Mean-field Estimates Research Articles

Cubic elasticity of porous materials produced by additive manufacturing: experimental analyses, numerical and mean-field modelling

Although the elastic properties of porous materials depend mainly on the volume fraction of pores, the details of pore distribution within the material representative volume are also important and may be the subject of optimisation. To study their effect, experimental analyses were performed on samples made of a polymer material with a predefined distribution of spherical voids, but with various porosities due to different pore sizes. Three types of pore distribution with cubic symmetry were considered and the results of experimental analyses were confronted with mean-field estimates and numerical calculations. The mean-field ‘cluster’ model is used in which the mutual interactions between each of the two pores in the predefined volume are considered. As a result, the geometry of pore distribution is reflected in the anisotropic effective properties. The samples were produced using a 3D printing technique and tested in the regime of small strain to assess the elastic stiffness. The digital image correlation method was used to measure material response under compression. As a reference, the solid samples were also 3D printed and tested to evaluate the polymer matrix stiffness. The anisotropy of the elastic response of porous samples related to the arrangement of voids was assessed. Young’s moduli measured for the additively manufactured samples complied satisfactorily with modelling predictions for low and moderate pore sizes, while only qualitatively for larger porosities. Thus, the low-cost additive manufacturing techniques may be considered rather as preliminary tools to prototype porous materials and test mean-field approaches, while for the quantitative and detailed model validation, more accurate additive printing techniques should be considered. Research paves the way for using these computationally efficient models in optimising the microstructure of heterogeneous materials and composites.

Critical behavior at ferromagnetic to paramagnetic phase transition in single crystalline MnNiSi ferromagnet

Ferromagnetic single crystalline MnNiSi samples were first fabricated through a Sn-flux growth technique, followed by measurements of their structural characteristics and intrinsic magnetic properties. Additionally, the critical behavior for second-order ferromagnetic to paramagnetic phase transition was investigated through utilization of techniques such as the modified Arrott plot, the Kouvel–Fisher method, and the magnetocaloric effect scaling law method. Through different methods of analysis, reliable critical exponents were obtained. Renormalization of interactions around the Curie temperature indicates the reliability of the obtained exponents. The obtained critical exponents are close to those theoretically predicted for a three-dimensional isotropic short-range Heisenberg ferromagnet but shift toward the long-range mean-field estimates. This may arise from the coupling of short- and long-range interactions as well as the competition between localized Mn–Mn magnetic interactions and the hybridization between p- and d-type orbitals.

Accelerating convergence of inference in the inverse Ising problem

Inferring modelling parameters of dynamical processes from observational data is an important inverse problem in statistical physics. In this paper, instead of passively observing the dynamics for inference, we focus on strategically manipulating dynamics to generate data that gives more accurate estimators within fewer observations. For this purpose, we consider the inference problem rooted in the Ising model with two opposite external fields, assuming that the strength distribution of one of the fields (labelled as passive) is unknown and needs to be inferred. In contrast, the other field (labelled active) is strategically deployed to interact with the Ising dynamics in such a way as to improve the accuracy of estimates of inferring the opposing passive field. By comparing to benchmark cases, we first demonstrate that it is possible to accelerate the inference by strategically interacting with the Ising dynamics. We then apply series expansions to obtain an approximation of the optimized influence configurations in the high-temperature region. Furthermore, by using mean-field estimates, we also demonstrate the applicability of the method in a more general scenario where real-time tracking of the system is infeasible. Last, analysing the optimized influence profiles, we describe heuristics for manipulating the Ising dynamics for faster inference. For example, we show that agents targeted more strongly by the passive field should also be strongly targeted by the active one.

Parameters of the Liquid-Gas-State Triangle for Hard-Core Attractive Yukawa Fluids.

We discuss the triangle of the liquid-gas concept within the fluid-lattice gas isomorphism approach and the Zeno-element, taking the hard-core Yukawa fluid (HCAYF) as an example. The applicability of such an isomorphism is demonstrated by the symmetrization of binodals with mapping onto the Ising model coexistence curve. We show that the parameters of the isomorphism transformation reflect the liquid-phase instability for hard-core Yukawa potential and its generalization. We also provide a simple mean-field estimate for the parameter z of the fluid-lattice gas transformation and use it to obtain the locus of the critical point.

Strong Magnetocaloric Coupling in Oxyorthosilicate with Dense Gd3+ Spins.

