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This work focuses on the semi-analytical methods for obtaining the solutions of time fractional partial integro-differential equations. Adomian decomposition method (ADM) and homotopy perturbation method (HPM) are successfully applied. Further, the modified version of homotopy perturbation method is applied which is comparatively more accurate than the other two methods. These methods are shown to be efficient and converge rapidly to the exact solution. Graphs are plotted and tabular data are recorded which represents the accuracy of the proposed techniques. [ABSTRACT FROM AUTHOR]

In this paper we prove the strong Sard conjecture for sub-Riemannian structures on 3-dimensional analytic manifolds. More precisely, given a totally nonholonomic analytic distribution of rank 2 on a 3-dimensional analytic manifold, we investigate the size of the set of points that can be reached by singular horizontal paths starting from a given point and prove that it has Hausdorff dimension at most 1. In fact, provided that the lengths of the singular curves under consideration are bounded with respect to a given complete Riemannian metric, we demonstrate that such a set is a semianalytic curve. As a consequence, combining our techniques with recent developments on the regularity of sub-Riemannian minimizing geodesics, we prove that minimizing sub-Riemannian geodesics in 3-dimensional analytic manifolds are always of class C 1 , and actually they are analytic outside of a finite set of points. [ABSTRACT FROM AUTHOR]

In this paper, the differential transformation method (DTM) is employed to find the semi-analytical solutions of SIS and SI epidemic models for constant population. Firstly, the theoretical background of DTM is studied and followed by constructing the solutions of SIS and SI epidemic models. Furthermore, the convergence analysis of DTM is proven by proposing two theorems. Finally, numerical computations are made and compared with the exact solutions. From the numerical results, the solutions produced by DTM approach the exact solutions which agreed with the proposed theorems. It can be seen that the DTM is an alternative technique to be considered in solving many practical problems involving differential equations. [ABSTRACT FROM AUTHOR]

We prove that the set of Segre-degenerate points of a real-analytic subvariety X in Cn is a closed semianalytic set. It is a subvariety if X is coherent. More precisely, the set of points where the germ of the Segre variety is of dimension k or greater is a closed semianalytic set in general, and for a coherent X, it is a real-analytic subvariety of X. For a hypersurface X in Cn, the set of Segre-degenerate points, X[n], is a semianalytic set of dimension at most 2n−4. If X is coherent, then X[n] is a complex subvariety of (complex) dimension n−2. Example hypersurfaces are given showing that X[n] need not be a subvariety and that it also need not be complex; X[n] can, for instance, be a real line. [ABSTRACT FROM AUTHOR]

Semi-analytical studies for the porosity action of a hollow sphere made of functionally graded piezoelectric material are presented. A semi-analytical technique for radial displacement is presented. A combination of internal and external pressures, temperature distribution, uniform hygrothermal distribution, and an electric potential variation has been discussed between the inner and outer surfaces of the sphere. The material physical properties for the present porous hollow sphere are varying through the thickness due to the power functions of the radius. Numerical outcomes are validated for radial displacement, electric potential, and stresses for the perfect and porous functionally graded hollow sphere. The effect of different mechanical, piezoelectric, and hygrothermal are investigated. [ABSTRACT FROM AUTHOR]

Given an n-dimensional, connected, analytic manifold M and analytic vector fields { f i } i = 0 m on M consider the affine control process 0.2 ξ ′ = f 0 (ξ) + ∑ i = 1 m u i f i (ξ). Let t → ξ x , u ¯ (t) be the solution curve satisfying the above differential equation with initial condition ξ (0) = x and u ¯ = (u 1 , u 2 , ... , u m) ∈ W T m ≡ L ∞ ([ 0 , T ] , R m) is a control function. For a fixed x ∈ M and T > 0 consider the evaluation map E x : W T m → M : E x (u ¯) = ξ x , u ¯ (T) . Given a compact, semi-analytic set K ⊂ M , we prove that, (Theorem 1.6), if the system satisfies SAP (strong accessibility property), at each x ∈ K , then the set of control functions u ¯ ∈ C ∞ ([ 0 , T ] , R m) at which the the map E x is a submersion, (uniformly as x varies over K), is dense in the set C ∞ ([ 0 , T ] , R m) of C ∞ control functions with the C ∞ topology. The proof of the uniform submersion theorem, uses a control theoretic notion of 'detectability' and is based on an important result, (Theorem 2.2), about existence and genericity of 'universal detectors'. [ABSTRACT FROM AUTHOR]

In this paper, we develop a Multilayer (ML) method for solving one-factor parabolic equations. Our approach provides a powerful alternative to the well-known finite difference and Monte Carlo methods. We discuss various advantages of this approach, which judiciously combines semi-analytical and numerical techniques and provides a fast and accurate way of finding solutions to the corresponding equations. To introduce the core of the method, we consider multilayer heat equations, known in physics for a relatively long time but never used when solving financial problems. Thus, we expand the analytic machinery of quantitative finance by augmenting it with the ML method. We demonstrate how one can solve various problems of mathematical finance by using our approach. Specifically, we develop efficient algorithms for pricing barrier options for time-dependent one-factor short-rate models, such as Black-Karasinski and Verhulst. Besides, we show how to solve the well-known Dupire equation quickly and accurately. Numerical examples confirm that our approach is considerably more efficient for solving the corresponding partial differential equations than the conventional finite difference method by being much faster and more accurate than the known alternatives. [ABSTRACT FROM AUTHOR]

