Well-defined Physical Meaning Research Articles

A nonlinear elastic-strain hardening model for frozen improved sandy soil under uniaxial compression loading condition

Artificial freezing is one of the most effective methods in the excavation of water-rich soils. This work aims at investigating the influence of cement‑sodium silicate grout (C-S grout) and organic polymer stabilizer (OPS) on the uniaxial compressive strength (UCS), stress-strain curve, and unfrozen water content of frozen sandy soil. A series of uniaxial compression tests and nuclear magnetic resonance (NMR) tests were conducted on the saturated frozen sandy soils improved by C-S grout and OPS (“C-S grout-improved soil” and “OPS-improved soil”) under different negative temperatures (i.e., −5 °C, −10 °C, −15 °C, and −20 °C). Based upon the experiment results and existing stress-strain models, including improved Duncan-Chang model and elastic-strain hardening model, a nonlinear elastic-strain hardening constitutive model for improved soils was proposed, in which each parameter has well-defined physical meaning. The results showed that, as the temperature decreases, the strengths of frozen improved soils gradually increase. The strength of OPS-improved soil first increases and then decreases with the increase of OPS dosage. Contrary to the UCS, the unfrozen water content of two improved soils was observed to gradually decrease with the decrease of temperature. As the OPS dosage increases, the unfrozen water content of improved soils decreases first and then increases. When the strain is <0.2, the stress-strain curves of frozen C-S grout-improved soil exhibits a behavior of yielding first and then hardening after the nonlinear elastic stage, while OPS-improved soil exhibits continuous strain hardening behavior. With temperature and unfrozen water content given, the new nonlinear elastic-strain hardening model can accurately predict the stress-strain behavior of frozen improved soils. This study is helpful to the stability analysis of artificial frozen walls and pre-control of environmental deformation during the excavation of water-rich sandy soils.

On the logarithmic nature of axial dispersion in Darcy flow through heterogeneous porous media

The present study provides novel insights in how spatial velocity variations in a heterogeneous porous medium cause the dispersion of a passive tracer. The study consists of two parts. The first part describes a series of numerical computations of the axial dispersion in the flow through heterogeneous porous media, idealized as Darcy flow through two-dimensional and three-dimensional patchwork geometries of zones with randomized permeability fields. Data on the axial dispersion were obtained using the mean age theory, which transforms the transient advection–diffusion equation into the steady-state mean age field equation, thus reducing the required computational effort by multiple orders of magnitude. This allowed to consider a sufficiently large number of randomizations to obtain a statistically representative ensemble average, as well as to consider sufficiently large systems to reduce the influence of boundary conditions. In the second part, it is shown that the relation between the axial dispersion coefficient and the velocity can be represented as a series, summing up the effect of velocity differences on all length scales, assuming the velocity differences are analogous to white noise. The sum can be closely fitted by a logarithmic law containing only two parameters with a well-defined physical meaning. A similar logarithmic dependency was also obtained by Saffman, Koch, and Brady. However, the logarithmic dependency obtained in the present work emerges from the heterogeneity of the porous medium, whereas the logarithmic dependency in the aforementioned works emerged from the no-slip boundary conditions at solid surfaces.

Utility of FRET in studies of membrane protein oligomerization: The concept of the effective dissociation constant

The activity of many membrane receptors is controlled through their lateral association into dimers or higher-order oligomers. Although Förster resonance energy transfer (FRET) measurements have been used extensively to characterize the stability of receptor dimers, the utility of FRET in studies of larger oligomers has been limited. Here we introduce an effective equilibrium dissociation constant that can be extracted from FRET measurements for EphA2, a receptor tyrosine kinase (RTK) known to form active oligomers of heterogeneous distributions in response to its ligand ephrinA1-Fc. The newly introduced effective equilibrium dissociation constant has a well-defined physical meaning and biological significance. It denotes the receptor concentration for which half of the receptors are monomeric and inactive, and the other half are associated into oligomers and are active, irrespective of the exact oligomer size. This work introduces a new dimension to the utility of FRET in studies of membrane receptor association and signaling in the plasma membrane.

