Exponential Method Research Articles

Nucleic Acid Amplification by Template-Dominated Click Chemistry for Ultrasensitive DNA/RNA Detection on an Electrochemical Readout Platform.

As an enzyme-free exponential nucleic acid amplification method, the click chemistry-mediated ligation chain reaction (ccLCR) has shown great prospects in the molecular diagnosis. However, the current optics-based ccLCR is challenged by remarkable nonspecific amplification, severely hindering its future application. This study demonstrated that the severe nonspecific amplification was generated probably due to high random collision in the high DNA probe concentration (μM level). To solve this hurdle, a nucleic acid template-dominated ccLCR was constructed using nM-level DNA probes and read on an electrochemical platform (cc-eLCR). Under the optimal conditions, the proposed cc-eLCR detected a low-level nucleic acid target (1 fM) with a single-base resolution. Furthermore, this assay was applied to detect the target of interest in cell extracts with a satisfactory result. The proposed cc-eLCR offers huge possibility for click chemistry-mediated enzyme-free exponential nucleic acid amplification in the application of medical diagnosis and biomedical research.

Analytical Solutions of the Fractional Complex Ginzburg-Landau Model Using Generalized Exponential Rational Function Method with Two Different Nonlinearities

The complex Ginzburg-Landau model appears in the mathematical description of wave propagation in nonlinear optics. In this paper, the fractional complex Ginzburg-Landau model is investigated using the generalized exponential rational function method. The Kerr law and parabolic law are considered to discuss the nonlinearity of the proposed model. The fractional effects are also included using a novel local fractional derivative of order α . Many novel solutions containing trigonometric functions, hyperbolic functions, and exponential functions are acquired using the generalized exponential rational function method. The 3D-surface graphs, 2D-contour graphs, density graphs, and 2D-line graphs of some retrieved solutions are plotted using Maple software. A variety of exact traveling wave solutions are reported including dark, bright, and kink soliton solutions. The nature of the optical solitons is demonstrated through the graphical representations of the acquired solutions for variation in the fractional order of derivative. It is hoped that the acquired solutions will aid in understanding the dynamics of the various physical phenomena and dynamical processes governed by the considered model.

Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant

AbstractRecently, the numerical methods for long‐time dynamics of PDEs with weak nonlinearity (or small potentials) have received more and more attention. For the Klein‐Gordon‐Dirac (KGD) equation with the small coupling constant , we propose two time symmetric and structure‐preserving exponential wave integrator Fourier pseudo‐spectral (TSSPEWIFP) methods under periodic boundary conditions. The new methods are proved to preserve the energy in discrete level and in addition the first one preserves the modified discrete mass. Through rigorous error analysis, we establish uniform error bounds of the numerical solutions at up to the time at for where and are the mesh size and time step, respectively, and depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGD equation with the small coupling constant. The tools for error analysis mainly include cut‐off technique and the standard energy method. We also extend the results on error bounds, structure‐preservation and time symmetry to the oscillatory KGD equation with wavelength at in time which is equivalent to the KGD equation with small coupling constant. Numerical experiments confirm that the theoretical results are correct. Our methods are novel because that to the best of our knowledge there has not been any energy‐preserving exponential wave integrator method and any relevant long time analysis for the KGD equation.

Interaction Characteristics of the Riemann Wave Propagation in the (2+1)-Dimensional Generalized Breaking Soliton System

In this study, the nonlinear (2+1)-dimensional generalized breaking soliton system has been studied by introducing an appropriate traveling wave transformation. The model under consideration is integrable with constant coefficients and demonstrates Riemann wave propagation characteristics, it principally transformed into a third-order nonlinear ODE. The reliable and robust method, namely the modified exponential function method, is applied to the nonlinear system for the first time. The main goal is to investigate and obtain some explicitly exact traveling waves, periodic waves, and soliton solutions. The obtained solutions are in the form of exponential functions, trigonometric hyperbolic functions, and combined structures of the trigonometric hyperbolic with logarithmic functions. Furthermore, the obtained solutions are new and significant in revealing the pertinent features of the physical phenomenon. The results have been expressed in several graphs, including two- and three-dimensional plots, for the best visual assessment of the physical significance and dynamic characteristics. The most potent and efficacious tools are the computer software packages we utilize to derive solutions and graphs.

