RESUMEN

In this paper, we propose a new approach for numerically simulating the growth of cracks in unidirectional composite materials, termed extended isogeometric analysis, evaluating the maximum stress intensity factor and T-stress. To validate our approach, we used a small anisotropic plate with two edge cracks, beginning with formulating the governing equations based on the energy integral method, Stroh's Formula, and the Elastic Law describing the behaviour of anisotropic materials, while considering boundary conditions and initial states. A MATLAB code was developed to solve these equations numerically and to post-process the tensile stress and the stress intensity factor (SIF) in the first mode. The results for the SIF closely match those obtained using the extended finite element method (X-FEM), with a discrepancy of only 0.0021 Pa·m0.5. This finding underscores the credibility of our approach. The extended finite element method has demonstrated robustness in predicting crack propagation in composite materials in recent years, leading to its adoption by several widely used software packages in various industries.

RESUMEN

In order to safeguard the surface structures from mining damage while optimizing the liberation of coal resources under the dense surface buildings of the Cedi River coal mine. Considering that the analysis of the structure and type of surface buildings and the geological mining conditions of the mine, a wide strip mining design with a retention width of 70 m and a mining width of 50 m was finally determined by using the pressure arch theory and Wilson's theory, combined with the actual layout of working faces 51,002, 51,004 and 51,006 at the site.The strip mining design is verified by probability integral method and FLAC3D numerical simulation calculation respectively, The findings indicate that the highest value of earth surface subsidence created by the mining of the wide strip is 210 mm, the surface horizontal deformation value is 1.0 to - 1.4 mm/m, the damage to surface buildings is less than Level I, which satisfying the prerequisites of the surface building protection level, and can realize the continuous advancement of mine 51,002, 51,004 and 51,006 working faces, The coal pillars of the retained strip have sufficient support strength and long-term consistency, and the movement and deformation of the overburden after mining will not cause undulating subsidence of the surface, which effectively solve the mine's technical difficulties in safely coal mining under surface buildings.

RESUMEN

The Poisson-Boltzmann (PB) model is a widely used electrostatic model for biomolecular solvation analysis. Formulated as an elliptic interface problem, the PB model can be numerically solved on either Eulerian meshes using finite difference/finite element methods or Lagrangian meshes using boundary element methods. Molecular surface generators, which produce the discretized dielectric interfaces between solutes and solvents, are critical factors in determining the accuracy and efficiency of the PB solvers. In this work, we investigate the utility of the Eulerian Solvent Excluded Surface (ESES) software for rendering conjugated Eulerian and Lagrangian surface representations, which enables us to numerically validate and compare the quality of Eulerian PB solvers, such as the MIBPB solver, and the Lagrangian PB solvers, such as the TABI-PB solver. Furthermore, with the ESES software and its associated PB solvers, we are able to numerically validate an interesting and useful but often neglected source-target symmetric property associated with the linearized PB model.

RESUMEN

The splenic interendothelial slits fulfill the essential function of continuously filtering red blood cells (RBCs) from the bloodstream to eliminate abnormal and aged cells. To date, the process by which 8 [Formula: see text]m RBCs pass through 0.3 [Formula: see text]m-wide slits remains enigmatic. Does the slit caliber increase during RBC passage as sometimes suggested? Here, we elucidated the mechanisms that govern the RBC retention or passage dynamics in slits by combining multiscale modeling, live imaging, and microfluidic experiments on an original device with submicron-wide physiologically calibrated slits. We observed that healthy RBCs pass through 0.28 [Formula: see text]m-wide rigid slits at 37 °C. To achieve this feat, they must meet two requirements. Geometrically, their surface area-to-volume ratio must be compatible with a shape in two tether-connected equal spheres. Mechanically, the cells with a low surface area-to-volume ratio (28% of RBCs in a 0.4 [Formula: see text]m-wide slit) must locally unfold their spectrin cytoskeleton inside the slit. In contrast, activation of the mechanosensitive PIEZO1 channel is not required. The RBC transit time through the slits follows a [Formula: see text]1 and [Formula: see text]3 power law with in-slit pressure drop and slip width, respectively. This law is similar to that of a Newtonian fluid in a two-dimensional Poiseuille flow, showing that the dynamics of RBCs is controlled by their cytoplasmic viscosity. Altogether, our results show that filtration through submicron-wide slits is possible without further slit opening. Furthermore, our approach addresses the critical need for in vitro evaluation of splenic clearance of diseased or engineered RBCs for transfusion and drug delivery.

