arXiv subjects

D. J. Priour Jr

Publications and source records attributed to D. J. Priour Jr.

At least 19 recordsLinked to original sources

arXiv2026

A Geometrically Exact Treatment of Percolation Through Voids around Faceted Regular and Structurally Disordered Grains

Fluid and charge flow through interstitial volumes among impermeable randomly placed grains in porous materials ceases to occur at a critical concentration where networks of void volumes are disrupted at macroscopic scales. This critical density for void percolation can be difficult to calculate due to the irregular shape of the void regions. We develop and implement a geometrically exact method, scaling only linearly in the system volume, for identifying the shape and size of contiguous voids. In this manner, we calculate percolation thresholds for both grain cluster percolation (where system spanning networks of overlapping grains begin to appear with increasing density) and void percolation at much higher grain concentrations where networks of interstitial volumes no longer exist on macroscopic scales. For both the former and the latter, we calculate critical concentrations for inclusions in the shape of the Platonic solids (as well as truncated icosahedra) for both aligned and randomly oriented grains. In the case of critical densities for void percolation, the accuracy of our results is significantly improved relative to prior benchmarks. We also incorporate structural disorder of inclusions by considering impermeable grains in the form of cubes subject to a series of randomly placed and oriented fracture planes to mimic aggressively fractured inclusions found in nature. As the number of sustained slices becomes large, we find that the critical porosity for void percolation tends to 5%

cond-mat.dis-nn↗

arXiv2025

The Phase Diagram for Percolating Free Surfaces in Disordered Assemblies of Faceted Grains

Percolation in systems made up of randomly placed impermeable grains is often examined in the context of system spanning clusters of connected solids forming above a relatively low critical grain density $ρ_{c1}$ or networks of interstitial void volumes ceasing to exist above a signficantly higher threshold $ρ_{c2}$. In this work, we interpret these percolation transitions as, respectively, the low and high density boundaries of percolating exposed surfaces which either ensheath clusters of impermeable particles or line tunnel-like voids. Moreover, we find in the thermodynamic limit exposed surfaces are either sheaths or tunnels with a second order phase transition from the former to the latter at a density threshold $ρ_{c*}$ intermediate between $ρ_{c1}$ and $ρ_{c2}$. We calculate critical inclusion densities with a new method which identifies exposed free surfaces in a geometrically exact manner with a computational cost scaling only linearly in the system volume. We obtain $ρ_{c1}$, $ρ_{c2}$, and $ρ_{c*}$ for a variety of grain geometries, including each of the Platonic solids, truncated icosahedra, and structurally disordered inclusions formed from cubes subject to a random sequence of slicing planes. In the case of the latter, we find a limiting value of $5\%$ for the critical porosity at the void percolation threshold as the number of sustained slices per cube becomes large.

cond-mat.dis-nn↗

arXiv2022

Percolation through Voids around Toroidal Inclusions

In the case of media comprised of impermeable particles, fluid flows through voids around impenetrable grains. For sufficiently low concentrations of the latter, spaces around grains join to allow transport on macroscopic scales, whereas greater impenetrable inclusion densities disrupt void networks and block macroscopic fluid flow. A critical grain concentration $ρ_{c}$ marks the percolation transition or phase boundary separating these two regimes. With a dynamical infiltration technique in which virtual tracer particles explore void spaces, we calculate critical grain concentrations for randomly placed interpenetrating impermeable toroidal inclusions; the latter consist of surfaces of revolution with circular and square cross sections. In this manner, we study for the first time continuum percolation transitions involving non-convex grains. As the radius of revolution increases relative to the length scale of the torus cross section, the tori develop a central hole, a topological transition accompanied by a cusp in the critical porosity for percolation. With a further increase in the radius of revolution, as constituent grains become more ring-like in appearance, we find that the critical porosity converges to that of high aspect ratio cylindrical counterparts only for randomly oriented grains.

