Semi-phenomenological Models Research Articles

Characterization, modeling and prediction of foam-formed softwood fiber sound absorption

The transition towards building materials with low or negative carbon-dioxide footprint is a pressing topic in nowadays society. Materials for thermal and acoustic insulation are among those attracting a growing number of research publications. Commonly used materials in the building sector are mostly mineral wools which demand huge amounts of energy during production by melting sand or stone. Cellulose-based materials are a promising substitute for the current market leaders. These materials are able to reach negative carbon footprints due to low embodied energy and their ability to store carbon dioxide in buildings for decades. Predicting the sound absorption behavior prior to manufacturing can further improve their usability. This study delves into the prediction and characterization of wood-based pulp fiber foams and their acoustic properties. By comparing analytical models, semi-phenomenological models and experimental measurements the prediction of sound absorption based on fiber diameter and bulk density is evaluated. The findings reveal that refining a recent analytical model for natural fibers through parameter fitting to non-acoustic parameters yields improved accuracy in predicting sound absorption curves. While the accuracy declines towards higher densities, this work lays the groundwork to create environmentally sustainable sound absorbers with carefully tailored sound absorption properties.

Inference of the acoustic properties of transversely isotropic porous materials

Transversely isotropic porous materials are well represented by equivalent fluid models based on semi-phenomenological models such as the Johnson-Champoux-Allard-Lafarge (JCAL) model and a set of material parameters. Direct measurements of these parameters, however, are often difficult or time consuming. As an alternative, inverse estimation methods provide a simple and fast framework to identify the JCAL model parameters, since they can be performed on single impedance tube measurements. In this work, we present a stochastic inverse identification method of the JCAL parameters for transversely isotropic materials. We consider the flow resistance and characteristic viscous length and the static tortuosity to be anisotropic and the frame to be fully rigid, resulting in nine unique parameters to be identified. The method is based on reflection factor measurements of a material in different orientations corresponding the transverse and isotropic principal axes. Hence, a priori knowledge of the orientation of the principal axes of the material is required. Results of the parameter inference are presented based on experimental data for a glass wool sample.

Numerical Equivalent Acoustic Material for Air-Filled Porous Absorption Simulations in Finite Different Time Domain Methods: Design and Comparison

Extracting the microscopic parameters of a porous material is a complex task, and attempts have been made to develop models that can simulate their characteristics, gathering the least amount of information possible. As a case in point, tests to evaluate macroscopic behaviors such as tortuosity, which depends directly on the microscopic fluid velocities, are highly susceptible to generate errors if the precision of the measurement devices is not correct, and the same goes for the other parameters. For this reason, in this paper, a sound propagation model in porous materials with a rigid frame is presented based on a local theory, which tries to simplify, even more, the way to obtain the basic characteristics of porous materials, such as their absorption coefficient at normal and random incidence, and their normal surface impedance. The proposed linearized equivalent fluid model presents four phenomenological coefficients, which characterize acoustic propagation trough the material. Their values are obtained from the material thickness and a measurement in an impedance tube following the ISO 10534 standard. Thus, what is only required is the measured absorption coefficient, either on one third or one octave bands, to fully represent the acoustic behavior in the finite different in time domain (FDTD) method. The model has been simulated with FDTD in porous and fibrous kernels, and the results show a strong agreement with the laboratory measurements and with the analytical results calculated with well-established semi-phenomenological models.

Optimal design of fibrous materials for sound absorption

Fibrous materials, which are typical porous materials, play a crucial role in noise control and improving sound quality in the building and automotive industries. Researchers have extensively investigated the acoustic properties of fibrous materials, including both natural and synthetic fibers. Additionally, various numerical and semi-phenomenological models have been employed to accurately predict their acoustic properties. Despite the existence of accurate models, most research on the acoustic properties of fibrous materials has been experiment-oriented. Furthermore, very few studies have focused on reliable and straightforward approaches to optimize these properties and guide the preparation process of fibrous materials. This work aims to develop a robust optimization approach for single-layer and multi-layer fibrous materials by combining numerical optimization methods with numerical and semi-phenomenological acoustic models. The ultimate goal of this optimization approach is to provide designed parameters for fabricating fibrous materials with excellent sound absorption properties. To validate and refine the optimization approach, the fabricated fibrous materials will be thoroughly measured.