We continue a series of papers devoted to construction of semi-analytic solutions for barrier options. These options are written on underlying following some simple one-factor diffusion model, but all the parameters of the model as well as the barriers are time-dependent. We managed to show that these solutions are systematically more efficient for pricing and calibration than, e.g., the corresponding finite-difference solvers. In this paper we extend this technique to pricing double barrier options and present two approaches to solving it: the General Integral transform method and the Heat Potential method. Our results confirm that for double barrier options these semi-analytic techniques are also more efficient than the traditional numerical methods used to solve this type of problems. [ABSTRACT FROM AUTHOR]

We generate constrained realizations (CRs) of the density and peculiar velocity fields within |$200 \, h^{-1} \, \mathrm{Mpc}$| from the final release of the Two-Micron All-Sky Redshift Survey (2MRS) – the densest all-sky redshift survey to date. The CRs are generated by combining a Wiener filter estimator in spherical Fourier-Bessel space with random realizations of log-normally distributed density fields and Poisson-sampled galaxy positions. The algorithm is tested and calibrated on a set of semi-analytic mock catalogues mimicking the environment of the Local Group (LG), to rigorously account for the statistical and systematic errors of the reconstruction method. By comparing our peculiar velocity CRs with the observed velocities from the Cosmicflows-3 catalogue, we constrain the normalized linear growth rate to |$f \sigma _8^{\text{lin}}= 0.367 \pm 0.060$|⁠ , which is consistent at the 1.1σ level with the latest Planck results as well as other direct probes. Simultaneously, we estimate a bulk flow contribution from sources beyond the 2MRS reconstruction volume of |$B^{\text{ext}}= 199 \pm 68 \, \mathrm{km} \, \mathrm{s}^{-1}$| towards l  = 299 ± 18°, b  = 8 ± 19°. The total reconstructed velocity field at the position of the LG, smoothed with a |$1 \, h^{-1} \, \mathrm{Mpc}$| Gaussian, is |$685 \pm 75 \, \mathrm{km} \, \mathrm{s}^{-1}$| towards l  = 270.6 ± 6.6°, b  = 35.5 ± 7.2°, in good agreement with the observed CMB dipole. The total reconstructed bulk flow within different radii is compatible with other measurements. Within a |$50 \, h^{-1} \, \mathrm{Mpc}$| Gaussian window we find a bulk flow of |$274 \pm 50 \, \mathrm{km} \, \mathrm{s}^{-1}$| towards l  = 287 ± 9°, b  = 11 ± 10°. The code used to generate the CRs and obtain these results, dubbed coras , is made publicly available. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a semi-analytic procedure for deriving the response spectrum of the synthetic acceleration records generated using the Double-Frequency Model (DFM). DFM is a filtered white noise method for fully non-stationarity synthetic acceleration records. The proposed semi-analytic procedure is based on the theory of the first passage problem, which precludes time and computationally extensive methods such as Monte Carlo simulations. Assuming a slowly-varying envelope and evolutionary transfer functions, the procedure of estimating the elastic response of a structure is implemented in both time and frequency domains. Comparing the results of our model with previous models and approximations, we concluded that for a set of 10000 realizations of the DFM model, the semi-analytic model produces an error of less than 10% for 92% of the realizations. The accuracy of estimations is higher in the short-period compared to the long-period ranges of the response spectrum. Comparing the accuracy of approximations used to arrive at peak factors, results show that Michaelov approximation executed in the frequency domain yields the best results compared to Poisson or Vanmarcke procedures. [ABSTRACT FROM AUTHOR]

This research article is concerned with the solution of hydrodynamic stability based linear and nonlinear fourteenth order differential problem, which has great significance in applied physics, astrophysics, applied mathematics, engineering departments. The homotopy perturbation method (HPM) and optimal homotopy asymptotic method (OHAM) are applied for the solution of the existed problem. These semi analytical techniques are continuously evolved to solve diverse range of linear and nonlinear problems with effective approximate agents which is a rapid approach to the exact solutions. This approach is effectively proposed with different numerical examples, which are taken from literature. Numerical results are accomplished by phrase of convergent series solutions and approach to the accurate solutions only by taking minimum steps. The numerical results are exercised with exact solutions, cubic polynomial spline technique (CPST) and cubic non-polynomial spline technique (CNPST), excellent agreement has been observed. The observations suggested that OHAM and HPM performed excellent in comparison to the CPST and CNPST in terms of solution, which demonstrated the effectiveness, potential and validity of suggested schemes in reality and acquired results are of top-level perfection. [ABSTRACT FROM AUTHOR]