Asunto(s)

RESUMEN

In order to improve the accuracy of detection results of debonding defects of aluminum alloy thin plate, the nonlinear ultrasonic technology is used to detect the simulated defect samples, aiming at problems such as near surface blind region caused by the interaction of incident wave, reflected wave and even second harmonic wave in a short time due to the small thickness of thin plates. An integral method based on energy transfer efficiency is proposed to calculate the nonlinear ultrasonic coefficient to characterize the debonding defects of thin plates. A series of simulated debonding defects of different sizes were made using aluminum alloy plates with four thicknesses of 1 mm, 2 mm, 3 mm and 10 mm. By comparing the traditional nonlinear coefficient with the integral nonlinear coefficient proposed in this paper, it is verified that both methods can quantitatively characterize the size of debonding defects. The nonlinear ultrasonic testing technology based on energy transfer efficiency has higher testing accuracy for thin plates.

RESUMEN

In response to the problem that the actual extent of coal mining impacts on the surface in thick loose layer mines significantly exceeds the theoretical predictions, based on the literature study, the form of influence of thick loose layer on the predicted parameters of the probability integral method is summarized and analyzed; taking into account the influence of the subsidence coefficient, the sine modification formula of the major influence radius and the logistic modification formula of the subsidence coefficient are established, respectively, and based on the characteristics of the major influence radius, a new subsidence basin demarcation point is proposed and a novel probability integral method segmental parameter modified prediction model is constructed. The simulated experiment and real data experiment results prove that the constructed probability integral method segmented parameter modified model can both reduce the convergence of surface subsidence basin edge better and take into account the predicted accuracy inside the subsidence basin. The research achievements provide scientific data support for disaster warning, pollution management, ecological restoration, and coordination between coal mining and surface city construction in thick loose layer mining areas.

Asunto(s)

RESUMEN

In this work, the properties of concrete modified with dosages of natural pozzolans (NP) in substitution of cement or superfine aggregates were evaluated. Proportions of 20/80 pozzolan/cement or pozzolan/superfine aggregates were selected for the additions of quarry and tuff pozzolans. Pozzolanic activity, durability, compressive strength, characteristic resistance, settling consistency, density, electrical resistivity, depth of water penetration, accessible porosity, and carbonation and chloride penetration were determined for the resulting concrete mixtures, and they were subsequently compared to the values obtained for the reference concrete batches without additions. The results of the cementitious mixtures supplemented with tuff (PZT) and quarry (PZQ) pozzolans, expressed in mmol/L, are consistent with the pozzolanism test, with [Ca(OH)2]/[OH-] ratios at 7 days are 6.03/60.19 for PZQ and 1.78/92.78 PZT. In addition to the pozzolanic activity at these dosages, the characteristic resistance and durability parameters required by EHE-08 were verified. Particular attention was given to the determination of the diffusion of chloride ions, introducing an instrumental modification of the accelerated integral method. The modification provides values of diffusion coefficients similar to those obtained by the other methods with the advantage of greater stability and quality of the measurement.

