Universal relationship between sample dimensions and cooperative phenomena: Effects of fractal dimension on electronic properties of high-TC cuprate observed using electron spin resonance

As demonstrated by the unique electronic properties of nanostructured materials, which are qualitatively different from the bulk properties of the same materials, there should be general relationship between dimensions of...

Concluding remarks: Cooperative phenomena in framework materials

A brief summary and personal perspectives on the virtual Faraday Discussion: Cooperative Phenomena in Framework Materials (13–16 October 2020).

Itinerant ferromagnetism in narrow-band metals

Since its introduction in 1963, the Hubbard model has becomes one of the most popular models used in the literature to study cooperative phenomena in narrow-band metals (ferromagnetism, metal-insulator transitions, charge-density waves, high-Tc superconductivity). Amongst all these cooperative phenomena, the problem of itinerant ferromagnetism in the Hubbard model has the longest history. However, in spite of an impressive research activity in the past, the underlying physics (microscopic mechanisms) that leads to the stabilization of itinerant ferromagnetism in Hubbard model (narrow-band metals) is still far from being understood. In this review we present our numerical results concerning this subject, which have been reached by small cluster exact diagonalization, density matrix renormalization group and quantum Monte Carlo calculations within various extensions of the Hubbard model. Particular attention is paid to a description of crucial mechanisms (interactions) that support the stabilization of the ferromagnetic state, and namely: (i) the long-range hopping, (ii) the correlated hopping, (iii) the long-range Coulomb interaction, (iv) the flat bands and (v) the lattice structure. Most of the presented results have been obtained for the one-dimensional case, but the influence of the increasing dimension of the system on the ferromagnetic state is also intensively discussed.

The Concept of Cooperative Dynamics in Simulations of Soft Matter

In this review we compiled recent advances concerning the cooperative motion in crowded soft matter systems. We tried to answer the question how to perform dynamic Monte Carlo simulations of dense macromolecular systems effectively. This problem is not simple due to the fact that the movement in such systems is strictly correlated which leads to cooperative phenomena. The influence of crowding was found interesting especially for two-dimensional cases, e.g., in membranes where the presence of macromolecules, proteins and cytoskeleton often changed the mean-square displacement as a function of the lag time and anomalous diffusion appeared. Simple models are frequently used to shed a light on molecular transport in biological systems. The emphasis was given to the Dynamic Lattice Liquid model. The latter model became a basis for a parallel algorithm that takes into account coincidences of elementary molecular motion attempts resulting in local cooperative structural transformations. The emphasis is put on influence of the model of molecular transport on the diffusion. The comparison to alternative approaches like single agent model was carried out.

Platelet adhesion and aggregate formation controlled by immobilised and soluble VWF

Background It has been demonstrated that von Willebrand factor (VWF) mediated platelet-endothelium and platelet-platelet interactions are shear dependent. The VWF’s mobility under dynamic conditions (e.g. flow) is pivotal to platelet adhesion and VWF-mediated aggregate formation in the cascade of VWF-platelet interactions in haemostasis. Results Combining microfluidic tools with fluorescence and reflection interference contrast microscopy (RICM), here we show, that specific deletions in the A-domains of the biopolymer VWF affect both, adhesion and aggregation properties independently. Intuitively, the deletion of the A1-domain led to a significant decrease in both adhesion and aggregate formation of platelets. Nevertheless, the deletion of the A2-domain revealed a completely different picture, with a significant increase in formation of rolling aggregates (gain of function). We predict that the A2-domain effectively ‘masks’ the potential between the platelet glycoprotein (GP) Ib and the VWF A1-domain. Furthermore, the deletion of the A3-domain led to no significant variation in either of the two functional characteristics. Conclusions These data demonstrate that the macroscopic functional properties i.e. adhesion and aggregate formation cannot simply be assigned to the properties of one particular domain, but have to be explained by cooperative phenomena. The absence or presence of molecular entities likewise affects the properties (thermodynamic phenomenology) of its neighbours, therefore altering the macromolecular function.

Platelet adhesion and aggregate formation controlled by immobilised and soluble VWF

BackgroundIt has been demonstrated that von Willebrand factor (VWF) mediated platelet-endothelium and platelet-platelet interactions are shear dependent. The VWF's mobility under dynamic conditions (e.g. flow) is pivotal to platelet adhesion and VWF-mediated aggregate formation in the cascade of VWF-platelet interactions in haemostasis.ResultsCombining microfluidic tools with fluorescence and reflection interference contrast microscopy (RICM), here we show, that specific deletions in the A-domains of the biopolymer VWF affect both, adhesion and aggregation properties independently. Intuitively, the deletion of the A1-domain led to a significant decrease in both adhesion and aggregate formation of platelets. Nevertheless, the deletion of the A2-domain revealed a completely different picture, with a significant increase in formation of rolling aggregates (gain of function). We predict that the A2-domain effectively ‘masks’ the potential between the platelet glycoprotein (GP) Ib and the VWF A1-domain. Furthermore, the deletion of the A3-domain led to no significant variation in either of the two functional characteristics.ConclusionsThese data demonstrate that the macroscopic functional properties i.e. adhesion and aggregate formation cannot simply be assigned to the properties of one particular domain, but have to be explained by cooperative phenomena. The absence or presence of molecular entities likewise affects the properties (thermodynamic phenomenology) of its neighbours, therefore altering the macromolecular function.

Evolution of Cooperation in the Presence of Higher-Order Interactions: From Networks to Hypergraphs

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise to network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.