A non-zero mutual information between morphology of a galaxy and its large-scale environment is known to exist in Sloan Digital Sky Survey (SDSS) upto a few tens of Mpc. It is important to test the statistical significance of these mutual information if any. We propose three different methods to test the statistical significance of these non-zero mutual information and apply them to SDSS and Millennium run simulation. We randomize the morphological information of SDSS galaxies without affecting their spatial distribution and compare the mutual information in the original and randomized data sets. We also divide the galaxy distribution into smaller subcubes and randomly shuffle them many times keeping the morphological information of galaxies intact. We compare the mutual information in the original SDSS data and its shuffled realizations for different shuffling lengths. Using a t -test, we find that a small but statistically significant (at |$99.9{{\ \rm per\ cent}}$| confidence level) mutual information between morphology and environment exists upto the entire length-scale probed. We also conduct another experiment using mock data sets from a semi-analytic galaxy catalogue where we assign morphology to galaxies in a controlled manner based on the density at their locations. The experiment clearly demonstrates that mutual information can effectively capture the physical correlations between morphology and environment. Our analysis suggests that physical association between morphology and environment may extend to much larger length-scales than currently believed, and the information theoretic framework presented here can serve as a sensitive and useful probe of the assembly bias and large-scale environmental dependence of galaxy properties. [ABSTRACT FROM AUTHOR]

We propose a mathematical model for two-dimensional continua in order to establish a solid theoretical foundation for the study of their complex topology, large geometric deformations, and topological changes such as merging in the context of multiphase flows. Our modeling space, named the Yin space, consists of regular open semianalytic sets with bounded boundaries, and is further equipped with constructive and algebraic definitions of Boolean operations. Major distinguishing features of our model include (a) topological information of fluids such as Betti numbers can be easily extracted in constant time, (b) topological changes of fluids are captured by nonmanifold points on fluid boundaries, and (c) Boolean operations on fluids correctly handle all degenerate cases and apply to arbitrarily complex topologies, yet they are simple and efficient in that they only involve determining the relative position of a point to a Jordan curve and intersecting a number of curve segments. Finally, utilities of (a) and (c) are demonstrated by combining the Yin space with the recent cubic MARS method to track a complex fluid in a single vortex flow. [ABSTRACT FROM AUTHOR]

Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the mild solution (m-solution) of a class of fractional dynamic systems (FDS). We deal with a new family of fractional m-solution in Rn for fractional dynamic systems. To accomplish it, we introduce first the concept of (F, ψ)-contraction based on the measure of noncompactness in some Banach spaces. Consequently, we establish requisite fixed point theorems (FPTs), which extend existing results following the Krasnoselskii FPT and coupled fixed point results as a outcomes of derived one. Finally, we give a numerical example to verify the considered FDS, and we solve it by iterative algorithm constructed by semianalytic method with high accuracy. The solution can be considered as bacterial growth system when the time interval is large. [ABSTRACT FROM AUTHOR]

Ubiquitous detections of cold/warm gas around galaxies indicate that the circumgalactic medium (CGM) is multiphase and dynamic. Recent state-of-the-art cosmological galaxy simulations have generally underproduced the column density of cold halo gas. We argue that this may be due to a mismatch of spatial resolution in the circumgalactic space and the relevant physical scales at which the cold gas operates. Using semi-analytic calculations and a set of magnetohydrodynamic simulations, we present a multiphase model of the gaseous haloes around galaxies, the circumgalactic mist (CGmist). The CGmist model is based on the idea that the observed cold halo gas may be a composite of cold, dense, and small cloudlets embedded in a hot diffuse halo, resembling terrestrial clouds and mist. We show that the resulting cold gas from thermal instabilities conforms to a characteristic column density of |$N_{\rm H}\approx 10^{17}\, \rm {cm^{-2}}$| as predicted by the cs t cool ansatz. The model implies a large number of cold clumps in the inner galactic halo with a small volume filling factor but a large covering fraction. The model also naturally gives rise to spatial extents and differential covering fractions of cold, warm, and hot gas. To self-consistently model the co-evolution of the CGM and star formation within galaxies, future simulations must address the mismatch of the spatial resolution and characteristic scale of cold gas. [ABSTRACT FROM AUTHOR]

A computational study of the effects of the intergranular exchange field and its dispersion on the cluster size in perpendicular recording media is presented. The dispersion arises from the grain size dispersion and the dispersion of intrinsic exchange coupling between individual grains. It is found that increasing the degree of dispersion reduces the cluster size due to weakly coupled grains acting as pinning sites against the expansion of the clusters. A simple semi-analytical model is proposed which gives good agreement with the numerical calculations in the limit of the large anisotropy constant. [ABSTRACT FROM AUTHOR]

Polymer chains, confined to cavities or polymer layers with dimensions less than the chain radius of gyration, appear in many phenomena, such as gel chromatography, rubber elasticity, viscolelasticity of high molar mass polymer melts, the translocation of polymers through nanopores and nanotubes, polymer adsorption, etc. Thus, the description of how the constraints alter polymer thermodynamic properties is a recurrent theoretical problem. A realistic treatment requires the incorporation of impenetrable interacting (attractive or repulsive) boundaries, a process that introduces significant mathematical complications. The standard approach involves developing the generalized diffusion equation description of the interaction of flexible polymers with impenetrable confining surfaces into a discrete eigenfunction expansion, where the solutions are normally truncated at the first mode (the “ground state dominance” approximation). This approximation is mathematically well justified under conditions of strong confinement, i.e., a confinement length scale much smaller than the chain radius of gyration, but becomes unreliable when the polymers are confined to dimensions comparable to their typically nanoscale size. We extend a general approach to describe polymers under conditions of weak to moderate confinement and apply this semianalytic method specifically to determine the thermodynamics and static structure factor for a flexible polymer confined between impenetrable interacting parallel plate boundaries. The method is first illustrated by analyzing chain partitioning between a pore and a large external reservoir, a model system with application to chromatography. Improved agreement is found for the partition coefficients of a polymer chain in the pore geometry. An expression is derived for the structure factor S(k) in a slit geometry to assist in more accurately estimating chain dimensions from scattering measurements for thin polymer films. [ABSTRACT FROM AUTHOR]