Multi-model sequential analysis of MRI data for microstructure prediction in heterogeneous tissue

We propose a general method for combining multiple models to predict tissue microstructure, with an exemplar using in vivo diffusion-relaxation MRI data. The proposed method obviates the need to select a single ’optimum’ structure model for data analysis in heterogeneous tissues where the best model varies according to local environment. We break signal interpretation into a three-stage sequence: (1) application of multiple semi-phenomenological models to predict the physical properties of tissue water pools contributing to the observed signal; (2) from each Stage-1 semi-phenomenological model, application of a tissue microstructure model to predict the relative volumes of tissue structure components that make up each water pool; and (3) aggregation of the predictions of tissue structure, with weightings based on model likelihood and fractional volumes of the water pools from Stage-1. The multiple model approach is expected to reduce prediction variance in tissue regions where a complex model is overparameterised, and bias where a model is underparameterised. The separation of signal characterisation (Stage-1) from biological assignment (Stage-2) enables alternative biological interpretations of the observed physical properties of the system, by application of different tissue structure models. The proposed method is exemplified with human prostate diffusion-relaxation MRI data, but has potential application to a wide range of analyses where a single model may not be optimal throughout the sampled domain.

Modeling Progression of Single Cell Populations Through the Cell Cycle as a Sequence of Switches.

Cell cycle is a biological process underlying the existence and propagation of life in time and space. It has been an object for mathematical modeling for long, with several alternative mechanistic modeling principles suggested, describing in more or less details the known molecular mechanisms. Recently, cell cycle has been investigated at single cell level in snapshots of unsynchronized cell populations, exploiting the new methods for transcriptomic and proteomic molecular profiling. This raises a need for simplified semi-phenomenological cell cycle models, in order to formalize the processes underlying the cell cycle, at a higher abstracted level. Here we suggest a modeling framework, recapitulating the most important properties of the cell cycle as a limit trajectory of a dynamical process characterized by several internal states with switches between them. In the simplest form, this leads to a limit cycle trajectory, composed by linear segments in logarithmic coordinates describing some extensive (depending on system size) cell properties. We prove a theorem connecting the effective embedding dimensionality of the cell cycle trajectory with the number of its linear segments. We also develop a simplified kinetic model with piecewise-constant kinetic rates describing the dynamics of lumps of genes involved in S-phase and G2/M phases. We show how the developed cell cycle models can be applied to analyze the available single cell datasets and simulate certain properties of the observed cell cycle trajectories. Based on our model, we can predict with good accuracy the cell line doubling time from the length of cell cycle trajectory.

Sound Absorption Properties and Accuracy of Prediction Models on Natural Fiber Based Nonwoven Materials

ABSTRACT In this work, the sound absorption performance of cotton fiber- and wool fiber-based nonwoven fabrics as well as one pure polyester nonwoven fabric were investigated. The Brüel & Kjær two-microphone impedance tube is used to conduct the measurement in the frequency of 50–6400 Hz. Empirical and semi-phenomenological models are used to predict the acoustical impedance and sound absorption coefficient of natural fiber-based nonwoven fabrics. The nonwoven fabric containing 60 wt.% cotton fiber and 40 wt.% polyester fiber shows a comparable sound absorption ability compared with the polyester nonwoven. At the same time, this property for wool-based nonwoven is relatively poor. Moreover, the prediction is still not acceptable, although the Voronina model exhibits better prediction for the natural fiber-based nonwoven materials compared with the other two prediction models. The modification on the Miki model was conducted to fit the cotton and wool fiber-based nonwovens. The modified Miki model demonstrates an accurate prediction on surface impedance and sound absorption coefficient for the natural fiber-based nonwovens.

