Thermodynamics, static properties and transport behaviour of fluids with competing interactions

Competing interaction fluids have become ideal model systems to study a large number of phenomena, for example, the formation of intermediate range order structures, condensed phases not seen in fluids driven by purely attractive or repulsive forces, the onset of particle aggregation under in- and out-of-equilibrium conditions, which results in the birth of reversible and irreversible aggregates or clusters whose topology and morphology depend additionally on the thermodynamic constrictions, and a particle dynamics that has a strong influence on the transport behaviour and rheological properties of the fluid. In this contribution, we study a system of particles interacting through a potential composed by a continuous succession of a short-ranged square-well, an intermediate-ranged square-shoulder and a long-ranged square-well. This potential model is chosen to systematically analyse the contribution of every component of the interaction potential on the phase behaviour, the microstructure, the morphology of the resulting aggregates and the transport phenomena of fluids described by competing interactions. Our results indicate that the inclusion of a barrier and a second well leads to new and interesting effects, which in addition result in variations of the physical properties associated to the competition among interactions.

Structural and Dynamical Behaviour of Colloids with Competing Interactions Confined in Slit Pores

Systems with short-range attractive and long-range repulsive interactions can form periodic modulated phases at low temperatures, such as cluster-crystal, hexagonal, lamellar and bicontinuous gyroid phases. These periodic microphases should be stable regardless of the physical origin of the interactions. However, they have not yet been experimentally observed in colloidal systems, where, in principle, the interactions can be tuned by modifying the colloidal solution. Our goal is to investigate whether the formation of some of these periodic microphases can be promoted by confinement in narrow slit pores. By performing simulations of a simple model with competing interactions, we find that both the cluster-crystal and lamellar phases can be stable up to higher temperatures than in the bulk system, whereas the hexagonal phase is destabilised at temperatures somewhat lower than in bulk. Besides, we observed that the internal ordering of the lamellar phase can be modified by changing the pore width. Interestingly, for sufficiently wide pores to host three lamellae, there is a range of temperatures for which the two lamellae close to the walls are internally ordered, whereas the one at the centre of the pore remains internally disordered. We also find that particle diffusion under confinement exhibits a complex dependence with the pore width and with the density, obtaining larger and smaller values of the diffusion coefficient than in the corresponding bulk system.

Elastic Modeling of Two-Step Transitions in Sterically Frustrated 1D Binuclear Spin-Crossover Chains

Among the large family of spin-crossover materials, binuclear systems play an important role due to their specific molecular configurations, allowing the presence of multi-step transitions and elastic frustration. Although this issue benefited from a significant number of spin-based theories, there is almost no elastic description of the spin transition phenomenon in binuclear systems. To overcome this deficiency, in this work we develop the first elastic modeling of thermal properties of binuclear spin-crossover solids. At this end, we investigated a finite spin-crossover open chain constituted of elastically coupled binuclear (A = B) blocks, ⋯A=B−A=B−A=B⋯, in which the considered equivalent A and B sites may occupy two configurations, namely low-spin (LS) and high-spin (HS) states. The sites of the binuclear unit interact via an intramolecular spring and couple to the neighboring binuclear units via other springs. The model also includes the change of length inside and between the binuclear units subsequent to the spin state changes. When injecting an elastic frustration inside the binuclear unit in the LS state, competing interactions between the intra- and the inter-binuclear couplings emerge. The latter shows that according to the intra- and inter-binuclear elastic constants and the strength of the frustration, multi-step transitions are derived, for which a specific self-organization of type (HS = HS)-(LS-LS)-(HS = HS)⋯ is revealed and discussed. Finally, we have also studied the relaxation of the metastable photoinduced HS states at low temperature, in which two relaxation regimes with transient self-organized states were identified when monitoring the elastic frustration rate or the ratio of intra- and intermolecular elastic interactions. These behaviors are reminiscent of the thermal dependence of the order parameters of the system. The present model opens several possibilities of extensions of elastic frustrations acting in polynuclear spin-crossover systems, which may lead to other types of spin-state self-organizations and relaxation dynamics.

