Inhomogeneous Model Research Articles

Numerical Investigation on Fracture Mechanisms and Energy Evolution Characteristics of Columnar Jointed Basalts With Different Model Boundaries and Confining Pressures

To reveal the mechanical mechanisms and energy release characteristics underlying progressive failure of columnar jointed basalts (CJBs) with various model boundaries and confining pressures, by combining the meso-damage mechanics, statistical strength theory, and continuum mechanics, inhomogeneous CJB models with different dip angles to the column axis are constructed. In the cases of plane stress, plane strain, and between plane stress and plane strain, the gradual fracture processes of CJBs are simulated under different confining pressures and the acoustic emission (AE) rules are obtained. The results show that: 1) in the case of plane stress, the fracture process of CJBs along direction I orthogonal to the column axis: at the initial stage of loading, the vertical joints and the transverse joints in the CJB specimen are damaged. Then, more columns in the upper middle part are cracked; 2) in the case between plane stress and plane strain, the fracture process of CJBs along the direction parallel to the column axis: at the initial stage of loading, the columnar joints are damaged. Then, the area of the damaged and broken columns at the top of the specimen increases and the crushing degree intensifies; 3) for the case between plane stress and plane strain, the AE energy accumulation before the peak stress is higher than the plane strain state along the direction orthogonal to the column axis. Meanwhile, along the direction parallel to the column axis, this value becomes larger when changing from the state between plane stress and plane strain to the plane strain state. These achievements will certainly improve our understanding of the fracture mechanism and energy evolution of CJBs and provide valuable insights into the instability precursor of CJBs.

BiGONLight: light propagation with bilocal operators in numerical relativity

BiGONLight, Bilocal Geodesic Operators framework for Numerical Light propagation, is a new tool for light propagation in numerical relativity. The package implements the bilocal geodesic operators formalism, a new framework for light propagation in general relativity. With BiGONLight it is possible to extract observables such as angular diameter distance, luminosity distance, magnification as well as new real-time observables like parallax and redshift drift within the same computation. As a test-bed for our code we consider two exact cosmological models, the ΛCDM and the inhomogeneous Szekeres model, and a simulated dust Universe. All our tests show an excellent agreement with known results.

Heat Transfer of Nanomaterial over an Infinite Disk with Marangoni Convection: A Modified Fourier’s Heat Flux Model for Solar Thermal System Applications

The demand for energy due to the population boom, together with the harmful consequences of fossil fuels, makes it essential to explore renewable thermal energy. Solar Thermal Systems (STS’s) are important alternatives to conventional fossil fuels, owing to their ability to convert solar thermal energy into heat and electricity. However, improving the efficiency of solar thermal systems is the biggest challenge for researchers. Nanomaterial is an effective technique for improving the efficiency of STS’s by using nanomaterials as working fluids. Therefore, the present theoretical study aims to explore the thermal energy characteristics of the flow of nanomaterials generated by the surface gradient (Marangoni convection) on a disk surface subjected to two different thermal energy modulations. Instead of the conventional Fourier heat flux law to examine heat transfer characteristics, the Cattaneo–Christov heat flux (Fourier’s heat flux model) law is accounted for. The inhomogeneous nanomaterial model is used in mathematical modeling. The exponential form of thermal energy modulations is incorporated. The finite-difference technique along with Richardson extrapolation is used to treat the governing problem. The effects of the key parameters on flow distributions were analyzed in detail. Numerical calculations were performed to obtain correlations giving the reduced Nusselt number and the reduced Sherwood number in terms of relevant key parameters. The heat transfer rate of solar collectors increases due to the Marangoni convection. The thermophoresis phenomenon and chaotic movement of nanoparticles in a working fluid of solar collectors enhance the temperature distribution of the system. Furthermore, the thermal field is enhanced due to the thermal energy modulations. The results find applications in solar thermal exchanger manufacturing processes.