We revisit different three-dimensional network-forming lattice models proposed in the literature to investigate water anomalies. We perform a semianalytical calculation based on a cluster-variation technique, showing a quite good agreement with independent Monte Carlo results. The method allows us to clarify the structure of the phase diagrams, which turn out to exhibit different kinds of orientationally ordered phases. We point out that certain “waterlike” thermodynamic anomalies, claimed by previous studies, are indeed artifacts of a homogeneity assumption made in the analytical treatment. We argue that such a difficulty is common to a whole class of lattice models for water and suggest a possible way to overcome the problem in terms of “equivalent” models defined on random lattices. [ABSTRACT FROM AUTHOR]

Abstract This paper presents semi-analytical solutions of two-dimensional plane strain consolidation for unsaturated soils under time-dependent loading using Fourier sine series and Laplace transform. The consolidation equations in form of two-order partial differential equations with three variables are firstly converted to that with two variables. Then four-order ordinary differential equations about excess pore-air and pore-water pressures are presented, and the semi-analytical solutions of excess pore-air and pore-water pressures and settlement are achieved in the Laplace transform domain. Two comparisons are performed to verify the exactness of the obtained solutions, and the consolidation behavior involving three time-dependent loadings is illustrated and discussed. [ABSTRACT FROM AUTHOR]

Abstract Most analytical approaches for the design of shallow plate and screw anchors in tension are based on the limit equilibrium of a rigid soil wedge for which a horizontal stress distribution acting on the failure plane is assumed. Finite element analysis for a wide range of soil properties was carried out to identify the shape of the failure mechanism and to study the stress distribution at failure. Results show that soil deformation modifies the stress field around the anchor and increases the uplift capacity. A semi-analytical approach is proposed to describe this stress distribution, based on peak friction angle. [ABSTRACT FROM AUTHOR]

Abstract A three dimensional model for solving steady state heat conduction in a semi-infinite domain containing an elementary cuboidal inhomogeneity is established in this paper. A set of analytical formulas for steady state heat conduction in a full space with an embedded cuboidal inclusion is derived. The temperature field of a half space distributed with arbitrarily shaped inhomogeneities is then obtained via the application of numerical discretization and the method of images. Benchmark comparisons involving a cuboidal/ellipsoidal inhomogeneity and double-inhomogeneity particle with the results produced by the finite element method (FEM) are conducted. Good agreements between the results of the two methods demonstrate the effectiveness and capability of the proposed model. Further, a case of heterogeneous material containing arrayed inhomogeneities is studied to explore the disturbance and interaction of the temperature field due to distributed inhomogeneities. [ABSTRACT FROM AUTHOR]

The use of adhesively bonded joints in industrial structures requires reliable tools for the estimation of the failure load. The necessary and sufficient condition to predict the strength of such joints involves the implementation of a coupled stress and energetic criteria. However, its application necessitates the identification of the stress distribution along the adhesive layer, which has been approximated in this paper by a previously published closed‐form solution. This analysis along with finite element modelling results are compared with experimental data issued from a double‐notched sample tested with the Arcan fixture at various load ratios. The results show good agreement; the use of the closed‐form solution permitted to predict the failure load more rapidly and in a conservative manner compared with the experimental results. The application of the methodology is also extended to a wider range of joint geometries by means of spatial interpolation using the Kriging model. [ABSTRACT FROM AUTHOR]

Abstract On the basis of three-dimensional elasticity theory, semi-analytical solutions that combine the state space technique (SST) and differential quadrature method (DQM) were developed for the free vibration of arbitrary angle-ply laminated cylindrical shells with simply-simply, simply-clamped and clamped-clamped support boundary conditions. The SST was applied in the radial direction while the DQM was employed to discretize the longitudinal direction of the cylindrical shells. The derived equation of motion was solved for the free vibration of general cylindrical shells, including the isotropic, orthotropic, or monoclinic material behavior. The theoretical solutions were verified by comparing the reported results of two-dimensional shell theory in the literature and the finite element results from commercial software. The effects of layer angle on natural frequencies were also investigated. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we consider numerical simulation of wormhole propagation with the Darcy–Brinkman–Forchheimer model. Matrix acidization in carbonate reservoirs is a widely practiced technique in the product enhancement of the oil and gas reservoir. A wormhole, i.e. a flow channel with high porosity, is generated during reactive dissolution of carbonates by the action of the injected acid. In the wormhole forming process, the porosity changes non-uniformly in space, and it even becomes close to unity in the central regions of a wormhole. The Darcy–Brinkman–Forchheimer model accounts for both the porous media and clear fluid area, so it can be used to model wormhole propagation perfectly. This model, however, strongly depends on porosity. Therefore, the time schemes for solving the evolutionary equation of porosity have a significant effect on accuracy and stability of the numerical simulation for wormhole propagation. We propose a semi-analytic time scheme, which solves the porosity equation analytically at each time step for given acid concentration. The proposed numerical method can improve the accuracy and stability of numerical simulation significantly. For theoretical analysis of the proposed time scheme for the wormhole simulation, we first reconstruct the analytical functions of porosity to analyze the time error of the porosity, and on the basis of error estimates of porosity, we employ a coupled analysis approach to achieve the estimates of pressure, velocity and solute concentration. The time error estimates for velocity, pressure, concentration and porosity are obtained in different norms. Finally, numerical results are provided to verify the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Modelling the vibrational response of railway tracks is a mandatory step to predict rolling noise. This article proposes a model based on the semi-analytical finite element method (SAFE) taking into account the three main characteristics of railway tracks: infinite length in the longitudinal direction, deformable cross-section, and periodic track support. Although this approach is ideally suited to predict rail vibrations, numerical instabilities undermine its reliability at low frequencies. Consequently, a new approach using the second-order Arnoldi reduction (SOAR) is used, which allows to provide the required numerical stability. Lastly, numerical results are compared with classical railway track behaviours described in the literature, as well as experimental data and 3D finite element simulations. [ABSTRACT FROM AUTHOR]

