Discontinuous Conditions Research Articles

Weak curvature asymptotics for Debye layers as electrohydrodynamic discontinuities.

Important microfluidic phenomena, such as droplet deformation and cell motion, are impacted by the formation of Debye layers at charged interfaces. Previous studies examined interface problems with leaky dielectrics or the formation of diffuse charge layers. In most cases, the results are derived for weakly curved spherical geometries. Moreover, many studies of streaming-potential phenomena at fluid-solid interfaces lack a macroscale description of effects that are higher than first order. An asymptotic methodology capturing both complex surface geometries and an accurate description of higher-order phenomena is presented in this study. For this purpose, we consider a generic streaming-potential problem. As a result, the complex three-dimensional electrohydrodynamics in the Debye layer are entailed in two-dimensional discontinuity conditions. The latter contain a free parameter, the layer thickness, which mathematically represents the discontinuity position within the Debye layer. It can be used to derive an alternative definition of the Debye thickness capturing the influence of the ζ potential. We introduce a virtual particle whose outer boundary envelopes the solid particle plus a fraction of the Debye layer. It interacts with the macroscopic flow while incorporating the detailed electrohydrodynamics inside the layer.

A compatible multiscale model for nanocomposites incorporating interface effect

The asymptotic homogenization theory is usually employed for analysis of composites with hierarchical microstructures, and the interface effect has to be considered for nanocomposites due to the fact that the surface-to-volume ratio of the nanofillers becomes significant. However, commonly-used two-dimensional surface theories of elasticity cannot be compatibly applied in conjunction with the asymptotic homogenization theory for analysis of nanocomposites due to traction discontinuity and the difficulty in specifying positive definiteness of elasticity tensor in terms of two-dimensional interface parameters. This study is focused on solving the incompatibility problem. A simple but useful three-dimensional interface theory is proposed, in which stress discontinuity conditions across two-dimensional interfaces are replaced by traction continuity on its two sides, and the requirement for positive definiteness of elasticity tensor can be easily specified. This three-dimensional interface theory is linked to the well-accepted two-dimensional models through energy-equivalence and kinematics of its middle surface. It is found that if the mechanical behavior of an interface can be well captured by commonly-used two-dimensional surface theories of elasticity, the three-dimensional interface can be characterized by constant elastic moduli as well as a size-independent thickness. Based on the proposed three-dimensional interface theory and the asymptotic homogenization theory, a compatible multiscale model is then developed and provides a practical way to examine the scaling law of effective moduli of typical nanocomposites. It is examined using numerical results that two-dimensional interface parameters can be easily extracted from the scaling law, and the way we link three-dimensional interfaces to two-dimensional counterparts is justified.

Effectiveness Of Incision Wound Healing Of Pandanus Amaryllifolius Roxb In Wistar Rats

The incision is a condition of tissue discontinuity that is commonly encountered with the risk of prolonged healing time, imperfect wound healing, infection, etc. Assessment of the wound healing activity of the incision is the purpose of this research, which includes an examination of wound contraction, the thickness of collagen fibers, and the number of new blood vessels formation. In total, 25 rats will be divided into 5 test groups, each consisting of 5 rats; the control group (cream base treated), standard group (Povidone Iodine), followed by the treated group with 10%, 20%, and 30% pandan leaf extract ointment. The preliminary screening of phytochemical analysisshowed the presence of alkaloids, saponins, flavonoids, tannins, triterpenoids, and steroids and glycosides, with the total content of phenols and flavonoids from the ethanolic extract of Pandan Wangi is 20.95 GAE mg/gram extract, and 23.57 TAE mg/gram extract. Wound contraction examination result showed a significant difference between the treatment groups on day 16 and a sign the pairs of groups after being given the ointment with each concentration (p <0.05), especially in the group with 30% fragrant leaves extract and the standard group. Examination of new blood vessels showed a significant difference (p <0.05), especially with 30% of the leaves extract ointment. There was also a significant difference in collagen density in the group given pandanus ethanol ointment, especially at the 30% pandanus extract content against the group that was only given the ointment base. This research strongly suggests that the fragrant pandan leaf extract ointment is effective in healing incisional wounds and promises the potential for further studies on the pharmacological aspects.