A second-order low-regularity correction of Lie splitting for the semilinear Klein–Gordon equation

The numerical approximation of nonsmooth solutions of the semilinear Klein–Gordon equation in the d-dimensional space, with d = 1, 2, 3, is studied based on the discovery of a new cancellation structure in the equation. This cancellation structure allows us to construct a low-regularity correction of the Lie splitting method (i.e., exponential Euler method), which can significantly improve the accuracy of the numerical solutions under low-regularity conditions compared with other second-order methods. In particular, the proposed time-stepping method can have second-order convergence in the energy space under the regularity condition $ (u,{\mathrm{\partial }}_tu)\in {L}^{\mathrm{\infty }}(0,T;{H}^{1+\frac{d}{4}}\times {H}^{\frac{d}{4}})$ . In one dimension, the proposed method is shown to have almost $ \frac{4}{3}$ -order convergence in L∞(0, T; H1 × L2) for solutions in the same space, i.e., no additional regularity in the solution is required. Rigorous error estimates are presented for a fully discrete spectral method with the proposed low-regularity time-stepping scheme. The numerical experiments show that the proposed time-stepping method is much more accurate than previously proposed methods for approximating the time dynamics of nonsmooth solutions of the semilinear Klein–Gordon equation.

Prediction of Three-Dimensional Consolidation Settlement: Observational Method and Its Applicability

This paper presents a closed form of the simplified three-dimensional (3D) (vertical and radial) consolidation solution, which has negligible errors for practical cases. Based on the simplified solution, two observational methods (namely, 3D modified curve fit and linear rule methods) that could predict the actual 3D consolidation settlement behaviors by reflecting the effect of sampling range were newly developed. The appropriateness of the proposed methods was verified by using 3D and two-dimensional (2D) theoretical data. Then, the proposed methods were applied to three case records. Back-analyzed results (i.e., the end of consolidation settlement S100 and consolidation coefficient ch(n)) were slightly affected by the differently approached methods and the inputted value of vertical consolidation coefficient (cv). S100 and ch(n) values obtained from the 3D modified methods were close to those secured from the 2D modified methods due to the insignificant effect of vertical drainage for the cases. Owing to incomplete measurement (93%–98% of S100, i.e., no consideration of sampling range effect), an existing 3D method and the original 2D Asaoka and exponential methods predicted a lower S100 and higher ch(n) than those predicted by the 3D or 2D modified curve fit methods. Therefore, the proposed 3D methods can be recommended for practical applications.

A Layer-Wise Coupled Thermo-Elastic Shell Model for Three-Dimensional Stress Analysis of Functionally Graded Material Structures

In this work, a coupled 3D thermo-elastic shell model is presented. The primary variables are the scalar sovra-temperature and the displacement vector. This model allows for the thermal stress analysis of one-layered and sandwich plates and shells embedding Functionally Graded Material (FGM) layers. The 3D equilibrium equations and the 3D Fourier heat conduction equation for spherical shells are put together into a set of four coupled equations. They automatically degenerate in those for simpler geometries thanks to proper considerations about the radii of curvature and the use of orthogonal mixed curvilinear coordinates α, β, and z. The obtained partial differential governing the equations along the thickness direction are solved using the exponential matrix method. The closed form solution is possible assuming simply supported boundary conditions and proper harmonic forms for all the unknowns. The sovra-temperature amplitudes are directly imposed at the outer surfaces for each geometry in steady-state conditions. The effects of the thermal environment are related to the sovra-temperature profiles through the thickness. The static responses are evaluated in terms of displacements and stresses. After a proper and global preliminary validation, new cases are presented for different thickness ratios, geometries, and temperature values at the external surfaces. The considered FGM is metallic at the bottom and ceramic at the top. This FGM layer can be embedded in a sandwich configuration or in a one-layered configuration. This new fully coupled thermo-elastic model provides results that are coincident with the results proposed by the uncoupled thermo-elastic model that separately solves the 3D Fourier heat conduction equation. The differences are always less than 0.5% for each investigated displacement, temperature, and stress component. The differences between the present 3D full coupled model and the the advantages of this new model are clearly shown. Both the thickness layer and material layer effects are directly included in all the conducted coupled thermal stress analyses.