Highlights • Addition of an error criterion allows the detection of artificial solutions. • Classification of solutions in large relative error, low relative error stable and low relative error unstable ones. • Application to nonlinear oscillators showing varieties of multiple solutions. Abstract Harmonic Balance is a very popular semi-analytic method in nonlinear dynamics. It is easy to apply and is known to produce good results for numerous examples. Adding an error criterion taking into account the neglected terms allows an evaluation of the results. Looking on the therefore determined error for increasing ansatz orders, it can be evaluated whether a solution really exists or is an artifact. For the low-error solutions additionally a stability analysis is performed which allows the classification of the solutions in three types, namely in large error solutions, low error stable solutions and low error unstable solution. Examples considered in this paper are the classical Duffing oscillator and an extended Duffing oscillator with nonlinear damping and excitation. Compared to numerical integration, the proposed procedure offers a faster calculation of existing multiple solutions and their character. [ABSTRACT FROM AUTHOR]

Highlights • A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves is proposed. • The fluid film forces calculated by the proposed method agree well with the results obtained by the finite-difference method. • The method facilitates the accurate calculation of the fluid film force of a journal bearing and saves computational costs. • The effects of the bearing parameters on the nonlinear fluid film forces are analyzed. Abstract A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves under the cavitation boundary condition is proposed. The pressure distribution of the Reynolds equation of a finitely long journal bearing with axial grooves is expressed as a particular solution and a homogeneous solution. The particular solution and the homogeneous solution are separated, respectively, into an additive form and a multiplicative form by the method of separation of variables. The circumferential separable function of the homogeneous solution can be expanded on the basis of the infinite series of trigonometric functions. The pressure distribution of the particular solution is obtained by the Sommerfeld transformation. The termination positions of the fluid film are determined by the continuity condition. The analytical expressions for the nonlinear fluid film forces of a finitely long journal bearing with two axial grooves are obtained. The fluid film forces calculated by the proposed method agree well with the results obtained by the finite-difference method. The effects of the bearing parameters on the nonlinear fluid film forces are analyzed. [ABSTRACT FROM AUTHOR]

Summary: A semianalytical procedure is proposed for evaluating the internal forces of circular tunnel with imperfect interface bonding in layered ground subjected to an obliquely incident plane P or SV wave. In this study, the hoop bending moment and hoop axial force are related to the free‐field responses of the ground. A one‐dimensional numerical approach is firstly presented to obtain the free‐field responses of a layered half‐space with an obliquely incident plane P or SV wave propagation. Then, the free‐field stress state is transformed and decomposed in the polar coordinate system. The internal forces of tunnel caused by the isotropic stress state and the pure shear state are calculated and then summed up to obtain the overall analytical solutions. Finally, the validity of the proposed semianalytical procedure is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper reported a size-dependent semi-analytical model (SAM) on the contact involving a functionally graded elastic film indented by a rigid frictionless cylinder, where Chen-Yao's surface elastic theory is employed to account for the effects of surface energy and surface strain. The model assumes that the film is perfectly bonded to a rigid substrate, and that the shear modulus of the film varies along the thickness direction following a simple exponential form. The core fundamental solutions of the elastic displacements and stresses for such an elastic thin film with respect to the unit applied force are derived firstly, incorporating the surface effects by means of Chen-Yao's surface elastic theory. Then the frequency response functions (FRFs) and their conversion into the corresponding influence coefficients (ICs), are analytical obtained. Efficient numerical techniques, supported by the conjugate gradient method (CGM) and the fast Fourier transform (FFT), are applied to obtain the unknown pressure and stress distributions. The combined effects of shear modulus ratio, film thickness, and surface energy on the contact behavior of the thin film are explored, and a schematic map is constructed to reveal the influences of film thickness and material characteristic length, which correlates the geometric configuration (i.e. a film or a half-space) and surface behaviors (i.e. with or without considering the surface effects). [ABSTRACT FROM AUTHOR]