The risks of sulfur addition on cadmium accumulation in paddy rice under different water-management conditions

Recently, the application of sulfur (S) has been recommended to control the accumulation of cadmium (Cd) in rice in contaminated paddy soil. However, the effects of exogenous S on Cd transfer in paddy rice systems under different water-management practices have not been systematically investigated. Pot experiments were performed to monitor the composition of soil pore water and the Cd accumulation in iron plaque and rice tissue were compared under different S (0 and 200 mg/kg Na2SO4) and water (continuous and discontinuous flooding) treatments. Sulfur application significantly increased Cd concentrations in soil pore water under discontinuous flooding conditions, but slightly reduced them under continuous flooding. Moreover, the oxidation/reduction potential (Eh) was the most critical factor that affected the Cd levels. When the Eh exceeded −42.5 mV, S became the second critical factor, and excessive S application promoted Cd dissolution. In addition, S addition elevated the Cd levels in iron plaque and reduced the Cd transfer from the iron plaque to rice roots. In rice, S addition inhibited Cd transfer from the rice roots to the straw; thus, more Cd was stored in the rice roots. Nevertheless, additional S application increased the Cd content in the rice grains by 72% under discontinuous flooding, although this effect was mitigated by continued flooding. Under simulated practical water management conditions, S addition increased the risk of Cd contamination in rice, suggesting that S application should be reconsidered as a paddy fertilization strategy.

A LIMITER OF DISCONTINUOUS FINITE ELEMENT METHOD FOR THERMAL RADIATION HEAT TRANSFER

Due to the irregular shape of the high-temperature equipment, the thermal radiation processes are susceptible to discontinuous and shielding effects. Achieving the high accuracy of numerical solution for such processes is still a significant challenge. In this paper, the discontinuous finite element method is developed to discretize the angle and space for the numerical solution of the radiative transfer equation. A limiter, which is based on the Barth-Jespersen limiter borrowing the hierarchical limiting strategy, is imposed for the angular and spatial domains of radiative intensity to suppress the nonphysical oscillations of numerical solutions. Several benchmark problems involving discontinuous boundary conditions or irregular geometrical systems with the participating medium are solved. Besides, by comparing numerical results with exact solutions of radiative intensity in azimuthal angle, it is verified that the limiter can effectively suppress the numerical oscillation caused by the shielding effect. Finally, the three-dimensional angular distributions of radiative intensity on space nodes are depicted. In a word, the limiter, which is specially designed for the discontinuous finite element method, is a useful technical means to solve radiative heat transfer with discontinuous boundary conditions or irregular geometrical systems.

On the basis properties of a system of eigenfunctions of a spectral problem for a second-order discontinuous differential operator in the weighted grand-Lebesgue space with a general weight

The question of the basis property of a system of eigenfunctions of one spectral problem for a discontinuous second-order differential operator with a spectral parameter under discontinuity conditions is considered in the weighted grand-Lebesgue spaces Lp),?(0, 1), 1 < p < +?, with a general weight ?(?). These spaces are non-separable and therefore it is necessary to define its subspace associated with differential equation. In this paper, using the shift operator, a subspace Gp),?(0, 1) is considered, in which the basis property of exponentials and trigonometric systems of sines and cosines is established when the weight function ?(?) satisfies the Muckenhoupt condition. It is proved that the system of eigenfunctions and associated functions of the discontinuous differential operator corresponding to the given problem forms a basis in the weighted space Gp),?(0, 1) ? C,1 < p < +? with the weight ?(?) satisfying the Muckenhoupt condition. The question of the defect basis property of the system of eigenfunctions and associated functions of the given problem in the weighted spaces Gp),?(0, 1),1 < p < +?, is considered.

