to explain the Ziegler paradox

The destabilization effect of damping on a class of general dynamical systems is discussed. The phenomenon of jump in the critical value of the bifurcation parameter, in passing from undamped to damped system, is view in a new perspective, according to which no discontinuities manifest themselves. By using asymptotic analysis, it is proved that all subcritically loaded undamped systems are candidate to become unstable, provided a suitable damping matrix is added. The mechanism of instability is explained by introducing the concept of modal dampings, as the components of the damping forces along the unit vectors of a non-orthogonal eigenvector basis. Such quantities can change sign while the load changes the eigenvectors of the basis, thus triggering instability. A paradigmatic, non-physical, minimal system has been built up, admitting closed-form solutions able to explain the essence of the destabilizing phenomenon. Series expansions carried out on the exact solution give information on how to deal more complex systems by perturbation methods.     

A solids mixing rate correlation for small scale fluidized beds

A new first degree solids mixing rate is proposed to evaluate the mixing of solids in small scale fluidized beds. Particle mixing experiments were carried out in a 2D fluidized bed with a cross-section of 0.02 m × 0.2 m and a height of 1 m. White and black particles with average diameters of 850 and 450 μm were used in our experiments. Image processing was used to measure the concentration of the tracers at different times. The effects of four representative operating parameters (superficial gas velocity, ratio of tracer particles to bed particles, tracer particle position, and particle size) on mixing are discussed with reference to the mixing index. We found that the Lacey index depends on the concentration of the tracers. The position of the tracers affects the initial mixing rate but not the final degree of mixing. However, the new mixing rate equation does not depend on the initial configuration of the particles because this situation is considered to be the initial condition. Using the data obtained in this work and that found in literature, an empirical correlation is proposed to evaluate the mixing rate constant as a function of dimensionless numbers (Archimedes, Reynolds, and Froude) in small scale fluidized beds. This correlation allows for an estimation of the mixing rate under different operating conditions and for the detection of the end point and/or the time of mixing.     

Adaptive dynamic programming-based stabilization of nonlinear systems with unknown actuator saturation

This paper addresses the stabilizing control problem for nonlinear systems subject to unknown actuator saturation by using adaptive dynamic programming algorithm. The control strategy is composed of an online nominal optimal control and a neural network (NN)-based feed-forward saturation compensator. For nominal systems without actuator saturation, a critic NN is established to deal with the Hamilton–Jacobi–Bellman equation. Thus, the online approximate nominal optimal control policy can be obtained without action NN. Then, the unknown actuator saturation, which is considered as saturation nonlinearity by simple transformation, is compensated by employing a NN-based feed-forward control loop. The stability of the closed-loop nonlinear system is analyzed to be ultimately uniformly bounded via Lyapunov’s direct method. Finally, the effectiveness of the presented control method is demonstrated by two simulation examples.     

Asymmetric bifurcations in a pressurised circular thin plate under initial tension

It has been known for some time that under certain circumstances the axisymmetric solution describing the deformation experienced by a stretched circular thin plate or membrane under sufficiently strong normal pressure does not represent an energy-minimum configuration. By using the method of adjacent equilibrium a set of coordinate-free bifurcation equations is derived here by adopting the Föppl–von Kármán plate theory. A particular class of asymmetric bifurcation solutions is then investigated by reduction to a system of ordinary differential equations with variable coefficients. The localised character of the eigenmodes is confirmed numerically and we also look briefly at the role played by the background tension on this phenomenon.     

Dynamics and control in an $$({\varvec{n}}+{\varvec{2}})$$ ( n + 2 ) -neuron BAM network with multiple delays

Nonlinear Dynamics - The issues of the stability and bifurcation for a delayed BAM network involving two neurons in the I-layer and arbitrary neurons in the J-layer are concerned in the present...     

Magic microfluidic T-junctions: Valving and bubbling

We develop and characterize a simple microfluidic component: a T-junction of two microfluidic channels conveying a gas and a liquid into the junction. It can either microvalve the two fluids or microbubble the gas with its functions switchable and controlled by the inlet pressure ratio of the two fluids. For the microvalving, it requires no actuating, moving and sealing components. Instead, the flow channels and the mechanisms of supplying the two fluids into them provide all these functions automatically. For microbubbling, it generates indistinguishable (monodispersed) bubbles steadily and stably with their size and generation frequency well-controlled.     

Why organizational networks in reality do not show scale-free distributions

This paper discusses chain of command networks that are most likely to exhibit the scale-free (SF) property in organizational networks, explaining why organizational networks do not show SF distributions. We propose an evolving hierarchical tree network model without explicit preferential attachment. The model simulates several kinds of chain of command networks with the span of control ranging from extreme homogeneity to extreme heterogeneity. In addition to traditional degree distribution, a new kind of cumulative-outdegree distribution p(K _cum =k _cum ) is introduced and discussed that gives a probability that a randomly selected node has exactly k _cum children nodes. Theoretical analysis and simulation results show that even if the network size is large enough to meet the demand of large-scale networks, the SF property can emerge only when a hierarchical tree lies in two extreme situations: (1) the exact same span of control exists at all levels of an organization; (2) the node outdegree (i.e. span of control) distribution obeys a power-law distribution. The empirical investigations show that real organization networks are between the two extreme situations. This is why organizational networks in reality do not show an SF degree distribution or SF cumulative-outdegree distribution. This finding shows that the SF property is the consequence of extreme situations, even though it is very common in nature and in society. In fact, the SF property is of no value in the study of problems in organizations.     

Measurement and evaluation of the metabolic capacity of an urban ecosystem

Cities as superorganisms confront disturbances from their metabolic processes, including large metabolic fluxes, low stocks of resources and products, and a low efficiency of the urban material metabolism. Based on ecological thermodynamics, an indicator system is established in this paper to evaluate the fluxes, stocks, and effiency of the urban material metabolism using emergy analysis. Also, a new model for the urban material metabolism is proposed to define the production possibility curve using a wealth index (WI) and an ecological effiency index (EEI). Then, six large Chinese cities including Beijing, Shanghai, Tianjin, Chongqing, Guangzhou, and Shenzhen are selected as typical cases to validate the proposed model. The results show that Shenzhen has the highest metabolic capacity, followed by Beijing, Shanghai, Guangzhou, Tianjin, and Chongqing. It is also reflected that different urban material metabolisms of the six cities are resulted from the varied regional metabolic capacities, thus providing insights into how cities improve their metabolic capacities. Meanwhile, Shenzhen has the highest WI and EEI, Chongqing has the lowest WI and EEI, and Beijing, Shanghai, Tianjin, and Guangzhou has low WI and high EEI. It is also shown that the sustainable operation of the urban material metabolism reflects the mutualism and symbiosis between socioeconomic development and ecological environment protection.