Critical Exponents Research Articles

An existence theory for superposition operators of mixed order subject to jumping nonlinearities

We consider a superposition operator of the form ∫[0,1](−Δ)sudμ(s), for a signed measure µ on the interval of fractional exponents [0,1] , joined to a nonlinearity whose term of homogeneity equal to one is ‘jumping’, i.e. it may present different coefficients in front of the negative and positive parts. The signed measure is supposed to possess a positive contribution coming from the higher exponents that overcomes its negative contribution (if any). The problem taken into account is also of ‘critical’ type, though in this case the critical exponent needs to be carefully selected in terms of the signed measure µ. Not only the operator and the nonlinearity considered here are very general, but our results are new even in special cases of interest and include known results as particular subcases. The possibility of considering operators ‘with the wrong sign’ is also a complete novelty in this setting.

Revolutionizing flexible Electronics: Integrating liquid metal DIW 3D printing by bimolecular interpenetrating network

Ultra-flexible liquid metal (LM) composites have significant potential in various applications, including soft robotics, wearable electronics, and human–machine interactions. This burgeoning field necessitates mass production at a critical scale alongside highly accurate and fully automated technology. In this study, a direct ink-writing (DIW) 3D all-printing strategy was developed, integrating cellulose nanofibrils (CNF), water-based polyurethane (WPU), and LM to fabricate high-performance LM-based electronic films, circuits, and diverse 2D or 3D structures. The stable ternary interface system was investigated, and bimolecular interpenetrating network system of CNF/WPU significantly enhanced the flexibility, reducing LM damage, mitigation, and leakage. Moreover, the systematic control of the DIW all-printing process facilitated high-resolution and excellent printability. The super-flexibility and precise electrical conductivity were demonstrated by investigating bending deformation and recyclable electrical signals. Electronics based on ultra-flexible LM, with a high LM content (78.0%), exhibited an accurate electrical response to bending deformation, extraordinary flexibility, and recyclable durability (up to 500 cycles). Notably, the all-printed system facilitates the complete automation, complex structuring, and precise moulding of various appliances. DIW 3D all-printing of LM has the potential to create complex conductive architectures for programmable and multi-material LM-based electronics, meeting high-precision, large-scale, and automated production requirements.

Predicting network congestion by extending betweenness centrality to interacting agents.

We present a simple model to predict network activity at the edge level by extending a known approximation method to compute betweenness centrality with a repulsive mechanism to prevent unphysical densities. By taking into account the strong interaction effects often observed in real phenomena, we aim to obtain an improved measure of edge usage during rush hours as traffic congestion patterns emerge in urban networks. In this approach, the network is iteratively populated by agents following dynamically evolving fastest paths who are progressively attracted towards uncongested parts of the network as the global traffic volume increases. Following the transition of the network state from empty to saturated, we study the emergence of congestion and the progressive disruption of global connectivity due to a relatively small fraction of crowded edges. We assess the predictive power of our model by comparing the speed distribution against a large experimental data set for the London area with remarkable results, which also translate into a qualitative similarity of the congestion maps. Also, percolation analysis confirms the quantitative agreement of the model with the real data for London. We perform simulations for seven other topologically different cities to obtain the Fisher critical exponent τ that shows no common functional dependence on the traffic level. The critical exponent γ, studied to assess the power-law decay of spatial correlation, is found to be inversely proportional to the number of vehicles for both real and simulated traffic. This simulation approach seems particularly fit to describe qualitative and quantitative properties of the network loading process, culminating in peak-hour congestion, by using only topological and geographical network features.

CMC/SWCNT biocomposites: A combined study on experiments, molecular simulations and continuum models

A comprehensive study is carried out including experimental, molecular dynamics (MD) simulations and continuum modelling of Carboxymethyl cellulose/Single walled carbon nanotube (CMC/SWCNT) biocomposites. The electrical, optical, and mechanical properties of CMC/SWCNT biocomposites were investigated in the experimental part of this work. In the result of measurements, it was determined that electrical conductivity (σdc), absorbance level (A) and tensile modulus (E) of the composites increased significantly with the increase of SWCNT content in the CMC matrix. These physical changes in the CMC/SWCNT composites were explained by the percolation theory and the electrical and optical percolation thresholds (Rσ and Rop) and the critical exponents (βσ and βop) of these composites were calculated. In addition, MD simulations were performed to estimate the material properties for the polymer composite structures. The results of the tensile test experiments were found to qualitatively overlap with the experiments at low concentration range. Moreover, a homogenous distribution of SWCNTs were observed in the CMC matrix together with a strong level of interactions in between. In the continuum modelling a two parameters augmentation model is used. A coupled Mori-Tanaka-self consistent method is utilized when obtaining effective properties of composites. Experimental, MD and continuum modelling results of composites were compared and reasonable agreement was obtained between results.