On a $q$-analogue of the Sturm-Liouville operator with discontinuity conditions

Исследуется $q$-аналог задачи Штурма-Лиувилля с условием разрыва на конечном интервале. Доказано, что $q$-задача Штурма-Лиувилля с условиями разрыва является самосопряженной в $L_q^2(0,\pi)$. Доказаны теорема о полноте и теорема о выборке. Приводится пример, иллюстрирующий полученные результаты.

MODELING THE EFFECT OF STOCHASTIC DEFECTS FORMED IN PRODUCTS DURING MACHINING ON THE LOSS OF THEIR FUNCTIONAL DEPENDENCIES

The article investigates the influence of hereditary defects formed in the surface layer of products from metals of heterogeneous structure on the quality of surfaces treated with finishing methods. The research is based on an integrated approach based on the results of the deterministic theory of defect development and methods of probability theory. The treated layer of the product is considered as a medium weakened by random defects that do not interact with each other, namely: structural changes, cracks, inclusions, the parameters of which are random variables with known laws of their probability distribution. The causes of structural changes, crack formation on the treated surface product depending on different types of probability distribution of dimensions are investigated: length, depth of defects, and their orientation. From these positions, technological possibilities of their elimination by definition of branch of combinations of the technological parameters providing necessary quality of the processed surfaces are considered. Modeling of thermomechanical processes in the treated surface containing hereditary defects is carried out based on thermoelastic equations with discontinuous boundary conditions in the places of their accumulation. The research used the apparatus of boundary value problems of mathematical physics equations, the method of singular integral equations for solving problems of fracture mechanics, Fourier-Laplace integral transformations for obtaining exact solutions, the method of constructing discontinuous functions. The dependences determining the intensity of stresses in the vertices of hereditary defects are obtained. A method for predicting the nature of crack formation depending on the probability distribution of defects, the values of heat flux entering the surface layer of the processed product has been developed. It is established that the increase in the homogeneity of the material leads to an increase in the value of heat flux, which corresponds to a fixed probability of failure.

Boundary-Value Problem for a Loaded Hyperbolic-Parabolic Equation with Degeneration of Order

In this paper, we study a boundary-value problem with discontinuous conjugation conditions on the line of type changing for a model equation of mixed hyperbolic-parabolic type with degeneration of order in the hyperbolicity domain. In the parabolic domain, the equation is the fractional diffusion equation, whereas in the hyperbolic domain it is the loaded one-speed transfer equation. We prove the uniqueness and existence theorem and propose an explicit solution of the problem in the parabolic and hyperbolic domains.

Pozitif Yarı Eksende Süreksizlik Koşuluna Sahip Sturm-Liouville Operatörünün Ters Saçılma Problemi

In this paper, we consider the inverse scattering problem for Sturm-Liouville operator with discontinuity conditions at some point on the positive half line. The scattering data of this boundary value problem is examined. The resolvent operator is constructed and the expansion formula with respect to the eigenfunctions of this boundary value problem is obtained. The main equation or modified Marchenko equation of the inverse scattering problem is derived and an algorithm of the construction of the potential function according to scattering data of this boundary value problem is given.

Lignocellulose Nanofiber Media for the Enhanced Removal of Copper From Aqueous Solutions

