Dilute Model Research Articles

In vitro pharmacodynamics of omadacycline against Escherichia coli and Acinetobacter baumannii.

The pharmacodynamics of omadacycline have been extensively studied against Gram-positive pathogens but less information is available for Gram-negative pathogens. We describe the pre-clinical pharmacodynamics of omadacycline against Escherichia coli and Acinetobacter baumannii. An in vitro dilutional pharmacokinetic model was used. Exposure experiments with fAUC/MIC ratios ranging from 0 to 1200 were performed using five strains of E. coli and five strains of A. baumannii. Reduction in bacterial load and changes in population profiles were measured. The fAUC/MIC targets against E. coli for 24 h static and -1 log reduction in load were 25.3 ± 17.2 and 42.7 ± 32.5, respectively. For A. baumannii the fAUC/MIC for 24 h static effect was 108.1 ± 38.6. Changes in population profiles were observed for E. coli at fAUC/MIC ratios of ≤200 and for A. baumannii up to 1200. MICs were increased 2-32 fold. fAUC/MIC targets for A. baumannii are greater than for E.coli and changes in population profiles more likely. E. coli fAUC/MIC targets align with in vivo data and will be useful in determining omadacycline dosing for this pathogen.

The organic preservation effect of hemodilution

Background: Organ donation in countries with Buddhist cultures was developed primarily from living donor. Organs from the source for brain death with a low rate and the rate of organ transplantation eligible for transplantation account for 1.8 organs/ brain death donor. With the current multi-organ collection model, there are often hemodynamic abnormalities, which can cause arterial clotting, affecting the quality and function of the donor organ. This study aims to initially evaluate the multi-suberculosis method of blood dilution. Methods: The study was conducted on experimental 30 pigs with the model of multi-organ blood dilution with the following steps: (1) animal preparation: pre-anesthesia with Atropine 1/4 mg (01 tube), Valium 10 mg (01 tube), and Ketamine 100 mg; anesthesia with Pentothal at 60 mg/kg body weight. Use Arduan 4 mg muscle relaxants and monitor over hemodynamic and central temperature. (2) Cause brain death in experimental animals using compression damage. (3) Place the cannula (20F) into the femoral artery (Scarpa triangle). Place two infusion tubes through the carotid vein and the thigh (7F). (4) Drop blood flowing slowly through the femoral cannula about 30% volume, simultaneously by intravenous (IV) infusion (Ringer lactate). Blood loss from 50%-60% began to appear hemodynamic disorders. Infuse IV Ringer lactate at 4°C. Monitor pulse, blood pressure, and cen tral temperature. (5) Blood flows in a stream through the femoral artery, quickly transfused through two veins (with phases Hep arin and Kaleorid). Monitor temperature and hemodynamics until the animal stops heart. (6) Infuse fluids and organ preservative solutions continuously. Open the chest and abdomen, take the organs in blocks (heart-lung, liver-pancreas-intestine, kidney, etc.), and bring to the dissection table. Do pathological surgery to evaluate the quality of organs. Results: Initial results showed that the central temperature decreased from 37.8°C to 32°C, and heart rate and blood pressure were stable until 68% of the blood was withdrawn. Evaluation of donor organs: white color accounts for 29/30 (96.67%), and white-pink accounts for 1/30 (3.33%). The density of sure organs is 30/30 (100%). The results of pathological anatomy: 360 samples showed that 10/360 (2.7%) of the samples had microscopic lesions. Performing pancreatic, kidney, and lung transplant: having post-transplant function accounts for 100%. The post-transplant survival rate followed up to 72 hours was 93.3% (14/15), 100% (15/15), and 93.3% (14/15). Conclusions: Initial results show that this is an effective multi-organ washing method.

Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models

We present a mapping of correlated multi-impurity Anderson models to a cluster model coupled to a number of effective conduction bands capturing its essential low-energy physics. The major ingredient is the complex single-particle self energy matrix of the uncorrelated problem that encodes the influence to the host conduction band onto the dynamics of a set of correlated orbitals. While the real part of the self-energy matrix generates an effective hopping between the cluster orbitals, the imaginary part determines the coupling to the effective conduction bands in the mapped model. The rank of the imaginary part determines the number of independent screening channels of the problem, and allows the replacement of the phenomenological exhaustion criterion by a rigorous mathematical statement. This rank provides a distinction between multi-impurity models of first kind and of second kind. For the latter, there are insufficient screening channels available, so that a singlet ground state must be driven by the inter-cluster spin correlations. This classification provides a fundamental answer to the question of why ferromagnetic correlations between local moments are irrelevant for the spin compensated ground state in dilute impurity models, whereas they compete with the Kondo-scale in dense impurity arrays, without evoking a spin density wave. The low-temperature physics of three examples taken from the literature are deduced from the analytic structure of the mapped model, demonstrating the potential power of this approach. NRG calculations are presented for up to five site cluster. We investigate the appearance of frustration induced non-Fermi liquid fixed points in the trimer, and demonstrate the existence of several critical points of KT type at which ferromagnetic correlations suppress the screening of an additional effective spin-$1/2$ degree of freedom.

MonteCarlo Renormalization Group for Classical Lattice Models with Quenched Disorder.

We extend to quenched-disordered systems the variational scheme for real-space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the MonteCarlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two- and three-dimensional lattices.

Does the Organ-Based N Dilution Curve Improve the Predictions of N Status in Winter Wheat?

Accurately summarizing Nitrogen (N) content as a prelude to optimal N fertilizer application is complicated during the vegetative growth period of all the crop species studied. The critical nitrogen (N) concentration (Nc) dilution curve is a stable diagnostic indicator, which performs plant critical N concentration trends as crop grows. This study developed efficient technologies for different organ-based (plant dry matters (PDM), leaf DM (LDM), stem DM (SDM), and leaf area index (LAI)) estimation of Nc curves to enrich the practical applications of precision N management strategies. Four winter wheat cultivars were planted with 10 different N treatments in Jiangsu province of eastern China. Results showed the SDM-based curve had a better performance than the PDM-based curve in N nutrition index (NNI) estimation, accumulated N deficit (AND) calculation, and N requirement (NR) determination. The regression coefficients ‘a’ and ‘b’ varied among the four critical N dilution models: Nc = 3.61 × LDM–0.19, R2 = 0.77; Nc = 2.50 × SDM–0.44, R2 = 0.89; Nc = 4.16 × PDM–0.41, R2 = 0.87; and Nc = 3.82 × LAI–0.36, R2 = 0.81. In later growth periods, the SDM-based curve was found to be a feasible indicator for calculating NNI, AND, and NR, relative to curves based on the other indicators. Meanwhile, the lower LAI-based curve coefficient variation values stated that leaf-related indicators were also a good choice for developing the N curve with high efficiency as compared to other biomass-based approaches. The SDM-based curve was the more reliable predictor of relative yield because of its low relative root mean square error in most of the growth stages. The curves developed in this study will provide diverse choices of indicators for establishing an integrated procedure of diagnosing wheat N status, and improving the accuracy and efficiency of wheat N fertilizer management.

A Modified Critical Nitrogen Dilution Curve for Winter Wheat to Diagnose Nitrogen Status Under Different Nitrogen and Irrigation Rates.

