Effective Boundary Conditions for the Heat Equation with Interior Inclusion

Of concern is the scenario of a heat equation on a domain that contains a thin layer,on which the thermal conductivity is drastically different from that in the bulk.The multi-scales in the spatial variable and the thermal conductivity lead to computational difficulties,so we may think of the thin layer as a thickless surface,on which we impose"effective boundary conditions"(EBCs).These boundary conditions not only ease the computational burden,but also reveal the effect of the inclusion.In this paper,by considering the asymptotic behavior of the heat equation with interior inclusion subject to Dirichlet boundary condition,as the thickness of the thin layer shrinks,we derive,on a closed curve inside a two-dimensional domain,EBCs which include a Poisson equation on the curve,and a non-local one.It turns out that the EBCs depend on the magnitude of the thermal conductivity in the thin layer,compared to the reciprocal of its thickness.

Experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering boundary effect

The boundary condition is a crucial factor affecting the permeability variation due to suffusion.An experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering the boundary effect is conducted,where the hydraulic head difference(DH)varies,and the boundary includes non-loss and soil-loss conditions.Soil samples are filled into seven soil storerooms connected in turn.After evaluation,the variation in content of fine sand(ΔR_(f))and the hydraulic conductivity of soils in each storeroom(C_(i))are analyzed.In the non-loss test,the soil sample filling area is divided into runoff,transited,and accumulated areas according to the negative or positive ΔR_(f) values.ΔR_(f) increases from negative to positive along the seepage path,and Ci decreases from runoff area to transited area and then rebounds in accumulated area.In the soil-loss test,all soil sample filling areas belong to the runoff area,where the gentle-loss,strengthened-loss,and alleviated-loss parts are further divided.ΔR_(f) decreases from the gentle-loss part to the strengthened-loss part and then rebounds in the alleviated-loss part,and C_(i) increases and then decreases along the seepage path.The relationship between ΔR_(f) and Ci is different with the boundary condition.Ci exponentially decreases with ΔR_(f) in the non-loss test and increases with ΔR_(f) generally in the soil-loss test.

Effect of boundary conditions on shakedown analysis of heterogeneous materials

The determination of the ultimate load-bearing capacity of structures made of elastoplastic heterogeneous materials under varying loads is of great importance for engineering analysis and design. Therefore, it is necessary to accurately predict the shakedown domains of these materials. The static shakedown theorem, also known as Melan's theorem, is a fundamental method used to predict the shakedown domains of structures and materials. Within this method, a key aspect lies in the construction and application of an appropriate self-equilibrium stress field(SSF). In the structural shakedown analysis, the SSF is typically constructed by governing equations that satisfy no external force(NEF) boundary conditions. However, we discover that directly applying these governing equations is not suitable for the shakedown analysis of heterogeneous materials. Researchers must consider the requirements imposed by the Hill-Mandel condition for boundary conditions and the physical significance of representative volume elements(RVEs). This paper addresses this issue and demonstrates that the sizes of SSFs vary under different boundary conditions, such as uniform displacement boundary conditions(DBCs), uniform traction boundary conditions(TBCs), and periodic boundary conditions(PBCs). As a result, significant discrepancies arise in the predicted shakedown domain sizes of heterogeneous materials. Built on the demonstrated relationship between SSFs under different boundary conditions, this study explores the conservative relationships among different shakedown domains, and provides proof of the relationship between the elastic limit(EL) factors and the shakedown loading factors under the loading domain of two load vertices. By utilizing numerical examples, we highlight the conservatism present in certain results reported in the existing literature. Among the investigated boundary conditions, the obtained shakedown domain is the most conservative under TBCs.Conversely, utilizing PBCs to construct an SSF for the shakedown analysis leads to less conservative lower bounds, indicating that PBCs should be employed as the preferred boundary conditions for the shakedown analysis of heterogeneous materials.