Nowadays, the entry of heavy metals entry into aqueous environments has jeopardized the health of human societies. The experiment was conducted in discontinuous conditions, and the study focused on examining the effect of five parameters including initial concentration, temperature, contact time, pH, and adsorbent dose on the adsorption of Cu heavy metals. In addition, the two-parameter models of Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich were studied and compared to evaluate isothermal absorption. The highest correlation coefficients were obtained for Freundlich (0.969) and Dubinin-Radushkevich (0.9603) models. Finally, thermodynamic parameters such as enthalpy and entropy changes and Gibbs-free energy were calculated as well. The pH parameters, adsorption dose, contact time, temperature, and initial Cu concentrations in the discontinuous system had a statistically significant effect on the adsorption process. The results showed that the maximum efficiency of Cu adsorption by Lignocellulose nanofiber (LCNF) occurred at the pH of 6, contact time of 60 minutes, the ambient temperature of 25°C, and adsorption dose of 0.2 g. In the case of adsorption kinetics, the pseudo-second order model and intra-particle diffusion had more fitness with the experimental data indicating a chemical equilibrium between the adsorbate and the absorbent. Thermodynamic studies demonstrated that the process (negative ΔG) is spontaneous (negative ΔG), endothermic (negative ΔH), and non-random (positive ΔS). Thus, LCNF can be used as an effective adsorbent in the removal of metals by having an extremely high surface area.

Modelling discontinuity control on the development of Hell\u2019s Mouth landslide

This paper focuses on numerical modelling and back analysis of the Hell’s Mouth landslide to provide improved understanding of the evolution of a section of the north coast of Cornwall, UK. Discontinuity control is highlighted through the formation of a ‘zawn’ or inlet, the occurrence of two successive landslides and evidence of ongoing instability through opening of tension cracks behind the cliff top. Several integrated remote sensing (RS) techniques have been utilised for data acquisition to characterise the slope geometry, landslide features and tension crack extent and development. In view of the structural control on the rock slope failures, a 3D distinct element method (DEM) code incorporating a discrete fracture network and rigid blocks has been adopted for the stability analysis. The onset and opening of tension cracks behind the modelled slope failure zones has also been studied by analysing the displacements of two adjoining landslide blocks, between which, a joint-related tension crack developed. In addition, a sensitivity analysis has been undertaken to provide further insight into the influence of key discontinuity parameters (i.e. dip, dip direction, persistence and friction angle) on the stability of this section of the coastline. Numerical modelling and field observations indicate that block removal and preferential erosion along a fault resulted in the formation of the inlet. The development of the inlet provides daylighting conditions for discontinuities exposed on the inlet slope wall, triggering the initial landslide which occurred on 23rd September 2011. Numerical modelling, and evidence from a video of the initial landslide, suggests that the cliff instability is characterised by a combination of planar sliding, wedge sliding and toppling modes of failure controlled by the discrete fracture network geometry.

Simulation of multicomponent material seepage in porous media under strong discontinuous conditions

Simulation of multicomponent material seepage in porous media under strong discontinuous conditions

Explicit Stable Finite Difference Methods for Diffusion-Reaction Type Equations

By the iteration of the theta-formula and treating the neighbors explicitly such as the unconditionally positive finite difference (UPFD) methods, we construct a new 2-stage explicit algorithm to solve partial differential equations containing a diffusion term and two reaction terms. One of the reaction terms is linear, which may describe heat convection, the other one is proportional to the fourth power of the variable, which can represent radiation. We analytically prove, for the linear case, that the order of accuracy of the method is two, and that it is unconditionally stable. We verify the method by reproducing an analytical solution with high accuracy. Then large systems with random parameters and discontinuous initial conditions are used to demonstrate that the new method is competitive against several other solvers, even if the nonlinear term is extremely large. Finally, we show that the new method can be adapted to the advection–diffusion-reaction term as well.

Accurate formulae for P-wave reflectivity and transmissivity for a non-welded contact interface with the effect of in situ vertical stress

