Search Results (94)

Electroencephalographic (EEG) signals provide macroscopic observables of complex neural dynamics. We introduce a horizon-inspired framework in which measured EEG signals are modeled as projections of a complex wave-like representation constrained by an effective boundary analogous to an event horizon. In this formulation the signal amplitude obeys a renormalization-group scaling relation while EEG spectral entropy parameterizes the accessibility of observable modes. The resulting solutions generate oscillatory structures whose geometry and spectral signatures can be explored through signal analysis and sonification. This mapping between entropy-based neural observables and wave-like signal representations provides a physically motivated framework linking entropy measures, scale-dependent dynamics, and observable neural oscillations. The work is intentionally conceptual. It provides a falsifiable framework intended to stimulate future empirical investigations. Full article

The critical brain hypothesis proposes that neural systems operate near a phase transition to optimize information processing. A key method for investigating this hypothesis is the phenomenological renormalization group (pRG), which looks for scale-invariant features across levels of coarse-graining. One such feature is the power-law scaling of eigenvalues of covariance matrices of coarse-grained variables. However, the estimation of this scaling exponent, $\mu$, often relies on linear regression over arbitrarily selected ranges of the plot of eigenvalues versus rank. This heuristic “eyeballing” introduces uncontrolled bias and complicates the interpretation of observed scaling relationships. In order to obtain a more robust estimation of $\mu$, we do not fit the standard eigenvalue-vs-rank relationship, but rather the density of eigenvalues, for which standard protocols exist for fitting power laws to empirical data distributions. We demonstrate this approach using a synthetic model that replicates the scaling signatures of neural data while providing control over the system’s exponents as well as neural data obtained from publicly available Neuropixels recordings. We also establish standards for the minimal data required to quantify power-law behavior in a pRG eigenvalue analysis. Our approach contributes a tool for understanding the fundamental limitations imposed by spatial and temporal constraints of experimental datasets, which is required to rigorously assess the neural criticality hypothesis. Full article

Quantum stochastic processes are widely used in describing open quantum systems and in the context of quantum foundations. Physically relevant quantum stochastic processes driven by multiplicative colored noise are generically non-Markovian and analytically intractable. Further, their Markovian limits are generically inequivalent when using either the Ito or Stratonovich conventions for the same quantum stochastic processes. We introduce a quantum noise homogenization scheme that temporally coarse-grains non-Markovian, colored-noise-driven quantum stochastic processes and connects them to their effective white-noise (Markovian) limits. Our approach uses a novel phase-space augmentation that maps the non-Markovian dynamics into a higher-dimensional Markovian system and then applies a controlled perturbative coarse-graining scheme in the characteristic time scales of the noise. This allows an explicit analytical algorithm to derive effective Markovian generators with renormalized coefficients and enables various physical constraints, such as causality, to be imposed on them. We thus resolve the Ito–Stratonovich ambiguity for multiplicative colored-noise-driven quantum stochastic processes, wherein we show that their consistent Markovian limit corresponds to the Stratonovich convention with renormalized coefficients as well as correction terms in Ito’s convention. By assuming their Markovian limit unravels causal, completely positive and trace-preserving dynamics, we further characterize a physically relevant family of non-Markovian quantum stochastic processes driven by multiplicative colored noise. Full article

We argue that turbulent irreversibility is best explained as an asymptotic feature of a singular inviscid limit—a reclassification of admissible entities and balances at $\nu \to 0$—rather than as a mere residual effect of molecular viscosity. Tracing a conceptual line from Euler and Kármán–Howarth to Onsager, Duchon–Robert, Kato/Prandtl, and modern convex integration results, we show that the limit theory reclassifies the admissible entities: from smooth Euler fields (energy conserving) to rough weak solutions equipped with a positive defect measure in the energy balance. The constant inter-scale process (energy flux) observed at high-Reynolds number therefore persists at $\nu =0$ as a structural feature of the limit ontology. We articulate three selection principles—the local energy inequality, the exact third-order law, and scale-locality—as ontological constraints that reconcile mathematical non-uniqueness with physical uniqueness. A brief conceptual history clarifies how the arrow of time in turbulence emerged through successive shifts of entities and invariants, and a comparison with other singular limit explanations (Boltzmannian irreversibility, shocks, renormalization) situates the account within general foundations of physics. Methodologically, we recast LES/closures as asymptotic mediators validated by flux plateaus and viscosity-free diagnostics, not microscopic subgrid fidelity. Full article

