Influence of Mixing Conditions on Morphologies and Properties of MMT/Epoxy Resin Composite Materials

Montmorillonite（MMT） was directly modified with hexadecyl trimethyl ammonium bromide. The interlayer spacing of the organophilic montmorillonite（organo-MMT） corresponding to the d（001） plane peak was 2.21 nm The influences of the content of organo-MMT and mixing conditions including mixing temperature and mixing time on the intercalation and exfoliation structures of MMT/epoxy resin composites were investigated by wide X-ray diffraction（WXRD）. The X-ray patterns reveal that organo-MMT was intercalated by the epoxy resin during mixing process. Only under certain mixing conditions, could the exfoliation nanocomposites be formed. The mechanical and thermal properties of the composites were measured. The results indicate that the composites have better mechanical properties and higher Tg than those of the pristine epoxy resin.

GENERALIZED STROH FORMALISM FOR ANISOTROPIC ELASTICITY FOR GENERAL BOUNDARY CONDITIONS

The Stroh formalism is most elegant when the boundary conditions are simple, namely,they are prescribed in terms of traction or displacement.For mixed boundary conditions such as there for a slippery boundary,the concise matrix expressions of the Stroh formalism are destroyed.We present a generalized Stroh formalism which is applicable to a class of general boundary conditions.The general boundary conditions in- clude the simple and slippery boundary conditions as special cases.For Green's functions for the half space, the general solution is applicable to the case when the surface of the half-space is a fixed,a free,a slippery, or other more general boundary.For the Griffith crack in the infinite space,the crack can be a slit-like crack with free surfaces,a rigid line inclusion(which is sometimes called an anticrack),or a rigid line with slippery surface or with other general surface conditions.It is worth mention that the modifications required on the Stroh formalism are minor.The generalized formalism and the final solutions look very similar to those of unmodified version.Yet the results are applicable to a rather wide range of boundary conditions.

Novel wavelet-homotopy Galerkin technique for analysis of lid-driven cavity flow and heat transfer with non-uniform boundary conditions

In this paper, a brand-new wavelet-homotopy Galerkin technique is developed to solve nonlinear ordinary or partial differential equations. Before this investigation,few studies have been done for handling nonlinear problems with non-uniform boundary conditions by means of the wavelet Galerkin technique, especially in the field of fluid mechanics and heat transfer. The lid-driven cavity flow and heat transfer are illustrated as a typical example to verify the validity and correctness of this proposed technique. The cavity is subject to the upper and lower walls’ motions in the same or opposite directions.The inclined angle of the square cavity is from 0 to π/2. Four different modes including uniform, linear, exponential, and sinusoidal heating are considered on the top and bottom walls, respectively, while the left and right walls are thermally isolated and stationary.A parametric analysis of heating distribution between upper and lower walls including the amplitude ratio from 0 to 1 and the phase deviation from 0 to 2π is conducted. The governing equations are non-dimensionalized in terms of the stream function-vorticity formulation and the temperature distribution function and then solved analytically subject to various boundary conditions. Comparisons with previous publications are given,showing high efficiency and great feasibility of the proposed technique.

EXISTENCE OF MULTIPLE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

The paper is concerned with the multiplicity of solutions for some nonlinear elliptic equations involving critical Sobolev exponents and mixed boundary conditions.

Static response of functionally graded multilayered two-dimensional quasicrystal plates with mixed boundary conditions

The unusual properties of quasicrystals(QCs)have attracted tremendous attention from researchers.In this paper,a semi-analytical solution is presented for the static response of a functionally graded(FG)multilayered two-dimensional(2 D)decagonal QC rectangular plate with mixed boundary conditions.Based on the elastic theory of FG 2 D QCs,the state-space method is used to derive the state equations composed of partial differential along the thickness direction.Besides,the Fourier series expansion and the differential quadrature technique are utilized to simulate the simply supported boundary conditions and the mixed boundary conditions,respectively.Then,the propagator matrix which connects the field variables at the upper interface to those at the lower interface of any homogeneous layer can be derived based on the state equations.Combined with the interface continuity condition,the static response can be obtained by imposing the sinusoidal load on the top surfaces of laminates.Finally,the numerical examples are presented to verify the effectiveness of this method,and the results are very useful for the design and understanding of the characterization of FG QC materials in their applications to multilayered systems.

Computational Fracture Analysis of an AFM-Specimen under Mixed Mode Loading Conditions

Fracture processes in ship-building structures are in many cases of a 3-D character. A finite element （FE） model of an all fracture mode （AFM） specimen was built for the study of 3-D mixed mode crack fracture behavior including modes Ⅰ,Ⅱ, and Ⅲ. The stress intensity factors （SIFs） were calculated by the modified virtual crack closure integral （MVCCI） method, and the crack initiation angle assessment was based on a recently developed 3-D fracture criterion--the Richard criterion. It was shown that the FE model of the AFM-specimen is applicable for investigations under general mixed mode loading conditions, and the computational results of crack initiation angles are in agreement with some available experimental findings. Thus, the applicability of the FE model of the AFM-specimen for mixed mode loading conditions and the validity of the Richard criterion can be demonstrated.

