arXiv subjects

John W. Lawson

Publications and source records attributed to John W. Lawson.

13 recordsLinked to original sources

arXiv2024

Thermodynamic Integration for Dynamically Unstable Systems Using Interatomic Force Constants without Molecular Dynamics

We demonstrate an efficient and accurate, general-purpose first-principles blueprint for calculating anharmonic vibrational free energy and predicting structural phase transition temperatures of solids. Thermodynamic integration is performed without molecular dynamics using only interatomic force constants to model analogues of the true potential and generate their thermal ensembles. By replacing \textit{ab initio} molecular dynamics (AIMD) with statistical sampling of ensemble configurations and trading density-functional theory (DFT) energy calculations on each configuration for a set of matrix operations, our approach enables a faster thermodynamic integration by 4 orders of magnitude over the traditional route via AIMD. Experimental phase transition temperatures of a variety of strongly anharmonic materials with dynamical instabilities including shape-memory alloys are recovered to largely within 25% error. Such a combination of speed and accuracy enables the method to be deployed at a large-scale for predictive mapping of phase transition temperatures.

cond-mat.mtrl-sci↗

arXiv2023

Energy-composition relations in Ni$_3$(Al$_{1-x}$X$_x$) phases

The secondary phase, such as Ni$_3$Al-based $L1_2$ $γ^\prime$, is crucially important for precipitation strengthening of superalloys. Composition-structure-property relations provide useful insights for guided alloy design. Here we use density functional theory combined with the multiple scattering theory to compute dependencies of the structural energies and equilibrium volumes versus composition for ternary Ni$_3$(Al$_{1-x}$X$_x$) alloys with X=(Ti, Zr, Hf; V, Nb, Ta; Cr, Mo, W) in $L1_2$, $D0_{24}$, and $D0_{19}$ phases with a homogeneous chemical disorder on the (Al$_{1-x}$X$_x$) sublattice. Our results provide a better understanding of the physics in Ni$_3$Al-based precipitates and facilitate design of next-generation nickel superalloys with precipitation strengthening.

cond-mat.mtrl-sci↗

arXiv2023

Energy landscape in NiCoCr-based middle-entropy alloys

NiCoCr middle-entropy alloy is known for its exceptional strength at both low and elevated operating temperatures. Mechanical properties of NiCoCr-based alloys are affected by certain features of the energy landscape, such as the energy difference between the hcp and fcc phases (which is known to correlate with the stacking fault energy in the fcc phase) and curvature of the energy surface. We compute formation energies in the Ni-Co-Cr ternary and related quaternary systems and investigate dependences of the relative energies on composition. Such computed composition-structure-property relations can be useful for tuning composition and designing next-generation alloys with improved strength.

cond-mat.mtrl-sci↗

arXiv2021

Cluster algebras from surfaces and extended affine Weyl groups

We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with every triangulation a basis in $V$, such that any mutation of a cluster (i.e., a flip of a triangulation) transforms the corresponding bases into each other by partial reflections. Furthermore, every triangulation gives rise to an extended affine Weyl group of type $A$, which is invariant under flips. The construction is also extended to exceptional skew-symmetric mutation-finite cluster algebras of types $E$.

math.CO↗

arXiv2016

Cluster automorphisms and the marked exchange graphs of skew-symmetrizable cluster algebras

Cluster automorphisms have been shown to have links to the mapping class groups of surfaces, maximal green sequences and to exchange graph automorphisms for skew-symmetric cluster algebras. In this paper we aim to generalise these results to the skew-symmetrizable case by introducing a marking on the exchange graph. Many skew-symmetrizable matrices unfold to skew-symmetric matrices and we consider how cluster automorphisms behave under this unfolding with applications to coverings of orbifolds by surfaces.

math.CO↗

arXiv2016

Properties of minimal mutation-infinite quivers

We study properties of minimal mutation-infinite quivers. In particular we show that every minimal-mutation infinite quiver of at least rank 4 is Louise and has a maximal green sequence. It then follows that the cluster algebras generated by these quivers are locally acyclic and hence equal to their upper cluster algebra. We also study which quivers in a mutation-class have a maximal green sequence. For any rank 3 quiver there are at most 6 quivers in its mutation class that admit a maximal green sequence. We also show that for every rank 4 minimal mutation-infinite quiver there is a finite connected subgraph of the unlabelled exchange graph consisting of quivers that admit a maximal green sequence.

math.CO↗

arXiv2008

Density matrix calculation of optical constants from optical to x-ray frequencies