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [ Appl. Math. Model. , 46:450–464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the depletion regions at the source and drain sides in a symmetric junctionless double‐gate metal‐oxide‐semiconductor field‐effect transistor with trapped charges working in subthreshold condition. The effects of depletion layers on the potential, threshold voltage, drain‐induced barrier lowering (DIBL), and the current of the device have been investigated. The channel of the transistor is divided into 4 regions: 2 regions without and with trapped charges and 2 depletion regions on either side of the channel. Solving the 2‐dimensional Poisson's equation, a semianalytical model for the potential is achieved in these regions and the threshold voltage, the DIBL, and the current are calculated. Also, the depletion widths are calculated during the modeling and their variation against the positive and negative trapped charges is investigated. To show the importance of the depletion layers, another junctionless double‐gate metal‐oxide‐semiconductor field‐effect transistor without depletion layers is considered and the mentioned electrical properties of the 2 devices are compared with each other. Smaller central potential, threshold voltage, and current and higher DIBL are achieved when the depletion layers are considered. Good agreement between the results of the proposed model and the simulated results by TCAD software shows the physical validity of the proposed model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to put forward a semi-analytical solution to conduct the free vibration analysis of thick orthotropic annular sector plates with general boundary conditions, internal radial line and circumferential arc supports for the first time. Based on the Mindlin plate theory, stationary energy principle and Rayleigh-Ritz method, the governing eigenvalue equation is derived for thick orthotropic annular sector plates of different radii, sector angles, thickness ratio, line/arc supports and various boundary conditions along the radial and circumference edges. The main innovation point of this paper lies in breaking the classical boundary barrier by using an improved Fourier series to replace the traditional Fourier series. By comparing with those results in open reported literature, the present method proves to be of excellent accuracy and reliability. In addition, in order to enrich the research, some results involving thick orthotropic annular sector plates with various boundary conditions are presented firstly, which can be acted as benchmark data for the future research. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration of the stepped doubly-curved shells of revolution is investigated by using a semi-analytical method with arbitrary boundary conditions. The stepped doubly-curved shells of revolution are divided into their segments in the meridional direction according to the steps of the structures, and the analysis of the theoretical model is formulated by using Flügge’s thin shell theory. The Jacobi polynomials along the revolution axis direction and the standard Fourier series along the circumferential direction consist of the displacement functions of shell segments. The boundary conditions at the ends of the stepped doubly-curved shells of revolution and the continuity conditions at two adjacent segments were enforced by penalty method. Then, the accurate solutions about the vibration characteristic of the stepped doubly-curved shells of revolution were solved by the method of Rayleigh–Ritz. For arbitrary boundary conditions, the present method does not need any changes to the mathematical model or the displacement functions, and it is very effective in the analysis of free vibration for the stepped doubly-curved shells of revolution. The accuracy and reliability of the proposed method are verified with the results of finite element method (FEM), and some numerical results are reported for free vibration of the stepped doubly-curved shells of revolution under arbitrary boundary conditions. Results of this paper can provide reference data for future studies in related field. [ABSTRACT FROM AUTHOR]

In the dynamical model of relative motion with circular reference orbit, the equilibrium points are distributed on the circle where the leader spacecraft is located. In this work, analytical solutions of periodic configurations around an arbitrary equilibrium point are constructed by taking Lindstedt-Poincaré (L-P) and polynomial expansion methods. Based on L-P approach, periodic motions are expanded as formal series of in-plane and out-of-plane amplitudes. According to the method of polynomial expansions, a pair of modal coordinates is chosen, and the remaining state variables are expressed as polynomial series about the modal coordinates. In order to check the validity of series solutions constructed, the practical convergence is evaluated. Considering the fact that relative motion model is a special case of restricted three-body problem, the periodic configurations constructed in the model of relative motion are taken as starting solutions to numerically identify the periodic orbits in restricted three-body problem by means of continuation technique with the mass of system as continuation parameter. [ABSTRACT FROM AUTHOR]

Power transformer design normally includes an optimization process which involves the assessment of a great number of design alternatives. This calculation process normally requires a high computation time and its reduction is always a desirable goal. Circulating currents in parallel connected conductors in transformer windings are a critical design aspect to be analyzed. This article presents a new methodology for the fast calculation of circulating currents for parallel connected conductors in power transformers. The formulation for solid conductor modeling has been developed using the same calculation strategy as in Semianalytic Integral Method (SAIM) [1], which allows a significant reduction of computational effort. A realistic case study of a 25 MVA transformer was used to validate the proposed methodology. As for the accuracy of the calculations, the comparison of the results obtained by the proposed methodology and those calculated using the Finite Element Method (FEM) shows an excellent agreement between both approaches. However, the computational performance of the new approach was found to be much higher than that of FEM. This makes the proposed method much more efficient for transformer design purposes. [ABSTRACT FROM AUTHOR]

