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The effects of indirect correlations between the neighboring interacting particles on the rates of the elementary stages of particle transitions according to the vacancy mechanism and on the label, mass, and momentum transfer coefficients were studied. The transition rate was calculated within the framework of the theory of absolute reaction rates, which allows for the difference between the interactions of particles in the ground states and the activated complex of the stage in the transition state. The simplest lattice structure (a homogeneous (100) flat face) is considered, for which the exact solution to the many-body problem is known. The local distributions of particles were constructed within the framework of the cluster variation method (CVM), which allows us to go beyond the quasichemical approximation (QCA), reflecting the effects of only direct correlations (or an isolated (2 × 1) pair in CVM terminology). The given characteristics, calculated for some simplest basic clusters (2 × 2, 2 × 3, k1s, 3 × 3) by CVM and in QCA, were compared. At temperatures below the particle condensation temperature, the effects of separation into two coexisting phases are taken into account. Inclusion of indirect correlations in the calculation for an increased size of the basic cluster leads to a difference between the current cluster approximation and QCA. These are quantitative differences, while the type of the concentration dependences of the label, mass, and momentum transfer coefficients in the QCA remains qualitatively unchanged. [ABSTRACT FROM AUTHOR]

Systematic studies on the lattice expansion and order-disorder phase equilibria are attempted for the A-B binary alloy on the two-dimensional square lattice. The atomic pair potentials are described by the Morse potential and the configurational entropy is formulated within the pair approximation of the Cluster Variation Method (CVM). The lattice expansion of the uniformly deformable lattice is enhanced by introducing lattice vibration effects through the Debye–Grüneisen model. The introduction of the local lattice distortion by continuous displacement CVM (CDCVM) further increases the lattice expansion. The transition temperature obtained for a uniformly deformable lattice is reduced by the thermal vibration effects, which is interpreted as the curvature effects of atomic pair potentials. The local lattice relaxation further reduced the transition temperature, which is ascribed to the additional freedom of distributing atomic pairs over a wide range of distances. [ABSTRACT FROM AUTHOR]

The effects of indirect correlations between the nearest adsorbed particles attracting each other on the rates of the elementary adsorption and desorption stages were studied. The calculation was performed within the framework of the theory of absolute reaction rates, including the difference between the interactions of particles in the ground states and the activated complex of the stage in the transition state. The local particle distributions were calculated within the framework of the cluster variation method (CVM), which allows us to go beyond the quasichemical approximation (QCA), reflecting the effects of only direct correlations or an isolated pair (2 × 1) in CVM terminology. The isothermal concentration dependences of the adsorption and desorption rates of adsorbed particles on the homogeneous (100) flat face, as well as the thermal desorption spectra, were calculated. The rates calculated for some simplest basic clusters (2 × 2, k1s, 3 × 3, 3 × 4) were compared with those calculated in QCA. At temperatures below the condensation temperature of the adsorbate, the effects of separation of the latter into two coexisting phases were taken into account. Inclusion of indirect correlations in calculation for increased basic cluster sizes leads to quantitative differences between the given cluster approximation and QCA, while the type of the concentration dependence of the adsorption/desorption rate and the thermal desorption spectrum remains qualitatively unchanged. [ABSTRACT FROM AUTHOR]

The influence of indirect correlations between the nearest interacting chemisorbed particles on the rates of elementary mono- and bimolecular stages of adsorption and desorption was studied. The calculation was performed within the framework of the theory of absolute reaction rates, in which the difference between the interactions of particles in the ground states and the activated complex of the stage in the transition state is taken into account. The local distributions of particles were constructed within the framework of the cluster variation method (CVM), which allows us to go beyond the limits of the quasi-chemical approximation (QCA), reflecting the effects of only direct correlations or an isolated pair (2 × 1) in the CVM terminology. The type of cluster approximation is determined by the size of the basic cluster in the CVM. As an illustration, calculations of adsorption and desorption rates are given including and neglecting molecular dissociation on a homogeneous flat (100) face for the isothermal concentration dependences of the rates and for the thermal desorption curves. The rates calculated for a number of simple basic clusters (2 × 2, k1s, 3 × 3, 3 × 4) and in QCA were compared. The calculations were performed near the critical temperature in the corresponding cluster approximation without taking into account the appearance of ordered structures of chemisorbed particles. In all versions of calculations including indirect correlations, an increase in the size of the basic cluster increases the differences between this cluster approximation and the QCA. These differences are quantitative, leaving the type of concentration and thermal desorption curves of adsorption and desorption rates qualitatively unchanged. [ABSTRACT FROM AUTHOR]