Image Force Corrections to Tung’s Inhomogeneous Schottky Barrier Model

The popular Tung model for Schottky barrier inhomogeneity considers how low-barrier patches (embedded in a high barrier background) impact the diode current. However, Tung's model fails to account for the image-force effect. We analyze how the image force alters the current through an inhomogeneous barrier and find that, in some circumstances, it will smooth the barrier, such that the current will effectively be that of a homogeneous diode. We also show that for a distribution of defect barriers and/or sizes, the diode current can be intermediate between that of a homogeneous diode and a diode dominated by the low-barrier patches. We calculate the parameter values associated with this transitional region. A survey of existing literature applications of Tung's model shows that many diodes are actually operating in this transition region, where Tung's equations are in error. We provide the corrected equations for this case and demonstrate their ability to model practical diode characteristics.

Assessing the Intestinal Permeability of Small Molecule Drugs via Diffusion Motion on a Multidimensional Free Energy Surface.

A protocol that accurately assesses the intestinal permeability of small molecule compounds plays an essential role in decreasing the cost and time in inventing a new drug. This manuscript presents a novel computational method to study the passive permeation of small molecule drugs based on the inhomogeneous solubility-diffusion model. The multidimensional free energy surface of the drug transiting through a lipid bilayer is computed with transition-tempered metadynamics that accurately captures the mechanisms of passive permeation. The permeability is computed by following the diffusion motion of the drug molecules along the minimal free energy path found on the multidimensional free energy surface. This computational method is assessed by studying the permeability of five small molecule drugs (ketoprofen, naproxen, metoprolol, propranolol, and salicylic acid). The results demonstrate a remarkable agreement between the computed permeabilities and those measured with the intestinal assay. The in silico method reported in this manuscript also reproduces the permeability measured from the intestinal assay (in vivo) better than the cell-based assays (e.g., PAMPA and Caco-2) do. In addition, the multidimensional free energy surface reveals the interplay between the structure of the small molecule and its permeability, shedding light on strategies of drug optimization.

Scale-space energy density for inhomogeneous turbulence based on filtered velocities

The energy spectrum is commonly used to describe the scale dependence of turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are mainly employed for inhomogeneous turbulence models. Attempts have been made to describe the scale dependence of inhomogeneous turbulence using the second-order structure function and two-point velocity correlation. However, unlike the energy spectrum, expressions for the energy density in the scale space fail to satisfy the requirement of being non-negative. In this study, a new expression for the scale-space energy density based on filtered velocities is proposed to clarify the reasons behind the negative values of the energy density and to obtain a better understanding of inhomogeneous turbulence. The new expression consists of homogeneous and inhomogeneous parts; the former is always non-negative, while the latter can be negative because of the turbulence inhomogeneity. Direct numerical simulation data of homogeneous isotropic turbulence and a turbulent channel flow are used to evaluate the two parts of the energy density and turbulent energy. It was found that the inhomogeneous part of the turbulent energy shows non-zero values near the wall and at the centre of a channel flow. In particular, the inhomogeneous part of the energy density changes its sign depending on the scale. A concave profile of the filtered-velocity variance at the wall accounts for the negative value of the energy density in the region very close to the wall.

Inhomogeneous asymmetric exclusion processes between two reservoirs: large deviations for the local empirical observables in the mean-field approximation

For a given inhomogeneous exclusion processes on N sites between two reservoirs, the trajectories probabilities allow to identify the relevant local empirical observables and to obtain the corresponding rate function at level 2.5. In order to close the hierarchy of the empirical dynamics that appear in the stationarity constraints, we consider the simplest approximation, namely the mean-field approximation for the empirical density of two consecutive sites, in direct correspondence with the previously studied mean-field approximation for the steady state. For a given inhomogeneous totally asymmetric model, this mean-field approximation yields the large deviations for the joint distribution of the empirical density profile and of the empirical current around the mean-field steady state; the further explicit contraction over the current allows to obtain the large deviations of the empirical density profile alone. For a given inhomogeneous asymmetric model, the local empirical observables also involve the empirical activities of the links and of the reservoirs; the further explicit contraction over these activities yields the large deviations for the joint distribution of the empirical density profile and of the empirical current. The consequences for the large deviations properties of time-additive space-local observables are also discussed in both cases.