The accuracy of nitrogen (N) diagnosis is essential to improve N use efficiency. The standard critical N concentration (standard Nc) dilution curves, an expression of the dynamics of N uptake and dry matter accumulation in plants, are widely used to diagnose the N status of crops. Several standard Nc dilution curves were proposed and validated for several crops, based on experiments involving different N fertilizer treatments. However, standard Nc dilution curves are affected by crop water status, e.g., resulting from differences in irrigation management. This paper aimed at developing a N diagnostic model under the coupling effect of irrigation and fertilizer managements. For this purpose, Nc dilution curves were developed under different irrigation rates. Additionally, plant water content (PWC), leaf water content (LWC), leaf area index (LAI), equivalent water thickness (EWT), and leaf area duration (LAD) were introduced into the model, to construct a modified Nc (mNc) dilution curve. The mNc dilution curves were designed using the principle of hierarchical linear model (HLM), introducing aboveground dry biomass (AGB) as the first layer of information, whereas the second layer of information included the different agronomic variables (PWC, LWC, LAI, EWT, and LAD). The results showed that parameters “a” and “b” of the standard Nc dilution curves ranged from 5.17 to 6.52 and −0.69 to −0.38 respectively. Parameter “a” was easily affected by different management conditions. The performance of standard Nc dilution models obtained by the cross-validation method was worse than that of mNc dilution models. The Nc dilution curve based on 4 years of data was described by the negative power equation Nc = 5.05 × AGB–0.47, with R2 and nRMSE of 0.63 and 0.21, respectively. The mNc dilution curve considers different treatments and was represented by the equation mNc = a×AGB−b, where a = 2.09 × PWC + 3.24, b = −0.02 × LAI + 0.51, with R2 and nRMSE of 0.79 and 0.13, respectively. For winter wheat, C3 crop, there would be a few problems in using standard Nc dilution methods to guide field management, however, this study provides a reliable method for constructing mNc dilution curves under different water and N fertilizer management. Due to the significant differences in hereditary, CO2 fixation efficiency and N metabolism pathways for C3 and C4 crops, the construction of mNc dilution curve suitable for different N response mechanisms will be conducive to the sustainable N management in crop plants.

Balance between strength and ductility of dilute Fe2B by high-throughput first-principles calculations

In boride ceramics, Fe2B typically functions as the primary wear-resistant phase owing to its high hardness, but the elastic and ductile-brittle properties of Fe2B greatly influence its wear resistance and industrial application. First-principles calculations using density functional theory (DFT) were utilized to systematically investigate the effects of Al, Si, and transition elements (including 3d, 4d, and 5d transition elements) on the mechanical properties and electronic structure of Fe31MB16 with a dilute solution model. The bulk modulus (B), shear modulus (G), and Young's modulus (E) were calculated through the stress-strain method. The Vickers hardness (HV) and fracture toughness (KIC) were calculated by semi-empirical models. The electronic structures and chemical bonding were analyzed using the charge density difference, electron localization function, and Mulliken bond population. Overall, Fe31YB16 had the largest moduli (B, G, and E) among all the Fe31MB16 compounds that were investigated, while Fe31CrB16 had the highest hardness. Compared with pure Fe2B, the ductility of Fe31MB16 improved to varying degrees according to the B/G and Poisson's ratio (σ) criteria, respectively. However, adding alloying elements in this concentration did not change the intrinsic brittleness of Fe2B. Moreover, the trends in the calculated KIC of Fe31MB16 (M = Cr, Mn, Mo, and W respectively) were consistent with those of experiments. The electronic structure and Mulliken population analysis showed that the differences in the mechanical properties of the Fe31MB16 compounds were primarily determined by the M-B and B–B bonds because the alloying element M replaced Fe. These results provide guidance for improving the ductility of Fe2B and its industrial application.

Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

Ferromagnetic and spin-glass-like transitions in nonequilibrium spin models in contact with two thermal baths with different temperatures are investigated. The models comprise the Sherrington-Kirkpatrick model and the dilute spin glass model which are the Ising models on complete and random graphs, respectively, with edges corresponding, with certain probability, to positive and negative exchange integrals. The spin flip rates are combinations of two Glauber rates at the two temperatures, and by varying the coefficients of this combination probabilities of contact of the model with each thermal bath and thus the level of thermal noise in the model are changed. Particular attention is devoted to the majority vote model in which one of the two above-mentioned temperatures is zero and the other one tends to infinity. Only in rare cases such nonequilibrium models can be mapped onto equilibrium ones at certain effective temperature. Nevertheless, Monte Carlo simulations show that transitions from the paramagnetic to the ferromagnetic and spin-glass-like phases occur in all cases under study as the level of thermal noise is varied, and the phase diagrams resemble qualitatively those for the corresponding equilibrium models obtained with varying temperature. Theoretical investigation of the model on complete and random graphs is performed using the TAP equations as well as mean-field and pair approximations, respectively. In all cases theoretical calculations yield reasonably correct predictions concerning location of the phase border between the paramagnetic and ferromagnetic phases. In the case of the spin-glass-like transition only qualitative agreement between theoretical and numerical results is achieved using the TAP equations, and the mean-field and pair approximations are not suitable for the study of this transition. The obtained results can be interesting for modeling opinion formation by means of the majority-vote and related models and suggest that in the presence of negative interactions between agents, apart from the ferromagnetic phase corresponding to consensus formation, spin-glass-like phase can occur in the society characterized by local rather than long-range ordering.Graphical abstract

A minimum dilution scenario for supernovae and consequences for extremely metal-poor stars

ABSTRACT To date no metal-free stars have been identified by direct observations. The most common method of constraining their properties is searching the spectra of the most metal-poor stars for the chemical elements created in the first stars and their supernova (SN). In this approach, modelled SN yields are compared to the observed abundance patterns in extremely metal-poor stars. The method typically only uses the abundance ratios, i.e. the yields are diluted to the observed level. Following the usual assumption of spherical symmetry we compute a simple lower limit of the mass an SN can mix with and find that it is consistent with all published simulations of early chemical enrichment in the interstellar medium. For three different cases, we demonstrate that this dilution limit can change the conclusions from the abundance fitting. There is a large discrepancy between the dilution found in simulations of SN explosions in minihaloes and the dilution assumed in many abundance fits. Limiting the dilution can significantly alter the likelihood of which supernovae are possible progenitors of observed CEMP-no stars. In particular, some of the faint, very low yield SNe, which have been suggested as models for the abundance pattern of SMSS0313−6708, cannot explain the measured metal abundances, as their predicted metal yields are too small by two orders of magnitude. Altogether, the new dilution model presented here emphasizes the need to better understand the mixing and dilution behaviour of aspherical SNe.

A Humidity Compensation Method for On-line Odor Detection System in the Vehicle

The paper introduce a humidity compensation method for the on-line detection system of odor in the vehicle. The method is based on theoretical model of dilution and humidity control, and the gas concentration of the sample to be measured under different dilution multiples is measured, and then the original gas concentration is calculated by linear fitting with the gas concentration data under the condition of low humidity, so that the humidity compensation of the measured sample gas can be carried out. After the humidity compensation method, the relative error of VOCs concentration of the sample A is about 15%, which is close to its real value, which significantly improves the accuracy of sample’s VOCs concentration measurement.

Developmental exposure to methylmercury and resultant muscle mercury accumulation and adult motor deficits in mice