Equations for the rates of elementary mono- and bimolecular stages for non-ideal reaction systems are derived within the theory of absolute reaction rates in the cluster variation model (CVM). The theory allows for the difference between the interaction of particles in the ground and activated (transition) states. Locally equilibrium distributions of particles are calculated in a CVM that considers the influence of indirect correlations, making it possible to go beyond the limits of the quasichemic approximation, which reflects only the effects of direct correlations between interacting particles. The rates refer to the elementary stages of adsorption and desorption with and without allowing for the dissociation of molecules on a homogeneous flat face (100), along with the rate of the thermal motion of molecular jumps to neighboring vacant sites. The condition of self consistency in describing the rates of elementary stages and the equilibrium state of the system is confirmed in CVM approximations, starting from the basic 2 × 2 square cluster used to approximate the probabilities of obtaining reaction clusters of mono- and bimolecular stages with sizes K1 and K2. The principle of approximating the calculation of multiparticle probabilities of sizes K1 and K2 in terms of the probabilities of smaller basic clusters is discussed. [ABSTRACT FROM AUTHOR]

Fundamentals of cluster variation (CV) are developed for locally heterogeneous spatially distributed systems. The theory is based on the principles of homogeneous CV in which all variants of the location of the basis cluster on a heterogeneous lattice are additionally considered when it is translated over the system. The structure of the statistical sum of homogeneous CV is shown to remain upon moving to a heterogeneous or homogeneous spatially distributed lattice. However, cofactors of the statistical sum, which previously corresponded to homogeneous clusters, must now consider all arrangements of heterogeneous sites inside each cluster. The general approach is to use a layered structure of the transitional region with variable density between vapor and fluid on a planar square lattice. Explicit expressions for a heterogeneous statistical sum of the transitional region are given on the basis of a 3 × 3 cluster. Using a 2 × 2 cluster, it is shown how an explicit equation for the equilibrium particle distribution in the transitional region can be obtained from the heterogeneous statistical sum. A gradual increase in the size of the m × n basis cluster in the transitional region converges to the exact solution. [ABSTRACT FROM AUTHOR]

Experimental evidence for short-range order (SRO) has been discovered for many alloys, and it affects several physical and mechanical properties of the alloys. Hence, treatment of SRO in the thermodynamic modeling of the phases is required for reliable description of alloy systems. In addition, the availability of first-principles-based thermochemical data has created the possibility for further improving existing thermodynamic descriptions. The present work uses the cluster expansion and cluster variation methods (CE-CVM) for the bcc solid phase to address these issues. Three binary Ti-X (X = Nb, V, Zr) alloys were thermodynamically accessed using existing experimental and calculated first-principles-based thermochemical data. Density functional theory (DFT), along with techniques, such as CE and special quasirandom structures (SQS), were used to calculate thermochemical data. Thermodynamic descriptions of binary Ti-X systems were obtained by optimizing all the available experimental, first-principles-based thermochemical, and phase diagram data. The phase diagram and thermodynamic properties calculated using model parameters agree well with the experimental data. The SRO of the bcc solid phase at various compositions and temperatures were determined using optimized model parameters. While the experimental determination of SRO remains a challenge, a CE-CVM based modeling approach offers a viable option for determining the SRO states of the alloys. [ABSTRACT FROM AUTHOR]