Influence of the boundary effect on the mechanical response test of pavement cushion under the wetting effect of silt

Through a self-developed model test system,the mechanical properties of silt and the deformation characteristics of airport runways were investigated during the period of subgrade wetting.Based on the test results,the reliability of the numerical simulation results was verified.Numerical models with different sizes were established.Under the same cushion parameter and loading width ranges,the effects of the cushion parameters and loading conditions on the mechanical responses of the cushion before and after subgrade wetting were analyzed.The results show that the internal friction angles of silt with different wetting degrees are approximately 34°.The cohesion is from 8 to 44 kPa,and the elastic modulus is from 15 to 34 MPa.Before and after subgrade wetting,the variation rates of the cushion horizontal tensile stresses with the same cushion parameters and loading width ranges are different under the influence of boundary effects.After subgrade wetting,the difference in the variation rates of the cushion horizontal tensile stresses under the same cushion parameter range decreases compared with that before subgrade wetting;however,this difference increases under the same loading width range.Before and after subgrade wetting,the influence of the boundary effect on the mechanical response evaluation of the cushion is not beneficial for optimizing the pavement design parameters.When the cushion thickness is more than 0.25 m,the influence of the boundary effect can be disregarded.

Tunable acoustic radiation pattern assisted by effective impedance boundary

The acoustic wave propagation from a two-dimensional subwavelength slit surrounded by metal plates decorated with Helmholtz resonators （HRs） is investigated both numerically and experimentally in this work. Owing to the presence of HRs, the effective impedance of metal surface boundary can be manipulated. By optimizing the distribution of HRs, the asymmetric effective impedance boundary will be obtained, which contributes to generating tunable acoustic radiation pattern such as directional acoustic beaming. These dipole-like radiation patterns have high radiation efficiency, no finger- print of sidelobes, and a wide tunable range of the radiation pattern directivity angle which can be steered by the spatial displacements of HRs.

Observation of size-dependent boundary effects in non-Hermitian electric circuits

The non-Hermitian systems with the non-Hermitian skin effect(NHSE)are very sensitive to the imposed boundary conditions and lattice sizes,which lead to size-dependent non-Hermitian skin effects.Here,we report the experimental observation of NHSE with different boundary conditions and different lattice sizes in the unidirectional hopping model based on a circuit platform.The circuit admittance spectra and corresponding eigenstates are very sensitive to the presence of the boundary.Meanwhile,our experimental results show how the lattice sizes and boundary terms together affect the strength of NHSE.Therefore,our electric circuit provides a good platform to observe size-dependent boundary effects in non-Hermitian systems.

Semi-analytical solution for drained expansion analysis of a hollow cylinder of critical state soils

The expansion of a thick-walled hollow cylinder in soil is of non-self-similar nature that the stress/deformation paths are not the same for different soil material points.As a result,this problem cannot be solved by the common self-similar-based similarity techniques.This paper proposes a novel,exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils.Considering stress-dependent elastic moduli of soils,new analytical stress and displacement solutions for the nonself-similar problem are developed taking the small strain assumption in the elastic zone.In the plastic zone,the cavity expansion response is formulated into a set of first-order partial differential equations(PDEs)with the combination use of Eulerian and Lagrangian descriptions,and a novel solution algorithm is developed to efficiently solve this complex boundary value problem.The solution is presented in a general form and thus can be useful for a wide range of soils.With the new solution,the non-self-similar nature induced by the finite outer boundary is clearly demonstrated and highlighted,which is found to be greatly different to the behaviour of cavity expansion in infinite soil mass.The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small-sized calibration chambers.

Elimination of boundary effect for laminated overburden model in pillar stability analysis

The laminated overburden model(La Model)has been widely used for pillar design and stability analysis.As a boundary element program,the La Model program is sensitive to the boundary condition,which should be considered before creating the model.To eliminate the boundary effect in a La Model pillar stability analysis,a suitable boundary buffer zone is needed around the model edge.The radius of influence(R)and the abutment load extent(D)are two major factors that affect the stresses and displacements calculated in LaM odel.To determine the optimum buffer zone extent,a database of case histories was analyzed using the La Model program.Values for R and D were varied until a buffer zone having negligible influence on the pillar stability factor(SF)of the active mining zone(AMZ)was determined.

THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS

A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.