cond-mat.soft↗

arXiv2020

Time Scales for Rounding of Rocks through Stochastic Chipping

For 3D geometries, we consider stones (modeled as convex polyhedra) subject to weathering with planar slices of random orientation and depth successively removing material, ultimately yielding smooth and round (i.e. spherical) shapes. An exponentially decaying acceptance probability in the area exposed by a prospective slice provides a stochastically driven physical basis for the removal of material in fracture events. With a variety of quantitative measures, in steady state we find a power law decay of deviations in a toughness parameter $γ$ from a perfect spherical shape. We examine the time evolution of shapes for stones initially in the form of cubes as well as irregular fragments created by cleaving a regular solid many times along random fracture planes. In the case of the former, we find two sets of second order structural phase transitions with the usual hallmarks of critical behavior. The first involves the simultaneous loss of facets original to the parent solid, while the second of these involves a shift to a spherical profile. Nevertheless, for mono-dispersed irregular solids, the loss of primordial facets is not simultaneous but occurs in stages. In the case of initially irregular stones, strong disorder obscures individual structural transitions, and relevant observables are smooth with respect to time. More broadly, we find that salient times scale quadratically in $γ$. We use the universal dependence of variables on the volume remaining to calculate time dependent variables for a variety of erosion scenarios with results from a single weathering scheme such as the case in which the fracture acceptance probability depends on the relative area of the prospective new face. We calculate time scales for the attainment of structural milestones, obtaining a closed form approximate expression which bounds direct simulation results from above.

cond-mat.stat-mech↗

arXiv2012

Percolation through Voids around Overlapping Spheres, a Dynamically based Finite Size Scaling Analysis

The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the impenetrable spheres and the spaces between them. To properly exploit finite size scaling, we examine multiple systems of differing sizes, with suitable averaging over disorder, and extrapolate to the thermodynamic limit. An order parameter based on the statistical sampling of stochastically driven dynamical excursions and amenable to finite size scaling analysis is defined, calculated for various system sizes, and used to determine the critical volume fraction phi_{c} = 0.0317 +/- 0.0004 and the correlation length exponent nu = 0.92 +/- 0.05.

cond-mat.dis-nn↗

arXiv2011

Critical Behavior and Extended States in 2D and 3D Systems with Gas-like Disorder

With a tight binding treatment we examine amorphous conductors with gas-like disorder, or no correlations among the site positions. We consider an exponentially decaying hopping integral with range $l$, and the Inverse Participation Ratio (IPR) is used to characterize carrier wave functions with respect to localization. With the aid of two complementary finite size scaling techniques to extrapolate to the bulk limit (both methods exploit critical behavior in different ways to find the boundary between domains of extended and localized wave functions) which nevertheless yield identical results, we obtain phase diagrams showing regions where states are extended and domains of localized states. In the 2D case, states are localized below a threshold length scale $l_{c}$ on the order of the interparticle separation $ρ^{-1/2}$ with a finite fraction of states extended for $l > l_{c}$. For $D = 3$, the extended phase is flanked by regions of localized states and bounded by two mobility edges. The swath of extended states, broad for $l \sim 1$, becomes narrower with decreasing $l$, though persisting with finite width even for $l < (1/5)ρ^{-1/3}$. Mobility edges are interpreted as lines of critical points, and we calculate the corresponding critical exponents.

cond-mat.dis-nn↗

arXiv2011

Electronic States in One, Two, and Three Dimensional Highly Amorphous Materials: A Tight Binding Treatment

In a tight binding framework, we analyze the characteristics of electronic states in strongly disordered materials (hopping sites are placed randomly with no local order) with tunneling matrix elements decaying exponentially in the atomic separation with various decay ranges l examined. We calculate the density of states (DOS) and the Inverse Participation Ratio (IPR) for amorphous atomic configurations in one, two, and three dimensions. With a finite size scaling analysis of the IPR statistical distributions, it is shown that states are either extended or localized for a particular energy, and phase portraits for wave functions are obtained showing extended and localized behavior in the thermodynamic limit. While we conclude that all states are localized in 1D, in the 2D case there is a threshold for l above which some eigenstates appear to be extended and below which wave functions are entirely localized. For 3D geometries, there are two mobility boundaries flanking an intermediate range of energies where states are extended with eigenstates localized for energies above or below this range. While a zone of extended states persists even for very short l, the width of the region tends to zero exponentially (i.e. scaling as exp{-A/l}) for very small decay length scales.

cond-mat.mtrl-sci↗

arXiv2010

The Thermodynamic Stability of Two Dimensional Crystals with an Extended Coupling Scheme