Exploiting Chemical Short-Range Order (CSRO) is a promising avenue for manipulating the properties of alloys. However, existing modeling frameworks are not sufficient to predict CSRO in multicomponent alloys (>3 components) in an efficient and reliable manner. In this work, we developed a hybrid computational thermodynamics framework by combining unique advantages from Cluster Variation Method (CVM) and CALculation of PHAse Diagram (CALPHAD) method. The key is to decompose the cumbersome cluster variables in CVM into fewer site variables of the basic cluster using the Fowler-Yang-Li (FYL) transform, which considerably reduces the number of variables that must be minimized for multicomponent systems. CSRO is incorporated into CALPHAD with a novel cluster-based solution model called FYL-CVM. This new framework brings more physics into CALPHAD while maintaining its practicality and achieves a good balance between accuracy and computational cost. It leverages statistical mechanics to yield a more physical description of configurational entropy and opens the door to cluster-based CALPHAD database development. The application of the FYL-CVM model in a prototype fcc AB alloy demonstrates its capability to calculate the phase diagram and thermodynamic properties with remarkable accuracy comparable to CVM. The hybrid CVM-CALPHAD framework represents a new methodology for thermodynamic modeling that enables atomic-scale order to be exploited for materials design. [Display omitted] [ABSTRACT FROM AUTHOR]

The Nb-Zr system was reassessed based on calculated theoretical data and available thermodynamic and phase equilibria data. The Gibbs energies of the bcc and hcp solid phases were described using cluster expansion and cluster variation methods (CE–CVM) to model short-range ordering (SRO) in the solid solution phases. Enthalpy of mixing data was calculated using density functional theory with special quasirandom structures and cluster expansion (CE) method. A sub-regular solution model was used for describing the Gibbs energy of the liquid phase. An optimal set of parameters has been obtained for describing the Gibbs energies of the liquid and solid phases in the Nb-Zr binary system. The modeled phase diagram and thermodynamic properties agree with the experimental data. The relevance of CE–CVM has been demonstrated in the present case by calculating the solid phase's short-range order (SRO) parameters as a function of composition and temperature. [ABSTRACT FROM AUTHOR]

Background: In the framework of cluster expansion—cluster variation methods (CE - CVM), the equilibrium values of the microscopic state variables called correlation functions (CFs) can be obtained by minimization of the Helmholtz energy. This involves solving the nonlinear equilibrium equations using numerical techniques. As an exception, Guggenheim obtained an analytical solution for the pair CF in the pair approximation of quasi-chemical theory for a binary alloy. Results: In this communication, analytical solutions for the CFs for the case of exclusive second neighbour pair interactions in binary A2 & B32 phases and A1 & L11 phases respectively under tetrahedron and tetrahedron–octahedron approximations of CVM are obtained as functions of the corresponding energy coefficient, temperature, and composition. Results obtained by results in the previous section and a few new results: Further, analytical expressions for the phase boundaries in phase separating and ordering systems have been obtained. Apart from these, thermodynamic quantities such as heat capacities have also been evaluated. In addition, the effect of composition and temperature dependence of the energy coefficient on the phase boundary is also discussed. Application: For the selected composition, the solution of CF reduces to a simple rational function. Taking this as a guide, the coefficients of the polynomials used to approximate the CFs are expressed as rational functions, which was discussed elsewhere. [ABSTRACT FROM AUTHOR]

A numerical technique has been developed on the basis of the cluster variation method (CVM) for calculating the spatial distribution of particles in the Ising lattice model. The lattice is approximated by a basic cluster, which makes it possible to obtain an exact solution to the problem by increasing the cluster size. Universal expressions for the microscopic distribution of particles in clusters of any size were derived by expanding the cluster probabilities in terms of the correlation factors determined on smaller clusters inside the basic cluster. For the sites of the basic cluster, new variables were introduced in order to preserve the structure of the relationships of probabilistic correlators with smaller clusters at any size of the basic cluster. It was shown that the correlation factor symmetrically reflects multisite spin correlations. It was found that expansion in terms of correlation factors allows one to avoid the difficulties in calculations in the CVM caused by the need to use the method of indefinite Lagrange multipliers for cluster probabilities. The difference between the new spin variables and the conventional variables in the CVM was discussed. The efficiency of the technique was demonstrated using a square planar lattice as an example, for which the exact Onsager solution is known. For clusters of 16 sites, the difference between the critical temperature and the exact value was found to be ~2%. [ABSTRACT FROM AUTHOR]