Dimensional regularization, Wilsonian RG, and the naturalness and hierarchy problem

While it is usually stated that dimensional regularization (DR) has no direct physical interpretation, consensus has recently grown on the idea that it might be endowed with special physical properties that would provide the mechanism that solves the naturalness/hierarchy problem. Comparing direct Wilsonian calculations with the corresponding DR ones, we find that DR indeed has a well-defined physical meaning, and we point out its limitations. In particular, our results show that DR cannot provide the solution to the naturalness/hierarchy problem. The absence of too large corrections to the Higgs boson mass is due to a secretly realized fine-tuning, rather than special physical properties of DR. We also investigate these issues within the Wilsonian RG framework and, by comparison with the usual perturbative RG analysis, we show that several popular proposals for the resolution of the problem, commonly considered as physical mechanisms free of fine-tuning, again secretly implement the tuning.

Remaining useful life prediction in embedded systems using an online auto-updated machine learning based modeling

Systems on Chips are increasingly involved in critical equipment in the fields of aeronautics, transportations, and energy. Therefore, monitoring their life cycle is a crucial issue for safety and hazard-prevention. This paper deals with a data-driven method for online prediction of the Remaining Useful Life (RUL) of the safety-critical System-on-Chips (SoC). This method is based on the detection and prediction of drifts in their operating temperatures. The work starts with a description of the formal relationships between temperature drifts and the degradation process of SoCs to justify the choice of the temperature as an indicator of the level of the degradation in the system. Then, temperature-based physical health indicators are constructed using data-driven analytical redundancy. Since temperature varies not just according to the degradation state of the system, but also according to its various normal operating points, data-driven analytical redundancy makes it possible to obtain a health indicator that has a well-defined physical meaning, and which is only sensitive to the SoC degradation process. To predict the remaining useful life of the chip, the trend of the drift is modeled using an auto-regressive neural (NAR) network. The latter is updated online according to the evolution of the temperature drift and the state of the system. Finally, forecasts of the remaining useful life of the SoC are obtained using a combination of temporal projection and threshold data. Simulations and experimental results highlight the effectiveness and accuracy of the proposed approach.

The Evolution of Star Formation Rate Density of Galaxies

We present a semi-analytical calculation of the global star formation density (SFD) by using the well constrained cold dark matter (CDM) halo mass function. Both, halo masses <I>M<SUB>H</SUB></I>(<i>z</i>) and stellar masses <I>M</I>_*(<i>z</i>) are taken from observations of Lyα emitter (LAEs) and/or Lyman break galaxies (LBGs). Most of them, spectroscopically selected, are characterized by high star formation rates. The view of galaxy formation is mainly based on the hierarchical (“botton-up”) cold dark matter model for structure formation. We have used the connection between the halo mass and the star formation rate in galaxies of the halo mass <I>M<SUB>H</SUB></I> at redshift <i>z</i>. Our model has the advantage that we are able to calculate the global star formation rate <i>ρ</i>_*(<i>z</i>) (in <I>M</I>ʘ<i>y</i>-1<i>Mpc</i>-3) by a closed equation. All parameters (<I>M<SUB>H</SUB></I>; <I>M</I>_* and <i>n</i>) have a well-defined physical meaning. From the CDM spectrum, the power law index of the halo mass function is well constrained. Our results are compiled in Table 1 and Figure 1. Here our results are compared with observations and hydrodynamical simulations. The physical meaning of the evolution of comoving cosmic star density as a function of redshift with three epochs is discussed. We find a good agreement between the SFD inferred from observations and our model in the range of redshifts <i>z</i> = 0 - 7.

Molecular Understanding of Calorimetric Protein Unfolding Experiments

Protein unfolding is a dynamic cooperative equilibrium between short lived protein conformations. The Zimm-Bragg theory is an ideal algorithm to handle cooperative processes. Here, we extend the analytical capabilities of the Zimm-Bragg theory in two directions. First, we combine the Zimm-Bragg partition function Z(T) with statistical-mechanical thermodynamics, explaining the thermodynamic system properties enthalpy, entropy and free energy with molecular parameters only. Second, the molecular enthalpy h0 to unfold a single amino acid residue is made temperature-dependent. The addition of a heat capacity term cv allows predicting not only heat denaturation, but also cold denaturation. Moreover, it predicts the heat capacity increase ΔC° p in protein unfolding. The theory is successfully applied to differential scanning calorimetry experiments of proteins of different size and structure, that is, gpW62 (62aa), ubiquitin (74aa), lysozyme (129aa), metmyoglobin (153aa) and mAb monoclonal antibody (1290aa). Particular attention was given to the so far neglected free energy. The DSC experiments reveal a zero free energy for the native protein with an immediate decrease to negative free energies upon cold and heat denaturation. This trapezoidal shape is precisely reproduced by the Zimm-Bragg theory, whereas the so far applied non-cooperative 2-state model predicts a parabolic shape with a positive free energy maximum of the native protein. We demonstrate that the molecular parameters of the Zimm-Bragg theory have a well-defined physical meaning. In addition to predicting protein stability, independent of protein size, they yield estimates of unfolding kinetics and can be connected to molecular dynamics calculations.

Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 2: Model Uncertainty and Optimal Parameterization

ABSTRACTIn a companion article, Safarshahi and Morozov (2020) argued that construction of distance- and frequency-dependent models for seismic-wave amplitudes should include four general elements: (1) a sufficiently detailed (parametric or nonparametric) model of frequency-independent spreading, capturing all essential features of observations; (2) model parameters with well-defined and nonoverlapping physical meanings; (3) joint inversion for multiple parameters, including the geometrical spreading, Q, κ, and source and receiver couplings; and (4) the use of additional dataset-specific criteria of model quality, while fitting the logarithms of seismic amplitudes. Some of these elements are present in existing models, but, taken together, they are poorly understood and require an integrated approach. Such an approach was illustrated by detailed analysis of an S-wave amplitude dataset from southern Iran. The resulting model is based on a frequency-independent Q, and matches the data closer than conventional models and across the entire epicentral-distance range. Here, we complete the analysis of this model by evaluating the uncertainties and trade-offs of its parameters. Two types of trade-offs are differentiated: one caused by a (possibly) limited model parameterization and the second due to statistical data errors. Data bootstrapping shows that with adequate parameterization, attenuation properties Q, κ, and geometrical spreading parameters are resolved well and show moderate trade-offs due to measurement errors. Using the principal component analysis of these trade-offs, an optimal (trade-off free) parameterization of seismic amplitudes is obtained. By contrast, when assuming theoretical values for certain model parameters and using multistep inversion procedures (as commonly done), parameter trade-offs increase dramatically and become difficult to assess. In particular, the frequency-dependent Q correlates with the distribution of the source and receiver-site factors, and also with biases in the resulting median data residuals. In the new model, these trade-offs are removed using an improved parameterization of geometrical spreading, constant Q, and model quality constraints.

Shape-Based Nonlinear Model Reduction for 1D Conservation Laws

We present a novel method for model reduction of one-dimensional conservation law to the dynamics of the parameters describing the approximate shape of the solution. Depending on the parametrization, each parameter has a well-defined physical meaning. The obtained ODE system can be used for the estimation and control purposes. The model reduction is performed by minimizing the divergence of flows between the original and reduced systems, and we show that this is equivalent to the minimization of the Wasserstein distance derivative. The method is then tested on the heat equation and on the LWR (Lighthill-Whitham-Richards) model for vehicle traffic.

Scatterer recognition via analysis of speckle patterns

Light scattering due to interaction with a material has long been known to create speckle patterns. We have demonstrated that even though speckle patterns from different objects are very similar, they contain minute dissimilarities that can be used to differentiate between the originating scatterers. We first approached this problem using a convolutional neural network—a deep learning algorithm—to show that indeed specific speckle patterns can be linked to the respective materials creating them. We then progressed to use recorded speckle patterns created from different materials in order to measure statistical parameters that possess a well-defined physical meaning. Using these parameters gave similar scatterer recognition abilities while gaining insight on the physical reasons for these material-dependent statistical deviations.

Magneto-dependent stress relaxation of magnetorheological gels

The stress relaxation behaviors of magnetorheological (MR) gels under stepwise shear loading are systematically investigated. The particle-enhanced effect, the magneto-induced effect, and the temperature-enhanced effect on the stress relaxation of MR gels (MRG) are discussed. For further analysis of the magneto-induced stress relaxation mechanism in MRG, a phenomenological model is established to describe the stress relaxation behavior of the matrix and the magnetic particle chains. All characteristic parameters introduced in the model, i.e. relaxation time, instantaneous modulus, and stable modulus, have well-defined physical meanings and are fitted based on the experimental results. The influence of each parameter on the macroscopic response is discussed and it is found that the relaxation stress induced by the magneto-mechanical coupling effect plays an important role in the stress relaxation process of MRG.

