Phenomenological Model Research Articles

Thermal cross section of poly(2-hydroxyethyl methacrylate) hydrogels for neutron dose calculation

Phantom materials are used to design radiation safety and protection strategies by means of numerical dose calculation. In the case of thermal neutrons, the radiation transport in the phantom relies on mass attenuation coefficients and total cross sections which are dependent on the physical and chemical properties of the material. Specifically for medical applications, such as neutron capture therapy, the neutron-induced dose is mainly related to the neutron absorption by hydrogen and nitrogen in the human tissue and body. Here, we investigate the use of poly(2-hydroxyethyl methacrylate) as a phantom material by experimental measurement and modeling of its total neutron scattering cross section and mass attenuation coefficient. We show that by varying the hydration level from 10 to 40 w%, one can obtain a neutron attenuation coefficient similar to polymethyl methacrylate or more representative of the human body, respectively. By benchmarking our phenomenological model on the experimental data, we provide a new example of how to use the average functional group approximation to accurately model total neutron cross sections in the framework of personalized medicine approaches.

Predicting initial microlayer thickness in nucleate boiling using Landau–Levich theory

A phenomenological model is proposed to estimate the initial thickness of the liquid microlayer forming beneath a vapour bubble growing on a solid surface upon nucleate boiling. The model employs an analogy between the microlayer formation and the classic plate withdrawal problem. It calculates the microlayer thickness by considering it as a Landau–Levich film, where the thickness is a function of the meniscus speed and radius of curvature. Given the nearly hemispherical shape of the bubble during the early growth stage when the microlayer is first deposited, we assume that the meniscus speed can be approximated by the bubble expansion rate, and estimate the meniscus curvature using the Rayleigh equations. Unlike previous theories that assume that the bubble radius growth is proportional to the square root of time, the proposed model does not rely on any specific law of growth for vapour bubbles. The model is validated for predicting the microlayer thickness in water and ethanol, showing good agreement with experimental measurements and empirical correlations. Subsequent analyses of the microlayer interface profile address inconsistent reports – some described a wedge-like shape, whereas others reported a slight outward curvature with decreasing thickness in the outer region. This discrepancy is attributed to a reduction in the expansion rate of the microlayer's outer edge, particularly when the bubble reaches its maximum width. Our model provides insights into microlayer dynamics, essential to boiling heat transfer, as the evaporative heat flux through the microlayer is very sensitive to its initial thickness.

Magnetic structures of PrMn7O12 : Intersublattice magnetoelastic coupling and incommensurate spin canting

We report on the magnetic structures of PrMn7O12, resolving both a high-temperature structure in common with the other R3+Mn7O12 systems and an additional low-temperature phase characterized by a superposed incommensurate (ICM) spin canting. A phenomenological model is developed to account for large magnetoelastic coupling immediately below the Curie temperature, demonstrating that A′B exchange is primarily responsible for the ferrimagnetic structures observed across the R3+Mn7O12 family. Finally, an analytical mean-field minimal model is presented that successfully accounts for all magnetic structures observed in this family of materials, including the canted commensurate and ICM ground states. Published by the American Physical Society 2024

Pseudoscalar mesons from a PNJL model at zero temperature

We study pseudoscalar π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi $$\\end{document}, K and η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document} meson properties, such as masses and couplings, in dense matter at zero temperature. We use a recently proposed phenomenological quark model, known as the PNJL0, which takes into account the confinement/deconfinement phase transition by means of the traced Polyakov loop (Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document}) which serves as an order parameter at zero temperature. We consider two different scenarios, namely, symmetric quark matter with equal chemical potentials for all the flavors, and the beta equilibrated matter. In the latter case the hadron-quark phase transition is implemented by a two model approach. For the hadron side we use a relativistic mean-field model with density dependent couplings. We show that Φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varPhi $$\\end{document} induces abrupt changes in the mesons properties with gap sizes regulated by the phenomenological gluonic sector of the model.