Developmental methylmercury (MeHg) exposure can have lasting consequences on neural development and motor function across the lifespan. Recent evidence for MeHg targeting of myogenic pathways has drawn attention to the possibility that developing skeletal muscle plays a role in the motor deficits stemming from early life MeHg exposure. In this study we examined a potential role for muscle in influencing MeHg developmental toxicity in offspring of female mice exposed to MeHg via drinking water. Dams had access to 0, 0.5 or 5.0 ppm MeHg chloride in drinking water from two weeks prior to mating through weaning. Blood, brain and muscle tissue was harvested from dams at weaning and pups at postnatal days (PND) 6, 21 and 60 for analysis of total Hg. Muscle tissue sections were examined with histological stains. Behavioral testing of offspring was conducted at PND 60 and included locomotor activity, inverted screen, grip strength and rotarod tests to assess motor function. Total Hg (tHg) levels in dam muscles at weaning were 1.7–3-fold higher than Hg levels in blood or brain. In PND6 male and female pups, muscle and brain tHg levels were 2 to 4-fold higher than blood tHg. Brain tHg levels decreased more rapidly than muscle tHg levels between PND 6 and 21. Premised on modeling of growth dilution, brain tissue demonstrated an elimination of tHg while muscle tissue exhibited a net uptake of tHg between PND 6 and 21. Despite overall elevated Hg levels in developing muscle, no gross morphological or cytological phenotypes were observed in muscle at PND 60. At the higher MeHg dose, grip strength was reduced in both females and males at PND 60, whereas only male specific deficits were observed in locomotor activity and inverted screen tests with marginally significant deficits on rotarod. These findings highlight a potential role for developing skeletal muscle in mediating the neuromuscular insult of early life MeHg exposure.

Local distributions of the 1D dilute Ising model

The local distributions of the one-dimensional dilute annealed Ising model with charged impurities are studied. Explicit expressions are obtained for the pair distribution functions and correlation lengths, and their low-temperature asymptotic behavior is explored depending on the concentration of impurities. For a more detailed consideration of the ordering processes, we study local distributions. Based on the Markov property of the dilute Ising chain, we obtain an explicit expression for the probability of any finite sequence and find a geometric probability distribution for the lengths of sequences consisting of repeating blocks. An analysis of distributions shows that the critical behavior of the spin correlation length is defined by ferromagnetic or antiferromagnetic sequences, while the critical behavior of the impurity correlation length is defined by the sequences of impurities or by the charge-ordered sequences. For the dilute Ising chain, there are no other repeating sequences whose mean length diverges at zero temperature. While both the spin correlation and the impurity correlation lengths can diverge only at zero temperature, the ordering processes result in a maximum of the specific heat at finite temperature defined by the maximum rate of change of the impurity-spin pairs concentration. A simple approximate equation is found for this temperature. We show that the non-ordered dilute Ising chains correspond to the regular Markov chains, while various orderings generate the irregular Markov chains of different types.

Family business succession roadblock model based on fuzzy linguistic preference relations

This study investigates how to reduce future barriers to succession and other problems related to family governance by constructing a succession roadblock map. The study explores succession roadblocks in family businesses and provides a succession planning tool that is based on empirical data from 42 director members of the Taiwan Institute of Directors. An analytical hierarchy of family business succession and succession roadblocks are divided into three categories: family roadblocks, institutional roadblocks, and market roadblocks. Next, this study calculates the weights and rankings of the severity of such roadblocks and the likelihood of their occurrence. Specifically, this study constructs a succession roadblock matrix that categorizes succession roadblocks into four categories: the ownership dilution model, sell or withdraw model, ownership management model, and dispersive ownership model. This study also establishes a roadblock strategy matrix for successor positioning and proposes suggestions for practical strategic planning to overcome the challenges of succession roadblocks.

Development of Lake Vesij\xe4rvi through four decades of remediation efforts

The diversion of sewage inputs in the mid-1970s led to an order of magnitude reduction in nutrient loading to Lake Vesijärvi, southern Finland. After the diversion, nutrient concentrations declined, consistent with a simple dilution model, and by the mid-1990s the chlorophyll concentration was reduced by 80%. The favourable development was supported by a 5-year mass removal of planktivorous and benthivorous fish and the stocking of predatory pikeperch (Sander lucioperca (L.)), although the exact mechanisms behind their effects remain obscure. Starting in 2010, oxygen-rich water from the top of the water column was pumped to the deepest parts of the lake, resulting in high deepwater oxygen concentration in winter. In summer, hypoxic or even anoxic conditions could not be avoided, but the duration of the anoxic period was markedly shortened. Because nitrate was never depleted, leaching of total nitrogen from the sediment was reduced and the same was also true for total phosphorus, but only in winter. The oxygenation stabilized deepwater nutrient concentrations to a low level, but this was not reflected in the epilimnetic total nutrient concentration or in a further decrease in the chlorophyll concentration.