Predicting resting-state brain functional connectivity from the structural connectome using the heat diffusion model: a multiple-timescale fusion method

Objective. Understanding the intricate relationship between structural connectivity (SC) and functional connectivity (FC) is pivotal for understanding the complexities of the human brain. To explore this relationship, the heat diffusion model (HDM) was utilized to predict FC from SC. However, previous studies using the HDM have typically predicted FC at a critical time scale in the heat kernel equation, overlooking the dynamic nature of the diffusion process and providing an incomplete representation of the predicted FC. Approach. In this study, we propose an alternative approach based on the HDM. First, we introduced a multiple-timescale fusion method to capture the dynamic features of the diffusion process. Additionally, to enhance the smoothness of the predicted FC values, we employed the Wavelet reconstruction method to maintain local consistency and remove noise. Moreover, to provide a more accurate representation of the relationship between SC and FC, we calculated the linear transformation between the smoothed FC and the empirical FC. Main results. We conducted extensive experiments in two independent datasets. By fusing different time scales in the diffusion process for predicting FC, the proposed method demonstrated higher predictive correlation compared with method considering only critical time points (Singlescale). Furthermore, compared with other existing methods, the proposed method achieved the highest predictive correlations of 0.6939 ± 0.0079 and 0.7302 ± 0.0117 on the two datasets respectively. We observed that the visual network at the network level and the parietal lobe at the lobe level exhibited the highest predictive correlations, indicating that the functional activity in these regions may be closely related to the direct diffusion of information between brain regions. Significance. The multiple-timescale fusion method proposed in this study provides insights into the dynamic aspects of the diffusion process, contributing to a deeper understanding of how brain structure gives rise to brain function.

Validating a Critical Consciousness Scale for Civil Engineers

Validating a Critical Consciousness Scale for Civil Engineers

Investigation of Magnetocaloric Effect and Critical Field Analysis of Nd0.7−xLaxSr0.3MnO3 (x = 0.0−0.3) Manganites

This research explored the temperature dependence magnetization, magnetocaloric effect, and critical field analysis of Nd0.7−xLaxSr0.3MnO3 (x = 0.0, 0.1, 0.2 and 0.3) manganites samples synthesized through solid state reaction route. The substitution of La3+ at Nd3+ site enhances the A-site average ionic radius ( rA ) from 1.321 Å (for x = 0.0) to 1.348 Å (for x = 0.3). An increase in rA reduced the internal chemical pressure inside the lattice such that the Mn–O–Mn bond angle approached 180°. In addition, an increase in Mn–O–Mn bond angle supresses the spin-lattice interaction, which consequently reduces the change in maximum magnetic entropy (ΔSMmax) at the magnetic transition temperature. This implies that variation of A-site average ionic radius influences the change in maximum magnetic entropy. The critical behavior of the manganite samples was addressed based on the data of magnetization measurements around the transition temperature TC. Various techniques such as modified Arrott plot, a Kouvel–Fisher method, and critical isotherm analysis were used to measure the values of the ferromagnetic transition temperature TC, as well as the critical exponents of β, γ, and δ. The magnetic order parameter n is very well obeyed with scaling relation with change in magnetic entropy.

Blume-Capel model analysis with a microcanonical population annealing method.

We present a modification of the Rose-Machta algorithm [N. Rose and J. Machta, Phys. Rev. E 100, 063304 (2019)2470-004510.1103/PhysRevE.100.063304] and estimate the density of states for a two-dimensional Blume-Capel model, simulating 10^{5} replicas in parallel for each set of parameters. We perform a finite-size analysis of the specific heat and Binder cumulant, determine the critical temperature along the critical line, and evaluate the critical exponents. The obtained results are in good agreement with those previously obtained using various methods-Markov chain Monte Carlo simulation, Wang-Landau simulation, transfer matrix, and series expansion. The simulation results clearly illustrate the typical behavior of specific heat along the critical lines and through the tricritical point.