Selection of a Ship Compressor Using Statistical Data Processing

INTRODUCTION: Compressors are essential for supplying compressed air at various pressures and flow rates to the ships power systems, and to the ship as a whole. An appropriate choice of the compressor is essential for the proper operation of water transport infrastructure. Hence, it is necessary to consider this issue in detail. If all variables, the compressor selection parameters to be considered, were measured in the same scales and units, it would be possible to suggest adding up all values, but this approach is very crude. The solution is to normalize the values of the variables and then calculate a final criterion based on them.
 AIM: Finding a formal criterion by which the selection of a particular compressor will be made.
 MATERIAL AND METHODS: The process of selecting a compressor for starting the ships engines and for the general operation of the ship is discussed based on exponential and linear rationing methods. Certain parameters of compressors from domestic and foreign manufacturers are offered for statistical processing. Subsequently, data processing was carried out using maximum likelihood estimation and logistic regression.
 RESULTS: The result of the study is a single formal criterion, the final rating, instead of several qualitative parameters. A set of characteristics has been determined that describes the optimal compressor based on the above calculations and data processing. A simulation of the probability of assigning a compressor, with a certain set of characteristics, to a positive or negative class has been performed. The training of the model was done using the available training data.
 CONCLUSION: Statistical methods of data processing can be applied to an object such as a compressor. Given a set of desired compressor characteristics, it is possible to teach the machine to determine the optimal compressor.

A convergent exponential B-spline collocation method for a time-fractional telegraph equation

A convergent exponential B-spline collocation method for a time-fractional telegraph equation

A novel FMEA approach for submarine pipeline risk analysis based on IVIFRN and ExpTODIM-PROMETHEE-II

The failure mode and effects analysis (FMEA) approach based on TODIM has been widely applied in risk analysis in several fields. To fill the gap in relevant research in the field of submarine pipeline risk analysis and to address possible problems in the classical TODIM method, a novel FMEA model is proposed in this paper. Firstly, an improvement to the existing interval-valued intuitionistic fuzzy rough number (IVIFRN) theory is made and used to collect expert opinions better to consider individual and group uncertainty. Secondly, ExpTODIM, which is more in line with prospect theory, is combined with the PROMETHEE-II method. And it also incorporates weight calculation methods such as the maximizing deviation method for ranking failure modes. Thirdly, the exponential entropy weight method based on the improved IVIFRN theory is combined with the analytical hierarchical process (AHP) for application in fuzzy comprehensive evaluation to complete the calculation of risk values. Fourthly, the proposed novel FMEA approach is applied to the risk analysis of the submarine pipeline to obtain its failure mode ranking and risk value results. Comparisons with other methods in concept and example analysis show that the proposed method is relatively reliable and has certain advantages over other current FMEA methods based on MCDM. In particular, the proposed method overcomes the theoretical problems of the classical TODIM and is more consistent with logic. It also improves the accuracy and comprehensiveness of analysis results, which can provide a valid and accurate reference for the practical engineering of submarine pipelines.

Simultaneous Inversion of the Space-Dependent Source Term and the Initial Value in a Time-Fractional Diffusion Equation

Abstract The inverse problem for simultaneously identifying the space-dependent source term and the initial value in a time-fractional diffusion equation is studied in this paper. The simultaneous inversion is formulated into a system of two operator equations based on the Fourier method to the time-fractional diffusion equation. Under some suitable assumptions, the conditional stability of simultaneous inversion solutions is established, and the exponential Tikhonov regularization method is proposed to obtain the good approximations of simultaneous inversion solutions. Then the convergence estimations of inversion solutions are presented for a priori and a posteriori selections of regularization parameters. Finally, numerical experiments are conducted to illustrate effectiveness of the proposed method.

Unconditional Convergence of Conservative Spectral Galerkin Methods for the Coupled Fractional Nonlinear Klein–Gordon–Schrödinger Equations

In this work, two novel classes of structure-preserving spectral Galerkin methods are proposed which based on the Crank–Nicolson scheme and the exponential scalar auxiliary variable method respectively, for solving the coupled fractional nonlinear Klein–Gordon–Schrödinger equation. The paper focuses on the theoretical analyses and computational efficiency of the proposed schemes, the Crank–Nicoloson scheme is proved to be unconditionally convergent and has maximum-norm boundness of numerical solutions. The exponential scalar auxiliary variable scheme is linearly implicit and decoupled, but lack of the maximum-norm boundness, also, the energy structure is modified. Subsequently, the efficient implementations of the proposed schemes are introduced in detail. Both the theoretical analyses and the numerical comparisons show that the proposed spectral Galerkin methods have high efficiency in long-time computations.