Screening the hurdles to sea disposal of desalination brine around the Mediterranean

As desalination develops, the impacts of brine ocean disposal rise increasing concerns. Here we present a screening of the hurdles to brine disposal through pressurized submerged outfalls in the broader Mediterranean region. Using first-tier dilution models, we analyze how different environmental quality standards reflect in terms of initial outfall velocity. We show that achieving moderate dilution is usually not problematic, while higher environmental quality standards would often require excessively high initial velocities. Although this may not be so overwhelming a problem as to undermine the feasibility of brine discharge, it indicates possible hurdles to arise in the permitting of a project.We also show that increasing water recovery (i.e. having more concentrated brine) reduces jet extents, hence allows disposal in shallower waters, with smaller pipelines, causing an appreciable reduction of costs, while also slightly reducing pumping energy demand (which is rather small anyway in comparison with the overall energy demand of the desalination process). This makes recovery of water from the brine a potentially interesting management option, to be appraised against the costs of increasing recovery, and the difficulties arising from the higher dilution required at the outfall.

Laser Additive Manufacturing- Direct Energy Deposition of Ti-15Mo Biomedical Alloy: Artificial Neural Network Based Modeling of Track Dilution

Direct energy deposition is one of the most popular laser additive manufacturing processes. However, the generation of geometry (or dilution and the resulting porosity) of the deposited tracks is not well understood as it is largely dependent on the laser process settings. In this work, the track dilution generated in single track deposition of Ti-15Mo alloy using the laser additive manufacturing – direct energy deposition (LAM-DED) process is accurately modeled and predicted, using the Matlab software based artificial neural network (ANN). Targeting a mean square error of zero, a 3–7-1 feed-forward, back-propagation, NN architecture with Levenberg-Marquardt training algorithm is developed. The percentage prediction error is calculated to validate the developed ANN model and is found to range between −0.981 and 0.584 establishing the goodness of the fitted model and the high prediction accuracy of track dilution. Further, regression analysis is also conducted for theoretical validation of the experimental track dilution. The correlation coefficient value obtained for 27 data is 0.982 which establishes high confidence in the fitted data. This study helps in accurate software based prediction of track dilution at different LAM-DED process parameter settings for possible fabrication of superior quality (low porosity) Ti-15Mo bio-implants.

Critical Behavior of a 2D Spin-Pseudospin Model in a Strong Exchange Limit

We study the 2D static spin-pseudospin model equivalent to the dilute frustrated antiferromagnetic Ising model with charge impurities. We present the results of classical Monte Carlo simulation on a square lattice with periodic boundary conditions in a strong exchange limit. In the framework of the finite-size scaling theory we obtained the static critical exponents for the specific heat $\alpha$ and the correlation length $\nu$ for a wide range of the local density-density interaction parameter $\Delta$ and charge density $n$. It was shown that the system exhibits non-universal critical behavior depending on these parameters.