From Koopman\u2013von Neumann theory to quantum theory

Koopman and von Neumann (KvN) extended the Liouville equation by introducing a phase space function S^{(K)}(q,p,t) whose physical meaning is unknown. We show that a different S(q, p, t), with well-defined physical meaning, may be introduced without destroying the attractive “quantum-like” mathematical features of the KvN theory. This new S(q, p, t) is the classical action expressed in phase space coordinates. It defines a mapping between observables and operators which preserves the Lie bracket structure. The new evolution equation reduces to Schrödinger’s equation if functions on phase space are reduced to functions on configuration space. This new kind of “quantization” does not only establish a correspondence between observables and operators, but provides in addition a derivation of quantum operators and evolution equations from corresponding classical entities. It is performed by replacing frac{partial }{partial p} by 0 and p by frac{hbar }{imath } frac{partial }{partial q}, thus providing an explanation for the common quantization rules.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory.

We describe a diabatic-at-construction (DAC) strategy for defining diabatic states to determine the adiabatic ground and excited electronic states and their potential energy surfaces using the multistate density functional theory (MSDFT). The DAC approach differs in two fundamental ways from the adiabatic-to-diabatic (ATD) procedures that transform a set of preselected adiabatic electronic states to a new representation. (1) The DAC states are defined in the first computation step to form an active space, whose configuration interaction produces the adiabatic ground and excited states in the second step of MSDFT. Thus, they do not result from a similarity transformation of the adiabatic states as in the ATD procedure; they are the basis for producing the adiabatic states. The appropriateness and completeness of the DAC active space can be validated by comparison with experimental observables of the ground and excited states. (2) The DAC diabatic states are defined using the valence bond characters of the asymptotic dissociation limits of the adiabatic states of interest, and they are strictly maintained at all molecular geometries. Consequently, DAC diabatic states have specific and well-defined physical and chemical meanings that can be used for understanding the nature of the adiabatic states and their energetic components. Here we present results for the four lowest singlet states of LiH and compare them to a well-tested ATD diabatization method, namely the 3-fold way; the comparison reveals both similarities and differences between the ATD diabatic states and the orthogonalized DAC diabatic states. Furthermore, MSDFT can provide a quantitative description of the ground and excited states for LiH with multiple strongly and weakly avoided curve crossings spanning over 10 Å of interatomic separation.

Statistical Assessment of Hydraulic Properties of Unsaturated Soils

The availability of statistical values for soil parameters is essential in reliability-based geotechnical design and sensitivity analysis. Unfortunately, there are few statistical studies available about unsaturated soil parameters. The primary objective of this paper is to present a methodology for the statistical assessment of hydraulic properties of unsaturated soil and to present the results of a statistical study carried out using a large database of soil properties. Two fundamental unsaturated soil properties are considered; namely, the soil-water characteristic curve (SWCC) and the hydraulic conductivity function. Appropriate nonlinear functions and fitting parameters with well-defined and unique physical and/or geometrical meanings were adopted. The main contribution of this article is the establishment of central tendency measures, standard deviations, and correlation coefficients for the unsaturated soil parameters, considering soil datasets grouped according to soil texture. It was determined based on the analyses results that the air-entry value, primary SWCC slope, residual SWCC slope, saturated hydraulic conductivity, and hydraulic conductivity function slope could be well described using lognormal probability density functions. Finally, general guidelines are provided regarding the statistical values to be adopted for the unsaturated soil properties studied.

Introduction of simplex-informational descriptors for QSPR analysis of fullerene derivatives

Rational approach towards the QSAR/QSPR modeling requires the selection of descriptors to be computationally efficient and physically and chemically meaningful. However, fullerenes and their derivatives represent challenging compounds in terms of QSPR modeling and there is a lack of efficient and comprehensible descriptors for them. Based on existing informational field model and simplex representation of molecular structure approach, an outline of descriptoral representation for fullerenes was developed. Solubility of fullerene derivatives was chosen as target property for the estimation of descriptors’ efficacy. Developed model provides well-defined physical meanings and obtained results are interpreted in terms of basic molecular properties.

