Mean-field Interaction Model Research Articles

Exploring spatial segregation induced by competition avoidance as driving mechanism for emergent coexistence in microbial communities.

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models, and we consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

Effective Interaction between Homo- and Heteropolymer Block of Poly(n-butyl acrylate)-b-poly(methyl methacrylate-r-styrene) Diblock Copolymers.

We investigated the segregation behavior of a molten diblock copolymer, poly(n-butyl acrylate)-b-poly(methyl methacrylate-r-styrene) (PBA-b-P(MMA-r-S)), wherein styrene (S) is incorporated as a comonomer in the second block to modulate the effective interaction between homopolymer and a random copolymer block. The temperature dependence of the effective interaction parameter χeff between n-butyl acrylate (BA) and the average monomer of the MMA-r-S random block was evaluated from small-angle X-ray scattering (SAXS) analysis using the random phase approximation (RPA) approach. The calculated χeff, as a function of the styrene fraction in the random copolymer block, shows a good agreement with the mean-field binary interaction model. This consistency indicates that the effective interaction between component BA and the average monomer of the random copolymer block is smaller than the interactions between pure components (χBA,MMA,χBA,S). The present study suggests that the introduction of a random copolymer block to a block copolymer can effectively reduce the degree of incompatibility of the block copolymer system without altering the constituent species, which may serve as a viable methodology in designing novel thermoplastic elastomers based on triblock or multiblock copolymers.

Mean field interaction model accounting for the spatial distribution of inclusions in elastic-viscoplastic composites

A cluster interaction model has been proposed to account for the spatial distribution and morphology of particles when estimating the effective properties of elastic and thermoelastic composites (Molinari and El Mouden, 1996). In the present paper this approach is extended to elastic-viscoplastic composites. To this end the tangent linearization of the non-linear viscoplastic law and the concept of additive interaction equation are used. Although the extension is formulated for the non-linear case, first applications are considered for linear viscoelastic composites, a situation rich enough to evaluate the interest of the cluster interaction approach. Results of the model are compared to numerical homogenization for periodic unit cells with two cubic configurations.

Exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits

The exact solution of spherical mean-field plus multi-pair interaction model with two non-degenerate j-orbits, which is an extension of the widely used standard (two-body) pairing model, is derived based on the Bethe–Richardson–Gaudin approach. The Bethe–Richardson–Gaudin equations in determining eigenstates and the corresponding eigen-energies of the model are provided and exemplified with up to three-pair interactions. With a suitable parameterization of the overall multi-pair interaction strengths, the model with one adjustable parameter and valence nucleons confined in the $$1d_{5/2}$$ and $$0g_{7/2}$$ orbits is applied to fit binding energies of $$^{102{\text {--}}112}$$Sn. It is shown that the ground-state occupation probabilities of nucleon pairs calculated from this model and those from the standard pairing model are almost the same with perfect ground-state overlap of the two models. A noticeable feature of the multi-pair interactions is that the even–odd staggering of pairing interaction strength appearing in the standard pairing model due to the Pauli-blocking is suppressed. As the result, the pairing interaction strength of the model only depends on the number of valence nucleon pairs in the system.

Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues

Consider a queueing network with a large number [Formula: see text] nodes, in which each queue has a dedicated input stream, and, in addition, there is an extra input stream, balancing the network load by directing its arrivals to the shortest queue(s). A mean field interaction model is set up to study the performance of this network in terms of limiting results. One of our results shows that the stationary behavior of any of the queues is approximated by that of the [Formula: see text] queue with a modified arrival rate when the queue length is around zero.

Shape phase transition in the odd Sm nuclei: effective order parameter and odd–even effect**Supported by National Natural Science Foundation of China (11375005, 11005056, 11175078, 11405080)

Some binding energy related quantities serving as effective order parameters have been used to analyze the shape phase transition in the odd Sm nuclei. It is found that the signals of phase transition in the odd Sm nuclei are greatly enhanced in contrast to the even Sm nuclei. A further analysis shows that the transitional behaviors related to pairing in the Sm nuclei can be well described by the mean field plus pairing interaction model, with a monotonic decrease in the pairing strength G.