Investigation of acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure

In this paper, the acoustic scale effects and boundary effects for the similitude model of underwater complex shell-structure are investigated. The similitude conditions and relations between the similitude model and its prototype were studied in the references. This paper investigates the acoustic scale effects for the similitude model, which are influenced by loss factor, shear and rotatory inertia. At the same time, the boundary effects which are influenced by surface sound reflection are investigated in the experiment of similitude model. The results show that the acoustic scale effects may be controlled with model designing, the boundary effects can be controlled with experimental designing between the similitude model and its prototype.

Volcanism at the Permian-Triassic Boundary in South China and Its Effects on Mass Extinction

This paper discusses the clayrocks widespread at the Permian-Triassic boundary, which are mostly of volcanic origin. Volcanogenetic textures, structures and minerals such as high-temperature quartz are found in clayrocks at the Permian-Triassic boundary in many places. Thousands of microspherules have been collected from the Boundary clayrocks, many of which exhibit the typical features of the process from melting to cooling and solidification. indicating that they were formed by volcanic eruption or extraterrestrial impact. Volcanic effects on the Permian-Triassic mass extinction may be reflected in conodonts, algae and ammonoids. The Boundary clayrocks are found in many Permian-Triassic sections along the coast of Tethys. Their orighin remains to be studied.

ABNORMAL GEOMAGNETIC FIELD RESPONSE AT INTRAPLATE TECTONIC BOUNDARY IN CONTINENT AND CONTINENTAL MARGIN IN SOUTHEASTERN CHINA

We used matched filter, spectrum analysis, and continuation methods of potential field for data processing and obtained the geomagnetic field distribution about the continent and continental margin in southeast China. On the basis of grid data, inversion was conducted and magnetic field distribution and magnetic structure on bedding of different depths were obtained. The new results show that: 1. The magnetic field characteristics are largely different in horizontal and vertical directions and they can be divided into zones according to the continental blocks of Yangtze, Cathaysia, Kangdian (Sichuan-Yunnan) and Qinling-Dabie. 2. The Tanlu fault extends southward along the Ganjiang fault and the Wuchuan-Sihui fault after it crossed over the Yangtze River and was offset locally in the east-west direction. The Tanlu fault finally slips into the South China Sea at Hainan Island. 3. The boundary between Yangtze and Cathaysia blocks starts from Hangzhou Bay in the east, extends along Jiangshao fault and passes through Nanchang, Changsha, and Guilin, and finally enters the sea at Qinzhou, Guangxi. 4. The distribution of buried structure zone is located at 24.5°-26° N.

Effect of P impurity on NiAlΣ5 grain boundary from first-principles study

First-principles calculations based on the density functional theory（DFT） and ultra-soft pseudopotential are employed to study the atomic configuration and charge density of impurity P in Ni Al Σ5 grain boundary（GB）. The negative segregation energy of a P atom proves that a P atom can easily segregate in the Ni Al GB. The atomic configuration and formation energy of the P atom in the Ni Al GB demonstrate that the P atom tends to occupy an interstitial site or substitute a Al atom depending on the Ni/Al atoms ratio. The P atom is preferable to staying in the Ni-rich environment in the Ni Al GB forming P–Ni bonds. Both of the charge density and the deformation charge imply that a P atom is more likely to bond with Ni atoms rather than with Al atoms. The density of states further exhibits the interactions between P atom and Ni atom, and the orbital electrons of P, Ni and Al atoms all contribute to P–Ni bonds in the Ni Al GB. It is worth noting that the P–Ni covalent bonds might embrittle the Ni Al GB and weakens the plasticity of the Ni Al intermetallics.

Effects of Turbulent Dispersion of Atmospheric Balance Motions of Planetary Boundary Layer

New Reynolds' mean momentum equations including both turbulent viscosity and dispersion are used to analyze atmospheric balance motions of the planetary boundary layer. It is pointed out that turbulent dispersion with r 0 will increase depth of Ekman layer, reduce wind velocity in Ekman layer and produce a more satisfactory Ekman spiral lines fit the observed wind hodograph. The wind profile in the surface layer including tur-bulent dispersion is still logarithmic but the von Karman constant k is replaced by k1 = 1 -2/k, the wind increasesa little more rapidly with height.

