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Showing 1 to 20 of 33 for “"Cluster expansion"”.
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Point processes in statistical mechanics : a cluster expansion approach
… Kerstan, Matthes and Mecke, with the method of cluster expansions from statistical mechanics. Here the starting point is a family of signed Radon measures, which defines on the one hand the Levy pseudo measure L, and on the other hand locally the point process. The relation between L and the …
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Cluster expansion approach and fluctuation results in mean field spin glass theory
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-08-01
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Unique cluster expansion for reliable first-principles prediction of alloy thermodynamics and phase diagrams
"A theoretical multi-scale approach based on the cluster expansion (CE) has been developed to aid materials design and discovery for scientific and engineering applications. Using structural energies from first-principles electronic theory, an effective (CE) Hamiltonian that is suitable for large …
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Ground state determination, ground state preserving fit for cluster expansion and their integration for robust CE construction
… ground state problem for arbitrary effective cluster interactions and construct ground state preserving cluster expansions. A full mathematical definition of our problem has been formalized to illustrate its generality and clarify our discussion. We review previous methods in material science …
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Spin cluster expansion approach to the interplay between short-range order and interstitial atoms in austenitic stainless steels
… essential for sampling alloy configurations. The cluster expansion (CE) method, combined with Monte Carlo (MC) simulations, provides a powerful computational framework for studying the thermodynamic properties of alloys. We present a detailed mathematical analysis of the conventional CE formalism, …
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Computational studies of cation and anion ordering in cubic yttria stabilized zirconia
… The first set of calculations uses the cluster expansion method. A guide to the practical implementation of the cluster expansion outlines methods for defining a goal and choosing structures and clusters that best model the system of interest. The cluster expansion of the yttria …
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Atomistic and ab initio prediction and optimization of thermoelectric and photovoltaic properties
… and demonstrate the feasibility of using the cluster expansion technique to parameterize KL. We find that the use of coarse graining and a meta cluster expansion approach is effective, in conjunction with a genetic algorithm, to find configurations which drastically lower KL. The low values of …
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First -Principles Prediction of Thermodynamics and Ordering in Metallic Alloys
After that we construct a grand-canonical cluster expansion for the hcp Al-Ag and perform ground-state search and Monte Carlo simulations to determine the metastable hcp Ag-Al phase diagram. We predict a new equilibrium hcp AgAl ground state with zero-energy domain boundary defects. From …
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Decoherence and Dynamical Decoupling in Solid-State Spin Qubits
… spin quantum computer architectures. A quantum cluster expansion method is motivated, developed, and tested for the spectral diffusion problem. The method is applicable to any ideal pulse sequence applied to the qubit. Dynamical decoupling sequences, which aim to prolong qubit coherence, are …
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Computational studies of hydrogen storage materials and the development of related methods
… including density functional theory and the cluster expansion formalism, are used to study materials for hydrogen storage. The storage of molecular hydrogen in the metal-organic framework with formula unit Zn40(02C-C6H6-COD3 is considered. It is predicted that hydrogen adsorbs at five sites …
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Computational structure analysis of multicomponent oxides
… (DFT) energy calculations combined with the cluster expansion and Monte Carlo techniques are used to understand the cation ordering patterns of multicomponent oxides. Specifically, the lithium ion battery cation material LiNi0.5Mn0.5O2 and the thermoelectric material P2-NaxCoO2 (0.5 =/< x =/< …
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A variational theory of nuclear matter
… rules are given and a general diagrammatic cluster expansion is derived. It is an expansion in powers of commutators of the non-central operators, and in their absence reduces to the usual Mayer cluster expansion. Evaluation of diagrams in the cluster expansion is complicated by the presence …
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Corrections to the Debye-Hückel Theory
<p>The cluster expansion theory of Mayer is rearranged to obtain expressions for the potential of average force and the internal potential energy of the electron gas through order n<sup>3/2</sup> in the density n. The order n result for the potential of average force is applied to ionic solutions, …
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First principles investigation of the thermodynamic and kinetic properties of lithium transition metal oxides
… local density approximation (LDA) along with the cluster expansion formalism. We have also developed a scheme to calculate from first principles, the diffusion coefficient in systems with significant configurational disorder. Building on previous first principles investigations of lithium …
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Many-body physics and non-equilibrium dynamics in ultracold atomic systems
… the normal phase. After that I develop a novel cluster expansion technique to model the dynamics of interacting fermions in a disordered optical lattice. Finally I apply a Ginzurg-Landau theory to model experimental studies of superfluid 3He embedded in nematically ordered aerogel, finding …
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Modeling the flexibility of alpha helices in protein interfaces : structure based design and prediction of helix-mediated protein-protein interactions
… by flexible-backbone methods and the use of cluster expansion to quickly map structural energies to sequence-based functions for increased efficiency.
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Spectral Properties of the Renormalization Group
… infinite volume limit at high temperature by a cluster expansion approach. The third part continues the theme of the third part, and shows that the matrix of partial derivatives of the RG map displays an approximate band property for finite-range and translation-invariant Hamiltonians at high …
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Computational Studies of PbS Quantum Dots
… well as a discretized and regularized manybody cluster expansion formulation alongside multilayer perceptrons, in training neural network potentials, as well as in directly accelerating geometry relaxations for PbS quantum dots. Noticing some unexpected nontrivial behavior during the geometry …
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Data-driven linear interatomic potentials
… permutation invariant polynomials' and 'atomic cluster expansion'. Both frameworks are linear models that can be used to create computationally efficient potentials that approximate the potential energy surface for materials and molecules with first-principles accuracy while preserving its …
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Surface phases and surface phase transitions: A renormalization-group calculation
… surface properties. In two dimensions a 4x4 cell-cluster approximation gives critical and thermodynamic properties in quantitative agreement with the. exact results of McCoy and Wu. In three dimensions a cruder (2-cell) approximation gives results which appear in qualitative agreement with what is …
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