Alternative Analytical Solution Research Articles

An alternative two-phase formulation and analytical solution for a Stefan problem in one-dimension accounting for volume change and sensible heat

Stefan problems, or free boundary problems, in the phase change process occur in many engineering problems. This paper develops a compact formula for a two-phase melting process in a one-dimensional semi-infinite slab with a novel approach. Unlike the classic Stefan problem, the novel approach considers volume change (or density difference) and the net-sensible-heat of the two phases. Furthermore, an analytical solution is proposed. To illustrate, the melting process of ice-water in a pipe is investigated. The results have been validated through an exact solution and comparisons with other relevant models. A special case of a one-phase problem is also proposed. The proposed model can be used as an alternative tool for engineers in estimating the position of the melt-front, depending on the dominant effect on the phase change process.

3D mechanical analysis of geothermal reservoir operations in faulted sedimentary aquifers using MACRIS

Accurate and efficient predictions of three-dimensional subsurface stress changes are required for the assessment of geothermal operations with respect to fault stability and the potential risk for induced seismicity. This work extends the model capabilities of Mechanical Analysis of Complex Reservoirs for Induced Seismicity (MACRIS) to account for high-resolution thermo-elastic stress evaluations in structurally complex (i.e. faulted) and matrix permeability dominated geothermal systems. By adopting a mesh-free approach suitable to industry standard flow simulation models, MACRIS is capable of preserving the complex 3D hydraulic development of the injected cold-water volume and the 3D geometrical complexities of the reservoir model. The workflow has been applied to three-dimensional models with clastic reservoir characteristics representative for low enthalpy geothermal exploitation in the Netherlands. The models are marked by a single fault, subject to no and normal offset. Comparison of simulated stress evolutions in MACRIS with alternative analytical solutions highlight the effects of stress arching involved in the poro- and thermo-elastic stress developments on complex faults intersected by or in direct contact with the cold-water volume. Results are in agreement with previous studies and show the effect of thermal stressing to be dominant, arching of stresses to occur at the rim of the cold-water volume, and in cooling reservoirs, the intersection area of the cold-water volume in direct contact with the fault plane to be the main driver for fault reactivation and subsequent seismic potential. Moreover, results show the effects of stress arching (i) to be enhanced in the case of reservoir throw and flow compartmentalization, and (ii) to be reduced by a relative increase in conductive heat transfer between the reservoir and surrounding formations.

New formulation of the state space approach for asymmetrically supported laminated composite plates

The 3D state space approach (SSA) allows accurate description of composite plate behavior, regardless of plate thickness. A new formulation of the SSA is proposed here for the hitherto unexplored case of an asymmetrically supported plate. This solution takes into account all independent elastic constants and satisfies all governing equations and boundary conditions. The new formulation is first derived and then compared to predictions by alternative analytical solutions including classical plate theory as well as the finite element method (FEM) for a number of case studies. Globally, the SSA solution compared well and produced greater accuracy than the FEM model.

Probability density of the Yukawa particle at the origin: Numerical calculation and analytical solution

The probability density of the Yukawa particle at the origin plays significant roles in fundamental physical quantities such as the darkonium production cross sections and matter-anti-matter annihilation rates. Inspired by the recent work of Napsuciale and Rodríguez (2021) [12,13] where the authors proposed a complete analytical solution of the Yukawa problem at small screening parameters to analyze the bound state eigenenergies and probability densities at the origin, we perform in this work high-precision numerical calculation of these quantities by employing the generalized pseudospectral method. The variational method based on one-, two-, and three-parameter trial wave functions is also developed to provide an alternative analytical solution to the Yukawa problem. It is shown that these trial functions manifest simple implementation and high accuracy in the entire range of screening parameters.

Social Networks for Threat Perception and Analysis

In the current era of massive knowledge, high volumes of valuable knowledge is simply collected and generated. Social networks square measure samples of generating sources of those huge knowledge. Users in these social networks square measure usually coupled by some interdependency like friendly relationship. As these huge social networks continue to grow, there square measure things during which Associate in Nursing individual user needs to seek out common teams of friends so he will suggest a similar teams to alternative users. Many users of social Network are not aware about the number of security risks in networks such as identity theft, privacy violations, sexual harassment etc,. Recent studies says that most of the social network users expose their personal information like their date of birth, email address, phone number, relationship status. If this type of data reached to the wrong person, then person used that information to harm the users. If the children are users of social network, then these risks become serious. In this paper we present an alternative data analytic solution by using pattern matching solution.

On the energy of topological defect lattices

Since the logarithm function is the solution of Poisson's equation in two dimensions, it appears as the Coulomb interaction in two dimensions, the interaction between Abrikosov flux lines in a type II superconductor, or between line defects in elastic media, and so on. Lattices of lines interacting logarithmically are, therefore, a subject of intense research due to their manifold applications. The solution of the Poisson equation for such lattices is known in the form of an infinite sum since the late 1990's. In this article we present an alternative analytical solution, in closed form, in terms of the Jacobi theta function.