Flow state transition induced by emergence of orbiting satellite eddies in two-dimensional turbulent Rayleigh–Bénard convection

We report a numerical investigation of a previously noticed but less explored flow state transition in two-dimensional turbulent Rayleigh–Bénard convection. The simulations are performed in a square domain over a Rayleigh number range of $10^7 \leq Ra \leq 2 \times 10^{11}$ and a Prandtl number range of $0.25 \leq Pr \leq 20$ . The transition is characterized by the emergence of multiple satellite eddies with increasing $Ra$ , which orbit around and interact with the main vortex roll in the system. Consequently, the main roll is squeezed to a smaller size compared with the domain and wanders around in the bulk region irregularly and extensively. This is in sharp contrast to the flow state before the transition, which is featured by a domain-sized circulatory roll with its vortex centre ‘condensed’ near the domain's centre. Detailed velocity field analysis reveals that there exists an abrupt increase in the energy fluctuations of the Fourier modes during the transition. Based on this phase-transition-like signal, the critical condition for the transition is found to follow a scaling relation as $Ra_t \sim Pr^{1.41}$ where $Ra_t$ is the critical Rayleigh number for the transition. This scaling relation is quantitatively explained by a phenomenological model grounded on the bistability behaviour (i.e. spontaneous and stochastic switching between the two flow states) observed at the edge of the transition. The model can also account for the effects of aspect ratio on the transition reported in the literature (van der Poel et al., Phys. Fluids, vol. 24, 2012).

The high-energy cyclotron line in 2S 1417-624 discovered with Insight-HXMT during the 2018 outburst

We report a detailed timing and spectral analysis of the X-ray pulsar 2S 1417-624 using the data from Insight-HXMT during the 2018 outburst. The pulse profiles are highly variable with respect to both unabsorbed flux and energy. A double-peaked pulse profile from the low flux evolved to a multi-peaked shape in the high-flux state. The pulse fraction is negatively correlated to the source flux in the range of sim (1--6)$\ $ erg cm$^ $ s$^ $, consistent with Rossi X-ray Timing Explorer (RXTE) studies during the 2009 giant outburst. The energy-resolved pulse profiles around the peak outburst showed a four-peak shape in the low-energy bands and gradually evolved to triple peaks at higher energies. The continuum spectrum is well described by typical phenomenological models, such as the cut-off power law and the power law with high-energy cut-off models. Notably, we discovered high-energy cyclotron resonant scattering features (CRSFs) for the first time, which are around 100 keV with a statistical significance of sim 7sigma near the peak luminosity of the outburst. This CRSF line is significantly detected with different continuum models and provides very robust evidence for its presence. Furthermore, pulse-phase-resolved spectroscopy confirmed the presence of the line, whose energy varied from 97 to 107 keV over the pulse phase and appeared to have a maximum value at the narrow peak phase of the profiles.

Phenomenological models of ferroelastics with a fully symmetric order parameter: classification by methods of equivariant catastrophe theory

Using the methods of the catastrophe theory, which take into account the symmetry of the thermodynamic system, phenomenological models of phase transitions in proper and pseudo-proper ferroelastics have been constructed for interacting order parameters, one of which is fully symmetric, invariant with respect to all symmetry transformations of the crystal. A classification of models based on the number of control parameters, which depend on external thermodynamic conditions, has been carried out. A phase diagram of one of the models has been constructed, and the theoretical temperature dependence of the heat capacity has been calculated. The comparison of theoretical and experimental data showed satisfactory qualitative agreement.

Calculation of the order parameter and dielectric susceptibility under the electric field near the incommensurate phase in NaNO2 using Landau model

ABSTRACT Temperature dependences of the order parameters (P and Ψ) and inverse susceptibilities (χp −1 and χΨ -1 ) are calculated for the ferroelectric(FE)-incommensurate (INC) – paraelectric (PE) transitions in NaNO2 at zero (E = 0) and constant electric fields E by the Landau phenomenological model. For the calculation of the polarisation P and the order parameter Ψ, the phase line equations are fitted to the observed data (E = 0) from the literature. On this basis, E-T phase diagram including the ferroelectric, incommensurate and paraelectric phases is constructed using the observed (E-T) data for NaNO2 as reported in the literature. In the presence of the polarisation P (secondary order parameter), which has a biquadratic coupling with the Ψ (primary order parameter) in the incommensurate phase, the Landau model presented here describes the observed behaviour of the FE-INC and INC-PE transitions in NaNO2. Under constant electric fields, our predictions can be compared with the experiments. This method of calculation can be applied to some other crystals exhibiting the incommensurate phase between the FE and PE phases.

