Abstract: Additive Manufacturing is utilized in medical automation to optimize and integrate materials in accordance to energy source type leading to treatment gaps in industrial designs for extreme biomechanical forces in relation with vibration, fluid transfer, and multi-physics performance. Elastic/piezoelectric materials are strongly ordered inter-metallics for characterization of distinct features that can provide excellent compositional strength, ductility, and uniformity for superelastic shape memory alloy on medical devices. Several theories can be derived to analyze and interpret complex problems on the application of functionally graded materials used in medical machinery for genome architecture. Numerical principles on fluid and thermodynamics such as Reynolds number, Darcy rule, Friction Factor and Heat Rate are integrated with fundamental equation of numerical vibrations using Helmholtz equation. Simulation by Large Eddy approach and genetic modeling can be done using Physical and Chemical Vapor Deposition following various theories on Carrera’s Unified Formulations by comparing with various Classical Plate Theories, Equivalent Single Layer Theories, Layer-Wise Theories, Zig-Zag Theories, and Mixed Refined Variational Theories. The subject is approached towards the application of ethical and legal problems in order to resolve issues on consent and return of results.
Abstract: This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As2S3 chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.
Abstract: In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.
Abstract: In this paper, the formulation of a new group explicit
method with a fourth order accuracy is described in solving the two
dimensional Helmholtz equation. The formulation is based on the
nine-point fourth order compact finite difference approximation
formula. The complexity analysis of the developed scheme is also
presented. Several numerical experiments were conducted to test the
feasibility of the developed scheme. Comparisons with other existing
schemes will be reported and discussed. Preliminary results indicate
that this method is a viable alternative high accuracy solver to the
Helmholtz equation.
Abstract: The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.
Abstract: This paper deals with the problem of non-uniform
torsion in thin-walled elastic beams with asymmetric cross-section,
removing the basic concept of a fixed center of twist, necessary in the
Vlasov-s and Benscoter-s theories to obtain a warping stress field
equivalent to zero. In this new torsion/flexure theory, despite of the
classical ones, the warping function will punctually satisfy the first
indefinite equilibrium equation along the beam axis and it wont- be
necessary to introduce the classical congruence condition, to take into
account the effect of the beam restraints. The solution, based on the
Fourier development of the displacement field, is obtained assuming
that the applied external torque is constant along the beam axis and
on both beam ends the unit twist angle and the warping axial
displacement functions are totally restrained.
Finally, in order to verify the feasibility of the proposed method
and to compare it with the classical theories, two applications are
carried out. The first one, relative to an open profile, is necessary to
test the numerical method adopted to find the solution; the second
one, instead, is relative to a simplified containership section,
considered as full restrained in correspondence of two adjacent
transverse bulkheads.
Abstract: We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.
Abstract: The problem addressed herein is the efficient management of the Grid/Cluster intense computation involved, when the preconditioned Bi-CGSTAB Krylov method is employed for the iterative solution of the large and sparse linear system arising from the discretization of the Modified Helmholtz-Dirichlet problem by the Hermite Collocation method. Taking advantage of the Collocation ma-trix's red-black ordered structure we organize efficiently the whole computation and map it on a pipeline architecture with master-slave communication. Implementation, through MPI programming tools, is realized on a SUN V240 cluster, inter-connected through a 100Mbps and 1Gbps ethernet network,and its performance is presented by speedup measurements included.
Abstract: In this paper, a novel wave equation for electromagnetic
waves in a medium having anisotropic permittivity has been derived
with the help of Maxwell-s curl equations. The x and y components
of the Maxwell-s equations are written with the permittivity () being
a 3 × 3 symmetric matrix. These equations are solved for Ex , Ey,
Hx, Hy in terms of Ez, Hz, and the partial derivatives. The Z
components of the Maxwell-s curl are then used to arrive to the
generalized Helmholtz equations for Ez and Hz.
Abstract: In the traditional theory of non-uniform torsion the
axial displacement field is expressed as the product of the unit twist
angle and the warping function. The first one, variable along the
beam axis, is obtained by a global congruence condition; the second
one, instead, defined over the cross-section, is determined by solving
a Neumann problem associated to the Laplace equation, as well as for
the uniform torsion problem.
So, as in the classical theory the warping function doesn-t punctually
satisfy the first indefinite equilibrium equation, the principal aim of
this work is to develop a new theory for non-uniform torsion of
beams with axial symmetric cross-section, fully restrained on both
ends and loaded by a constant torque, that permits to punctually
satisfy the previous equation, by means of a trigonometric expansion
of the axial displacement and unit twist angle functions.
Furthermore, as the classical theory is generally applied with good
results to the global and local analysis of ship structures, two beams
having the first one an open profile, the second one a closed section,
have been analyzed, in order to compare the two theories.