Alternative Solutions for Consolidation Problems in Isotropic Clay Stratum Using Laplace Heaviside’s Theorem

This study offers an alternative analytical solution, for one and two-dimensional consolidation problem, for functionally-homogenous isotropic clay layer. The fundamental analytical solution presented in this study is derived based on the Laplace transform which eliminates the time-dependent and Heaviside's inversion theorem to extract the inverse. The alternative solutions have been derived based on the governing available fundamental consolidation equations solution. The derived solutions have shown good estimation with the exact solution. The two dimensions of isotopic permeability expressed significant influence on the accumulated excess pore water pressure and approximate time for full consolidation. The analytical solution shows identical results with the numerical one.

Electromagnetic Field Coupling Between a Horizontal Loop Antenna and a Transmission Line: An Analytical Time-Domain Model

The time-domain electromagnetic (EM) reciprocity theorem and the Cagniard–DeHoop technique are applied to analyze the pulsed EM coupling between a horizontal small loop antenna and a finite transmission line above the perfect ground. It is demonstrated that this approach yields closed-form analytical formulas describing the impact of transmission, EM propagation, and reception on the exciting pulse signature. Moreover, approximate expressions applying to relatively short transmission lines are given and discussed, thus revealing similarities with the loop-to-loop EM coupling. Numerical results are presented and validated using an alternative analytical solution and an EM computational tool.

Concept of stress dead zone in cracked plates: Theoretical, experimental, and computational studies

AbstractThis paper presents a study on stress dead zone implications and its characterization with uniaxial tensile testing on MT polycarbonate plate specimens. To obtain the experimental solution, digital image correlation (DIC) is used. Numerically, based on LEFM, the problem is solved using advanced discretization techniques, finite element, and meshless methods. Considering stress dead zone notion, it aims to determine alternative analytical solution of the SIF. Thus, the compliance method is adopted, which is associated with the specimen's dead zone region that does not involve the cracking resistance. Hence, LEFM formulations complying with strain energy release rate criterion are assumed. A proper comparison is made amongst results obtained from all theoretical, experimental, and numerical analyses. Furthermore, this work focuses on the variational fields' evaluation and, in particular, verification on the theoretical assumption of dead zone characteristics. The obtained results support adopted methodologies and are encouragingly robust and cost‐effective.

Alternative Analytical Solution of Consolidation at Constant Rate of Deformation

In this paper, we present an alternative solution of consolidation at constant rate of deformation (CRD). Governing equation of CRD consolidation is formulated considering excess pore water pressure as primary variable. Formulation of the governing equation is done for soil as linear as well as nonlinear materials. An analytical solution to the governing equation is derived which consists of transient state and steady state components. The solution derived herein yields profile of excess pore water pressure distribution with depth at any time during the test. The present paper analyzes the excess pore water pressure distribution profile during CRD consolidation and factors affecting it in detail. Analysis of the obtained solution indicates the existence of moving boundary condition within the test specimen at early stage of the test where transient state condition prevails. It also indicates that the pore water pressure ratio affects significantly the excess pore water distribution profile, in turn, average value of pore water pressure and average effective stress in the specimen. An expression for consolidation parameters for steady state condition are derived using the present solution. Further, evolution of excess pore water pressure at the base of CRD consolidation test specimen during the test is predicted for normally consolidated as well as for over consolidated soils at different rates of deformation.

Analytical Solutions of Eddy-Current Problems in a Finite Length Cylinder

Magnetic field and eddy currents in a cylinder of finite length are calculated by separation of variables. The magnetic field outside the cylinder or inside the bore of the hollow cylinder and shell is expressed in terms of Bessel functions. Both axial and transverse applied fields are considered for the solid and hollow cylinders. The equations for the vector potential components are transformed in one-dimensional equations along the radial coordinate with the consequent integration by the method of variation of parameters. The equation for the scalar electric potential when required is also integrated analytically. Expressions for the magnetic moment and loss are derived. An alternative analytical solution in terms of scalar magnetic potential is derived for the finite length thin shells. All formulas are validated by the comparison with the solutions by finite–element and finite-difference methods.