Circuit-theoretic phenomenological model of an electrostatic gate-controlled bi-SQUID

Abstract A numerical model based on a lumped circuit element approximation for a bi-superconducting quantum interference device (bi-SQUID) operating in the presence of an external magnetic field is presented in this paper. Included in the model is the novel ability to capture the resultant behaviour of the device when a strong electric field is applied to its Josephson junctions by utilising gate electrodes. The model is used to simulate an all-metallic SNS (Al-Cu-Al) bi-SQUID, where good agreement is observed between the simulated results and the experimental data. The results discussed in this work suggest that the primary consequences of the superconducting field effect induced by the gating of the Josephson junctions are accounted for in our minimal model; namely, the suppression of the junctions super-current. Although based on a simplified semi-empirical model, our results may guide the search for a microscopic origin of this effect by providing a means to model the voltage response of gated SQUIDs. Also, the possible applications of this effect regarding the operation of SQUIDs as ultra-high precision sensors, where the performance of such devices can be improved via careful tuning of the applied gate voltages, are discussed at the end of the paper.

Silver Nanowire Aerogel Support Promotes Stable Hydrogen Evolution Reaction at High Current Density.

The stability of electrocatalysts during the hydrogen evolution reaction (HER) is vital for efficient production of hydrogen energy. Herein, we demonstrate that silver nanowire aerogel-based support (AABS) could facilitate the construction of HER catalysts with extraordinary long-term stability. A full nanostructure catalyst of nickel phosphide based formed on AABS (Ni2P-Ni5P4@AABS) was prepared to achieve an overpotential of 687 mV (without iR compensation) for HER at the current density of 1 A cm-2 in 0.5 M H2SO4. Excitingly, the stable HER performance was kept for 42 days during the long-term stability (i-t) test at high current density (0.5-1 A cm-2). The excellent HER performance of the Ni2P-Ni5P4@AABS catalyst is attributed to rapid electron transport pathways, numerous more accessible active sites, and support induced enhanced catalytic activity. The support effect was highlighted by a proposed phenomenological two-channel model for electron transport, which provides fresh insights into the design strategy for energy storage and delivery.

FORMALISM OF PHENOMENOLOGICAL THEORY IN MATHEMATICAL MODELING OF ECONOMIC PROCESSES

Introduction: In contrast to neoclassical economics, where agents are rational, their actions are rational, and they strive for equilibrium, complex economics proposes to consider systems as evolving, complex, and not necessarily striving for equilibrium. The application of complex economics is particularly relevant in conditions of uncertainty and rapidly changing economic conditions. To develop the tools of complex economics, it is necessary to search for new mathematical approaches; a revolutionary approach in economics could be an approach based on the formalism of phenomenological theory. Methods: The formalism of phenomenological theory is used. Results: Four economic models are considered that can be built using the formalism of phenomenological theory. Using the example of analyzing changes in economic indicators caused by external factors such as magnetic storms, a modeling algorithm was implemented using phenomenological theory. Available data: No available data Discussion: The article shows that phenomenological formalism can be used in both traditional and more modern economic paradigms, expanding the boundaries of theoretical and applied analysis. Based on observed patterns and empirical data, phenomenological models allow us to study the macroscopic characteristics of economies without delving into microscopic details. As shown above, the formalism of phenomenological theory can be used both within the framework of neoclassical economics and complex economics. The phenomenological approach is universal and applicable in various areas of economic analysis, and the use of phenomenological theory allows us to take into account the elements of randomness and irrationality inherent in real economic processes, which is especially relevant for a complex economy.

Constraints on VHE gamma-ray emission of flat spectrum radio quasars with the MAGIC telescopes

ABSTRACT Flat spectrum radio quasars (FSRQs) constitute a class of jetted active galaxies characterized by a very luminous accretion disc, prominent and rapidly moving line-emitting cloud structures (broad-line region, BLR), and a surrounding dense dust structure known as dusty torus. The intense radiation field of the accretion disc strongly determines the observational properties of FSRQs. While hundreds of such sources have been detected at GeV energies, only a handful of them exhibit emission in the very-high-energy (VHE, E$\gtrsim 100$ GeV) range. This study presents the results and interpretation derived from a cumulative observation period of 174 h dedicated to nine FSRQs conducted with the Major Atmospheric Gamma-ray Imaging Cherenkov telescopes from 2008 to 2020. Our findings indicate no statistically significant ($\ge$5$\sigma$) signal for any of the studied sources, resulting in upper limits on the emission within the VHE energy range. In two of the sources, we derived quite stringent constraints on the gamma-ray emission in the form of upper limits. Our analysis focuses on modelling the VHE emission of these two sources in search for hints of absorption signatures within the BLR radiation field. For these particular sources, constraints on the distance between the emission region and the central black hole are derived using a phenomenological model. Subsequently, these constraints are tested using a framework based on a leptonic model.

