Computational and Mathematical Methods最新文献

One of major problems in celestial mechanics is the management of the long developments in Fourier or Poisson series used to describe the perturbed motion in the planetary system. In this work we will develop a software package suitable for managing these objects. This package includes the ordinary arithmetic operations with Poisson series—such as sum or product—as well as the most commonly used functions $��\sin �$, $��\cos �$, or $��\exp �$, among others. Derivation or integration procedures with respect to time of these objects have been implemented and inversion or serialization procedures are also attainable to obtain such series. All the programming has been accomplished overloading the arithmetic and functional operators natural to C++ with the intention of allowing the programmer to work in a more friendly way and treating the series as if they were mere numbers. In this work we extend the processor in order to obtain the solution to perturbed problems which solution is in the form of a Poisson series. These algorithms have been written in C++.

We describe a method for computing the number of Hamilton cycles in cubic polyhedral graphs. The Hamilton cycle counts are expressed in terms of a finite-state machine, and can be written as a matrix expression. In the special case of polyhedral graphs with repeating layers, the state machines become cyclic, greatly simplifying the expression for the exact Hamilton cycle counts, and let us calculate the exact Hamilton cycle counts for infinite series of graphs that are generated by repeating the layers. For some series, these reduce to closed form expressions, valid for the entire infinite series. When this is not possible, evaluating the number of Hamiltonian cycles admitted by the series' k-layer member is found by computing a (k − 1)^th matrix power, requiring $��𝒪��\left(��{�\log �}_{�2�}�\left(�k�\right)��\right)��$ matrix-matrix multiplications. We demonstrate our technique for the two infinite series of fullerene nanotubes with the smallest caps. In addition to exact closed form and matrix expressions, we provide approximate exponential formulas for the number of Hamilton cycles.

In this work we consider a particular randomized kinetic model for reaction–deactivation of hydrogen peroxide decomposition. We apply the random variable transformation technique to obtain the first probability density function of the solution stochastic process under general conditions. From the first probability density function, we can obtain fundamental statistical information, such as the mean and the variance of the solution, at every instant time. The transformation considered in the application of the random variable transformation technique is not unique. Then, the first probability density function can take different expressions, although essentially equivalent in terms of computing probabilistic information. To motivate this fact, we consider in our analysis two different mappings. Several numerical examples show the capability of our approach and of the obtained results as well. We show, through simulations, that the choice of the transformation, that permits computing the first probability density function, is a crucial issue regarding the computational time.

This study proposes a new index for projection pursuit used to reduce the dimensions of groups of variables using multiple factor analysis. The main advantage with respect to other indexes is that the methodological procedure preserves the variance and covariance structures to perform singular value decomposition, when the index is used to compare groups of variables. Among other contributions, the study presents a modification in the grand tour algorithm with simulated annealing, adapting it to deal with groups of variables. The methodology used to assess the proposed index was based on Monte Carlo simulations, in several scenarios and with configurations of the following factors: degrees of correlation between the variables; and number of groups and degrees of heterogeneity among groups of variables. The proposed index was compared with thirteen indexes known in the literature. It was concluded that the proposed index was efficient in the reduction of data to use multiple factor analysis. This index is recommended for situations in which the groups exhibit low or high heterogeneity and a strong degree of correlation between the variables $���\left(��\rho �=�0�.�9��\right)��$. In general terms, indexes are affected by the increase in the number of groups, depending on the scenarios assessed.

We present an accurate semi-Lagrangian finite element method for the numerical solution of groundwater flow problems in porous media with natural convection. The mathematical model consists of the Darcy problem for the flow velocity and pressure subject to the Boussinesq approximation of low density variations coupled to a convection–diffusion equation for the concentration. The main idea is to combine the semi-Lagrangian method for time integration with finite element method for space discretization, so that the standard Courant–Friedrichs–Lewy condition is relaxed and the time truncation errors are reduced in the diffusion part of the governing equations. We also use a local L²-projection stabilization technique in order to improve the accuracy of the presented method. Numerical simulations are carried out for a test example of a natural convection in an aquifer system with natural boundaries. The obtained results demonstrate the ability of the proposed semi-Lagrangian finite element method to offer efficient and accurate simulations for natural convection in Darcy flows.