This article is the first in a series about the thermal design of Earth-to-Air Heat Exchanger, EAHE, using a new developed semi-analytical method. The temperature distribution in the soil surrounding the EAHE is studied in the goal to determine the soil radius as a function of the operation duration. This radius is the first distance from the pipe axis where there is no effect of heat from EAHE. For that, a new transient semi-analytical model is developed in particular to facilitate the thermal design of EAHEs. The main application of the developed model is to predict the deterioration in EAHE's thermal performance as a function of the duration operation. This deterioration can be caused by soil thermal saturation where the nearby subsoil temperature becomes almost equal to the inlet air temperature resulting in minimum heat transfer between air and soil. The analytical solution of the proposed model has been integrated by means of the Bessel function method, for a constant heat flux per unit of length at the pipe surface in the radial dimension and constant inlet air temperature. The model has been verified with several results obtained from the literature. In addition, an investigation of continuous operation of an EAHE is made on thermal performance of the EAHE in the soil of the region of Biskra (Southern Algeria) (34°47′N - 005°43′E) by applying extreme ambient air temperature (57 °C). Results show that the deterioration in thermal performance of EAHE is observed for longer duration in hot and dry climate. In the case of 6 h of continuous operation, the soil radius can reach 0.55 m from the pipe surface. The model proposed in this paper can be considered as the first of its kind which gives a formula for calculating the soil radius (thickness) as a function of the: i) duration of operation, ii) soil thermal diffusivity, iii) pipe diameter and iv) air temperature. [ABSTRACT FROM AUTHOR]

Single-frequency networks (SFN) are widely adopted in terrestrial broadcast networks based on high-power high-tower (HPHT) deployments. The mobile broadcasting standard Evolved Multimedia Broadcast Multicast Service (eMBMS) has been enhanced in Release 14 to enable SFN operation with larger CP duration which may allow for the deployment of large area SFNs and even the combined operation between HPHT and low-power low-tower (LPLT) cellular stations. The knowledge of the signal-to-interference-plus-noise ratio (SINR) distribution over an SFN area may facilitate the selection of transmission parameters according to the network topology. This paper presents a semianalytical method for the calculation of the SINR distribution in SFNs with low computational complexity compared to Monte Carlo simulations. The method, which builds on previous work developed for cellular communications, is applied to HPHT+LPLT SFNs and evaluated against different transmission and network parameters. [ABSTRACT FROM PUBLISHER]

We have developed a semi-analytic framework to model the large-scale evolution of the first Population III (Pop III) stars and the transition to metal-enriched star formation. Our model follows dark matter haloes from cosmological N-body simulations, utilizing their individual merger histories and three-dimensional positions, and applies physically motivated prescriptions for star formation and feedback from Lyman-Werner (LW) radiation, hydrogen ionizing radiation, and external metal enrichment due to supernovae winds. This method is intended to complement analytic studies, which do not include clustering or individual merger histories, and hydrodynamical cosmological simulations, which include detailed physics, but are computationally expensive and have limited dynamic range. Utilizing this technique, we compute the cumulative Pop III and metal-enriched star formation rate density (SFRD) as a function of redshift at z = 20. We find that varying the model parameters leads to significant qualitative changes in the global star formation history. The Pop III star formation efficiency and the delay time between Pop III and subsequent metal-enriched star formation are found to have the largest impact. The effect of clustering (i.e. including the three-dimensional positions of individual haloes) on various feedback mechanisms is also investigated. The impact of clustering on LW and ionization feedback is found to be relatively mild in our fiducial model, but can be larger if external metal enrichment can promote metal-enriched star formation over large distances. [ABSTRACT FROM AUTHOR]

An investigation on non-equilibrium condensing steam flow is conducted to attain a semi-analytical model for the prediction of the Wilson point up to the critical point. The database for the analysis includes experimental observations in various nozzles and conditions (ranging from 20 to 150 bar) taken from the literature as well as additional data at lower and higher reduced pressures, generated by means of a calibrated quasi-1D model based on the method of moments. The simplified model is based on a reformulation of the Wilson point in terms of activation time, defined as the temporal interval between the instant at which the flow is at saturation conditions and the inception stable of condensation. This allows to incorporate the dependency of the Wilson point on the cooling rate and dew-point temperature, which are found the key parameters affecting the delay of condensation. The accuracy of the approach is proved by predicting the degree of subcooling on four different test cases, with deviations against experiments in the range of 1 − 10 % . As demonstrated, the same approach can be exploited to design nozzles free of condensation. [ABSTRACT FROM AUTHOR]

In this note, we will show that for a closed subanalytic subset A ⊂ Rn, the Clarke tangential regularity of A at x0 ∈ A is equivalent to the coincidence of the Clarke tangent cone to A at x0 with the set L(A, x0) :={ċ+(0) ∈ Rn : c : [0, 1] → A is Lipschitz, c(0) = x0}, where ċ+(0) denotes the right-strict derivative of c at 0. The results obtained are used to show that the Clarke regularity of the epigraph of a function may be characterized by a new formula of the Clarke subdifferential of that function. [ABSTRACT FROM AUTHOR]

Fractional differential equation has been introduced to the financial theory, which presents new ideas and tools for the theoretical researches and the practical applications. In the work, an approximate semianalytical solution of the time-fractional European option pricing model is derived using the method of combining the enhanced technique of Adomian decomposition method with the finite difference method. And then the result is introduced in China’s financial market. The work makes every effort to test the feasibility of the fractional derivative model in the actual financial market. [ABSTRACT FROM AUTHOR]