Boundary Effect of Planar Glow Dielectric Barrier Discharge and Its Influence on the Discharge Structure

The dielectric barrier discharge （DBD） in the glow regime in neon has been investigated by experiment and two-dimensional （2D） fluid modeling. The discharge was carried out in a planar DBD system with segmented-electrodes driven by square-wave voltage. The results show that the glow DBD originates in the center of the electrode and expands outward to the electrode edge during each half cycle of the voltage, forming a radial structure. The discharge decays firstly in the inner area but sustains longer in the edge area, showing a reversed discharge area. The discharge cannot completely cover the entire electrode surface, but remains a border of nonor weak discharge. The fluid modeling shows a similar result in agreement with the experiments. The simulations indicate that the electric field in the edge area is distorted due to the boundary effect so that the electric field and charge distribution are different from that in the inner part. The distorted field reduces the longitudinal component near the edge and causes the local field to be lower than that in the center, and hence makes the discharge behindhand. It also induces a transverse field that makes the discharge extend radially outward to the edge. The boundary effect plays an important role in the glow DBD structure.

Boundary effect of toppling failure based on three-dimensional mechanical model

Previous researches on the mechanical model of toppling failure mainly concentrated on twodimensional mechanical model(TwDM) analysis. The TwDM analysis assumes the width of the slab beam is unit width without considering the lateral constraint force. The assumed conditions are obviously different from the site conditions, thus there is a certain difference between the calculated results and the field work. A three-dimensional mechanical model(ThDM)of toppling failure was established, considering that the slab beam was mainly subject to self-weight, the frictional resistance of interlayer and lateral constraint force. Due to the progressive characteristics of toppling failure, the concept and the formula of the first fracture depth(FFD) of toppling was raised and constructed. The case study indicates that the ThDM is more effective and can be accurately used to calculate the toppling fracture depth of the slab beam. The FFD decreases proportionally with the increase of slab beam width. FFD grows fast when the slab beam width is less than 2.0 m and it tends to be stable when the slab beam width is above 2.0 m. The FFD decreases with the increase of the lateral constraint coefficient, indicating that the boundary condition of the free space is positively correlated with the stability and depth of toppling. This is a good explanation of the free space effect. This study provides a reference for the stability evaluation and prevention-control design of toppling slope in the future.

Influence of Boundary Effect on Fracture of Concrete

The recently-developed boundary effect concept and the associated asymptotic model are used to analyze size-dependent fracture of concrete specimens.It is shown that the dependence of concrete fracture on specimen size,crack and/or ligament length is due to the same mechanism,i.e.the interactions between the crack tip fracture process zone and specimen's boundaries.By introducing an equivalent crack length ae,dimension dependent fracture becomes equivalent to fracture of a large plate with a small edge crack,and therefore,follows the same relationship of the 'net' nominal strength σn versus ae.As a result,the size dependent fracture can be predicted using the data measured on different types of specimens.To demonstrate the flexibility and effectiveness of the asymptotic boundary effect model,previously published results of three test series are analyzed.Excellent agreement has been found.Implications of the successful prediction are discussed.

The K Method for Estimating Earthquake Activity Parameters and Effect of the Boundary Uncertainty of the Source Region:Discussion on the Seismic Zoning Method

Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.

Effect of Boundary Condition on Impact Response and Damage Meso-mechanism for Scarf Bonded Repair of Load-bearing Composite Structures

Composite scarf repair is applied in airplane load-bearing structures. But the repairs would have different boundary supports in real situation, such as simply support, clamped support and flexible support. With different boundary supports, the bonded scarf repair of composite structures could have diverse damage mechanisms and responses. This work intends to study the impact performance of different boundaries. For this purpose, experimental tests were carried out on the specimens with two sides support and four sides support. The impact load and deflection was monitored during the tests. After impact being finished, the meso-mechanism was studied by means of micro-cracks of the side section for two sides support condition and cross section for the four sides support condition. It was possible to conclude that the four sides boundary possess higher impact resistance maximum loads, lower displacements and lower extent load dropping. In terms of damage modes, as the impact energy relative low 12 J and 16 J, the central position of scarf bonding zone for two sides support appears adhesive cohesive failure and adhesive-composite interface failure. When the energy increases to 20 J, the dominated damage of two sides support moves down to the feathered tip. For four sides support, the critical energy level is 25 J, under which the scarf adhesive begins to be damaged.