We calculate mean square deviations for crystals in one and two dimensions. For the two dimensional lattices, we consider several distinct geometries (i.e. square, triangular, and honeycomb), and we find the same essential phenomena for each lattice structure. We investigate the stability of long-range crystalline order for a variety of coupling schemes, including short-range exponentially decaying inter-atomic potentials and long-range interactions with a power law dependence r^{-alpha}. For the latter in the 1D case, we find a critical value alpha_c(1D) = 1.615 +/- 0.005 for the power law decay exponent below which crystalline order is intact, and above which thermal fluctuations destroy long-range order when T > 0. The corresponding critical value for two dimensional lattices with displacements confined to the plane is alpha_c(2D) = 3.15 +/ 0.025. If motion perpendicular to the crystal plane is permitted, thermally induced distortions diverge rapidly (i.e. linearly) in dual layer systems with local stiffness provided by an extended coupling scheme, even if the interaction is long ranged, decaying as a power law in the separation between lattice sites.

cond-mat.mtrl-sci↗

arXiv2010

Critical behavior of diluted magnetic semiconductors: the apparent violation and the eventual restoration of the Harris criterion for all regimes of disorder

Using large-scale Monte Carlo calculations, we consider strongly disordered Heisenberg models on a cubic lattice with missing sites (as in diluted magnetic semiconductors such as Ga_{1-x}Mn_{x}As). For disorder ranging from weak to strong levels of dilution, we identify Curie temperatures and calculate the critical exponents nu, gamma, eta, and beta finding, per the Harris criterion, good agreement with critical indices for the pure Heisenberg model where there is no disorder component. Moreover, we find that thermodynamic quantities (e.g. the second moment of the magnetization per spin) self average at the ferromagnetic transition temperature with relative fluctuations tending to zero with increasing system size. We directly calculate effective critical exponents for T > T_{c}, yielding values which may differ significantly from the critical indices for the pure system, especially in the presence of strong disorder. Ultimately, the difference is only apparent, and eventually disappears when T is very close to T_{c}.

cond-mat.mtrl-sci↗

arXiv2010

Phonon Density of States and Thermodynamic Behavior in Highly Amorphous Media

We calculate the phonon density of states (DOS) for strongly amorphous materials with a short-ranged interatomic potential. Exponentially decaying and abruptly truncated interatomic potentials are examined. Thermally excited mean square deviations from equilibrium are calculated with rapid increases noted as the average number of neighbors is reduced. The Inverse Participation Ratio (IPR) is used to characterize the phonon states and identify localized phonon modes as the bonding range (and hence the average number of neighbors per atom) is diminished. For the truncated potential, the characteristics of the IPR histogram change qualitatively below $n_{\mathrm{neigh}}$ with the appearance of localized phonon modes below $n_{\mathrm{neigh}} = 6.0$.

cond-mat.mtrl-sci↗

arXiv2009

A Convenient Alternative for Series Manipulation via the Translation Operator

We derive and discuss a technique for manipulating power series which is complementary to standard procedures. We begin with the translation operator, but we express the operator as an infinite product instead of expanding it as a series and we apply combinatorial arguments to generate the terms in the series in an efficient manner with a minimum of clutter and intermediate calculations. The method is effective for developing multivariate expansions, and may also be used to manipulate series, e.g. in operations where one must take the reciprocal of a power series or raise it to a power that may be fractional or irrational. In the case of two component perturbations, we obtain analytic expressions for the expansion coefficients. We use our technique to generate an electrostatic multipole expansion as a demonstration of its utility in producing coefficients of special functions such as the Legendre and Hermite polynomials.

math-ph↗

arXiv2006

Clustering in disordered ferromagnets: The Curie temperature in diluted magnetic semiconductors

We theoretically investigate impurity correlation and magnetic clustering effects on the long-range ferromagnetic ordering in diluted magnetic semiconductors, such as $\textrm{Ga}_{1-x}\textrm{Mn}_{x}\textrm{As}$, using analytical arguments and direct Monte Carlo simulations. We obtain an analytic formula for the ferromagnetic transition temperature $T_{c}$ which becomes asymptotically exact in the strongly disordered, highly dilute (i.e. small $x$) regime. We establish that impurity correlations have only small effects on $T_{c}$ with the neutrally correlated random disorder producing the nominally highest $T_{c}$. We find that the ferromagnetic order is approached from the high temperature paramagnetic side through a random magnetic clustering phenomenon consistent with the percolation transition scenario.