Investigation of the critical behaviour and magnetocaloric effect in γ-Fe49Ni29Cr22 disordered austenitic stainless steel alloy by using the field dependence of magnetic entropy change

We have reported here the critical behaviour and magnetocaloric effect (MCE) around the ferromagnetic (FM) → paramagnetic (PM) phase transition temperature (Tc) in a γ-Fe49Ni29Cr22 disordered austenitic stainless steel alloy system through detailed ac and dc magnetization study. The value of critical exponents have been estimated using the recorded M−H isotherms SQUID data using different techniques such as modified Arrott plots, Kouvel–Fisher plots, and critical isotherm analysis. The critical exponents values of γ-Fe49Ni29Cr22 alloy are found to be β = 0.440 (7), γ = 1.340 (16) and δ = 3.336 (5) with Tc = (124.82 ± 0.01) K. From the detailed DC magnetization study, the observed non-hysteretic M-T data in FCC and FCW mode, positive slope in the entire range of the Arrott plots near TC (Banerjee criterion), it confirms a second order FM → PM phase transition at TC. Though the nature of this transition is found to be of second order, the estimated critical exponent values β, γ, and δ are in between the theoretically predicted values for 3d Heisenberg and mean-field spin interaction models. However, it is important that these critical exponents obeyed the single scaling relations [M(H,ε)=|ε|βf±(H,|ε|−(β+γ))] indicating renormalization of interactions around the Curie temperature (TC). Temperature variation in effective critical exponents (βeff and γeff) resemble with those for various disordered ferromagnets as found in our γ-Fe49Ni29Cr22 alloy system. We have also estimated the normal MCE with maximum entropy change of 1.8 J/kg-K at 125.5 K under an external magnetic field change of 5 T in the austenite phase of the alloy.

Second order magnetic phase transition and scaling analysis in iron doped manganite La0.7Ca0.3Mn1−xFexO3 compounds

We investigated magnetic properties of La0.7Ca0.3Mn1−xFexO3 (x=0.09 and 0.11) compounds in terms of isothermal magnetization analysis and scaling behavior with various critical exponents. From the Landau theory of magnetic phase transition, we found that the paramagnetic to ferromagnetic phase transition in La0.7Ca0.3Mn1−xFexO3 (x=0.09 and 0.11) compounds is the type of second order magnetic transition (SOMT), which contrary to the first order magnetic transition (FOMT) for low Fe-doped compounds (x<0.09) in previous reports. When we investigate the critical behavior of the compounds near T=Tc by the modified Arrott plot, Kouvel–Fisher plots, and critical isothermal analysis, the estimated critical exponents β, γ, and δ are in between the theoretically predicted values for three-dimensional Heisenberg and mean-field interaction models. It is noteworthy that the scaling relations are obeyed in terms of renormalization magnetization m=ε−βM(H,ε) and renormalized field h=|ε|β+γH. Temperature-dependent effective exponents βeff and γeff correspond to the ones of disordered ferromagnets. It is shown that the magnetic state of the compounds is not fully described by the conventional localized-spin interaction model because the ferromagnetic interaction has itinerant character by increasing Fe-doping concentration.

Critical behavior and spontaneous magnetization estimation in La0.5Sr0.5MnO3 compound

We report the critical behavior in La0.5Sr0.5MnO3 perovskite oxide manganite using methods including modified Arrott plot, Kouvel–Fisher plot, and critical isotherm analysis. By means of the above techniques around the ferromagnetic–paramagnetic (FM–PM) transition, the magnetic data analyzed shows the sample attending the second-order magnetic phase transition with the critical parameters β = 0.553±0.020 with TC=352.02±0.63K (from the spontaneous magnetization MS(T) below TC) and γ =1.169±0.058 with TC=352.49±0.85K (from the inverse initial susceptibility χ0−1(T) above TC). The exponent δ =3,216 independently obtained from the critical magnetization isotherm satisfies the Widom scaling relationδ=1+β/γ. Moreover, the critical exponents are in the theoretically expected values for mean-field interaction model rather than the other universal theory and also follow the single scaling equation of M(H,ε)ε−β=f±(H/εβ+γ). Furthermore, to estimate the spontaneous magnetization of La0.5Sr0.5MnO3 perovskite, we used the magnetic entropy change (−ΔSM), obtained from isothermal magnetization. The results of this approach are compared to results obtained from classical analysis using Arrott curves.