On the estimation of the structural index from low-pass filtered magnetic data

The estimation of the structural index and of the depth to the source is the main task of many popular methods used to analyze potential field data, such as Euler deconvolution. However, these estimates are unstable even in the presence of a weak amount of noise, and Euler deconvolution of noisy data leads to an underestimation of structural index and depth. We have studied how the structural index and depth estimates are affected by applying low-pass filtering to the data. Physically based low-pass filters, such as upward continuation and integration, have been shown to be the best choice over a range of altitudes (upward continuation) or orders (integration filters), mainly because their outputs have a well-defined physical meaning. In contrast, mathematical low-pass filters require that the filter parameters be tuned carefully by means of several trial tests to produce optimally smoothed fields. The C-norm criterion is a reliable strategy to produce a stabilized vertical derivative, and we discourage Butterworth filters because they tend to a vertical integral filter, for a high cutoff wavenumber, thus complicating the interpretation of the estimated structural index. We found that the estimated structural index and depth to source increase proportionally with the amount of smoothing, unless in the case of overfiltering. In that case, the severe distortion of the original field may cause a decrease of the estimated structural index and depth to source.

Decay of Phosphorescent Warning Design on Textile Substrates

The present paper reports the decay of phosphorescence. Besides its interest for measurement techniques, the knowledge of phosphorescence decay curves is, in itself, of fundamental importance in physics and photochemistry. In point of view of development new functional warning design, which is usable for sportswear and outdoor clothes generally, phosphorescence brings additional impulse for safety improvement. On the basis of phosphorescence spectral effectiveness function was shown effect of different colors of used background on phosphorescence visibility. For instance, the agreement, found in this work, between decay curves, kinetic equations and background reflectance give experimental evidence that the theoretical model for the anisotropy decay approximates to a three-exponential function. This model has a few fitting parameters with well-defined physical meanings as compared to the current empirical one.

New approach to kinetic description of partially-reversible catalytic processes: Kinetics of the CH3OH synthesis at Zn/Cu-containing catalysts as an example

A new ideology and procedure for consideration of the contribution of inverse reactions to the analytic descriptions of the kinetics of heterogeneous catalytic processes (gross-reactions, GRs), which proceed with rate-determining steps (RDSs) and residual equilibrium portions (ExEqms), are proposed instead of the ordinary ideology and procedure that use the notion of the rate-determining step stoichiometric number (RDSSN). Instead of the RDSSNs, the notion of the matching coefficients (MCs) of stoichiometric nature is used. As was first shown by Weller [Catal Rev – Sci Eng 1992;34:227–80], the notion of the RDSSNs has no well-defined physical meaning and the repeated attempts of their experimental measurements gave no reproducible results. The MCs co-ordinate RDS, ExEqm, and GR equations with each other; they are determinable for any GR by a simple chemico-algebraic procedure. The procedures for determination of their values and deduction of kinetic equations are considered by the example of the CH3OH synthesis from H2 and carbon oxides at Zn/Cu-containing catalysts. An improved kinetic equation is deduced and successfully applied to description of available data on the CH3OH synthesis at 0.1 (453 and 473K) and 4.5 (513K) MPa.

Modeling hydrodynamic properties of open-cell metal foams

Modeling the hydrodynamics of open-cell aluminum foam still is a challenging task because of the large range of length-scales, own to the physical phenomena which occur in the complex structure. Upscaling the classical conservation equations is a promising approach, but introduces the problem of modeling closure terms. This is dealt with via the well-known porous properties, i.e., permeability and inertial loss factor.Derivation of these properties is commonly done by linking pressure drop data to velocity via a second order interpolation. This, however, introduces significant deviation between the available data set, up to anorder of magnitude, which in turn results in difficulties to predict pressure drop during desing the desing phase of an applicaiton. As the closure terms have a well-defined physical meaning, it should be possible to compute them with better accuracy. This forms the topic of this paper.

Study of Numerical Method for Magnetic Shielding Problem Considering Actual Measurement of Magnetic Environment

A critical consideration in the optimal design of magnetically shielded rooms is the manner in which an external magnetic field, which should be shielded, is imposed on a target area. In this paper, we examined the possibility of applying the <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> method (the method of which the magnetic field <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> in the analyzed region is given) to the shielding problem with a measurement-based magnetic field, which includes an irrotational field component as noise, and, therefore, is inconsistent with Maxwell's equations. We show that the <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> method has a well-defined physical meaning for such an irrotational field component. Furthermore, we explain why the convergence and the accuracy of the <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> method are better than those of the A method.