RESUMEN

Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method. The article begins with a short overview of the literature connected to the methodology for obtaining exact solutions of nonlinear differential equations. This overview includes research on nonlinear waves, research on the methodology of the Inverse Scattering Transform method, and the method of Hirota, as well as some of the nonlinear equations studied by these methods. The overview continues with articles devoted to the phenomena described by the exact solutions of the nonlinear differential equations and articles about mathematical results connected to the methodology for obtaining such exact solutions. Several articles devoted to the numerical study of nonlinear waves are mentioned. Then, the approach to the SEsM is described starting from the Hopf-Cole transformation, the research of Kudryashov on the Method of the Simplest Equation, the approach to the Modified Method of the Simplest Equation, and the development of this methodology towards the SEsM. The description of the algorithm of the SEsM begins with the transformations that convert the nonlinearity of the solved complicated equation into a treatable kind of nonlinearity. Next, we discuss the use of composite functions in the steps of the algorithms. Special attention is given to the role of the simple equation in the SEsM. The connection of the methodology with other methods for obtaining exact multisoliton solutions of nonlinear differential equations is discussed. These methods are the Inverse Scattering Transform method and the Hirota method. Numerous examples of the application of the SEsM for obtaining exact solutions of nonlinear differential equations are demonstrated. One of the examples is connected to the exact solution of an equation that occurs in the SIR model of epidemic spreading. The solution of this equation can be used for modeling epidemic waves, for example, COVID-19 epidemic waves. Other examples of the application of the SEsM methodology are connected to the use of the differential equation of Bernoulli and Riccati as simple equations for obtaining exact solutions of more complicated nonlinear differential equations. The SEsM leads to a definition of a specific special function through a simple equation containing polynomial nonlinearities. The special function contains specific cases of numerous well-known functions such as the trigonometric and hyperbolic functions and the elliptic functions of Jacobi, Weierstrass, etc. Among the examples are the solutions of the differential equations of Fisher, equation of Burgers-Huxley, generalized equation of Camassa-Holm, generalized equation of Swift-Hohenberg, generalized Rayleigh equation, etc. Finally, we discuss the connection between the SEsM and the other methods for obtaining exact solutions of nonintegrable nonlinear differential equations. We present a conjecture about the relationship of the SEsM with these methods.

RESUMEN

When red blood cells (RBCs) experience non-physiologically high stresses, e.g., in medical devices, they can rupture in a process called hemolysis. Directly simulating this process is computationally unaffordable given that the length scales of a medical device are several orders of magnitude larger than that of a RBC. To overcome this separation of scales, the present work introduces an affordable computational framework that accurately resolves the stress and deformation of a RBC in a spatially and temporally varying macroscale flow field such as those found in a typical medical device. The underlying idea of the present framework is to treat RBCs as one-way coupled tracers in the macroscale flow by capturing the effect of the flow on their dynamics but neglecting their effect on the flow at the macroscale. As a result, the RBC dynamics are simulated after those of the flow in a postprocessing step by receiving the fluid velocity gradient tensor measured along the RBC trajectory as the input. To resolve the fluid velocity in the immediate vicinity of the RBC as well as the motion of the membrane, we employ the boundary integral method coupled to a structural solver. The governing equations are discretized in space using spherical harmonics, yielding spectral integration accuracy. The predictions produced by this formulation are in good agreement with those obtained from simulations of spherical capsules in shear flows and optical tweezers experiments. The accuracy of the present method is evaluated using unbounded shear flow as a benchmark. Its computational cost grows proportional to p 5, where p is the degree of the spherical harmonic. It also exhibits a fast convergence rate that is approximately O ( p 6 ) for p ⪅ 20.

RESUMEN

In a blind adaptive deconvolution problem, the convolutional noise observed at the output of the deconvolution process, in addition to the required source signal, is-according to the literature-assumed to be a Gaussian process when the deconvolution process (the blind adaptive equalizer) is deep in its convergence state. Namely, when the convolutional noise sequence or, equivalently, the residual inter-symbol interference (ISI) is considered small. Up to now, no closed-form approximated expression is given for the residual ISI, where the Gaussian model can be used to describe the convolutional noise probability density function (pdf). In this paper, we use the Maximum Entropy density technique, Lagrange's Integral method, and quasi-moment truncation technique to obtain an approximated closed-form equation for the residual ISI where the Gaussian model can be used to approximately describe the convolutional noise pdf. We will show, based on this approximated closed-form equation for the residual ISI, that the Gaussian model can be used to approximately describe the convolutional noise pdf just before the equalizer has converged, even at a residual ISI level where the "eye diagram" is still very closed, namely, where the residual ISI can not be considered as small.