Micro-electromechanical system-based cryogenic and heating in situ transmission electron microscopy for investigating phase transitions and domain evolution in single-crystal BaTiO3

Investigating phase transitions between ferroelectric states is crucial for understanding the nucleation, dynamics, and kinetics of domains, both before and after transformation. Here, we assess all phase transitions and domain evolutions in single-crystal BaTiO3 by implementing microelectromechanical systems (MEMS)-based in situ cryogenic (cryo-) and heating transmission electron microscopy (TEM) by continuously varying sample temperatures from -175 °C to 200 °C. Every possible phase-cubic, tetragonal, orthorhombic, and rhombohedral - was identified. An ultra-stable imaging condition was achieved with a mean drift speed of 1.52 nm/min, providing unique opportunities for atomic resolution in situ scanning TEM with a wide temperature range. Furthermore, domain nucleation and evolution across phase transitions were investigated using complementary dielectric measurements, optical microscopy, and a phenomenological model. This study underscores the effectiveness and utility of MEMS-based in situ cryo-/heating TEM in revealing phase transitions and domain structures in ferroelectric materials.

Time delay of light in the gravitational lensing of supermassive black holes in dark matter halos

AbstractThe dark matter halo has non-negligible effects on the gravitational lensing of supermassive black hole in the galaxy center. Our work presents a study on the time-delay of light in gravitational lensing of black holes enclosed by dark matter halos. To provide a precise description on the distribution of dark matter in galaxies, we choose several famous phenomenological dark matter halo models in astrophysics, including the NFW, Beta, Burkert and Moore models, to carry out the present study. Through numerically calculating the time-delay of light in gravitational lensing, a comparative analysis of the dark matter effects within different halo models has been performed. Assuming typical length scales associated with the galactic gravitational lensing, numerical results indicate that the NFW, Beta, Burkert and Moore dark matter halos can significantly enhance the time delay of light in gravitational lenisng of central supermassive black holes. The enhancing effect becomes more pronounced with a small dark matter halo scale and an increasing dark matter halo mass.

Analysis and control of hydrofoil vortex-induced vibration

This paper primarily investigates the relationship between the wake vortices and vortex-induced vibrations in hydrofoil structures, as well as explores effective methods to suppress structural vibrations in hydrofoils using a piezoelectric control system. By combining CFD simulations with PIV experiments, the study compared the vortex characteristics at the trailing edge of hydrofoils with different geometries. Furthermore, by integrating the results from the water tank experiments, the research revealed the sensitivity of vortex-induced resonance to the regularity and periodicity of the von Kármán vortex street. Subsequently, the FxLMS algorithm was fine-tuned based on a phenomenological model of vortex-induced resonance. Active control experiments on vortex-induced vibrations of the hydrofoil were conducted using a piezoelectric control system built on this algorithm, achieving a maximum vibration reduction rate of 56%. Finally, the instability and limitations of the control effectiveness were analyzed, and future research directions were proposed to improve control strategies and the system's temporal responsiveness.

Vacuum energy of nonsupersymmetric S˜ heterotic string models

We use the free fermionic formulation of the heterotic string in four dimensions to study the vacuum structure and energy of nonsupersymmetric tachyon free models that correspond to compactifications of tachyonic vacua of the ten-dimensional heterotic string. We explore the class of heterotic SO(10) nonsupersymmetric models constructed from the S˜ model in the free fermionic formalism and investigate the dependence of the potential on the geometric moduli. This paper will explore a sample of 109 string vacua to find the frequency of viable models, classifying these vacua by the following fertility criteria: tachyon presence, number of spinorial 16/16¯ representations, vectorial 10 states, and top quark mass coupling compatibility. Of these we find those that mimic supersymmetric models with equal number of bosons and fermions at the massless level: a00=0. Tachyon free models occur with a frequency of 5.309×10−3. Furthermore, models that fulfil the rest of the phenomenological fertility conditions and the additional condition on a00 occur with probability 4.0×10−9 We analyze the partition functions and study the moduli dependence of such models, finding that almost all fertile models have finite, positive potential at the free fermionic point, with 2 out of 84 of the fertile cores having negative, finite potential. We demonstrate that the free fermionic point is not necessarily a minimum in the potential. This work provides further evidence that supersymmetry may not be a necessary ingredient of phenomenological models, recreating many of the desirable features of such models without employing supersymmetry. Published by the American Physical Society 2024

Up-scattering production of a sterile fermion at DUNE: complementarity with spallation source and direct detection experiments