Analytical method for computing assembly errors in modular antenna during on-orbit assembly

AbstractTo meet the increasing communication demands, the satellites need to be equipped with the high-accuracy and large-aperture antennas. One of the effective methods to construct the modular antennas with ultra-high accuracy and ultra-large aperture is on-orbit assembly technology. During the on-orbit assembly missions, the assembly error is a key factor to affect the surface accuracy of the modular antennas. This paper studies the node design of each module and the assembly error analysis of the modular antennas. A design method of the module nodes is presented with consideration of the assembly gap between two modules. Meanwhile, a soft connection mechanism is designed to ensure the mobility among the assembly modules. To investigate the transmission law of the assembly errors, an analytical model of assembly error is derived based on the exponential product method. In order to establish the deformation surface with rotation and displacement assembly errors, an error ball concept is proposed by the analytical model. To decrease the assembly errors, the actuators are installed among some modules. Moreover, an adjustment method is proposed to obtain the adjustment amounts of actuators. Finally, the correctness of analytical model and the effectiveness of the adjustment method are demonstrated by the numerical simulations.

Analysis of Exponential Frequency-Diverse Array for Short-Range Beam-Focusing Technology

The frequency-diverse array (FDA) is a promising technology because of its angle- and range-dependent beam pattern. The FDA has unique properties, such as beam scanning and focusing, which are difficult to achieve using the conventional phased antenna array theory. In this study, the relationship between range and frequency increment is analyzed, and the fundamental operation principle of FDA is thoroughly investigated. The effect of coupling among antenna elements is also discussed to analyze the FDA theory. Furthermore, a novel exponential FDA method for short-range beam focusing is presented based on the proposed FDA analysis method. The proposed method has been investigated through various case studies and applied to research efforts on FDA methods. The FDA design procedures and analysis methods are also presented in this article.

On the Construction of Short Addition-Subtraction Chains and their Applications

Abstract The problem of computing xn effciently, such that x and n are known to be very interesting, specially when n is very large. In order to find effcient methods to solve this problem, addition chains have been much studied, and generalized to addition-subtraction chains. These various chains have been useful in finding effcient exponentiation algorithms. In this paper, we present a new method to recover all existing exponentiation algorithms. It will be applied to design a new fast exponentiation method.

Analisis Perbandingan Dempster Shafer dan Case Base Reasoning Dalam Diagnosis Penyakit Mastocytosis Menggunakan Metode Perbandingan Eksponensial

Diseases pose a major challenge in the medical world. Accurate and precise diagnosis is a crucial key in disease management, including the case of mastocytosis. Mastocytosis is a disorder characterized by the proliferation of mast cells that can affect various organ systems in the human body. There are various variations of mastocytosis, but they can generally be categorized into two main types: cutaneous mastocytosis, which primarily affects the skin and is the most common form, and systemic mastocytosis, which is a more severe form involving the accumulation of mast cells in organs and tissues throughout the body, not just the skin. Planning a successful course of therapy and providing a positive outlook for patients heavily relies on an accurate and timely diagnosis of mastocytosis. This study utilizes an exponential comparison strategy to compare and contrast the Dempster-Shafer (DS) and Case Based Reasoning (CBR) techniques in detecting mastocytosis. The Dempster-Shafer technique is employed in this study to gather and evaluate data from various ambiguous and inadequate sources. This method utilizes the theory of mass variability to represent uncertainty in disease diagnosis. On the other hand, Case Based Reasoning is an approach that relies on past experiences and utilizes existing knowledge in the form of previously encountered cases to make diagnoses. In this study, exponential comparison is used to assign greater weight to certain attributes considered more important in the diagnosis process. This exponential comparison method allows for more flexible attribute weighting, enabling more accurate modeling of symptoms and related factors in mastocytosis. The aim of this research is to use the exponential comparison approach to develop, analyze, and compare both strategies in detecting mastocytosis. With the lowest rate for cutaneous mastocytosis and the highest percentage for systemic mastocytosis, the research findings indicate that both approaches yield comparable results. The Dempster-Shafer approach has proven to be more accurate in mastocytosis diagnosis when comparing the calculations of these two methods with the exponential comparison method

The applications of symbolic computation to exact wave solutions of two HSI-like equations in (2+1)-dimensional

It is renowned that Hirota–Satsuma–Ito (HSI) equation is widely used to study wave dynamics of shallow water. In this work, two new HSI-like equations are investigated which could be extended to diversify problems in natural phenomena and give admirable contributions by applying the generalized exponential rational function method (GERFM). With the aid of symbolic calculations, various constraints on the free parameters are given, while classes of wave solutions are explicitly constructed from the coefficients of the combined non-linear and dissipative terms. After specifying values for free parameters, singular, periodic singular and anti-kink waves are demonstrated in 3D figures to exhibit different kinds of wave propagations. The fact that parameters directly influence the wave amplitude and speed of traveling waves is illustrated. The derived results are innovative and have important applications in the current field of mathematical physics research. Eventually, we show that generalized exponential rational function method is effective and straightforward to solve higher-order and high-dimensional non-linear evolution equations.