On the behaviors of solutions of a nonlinear diffusion system with a source and nonlinear boundary conditions

We study the global solvability and unsolvability of a nonlinear diffusion system with nonlinear boundary conditions in the case of slow diffusion. We obtain the critical exponent of the Fujita type and the critical global existence exponent, which plays a significant part in analyzing the qualitative characteristics of nonlinear models of reaction-diffusion, heat transfer, filtration, and other physical, chemical, and biological processes. In the global solvability case, the key components of the asymptotic solutions are obtained. Iterative methods, which quickly converge to the exact solution while maintaining the qualitative characteristics of the nonlinear processes under study, are known to require the presence of an appropriate initial approximation. This presents a significant challenge for the numerical solution of nonlinear problems. A successful selection of initial approximations allows for the resolution of this challenge, which depends on the value of the numerical parameters of the equation, which are primarily in the computations recommended using an asymptotic formula. Using the asymptotics of self-similar solutions as the initial approximation for the iterative process, numerical calculations and analysis of the results are carried out. The outcomes of numerical experiments demonstrate that the results are in excellent accord with the physics of the process under consideration of the nonlinear diffusion system.

A threshold criterion of stress intensity range in a steel sheet

Fatigue fractures often originate and propagate from geometric discontinuities or material defects in equipment or components. The occurrence and propagation of cracks near the fatigue limit were observed in notched specimens of a steel sheet that simulated this situation, and analyzed using fracture mechanics parameters. The notch caused strain concentration, and local plastic strain arose even at low stress amplitudes. Transgranular fracture occurred, and arrested cracks were observed near the threshold stress amplitude Δσth. The threshold stress intensity range ΔKth had a good power function correlation with the effective notch length aef, but it depended on the length and did not reach a constant value. By identifying and applying the critical power exponent, we proposed a prediction model using the function ΔKthc=Yπ1/2Δσthaef1/κ, which is the critical threshold stress intensity range that has a constant value. κ is equal to 5 for the steel sheet under transverse bending. Since ΔKth c obtained using this critical exponent method does not depend on the crack length, it can be used as a material constant and a failure criterion, and can be applied as a new strength prediction model.

A comparative study of magnetic behaviours in bulk and ribbon samples of PrMn2Ge2 compound

The magnetic properties of PrMn2Ge2 samples in both the as-cast bulk and melt-spun ribbon forms have been investigated in detail by a comprehensive set of x-ray and neutron powder diffraction, magnetic and heat capacity measurements and corresponding sets of data analyses. Thermal expansion measurements indicate the presence of magnetoelastic coupling effects around all transition temperatures in the bulk sample. The bulk modulus K0 = 42.0 GPa and its first derivative K0’ = 18.7 have been derived from the pressure-volume data. The Curie temperature from the intralayer antiferromagnetism (AFl) of PrMn2Ge2 to a canted spin structure (Fmc) is TCinter = 332 K for the bulk sample, decreasing to TCinter = 320 K for the ribbon sample. The critical components γ, β and δ of this second order magnetic transition as determined from Kouvel-Fisher analyses, indicate long range magnetic interactions around TCinter. Based on these critical exponents the magnetization, field and temperature data around TCinter collapse onto two curves obeying the single scaling equation M(H,ε)=εβf±(Hεβ+γ). The Debye temperatures and the density of states at the Fermi level are θD=306K and N(EF)=3.47state/eVatom for the bulk sample and θD=320K and (EF)=2.18state/eVatom for the ribbon sample with the nuclear specific heat coefficient for bulk PrMn2Ge2 derived from the splitting of the nuclear hyperfine levels as CN = 517 mJ mol−1 K−1. With a field change of ΔB = 5 T, the maximum values of the magnetic entropy changes -ΔSmax in the region around TCinter are -ΔSmax = 3.00 J/kg K and 2.35 J/kg K for the bulk and ribbon samples respectively, while the relative cooling power (RCP) for the ribbon-spun sample, RCP = 135.9 J/kg, is significantly higher than the value of RCP = 116.6 J/kg for the bulk sample. These findings indicate that PrMn2Ge2 could be a promising candidate for magnetic refrigeration applications in the room temperature region.

Ideas and perspectives: Sensing energy and matter fluxes in a biota-dominated Patagonian landscape through environmental seismology – introducing the Pumalín Critical Zone Observatory

