Infinite Cluster Research Articles

The piezoelectric activity in the HfO2 nanoclusters

In this paper the piezoelectric effects in infinite free-standing HfO2 film and HfO2 cluster under mechanical action are studied by methods of the density functional theory and first-principles pseudopotential based on own program code. The spatial distribution of valence electron density, the forces that act on an individual atom from the electronic and ionic subsystems, and Coulomb potential along transverse direction are calculated. It was found that a polarization charge distribution of valence electrons, which leads to piezoelectric effects, was observed in HfO2 nanofilms, while in HfO2 nanoclusters the charge distribution remained uniform both in the uncompressed and in the compressed state.

Corrections: On the capacity functional of the infinite cluster of a Boolean model

Corrections: On the capacity functional of the infinite cluster of a Boolean model

Specific surface area of mannitol rather than particle size dominant the dissolution rate of poorly water-soluble drug tablets: A study of binary mixture

The dissolution behavior of tablets, particularly those containing poorly water-soluble drugs, is a critical factor in determining their absorption and therapeutic efficacy. Traditionally, the particle size of excipients has been considered a key property affecting tablet dissolution. However, lurasidone hydrochloride (LH) tablets prepared by similar particle size mannitol, namely M200 (D90 = 209.68 ± 1.42 μm) and 160C (D90 = 195.38 ± 6.87 μm), exhibiting significant differences in their dissolution behavior. In order to find the fundamental influential factors of mannitol influencing the dissolution of LH tablets, the properties (particle size, water content, true density, bulk density, tapped density, specific surface area, circularity, surface free energy, mechanical properties and flowability) of five grades mannitol including M200 and 160C were investigated. Principal component analysis (PCA) was used to establish a relationship between mannitol properties and the dissolution behavior of LH. The results demonstrated that specific surface area (SSA) emerged as the key property influencing the dissolution of LH tablets. Moreover, our investigation based on the percolation theory provided further insights that the SSA of mannitol influences the probability of LH-LH bonding and LH infinite cluster formation, resulting in the different percolation threshold states, then led to different dissolution behaviors. Importantly, it is worth noting that these findings do not invalidate previous conclusions, as reducing particle size generally increases SSA, thereby affecting the percolation threshold and dissolution behavior of LH. Instead, this study provides a deeper understanding of the underlying role played by excipient SSA in the dissolution of drug tablets. This study provides valuable guidance for the development of novel excipients aimed at improving drug dissolution functionality.

Inhomogeneous long-range percolation in the weak decay regime

We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters.

Fascinating inclusion of metal–organic complex moieties in dinuclear Mn(II) and Zn(II) compounds involving pyridinedicarboxylates and phenanthroline: Experimental and theoretical studies

In the present study, we have reported the synthesis of two new dinuclear Mn(II) and Zn(II) metal–organic compounds, [Mn(2,5-PDC)(phen)2][Mn(phen)2(H2O)2]2Cl·10H2O (1) and [Zn(phen)3][Zn(2,6-PDC)2]·11.5H2O (2) (where, 2,5-PDC = 2,5-pyridinedicarboxylate, 2,6-PDC = 2,6-pyridinedicarboxylate, phen = 1,10-phenanthroline) at room temperature which have been characterized by elemental analysis, TGA, spectroscopic (FTIR, electronic) and single crystal X-ray diffraction techniques. A fascinating chloride-water supramolecular cluster in 1 and (H2O)13 H-bonded cluster in 2 along with π-stacked assemblies stabilize the solid state structures. The most interesting aspect of the crystal structure of 1 is the inclusion of complex cationic moieties within the infinite self-assembled chloride-water cluster. Similarly the inclusion of cationic complex moieties in compound 2 inside the supramolecular cavity formed by the anionic complex provides rigidity to the crystal structure. DFT calculations, molecular electrostatic potential (MEP) surface analysis, quantum theory of atoms-in-molecules (QTAIM) and the non-covalent index plot (NCI plot) analysis were performed to investigate the supramolecular assemblies of the compounds. The studies reveal that the antiparallel π-stacking interactions are energetically significant synthons for the assemblies. However, the assemblies in 2 have been dominated mostly by Columbic attraction of the cationic and anionic complex moieties.

