arXiv subjects

Matthew P. Clay

Publications and source records attributed to Matthew P. Clay.

5 recordsLinked to original sources

arXiv2026

Pressure-Induced Stacking Disorder and Suppression of Long-Range Sm-type Order in Medium-Entropy Rare-Earth Alloys

Rare-earth medium-entropy alloys provide a platform for investigating how chemical disorder modifies the well-established pressure-induced structural evolution of close-packed $4f$ lanthanides. Here, we study TbHoEr and TbHoDy using synchrotron X-ray diffraction in diamond anvil cells. Both alloys transform from the ambient hexagonal close-packed (hcp) structure to a double hexagonal close-packed (dhcp) phase, while no well-resolved bulk Sm-type intermediate phase is observed. For TbHoEr, compression to 70 GPa further reveals a high-pressure rhombohedral hR24 phase. Unlike the constituent heavy lanthanides, however, both alloys bypass the intermediate Sm-type phase. Two-dimensional diffraction images further reveal streak-like diffuse scattering in the transition region, indicating stacking disorder and limited stacking coherence along the close-packed direction. These observations indicate that the transformation proceeds through a stacking-disordered close-packed state rather than through a well-ordered bulk Sm-type phase. We propose that configurational disorder, local lattice distortion, stacking-fault energetics, and transformation kinetics collectively suppress the development of long-range Sm-type order. The results demonstrate that medium-entropy alloying can fundamentally modify pressure-induced stacking pathways in rare-earth materials under extreme conditions.

cond-mat.mtrl-sci↗

arXiv2024

First-Principles Calculation of Hubbard U for Terbium Metal under High Pressure

Using density functional theory (DFT) and linear response approaches, we compute the on-site Hubbard interaction $U$ of elemental Terbium (Tb) metal in the pressure range $\sim 0-65$ GPa. The resulting first-principles $U$ values with experimental crystal structures enable us to examine the magnetic properties of Tb using a self-consistent DFT+U method. The lowest-energy magnetic states in our calculations for different high-pressure Tb phases -- including hcp, $α$-Sm, and dhcp -- are found to be compatible with the corresponding magnetic ordering vectors reported in experiments. The result shows that the inclusion of Hubbard $U$ substantially improves the accuracy and efficiency in modeling correlated rare-earth materials. Our study also provides the necessary $U$ information for other quantum many-body techniques to study Tb under extreme pressure conditions.

cond-mat.str-el↗

arXiv2021

Small-scale isotropy and ramp-cliff structures in scalar turbulence

Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to $8192^3$ at high Péclet numbers to understand this anomaly as the scalar diffusivity, $D$, diminishes, or as the Schmidt number, $Sc = ν/D$, increases; here $ν$ is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and $Sc$ varies from 1 to 512. A simple model for the ramp-cliff structures is shown to characterize the scalar derivative statistics extremely well. It accurately captures how the small-scale isotropy is restored in the large-$Sc$ limit, and additionally suggests a slight correction to the Batchelor length scale as the relevant smallest scale in the scalar field.

physics.flu-dyn↗

arXiv2021

Turbulence is an ineffective mixer when Schmidt numbers are large

We solve the advection-diffusion equation for a stochastically stationary passive scalar $θ$, in conjunction with forced 3D Navier-Stokes equations, using direct numerical simulations in periodic domains of various sizes, the largest being $8192^3$. The Taylor-scale Reynolds number varies in the range $140-650$ and the Schmidt number $Sc \equiv ν/D$ in the range $1-512$, where $ν$ is the kinematic viscosity of the fluid and $D$ is the molecular diffusivity of $θ$. Our results show that turbulence becomes an ineffective mixer when $Sc$ is large. First, the mean scalar dissipation rate $\langle χ\rangle = 2D \langle |\nabla θ|^2\rangle$, when suitably non-dimensionalized, decreases as $1/\log Sc$. Second, 1D cuts through the scalar field indicate increasing density of sharp fronts on larger scales, oscillating with large excursions leading to reduced mixing, and additionally suggesting weakening of scalar variance flux across the scales. The scaling exponents of the scalar structure functions in the inertial-convective range appear to saturate with respect to the moment order and the saturation exponent approaches unity as $Sc$ increases, qualitatively consistent with 1D cuts of the scalar.

physics.flu-dyn↗

arXiv2014

Renyi's Parking Problem Revisited

Rényi's parking problem (or $1D$ sequential interval packing problem) dates back to 1958, when Rényi studied the following random process: Consider an interval $I$ of length $x$, and sequentially and randomly pack disjoint unit intervals in $I$ until the remaining space prevents placing any new segment. The expected value of the measure of the covered part of $I$ is $M(x)$, so that the ratio $M(x)/x$ is the expected filling density of the random process. Following recent work by Gargano {\it et al.} \cite{GWML(2005)}, we studied the discretized version of the above process by considering the packing of the $1D$ discrete lattice interval $\{1,2,...,n+2k-1\}$ with disjoint blocks of $(k+1)$ integers but, as opposed to the mentioned \cite{GWML(2005)} result, our exclusion process is symmetric, hence more natural. Furthermore, we were able to obtain useful recursion formulas for the expected number of $r$-gaps ($0\le r\le k$) between neighboring blocks. We also provided very fast converging series and extensive computer simulations for these expected numbers, so that the limiting filling density of the long line segment (as $n\to \infty$) is Rényi's famous parking constant, $0.7475979203...$.

math.PR↗