Abstract. The coastal temperate rainforests (CTRs) of Chilean Patagonia are a valuable forest biome on Earth given their prominent role in biogeochemical cycling and the ecological value and dynamics of surface processes. The Patagonian CTRs are amongst the most carbon-rich biomes on Earth. Together with frequent landscape disturbances, these forests potentially allow for episodic and massive release or sequestration of carbon into and from the atmosphere. We argue that, despite their particular biogeographic, geochemical, and ecological roles, the Patagonian CTRs in particular and the global CTRs in general are not adequately represented in the current catalog listing critical zone observatories (CZOs). Here, we present the Pumalín CZO as the first of its kind, located in Pumalín National Park in northern Chilean Patagonia. We consider our CZO a representative end-member of undisturbed ecosystem functioning of the Patagonian CTRs. We have identified four core research themes for the Pumalín CZO around which our activities circle in an integrative, quantitative, and generic approach using a range of emerging techniques. Our methodological blend includes an environmental seismology that also fills a critical spatiotemporal scale in terms of monitoring critical zone and surface processes with a minimum intervention in those pristine forests. We aim to gain quantitative understanding of these topics: (1) carbon sink functioning; (2) biota-driven landscape evolution; (3) water, biogeological, and energy fluxes; and (4) disturbance regime understanding. Our findings highlight the multitude of active functions that trees in particular and forests in general may have on the entire cascade of surface processes and the concomitant carbon cycling. This highlights the importance of an integrated approach, i.e., “one physical system”, as proposed by Richter and Billings (2015), and accounts for the recent advances in pushing nature conservation along the Chilean coast.

When correlations exceed system size: finite-size scaling in free boundary conditions above the upper critical dimension

We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation length is not bound by the system's physical size, a belief that long held sway. Instead, two scaling regimes can be observed — at the critical and pseudo-critical temperatures. We demonstrate that both are manifest for free boundaries. We use numerical simulations of the d = 5 Ising model to analyse the magnetization, susceptibility, magnetization Fourier modes and the partition function zeros. While some of the response functions hide the dual finite-size scaling, the precision enabled by the analysis of Lee–Yang zeros allows this be brought to the fore. In particular, finite-size scaling of leading zeros at the pseudo-critical point confirms recent predictions coming from correlations exceeding the system size. This paper is dedicated to Jaroslav Ilnytskyi on the occasion of his 60th birthday.

Some results for a weakly coupled system of semi-linear structurally damped σ-evolution equations

Abstract In this paper, we are interested in studying the Cauchy problem for a weakly coupled system of two semi-linear structurally damped σ k {\sigma_{k}} -evolution equations, where σ k ≥ 1 {\sigma_{k}\geq 1} for k = 1 , 2 {k=1,2} . Our first purpose involves the proof of global (in time) existence of small data energy solutions by mixing additional L m k {L^{m_{k}}} regularity for the data, where m k ∈ [ 1 , 2 ) {m_{k}\in[1,2)} . We want to point out that in some cases of choosing suitable parameters m k {m_{k}} , with k = 1 , 2 {k=1,2} , the obtained lower bound of one exponent p or q related to power nonlinearities on the right-hand sides is really smaller than the critical exponent, the so-called modified Fujita exponent. The second aim of this paper is to discuss a blow-up result for Sobolev solutions with any different fractional values of σ k ≥ 1 {\sigma_{k}\geq 1} when m 1 = m 2 {m_{1}=m_{2}} .

Critical behavior in the ferromagnet

High-Curie-temperature ferromagnets are promising candidates for designing new spintronic devices. Here we have successfully synthesized the single crystal of the itinerant ferromagnet Mn5Ge3 using flux method. Its critical properties were investigated by means of bulk dc magnetization at the boundary of the paramagnetic (PM) and ferromagnetic (FM) phase to determine intrinsic magnetic interactions. Critical exponents with a critical temperature K and with K are acquired by the modified Arrott plot, whereas is deduced by a critical isotherm analysis at K. The self-consistency and reliability of these critical exponents are verified by the Widom scaling law and the scaling equations. Further analysis reveals that the spin interaction in Mn5Ge3 exhibits three-dimensional Ising-like behavior. The magnetic exchange interaction is found to decay as , meaning that the spin interactions exceed the nearest neighbors, which may be related to the different Mn-Mn interactions with inequal exchange strengths.

Scaling towards the critical point in the combined reaction/Gibbs ensemble

We explore the impact of force field parameters and reaction equilibrium on the scaling behavior towards the critical point in reactive binary systems, focusing on NO2/N2O4. This system can be considered as a special single-component system since NO2 and N2O4 are in chemical equilibrium via the chemical reaction 2NO2⇌N2O4. We simplify the system by representing both components as single LJ particles, achieving excellent agreement with densities computed using molecular simulations in which all-atom force fields were used. We investigate the effect of force field parameters (ɛ and σ) on phase behavior and show that the critical exponent β remains constant, which means that intermolecular interactions do not affect the scaling to the critical point when the chemical reaction takes place. We also investigate the sensitivity of the reaction equilibrium constant and show that even small changes in isolated molecule partition functions lead to large differences in chemical equilibria. We show that the critical exponent β is different for systems with different reaction equilibrium constants, so a careful parameterization of β is needed for an accurate computation of critical temperatures of reactive mixtures. We perform a screening of reactive binary mixtures for a wide range of ideal gas reaction equilibrium constants, revealing key insights into the thermodynamic behavior and critical properties. Thereby we facilitate the efficient screening of reactive binary mixtures for various applications. Our results emphasize the importance of accurately parameterizing β and provide valuable insights into the critical scaling behavior of complex reactive systems.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