Effect of Zn doping on the magneto-caloric effect and critical constants of Mott insulator MnV2O4

X-ray absorption near edge spectra (XANES) and magnetization of Zn doped MnV2O4 have been measured and from the magnetic measurement the critical exponents and magnetocaloric effect have been estimated. The XANES study indicates that Zn doping does not change the valence states in Mn and V. It has been shown that the obtained values of critical exponents β, γ and δ do not belong to universal class and the values are in between the 3D Heisenberg model and the mean field interaction model. The magnetization data follow the scaling equation and collapse into two branches indicating that the calculated critical exponents and critical temperature are unambiguous and intrinsic to the system. All the samples show large magneto-caloric effect. The second peak in magneto-caloric curve of Mn0.95Zn0.05V2O4 is due to the strong coupling between orbital and spin degrees of freedom. But 10% Zn doping reduces the residual spins on the V-V pairs resulting the decrease of coupling between orbital and spin degrees of freedom.

Tuned Critical Avalanche Scaling in Bulk Metallic Glasses

Ingots of the bulk metallic glass (BMG), Zr64.13Cu15.75Ni10.12Al10 in atomic percent (at. %), are compressed at slow strain rates. The deformation behavior is characterized by discrete, jerky stress-drop bursts (serrations). Here we present a quantitative theory for the serration behavior of BMGs, which is a critical issue for the understanding of the deformation characteristics of BMGs. The mean-field interaction model predicts the scaling behavior of the distribution, D(S), of avalanche sizes, S, in the experiments. D(S) follows a power law multiplied by an exponentially-decaying scaling function. The size of the largest observed avalanche depends on experimental tuning-parameters, such as either imposed strain rate or stress. Similar to crystalline materials, the plasticity of BMGs reflects tuned criticality showing remarkable quantitative agreement with the slip statistics of slowly-compressed nanocrystals. The results imply that material-evaluation methods based on slip statistics apply to both crystalline and BMG materials.

On incentivizing upload capacity in P2P-VoD systems: Design, analysis and evaluation

Free riding has long been a serious problem in peer-to-peer (P2P) systems due to the selfish behavior of individual users. To conquer this problem, a key design issue of the P2P systems is to appropriately incentivize users to contribute resources. In P2P Video-on-Demand (VoD) applications, content providers need to incentivize the peers to dedicate bandwidth and upload data to one other so as to alleviate the upload workload of their content servers. In this paper, we design a simple yet practical incentive mechanism that rewards each peer based on its dedicated upload bandwidth. We use a mean field interaction model to characterize the distribution of number of peers in different video segments, based on which we characterize the content providers’ uploading cost as a function of the peers’ contribution. By using a game theoretic framework, we analyze the interaction between a content provider’s rewarding strategy and the peers’ contributing behaviors and derive a unique Stackelberg equilibrium. We further analyze the system efficiency in terms of the price of anarchy and study the long term behavior of the system under a repeated game setting. Via extensive simulations, we validate the stability and efficiency of our incentive scheme.

The stationary behaviour of fluid limits of reversible processes is concentrated on stationary points

Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called “mean field limit”, or “hydrodynamic limit”). A common practice, often called the “fixed point approximation” consists in approximating the stationary behaviour of the stochastic process by the stationary points of the fluid limit. It is known that this may be incorrect in general, as the stationary behaviour of the fluid limit may not be described by its stationary points. We show however that, if the stochastic process is reversible, the fixed point approximation is indeed valid. More precisely, we assume that the stochastic process converges to the fluid limit in distribution (hence in probability) at every fixed point in time. This assumption is very weak and holds for a large family of processes, among which many mean field and other interaction models. We show that the reversibility of the stochastic process implies that any limit point of its stationary distribution is concentrated on stationary points of the fluid limit. If the fluid limit has a unique stationary point, it is an approximation of the stationary distribution of the stochastic process.