An algorithm to compute the strength of competing interactions in the Bering Sea based on pythagorean fuzzy hypergraphs

The networks of various problems have competing constituents, and there is a concern to compute the strength of competition among these entities. Competition hypergraphs capture all groups of predators that are competing in a community through their hyperedges. This paper reintroduces competition hypergraphs in the context of Pythagorean fuzzy set theory, thereby producing Pythagorean fuzzy competition hypergraphs. The data of real-world ecological systems posses uncertainty, and the proposed hypergraphs can efficiently deal with such information to model wide range of competing interactions. We suggest several extensions of Pythagorean fuzzy competition hypergraphs, including Pythagorean fuzzy economic competition hypergraphs, Pythagorean fuzzy row as well as column hypergraphs, Pythagorean fuzzy k-competition hypergraphs, m-step Pythagorean fuzzy competition hypergraphs and Pythagorean fuzzy neighborhood hypergraphs. The proposed graphical structures are good tools to measure the strength of direct and indirect competing and non-competing interactions. Their aptness is illustrated through examples, and results support their intrinsic interest. We propose algorithms that help to compose some of the presented graphical structures. We consider predator-prey interactions among organisms of the Bering Sea as an application: Pythagorean fuzzy competition hypergraphs encapsulate the competing relationships among its inhabitants. Specifically, the algorithm which constructs the Pythagorean fuzzy competition hypergraphs can also compute the strength of competing and non-competing relations of this scenario.

Inter-specific competition among trees in pythagorean fuzzy soft environment

A Pythagorean fuzzy set is very effective mathematical framework to represent parameter-wise imprecision which is the property of linguistic communication. A Pythagorean fuzzy soft graph is more potent than the intuitionistic fuzzy soft as well as the fuzzy soft graph as it depicts the interactions among the objects of a system using Pythagorean membership grades with respect to different parameters. This article addresses the content of competition graphs as well as economic competition graphs like k-competition graphs, m-step competition graphs and p-competition graphs in Pythagorean fuzzy soft environment. All these concepts are illustrated with examples and fascinating results. Furthermore, an application which describes the competition among distinct forest trees, that grow together in the mixed conifer forests of California, for plant resources is elaborated graphically. An algorithm is also designed for the construction of Pythagorean fuzzy soft competition graphs. It is worthwhile to express the competing and non-competing interactions in various networks with the help of Pythagorean fuzzy soft competition graphs wherein a variation in competition relative to different attributes is visible.

Inhibitory and Stimulatory Micropeptides Preferentially Bind to Different Conformations of the Cardiac Calcium Pump

The ATP-dependent ion pump SERCA sequesters Ca2+ in the endoplasmic reticulum to establish a reservoir for cell signaling. Because of its central importance in physiology, this transporter is tightly controlled by physical interactions with tissue-specific regulatory micropeptides that tune SERCA function to match changing physiological conditions. In the heart, phospholamban (PLB) inhibits SERCA, while dwarf open reading frame (DWORF) stimulates SERCA. These competing interactions determine cardiac performance by modulating the amplitude of Ca2+ signals that drive the contraction/relaxation cycle. The distinct functions of these peptides may relate to their reciprocal preferences for SERCA binding. While SERCA binds PLB more avidly at low cytoplasmic Ca2+, it binds DWORF better at high Ca2+. In the present study, we determined that this opposing Ca2+ sensitivity is due to preferential binding of DWORF and PLB to different intermediate conformations that the pump samples during the Ca2+ transport cycle. The results suggest a mechanistic basis for inhibitory and stimulatory micropeptide function. In addition, fluorescence resonance energy transfer (FRET) measurements revealed dynamic shifts in SERCA-micropeptide binding equilibria during cellular Ca2+ elevations. The data suggest Ca2+-dependent dynamic exchange of inhibitory and stimulatory micropeptides from SERCA during the cardiac cycle. Together, these mechanisms provide beat-to-beat modulation of cardiac Ca2+ handling and contribute to the heart's adaptation to the increased physiological demands of exercise.