A Variational Principle for the Steady-State Heat Transfer Process in a Rigid Continuous Mixture

The subject of this paper is the steady-state heat transfer process in a rigid mixture with N continuous constituents, each of them representing a given continuous body. A continuous mixture consists of a convenient representation for bodies composed by several different materials or phases, in which the actual interfaces do not allow an adequate Classical Continuum Mechanics approach, once that the boundary conditions make the mathematical description of the problem unfeasible (as for instance in reinforced concrete, polymer strengthened concrete, and porous media). The phenomenon is mathematically described by a set of N partial differential equations coupled by temperature-dependent terms that play the role of internal energy sources. These internal energy sources arise because, at each spatial point, there are different temperatures, each one associated with one constituent of the mixture. The coupling among the partial differential equations arises from the thermal interchange among continua in a thermal nonequilibrium context (different temperature levels). In this work, it is presented a functional whose minimization is equivalent to the solution of the original steady-state problem (variational principle). The features of this functional give rise to proofs of solution existence and solution uniqueness. It is remarkable that, with the functional to be proposed here, instead of solving a system of N coupled partial differential equations, we need to look only for the minimum of a single functional.

Multiplicative Decomposition of Heterogeneity in Mixtures of Continuous Distributions

A system’s heterogeneity (diversity) is the effective size of its event space, and can be quantified using the Rényi family of indices (also known as Hill numbers in ecology or Hannah–Kay indices in economics), which are indexed by an elasticity parameter q≥0. Under these indices, the heterogeneity of a composite system (the γ-heterogeneity) is decomposable into heterogeneity arising from variation within and between component subsystems (the α- and β-heterogeneity, respectively). Since the average heterogeneity of a component subsystem should not be greater than that of the pooled system, we require that γ≥α. There exists a multiplicative decomposition for Rényi heterogeneity of composite systems with discrete event spaces, but less attention has been paid to decomposition in the continuous setting. We therefore describe multiplicative decomposition of the Rényi heterogeneity for continuous mixture distributions under parametric and non-parametric pooling assumptions. Under non-parametric pooling, the γ-heterogeneity must often be estimated numerically, but the multiplicative decomposition holds such that γ≥α for q>0. Conversely, under parametric pooling, γ-heterogeneity can be computed efficiently in closed-form, but the γ≥α condition holds reliably only at q=1. Our findings will further contribute to heterogeneity measurement in continuous systems.

Automation of physical experiments regarding explosions of air-methane mixtures

In the following study, experimental results are obtained from an automated stand. With the help of this experimental stand, visualization techniques such as Schlieren and Shadowgraph can be applied, to study the flame front propagation of air and inflammable gas mixtures initiation. In parallel, an infrared sensor was used to control a push-pull solenoid to open the gas escape diaphragm of the stand. To obtain the explosive gas mixture at various concentrations (between the lower explosion limit and the upper explosion limit) an original programmable mixer was used, based on computational algorithms for accurate control of stepper motors which allow attainment of air and inflammable gas flows in order to achieve a homogeneous and continuous mixture at the desired concentration. The performed experiments allow for a better understanding of the flame front production and propagation, facilitating the knowledge and optimization of the operating times from the reduction mechanisms for reducing the effects of explosions of the flammable gas-air mixtures.

Design of a new-concept conical positive displacement slurry pump for continuous de-clogging

Slurry pumps are extensively used in the construction industry while positive displacement screw pumps are used in most mobile concrete pump applications. The aggregate size is known to significantly affect pump performance in terms of clogging. Large aggregates tend to be trapped against the stator-rotor interface, blocking the continuous and smooth operation of the screw pump. In order to avoid the development of excessive stress values able to damage the rotor-stator mechanism of the pump, the typical de-clogging mechanism deployed by most positive displacement screw slurry pumps includes reversing the rotation of the pump driving motor thus allowing the aggregates to be carried away with the mixture, so that the pump can soon resume its operation. This procedure causes frequent start-stops of the pump resulting in dis-continuation of the pumped mixture lasting a few seconds, that while being of little importance in most construction applications, can be of significance in applications requiring higher levels of accuracy and continuous mixture flow. In the context of this work, a novel concept of positive displacement screw slurry pump is presented, including a continuous de-clogging mechanism, without the need to reverse the rotation of the driving motor. This de-clogging operation is achieved through the modification of the geometry of both the rotor and stator introducing a conical form along the axial direction. This configuration of the rotor-stator, allows for small displacements along the axial direction, which in turn increases the size of the cavities facilitating the de-clogging of the pump. Variable pitch is also introduced to both the rotor and stator in order to ensure constant mass flow of the mixture throughout the length of the screw pump covering for the velocity increase as a result of the conical geometry. The axial movement of the rotor in relation to the fixed stator, is achieved through the elastic support of the rotor in the axial direction, that allows for small axial displacements, when stresses induced from trapped aggregates exceed the stiffness of the support. The proposed concept comprises a passive real-time de-clogging mechanism that greatly reduces pump idle time compared to the conventional mechanism described earlier, providing smoother operation and stable mass flow of the mixture.

Semisoft clustering of single-cell data

Motivated by the dynamics of development, in which cells of recognizable types, or pure cell types, transition into other types over time, we propose a method of semisoft clustering that can classify both pure and intermediate cell types from data on gene expression from individual cells. Called semisoft clustering with pure cells (SOUP), this algorithm reveals the clustering structure for both pure cells and transitional cells with soft memberships. SOUP involves a two-step process: Identify the set of pure cells and then estimate a membership matrix. To find pure cells, SOUP uses the special block structure in the expression similarity matrix. Once pure cells are identified, they provide the key information from which the membership matrix can be computed. By modeling cells as a continuous mixture of K discrete types we obtain more parsimonious results than obtained with standard clustering algorithms. Moreover, using soft membership estimates of cell type cluster centers leads to better estimates of developmental trajectories. The strong performance of SOUP is documented via simulation studies, which show its robustness to violations of modeling assumptions. The advantages of SOUP are illustrated by analyses of two independent datasets of gene expression from a large number of cells from fetal brain.

A continuous mixture of two different dimers in liquid water

Liquid water is formed by a continuous mixture of two different dimers (cis and trans) with distinct energies related to different relative water molecule orientations.