Theoretical vs. empirical classification and prediction of congested traffic states

Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss the terminology of traffic phases and give empirical evidence for the existence of a phase diagram of traffic states. In contrast to previously presented phase diagrams, it is shown that “widening synchronized patterns” are possible, if the maximum flow is located inside of a metastable density regime. Moreover, for various kinds of traffic models with different instability diagrams it is discussed, how the related phase diagrams are expected to approximately look like. Apart from this, it is pointed out that combinations of on- and off-ramps create different patterns than a single, isolated on-ramp.     

Paradoxes and paradigms: influence of the power of z on the estimation of entropies of formation of aqueous anions using simple parameters

We continue our use of “simple” energetic patterns, where simple means the use of parameters derived only from the stoichiometry of these species in our studies of the entropy of formation (TΔ_f S ^o) of aqueous anions. Relationships between the entropy of formation and different parameters such as the number of oxygen atoms, the natural logarithm of the molecular weight and the total number of atoms are explored. The charge of the species, z− continues to be explicitly considered where we now explore various choices of p and use of z ^p as a parameter.     

On the statistics of area size in two-dimensional thick Voronoi diagrams

Cells of Voronoi diagrams in two dimensions are usually considered as having edges of zero width. However, this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large. In this paper, the concept of a thick Voronoi tessellation, that is with edges of non-zero width, is introduced and the statistics of cell areas, as thickness changes, are analyzed.     

Teacher flexibility in mathematical discussion

The significance of discussion in mathematics classes has been prominently debated in the research literature. Different studies have stressed the importance of teacher flexibility in orchestrating the discussion. We introduce an operational definition of teacher flexibility. In a case study with one secondary-school mathematics teacher, we microanalyzed discussion situations in which the teacher had to change her plan according to unforeseen student replies. The analysis was aimed at characterizing situations in which the teacher was either flexible or inflexible in her interactions with students and describing the factors that affected her flexibility. We suggest four basic patterns of teacher flexibility and discuss the complexity of the factors that shape them.     

Transitions and heteroclinic cycles in the general Gierer-Meinhardt equation and cardiovascular calcification model

The article is concerned with transitions and pattern selection analysis of the inhibitor-activator system proposed in connection with recent studies of cardiovascular calcification patterns. Explicit criteria are derived to enable us to distinguish between stable and metastable patterns. By deriving a reduced system of equations, the existence of certain complicated structures is discussed; in particular, heteroclinic cycles are identified and their properties are studied. It is also discussed that the change of boundary conditions can affect the transitions of the system. In this connection, we will also study asymptotic behavior of patterns after transitions and will compare the results with numerical simulations.     

Pure patterns of order 2

We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance of order 2, showing that the latter characterize the proof-theoretic ordinal $1^{\infty }$ of the fragment ${\mathrm{\Pi }}_1^1$–${\mathrm{CA}}_0$ of second order number theory, or equivalently the set theory $\mathrm{KP}{?}_0$. As a corollary, we prove that Carlson's result on the well-quasi orderedness of respecting forests of order 2 implies transfinite induction up to the ordinal $1^{\infty }$. We expect that our approach will facilitate analysis of more powerful systems of patterns.     

大气压氩气放电六边形斑图的电子激发温度研究

采用特殊设计的气体介质阻挡放电实验装置,对大气压氩气放电六边形斑图的放电信号及激发光谱进行了测量。采用发射光谱强度比法,计算了放电丝呈六边形斑图时的电子激发温度。实验发现,随着驱动电压频率的升高,六边形斑图的电子激发温度明显升高,各放电通道之间的放电时间相关程度提高。该工作对控制斑图的形成和研究斑图动力学具有重要参考价值。     

Design of Multicomponent Peptide Fibrils with Ordered and Programmable Compositional Patterns

Advanced applications of biomacromolecular assemblies require a stringent degree of control over molecular arrangement, which is a challenge to current synthetic methods. Here we used a neighbor-controlled patterning strategy to build multicomponent peptide fibrils with an unprecedented capacity to manipulate local composition and peptide positions. Eight peptides were designed to have regulable nearest neighbors upon co-assembly, which, by simulation, afforded 412 different patterns within fibrils, with varied compositions and/or peptide positions. The fibrils with six prescribed patterns were experimentally constructed with high accuracy. The controlled patterning also applies to functionalities appended to the peptides, as exemplified by arranging carbohydrate ligands at nanoscale precision for protein recognition. This study offers a route to molecular editing of inner structures of peptide assemblies, prefiguring the uniqueness and richness of patterning-based material design.     

Prospective elementary teachers use of representation to reason algebraically

We used a teaching experiment to evaluate the preparation of preservice teachers to teach early algebra concepts in the elementary school with the goal of improving their ability to generalize and justify algebraic rules when using pattern-finding tasks. Nearly all of the elementary preservice teachers generalized explicit rules using symbolic notation but had trouble with justifications early in the experiment. The use of isomorphic tasks promoted their ability to justify their generalizations and to understand the relationship of the coefficient and y-intercept to the models constructed with pattern blocks. Based on critical events in the teaching experiment, we developed a scale to map changes in preservice teachers’ understanding. Features of the tasks emerged that contributed to this understanding.