Standard and inverse site percolation of triangular tiles on triangular lattices: Isotropic and perfectly oriented deposition and removal.

Numerical simulations and finite-size scaling analysis have been carried out to study standard and inverse percolation of triangular tiles of side k (k-tiles) on triangular lattices. In the case of standard percolation, the lattice is initially empty. Then, k-tiles are randomly and sequentially deposited on the lattice. In the case of inverse percolation, the process starts with an initial configuration where all lattice sites are occupied by single monomers (each monomer occupies one lattice site) and, consequently, the opposite sides of the lattice are connected by nearest-neighbor occupied sites. Then, the system is diluted by randomly removing k-tiles [composed by k(k+1)/2 monomers] from the lattice. Two schemes are used for the depositing and removing process: the isotropic scheme, where the deposition (removal) of the objects occurs with the same probability in any lattice direction; and the anisotropic (perfectly oriented or nematic) scheme, where one lattice direction is privileged for depositing (removing) the tiles. The study is conducted by following the behavior of four critical concentrations with the size k: (i)[(ii)] standard isotropic (oriented) percolation threshold θ_{c,k} (ϑ_{c,k}), which represents the minimum concentration of occupied sites at which an infinite cluster of occupied nearest-neighbor sites extends from one side of the system to the other. θ_{c,k} (ϑ_{c,k}) is reached by isotropic (oriented) deposition of k-tiles on an initially empty lattice; and (iii)[(iv)] inverse isotropic (oriented) percolation threshold θ_{c,k}^{i} (ϑ_{c,k}^{i}), which corresponds to the maximum concentration of occupied sites for which connectivity disappears. θ_{c,k}^{i} (ϑ_{c,k}^{i}) is reached after removing isotropic (completely aligned) k-tiles from an initially fully occupied lattice. The obtained results indicate that (1)θ_{c,k} (θ_{c,k}^{i}) is an increasing (decreasing) function of k in the range 1≤k≤6. For k≥7, all jammed configurations are nonpercolating (percolating) states and, consequently, the percolation phase transition disappears. (2)ϑ_{c,k} (ϑ_{c,k}^{i}) show a behavior qualitatively similar to that observed for isotropic deposition. In this case, the minimum value of k at which the phase transition disappears is k=5. (3) For both isotropic and perfectly oriented models, the curves of standard and inverse percolation thresholds are symmetric to each other with respect to the line θ(ϑ)=0.5. Thus, a complementary property is found θ_{c,k}+θ_{c,k}^{i}=1 (and ϑ_{c,k}+ϑ_{c,k}^{i}=1), which has not been observed in other regular lattices. (4) Finally, in all cases, the jamming exponent ν_{j} was measured, being ν_{j}=1 regardless of the orientation (isotropic or nematic) or the size k considered. In addition, the accurate determination of the critical exponents ν,β, and γ reveals that the percolation phase transition involved in the system, which occurs for k varying between one and five (three) for isotropic (nematic) deposition scheme, has the same universality class as the standard percolation problem.

Self-assembled infinite silver cluster with atomic precision as a scalable catalyst for CO2-electroreduction under industry-relevant reaction rates

Scalable infinite silver acetylide cluster as a CO2 reduction catalyst with high selectivity for CO at industry-relevant rates.

The variance of the graph distance in the infinite cluster of percolation is sublinear

The variance of the graph distance in the infinite cluster of percolation is sublinear

Continuous percolation in a Hilbert space for a large system of qubits

AbstractThe development of percolation theory was historically shaped by its numerous applications in various branches of science, in particular in statistical physics, and was mainly constrained to the case of Euclidean spaces. One of its central concepts, the percolation transition, is defined through the appearance of the infinite cluster, and therefore cannot be used in compact spaces, such as the Hilbert space of an N-qubit system. Here, we propose its generalization for the case of a random space covering by hyperspheres, introducing the concept of a “maximal cluster”. Our numerical calculations reproduce the standard power-law relation between the hypersphere radius and the cover density, but show that as the number of qubits increases, the exponent quickly vanishes (i.e., the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient). Therefore the percolation transition is not an efficient model for the behavior of multiqubit systems, compared to the random walk model in the Hilbert space. However, our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.