Physical parameters influence on the transmitted signal through a rigid porous medium in the low-frequency range of ultrasound

The acoustic characterization of porous materials with rigid structure plays an important role in the prediction of the acoustic behavior of these media. In order to obtain an accurate prediction of its response as a function of frequency, several parametric models have been proposed. However, semi-phenomenological models are the most used to describe the acoustic behavior of porous materials with rigid or flexible structures according to a certain number of macroscopic physical properties related to the internal structure of the material and essential for their valuation. Among these models, the one proposed by Johnson et al. to describes the complex density of an acoustic porous material with an immobile skeleton having arbitrary pore shapes. The objective of this work is to study the effect of these parameters involved in Johnson's model as well as other new parameters, recently introduced by Sadouki [ Phys. Fluids 33, (2021)), on the transmitted signal in the low-frequency regime of ultrasound.

Nonclassical Exciton Diffusion in Monolayer WSe_{2}.

We experimentally demonstrate time-resolved exciton propagation in a monolayer semiconductor at cryogenic temperatures. Monitoring phonon-assisted recombination of dark states, we find a highly unusual case of exciton diffusion. While at 5K the diffusivity is intrinsically limited by acoustic phonon scattering, we observe a pronounced decrease of the diffusion coefficient with increasing temperature, far below the activation threshold of higher-energy phonon modes. This behavior corresponds neither to well-known regimes of semiclassical free-particle transport nor to the thermally activated hopping in systems with strong localization. Its origin is discussed in the framework of both microscopic numerical and semiphenomenological analytical models illustrating the observed characteristics of nonclassical propagation. Challenging the established description of mobile excitons in monolayer semiconductors, these results open up avenues to study quantum transport phenomena for excitonic quasiparticles in atomically thin van der Waals materials and their heterostructures.

Semiphenomenological model to predict hardening of solid–liquid–liquid systems by liquid bridges

In this study, we developed two semiphenomenological models to quantitatively predict the rheological properties of capillary suspensions. These models can be used to estimate the critical volume fraction of an additional immiscible fluid above which liquid bridges have formed between all neighboring particles, causing gelation. The models can also be used to estimate the numerical value of the yield stress. This model was derived from the mass balance between the net volume of the liquid bridge and the volume fraction of the secondary fluid assuming monodisperse particles and a cylindrical liquid bridge. The yield stress was constructed based on Rumpf’s equation. The calculation results demonstrated good agreement with the experimental data. We also used the developed model to investigate the effect of particle size on the yield stress. This model qualitatively described the experimental data and reference data, and revealed the mechanism of the particle size dependence of the yield stress. The model applies to capillary suspensions in the pendular state.

Finite element modeling of fluid-saturated metallic foams from micro-computed tomography

Open-cell metallic foams are high stiffness-to-weight cellular materials whose microstructure allows for saturation of viscous liquid. Such a composite has advantages for underwater sound absorption over traditional rubbers due to minimal compression from hydrostatic pressure, composite tunability, and potential for specific gravity less than one. Semi-phenomenological and hybrid numerical models have been shown to predict sound absorption performance of metallic foams, however difficulty arises in determining parameters for the numerical models such as tortuosity, viscous characteristic length, thermal characteristic length, and flow resistivity. Such models also assume that the porous frame is rigid, an assumption valid for only a limited frequency range. In this presentation, finite element models of fluid-saturated metallic foams are created from micro-computed tomography scans and analyzed to determine sound absorption performance. The advantage of this method is that the entire foam microstructure and surrounding fluid can be accurately modeled through a finite element mesh. In addition, experimental measurement of model parameters is not required and the rigid frame assumption can be removed.