The binary prototype phase diagrams for fcc structures calculated with the tetrahedron, tetrahedron–octahedron and quadruple tetrahedron approximations of the cluster variation method and Monte-Carlo simulations (MCS) for first neighbor interactions show significant differences in the computed triple points of the A1, L 1 0 and L 1 2 phases. The finite number of terms retained in the cluster variation method entropy functional in different approximations leads to differences in the accuracy of the approximation. In general, larger cluster approximations and MCS results are accepted to be more accurate, but are associated with large computational burden. The multiplicities of the basic clusters in the entropy functional for tetrahedron–octahedron approximation were earlier modified to reproduce many of the results of larger clusters with lower computational burden. In the present communication, a similar approach is adopted for the case of tetrahedron approximation for binary fcc phases. This approximation has a smaller number of variables, but yields the results which are in good agreement with the best known results. [ABSTRACT FROM AUTHOR]

Biological forms depend on a progressive specialization of pluripotent stem cells. The differentiation of these cells in their spatial and functional environment defines the organism itself; however, cellular mutations may disrupt the mutual balance between a cell and its niche, where cell proliferation and specialization are released from their autopoietic homeostasis. This induces the construction of cancer niches and maintains their survival. In this paper, we characterise cancer niche construction as a direct consequence of interactions between clusters of cancer and healthy cells. Explicitly, we evaluate these higher-order interactions between niches of cancer and healthy cells using Kikuchi approximations to the free energy. Kikuchi’s free energy is measured in terms of changes to the sum of energies of baseline clusters of cells (or nodes) minus the energies of overcounted cluster intersections (and interactions of interactions, etc.). We posit that these changes in energy node clusters correspond to a long-term reduction in the complexity of the system conducive to cancer niche survival. We validate this formulation through numerical simulations of apoptosis, local cancer growth, and metastasis, and highlight its implications for a computational understanding of the etiopathology of cancer.

The path probability method (PPM), which is a natural extension of the cluster variation method (CVM) to a time domain, has been employed in a relaxation process of atomic configurations in alloy systems. Although the vacancy mechanism is the main atomic migration process in an alloy system, most studies of PPM have used the spin flipping mechanism (or the direct exchange mechanism) because of the huge computational burden imposed by the vacancy mechanism. In this paper the computational problem is circumvented by treating various path variables in the PPM as cluster probabilities in the CVM, and the vacancy mechanism is explicitly taken into account in the theoretical framework. The method is employed to explore the relaxation process in a Ni 3 Al ordered phase within the tetrahedron approximation, and the effect of vacancy concentration is investigated. [ABSTRACT FROM AUTHOR]

The model J1-J2 has provided a good theoretical benchmark for the study of frustrated magnets. This model is studied from the perspective of the Cluster Variation Method (CVM). In a first moment, Bethe approximation is considered. In this context it is possible to obtain a phase diagram where a stripes phase and a paramagnetic phase are observed, though separated by a non convergence zone. Secondly, plaquette approximation is considered and a complete phase diagram is obtained. In the latter it is observed an additional nematic phase with orientational but not positional order, which was not possible to observe using the Bethe approximation. [ABSTRACT FROM AUTHOR]

Abstract In a previous work by the present authors (Acta Mater. 148, 2018, 263–279), the thermodynamics of V–Nb–Ta–Mo–W highly concentrated alloy at equiatomic concentration was investigated using the cluster variation method in the irregular tetrahedron approximation. It was shown that the disordered solid solution is stabilized in this highly concentrated area of the system as prescribed by the high entropy alloy (HEA) paradigm. The configurational entropy, however, has only a minor (and sometimes contrary) influence in this stabilization. It was then postulated that configurational frustration, i.e. the competition between conflicting interactions, is the more relevant factor in the stabilization of the highly-concentrated alloys. The present work elaborates this idea by further considering the cases of V–Nb–Mo–Al and V–Nb–W–Al quaternary systemas and the corresponding quinary systems with Ta addition. The quaternary system are characterized by strong Al – M pair interactions that could enhance configurational frustration. The introduction of Ta, with weaker Ta – Al and practically non-existing Ta – Nb interactions, is meant to disrupt the frustration, hence leading to a decrease of the stability of the disordered alloys. It was shown that V–Nb–Mo–Al and its quinary do not exhibit configurational frustration as expected, since a stable compound with stoichiometry VMoNbAl is formed, and the stability of their disordered alloys (A2) is low. On the contrary, V–Nb–W–Al and its quinary demonstrated strong configurational frustration and correspondingly a stronger A2 stabilization. Deviations from equiatomic composition were also investigated and even stronger A2 stabilization was observed in this case. These results show that the stabilization of the disordered phase can only be attributed to configurational frustration, corroborating the previous work's conclusion that the effect of configurational entropy is only marginal in this stabilization. Graphical abstract Image 1 Highlights • Systems V – Nb – (Ta) – Mo – Al and V – Nb – (Ta) – W – Al behave differently. • Thermodynamics of disordered highly concentrated alloys is defined by the enthalpy. • Deviations of the ideal activity are large and even non-linear both in x and T. • Short-range order parameters are large and even non-linear in T. • Role of the entropy is secondary and thus no need to restrain to equiatomic alloys. [ABSTRACT FROM AUTHOR]

