An airplane boarding model, introduced earlier by Hemmer and Frette, is considered. In this model, N passengers have reserved seats, but enter the airplane in arbitrary order. Here we focus on the blocking relations between passengers. The total boarding time is equal to the longest blocking sequence, represented by a line, connecting points of the two-dimensional q versus r scatter plot. Here, q=i/N">q=i/N q=i/N and r=j/N">r=j/N r=j/N , i and j being sequential numbers of passengers in the queue and their seat numbers, respectively. Such blocking sequences have been studied theoretically by Bachmat. We have developed an algorithm for numerical simulation of the longest blocking sequences, and have compared the results with analytical predictions for N→∞">N→∞ N→∞ .

Iron ore pellets consist of variety of mineral particles and are an important refined product used in steel manufacturing. Production of high-quality pellets requires good understanding of interactions between different constituents, such as magnetite, gangue residues, bentonite, and additives. Much research has been reported on magnetite, silica, and bentonite surface properties and their effect on pellet strength but more scant with a focus on a fundamental particle–particle interaction. To probe such particle interaction, atomic force microscopy (AFM) using colloidal probe technique has proven to be a suitable tool. In this work, the measurements were performed between magnetite–magnetite, bentonite–magnetite, silica–bentonite, and silica–magnetite particles in 1 mM CaCl2 solution at various pH values. The interaction character, i.e., repulsion or attraction, was determined by measuring and analyzing AFM force curves. The observed quantitative changes in interaction forces were in good agreement with the measured zeta-potentials for the particles at the same experimental conditions. Particle aggregation was studied by measuring the adhesion force. Absolute values of adhesion forces for different systems could not be compared due to the difference in particle size and contact geometry. Therefore, the relative change of adhesion force between pH 6 and 10 was used for comparison. The adhesion force decreased for the magnetite–magnetite and bentonite–silica systems and slightly increased for the magnetite–bentonite system at pH 10 as compared to pH 6, whereas a pronounced decrease in adhesion force was observed in the magnetite–silica system. Thus, the presence of silica particles on the magnetite surface could have a negative impact on the interaction between magnetite and bentonite in balling due to the reduction of the adhesion force.

Driving of cars on a highway is a complex process which can be described by deterministic and stochastic forces. It leads to equations of motion with asymmetric interaction and dissipation as well as to new energy flow law already presented at previous TRAFFIC AND GRANULAR FLOW meetings. Here we consider a model, where motion of an asymmetric random walker on a ring with periodic boundary conditions takes place. It is related to driven systems with active particles, energy input and depot. This simple model can be further developed towards more complicated ones, describing vehicular or pedestrian traffic. Three particular cases are considered, starting with discrete coordinate and time, then making time continuous and, finally, considering a drift–diffusion equation in a continuum limit.

Natural magnetite is used for producing iron ore pellets, one of the raw materials in steel production. The quality of produced pellets depends on many factors, including the properties of the magnetite concentrate fed to pelletization. To be able to minimize the effect of the variations in feed properties on pellets quality, investigation of magnetite particle interaction with a focus on the surface properties is required. Atomic force microscopy (AFM), using the colloidal probe technique, is a suitable tool for measuring such particle-particle interaction in-situ. Natural particles are usually of micro-sizes (m-s) and have different sizes and shapes, which complicates an accurate investigation of particle interaction with AFM. To overcome such difficulties, synthetic nanoparticles are used instead. Process water chemistry is one of the factors affecting magnetite surface properties. Partial dissolution of calcite and apatite minerals, present in iron ore, results in high Ca2+ concentrations in the process water, which has been shown to have a major effect on the charge of the magnetite particles [1, 2]. The aim of this study was therefore to investigate forces and aggregation between magnetite particles, of micro- and nano-size (n-s), in Ca2+ solutions at various pH values. The spherical monodispersed magnetite nano-sized particles, with a diameter of approx. 10 nm, were synthesized by the precipitation technique [3]. Measurements were performed for m-s probe/m-s layer and m-s probe/n-s layer systems. Natural magnetite particles of 10-30 µm size were glued to NP-S cantilevers (Digital Instruments/Bruker, Santa Barbara, CA) with a measured spring constant of 0.12 N/m. Nano-sized particles were deposited on the glass slides by dip-coating. Roughness (Ra) of the n-s layers was measured with AFM and was about 10 nm for areas 1×1µm2, a representative high-resolution image is shown in Figure 1. Particle interaction was similar for m-s and n-s magnetite particles at pH 4 and 6. At pH 10, the interaction behavior was different due to probable surface modification of natural magnetite particles by ions from process water. The adhesion force for both interacting systems was measured, see ref. [4] for a detailed description of the results. To verify that ϛ-potential measurements could be used to predict the interaction between charged particles (in this case silica and magnetite) in solutions containing inorganic ions, force measurements between n-s magnetite layer and a SiO2 spherical probe (3.5 µm in diameter) were performed and correlated with the ϛ-potential results for these particles in the same solutions. Also, a DLVO simulation was performed to theoretically confirm the experimental interaction based on surface charge trends. An example of the simulated force curves is shown in Figure 2. The interaction between the probe and the magnetite surface was attractive at pH 4 and 6 but became repulsive at pH 8 and 10, which is in agreement with what could be expected from the ϛ-potential results for these particles.

Force interactions between a microsize (m-s) magnetite probe and thin layers of synthesized magnetite particles as well as microsize (m-s) magnetite particles from magnetite concentrate were investigated using atomic force microscopy (AFM). Of special interest was the influence of Ca2 + ions and pH on the interaction between the probe and the two different magnetite particle surfaces. The probe and the magnetite surfaces were immersed in aqueous Ca2 + solutions (100, 10, and 1 mM) at various pH values (4, 6, and 10). The colloidal probe technique and a self-made computer program for automatic evaluation of adhesion forces were used. The analysis revealed an increase in adhesion force with increased calcium concentration at pH 6 for both the systems investigated. However, the adhesion behavior between the probe and the m-s and n-s magnetite particle surfaces is different at pH 10. The possible appearance of calcium carbonate precipitated onto the magnetite surfaces as well as the possible influence of already adsorbed silicate on magnetite particles from the concentrate is discussed. In addition to Ca, Cl and Na atoms, added to the working solutions, and the Fe and O detected signals, the SEM-EDS analysis also detected Si atoms on the surface of the m-s particles.

We have studied the optimal velocity model (Bando et al., Jpn J Indust Appl Math 11:203, 1994; Phys Rev E 51:1035, 1995; J Phys I Fr 5:1389, 1995) for highway traffic. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. We define an intrinsic energy of the model. We find a latent heat when the system undergoes a phase transition from single phase traffic (free flow) to a phase that contains two different, a dense and a dilute phase (congested or stop-and-go flow). Here we report on properties of the latent heat