cond-mat.mtrl-sci↗

arXiv2005

Two Dimensional Diluted Magnetic Semiconductor Systems

We develop a theory for two-dimensional diluted magnetic semiconductor systems (e.g. $\textrm{Ga}_{1-x}\textrm{Mn}_{x}\textrm{As}$ layers) where the itinerant carriers mediating the ferromagnetic interaction between the impurity local moments, as well as the local moments themselves, are confined in a two-dimensional layer. The theory includes exact spatial disorder effects associated with the random local moment positions within a disordered RKKY lattice field theory description. We predict the ferromagnetic transition temperature ($T_{c}$) as well as the nature of the spontaneous magnetization. The theory includes disorder and finite carrier mean free path effects as well as the important correction arising from the {\it finite temperature} RKKY interaction, finding a strong density dependence of $T_{c}$ in contrast to the simple virtual crystal approximation.

cond-mat.mtrl-sci↗

arXiv2004

Enhancing $T_c$ in ferromagnetic semiconductors

We theoretically investigate disorder effects on the ferromagnetic transition ('Curie') temperature $T_c$ in dilute III$_{1-x}$Mn$_x$V magnetic semiconductors (e.g. Ga$_{1-x}$Mn$_x$As) where a small fraction ($x \approx 0.01-0.1$) of the cation atoms (e.g. Ga) are randomly replaced by the magnetic dopants (e.g. Mn), leading to long-range ferromagnetic ordering for $T<T_c$. We find that $T_c$ is a complicated function of at least eight different parameters including carrier density, magnetic dopant density, and carrier mean free path; nominally macroscopically similar samples could have substantially different Curie temperatures. We provide simple physically appealing prescriptions for enhancing $T_c$ in diluted magnetic semiconductors, and discuss the magnetic phase diagram in the system parameter space.

cond-mat.mtrl-sci↗

arXiv2003

Vortex States of a Superconducting Film from a Magnetic Dot Array

Using Ginzburg-Landau theory, we find novel configurations of vortices in superconducting thin films subject to the magnetic field of a magnetic dot array, with dipole moments oriented perpendicular to the film. Sufficiently strong magnets cause the formation of vortex-antivortex pairs. In most cases, the vortices are confined to dot regions, while the antivortices can form a rich variety of lattice states. We propose an experiment in which the perpendicular component of the dot dipole moments can be tuned using an in-plane magnetic field. We show that in such an experiment the vortex-antivortex pair density shows broad plateaus as a function of the dipole strength. Many of the plateaus correspond to vortex configurations which break dot lattice symmetries. In some of these states, the vortex cores are strongly distorted. Possible experimental consequences are mentioned.

cond-mat.supr-con↗

arXiv2003

A disordered RKKY lattice mean field theory for ferromagnetism in diluted magnetic semiconductors

We develop a lattice mean field theory for ferromagnetic ordering in diluted magnetic semiconductors by taking into account the spatial fluctuations associated with random disorder in the magnetic impurity locations and the finite mean free path associated with low carrier mobilities. Assuming a carrier-mediated indirect RKKY exchange interaction among the magnetic impurities, we find substantial deviation from the extensively used continuum Zener model Weiss mean-field predictions. Our theory allows accurate analytic predictions for Tc, and provides simple explanations for a number of observed anomalies including the non-Brillouin function magnetization curves, the suppressed low-temperature magnetization saturation, and the dependence of Tc on conductivity.

cond-mat.mtrl-sci↗

arXiv2002

Deformation and Depinning of Superconducting Vortices from Artificial Defects: A Ginzburg-Landau Study

Using Ginzburg-Landau theory, we have performed detailed studies of vortices in the presence of artificial defect arrays, for a thin film geometry. We show that when a vortex approaches the vicinity of a defect, an abrupt transition occurs in which the vortex core develops a ``string'' extending to the defect boundary, while simultaneously the supercurrents and associated magnetic flux spread out and engulf the defect. Current induced depinning of vortices is shown to be dominated by the core string distortion in typical experimental situations. Experimental consequences of this unusual depinning behavior are discussed.

cond-mat.supr-con↗

arXiv2001

London equation studies of thin-film superconductors with a triangular antidot lattice

We report on a study of vortex pinning in nanoscale antidot defect arrays in the context of the London Theory. Using a wire network model, we discretize the array with a fine mesh, thereby providing a detailed treatment of pinning phenomena. The use of a fine grid has enabled us to examine both circular and elongated defects, patterned in the form of a rhombus. The latter display pinning characteristics superior to circular defects constructed with the similar area. We calculate pinning potentials for defects containing zero and single quanta, and we obtain a pinning phase diagram for the second matching field, $H = 2 Φ_{o}$.

cond-mat.supr-con↗