SUMMARY A detailed knowledge of wave reflectivity parametrization for non-welded interface plays an important role in fracture characterization and reservoir prediction. However, the effect of in situ stress on reflectivity formulae for non-welded contact interface remains unclear. Here based on the linear-slip theory and acoustoelasticity theory, we propose the accurate P-wave reflectivity and transmissivity formulae for planar P wave incident upon the non-welded interface between two elastic half-spaces under the in situ vertical stress. The discontinuous boundary conditions coupled with vertical stress is used to represent the non-welded contact interface for the elastic and viscous cases. Then accurate formulae are derived by solving the boundary conditions. Numerical results show that the proposed formulae are frequency-dependent and the non-welded interface performs as high- and low-pass filters for reflected and transmittedP wave at low stress, respectively. Moreover, initial vertical stress can change the maximum amplitudes of reflection and transmission coefficients and the corresponding critical angles. Particularly, vertical stress weakens the fracture-induced anomalous seismic reflections in zones lack of significant impedance contrasts at low incidence angles. The sensitivity analysis suggests a non-welded interface transforms into a welded interface at normal compliance ${\Delta _N} \le 5 \times {10^{ - 11}}$ m Pa−1. The phases and amplitudes of the four coefficients reach the maximum values at the specific viscosity $\eta \approx {10^6}$ Pa·s m−1 for the case of P wave obliquely incident upon the viscous interface at incidence angle 30°. Finally, we describe a method for simulating seismic reflection at the interface of two elastic media with experimental measurement.

ON AN INVERSE PROBLEM FOR THE SYSTEM OF DIRAC EQUATIONS WITH DISCONTINUITY CONDITIONS ON THE WHOLE AXIS

ON AN INVERSE PROBLEM FOR THE SYSTEM OF DIRAC EQUATIONS WITH DISCONTINUITY CONDITIONS ON THE WHOLE AXIS

The evolution of dynamic energy during drop hammer testing of Brazilian disk with non-persistent joints: An extensive experimental investigation

Rock mass is well known as a discontinuous, heterogeneous, and anisotropic material. The behavior and strength of rock mass is heavily controlled by the condition and orientation of discontinuities (faults, joints, bedding planes) and discontinuity sets. Under dynamic loading conditions, rock bridges along non-persistent discontinuity planes may crack, and a fully persistent discontinuity may form, potentially affecting the stability of a rock structure. The study of the dynamic behavior of rock discontinuities has critical implications for civil engineering, the mining industry, and any other areas where rock mass is utilized as a structural foundation in areas prone to dynamic loading conditions, such as those formed during earthquake events. In this paper, cement-mortar-based Brazilian disks containing open, non-persistent joints were constructed and subjected to impact loading to investigate their impact energy behavior. The effect of some parameters, such as joint continuity factor (the relationship between joint length and rock bridge length), bridge angle, joint spacing, joint orientation, and impact angle were investigated to estimate the required Dynamic Energy for Crack Initiation (DECI), Dynamic Energy for Crack Coalescence (DECC) and failure pattern of specimens. The results of the experiments revealed an increasingly continuous joint reduces the DECI and DECC, while larger joint spacings past the middle value of those experimented increase the DECI and DECC. The bridge angle and loading direction do not affect DECI, but by increasing bridge angle DECC decreases, and it increases by increasing loading direction angle. Finally, an optimization analysis was conducted which showed that joint spacing and joint continuity factors significantly affects DECI, and joint continuity factor and loading direction have significant effect on DECC.

The Structuring and Empowerment Policy of Losari Beach Street Vendors Based on The Concept of Smart City

Mining activities in open pit and underground mines will always be associated with rock breaking or stripping activities (both mechanical and blasting), so that this can affect the structure and strength of rocks. The strength of the rock is strongly influenced by the presence of initial cracks (pre-existing cracks) and rock anisotropy conditions associated with discontinuous plane conditions. Fracture mechanics is a science that illustrates how a fracture can occur and propagate during applied stress on material. The main parameter in fracture mechanics is called fracture toughness which shows the resistance of the material to propagate the crack. There are several mode in determining type I fracture toughness, one of which is type I fracture toughness Flattened Brazilian Disc (FBD) mode. Type I fracture toughness test is carried out using a compression machine in a laboratory and is conducted on concrete samples consisting of 3 (three) various samples, with a ratio of cement and sand composition of 1:1, 1:2, and 2:1. This test also uses different loading rate values, namely 2.50 mm/min, 2.70 mm/min, and 2.83 mm/min. The results of the type I fracture toughness value from each loading rate will be compared to determine the effect of the loading rate on the value of type I fracture toughness. The obtained fracture toughness value is also related to the physical and mechanical properties of the samples. Based on the results of tests, it can be seen that the loading rate affects the value of fracture toughness, the increase in fracture toughness value is followed by the higher loading rate. In addition, it can be seen that the fracture toughness value is directly proportional to the uniaxial compressive strength value and the indirect tensile strength value. The average correlation value obtained is R2 = 0.9884 (indicating a strong relationship).