Three-Nucleon Forces and Triplet Pairing in Neutron Matter

The existence of superfluidity of the neutron component in the core of a neutron star, associated specifically with triplet $P-$wave pairing, is currently an open question that is central to interpretation of the observed cooling curves and other neutron-star observables. Ab initio theoretical calculations aimed at resolving this issue face unique challenges in the relevant high-density domain, which reaches beyond the saturation density of symmetrical nuclear matter. These issues include uncertainties in the three-nucleon (3N) interaction and in the effects of strong short-range correlations -- and more generally of in-medium modification of nucleonic self-energies and interactions. A survey of existing solutions to the gap equations in the triplet channel shows that the separate or combined impacts of 3N forces, coupled channels, and mass renormalization range from moderate to strong to devastating, thus motivating a detailed analysis of the competing effects. In the present work we track the effects of the 3N force and in-medium modifications in the representative case of the $^3P_2$ channel, based on the Argonne V18 two-nucleon (2N) interaction supplemented by 3N interactions of the Urbana IX family. Sensitivity of the results to the input interaction is clearly demonstrated, while consistency issues arise with respect to the simultaneous treatment of 3N forces and in-medium effects. We consider this pilot study as the first step towards a systematic and comprehensive exploration of coupled-channel $^3P F_2$ pairing using a broad range of 2N and 3N interactions from the current generation of refined semi-phenomenological models and models derived from chiral effective field theory.

Sound propagation in porous materials with annular pores.

Long-wavelength sound propagation in porous materials with annular pores is investigated in this paper. Closed-form analytical expressions for the effective acoustical properties of this type of material were obtained. These are compared with both direct numerical calculations of the effective properties and their calculations obtained by using semi-phenomenological models. Analytical expressions for the input parameters of the latter, i.e., static viscous and thermal permeabilities, viscous and thermal characteristic lengths, and tortuosity, are also provided. The introduced model is successfully validated by comparing its predictions with measured data taken from literature. A parametric analysis that allows highlighting the influence of the different geometrical parameters of porous materials with annular pores on their sound absorptive properties is also presented.

Evidence of protein-free homology recognition in magnetic bead force-extension experiments.

Earlier theoretical studies have proposed that the homology-dependent pairing of large tracts of dsDNA may be due to physical interactions between homologous regions. Such interactions could contribute to the sequence-dependent pairing of chromosome regions that may occur in the presence or the absence of double-strand breaks. Several experiments have indicated the recognition of homologous sequences in pure electrolytic solutions without proteins. Here, we report single-molecule force experiments with a designed 60 kb long dsDNA construct; one end attached to a solid surface and the other end to a magnetic bead. The 60 kb constructs contain two 10 kb long homologous tracts oriented head to head, so that their sequences match if the two tracts fold on each other. The distance between the bead and the surface is measured as a function of the force applied to the bead. At low forces, the construct molecules extend substantially less than normal, control dsDNA, indicating the existence of preferential interaction between the homologous regions. The force increase causes no abrupt but continuous unfolding of the paired homologous regions. Simple semi-phenomenological models of the unfolding mechanics are proposed, and their predictions are compared with the data.

Prediction of acoustic foam properties by numerical simulation of polyurethane foaming process

This work aims to model and to simulate the polyurethane foaming process. Models taking into account the two main chemical reactions of the formation of polyurethane, the exothermic effect of these reactions as well as the thermo-rheo-kinetic coupling characterizing this process are proposed and implemented in the software NOGRID-points based on a meshless method (Finite Pointset Method). A prediction of some acoustic foam characteristics is also proposed based on the results of the numerical simulation of the foaming process and semi-phenomenological models.

Visco-thermal dissipations in heterogeneous porous media

Semi-phenomenological models have been widely used since the 1990’s for modeling visco-thermal dissipations of acoustical energy through porous media. These dissipations are taken into account by two complex frequency-dependent functions (the dynamic density ρeq (ω) and the dynamic bulk modulus Keq (ω)), which are analytically derived from macroscopic parameters. Other models were derived for modeling perforated plates [J. Sound Vib. 303 (2007)], double porosity media [J. Acoust. Soc. Am. 114(1) (2003)] or, more recently, porous composites made of porous inclusions in a substrate porous media [Acta Acoust. 96 (2010)]. So far, this latter model is not able to consider the shape of the host and the client media. This model can neither be extended to limiting cases of perforated plate model nor double porosity model. Based on a modified equivalent fluid model, this work proposes a unified model which accounts, analytically, for the shape of the inclusions, might they be porous or not. This model enables to describe the acoustic behavior of any kind of composite media from perforated plates to arbitrarily shaped porous composites including configurations of porous inclusions in solid matrix or double porosity media. In addition, possible pressure interactions between the substrate material and the inclusions are accounted for.