Searching for working refrigerant materials is the key element in the design of magnetic cooling devices. Herein, we report on the thermodynamic and magnetocaloric parameters of an X1 phase oxyorthosilicate, Gd2SiO5, by field-dependent static magnetization and specific heat measurements. An overall correlation strength of |J|S2 ≈ 3.4 K is derived via the mean-field estimate, with antiferromagnetic correlations between the ferromagnetically coupled Gd-Gd layers. The magnetic entropy change -ΔSm is quite impressive, reaches 0.40 J K-1 cm-3 (58.5 J K-1 kg-1) at T = 2.7 K, with the largest adiabatic temperature change Tad = 23.2 K for a field change of 8.9 T. At T = 20 K, the lattice entropy SL is small enough compared to the magnetic entropy Sm, Sm/SL = 21.3, which warrants its potential in 2 -20 K cryocoolers with both the Stirling and Carnot cycles. Though with relatively large exchange interactions, the layered A-type spin arrangement ultimately enhances the magnetocaloric coupling, raising the possibilities of designing magnetic refrigerants with a high ratio of cooling capacity to volume.

Modeling spatial inhomogeneities in a crossbridge ensemble reveals where mean-field estimates of sarcomere stiffness break down.

How actomyosin crossbridges share and transmit loads between the thick and thin filaments in a sarcomere underlies the emergence of muscle's stimulus-dependent material properties. In particular, stiffness, the resistance to external length perturbations, is of interest because of its importance to muscle's in vivo function. Following A.F. Huxley's original work, many sarcomere models treat the thick and thin filaments as rigid and lump their compliance into a single series elastic element. Under this approximation, the crossbridges act as parallel elastic force generators. So their stiffnesses are thought to add linearly and their collective dynamics are captured by the ensemble mean. In this work, we investigate the accuracy of this approximation by exactly deriving the stiffness of a spring network that accounts for the spatially distributed filament and crossbridge compliances. We show that even the small degree of measured filament compliance in a sarcomere leads to a profound deviation of the mechanical behavior from the ensemble mean. Unlike the lumped compliance approximation, the exact accounting finds that the emergent stiffness depends on the spatial distribution of crossbridges; a property that cannot be captured by a mean model. Moreover, under physiologically relevant crossbridge numbers, the lumped compliance approximation underestimates the net stiffness of a pair of filaments by over two-fold. Further analyses show that crossbridge clusters may be thermodynamically favored because they lower the total system strain energy that arises from externally applied loads at the filament boundaries and the internal forces applied by the myosin powerstroke. We speculate that the dependence of stiffness and strain energy on the spatial inhomogeneity of crossbridges has mechanochemical consequences that affect the development and cycling of crossbridges in actomyosin networks.

Analysis and mean-field derivation of a porous-medium equation with fractional diffusion

A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a fractional Laplacian, and the limit equation can be interpreted as a transport equation with a fractional pressure. The proof is based on Oelschläger’s approach and a priori estimates for the associated diffusion equations, coming from energy-type and entropy inequalities as well as parabolic regularity. An existence analysis of the fractional porous-medium equation is also provided, based on a careful regularization procedure, new variants of fractional Gagliardo–Nirenberg inequalities, and the div-curl lemma. A consequence of the mean-field limit estimates is the propagation of chaos property.

Electronic structure and magnetic properties of bulk and (001) surfaces of [formula omitted]-Fe4C from first principles

We report first principles investigation of the electronic structure and magnetic properties of bulk γ′-Fe4C and its (001) surfaces within density functional theory. The bulk equilibrium lattice parameter (a0 = 3.81Å ) and bulk modulus (B0=141.2 GPa) were determined by first relaxing the cell volume while keeping the atoms located at their ideal positions. The corresponding magnetic moments were found to be 3.10 μB and 1.77 μB on the two inequivalent iron sites. The magnetic exchange parameters between the magnetic spin moments were computed as functions of inter-atomic distances up to four times the lattice parameter, from which the mean-field estimates of the Curie temperature were obtained. Effects of disorder, due in one case to substitution of carbon atoms by nitrogen atoms, and in an other to a small concentration of vacancies on the iron sites, on the Curie temperature were also investigated within the coherent potential approximation. We found that disorder has a dramatic effect on the transition temperature, especially in the second case. The electronic structure and magnetic profile of the γ′-Fe4C (001) surface with Fe2C termination was studied in the supercell geometry. Substantial surface relaxations were found to occur, but they do not induce significant changes in the magnetic moments when compared to those of the unrelaxed surface. No notable charge transfers were found either in the bulk or at the surface.