One of the biggest challenges in characterizing 2-D image topographies is finding a low-dimensional parameter set that can succinctly describe, not so much image patterns themselves, but the nature of these patterns. The 2-D cluster variation method (CVM), introduced by Kikuchi in 1951, can characterize very local image pattern distributions using configuration variables, identifying nearest-neighbor, next-nearest-neighbor, and triplet configurations. Using the 2-D CVM, we can characterize 2-D topographies using just two parameters; the activation enthalpy (ε0) and the interaction enthalpy (ε1). Two different initial topographies (“scale-free-like” and “extreme rich club-like”) were each computationally brought to a CVM free energy minimum, for the case where the activation enthalpy was zero and different values were used for the interaction enthalpy. The results are: (1) the computational configuration variable results differ significantly from the analytically-predicted values well before ε1 approaches the known divergence as ε1→0.881, (2) the range of potentially useful parameter values, favoring clustering of like-with-like units, is limited to the region where ε0<3 and ε1<0.25, and (3) the topographies in the systems that are brought to a free energy minimum show interesting visual features, such as extended “spider legs” connecting previously unconnected “islands,” and as well as evolution of “peninsulas” in what were previously solid masses.

Due to the importance of phase diagrams in a wide range of material based industries, additional efforts should be dedicated to their elaboration techniques. The cluster variation method is a promising technique to model the entropy within different plane lattices and is recognized by the materials physics community as a powerful modeling framework. Motivated by the efficiency of genetic algorithms in solving numerous types of optimization problems, our aim in this work is to investigate their performance in minimizing the grand potential in the context of the cluster variation method. A comparison is conducted with respect to numerical iterative techniques namely the Newton-Raphson and natural iteration methods, where many performance criteria are computed and compared. The obtained results allow the ranking of the considered approaches according to their performance measures and suggest a more profound investigation of metaheuristics particularly for complicated cluster structures in the future. [ABSTRACT FROM AUTHOR]

Following our previous study on distorted to non-distorted displacive phase transformation in the two-dimensional square lattice based on the continuous displacement cluster variation method (CDCVM) within the Bragg–Williams (BW) approximation, we performed a higher order approximation, four-body approximation, in the entropy term and compared the results obtained by the two approximations. The transformation temperature decreases with the higher order approximation, which shares the common feature with conventional CVM studies on replacive transformations. The present study predicts the first-order transformation, which is markedly different from the previous study based on the BW approximation. Furthermore, by employing the four-body approximation, we are able to reproduce the o-type distribution of displaced atoms around a Bravais lattice point by changing the atomic interaction energy, which was by no means possible by the BW approximation. [ABSTRACT FROM AUTHOR]

High Entropy Alloys (HEAs) designate a class of multicomponent metallic alloys in nearly equiatomic compositions. According to the constituting postulate, a larger number of constituents in a solid solution increases its configurational entropy, which has a maximal value when constituents exist in equiatomic concentrations and this is sufficient to overcome enthalpic contributions between the alloy components which would otherwise favor compound formation or phase separation. This entropy effect would, thus, stabilize disordered, crystallographically simple, solid solutions. Since then, numerous HEA candidate systems have been experimentally studied. It is unclear, however, if, and to which extent, the configurational entropy can be accessed by the system in the way it is suggested. The present work deals with this question using theoretical/computational methods. First, a series of model Body Centered Cubic (BCC) systems involving strong symmetric interactions between unlike atom pairs (referred to as “equinteracting” systems), containing up to five components, is investigated using the Cluster Variation Method in the irregular tetrahedron approximation. The symmetry of interactions, though artificial, allows for the straightforward presentation of phase diagram sections even for quaternary and quinary systems. Next, a “real” HEA candidate system, VNbTaMoW, which presents the BCC structure, is investigated by ab initio calculations, allowing to extend the conclusions to a realistic case with asymmetric interactions. The results show that configurational entropy has a small, even marginal, effect on phase transitions and the competition between conflicting interactions in the solid solution ( i.e. frustration ) seems to be the relevant factor behind the observed stabilization in the disordered states in HEA systems. [ABSTRACT FROM AUTHOR]