Determination of short circuit location in the electric railway traction

This article discusses the problem of improving the accuracy of determining the location of a short circuit in the AC railways traction networks. Finding a short circuit can take several hours. An urgent task is reducing the time to search for a fault location. The purpose of the study is to develop a method that increases the accuracy of determining the location of a short circuit in AC traction networks. The method is based on computer modeling of inhomogeneities in the structure of the traction network and the arc. The proposed method makes it possible to take into account the arc resistance. The method was tested on the traction network active section. The error of the method is 200-300 meters. The method can find practical application in the work of dispatchers.

Horizontal Refraction of Acoustic Waves in Shallow-Water Waveguides Due to an Inhomogeneous Bottom Structure

Three-Dimensional (3-D) sound propagation in a shallow-water waveguide with a constant depth and inhomogeneous bottom is studied through numerical simulations. As a model of inhomogeneity, a transitional region between an acoustically soft and hard bottom is considered. Depth-averaged transmission loss simulations using the “horizontal rays and vertical modes” approach and mode parabolic equations demonstrate the horizontal refraction of sound in this region, even if the water column is considered homogeneous. The observed wave effect is prominent at low frequencies, at which the water depth does not exceed a few acoustic wavelengths. The obtained results within the simplified model are verified by the simulations for a real seabed structure in the Kara Sea.

A framework for automatically choosing the optimal parameters of finite-difference scheme in the acoustic wave modeling

An effective finite-difference (FD) scheme requires suitable FD parameters to ensure stability while having sufficient accuracy in the seismic modeling. The FD parameters such as time step, grid spacing and FD operator also affect the computational costs and storage requirements significantly. Thus, choosing the FD parameters should be the optimal trade-off between the stability, numerical accuracy and computational efficiency. However, the FD parameters usually be chosen through repeated manual tests, which is prone to unnecessary consumption. In this paper, we propose a framework for automatically choosing the FD parameters to achieve the optimal FD scheme in the acoustic wave modeling. Considering the computational efficiency, the proposed framework provides the maximum admissible time step under the stability condition. On the premise of the maximum time step, the proposed framework can find suitable parameters to ensure that the FD scheme has sufficient wavenumber bandwidth to deal with the maximum wavenumber or frequency of the wavefield. Dispersion and stability analyses prove that the FD parameters determined by our framework can effectively avoid dispersion errors while ensuring stability under the given conditions. Numerical experiments also prove the effectiveness of the framework in choosing FD parameters for the inhomogeneous velocity model. The framework can easily obtain the optimal FD parameters and can be recommended as a routine step for the FD methods.

Fractional inhomogeneous multi-state models in life insurance

In this paper, we demonstrate through the use of matrix calculus a transparent analysis of fractional inhomogeneous Markov models for life insurance where transition matrices commute. The resulting formulae are intuitive matrix generalizations of their single-state counterparts, and the absorption times are matrix versions of well-known scalar distributions. A further advantage of this approach is that it allows extending the analysis to the non-Markovian case where sojourns are Mittag-Leffler distributed, and where the absorption times are fractional phase-type distributed. Considering deterministic time transforms gives rise to fractional inhomogeneous phase-type distributions as absorption times. The latter underlying processes are an example of a regime where not only the present but also the history of a policyholder influences its future evolution. The sub-exponential nature of stable distributions translates into the multi-state insurance model as a random longevity risk at any given state of the chain.

Evaluation of the RF-induced lead-tip heating of AIMDs using a Volume-Weighed Tissue-Cluster Model for 1.5T MRI.