Investigations on the sensitivity of the relationships between sound absorption characteristics and microstructure related parameters for polyurethane foams

Straightforward semi-phenomenological models have been developed for highly porous polyurethane foams to predict the macroscopic non-acoustic parameters involved in the classical Johnson-Champoux-Allard model (i.e., porosity, airflow resistivity…) from microstructure properties (i.e., strut length, strut thickness, and reticulation rate). These microstructure properties are measured using sophisticated optical methods (i.e., optical microscope, SEM) and a large variability can be observed due to great complexity of the 3D microstructure; variability also depends on the precision of the measurement device. This work investigates how the variability associated with the model inputs affects the model outputs (i.e., non-acoustic parameters, surface impedance, and sound absorption coefficient). The sensitivity analysis is based on the Fourier Amplitude Sensitivity Test (FAST). It helps quantify the correlation between the input parameters and identify the parameters contributing the most to output variability, thus requiring precise measurement. This study illustrates the preponderant impact of the reticulation rate (i.e., open pore content) on acoustic performances and guides the user on the required optical measurement device.

A semi-phenomenological model to predict the acoustic behavior of fully and partially reticulated polyurethane foams

This paper proposes simple semi-phenomenological models to predict the sound absorption efficiency of highly porous polyurethane foams from microstructure characterization. In a previous paper [J. Appl. Phys. 110, 064901 (2011)], the authors presented a 3-parameter semi-phenomenological model linking the microstructure properties of fully and partially reticulated isotropic polyurethane foams (i.e., strut length l, strut thickness t, and reticulation rate Rw) to the macroscopic non-acoustic parameters involved in the classical Johnson-Champoux-Allard model (i.e., porosity ϕ, airflow resistivity σ, tortuosity α∝, viscous Λ, and thermal Λ′ characteristic lengths). The model was based on existing scaling laws, validated for fully reticulated polyurethane foams, and improved using both geometrical and empirical approaches to account for the presence of membrane closing the pores. This 3-parameter model is applied to six polyurethane foams in this paper and is found highly sensitive to the microstructure characterization; particularly to strut's dimensions. A simplified micro-/macro model is then presented. It is based on the cell size Cs and reticulation rate Rw only, assuming that the geometric ratio between strut length l and strut thickness t is known. This simplified model, called the 2-parameter model, considerably simplifies the microstructure characterization procedure. A comparison of the two proposed semi-phenomenological models is presented using six polyurethane foams being either fully or partially reticulated, isotropic or anisotropic. It is shown that the 2-parameter model is less sensitive to measurement uncertainties compared to the original model and allows a better estimation of polyurethane foams sound absorption behavior.

The hard X-ray emission of X Persei

We present an analysis of the spectral properties of the peculiar X-ray pulsar X Per based on INTEGRAL observations. We show that the source exhibits an unusually hard spectrum and is confidently detected by ISGRI up to more than 100 keV. We find that two distinct components may be identified in the broadband 4-200 keV spectrum of the source. We interpret these components as the result of thermal and bulk Comptonization in the vicinity of the neutron star and describe them with several semi-phenomenological models. The previously reported absorption feature at ~30 keV is not required in the proposed scenario and therefore its physical interpretation must be taken with caution. We also investigated the timing properties of the source in the framework of existing torque theory, concluding that the observed phenomenology can be consistently explained if the magnetic field of the neutron star is ~10^14 G.

5d–4f luminescence of Ce 3+, Gd 3+ and Lu 3+ in LiCaAlF 6

The emission and excitation spectra as well as decay kinetics of luminescence due to 5d–4f transitions in Ce 3+, Gd 3+ and Lu 3+ ions doped into LiCaAlF 6 crystals have been analyzed with high spectral and time resolution using synchrotron radiation for excitation. The rich fine structure originating from electronic origins of transitions and their phonon replica has been well resolved and identified. Experimental data are compared with the spectra simulated in the framework of the semiphenomenological models of the crystal field and the crystal lattice dynamics.