Assessing the Eutrophic Susceptibility of New Zealand Estuaries

We developed a method to predict the susceptibility of New Zealand estuaries to eutrophication. This method predicts macroalgae and phytoplankton responses to potential nutrient concentrations and flushing times, obtained nationally from simple dilution models, a GIS land-use model and physical estuary properties. Macroalgal response was based on an empirically derived relationship between potential nitrogen concentrations and an established macroalgal index (EQR) and phytoplankton response using an analytical growth model. Intertidal area was used to determine which primary producer was likely to lead to eutrophic conditions within estuaries. We calculated the eutrophication susceptibility of 399 New Zealand estuaries and assigned them to susceptibility bands A (lowest expected impact) to D (highest expected impact). Twenty-seven percent of New Zealand estuaries have high or very high eutrophication susceptibilities (band C or D), mostly (63% of band C and D) due to macroalgae. The physical properties of estuaries strongly influence susceptibility to macroalgae or phytoplankton blooms, and estuaries with similar physical properties cluster spatially around New Zealand’s coasts. As a result, regional patterns in susceptibility are apparent due to a combination of estuary types and land use patterns. The few areas in New Zealand with consistently low estuary eutrophication susceptibilities are either undeveloped or have estuaries with short flushing times, low intertidal area and/or minimal tidal influx. Estuaries with conditions favourable for macroalgae are most at risk. Our approach provides estuary-integrated susceptibility scores likely to be of use as a regional or national screening tool to prioritise more in-depth estuary assessments, to evaluate likely responses to altered nutrient loading regimes and assist in developing management strategies for estuaries.

Compressible liquid/gas inclusion with high initial pressure in plane deformation: Modified boundary conditions and related analytical solutions

In the analysis of the elastic behavior of a composite system composed of a solid matrix and a number of compressible liquid/gas inclusions, it is customary to incorporate the change in the magnitude of an inclusion's internal pressure (induced by the change in its volume) during deformation. However, when an inclusion has a relatively high initial pressure, the change in the direction of the pressure during deformation may also be significant, particularly in establishing an accurate boundary condition on the inclusion-matrix interface. This can be attributed to the fact that, during deformation, the change in the direction of the normal to the inclusion's boundary is of the same order as the change in its volume. Accordingly, in this paper, we propose two modified boundary conditions for a general compressible liquid/gas inclusion surrounded by a solid matrix subjected to plane deformation. Specifically, we incorporate changes in both the magnitude and direction of the inclusion's internal pressure during deformation. The corresponding boundary value problems are formulated using complex variable methods with explicit analytical solutions obtained in the particular case when the initial shape of the inclusion is circular and the surrounding matrix is infinite. Concise explicit formulae are also given for evaluating the effective moduli of the corresponding composite system based on the dilute model and the Mori-Tanaka method. Numerical results are presented to illustrate our solutions and to draw comparison with the classical solution in the case of an air bubble inclusion in a soft gel matrix. We find that when the inclusion has a relatively high initial pressure, the classical solution may indeed overestimate the external loading-induced stress concentration around the inclusion and underestimate the effective moduli of the corresponding composite system. In particular, it is shown that a porous material could be significantly strengthened in resisting shear deformation when filled with liquid/gas inclusions of a relatively high pressure even if surface tension effects are neglected: this phenomenon is not captured in classical models.

Parameterization of dilute Ising model for iron-containing lanthanum gallate and aluminate solid solutions based on first-principles calculations

Calculations of the cubic models of two solid solutions LaGa0.5Fe0.5O3 and LaAl0.5Fe0.5O3 have been performed within the hybrid density functional theory. Multiple configurations have been considered for the solid solutions resulting from a different distribution of Fe atoms over the p-metal (Ga or Al) positions accounting for different spin orientation for Fe atoms themselves. It was demonstrated that 27 structures for both LaGa0.5Fe0.5O3 and LaAl0.5Fe0.5O3 should be treated to account for all the possible configurations in case of cubic 2 × 2 × 2 supercell. Optimized geometry, energy, and electron properties were calculated for all the obtained configurations. Statistical weights and probabilities were estimated for each symmetry non-equivalent configuration of the solid solutions within the canonical ensemble. A new parameterization for the dilute Ising model has been proposed. In this model, we account for non-magnetic contributions, which are absent in the simple Ising model, using the lattice approach based on the concept of interchange energy. Two model parameters (the magnetic coupling constant and interchange energy) were fitted to the calculated total energies of all considered configurations of both solid solutions. The dilute Ising model confirmed the benefit of Fe-clustering in doped lanthanum gallate against aluminate. Different signs of the estimated interchange energy enable us to explain the reasons for such differences.