The mean-field limit of the Cucker-Smale model on complete Riemannian manifolds

We study the mean-field limit of the Cucker-Smale (C-S) model for flocking on complete smooth Riemannian manifolds. For this, we first formally derive the kinetic manifold C-S model on manifolds using the BBGKY hierarchy and derive several a priori estimates on emergent dynamics. Then, we present a rigorous mean-field limit from the particle model to the corresponding kinetic model by using the generalized particle-in-cell method. As a byproduct of our rigorous mean-field limit estimate, we also establish a global existence of a measure-valued solution for the derived kinetic model. Compared to the corresponding results on R d \mathbb {R}^d , our procedure requires additional assumption on holonomy and proper a priori bound on the derivative of parallel transports. As a concrete example, we verify that hyperbolic space H d \mathbb {H}^d satisfies our proposed standing assumptions.

Modelling Aboveground Biomass of Miombo Woodlands in Niassa Special Reserve, Northern Mozambique

Aboveground biomass (AGB) estimation plays a crucial role in forest management and carbon emission reporting, especially for developing countries wishing to address REDD+ projects. Both passive and active remote-sensing technologies can provide spatially explicit information of AGB by using a limited number of field samples, thus reducing the substantial budgetary cost of field inventories. The aim of the current study was to estimate AGB in the Niassa Special Reserve (NSR) using fusion of optical (Landsat 8/OLI and Sentinel 2A/MSI) and radar (Sentinel 1B and ALOS/PALSAR-2) data. The performance of multiple linear regression models to relate ground biomass with different combinations of sensor data was assessed using root-mean-square error (RMSE), and the Akaike and Bayesian information criteria (AIC and BIC). The mean AGB and carbon stock (CS) estimated from field data were estimated at 56 Mg ha−1 (ranging from 11 to 95 Mg ha−1) and 28 MgC ha−1, respectively. The best model estimated AGB at 63 ± 20.3 Mg ha−1 for NSR, ranging from 0.6 to 200 Mg ha−1 (r2 = 87.5%, AIC = 123, and BIC = 51.93). We obtained an RMSE % of 20.46 of the mean field estimate of 56 Mg ha−1. The estimation of AGB in this study was within the range that was reported in the existing literature for the miombo woodlands. The fusion of vegetation indices derived from Landsat/OLI and Sentinel 2A/MSI, and backscatter from ALOS/PALSAR-2 is a good predictor of AGB.

Evaluating the Harvest Rate Recommendation for Northern Bobwhites in South Texas

The current harvest rate recommendation for northern bobwhites (Colinus virginianus; hereafter, bobwhite) in South Texas, USA is 20% of the autumn population, including crippling loss. This recommendation is based on population simulations of empirical data. We completed the first field evaluation of the 20% harvest recommendation by comparing prehunting and posthunting bobwhite density estimates on a hunted and nonhunted site in South Texas during the 2018–2019, 2019–2020, and 2020–2021 statewide bobwhite hunting seasons in Jim Hogg County, Texas. We conducted line-transect distance sampling surveys on 4 occasions per year (early November, mid-December, late January, early March) from a helicopter platform and prescribed the 20% annual bobwhite harvest from the November density estimate. According to our bobwhite density estimates, we found that bobwhite mortality (e.g., population decline) varied seasonally between hunted ( = 54% ± 3%) and nonhunted sites ( = 46% ± 5%). Our spring density estimates on both sites (i.e., hunted vs. nonhunted) were similar through the first 2 years but diverged in 2020–2021, with bobwhite densities that were 129% higher on the nonhunted site. Comparing our annual spring density results to the means reported from population models (i.e., 100-year simulations) used to create the 20% harvest recommendation, we found that the mean spring density of the model simulations was higher than our mean field estimates on both our hunted (+59%) and nonhunted sites (+77%). We recommend a conservative approach to prescribing a bobwhite harvest in South Texas, such as using the lower 95% confidence interval of a bobwhite abundance estimate for calculating harvest prescriptions, due to variability within density estimates and bobwhite survival in semiarid ranges.