RESUMEN

This paper introduces a novel methodology to optimize the design of a ratiometric rotary inductive position sensor (IPS) fabricated in printed circuit board (PCB) technology. The optimization aims at reducing the linearity error of the sensor and amplitude mismatch between the voltages on the two receiving (RX) coils. Distinct from other optimization techniques proposed in the literature, the sensor footprint and the target geometry are considered as a non-modifiable input. This is motivated by the fact that, for sensor replacement purposes, the target has to fit a predefined space. For this reason, the original optimization technique proposed in this paper modifies the shape of the RX coils to reproduce theoretical coil voltages as much as possible. The optimized RX shape was obtained by means of a non-linear least-square solver, whereas the electromagnetic simulation of the sensor is performed with an original surface integral method, which are orders of magnitude faster than commercial software based on finite elements. Comparisons between simulations and measurements performed on different prototypes of an absolute rotary sensor show the effectiveness of the optimization tool. The optimized sensors exhibit a linearity error below 0.1% of the full scale (FS) without any signal calibration or post-processing manipulation.

Asunto(s)

RESUMEN

The spectral boundary integral method is popular for simulating fault, fracture, and frictional processes at a planar interface. However, the method is less commonly used to simulate off-fault dynamic fields. Here we develop a spectral boundary integral method for poroelastodynamic solid. The method has two steps: first, a numerical approximation of a convolution kernel and second, an efficient temporal convolution of slip speed and the appropriate kernel. The first step is computationally expensive but easily parallelizable and scalable such that the computational time is mostly restricted by computational resources. The kernel is independent of the slip history such that the same kernel can be used to explore a wide range of slip scenarios. We apply the method by exploring the short-time dynamic and static responses: first, with a simple source at intermediate and far-field distances and second, with a complex near-field source. We check if similar results can be attained with dynamic elasticity and undrained pore-pressure response and conclude that such an approach works well in the near-field but not necessarily at an intermediate and far-field distance. We analyze the dynamic pore-pressure response and find that the P-wave arrival carries a significant pore pressure peak that may be observed in high sampling rate pore-pressure measurements. We conclude that a spectral boundary integral method may offer a viable alternative to other approaches where the bulk is discretized, providing a better understanding of the near-field dynamics of the bulk in response to finite fault ruptures.

RESUMEN

In this paper we use an approximate analytical method for numerical solution of one dimensional moving boundary problem. We consider the oxygen diffusion problem where the oxygen is allowed to diffuse into a sick cell which absorbs and immobilizes oxygen at a constant rate. Our main problem consists in tracking the moving boundary that represents the oxygen penetration depth inside the sick cell. We can find an accurate solution which is obtained by a polynomial of third and fourth degree and we show some mistakes in the paper published by Seval Çatal in (App.Math.Comput 145:361-369, 2003).

Asunto(s)

RESUMEN

The main objective of this work is to predict the exact value of the fracture toughness (KQ) of fiber-reinforced polymer (FRP). The drawback of the American Society for Testing Materials (ASTM) E1922 specimen is the lack of intact fibers behind the crack-tip as in the real case, i.e., through-thickness cracked (TTC) specimen. The novelty of this research is to overcome this deficiency by suggesting unprecedented cracked specimens, i.e., matrix cracked (MC) specimens. This MC exists in the matrix (epoxy) without cutting the glass fibers behind the crack-tip in the unidirectional laminated composite. Two different cracked specimen geometries according to ASTM E1922 and ASTM D3039 were tested. 3-D FEA was adopted to predict the damage failure and geometry correction factor of cracked specimens. The results of the TTC ASTM E1922 specimen showed that the crack initiated perpendicular to the fiber direction up to 1 mm. Failure then occurred due to crack propagation parallel to the fiber direction, i.e., notch insensitivity. As expected, the KQ of the MC ASTM D3039 specimen is higher than that of the TTC ASTM D3039 specimen. The KQ of the MC specimen with two layers is about 1.3 times that of the MC specimen with one layer.

RESUMEN

This paper presents direct computations of 3-D fracture parameters including stress intensity factors (SIFs) and T-stress for straight and curved planar cracks with the p-version finite element method (P-FEM) and contour integral method (CIM). No excessive singular element or enrichment function is required for the computation. To demonstrate the accuracy and efficiency of the proposed approaches, several benchmark numerical models of 3-D planar straight and curved cracks with single and mixed-mode fractures are considered and analyzed: a through thickness edge straight crack in a homogeneous material, a through thickness inclined straight crack, a penny-shaped crack embedded in a cube and a central ellipse shaped crack in a homogeneous cube. Numerical results are analyzed and compared with analytical solutions and those reported by the extended finite element method (XFEM) and the scaled boundary finite element method (SBFEM) in the available literature. Numerical experiments show the accuracy, robustness and effectiveness of the present method.