We apply all-atom molecular dynamics simulations to investigate interactions of amyloid beta (A$��\beta �$) fibril seeds with natively disordered A$��\beta �$ chains, a process associated with the onset of Alzheimer's disease. The simulations captured attachment of A$��\beta �$ chains to the fibrils suggesting an onset of both fibril's elongation and secondary nucleation, with a stronger affinity of attachment leading to elongation. Choice of fibril's model appears important for the propensity to recruit A$��\beta �$ chains from solution and retain them adsorbed. Nuclear magnetic resonance-based and cryo-electron microscopy derived models of A$��\beta �$ fibrils exhibited significant differences in the interaction with individual A$��\beta �$ chains, as well as in structural and dynamical stability in solution.

In this article, the study of magnetohydrodynamics Darcy-Forchheimer flow is carried out. Viscous dissipation and thermal radiation are also deliberated for the flow system over a stretching and porous surface. Buongiorno model has been utilized to elaborate thermophoresis and Brownian dispersion impacts. The physical quantities such as viscosity, density, and specific heat play a key role in liquid flow behavior. The modeled equations are transformed to nonlinear ordinary differential equations and then solved by semi-analytical technique HAM. It is found in this assessment that expanding estimations of the magnetic parameter builds Lorentz force and henceforth decreases the velocity profile. Moreover, velocity is also a reducing function of porosity and inertial parameters. The temperature of nanofluid diminishes with enhancement in the Prandtl number and porosity parameter while it increases with Brownian motion, radiation, thermophoretic parameters, and Brinkman number. The concentration profile is a growing function of the thermophoretic parameter and a reducing function of the Brownian motion parameter and Lewis number.

This article presents a simple technique to couple the finite element method (FEM) and the smooth particle hydrodynamics (SPH) method in the Lagrangian framework for the simulation of problems involving solids and structures under shock loading that cause large deformations, such as rock blasting. For such problems FEM suffers from mesh distortion and thus requires some numerical corrective measures such as element erosion or remeshing to proceed with the solution. These cause some artificial effects and a sufficient increase in the computational time. Mesh-less particle based methods such as SPH, on the other hand offer the flexibility to handle high-speed motion inherently. But the SPH method is more computationally demanding and requires special treatment for application of boundary conditions. For the simulation of certain process that involve high impact by fluid on solids or structures such as blasting, a coupled FEM-SPH procedure might be more efficient where regions of large deformations are modeled with SPH particles and regions far off are modeled with FEM. An adaptive procedure of coupling FEM-SPH is developed in this work so that highly distorted elements in the model are replaced by SPH particles on the fly but remain linked to the model thus maintaining the consistency in solution. The article provides the details of this adaptive procedure. Validation of this coupling method is done by analyzing a two-dimensional (2D) elastic impact problem and then is applied for the 2D simulation of fragmentation in brittle rocks induced by high impact blast loads from explosions considering a continuum damage model under plain strain conditions. Since detailed three-dimensional (3D) FSI simulations require, even for the lone SPH or FEM solver, quite powerful computer resources, most examples in this article are restricted to two dimensions assuming plane symmetry and can easily be extended for 3D analyses.

In this paper, we prove some general common fixed point theorems using generalized contractive condition of Meir-Keeler type for two pairs of weakly compatible self-mappings in Menger spaces. Some suitable examples are also given to support our theorems.

In this article, we introduce a new general family of distributions. The submodels of the general family accommodate various shapes of pdf and hazard rate, involving decreasing, increasing, bathtub and J-shapes. Hence, it can provide analysis for many practical datasets. Mathematical expressions for the family are obtained, including moments, moment generating and quantile functions, stochastic ordering, and entropy. Some submodels of the family are inserted based on the baseline distributions: Exponential, Gompertz, Lindley, and weight exponential distributions. Estimation of the model parameters is justified by the method of maximum likelihood. Capability of the family is shown by fitting three practical datasets to the mentioned submodels.