The RF-induced lead-tip heating of AIMDs is related to the tangential electric field distribution along the AIMD lead paths in patients and the electromagnetic behavior (represented by the transfer function model) of the AIMDs. To evaluate the in-vivo RF-induced lead-tip heating of AIMDs using in-vitro methods, the electric field distribution is critical. In this paper, we proposed a Volume-Weighed Tissue-Cluster Model, a feasible bench method, to simplify the evaluation of the in-vivo RF-induced lead-tip heating of AIMDs. The incident electric field distribution inside this simplified model is highly correlated to that of the original inhomogeneous human body model. Compared to the RF-induced lead-tip heating results in the original model, the maximum error of the lead-tip heating in this Volume-Weighed Tissue-Cluster Model is less than 1 °C. The correlation coefficients of the temperature rise between the two models are higher than 0.997.Clinical Relevance- Simplified and accurate anatomical models can be used to emulate the in-vivo heating assessment for MRI safety.

Investigation of Interphase Drag Force Affected by Clouded Bubble via a Computational Fluid Dynamics–Discrete Element Method Approach

Bubbles as mesoscale structures play an important role in the development of the inhomogeneous drag force model, which is key to the prediction of fluidized beds. A coupled computational fluid dynamics–discrete element method is employed in this work to investigate the distribution of interphase drag force around a clouded bubble in an incipiently fluidized bed. A method for the determination of the bubble boundary is proposed. The results reveal that there is a stronger positive effect of drag force around the clouded bubble because of the presence of bubble crown and wake, which is different from the cloudless bubble. The bubble-induced local inhomogeneous coefficient is also proposed to evaluate the ensemble inhomogeneous impact around the bubble.

Functional brain-heart interplay extends to the multifractal domain.

The study of functional brain–heart interplay has provided meaningful insights in cardiology and neuroscience. Regarding biosignal processing, this interplay involves predominantly neural and heartbeat linear dynamics expressed via time and frequency domain-related features. However, the dynamics of central and autonomous nervous systems show nonlinear and multifractal behaviours, and the extent to which this behaviour influences brain–heart interactions is currently unknown. Here, we report a novel signal processing framework aimed at quantifying nonlinear functional brain–heart interplay in the non-Gaussian and multifractal domains that combines electroencephalography (EEG) and heart rate variability series. This framework relies on a maximal information coefficient analysis between nonlinear multiscale features derived from EEG spectra and from an inhomogeneous point-process model for heartbeat dynamics. Experimental results were gathered from 24 healthy volunteers during a resting state and a cold pressor test, revealing that synchronous changes between brain and heartbeat multifractal spectra occur at higher EEG frequency bands and through nonlinear/complex cardiovascular control. We conclude that significant bodily, sympathovagal changes such as those elicited by cold-pressure stimuli affect the functional brain–heart interplay beyond second-order statistics, thus extending it to multifractal dynamics. These results provide a platform to define novel nervous-system-targeted biomarkers.This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.

Numerical investigation of the transient interfacial material behavior during laser impact welding

During laser impact welding, severe plastic strains and temperature spikes occurring in less than 1 µs make experimental observation impractical and necessitate computational modeling to characterize in-situ behavior. To understand the effects of microstructure and the associated inhomogeneity/anisotropy in laser impact welding, an Eulerian framework featuring aluminum 1100 flyer and stainless steel 304 target foils is applied to simulate cases with and without microstructure modeling. The transient thermomechanical phenomena revealed by the dynamic simulation provide insights into evolution of the in-situ structure-property relationship, including microstructural variation, phase transformation, and material jetting. In contrast to the homogeneous model, the inhomogeneous model suggests a 10 µm-thick zone of grain refinement at the weld interface establishing new grains 0.1-1 µm in diameter in the flyer, and causing partial martensitic phase transformation in the target, attributable to rapidly induced equivalent plastic strains of up to 10.71 in the flyer and 0.98 in the target.