Design of Groundwater Sustain Irrigation Network System in Panca Lautang Area, Sidrap Regency, South Sulawesi

Mining activities in open pit and underground mines will always be associated with rock breaking or stripping activities (both mechanical and blasting), so that this can affect the structure and strength of rocks. The strength of the rock is strongly influenced by the presence of initial cracks (pre-existing cracks) and rock anisotropy conditions associated with discontinuous plane conditions. Fracture mechanics is a science that illustrates how a fracture can occur and propagate during applied stress on material. The main parameter in fracture mechanics is called fracture toughness which shows the resistance of the material to propagate the crack. There are several mode in determining type I fracture toughness, one of which is type I fracture toughness Flattened Brazilian Disc (FBD) mode. Type I fracture toughness test is carried out using a compression machine in a laboratory and is conducted on concrete samples consisting of 3 (three) various samples, with a ratio of cement and sand composition of 1:1, 1:2, and 2:1. This test also uses different loading rate values, namely 2.50 mm/min, 2.70 mm/min, and 2.83 mm/min. The results of the type I fracture toughness value from each loading rate will be compared to determine the effect of the loading rate on the value of type I fracture toughness. The obtained fracture toughness value is also related to the physical and mechanical properties of the samples. Based on the results of tests, it can be seen that the loading rate affects the value of fracture toughness, the increase in fracture toughness value is followed by the higher loading rate. In addition, it can be seen that the fracture toughness value is directly proportional to the uniaxial compressive strength value and the indirect tensile strength value. The average correlation value obtained is R2 = 0.9884 (indicating a strong relationship).

The Effect of Loading Rate on Fracture Toughness of Concrete using Type I Fracture Toughness Test Flattened Brazilian Disc (FBD) Mode

Mining activities in open pit and underground mines will always be associated with rock breaking or stripping activities (both mechanical and blasting), so that this can affect the structure and strength of rocks. The strength of the rock is strongly influenced by the presence of initial cracks (pre-existing cracks) and rock anisotropy conditions associated with discontinuous plane conditions. Fracture mechanics is a science that illustrates how a fracture can occur and propagate during applied stress on material. The main parameter in fracture mechanics is called fracture toughness which shows the resistance of the material to propagate the crack. There are several mode in determining type I fracture toughness, one of which is type I fracture toughness Flattened Brazilian Disc (FBD) mode. Type I fracture toughness test is carried out using a compression machine in a laboratory and is conducted on concrete samples consisting of 3 (three) various samples, with a ratio of cement and sand composition of 1:1, 1:2, and 2:1. This test also uses different loading rate values, namely 2.50 mm/min, 2.70 mm/min, and 2.83 mm/min. The results of the type I fracture toughness value from each loading rate will be compared to determine the effect of the loading rate on the value of type I fracture toughness. The obtained fracture toughness value is also related to the physical and mechanical properties of the samples. Based on the results of tests, it can be seen that the loading rate affects the value of fracture toughness, the increase in fracture toughness value is followed by the higher loading rate. In addition, it can be seen that the fracture toughness value is directly proportional to the uniaxial compressive strength value and the indirect tensile strength value. The average correlation value obtained is R2 = 0.9884 (indicating a strong relationship).