In this work, the Renormalization Method (RM) is used to analyze the dynamics of a nonlinear two-degree-of-freedom (2DOF) system under parametric excitation, with a focus on fractal vibration behavior. This procedure comprises transforming the system into a comparable form. An equivalent linearized model is produced by isolating the system’s nonlinear interactions using a two-scale formulation and mean-square analysis. The non-autonomous fractal equations are transformed into an autonomous representation using the RM, and then the system is described in traditional derivative form using El-Dib’s fractal transformation. The fractal-coupled Mathieu system’s stability behavior can be effectively identified using this framework. An agreement with the analytical solutions is shown by numerical results. All things considered, the integrated RM-based approach provides a reliable tool for forecasting and managing intricate nonlinear fractal systems. Full article

University campuses located within cities function as small-scale urban living areas and are expected to be designed to ensure easy and equitable access for all segments of society. In this context, in the first stage of the present study, the criteria identified from the literature on campus-scale accessibility were presented to experts for weighting. The weighted criteria were scored using the AHP method by an expert group across four commonly used pedestrian axes within the campus. In the second stage, a Geographic Information System (GIS)-based composite Accessibility Suitability Index (ASI) was applied across the entire campus pedestrian network. Then, this index was combined with the renormalized AHP weights. The analyses revealed that at Osmaniye Korkut Ata University, Axis 1 fell into the “medium” category, while the other three axes were classified as “low.” Improvement proposals were developed to address the deficiencies identified in the study area. These recommendations are expected to positively influence environmental factors and boost pedestrian use on the Karacaoğlan Campus of Osmaniye Korkut Ata University. Full article

Interfaces of rather different natures—as, e.g., bacterial colony or forest fire boundaries, or semiconductor layers grown by different methods (MBE, sputtering, etc.)—are self-affine fractals, and feature scaling with universal exponents (depending on the substrate’s dimensionality d and global topology, as well as on the driving randomness’ spatial and temporal correlations but not on the underlying mechanisms). Adding lateral growth as an essential (non-equilibrium) ingredient to the known equilibrium ones (randomness and interface relaxation), the Kardar–Parisi–Zhang (KPZ) equation succeeded in finding (via the dynamic renormalization group) the correct exponents for flat $d=1$ substrates and (spatially and temporally) uncorrelated randomness. It is this interplay which gives rise to the unique, non-Gaussian scaling properties characteristic of the specific, universal type of non-equilibrium roughening. Later on, the asymptotic statistics of process $h\left(x\right)$ fluctuations in the scaling regime was also analytically found for $d=1$ substrates. For $d>1$ substrates, however, one has to rely on numerical simulations. Here we review a variational approach that allows for analytical progress regardless of substrate dimensionality. After reviewing our previous numerical results in $d=1$, 2, and 3 on the time evolution of one of the functionals—which we call the non-equilibrium potential (NEP)—as well as its scaling behavior with the nonlinearity parameter $\lambda$, we discuss the stochastic thermodynamics of the roughening process and the memory of process $h\left(x\right)$ in KPZ and in the related Golubović–Bruinsma (GB) model, providing numerical evidence for the significant dependence on initial conditions of the NEP’s asymptotic behavior in both models. Finally, we highlight some open questions. Full article

In the immediate aftermath of the Big Bang, the universe existed in an extremely hot, dense state in which particle interactions occurred not in vacuum but within a thermal medium. Under such conditions, the standard framework of quantum field theory (QFT) requires a finite-temperature extension, wherein propagators—and hence the fundamental structure of the theory—are modified to reflect thermal background effects. These thermal modifications are central to understanding the nature of electroweak symmetry breaking (EWSB) as a high-temperature phase transition, potentially leading to qualitatively different vacuum structures for the Higgs field as the universe cooled. Finite-temperature corrections naturally regulate ultraviolet divergences in propagators, hinting at a possible route toward ultraviolet completion. However, these same thermal effects exacerbate infrared pathologies and can lead to imaginary contributions to the effective potential, particularly when analyzing metastable or multi-vacuum configurations. Additional theoretical challenges, such as gauge dependence and renormalization scale ambiguity, further obscure the precise characterization of the electroweak phase transition—even in minimal extensions of the Standard Model (SM). This review presents the theoretical foundations of finite-temperature QFT with an emphasis on how different field species respond to thermal effects, identifying the bosonic sector as the primary source of key theoretical subtleties. We focus particularly on the scalar extension of the SM, which offers a compelling framework for realizing first-order electroweak phase transitions, electroweak baryogenesis, and accommodating dark matter candidates depending on the underlying ${\mathbb{Z}}_2$ symmetry structure. Full article