Density dependence and spatial heterogeneity limit the population growth rate of invasive pines at the landscape scale

Determining population growth across large scales is difficult because it is often impractical to collect data at large scales and over long timespans. Instead, the growth of a population is often only measured at a small, plot‐level scale and then extrapolated to derive a mean field estimate. However, this approach is prone to error since it simplifies spatial processes such as the neighbourhood effects of density and dispersal. We present a novel approach that estimates how spatial processes derived from the effects of density and dispersal affect population growth between plot scales and landscape scales. The method is based on a scale transition theory and calculates a transition term to measure the spatial scaling of population growth, which we extend to unstable, expanding populations in order to assess whether landscape‐scale population dynamics are different from those estimated at smaller spatial scales. We illustrate this approach using aerial imagery of eight locations in New Zealand experiencing non‐native pine invasions. Analyses examined the dynamics at a plot scale (1 ha) and compared this to estimates across entire landscapes (between 24 and 1600 ha), in several cases for more than one time period. We used a Bayesian spatial random effects model to examine population growth and to account for neighbourhood effects and dispersal between plots in a rapidly changing system.We found that the estimates of the scale transition term were typically 10–25% of the mean field estimates, which led to mean field estimates of population growth extrapolated from plots being considerably higher than landscape estimates. The approach we have developed will not only have applications for predicting the populations' growth of invasive species, but also for studies examining the scaling of landscape‐scale phenomena.

Effects of dynamical screening on the BCS-BEC crossover in double bilayer graphene: Density functional theory for exciton bilayers

We derive a gap equation for bilayer excitonic systems based on density functional theory and benchmark our results against quantum Monte Carlo simulations and recent experiments on double bilayer graphene. The gap equation has a mean-field form but includes a consistent treatment of dynamical screening. We show that the gap survives at much higher densities than previously thought from mean-field estimates which gives strong indications that the double-bilayer graphene systems at zero magnetic field can be used as model systems to investigate the BCS-BEC crossover. Furthermore, we show that Josephson-like transfer of pairs can be substantial for small band gaps and densities.

Diagrammatic study of optical excitations in correlated systems

The optical conductivity contains relevant information on the properties of correlated electron systems. In infinite dimensions, where dynamical mean field theory becomes exact, vertex corrections can be neglected and the conductivity computed from particle-hole bubbles. An interesting question concerns the nature and effect of the most relevant vertex corrections in finite-dimensional systems. A recent numerical study showed that the dominant vertex correction near an ordering instability with wave vector {\pi} comes from a vertical ladder, analogous to the Maki-Thompson diagram. Since the RPA version of this ladder diagram, dubbed {\pi}-ton, can be easily evaluated, this suggests a simple procedure for incorporating antiferromagnetic or charge density wave fluctuations into dynamical mean field estimates of the optical conductivity and related susceptibilities. We implement this procedure for the half-filled Hubbard model, considering the {\pi}-ton and a double-ladder extension of the {\pi}-ton, and reveal the spectral signatures of these vertex corrections.

Proton fraction in neutron star matter: dynamical mean-field approach

Dynamical mean field theory (DMFT) is used to study neutron matter, both with and without admixture of the proton fraction. The system is approximated by the lattice Hubbard model. The corresponding equation of state as a function of temperature/density/asymmetry is investigated. The results are compared with the standard mean field (MF) approach where the effect of local correlations is neglected. Whereas the influence of the correlations on the properties of a pure neutron matter is found to be moderate, it becomes strong when the proton admixture is taken into account. In particular, we calculate the proton fraction, energy density and pressure in outer core of neutron stars, taking into account the beta equilibrium condition. The DMFT predicts that the proton fraction is several times the MF based calculations, whereas the DMFT results for energy density and pressure are 30%–40% lower than the corresponding MF estimates. Physical implications of our findings for a neutron star dynamics are discussed.

Electrically controlled two-dimensional electron-hole fluids

We study the electronic properties of dual-gated electron-hole bilayers in which the two layers are separated by a perfectly opaque tunnel barrier. Combining an electrostatic and thermodynamic analysis with mean-field theory estimates of interacting system chemical potentials, we explain the dependence of the electron and hole densities on the two gate voltages. Because chemical potential jumps occur for both electrons and holes at neutrality, there is a finite area in gate voltage parameter space over which electron and hole densities are equal. In that regime the electron-hole pair density depends only on the sum of the two gate voltages. We are able to explain a recent experimental study of electrically controlled bilayers by allowing for interlayer tunneling and using a non-equilibrium steady-state transport picture.

Different time scales in dynamic systems with multiple outcomes.

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each specific outcome, effectively corresponding to a single-exit process and assuming the independence of each exit process. However, the presence of other exits influences the statistical properties and dynamics measured at any specific exit. Here, we present theoretical arguments to explicitly show the existence of different time scales, such as mean exit times and inverse exit fluxes, for dynamic processes with multiple exits. This implies that the statistics of any specific exit dynamics cannot be considered without taking into account the presence of other exits. Several illustrative examples are described in detail using analytical calculations, mean-field estimates, and kinetic Monte Carlo computer simulations. The underlying microscopic mechanisms for the existence of different time scales are discussed. The results are relevant for understanding the mechanisms of various biological, chemical, and industrial processes, including transport through channels and pores.