МЕТОДЫ ИНТЕРПРЕТАЦИИ ЧЕРНЫХ ЯЩИКОВ МАШИННОГО ОБУЧЕНИЯ И ИХ ПРИМЕНЕНИЕ ДЛЯ СОЗДАНИЯ СИСТЕМ ПОДДЕРЖКИ ПРИНЯТИЯ РЕШЕНИЙ

. Modified theories of gravity have become a kind of paradigm in modern physics because they seem to solve several shortcomings of the standard General Theory of Relativity (GTR) related to cosmology, astrophysics and quantum field theory. The most famous modified theories of gravity are F(R) and F(T) theories of gravity. A generalization of these two modified theories and gravitations, which was first proposed by Myrzakulov Ratbay. In this paper, we study an inhomogeneous isotropic cosmological model with a fermion field f-essence whose action has the form , where R is the scalar of curvature, and T is the torsion scalar, and Lm is the Lagrangian f-essence. A particular case is studied in detail when parameters are obtained that describe the current accelerated expansion of the Universe. The type of Lagrangian f-essence of this model is determined. The presented results show that gravity with f-essence can describe inflation in the early evolution of the Universe. A modified F(R, T) gravity with f-essence is considered. Equations of motion were obtained and the inflationary period of the early Universe was considered. To describe the inflationary period, the form of the Hubble parameter and the slow-roll parameter were determined.

An Overview on the Nature of the Bounce in LQC and PQM

We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.

Remark on Justification of Asymptotics of Spectra of Cylindrical Waveguides with Periodic Singular Perturbations of Boundary and Coefficients

To perform an asymptotic analysis of spectra of singularly perturbed periodic waveguides, it is required to estimate remainders of asymptotic expansions of eigenvalues of a model problem on the periodicity cell uniformly with respect to the Floquet parameter. We propose two approaches to this problem. The first is based on the max–min principle and is sufficiently easily realized, but has a restricted application area. The second is more universal, but technically complex since it is required to prove the unique solvability of the problem on the cell for some value of the spectral parameter and the Floquet parameter in a nonempty closed segment, which is verified by constructing an almost inverse operator of the operator of an inhomogeneous model problem in variational setting. We consider boundary value problems on the simplest periodicity cell: a rectangle with a row of fine holes.

Microseismic P-Wave Travel Time Computation and 3D Localization Based on a 3D High-Order Fast Marching Method.

The travel time computation of microseismic waves in different directions (particularly, the diagonal direction) in three-dimensional space has been found to be inaccurate, which seriously affects the localization accuracy of three-dimensional microseismic sources. In order to solve this problem, this research study developed a method of calculating the P-wave travel time based on a 3D high-order fast marching method (3D_H_FMM). This study focused on designing a high-order finite-difference operator in order to realize the accurate calculation of the P-wave travel time in three-dimensional space. The method was validated using homogeneous velocity models and inhomogeneous layered media velocity models of different scales. The results showed that the overall mean absolute error (MAE) of the two homogenous models using 3D_H_FMM had been reduced by 88.335%, and 90.593% compared with the traditional 3D_FMM. On that basis, the three-dimensional localization of microseismic sources was carried out using a particle swarm optimization algorithm. The developed 3D_H_FMM was used to calculate the travel time, then to conduct the localization of the microseismic source in inhomogeneous models. The mean error of the localization results of the different positions in the three-dimensional space was determined to be 1.901 m, and the localization accuracy was found to be superior to that of the traditional 3D_FMM method (mean absolute localization error: 3.447 m) with the small-scaled inhomogeneous model.

On the Higher-Order Inhomogeneous Heisenberg Supermagnetic Models

This paper is concerned with the construction of the fifth-order inhomogeneous Heisenberg supermagnetic models. Moreover, the Lax representations of the models are presented. By means of the gauge transformation, we establish their gauge equivalent equations with different quadratic constraints, i.e., the super and fermionic fifth-order inhomogeneous nonlinear Schrödinger equations, respectively. In addition, we investigate their Lax representations and Bäcklund transformations from which the solutions of the super integrable systems have been discussed.