The flow field evolution in the first turn of the spiral concentrator is decisive for the separation efficiency of solid particles. A laboratory-scale Φ300 mm spiral concentrator was employed as the study subject. The fluid phase was simulated using the RNG k-ε (Renormalization Group) turbulence model and the VOF (Volume of Fluid) multiphase model, while the particles were calculated with an Eulerian multi-fluid VOF model that incorporates the Bagnold effect. The influence of the cross-sectional curve equation on the evolution of flow field parameters in the first turn and on the separation behavior of hematite and quartz particles was systematically investigated. The results indicated that the evolution characteristics of fluid parameters, such as the depth of flow film, the tangential velocity of surface flow, the velocity of secondary circulation, and radial flux, were similar. All parameters were observed to undergo an initial decrease or increase, eventually stabilizing as the longitudinal travel progressed. A negative correlation was identified between the index of the cross-sectional curve equation and both the depth of flow film and the tangential velocity of surface flow in the inner half of the trough, whereas an inverse relationship was noted in the outer half. With an increase in the index of the cross-sectional curve equation, the outward circulation velocity in the initial stage and its radial flux in the outer zone were enhanced, while the fluctuations in the evolution of local fluid parameters were suppressed, with more active fluid radial migration observed at the indices of the cross-sectional curve equation of 2.5 and 3. As the flow field evolved, axial separation between hematite and quartz particles was progressively achieved by gravity due to their density difference. In the middle and inner-outer zones, the migration directions of hematite and quartz were observed to become opposite in the later stage of evolution, while the difference in their migration magnitudes was also found to be widened. With an increase in the index of the cross-sectional curve equation, the disparity in the axial separation and movement between hematite and quartz was enhanced, albeit with a diminishing rate of increase. The maximum separation efficiency between hematite and quartz particles was significantly improved with increased longitudinal travel, reaching over 60% by the end of the first turn; higher indices were determined to be more favorable for achieving this performance. Based on the previous research, the variation in separation indices in the third turn was investigated under both independent adjustment of the index of the cross-sectional curve equation and its combined adjustment with the downward bevel angle. Relatively high and stable separation performance was achieved with the indices of the cross-sectional curve equation of 2.5 and 3, where a maximum separation efficiency of 82.02% was obtained, thereby validating the high efficiency and suitability of the selected spiral concentrator profile. This research elucidated the decisive role of the flow field evolution through the first turn in particle separation behavior from the perspective of quantitative description of hydrodynamic parameters, providing beneficial references for the cross-sectional structure design of spirals and the prediction of the separation index of specific feed. Full article

Cities are complex systems with socioeconomic activities exhibiting diverse spatial distributions, where selecting an appropriate observation scale is vital for understanding urban complexity. However, the traditional methods for this task are often limited, either because they rely on subjective judgments or lack generalizability before being applied across the diverse functions of a city. To address this issue, we introduce a complexity–heterogeneity balancing method, which employs renormalization group techniques to generate distribution matrices across different scales, striking a balance between complexity and heterogeneity to objectively identify appropriate observation scales. We implement this method on freight, enterprise and restaurant distribution data derived from major Chinese cities to identify their appropriate spatial scales. The results properly reflect the characteristic spatial organization structure of each urban function, meaning that the method provides a robust framework for determining appropriate scales in urban spatial analysis tasks. Our study has potential applications in enhancing the logistics optimization, industrial zoning and commercial planning processes and identifying urban functions and morphological features, thereby contributing to sustainable urban development. Full article

The effective design and operation of hydraulic structures, particularly open channel spillways, are crucial for water resource management and flood risk reduction in dams. A clear understanding of flow properties, such as velocity fluctuations and discharge, across various depths is essential for optimizing performance. In this study, experimental analysis and numerical simulation using FLOW-3D were combined to investigate the hydraulic parameters of a scaled model of the Romaine IV spillway located in Quebec, Canada. Measurements focused on flow properties, including velocity fluctuations at various discharge rates in specific flow depths, at selected points along the spillway. The numerical model was assessed by reproducing experimental geometry, initial water levels, and boundary conditions, and through sensitivity analyses to ensure accurate flow representation. Comparisons of flow rates of 180, 240, and 340 L/s showed that while simulations with the renormalized group (RNG) turbulence model reliably predicted average velocities, they underestimated maximum values and overestimated minimum values, especially at higher discharges. The results highlight the difficulty of accurately capturing velocity extremes in turbulent flows and the need for further model refinement. This was evident from the 60% discrepancy in minimum velocities observed at the channel center. Despite these discrepancies, the study advances our understanding of spillway performance and identifies avenues to improve the accuracy of numerical modeling in hydraulic engineering. Full article