We investigate the possible production of a MeV-scale sterile fermion through the up-scattering of neutrinos on nuclei and atomic electrons at different facilities. We consider a phenomenological model that adds a new fermion to the particle content of the Standard Model and we allow for all possible Lorentz-invariant non-derivative interactions (scalar, pseudoscalar, vector, axial-vector and tensor) of neutrinos with electrons and first-generation quarks. We first explore the sensitivity of the DUNE experiment to this scenario, by simulating elastic neutrino-electron scattering events in the near detector. We consider both options of a standard and a tau-optimized neutrino beams, and investigate the impact of a mobile detector that can be moved off-axis with respect to the beam. Next, we infer constraints on the typical coupling, new fermion and mediator masses from elastic neutrino-electron scattering events induced by solar neutrinos in two current dark matter direct detection experiments, XENONnT and LZ. Under the assumption that the new mediators couple also to first-generation quarks, we further set constraints on the up-scattering production of the sterile fermion using coherent elastic neutrino-nucleus scattering data from the COHERENT experiment. Moreover, we set additional constraints assuming that the sterile fermion may decay within the detector. We finally compare our results and discuss how these facilities are sensitive to different regions of the relevant parameter space due to kinematics arguments and can hence provide complementary information on the up-scattering production of a sterile fermion.

Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

We produce a general formalism to study the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. When a quantum solid of graphene is subjected to an intense electric field in the optical frequency range, the observation of a nonlinear response is facilitated by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in a spin-boson model of dissipative quantum statistical mechanics. Our results reveal the nonlinear steady-state regime’s population inversion and decoherence. The present method enables us to investigate further the nonlinear interband optical conductivity of pristine and gapped graphene characterized by a single dimensionless parameter at finite temperatures. Different bath spectra’ effects on phonons and electrons are examined in detail. The temperature dependence of conductivity reveals that changing temperature can enable us to make a transition from the linear to the nonlinear regime for fixed optical field parameters. Interestingly, a fascinating switching-like behavior is observed for the low-temperature optical conductivity of the gapped graphene while we vary the energy gap as well as the frequency of the externally applied field. Although our general formulation can address a variety of nonequilibrium responses of the two-band system, it also facilitates a connection with the phenomenological modeling of nonlinear optical conductivity.

Nonlinear geometrically exact dynamics of hyperelastic pipes conveying fluid: Comparative study of different hyperelastic models

This work presents a comparative analysis of the nonlinear dynamic responses of fluid-conveying pipes modelled by four different phenomenological hyperelastic constitutive models, namely the Mooney-Rivlin model, the Neo-Hookean model, the Yeoh model, and the Ogden model. Based on the strain energy density functions and the exact geometric relation, the geometrically exact dynamic models corresponding to different hyperelastic contitutive models are established. Then the Galerkin's truncation is adopted to transfer the obtained nonlinear integral-partial differential equations into the nonlinear ordinary differential equations. Subsequently, linear dynamic study and finite difference method are taken to explore the natural frequencies and stabilities and nonlinear dynamic responses of the pipe, respectively. And the fitting coefficients for various models obtained from Treloar's experiment data are utilized in the numerical calculation. It is found the Hopf bifurcation and the limit cycle oscillations in the post-flutter status are influenced by the choice of the hyperelastic models, particularly under large flow velocity. However, hyperelastic constitutive models do not exert a significantly extreme influence on the results, which can be attributed to the relatively small strains even though large deformations occur in the pipe. Mathematically, it is proven that the symmetry observed in the pipe's displacement response stems from the symmetry of its cross-section and the inextensibility assumption of the centerline, with hyperelasticity having no effect on this symmetry.

A model of task-level human stepping regulation yields semistable walking.

A simple lateral dynamic walker, with swing leg dynamics and three adjustable input parameters, is used to study how motor regulation affects frontal-plane stepping. Motivated by experimental observations and phenomenological models, we imposed task-level multi-objective regulation targeting the walker's optimal lateral foot placement at each step. The regulator prioritizes achieving step width and lateral body position goals to varying degrees by choosing a mixture parameter. Our model thus integrates a lateral mechanical template, which captures the fundamental mechanics of frontal-plane walking, with a lateral motor regulation template, an empirically verified model of how humans manipulate lateral foot placements in a goal-directed manner. The model captures experimentally observed stepping fluctuation statistics and demonstrates how linear empirical models of stepping dynamics can emerge from first-principles nonlinear mechanics. We find that task-level regulation gives rise to a goal-equivalent manifold in the system's extended state space of mechanical states and inputs, a subset of which contains a continuum of period-1 gaits forming a semistable set: perturbations off of any of its gaits result in transients that return to the set, though typically to different gaits.