In this paper we argue that verb clusters in Dutch varieties are merged and linearized in fully ascending (1-2-3) or fully descending (3-2-1) orders. We argue that verb clusters that deviate from these orders involve non-verbal material: adjectival participles, or nominal infinitives. As a result, our approach does not involve any unmotivated movements that are specific for verb clusters. Support for our analysis comes from (i) the interpretation of verb clusters; (ii) the fact that order variation depends on the types of verbs involved, which can be explained by selectional requirements of the verbs; and (iii) the geographic co-occurrence patterns of various orders. First, the 1-3-2 and 3-1-2 orders are argued to be ascending orders with a non-verbal 3. Indeed these orders occur in grammars that have ascending, rather than descending, verb clusters. Secondly, the 1-3-2 order is argued to be an interrupted V1-V2 cluster with a non-verbal 3. Indeed, this order is most common in the region where non-verbal material can interrupt the verb cluster. Our analysis of word order variation in verb clusters in terms of principles of grammar is further supported by an experiment in which we asked a large number of speakers distributed over the Dutch language area to rank all logically possible orders, including orders that are not common in their own variety of Dutch. The results demonstrate that speakers apply their syntactic knowledge to rank verb cluster orders that they do not use themselves. We argue that this knowledge cannot be due to familiarity with the various orders. [ABSTRACT FROM AUTHOR]

We present atomic-scale investigations of the thermodynamic properties of quinary bcc-based multi-principal-element alloys (MPEAs) within {Al,Co,Cr,Fe,Mn,Mo,Ni}, by means of short-range pair energetics and the cluster variation method (CVM) in the irregular tetrahedron approximation. We focus on an essential couple of key-properties detrimental for potential applications of MPEAs, namely the trends to (i) long-range ordering (LRO) and (ii) phase separation (PS). While the CVM has been more commonly employed in a grand canonical frame controlled by chemical potentials (δμ), we propose an original δμ-driven CVM scheme which allows an easier exploration of wide composition spaces typical of MPEAs. This modified scheme yields a slice-by-slice analysis of this space, by means of pseudo-ternary isothermal sections, which demonstrates the ability of the CVM to lead, with moderate computational effort, to full phase diagrams of MPEAs. In particular, our CVM calculations provide elements to interpret recent unexpected experimental trends of AlCrFeMnMo. Comparison with earlier studies of the same MPEAs using the less accurate point-mean-field (PMF) approximation indicates that CVM and PMF have global agreement for LRO at higher temperatures, whereas CVM should definitely be preferred as soon as PS begins to occur. Both approaches, employed more systematically in future MPEA studies in conjunction with ab initio electron theory and dedicated experiments, may offer convenient tools to check the merits of, and even improve, the various sets of effective pair interactions nowadays increasingly available for atomic-scale simulations of MPEAs, thus helping to identify composition domains relevant to avoid trends (i) and (ii) and design more reliable MPEAs. • Multi-principal-element alloys (MPEAs) are a poorly known class of materials. • Control of long-range order and phase separation is critical for MPEAs. • A cluster-variation (CVM) scheme is designed to explore MPEA composition space. • Our scheme allows drawing pseudo-ternary sections of MPEA phase diagrams. • Our study helps interpreting unexpected experimental trends of AlCrFeMnMo. [ABSTRACT FROM AUTHOR]

The magnetocaloric properties of the J x − J y Blume–Capel model with J x / J y = − 0. 5 are studied using the two point approximation of the Cluster Variation Method. The phase diagrams exhibit different phases depending on the anisotropy parameter, magnetic field, temperature and exchange interaction ratio. It is shown how the nature of the phase transition changes as parameters are varied. For an anisotropy parameter value of D = 1. 45 , a tricritical point and a reentrant behavior are identified. It was found inverse and direct magnetocaloric effect. The inverse magnetocaloric effect of the model is enhanced at low fields and temperatures around jumps between plateaus of magnetization. • Obtain the phase diagrams of the J x − J y Blume–Capel model in an external field. • Analyze the magnetocaloric properties of the J x − J y BC model. • The changes in entropy and adiabatic temperature are discontinuous around firt order transitions. • The magnetocaloric properties are enhanced around regions where there is a change in the magnetization pattern. [ABSTRACT FROM AUTHOR]