A simple hydrodynamic model of a laminar free-surface jet in horizontal or vertical flight

A useable model for laminar free-surface jet evolution during flight, for both horizontal and vertical jets, is developed through joint analytical, experimental, and simulation methods. The jet’s impingement centerline velocity, recently shown to dictate stagnation zone heat transfer, encompasses the entire flow history: from pipe-flow velocity profile development to profile relaxation and jet contraction during flight. While pipe-flow is well-known, an alternative analytic solution is presented for the centerline velocity’s viscous-driven decay. Jet-contraction is subject to influences of surface tension (We), pipe-flow profile development, in-flight viscous dissipation (Re), and gravity (Nj = Re/Fr). The effects of surface tension and emergence momentum flux (jet thrust) are incorporated analytically through a global momentum balance. Though emergence momentum is related to pipe flow development, and empirically linked to nominal pipe flow-length, it can be modified to incorporate low-Re downstream dissipation as well. Jet contraction’s gravity dependence is extended beyond existing uniform-velocity theory to cases of partially and fully developed profiles. The final jet-evolution model relies on three empirical parameters and compares well to present and previous experiments and simulations. Hence, micro-jet flight experiments were conducted to fill-in gaps in the literature: jet contraction under mild gravity-effects, and intermediate Reynolds and Weber numbers (Nj = 5–8, Re = 350–520, We = 2.8–6.2). Furthermore, two-phase direct numerical simulations provided insight beyond the experimental range: Re = 200–1800, short pipes (Z = L/d · Re ≥ 0.01), variable nozzle wettability, and cases of no surface tension and/or gravity.

A hybrid analysis method for displacement-monitored segmented circular tunnel rings

Segmented tunnel rings exhibit load-induced interfacial dislocations. In order to facilitate structural analysis, a hybrid method is developed and applied to a real-scale test of a segmented tunnel ring. Point loads, imposed on the tested ring, and measured interfacial discontinuities serve as input for the analysis. Moreover, the method accounts for the structural behavior of the individual segments by means of newly derived transfer relations. They represent analytical solutions of the first-order theory of slender circular arches, exhibiting constant cross-sectional properties. The tool for the development of this basically well-known theory is the principle of virtual power. Its involvement is motivated by the possibility of a mechanically consistent derivation of relations, some of which have been used for a long time without analyzing their scientific background. The validity and the usefulness of the transfer relations follow from a comparison of newly derived solutions with (i) alternative analytical solutions, (ii) Finite Element solutions, and (iii) experimental data. The computational efficiency and the usefulness of the developed hybrid method are demonstrated by structural analysis of a segmented tunnel ring. It provides valuable insight into the load-carrying behavior of the tested structure without the need to describe the nontrivial behavior of segment-to-segment interfaces.

Incremental laplacian regularization extreme learning machine for online learning

The past decade has witnessed an explosive growth of data streams in Internet, biometrics, remote sensing and other fields. Nowadays many supervised incremental/online learning approaches have been developed, to avoid retraining and reduce the computational complexity when data come chunk by chunk. However, these methods can’t obtain satisfied performance when the labeled samples are limited. In this paper, we propose an Incremental Laplacian Regularization Extreme Learning Machine (ILR-ELM) for semi-supervised online learning, by utilizing both labeled and unlabeled samples. Unlike most of the existing semi-supervised incremental/online learning algorithms, this paper not only proposes incremental/online learning mechanism for data chunk containing both labeled and unlabeled samples but also proposes incremental/online learning mechanism for data chunk containing only unlabeled samples. The latter case is more common in practical applications because there is usually no enough time to label the samples for continuously arriving data stream. The alternative analytical solutions of ILR-ELM for the two incremental/online learning mechanisms are also presented. The performance of ILR-ELM is evaluated on three benchmark machine learning data, and the results show that it can achieve near accurate and robust classification/regression with a small number of labeled data, and outperforms the incremental/online learning approaches. Compared with the supervised and the comparative semi-supervised incremental/online learning methods, the generalization accuracy of ILR-ELM is increased by nearly 9% and 2% respectively for the classification problem. For the regression problem, the generalization error of ILR-ELM is reduced by nearly 14% than the supervised incremental/online learning methods and 1% than compared semi-supervised incremental/online learning methods Furthermore, ILR-ELM can achieve comparable prediction to semi-supervised batch learning, using less time and Random Access Memory (RAM).

A reflected wave superposition method for vibration and energy of a travelling string

This paper considers the analytical free time domain response and energy in an axially translating and laterally vibrating string. The domain of the string is either a constant or variable length, dependent upon the general initial conditions. The translating tensioned strings possess either fixed-fixed or fixed-free boundaries. An alternative analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycles of vibration for both constant and variable length strings are provided, which for the latter are dependent upon the variable string length. Each cycle is divided into three time intervals according to the magnitude and the direction of the translating string velocity. Applying d’Alembert's method combined with the reflection properties, expressions for the reflected waves at the two boundaries are obtained. Subsequently, superposition of all of the incident and reflected waves provides results for the free vibration of the string over the three time intervals. The variation in the total mechanical energy of the string system is also shown. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-Beta method solution and an existing state space function representation of the string dynamics.

Analytical solution for compositional profile driven by gravitational segregation and diffusion.