Pauli limited d-wave superconductors: quantum breached pair phase and thermal transitions

We report a quantum phase transition in Pauli limited d-wave superconductors and give the mean field estimates of the associated quantum critical point. For a population imbalanced d-wave superconductor a stable ground state phase viz quantum breached pair phase has been identified which comprises of spatial coexistence of gapless superconductivity and nonzero magnetization. Based on the thermodynamic and quasiparticle indicators we for the first time analyze this phase, discuss the thermal behavior of Pauli limited d-wave superconductor, give accurate estimates of the thermal scales associated with such systems and map out the pseudogap regime. Our work shows that while the Pauli limited superconductors are known to exhibit exotic modulated superconducting phase at large imbalance of fermion populations; in the regime of weak imbalance an intriguing phase of competing orders is realized. We have established that rather than the superconducting pairing field, it is the average magnetization of the system that quantifies this quantum phase transition. Given that the existing Pauli limited superconductors possess unconventional pairing state symmetry of the superconducting order, our work promises to open up new avenues in the experimental research of these materials. We have also demonstrated an alternate scenario wherein the quantum breached pair phase is a natural outcome for a d-wave superconductor with unequal effective masses of the fermion species.

Complex interplay of magnetic interactions in 5f -electron systems: The case of U2Ni2Sn

Recent experiments on a single crystal of ${\mathrm{U}}_{2}{\mathrm{Ni}}_{2}\mathrm{Sn}$ established a strong uniaxial magnetic anisotropy and an unusual magnetic structure that is antiferromagnetic both inside the U layers and between the layers. We apply fully relativistic first-principles calculations to investigate various magnetic configurations of the system. The calculations confirmed both the character of the magnetic anisotropy and the type of the ground-state magnetic structure. The study of the electron density of states shows that the lowest energy of the ground-state structure is related to the doubling of the magnetic unit cell and corresponding reduction of the Brillouin zone, leading to the formation of the energy gaps in the electronic structure. The mapping of the energies of the magnetic structures on the Heisenberg Hamiltonian of interacting atomic moments leads to a surprising result that only one of the interatomic exchange interactions is antiferromagnetic. We explain how this one antiferromagnetic interaction competing with several ferromagnetic interactions leads to the simultaneous presence of two types of antiferromagnetic behavior. We provide a simple mean-field estimate of the N\'eel temperature and conclude that short-range magnetic order, neglected on the mean-field level, may play an important role at temperatures around the critical temperature. We demonstrate the existence of self-consistent noncollinear magnetic states that limits the accuracy of treating ${\mathrm{U}}_{2}{\mathrm{Ni}}_{2}\mathrm{Sn}$ as a pure Ising magnet. We apply $\mathrm{GGA}+U$ method to examine the influence of the Hubbard parameter $U$ on the magnetic moments and energies of the magnetic configurations. An estimation of the influence of the contraction of the lattice on the magnetic properties is reported.

Strain-induced superconductor-insulator transition on a Lieb lattice

We report the numerical investigation of strain induced superconductor-insulator quantum phase transition on a Lieb lattice. Based on a non perturbative Monte Carlo technique, we show that in two dimensions an s-wave superconductor undergoes transition to a highly correlated bosonic insulator under the influence of strain, applied as staggered hopping amplitudes. We further demonstrate a strain induced BCS-BEC like crossover in the superconducting state, such that the superconductor-insulator transition takes place between a bosonic superconductor and a bosonic insulator. Our results suggest that it is the contribution of the dispersive bands towards the superconducting order, which dictates this crossover. To the best of our knowledge, this is the first work to report theoretical investigation of "disorder free" superconductor-insulator phase transition in systems with Lieb lattice structure. With the recent experimental realization of the Lieb lattice in ultracold atomic gases, photonic lattices as well as in solid state systems, we believe that the results presented in this paper would be of importance to initiate experimental investigation of such novel quantum phase transitions. We further discuss the fate of such systems at finite temperature, highlighting the effect of fluctuations on the superconducting pair formations, thermal scales and quasiparticle behavior. Our non perturbative numerical approach to the problem enables us to capture the thermal scales of the system accurately and provides us with mean field estimates of the ground state properties. The high temperature quasiparticle signatures discussed in this paper are expected to serve as benchmarks for experiments such as radio frequency and momentum resolved radio frequency spectroscopy measurements carried out on systems such as ultracold atomic gases.