Configuration entropy is believed to stabilize disordered solid solution phases in multicomponent systems at elevated temperatures over intermetallic compounds by lowering the Gibbs free energy. Traditionally, the increment of configuration entropy with temperature was computed by time-consuming thermodynamic integration methods. In this work, a new formalism based on a hybrid combination of the Cluster Expansion (CE) Hamiltonian and Monte Carlo simulations is developed to predict the configuration entropy as a function of temperature from multi-body cluster probability in a multi-component system with arbitrary average composition. The multi-body probabilities are worked out by explicit inversion and direct product of a matrix formulation within orthonomal sets of point functions in the clusters obtained from symmetry independent correlation functions. The matrix quantities are determined from semi canonical Monte Carlo simulations with Effective Cluster Interactions (ECIs) derived from Density Functional Theory (DFT) calculations. The formalism is applied to analyze the 4-body cluster probabilities for the quaternary system Cr-Fe-Mn-Ni as a function of temperature and alloy concentration. It is shown that, for two specific compositions (Cr 25Fe 25Mn 25Ni 25 and Cr 18Fe 27Mn 27Ni 28), the high value of probabilities for Cr-Fe-Fe-Fe and Mn-Mn-Ni-Ni are strongly correlated with the presence of the ordered phases L1 2 -CrFe 3 and L1 0-MnNi, respectively. These results are in an excellent agreement with predictions of these ground state structures by ab initio calculations. The general formalism is used to investigate the configuration entropy as a function of temperature and for 285 different alloy compositions. It is found that our matrix formulation of cluster probabilities provides an efficient tool to compute configuration entropy in multi-component alloys in a comparison with the result obtained by the thermodynamic integration method. At high temperatures, it is shown that many-body cluster correlations still play an important role in understanding the configuration entropy before reaching the solid solution limit of high-entroy alloys (HEAs).

Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi-Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In combinatorial language, a brane tiling is a bipartite graph on a torus and its perfect matchings are of interest to both combinatorialists and physicists alike. A cluster algebra may also be associated to such quivers and in this paper we study the generators of this algebra, known as cluster variables, for the quiver associated to the cone over the del Pezzo surface d P . In particular, mutation sequences involving mutations exclusively at vertices with two in-coming arrows and two out-going arrows are referred to as toric cascades in the string theory literature. Such toric cascades give rise to interesting discrete integrable systems on the level of cluster variable dynamics. We provide an explicit algebraic formula for all cluster variables that are reachable by toric cascades as well as a combinatorial interpretation involving perfect matchings of subgraphs of the d P brane tiling for these formulas in most cases. [ABSTRACT FROM AUTHOR]

We prove a conjecture of Fock and Goncharov which provides a birational equivalence of a cluster variety called the cluster symplectic double and a certain moduli space of local systems associated to a surface. [ABSTRACT FROM AUTHOR]

We develop and test cluster approximations, which generalize simple mean-field by taking into account more and more local correlations, for the Totally Asymmetric Simple Exclusion Process with open boundaries. We consider in detail the pair and triplet approximations, discussing the improvements with respect to mean field in various steady state properties. Moreover, we analyze the recently discovered dynamical transition, describing how the spectrum of the relaxation matrix changes at the transition. [ABSTRACT FROM AUTHOR]