Slightly supercritical percolation on nonamenable graphs II: growth and isoperimetry of infinite clusters

Slightly supercritical percolation on nonamenable graphs II: growth and isoperimetry of infinite clusters

Monolayers of amino acid-type amphiphiles

The monolayer characteristics of selected N-alkanoyl substituted α-amino acid are studied with the objective to demonstrate the specific effect of the chemical structure of the polar head group which is highlighted with the D- and L-enantiomers of the following selected examples: R-alanine, R-serine, R-threonine, R-allo-threonine, and R-aspartic acid (R = C16, C18). The thermodynamic effect of the head group variation is studied. Experimental π-A isotherms of the N-tetradecyl-L-alanine monolayers show similar behavior as those of usual amphiphiles. The -CH3-group in R-alanine with the simplest head group structure is substituted by a -CH2-OH group in R-serine and serine methylester and by a -CH- CH3-OH group in R-threonine (or allo-threonine) and threonine methylester. The introduction of the methyl group in 3-position of serine (serine to 3-methyl-serine = threonine) shifts the characteristic temperatures by >20 K to lower values determined for N-C16-Dl-serine. The formation of the corresponding methylester decreases these temperatures by 15 K for serine with the shorter (C16) alkyl chain and only by ∼5 K for threonine with the longer chain (C18). The π–A curves of the enantiomeric and racemic allo-forms show similar features to those of N-stearoyl-threonine. The absolute T0-values (disappearance of the LE/LC-transition) are 4–5 K larger compared with the corresponding N-stearoyl-threonines, but the ΔT0 between the enantiomeric (D) and the racemic (DL) forms is only slightly larger than that of N-stearoyl-threonine.Monolayers of different N-alkanoyl substituted α-amino acid amphiphiles have been mesoscopically characterized. Substantial topological differences are observable at the condensed phase domains of several amino acid amphiphiles, such as, N-palmitoyl aspartic acid, N-palmitoyl- or N-stearoyl serine methyl ester, N-stearoyltyrosine, N-palmitoyl or N-myristoyl alanine. Many fascinating domain shapes are found, but always the curvatures of the two enantiomeric forms are directed in an opposite sense. The domain shape of the 1:1 racemic mixtures is usually different, but very often oppositely curved texture elements are observable.GIXD is used to study the characteristic features of the lattice structure of condensed monolayer phases on the Angstrom scale. Specific for all structures is the large tilt angle with respect to the surface normal, which decreases only marginally by compression. The large size of the head groups and strong interactions between them dominate the monolayer structure. As presented for NC16 and N-C18-threonine, N-C16-DL -serine, N-C16-L -serine, NC16 DL -serine-ME, NC16 L -serine-ME, NC18 DL -threonine-ME, and NC18 L -threonine-ME the enantiomers form an oblique lattice structure (3 diffraction peaks), whereas two peaks are observed for the racemates forming NNN tilted orthorhombic structures. A complete phase diagram of mixed monolayers of the D- and L-enantiomers of N-stearoyl-threonine with two eutectic points at xD ≈ 0.25 and xD ≈ 0.75 is proposed.The quantum chemical semiempirical PM3 method is applied to calculate the thermodynamic and structural parameters of clusterization in finite and infinite clusters for N-alkanoyl-substituted alanine with n = 8–17 carbon atoms in the chain at the air/water interface with the aim to obtain a new theoretical verification of the experimental results.

A study on the fractal and permeability characteristics of coal-based porous graphite for filtration and impregnation

Abstract In order to distinguish the differences in the heterogeneous fractal structure of porous graphite adopted in the filtration and impregnation, the fractal dimensions (FDs) were obtained by the mercury intrusion porosimetry (MIP) to calculate the volumetric FDs of ten graphite samples, following the fractal theory. The FD expression of the tortuosity along with all the parameters from the MIP test was optimized to simplify the calculation. In addition, the percolation evolution process of mercury in the porous media was analyzed based on the data collected in the experiment. According to the analysis conducted, the FDs in the backbone formation regions of samples varied from 2.695 to 2.984, with 2.923 to 2.991 in the percolation regions and 1.224 to 1.544 in the tortuosity. Based on the correlation coefficients ( R 2 ) ({R}^{2}) ranging between 0.906 and 0.999, and the root mean square errors ranging between 0.0001 and 0.0065 mL g−1, a high level of reliability was identified. According to the MIP test, the mercury distribution in porous graphite demonstrated a transitional process from the local aggregation, the gradual expansion, the infinite cluster connection to the global connection.