RESUMEN

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a "small" parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.

RESUMEN

The present article is focused on the shapes of dendritic tips occurring in undercooled binary systems in the absence of convection. A circular/globular shape appears in limiting cases of small and large Péclet numbers. A parabolic/paraboloidal shape describes the tip regions of dendrites whereas a fractional power law defines a shape behind their tips in the case of low/moderate Péclet number. The parabolic/paraboloidal and fractional power law shapes are sewed together in the present work to describe the dendritic shape in a broader region adjacent to the dendritic tip. Such a generalized law is in good agreement with the parabolic/paraboloidal and fractional power laws of dendritic shapes. A special case of the angled dendrite is considered and analysed in addition. The obtained results are compared with previous experimental data and the results of numerical simulations on dendritic growth. This article is part of the theme issue 'Patterns in soft and biological matters'.

RESUMEN

The effect of particle size on the combustion and explosion properties of grain dust is investigated by Hartmann tube, cone calorimeter (CC), and thermogravimetry (TG), it aims to provide fundamental experimental data of grain dust for an in-depth study on its potential risk. The fine-grain dust facilitates the decrease in the minimum ignition temperature (MIT) of dust layer and dust cloud, as well as the obvious increases in the maximum explosion pressure P max (climbs from 0.36 to 0.49 MPa) and pressure rising rate dP/dt (rises from 6.05 to 12.12 MPa s-1), leading to the increases in maximum combustion rate (dw/dτ)max and combustion characteristic index S, corresponding to the greater or severer potential risk. Because the E corresponding to combustion increases from 106.05 (sample with a particle size of 180-1250 µm) to 153.45 kJ mol-1 for the sample of 80-96 µm, the combustion process gradually transforms from diffusion-controlled into a kinetically controlled mode with the decreasing particle size of grain dust, together with the retardation of initially transient charring. It determines that the competition between the charring and combustion dominates the decomposition, and the combustion prevails for the coarse particle, while the charring controls the combustion for the fine-grain dust.

RESUMEN

In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient uptake rates inside and outside the tumor, this introduces variability in spatial diffusion gradients. Linear stability analysis suggests that the uptake rate in the tumor microenvironment, together with chemotaxis, may induce unstable growth, especially when the nutrient gradients are large. We investigate the fully nonlinear dynamics using a spectrally accurate boundary integral method. Our nonlinear simulations reveal that vascular heterogeneity plays an important role in the development of morphological instabilities that range from fingering and chain-like morphologies to compact, plate-like shapes in two dimensions.

Asunto(s)

RESUMEN

Various bubble dynamics near the boundary in an acoustic field play a significantly important role in destructive erosion which has been associated with applications in industry cleaning, chemical engineering and biomedicine. But the effect mechanism of the high pressure on the boundary induce by single acoustic cavitation bubble has not been fully elucidated, which is vital for further application. The objective of this paper is to investigate the behaviors of a gas bubble near a rigid wall in a low frequency ultrasonic field. The temporal evolution of the bubble was recorded by means of synchronous high-speed recordings. Meanwhile, the time of bubble collapse, velocity of the bubble margin and the characteristics of the liquid jet were analyzed. In addition, the bubble dynamics were simulated based on potential flow theory coupled with the boundary integral method (BIM). Results are presented for a single bubble generated near the rigid wall with the normalized standoff distance γ = 1.85 under a wide range of ultrasonic power. The results show that the dynamics of the bubble can be divided into four phases: oscillation, movement, collapse and rebound. And when the applied ultrasonic power increases, the time of bubble collapse has a clear trend to decrease and the maximum velocity of the bubble margin increases apparently. Furthermore, the bubble behaviors after its first collapse, such as the number and the velocity of the effective jets, also vary evidently as the increase of the ultrasonic power. These results about bubble dynamics in ultrasonic field may be significant to determine or correct the main mechanisms of acoustic cavitation.