Motion of dislocations is a common mechanism of plasticity in many materials. Dislocation-mediated deformation is essentially an inhomogeneous process, which is manifest in the formation of slip lines and complicated cell wall structures. An adequate description of these processes is an important goal of Materials Theory, which aims to describe the mechanical properties of materials and their reliability in service. This publication advances the thermodynamically consistent theory of dislocation-mediated plasticity to include the spatial gradients of the independent variables. We conducted the renormalization group scaling analysis of deformation and obtained the low-energy dislocation structures as ordinary solutions of the equilibrium equations without any arbitrary assumptions. We matched the emerging theoretical structures with the experimentally observed and made several predictions regarding possible experiments. Full article

The increasing integration of artificial intelligence agents (AIAs) based on large language models (LLMs) is transforming many spheres of society. These agents act as human assistants, forming Distributed Intelligent Systems (DISs) and engaging in opinion formation, consensus-building, and collective decision-making. However, complex DIS network topologies introduce significant uncertainty into these processes. We propose a quantum-inspired graph signal processing framework to model collective behavior in a DIS interacting with an external environment represented by an influence matrix (IM). System topology is captured using scale-free and Watts–Strogatz graphs. Two contrasting interaction regimes are considered. In the first case, the internal structure fully aligns with the external influence, as expressed by the commutativity between the adjacency matrix and the IM. Here, a renormalization-group-based scaling approach reveals minimal reservoir influence, characterized by full phase synchronization and coherent dynamics. In the second case, the IM includes heterogeneous negative (antagonistic) couplings that do not commute with the network, producing partial or complete spectral disorder. This disrupts phase coherence and may fragment opinions, except for the dominant collective (Perron) mode, which remains robust. Spectral entropy quantifies disorder and external influence. The proposed framework offers insights into designing LLM-participated DISs that can maintain coherence under environmental perturbations. Full article

We calculate the Doniach phase diagram of heavy-fermion systems containing Ce and Eu ions, using the scaling solution of the periodic Anderson model, and compare the results with the experimental data on CeRu₂Ge₂ and EuCu₂(Ge_1−xSi_x)₂. The temperature–pressure (T–p) phase diagram emerges from the competition between the pressure-dependent Kondo interaction and the temperature- and pressure-dependent RKKY interaction. Both are derived using scaling equations in the presence of crystal-field effects: Kondo temperature $T_K$ is related to the coupling constant g(p), where p is the control parameter, and the temperature-dependent renormalized coupling $g(T,T_K(g))$. For comparison with the experiment, we assume a linear dependence of g on the control parameter, which could be pressure or composition. The Néel temperature $T_N(p)$ is obtained by comparing the free energies of the system in the antiferromagnetic and paramagnetic states. The resulting asymmetric $T_N(p)$ arises naturally from the exponential growth of $T_K(p)$ and a much slower polynomial growth of the RKKY interaction. Phase diagrams for CeRu₂Ge₂ and EuCu₂(Ge_1−xSi_x)₂ successfully capture key experimental features: pressure-induced suppression of magnetic order, the peak of RKKY interaction energy, and crossover to a heavy-Fermi-liquid regime at high coupling strength. Our work provides the first quantitative, material-specific construction of Doniach diagrams, clarifies the entropy removal at low temperatures and offers predictive insight for future experiments under extreme conditions. Full article

A real-space renormalization group (RG) framework is formulated for classical SO(n) spin models defined on d-dimensional crystal lattices composed of corner-sharing hyper-tetrahedra, a class of geometrically frustrated crystal structures. This includes, as specific instances, the classical Heisenberg model on the kagome and pyrochlore crystals. The approach involves computing the partition function and corresponding order parameters for spin clusters embedded in the crystal, to leading order in symmetry-breaking fields generated by surrounding spins. The crystal geometry plays a central role in determining the scaling relations and the associated critical behavior. To illustrate the efficacy of the method, a reduced manifold of symmetry-allowed ordered states for isotropic nearest-neighbor interactions is analyzed. The RG flow systematically excludes the emergence of a $\overrightarrow{q}=\mathbf{0}$ ordered phase within the antiferromagnetic sector, independently of both the spatial dimensionality of the crystal and the number of spin components. Extensions to incorporate more elaborate crystal-symmetry-induced ordering patterns and fluctuation-driven phenomena—such as order-by-disorder—are also discussed. Full article