Cluster structures for the A∞$A_\infty$ singularity

AbstractWe study a category of ‐graded maximal Cohen‐Macaulay (MCM) modules over the curve singularity and demonstrate that it has infinite type cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategory) is stably equivalent to the infinite type cluster categories of Holm–Jørgensen, Fisher and Paquette–Yıldırım. As a consequence, has cluster tilting subcategories modelled by certain triangulations of the (completed) ‐gon. We use the Frobenius structure to extend this further to consider maximal almost rigid subcategories, and show that these subcategories and their mutations exhibit the combinatorics of the completed ‐gon.

Equality of critical parameters for percolation of Gaussian free field level sets

We consider upper level sets of the Gaussian free field (GFF) on Zd, for d≥3, above a given real-valued height parameter h. As h varies, this defines a canonical percolation model with strong, algebraically decaying correlations. We prove that three natural critical parameters associated with this model, respectively describing a well-ordered subcritical phase, the emergence of an infinite cluster, and the onset of a local uniqueness regime in the supercritical phase, actually coincide. At the core of our proof lies a new interpolation scheme aimed at integrating out the long-range dependence of the GFF. Due to the strength of correlations, its successful implementation requires that we work in an effectively critical regime. Our analysis relies extensively on certain novel renormalization techniques that bring into play all relevant scales simultaneously. The approach in this article paves the way to a complete understanding of the off-critical phases for strongly correlated disordered systems.

Superhighways and roads of multivariate time series shock transmission: Application to cryptocurrency, carbon emission and energy prices

Inferring the heterogeneous connection pattern of a networked system of multivariate time series observations is a key issue. In finance, the topological structure of financial connectedness in a network of assets can be a central tool for risk measurement. Against this, we propose a topological framework for variance decomposition analysis of multivariate time series in time and frequency domains. We build on the network representation of time–frequency generalized forecast error variance decomposition (GFEVD), and design a method to partition its maximal spanning tree into two components: (a) superhighways, i.e. the infinite incipient percolation cluster, for which nodes with high centrality dominate; (b) roads, for which low centrality nodes dominate. We apply our method to study the topology of shock transmission networks across cryptocurrency, carbon emission and energy prices. Results show that the topologies of short and long run shock transmission networks are starkly different, and that superhighways and roads considerably vary over time. We further document increased spillovers across the markets in the aftermath of the COVID-19 outbreak, as well as the absence of strong direct linkages between cryptocurrency and carbon markets.

Rationally Designed Manganese-Based Metal-Organic Frameworks as Altruistic Metal Oxide Precursors for Noble Metal-Free Oxygen Reduction Reaction.

The sluggish oxygen reduction reaction (ORR) at the cathode is challenging and hinders the growth of hydrogen fuel cells. Concerning kinetic values, platinum is the best known catalyst for ORR; however, its less abundance, high cost, and corrosive nature warrant the development of low-cost catalysts. We report the hydrothermal synthesis of two novel Mn-based metal-organic frameworks (MOFs), [Mn2(DOT)(H2O)2]n (Mn-SKU-1) and [Mn2(DOT)2(BPY)2(THF)]n (Mn-SKU-2) (DOT = 2,5-dihydroxyterephthalate; BPY = 4,4'-bipyridine). Mn-SKU-1 contains dimeric Mn(II) centers where the two corner-shared MnO6 octahedra fuse to give rise to an infinite Mn2O10 cluster, whereas the two Mn(II) ions coordinate to DOT and BPY moieties to give rise to a pillared structure in Mn-SKU-2 and form a 3D → 3D homo-interpenetration MOF with a twofold interpenetrated net. The pyrolysis of as-synthesized Mn-MOFs at 600 °C under N2 produced exclusively porous α-Mn2O3 composites (PSKU-1 and PSKU-2), with the BET surface area of 90.8 (for PSKU-1) and 179.3 m2 g-1 (for PSKU-2). These mesoporous MOF-derived α-Mn2O3 composites were modified as cathode materials for the electrocatalytic reduction of oxygen. The onset potential for the oxygen reduction reaction was found to be 0.90 V for PSKU-1 and 0.93 V for PSKU-2 versus RHE in 0.1 M KOH solution, with the current density of 4.8 and 6.0 mA cm-2, respectively, at 1600 rpm. Based on the RDE/RRDE results, the electrocatalytic oxygen reduction occurs majorly via the four-electron process. The electrocatalyst PSKU-2 is cheap, easy to use, retains 90% of its activity after 10 h of continuous use, and offers higher recyclability than Pt/C. The onset potential maximum current density and kinetic values (Jk = 11.68 mA cm-2 and Tafel slope = 85.0 mV dec-1) obtained in this work are higher than the values reported for pure Mn2O3.