We present a theory of linear optical constants based on a single-particle density matrix and implemented in an extension of the real-space multiple scattering code FEFF. This approach avoids the need to compute wave-functions explicitly, and yields efficient calculations for frequencies ranging from the IR to hard x-rays, and applicable to arbitrary aperiodic systems. Our approach is illustrated with calculations of optical properties and applications for several materials.

cond-mat.mtrl-sci↗

arXiv2007

Current-voltage curves for molecular junctions: the effect of substituents

We present current-voltage (I-V) curves for phenylene ethynylene oligomers between two Au surfaces computed using a Density Functional Theory/Green's Function approach. In addition to the parent molecule, two different substituents are considered: one where all the hydrogens are replaced by chlorines and a second where one H is replaced by an NO2 group. In this way, we can study the difference between electron withdrawing and pi orbital effects. For low biases, a reduced current for the derived species is consistent with a shift of HOMO to lower energy due to the electron withdrawal by Cl or NO2. At higher biases, the LUMO becomes important, and the Cl and NO2 substituted species carry more current than the parent because the LUMO is stabilized (shifted to lower energy) due to the withdrawal of electrons by the Cl and NO2. In these molecules, the C2 bridging units as well as the thiol anchor group are shown to create bottlenecks to current flow.

cond-mat.mes-hall↗

arXiv2006

Adaptive Programming of Unconventional Nano-Architectures

Novel assembly processes for nanocircuits could present compelling alternatives to the detailed design and placement currently used for computers. The resulting architectures however may not be programmable by standard means. In this paper, nanocomputers with unconventional architectures are programmed using adaptive methods. The internals of the device are treated as a "black box" and programming is achieved by manipulating "control voltages". Learning algorithms are used to set the controls. As examples, logic gates and simple arithmetic circuits are implemented. Additionally, similar methods allow for reconfiguration of the devices, and makes them resistant to certain kinds of faults.

cond-mat.mtrl-sci↗

arXiv2006

Current-Voltage Curves for Molecular Junctions Computed Using All-Electron Basis Sets

We present current-voltage (I-V) curves computed using all-electron basis sets on the conducting molecule. The all-electron results are very similar to previous results obtained using effective core potentials (ECP). A hybrid integration scheme is used that keeps the all-electron calculations cost competitive with respect to the ECP calculations. By neglecting the coupling of states to the contacts below a fixed energy cutoff, the density matrix for the core electrons can be evaluated analytically. The full density matrix is formed by adding this core contribution to the valence part that is evaluated numerically. Expanding the definition of the core in the all-electron calculations significantly reduces the computational effort and, up to biases of about 2 V, the results are very similar to those obtained using more rigorous approaches. The convergence of the I-V curves and transmission coefficients with respect to basis set is discussed. The addition of diffuse functions is critical in approaching basis set completeness.

cond-mat.mes-hall↗

arXiv2006

Transport in Molecular Junctions with Different Metallic Contacts

Ab initio calculations of phenyl dithiol connected to Au, Ag, Pd, and Pt electrodes are performed using non-equilibrium Green's functions and density functional theory. For each metal, the properties of the molecular junction are considered both in equilibrium and under bias. In particular, we consider in detail charge transfer, changes in the electrostatic potential, and their subsequent effects on the IV curves through the junctions. Gold is typically used in molecular junctions because it forms strong chemical bonds with sulfur. We find however that Pt and Pd make better electrical contacts than Au. The zero-bias conductance is found to be greatest for Pt, followed by Pd, Au, and then Ag.

cond-mat.mes-hall↗

arXiv1995

Source Galerkin Calculations in Scalar Field Theory

In this paper, we extend previous work on scalar $ϕ^4$ theory using the Source Galerkin method. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using polynomial expansions for the generating functional $Z$, we calculate propagators and mass-gaps for a number of systems. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. The use of polynomial expansions illustrates in a clear and simple way the ideas of the Source Galerkin method. But at the same time, this choice has serious limitations. Even after exploiting symmetries, the size of calculations become prohibitive except for small systems. The calculations in this paper were made on a workstation of modest power using a fourth order polynomial expansion for lattices of size $8^2$,$4^3$,$2^4$ in $2D$, $3D$, and $4D$. In addition, we present an alternative to the Galerkin procedure that results in sparse matrices to invert.

hep-th↗

arXiv1995

New Numerical Method for Fermion Field Theory

A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using Grassmann polynomial expansions for the generating functional $Z$, we calculate propagators for systems of interacting fermions. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. Because it is not based on a statistical technique, it does not have many of the difficulties often encountered when simulating fermions. Since no determinant is ever calculated, solutions to problems with dynamical fermions are handled more easily. This approach is very flexible, and can be taylored to specific problems based on convenience and computational constraints. We present simple examples to illustrate the method; more general schemes are desirable for more complicated systems.

hep-th↗