Influence of cobalt on the structural, magnetic and magnetocaloric properties of La0.67Ca0.33MnO3

The critical properties and magnetocaloric effect of perovskite manganite La0.67Ca0.33Mn1−xCoxO3 (x=0.03, 0.1 and 0.15) are investigated. Structural study using Reitveld refinement of X-ray diffraction pattern indicates an orthorhombic structure with Pnma space group for all compositions. The Curie temperature and magnetic moment decrease with increase of cobalt doping concentration and the samples exhibit characteristics of spin/cluster glass state which is evident from magnetization (zero field cooled and field cooled) vs temperature curves. The magnetic data is analyzed in the critical region using the modified Arrott plot method. The obtained values of critical exponents are in agreement with the values predicted by mean field interaction model. LCMCo0.03 compound shows a large magnetic entropy change (ΔSM) of 4J/kgK at a magnetic field of 50kOe. The relative cooling power (RCP) is found to be about ∼184J/kg for LCMCo0.03 and ∼114J/kg in the case of LCMCo0.1 in a magnetic field change of 50kOe. The field dependance of ΔSM and RCP are showing a power dependence at their respective transition temperatures. An increase in resistance and a diminution of magnetic entropy change were observed as a consequence of Co doping. An enhanced magnetoresistance up to 87% and considerable magnetic entropy change were observed for these cobalt doped compounds.

Fluid limit analysis of FIFO and RR caching for independent reference models

We study the fluid limit analysis of random replacement (RR) caching for the independent reference model. Applying the limit theorem for the mean field interaction model, we derive the fluid limit of fault probability in the transient state as well as in the steady state. Since the stationary fault probability for the RR cache is identical to that for the first-in first-out (FIFO) cache, our results on the stationary fault probability are available for the FIFO caching. We see that the fluid limit of stationary fault probability that we obtain is coincident with the existing heuristic approximation of stationary fault probability. That is, our fluid limit analysis gives a rigorous theoretical foundation to the heuristic approximation.

Sweep rate and temperature dependence of the coercivity in [formula omitted], x=0, 2 and 4, bulk amorphous ferromagnets

Bulk amorphous ferromagnet alloys of composition Nd60−xFe30Al10Dyx, x=0, 2 and 4, have been prepared. At room temperature all the alloys exhibit hard magnetic properties, and the intrinsic coercivity (μ0Hci) is seen to increase with increasing dysprosium content i.e. from 0.337T, x=0, to 0.537T, x=4. Measurements of the intrinsic coercivity as a function of magnetic field sweep rate are made, and from these measurements the fluctuation field, Hf, for each alloy, is determined. Measurements of the intrinsic coercivity were made for each alloy from 300K to 10K, and in all cases with decreasing temperature the intrinsic coercivity increases, reaching a maximum around 40–70K, before decreasing rapidly. For each alloy, in the temperature region above its peak to 300K, the temperature dependence of the intrinsic coercivity is well explained by the strong pinning model of domain walls of Gaunt (1983) [11]. Further insight into the magnetic properties of these alloys is gained from examining the behaviour of the demagnetization curve in the first quadrant, using a mean field interaction model. This enables determination of the behaviour of the saturation magnetization, anisotropy field and anisotropy constant for each alloy as a function of increasing dysprosium content.

Observation of magnetic cluster phase above Curie temperature in Fe2CrAl Heusler alloy

We present a detailed magnetic critical behavior study of Fe2CrAl Heusler alloy, for the first time, with rigorous analysis of high precision magnetization data obtained over the critical temperature region. Our studies confirm that B2 type site-disordered in Fe2CrAl alloy exhibits long-range ferromagnetic order below a well defined Curie temperature (T=208K). Though the nature of this transition is found to be of second order, the estimated critical exponents β=0.42, γ=1.356 and δ=4.25, are in between the theoretically predicted values for three-dimensional Heisenberg and mean-field interaction models. However, it is noteworthy that the scaling relations are obeyed indicating renormalization of interactions around the Curie temperature (TC), where magnetization data collapse into two separate branches, above and below TC. This conclusively shows that calculated critical exponents as well as critical temperature are unambiguous and intrinsic to the system. However, magnetization vs temperature data shows another magnetic transition (at T=313K) above the Curie temperature. It is shown that the short range magnetic correlation exist even beyond TC with cluster moment ∼102μB. This is attributed to a site disorder which results in formation of Cr clusters with short range ferromagnetic order.