Model-based clustering for multidimensional social networks

Abstract Social network data are relational data recorded among a group of actors, interacting in different contexts. Often, the same set of actors can be characterised by multiple social relations, captured by a multidimensional network. A common situation is that of colleagues working in the same institution, whose social interactions can be defined on professional and personal levels. In addition, individuals in a network tend to interact more frequently with similar others, naturally creating communities. Latent space models for network data are useful to recover clustering of the actors, as they allow to represent similarities between them by their positions and relative distances in an interpretable low-dimensional social space. We propose the infinite mixture latent position cluster model for multidimensional network data, which enables model-based clustering of actors interacting across multiple social dimensions. The model is based on a Bayesian non-parametric framework that allows to perform automatic inference on the clustering allocations, the number of clusters, and the latent social space. The method is tested on extensive simulated data experiments. It is also employed to investigate the presence of communities in two multidimensional workplace social networks recording relations of different types among colleagues.

Isoperimetric planar clusters with infinitely many regions

<abstract><p>In this paper we study infinite isoperimetric clusters. An infinite cluster $ {\bf{E}} $ in $ \mathbb R^d $ is a sequence of disjoint measurable sets $ E_k\subset \mathbb R^d $, called regions of the cluster, $ k = 1, 2, 3, \dots $ A natural question is the existence of a cluster $ {\bf{E}} $ with given volumes $ a_k\ge 0 $ of the regions $ E_k $, having finite perimeter $ P({\bf{E}}) $, which is minimal among all the clusters with regions having the same volumes. We prove that such a cluster exists in the planar case $ d = 2 $, for any choice of the areas $ a_k $ with $ \sum \sqrt a_k < \infty $. We also show the existence of a bounded minimizer with the property $ P({\bf{E}}) = \mathcal H^1({\tilde\partial} {\bf{E}}) $, where $ {\tilde\partial} {\bf{E}} $ denotes the measure theoretic boundary of the cluster. Finally, we provide several examples of infinite isoperimetric clusters for anisotropic and fractional perimeters.</p></abstract>

Transience and anchored isoperimetric dimension of supercritical percolation clusters

We establish several equivalent characterisations of the anchored isoperimetric dimension of supercritical clusters in Bernoulli bond percolation on transitive graphs. We deduce from these characterisations together with a theorem of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin (Duke Math. J. 2020) that if G is a transient transitive graph then the infinite clusters of Bernoulli percolation on G are transient for p sufficiently close to 1. It remains open to extend this result down to the critical probability. Along the way we establish two new cluster repulsion inequalities that are of independent interest.

Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd

Ising and Potts models can be studied using the Fortuin–Kasteleyn representation through the Edwards–Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength h > 0. In this representation, which is also known as the random-cluster model, the Kertész line is the curve that separates two regions of the parameter space defined according to the existence of an infinite cluster in Zd. This signifies a geometric phase transition between the ordered and disordered phases even in cases where a thermodynamic phase transition does not occur. In this article, we prove strict monotonicity and continuity of the Kertész line. Furthermore, we give new rigorous bounds that are asymptotically correct in the limit h → 0 complementing the bounds from the work of Ruiz and Wouts [J. Math. Phys. 49, 053303 (2008)], which were asymptotically correct for h → ∞. Finally, using a cluster expansion, we investigate the continuity of the Kertész line phase transition.