A lumped element model for the axial movement of an oil-well drillstring is presented. In this paper, the model is restricted to vertical holes, where damping is due to skin friction from time dependent Newtonian annular Couette-Poiseuille flow. The drillstring is constructed of pipes with different diameters and the diameter of the hole varies as a function of depth. Under these assumptions, the axial movement anywhere in the drillstring is basically a convolution between the axial movement on the top and a semi-analytical function that is derived in this paper. Expressions are given for transfer functions for downhole movements and pressures (surge and swab). In a vertical drilling situation, the motion is clearly underdamped, even when the hole is tight. The semi-analytical model illuminates various factors that are shown to be important for describing downhole pressure and motion. In particular the effect of added mass, the steady state viscous forces, the Basset viscous forces and the distribution of pipe sizes in the hole. The latter have non-neglectable impacts on where the resonant frequencies are located, how much they are amplified and what happens to the downhole pressure. Together with statistical power spectra of ocean wave patterns and the response amplitude operators for a floating structure, this model illustrates design concerns related to heave motion and how fast one can run the drillstring into the hole. Moreover, because of the computational simplicity of computing the convolution, the model is well suited for a real-time implementation. [ABSTRACT FROM AUTHOR]

The positive semidefinite Procrustes (PSDP) problem is the following: given rectangular matrices X and B , find the symmetric positive semidefinite matrix A that minimizes the Frobenius norm of A X − B . No general procedure is known that gives an exact solution. In this paper, we present a semi-analytical approach to solve the PSDP problem. First, we characterize a family of positive semidefinite matrices that either solve the PSDP problem when the infimum is attained or give arbitrary accurate approximations to the infimum when it is not attained. This characterization requires the unique optimal solution of a smaller PSDP problem where B is square and X is diagonal with positive diagonal elements. Second, we propose a very efficient strategy to solve the PSDP problem, combining the semi-analytical approach, a new initialization strategy and the fast gradient method. We illustrate the effectiveness of the new approach, which is guaranteed to converge linearly, compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

It is now possible for hydrodynamical simulations to reproduce a representative galaxy population. Accordingly, it is timely to assess critically some of the assumptions of traditional semi-analytic galaxy formation models. We use the EAGLE simulations to assess assumptions built into the GALFORM semi-analytic model, focusing on those relating to baryon cycling, angular momentum and feedback. We show that the assumption in GALFORM that newly formed stars have the same specific angular momentum as the total disc leads to a significant overestimate of the total stellar specific angular momentum of disc galaxies. In EAGLE, stars form preferentially out of low-specific angular momentum gas in the interstellar medium due to the assumed gas density threshold for stars to form, leading to more realistic galaxy sizes. We find that stellar mass assembly is similar between GALFORM and EAGLE but that the evolution of gas properties is different, with various indications that the rate of baryon cycling in EAGLE is slower than is assumed in GALFORM. Finally, by matching individual galaxies between EAGLE and GALFORM, we find that an artificial dependence of active galactic nucleus feedback and gas infall rates on halo mass-doubling events in GALFORM drives most of the scatter in stellar mass between individual objects. Put together our results suggest that the GALFORM semi-analytic model can be significantly improved in light of recent advances. [ABSTRACT FROM AUTHOR]

Efficient and accurate predictions of wave propagation are a vital component of wave-based non-destructive interrogation techniques. Although a variety of models are available in the literature, most of them are suited to a particular wave type or a specific frequency regime. In this paper we present a multi-wave model for wave propagation in axisymmetric fluid-filled waveguides, either buried or submerged in a fluid, based on the semi-analytical finite elements. The cross-section is discretised with high-order spectral elements to achieve high efficiency, and the singularities resulting from adopting a Lobatto scheme at the axis of symmetry are handled appropriately. The surrounding medium is modelled with a perfectly matched layer, and a practical rule of choice of its parameters, based only on the material properties and the geometry of the waveguide, is derived. To represent the fluid and the solid-fluid coupling, an acoustic SAFE element and appropriate coupling relationships are formulated. The model is validated against both numerical results from the literature and experiments, and the comparisons show very good agreement. Finally, an implementation of the method in Python is made available with this publication. [ABSTRACT FROM AUTHOR]

The paper deals with guided wave propagation and diffraction in an elastic plate with two and more parallel grooves (notches). It is a continuation of the preceding studies of a single-notch diffraction focused on the manifestation of the trapped mode and resonance transmission effects in the case of several obstacles. Those effects occur at the frequencies close to the nearly real scattering resonance poles, and the forms of wave localization near the notches are predetermined by the eigenforms associated with these poles. Therefore, the change of location of nearly real poles with additional notches and its dependence on their spacing are the issues of prime concern. The increase in number and assembling in groups of resonance poles and transmission peaks, which was known for multi-obstacle guides of other nature, have also been revealed and experimentally confirmed. The theoretical research is conducted on the basis of low-cost semi-analytical models, and the numerical simulation is experimentally validated through the laser Doppler vibrometry. [ABSTRACT FROM AUTHOR]

This work presents a semi-analytical methodology to select design environmental conditions based on long-term cross-section utilization ratios at the TDZ (Touchdown Zone) for steel catenary risers. This approach uses simplified analytical models to calculate time series of short-term utilization ratios, defined according to the DnV-OS-F201 (2010) standard. After processing these time series, long-term utilization ratios can be determined with relatively low computational cost. By evaluating long-term utilization ratios, it is possible to define short-term design environmental conditions, defined as short-term conditions for which the extreme riser responses are equal to the long-term ones. This kind of methodology may represent a substantial change to the traditional focus given to riser design, which is based on responses obtained from extreme environmental conditions, instead of on the extreme responses. [ABSTRACT FROM AUTHOR]