Potential Application of iRap for Road Safety Assessment under Mixed Traffic Condition Case Study: Le Van Viet Street in Ho Chi Minh City

Road transport safety policies have emphasized road infrastructure safety design and engineering as a core function.However,in developing countries like Vietnam,this approach has been slower to adopt,resulting in substandard roads.In-depth studies of accident locations indicate that road environment factors contribute significantly to road accidents in Vietnam and road design features are associated with specific accident types and hazards.Proactive and reactive approaches,such as road safety audit,inspection,assessment,and treatment of hazardous locations,are necessary to ensure that the road and its environment are safe.This paper provides an overview of road safety in Vietnam in general,and Ho Chi Minh in particular,including its factors and characteristics,as well as road infrastructure safety improvements.The iRap tool for road safety inspection and assessment is highlighted as a potential method for systematically analyzing road infrastructure deficiencies and providing targeted countermeasures to improve road safety under mixed traffic conditions.

Dynamic response analysis of a multiple-beam structure subjected to a moving load

In this study,the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated.The boundary conditions and properties of each beam vary,and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations.By examining a high-speed railway(HSR)with mixed boundary conditions,the rationality for the newly proposed method is verified,the difference in simulated multiple-beam models with different beam numbers is explored,and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined.Results suggest that the number of beams in the model should be as close to the actual beam number as possible.Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure.Neglecting the track-structure can overestimate the resonant speed of a high-speed railway,simply-supported beam bridge.The effective interval of foundation stiffness(EIFS)can provide a reference for future engineering designs.

Structured condition numbers and statistical condition estimation for the LDU factorization

In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.

A LOWER BOUND FOR FIRST EIGENVALUE WITH MIXED BOUNDARY CONDITIOIN

Let M be an n-dimensional compact Riemannian manifold with or without boundary,and its Ricci curvature Ric M≥n-1.The paper obtains an inequality for the first eigenvalue η 1 of M with mixed boundary condition,which is a generalization of the results of Lichnerowicz,Reilly,Escobar and Xia.It is also proved that η 1≥n for certain n-dimensional compact Riemannian manifolds with boundary,which is an extension of the work of Cheng,Li and Yau.

On Iterative Algorithm and Perturbation Analysis for the Nonlinear Matrix Equation

In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=In.Explicit expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix equation.Comparative analysis for the derived condition numbers and the proposed algorithm are presented.The proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line searches.Componentwise condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.

Re ned rigorous perturbation bounds for the SR decomposition

In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.

Spectral Asymptotics for Laplacian with Mixed Boundary-value Condition

Let Ω be a non-empty bounded open set in Rn(n ≥1) with boundary (?)Ω=Γ1∪Γ2. WedefineIn this paper, we consider the following variational eigenvalue problem:where △ denotes the Laplacian in Ω. We say that the scalar λ is an eigenvalue of (P) if

Existence theory for Rosseland equation and its homogenized equation

The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.

CA-YOLOv5: Detection model for healthy and diseased silkworms in mixed conditions based on improved YOLOv5

The accurate identification and localization of diseased silkworms is an important task in the research of disease precision control technology and equipment development in the sericulture industry. However, the existing deep learning-based methods for this task are mainly based on image classification, which fails to provide the location information of diseased silkworms. To this end, this study proposed an object detection-based method for identifying and locating healthy and diseased silkworms. Images of mixed healthy and diseased silkworms were collected using a mobile phone, and the category and location of each silkworm were labeled using LabelImg as a labeling tool to construct an image dataset for object detection. Based on the one-step detection model YOLOv5s, the ConvNeXt-Attention-YOLOv5 (CA-YOLOv5) model was designed in which the large kernel with depth-wise separable convolution (7×7 dw-conv) of ConvNeXt was adopted to expand receptive fields and the channel attention mechanism ECANet was added to enhance the capability of feature extraction. Experiments showed that the mean average precision (mAP) values of CA-YOLOv5 for healthy and diseased silkworms reached 96.46%, which is 1.35% better than that achieved via YOLOv5s. At the same time, the overall performance of CA-YOLOv5 was significantly better than state-of-the-art one-step models, such as Single Shot MultiBox Detector (SSD), CenterNet, and EfficientDet, and even improved YOLOv5 using image attention mechanism and a lightweight backbone, like SENet-YOLOv5 and MobileNet-YOLOv5. The results of this study can provide an important basis for the accurate positioning of diseased silkworms in precision disease control technology and equipment development.

DOUBLE FLIP MOVE FOR ISING MODELS WITH MIXED BOUNDARY CONDITIONS

This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of the spin lattice followed by a spin value flip.Both symmetric and approximately symmetric models are considered.We prove the detailed balance of the double flip move and demonstrate its empirical efficiency in mixing.

Tunnelling through weak and fragile rocks of Himalayas

A considerable amount of tunnelling has been going on in India for various projects such as hydroelectric power, irrigation, roads and railways. Most of these projects are located in Himalayas, far away from the urban areas. Tunnelling through weak and jointed rock masses such as the one in the Himalayas is a challenging task for the planners, designers, engineers and geologists because of high overburden, thickly vegetated surface, weak, poor and fragile rocks and highly varying geology with the presence of numerous small and big shear zones, faults, etc. Due to these reasons, various tunnelling problems have been faced in the past and are still being encountered. Failures and the problems may be regarded as challenges and opportunities for generating new knowledge base and thereby increasing self-reliance in tunnelling. The experiences of Himalayan tunnelling through weak and fragile rocks covering varying and mixed geology, understanding on tunnelling in squeezing ground conditions and applicability of TBM in Himalayas are presented. It has also been highlighted that the probe holes planning, drilling and monitoring shall be followed seriously to reduce the geological surprises.

Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs

In this paper,we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs.Firstly,we prove the local existence of solutions via Schauder fixed point theorem.Then,under certain conditions we obtain the estimates of quenching time and quenching rate.Finally,numerical experiments are shown to explain the theoretical results.