Motivation: Patient stratification or disease subtyping is crucial for precision medicine and personalized treatment of complex diseases. The increasing availability of high-throughput molecular data provides a great opportunity for patient stratification. Many clustering methods have been employed to tackle this problem in a purely data-driven manner. Yet, existing methods leveraging high-throughput molecular data often suffers from various limitations, e.g. noise, data heterogeneity, high dimensionality or poor interpretability. Results: Here we introduced an Entropy-based Consensus Clustering (ECC) method that overcomes those limitations all together. Our ECC method employs an entropy-based utility function to fuse many basic partitions to a consensus one that agrees with the basic ones as much as possible. Maximizing the utility function in ECC has a much more meaningful interpretation than any other consensus clustering methods. Moreover, we exactly map the complex utility maximization problem to the classic K-means clustering problem, which can then be efficiently solved with linear time and space complexity. Our ECC method can also naturally integrate multiple molecular data types measured from the same set of subjects, and easily handle missing values without any imputation. We applied ECC to 110 synthetic and 48 real datasets, including 35 cancer gene expression benchmark datasets and 13 cancer types with four molecular data types from The Cancer Genome Atlas. We found that ECC shows superior performance against existing clustering methods. Our results clearly demonstrate the power of ECC in clinically relevant patient stratification. [ABSTRACT FROM AUTHOR]

As online learning and the use of online technological tools in higher education continues to grow exponentially, higher education faculty are expected to incorporate these tools into their instruction. However, many faculty members are reluctant to embrace such tools, for a variety of professional and personal reasons. This study employs survey data from the 2012 Ithaka S+R faculty survey utilizing a multi-level binary (HGLM) model in order to explore the relationship between academic field, gender, age, years of experience and years in current position and the likelihood that faculty will utilize online technological tools in their instruction. The analysis found that only gender was a significant predictor of faculty online tool usage, when accounting for all other covariates, while the other predictors of age, years of experience and years in position were only significant when analyzed individually. The cluster variable field was not found to be statistically significant. [ABSTRACT FROM AUTHOR]

The phase boundary between B2 ordered and disordered phases in the Fe-rich region of the Fe-Si binary system is calculated by Cluster Variation Method (CVM). The configurational entropy is formulated within the tetrahedron approximation of CVM, and the internal energy is derived by Cluster Expansion Method (CEM) operated on a set of total energies calculated by DFT. The Debye Gruneisen model is employed to introduce the vibrational effect. The second order transition for the B2 order-disorder transition is confirmed, which is in agreement with the published phase diagram data and the results of previous CALPHAD calculations. The calculated transition temperature in the present study is higher around the stoichiometric composition and lower in the Fe-rich region compared to the experimental transition temperature. One reason for this overestimation and underestimation of the transition temperature may stem from the facts that the local atomic displacement and wide range atomic correlations are not considered in the present study. The transition temperature is also determined using Thermo-Calc software with the SSOL4 database. The transition temperature obtained by Thermo-Calc calculations accurately reproduces the experimental results. Hence, it is considered that the interaction parameters and the ordering parameters of CALPHAD free energy implicitly include the contributions of short range ordering and local atomic displacement. [ABSTRACT FROM AUTHOR]

We compute the structure factor of the J 1 - J 2 Ising model in an external field on the square lattice within the Cluster Variation Method. We use a four point plaquette approximation, which is the minimal one able to capture phases with broken orientational order in real space, like the recently reported Ising-nematic phase in the model. The analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against temperature and external field. Although the nematic susceptibility is not directly related to the structure factor, we show that because of the close relationship between the nematic order parameter and the structure factor, the latter shows unambiguous signatures of the presence of a nematic phase, in agreement with results from direct minimization of a variational free energy. The disorder variety of the model is identified and the possibility that the CVM four point approximation be exact on the disorder variety is discussed. [ABSTRACT FROM AUTHOR]

The claim that Ward’s linkage algorithm in hierarchical clustering is limited to use with Euclidean distances is investigated. In this paper, Ward’s clustering algorithm is generalised to use with l1 norm or Manhattan distances. We argue that the generalisation of Ward’s linkage method to incorporate Manhattan distances is theoretically sound and provide an example of where this method outperforms the method using Euclidean distances. As an application, we perform statistical analyses on languages using methods normally applied to biology and genetic classification. We aim to quantify differences in character traits between languages and use a statistical language signature based on relative bi-gram (sequence of two letters) frequencies to calculate a distance matrix between 32 Indo-European languages. We then use Ward’s method of hierarchical clustering to classify the languages, using the Euclidean distance and the Manhattan distance. Results obtained from using the different distance metrics are compared to show that the Ward’s algorithm characteristic of minimising intra-cluster variation and maximising inter-cluster variation is not violated when using the Manhattan metric. [ABSTRACT FROM AUTHOR]