Equivalent linear method with complex frequency for response analyses of the ground subject to fling-step displacements

The equivalent linear (EL) method is one of the most commonly used methods for seismic ground response analyses in engineering practice. However, it cannot be used to directly calculate the displacement response of the ground subject to fling-step displacements because these are characterized by non-zero final values and ordinary Fourier transform with real frequency breaks down. This article shows that this difficulty can be overcome by introducing a complex frequency in the equivalent linear method. The technique of using complex frequency was used in existing studies for analyses of undamped structures and is known as the exponential window method (EWM). In essence, the same approach is effective for the analysis of fling-step displacement. Herein, why this works for fling-step displacements is described and an application to a vertical array record which captured near-fault fling-step displacements is shown. The reasonable agreement between the observed and synthetic time histories, both for acceleration and displacement, illustrates the applicability of the method to the response analyses of the ground subject to fling-step displacements.

CP3d: A comprehensive Euler-Lagrange solver for direct numerical simulation of particle-laden flows

We present a comprehensive Euler-Lagrange solver, CP3d, for the direct numerical simulation of particle-laden flows. The solver can handle one-way, two-way, interface-unresolved four-way and interface-resolved coupling regime. To make the solver versatile, different numerical approaches are available for fluid, particle as well as the coupling sub-solver. For the sake of computational accuracy and efficiency, a third-order exponential approximation method is proposed for Basset history force in interface-unresolved regime, and a new simplified lubrication force model based on the averaged integration is utilized in interface-resolved simulation to account for the short-range hydrodynamic force. The volume integration approach is also modified to adapt the staggered mesh configuration. The present solver is intensively validated against several benchmarks. A 2D pencil-like domain decomposition is implemented for parallel communication. The resulting solver is able to simulate large scale cases with billions of grid points and millions of moving particles in interface-resolved four-way regime, using only hundreds of computational cores. In addition, a nearly perfect linear strong scaling performance is achieved. In our test, CP3d is more than ten times faster than other similar solver reported in the literature. Program summaryProgram Title: Channel-Particle 3D, CP3d.CPC Library link to program files:https://doi.org/10.17632/7j6kcf8629.1.Developer's repository link:https://github.com/gongzheng-justin/CP3d.Code Ocean capsule:https://codeocean.com/capsule/0609843.Licensing provisions: MIT License.Programming language: Fortran 95, parallelized using MPI.External libraries: FFTW.Nature of problem:CP3d provides a comprehensive tool to perform the direct numerical simulation for particle-laden flows. One-way, two-way, interface-unresolved four-way and interface-resolved coupling regimes can be conducted.Solution method: the code employs second-/fourth-order finite-difference discretization for the fluid Navier-Stokes equation, and numerically solves the Maxey-Riley equation for the particle phase. In four-way regime, particle collisions are considered by discrete-element method. Immersed boundary method is utilized in the interface-resolved coupling regime.

Traveling wave and general form solutions for the coupled Higgs system

In this study, the coupled Higgs system, which is a special case of the coupled Higgs field equation, which is effective in energy transport in the sub‐particles of the atom, is discussed. With the help of the modified generalized exponential rational function method, which is an important instrument in obtaining traveling wave solutions, both the propagating wave solutions and general form solutions of coupled Higgs system are presented. These solutions are examined under some restrictive conditions as they are presented. It is argued that these solutions differ from the literature. The advantages and disadvantages of the method discussed in the conclusion and discussion section are discussed. In addition, the changes in the behavior of the traveling wave solution are discussed by giving physical meaning to some constants in the traveling wave solutions produced by the method. The effects on the traveling wave solution are analyzed for different values of wave number, wave velocity, and wave frequency, which have physically important meanings. In addition, the behaviors caused by these effects are supported with the help of simulation.