Abstract We obtain an exact solution of spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter (PFDM). Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable, we analyse the thermodynamics of our black holes in the extended phase space. Owing to the background clouds of strings parameter ($a$) and the parameter endowed with PFDM ($\beta$), we analyse the Hawking temperature, entropy and specific heat. We also investigate the relationship between the photon sphere radius and the phase transition for the Letelier AdS black holes immersed in PFDM. Through the analysis, we find with a particular condition, there are non-monotonic behaviours between the photon sphere radius, the impact parameter, the PFDM parameter, temperature, and pressure. We can regard both the changes of photon sphere radius and impact parameter before and after phase transition as the order parameter; their critical exponents near the critical point are equal to the same value 1/2, just like ordinary thermal systems. These indicate that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

Coexistence of critical phenomena: the concept of manifold multi-spectral criticality

Prompted by the ubiquity of empirical observations of critical phenomena, often in non-equilibrium macrostates, we developed a modelling approach in which several critical phenomena coexist. Instead of a single critical point, many coexisting critical points in the system are identified, forming a one-dimensional critical manifold. Identified within our game-of-life-like heterogeneous agent-based simulation model, where agents can be created and annihilated in the presence of a catalyst, each critical point belonging to the critical manifold is associated with a multi-spectrum of critical exponents. We find this situation in non-equilibrium mixed percolation-like macrostates obeying continuous phase transitions. These macrostates are quasi-stationary, where some system characteristics are time-independent while others are not. This novel look at universality signals the existance of complexity of critical phenomena richer than described to date.

Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity.

We investigate the impact of nonreciprocity on universality and critical phenomena in open quantum interacting many-body systems. Nonreciprocal open quantum systems often have an exotic spectral sensitivity to boundary conditions, known as the Liouvillian skin effect (LSE). By considering an open quantum XXZ spin chain that exhibits LSE, we demonstrate the existence of a universal scaling regime that is not affected by the presence of the LSE. We resolve the critical exponents, which differ from those of free fermions, via tensor network methods and demonstrate that observables exhibit a universal scaling collapse, irrespective of the reciprocity. We find that the LSE only becomes relevant when a healing length scale ξ_{heal} at the system's edge (which is different from the localization length of the eigenstate of the Liouvillian) exceeds the system size, allowing edge properties to dominate the physics. We expect this result to be a generic feature of nonreciprocal models in the vicinity of a critical point. The driven-dissipative quantum criticality we observe has no classical analog and stems from the existence of multiple dark states.

The study of structural, electronic, magnetic and magnetocaloric properties of antiperovskite carbides M3AlC (M=Mn and Fe): DFT combined with Monte Carlo simulation

This work aims to investigate the structural stability, magnetic and electronic properties of M3AlC antiperovskites using density functional theory (DFT) and Monte Carlo simulation. The obtained ground state results reveal that the antiperovskites M3AlC are stable in the ferromagnetic (FM) state with a metallic character. The calculated total magnetic moments are 5.21[Formula: see text] and 3.34[Formula: see text] for Mn3AlC and Fe3AlC, respectively, with the total moments mainly from the M atom. The ferromagnetic behavior is confirmed by computing the density of state at Fermi level and verified the Stoner criterion. The magnetic and magnetocaloric behavior of M3AlC is investigated using Monte Carlo simulation and the obtained results demonstrate that the transition from ferromagnetic to paramagnetic state occurs at [Formula: see text][Formula: see text]K and [Formula: see text][Formula: see text]K for Mn3AlC and Fe3AlC, respectively. These values of [Formula: see text] are in good agreement with the experimental results. The magnetocaloric effect and critical behavior are studied and the obtained values of magnetic entropy change [Formula: see text] at 4.5[Formula: see text]T is about 4.242[Formula: see text]J/kg.K and 3.666[Formula: see text]J/kg.K and the relative cooling power (RCP) are 342.434[Formula: see text]J/kg.K and 325.26[Formula: see text]J/kg.K for Mn3AlC and Fe3AlC at 4.5T, indicating that these compounds are more appropriate for magnetic refrigeration. Finally, the critical exponents ([Formula: see text],[Formula: see text],[Formula: see text]) are calculated and the obtained values are close to the values of mean-field model.