An alternative analytical solution is presented, based on irreversible thermodynamics, that describes the equilibrium distribution of the components of a nonideal fluid mixture in a one-dimensional hydrostatic and isothermal system. In such a system, the vertical compositional profile of the fluid at equilibrium will be determined by the interaction of gravitational and chemical potentials. Our alternative analytical solution estimates this profile from the overall composition of the fluid. It is thus more general than the existing solution, which requires knowledge of the fluid composition at a given depth and assumes that the vertical compositional profile of this fluid is already at equilibrium. The solution is demonstrated by comparison against results obtained from previously published molecular dynamics simulations of segregation in a binary mixture and against numerical simulations of a real hydrocarbon reservoir system.

Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay

This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs) with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. The proposed series solutions are found to converge to exact solution rapidly. To confirm the efficiency and validity of FRDTM, the computation of three test problems of TFPDEs with proportional delay was presented. The scheme seems to be very reliable, effective, and efficient powerful technique for solving various types of physical models arising in science and engineering.

Accurate reliability analysis of concurrent checking circuits employing an efficient analytical method

Transient faults are important concerns in emerging ICs built from deep semiconductors. Concurrent error detection (CED) scheme has been proved to be an efficient technique in such a context. On the other hand, the increase of multiple faults can be foreseeable in future ICs. However, reported efforts applied to quantify the efficiency of CED schemes mostly consider single faults or suppose that implemented checker mechanisms are fault-free. This paper describes an alternative analytical solution for CED circuits analysis under a more realistic hypothesis. In addition to the assumption of the whole fault-prone circuit (including checker mechanisms), different failure rates of logic gate are considered as well. The proposed approach is based on probabilistic transfer matrices and then can deal with multiple faults. The time efficiency of the proposed solution is demonstrated through arithmetic circuits. By applying this solution, classical CED schemes are discussed according to different failure rates of transistor.

Fracture Toughness Determined by the Centrally Cracked Brazilian-Disc Test: Some Critical Issues in the Light of an Alternative Analytic Solution

Abstract The centrally cracked Brazilian-disc test is among the configurations proposed for the experimental determination of fracture toughness of brittle rock-like materials. In spite of its wide use and the fact that the test is already standardized by the International Society for Rock Mechanics (ISRM), quite a few issues are still open related especially to the exact expressions of the respective stress intensity factors (SIFs) and the actual shape of the crack during loading. The latter is crucial since for specific crack inclinations, the crack lips are coming in contact and contact stresses appear which alter the boundary conditions, rendering analytic solutions erroneous. In this context, an alternative analytic approach is here introduced assuming that the cracked disc is under uniform pressure along two finite symmetric arcs of its periphery. The main advantage of the present approach is that it provides physically acceptable results independently of whether the crack is under opening- or closing-mode. The results of the analysis are validated against experimental data obtained using the method of Caustics and the Digital Image Correlation (DIC) technique. Based on the analytic solution, some critical practical aspects of the cracked Brazilian-disc test are explored including the influence of the loading type and the length of the loaded arc, the role of the specimen's thickness, the range of crack inclination angles for which generation of contact stress is unavoidable, and the rotation of the crack axis. Moreover, a redefinition of the SIFs in case of Mixed Fundamental problems is proposed. The limitations of the analysis are critically considered and finally some thoughts about the future steps concerning the fracture toughness determination using the cracked Brazilian-disc test are discussed.

Paraxial light distribution in the focal region of a lens: a comparison of several analytical solutions and a numerical result

The distribution of the complex field in the focal region of a lens is a classical optical diffraction problem. Today, it remains of significant theoretical importance for understanding the properties of imaging systems. In the paraxial regime, it is possible to find analytical solutions in the neighborhood of the focus, when a plane wave is incident on a focusing lens whose finite extent is limited by a circular aperture. For example, in Born and Wolf’s treatment of this problem, two different, but mathematically equivalent analytical solutions, are presented that describe the 3D field distribution using infinite sums of and type Lommel functions. An alternative solution expresses the distribution in terms of Zernike polynomials, and was presented by Nijboer in 1947. More recently, Cao derived an alternative analytical solution by expanding the Fresnel kernel using a Taylor series expansion. In practical calculations, however, only a finite number of terms from these infinite series expansions is actually used to calculate the distribution in the focal region. In this manuscript, we compare and contrast each of these different solutions to a numerically calculated result, paying particular attention to how quickly each solution converges for a range of different spatial locations behind the focusing lens. We also examine the time taken to calculate each of the analytical solutions. The numerical solution is calculated in a polar coordinate system and is semi-analytic. The integration over the angle is solved analytically, while the radial coordinate is sampled with a sampling interval of and then numerically integrated. This produces an infinite set of replicas in the diffraction plane, that are located in circular rings centered at the optical axis and each with radii given by , where is the replica order. These circular replicas are shown to be fundamentally different from the replicas that arise in a Cartesian coordinate system.