A quadrature based method of moments for nonlinear Fokker–Planck equations

Fokker–Planck equations which are nonlinear with respect to their probability densities andoccur in many nonequilibrium systems relevant to mean field interaction models, plasmas,fermions and bosons can be challenging to solve numerically. To address some underlyingchallenges, we propose the application of the direct quadrature based method of moments(DQMOM) for efficient and accurate determination of transient (and stationary) solutionsof nonlinear Fokker–Planck equations (NLFPEs). In DQMOM, probability density (orother distribution) functions are represented using a finite collection of Dirac deltafunctions, characterized by quadrature weights and locations (or abscissas) that aredetermined based on constraints due to evolution of generalized moments. Three particularexamples of nonlinear Fokker–Planck equations considered in this paper includedescriptions of: (i) the Shimizu–Yamada model, (ii) the Desai–Zwanzig model (both ofwhich have been developed as models of muscular contraction) and (iii) fermions andbosons. Results based on DQMOM, for the transient and stationary solutions of thenonlinear Fokker–Planck equations, have been found to be in good agreementwith other available analytical and numerical approaches. It is also shown thatapproximate reconstruction of the underlying probability density function from momentsobtained from DQMOM can be satisfactorily achieved using a maximum entropymethod.

Application of the Stoner–Wohlfarth model with interaction for the determination of the saturation magnetisation, anisotropy field, and mean field interaction in bulk amorphous ferromagnets

Magnetic hysteresis curves of bulk amorphous ferromagnet alloys of composition Nd 60Fe 30Al 10, Nd 60Fe 20Co 10Al 10 and Pr 58Fe 24Al 18 have been measured in applied magnetic fields up to 9 T at temperatures in the range 10–350 K. The behaviour of the demagnetisation curve in the first quadrant is interpreted using a mean field interaction model as proposed by Callen et al. [Phys. Rev. B 16 (1977) 263], which extends the Stoner–Wohlfarth model [Philos. Trans. Roy. Soc. A 240 (1948) 599] for a random distribution of non-interacting uniaxial grains. Application of the mean field interaction model enables the determination of the saturation magnetisation M s, anisotropy field H a, and interaction parameter d, and from these other magnetic parameters, such as the anisotropy constant, K, are deduced. For the three alloys, the temperature dependent behaviour of M s, H a, d and K over the range 20–350 K are found to be qualitatively similar, though there are quantitative differences. In all cases M s increases with decreasing temperature, both H a and K increase with decreasing temperature, reaching a peak in the range 75–120 K, and then decreasing, and d decreases approximately linearly as the temperature decreases. The physical mechanisms responsible for coercivity in these materials are discussed in the context of random anisotropy and a strong pinning model of domain walls.

New exact solutions of the standard pairing model for well-deformed nuclei

A new step-by-step diagonalization procedure for evaluating exact solutions of the nuclear deformed mean-field plus pairing interaction model is proposed via a simple Bethe ansatz in each step from which the eigenvalues and corresponding eigenstates can be obtained progressively. This new approach draws upon an observation that the original one- plus two-body problem in a $k$-particle Hilbert subspace can be mapped onto a one-body grand hard-core boson picture that can be solved step by step with a simple Bethe ansatz known from earlier work. Based on this new procedure, it is further shown that the extended pairing model for deformed nuclei [Feng Pan, V. G. Gueorguiev, and J. P. Draayer, Phys. Rev. Lett. 92, 112503 (2004)] is similar to the standard pairing model with the first step approximation, in which only the lowest energy eigenstate of the standard pure pairing interaction part is taken into consideration. Our analysis shows that the standard pairing model with the first step approximation displays similar pair structures of the first few exact low-lying states of the model, which, therefore, provides a link between the two models.