Abstract: This paper consider the solution of the matrix
differential models using quadratic, cubic, quartic, and quintic
splines. Also using the Taylor’s and Picard’s matrix methods, one
illustrative example is included.
Abstract: Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. The roots of spline function versus Cantor sets used as the controller admin. The roots calculated by the numerical Newton – Raphson's method. The result of this algorithm was promised.
Abstract: Linear two-point boundary value problems of order
two are solved using cubic trigonometric B-spline interpolation
method (CTBIM). Cubic trigonometric B-spline is a piecewise
function consisting of trigonometric equations. This method is tested
on some problems and the results are compared with cubic B-spline
interpolation method (CBIM) from the literature. CTBIM is found to
approximate the solution slightly more accurately than CBIM if the
problems are trigonometric.
Abstract: An attempt has been made to develop a
seminumerical model to study temperature variations in dermal
layers of human limbs. The model has been developed for two
dimensional steady state case. The human limb has been assumed to
have elliptical cross section. The dermal region has been divided
into three natural layers namely epidermis, dermis and subdermal
tissues. The model incorporates the effect of important physiological
parameters like blood mass flow rate, metabolic heat generation, and
thermal conductivity of the tissues. The outer surface of the limb is
exposed to the environment and it is assumed that heat loss takes
place at the outer surface by conduction, convection, radiation, and
evaporation. The temperature of inner core of the limb also varies at
the lower atmospheric temperature. Appropriate boundary conditions
have been framed based on the physical conditions of the problem.
Cubic splines approach has been employed along radial direction and
Fourier series along angular direction to obtain the solution. The
numerical results have been computed for different values of
eccentricity resembling with the elliptic cross section of the human
limbs. The numerical results have been used to obtain the
temperature profile and to study the relationships among the various
physiological parameters.
Abstract: The study of the Andaman Sea can be studied by
using the oceanic model; therefore the grid covering the study area
should be generated. This research aims to generate grid covering
the Andaman Sea, situated between longitudes 90◦E to 101◦E and
latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear
with 87 × 217 grid points. The methods used in this study are
cubic spline and bilinear interpolations. The boundary grid points
are generated by spline interpolation while the interior grid points
have to be specified by bilinear interpolation method. A vertical grid
is sigma coordinate with 15 layers of water column.
Abstract: High precision in motion is required to manipulate the
micro objects in precision industries for micro assembly, cell
manipulation etc. Precision manipulation is achieved based on the
appropriate mechanism design of micro devices such as
microgrippers. Design of a compliant based mechanism is the better
option to achieve a highly precised and controlled motion. This
research article highlights the method of designing a compliant based
three fingered microgripper suitable for holding asymmetric objects.
Topological optimization technique, a systematic method is
implemented in this research work to arrive a topologically optimized
design of the mechanism needed to perform the required micro
motion of the gripper. Optimization technique has a drawback of
generating senseless regions such as node to node connectivity and
staircase effect at the boundaries. Hence, it is required to have post
processing of the design to make it manufacturable. To reduce the
effect of post processing stage and to preserve the edges of the image,
a cubic spline interpolation technique is introduced in the MATLAB
program. Structural performance of the topologically developed
mechanism design is tested using finite element method (FEM)
software. Further the microgripper structure is examined to find its
fatigue life and vibration characteristics.
Abstract: In this paper, a numerical solution based on nonpolynomial
cubic spline functions is used for finding the solution of
boundary value problems which arise from the problems of calculus
of variations. This approximation reduce the problems to an explicit
system of algebraic equations. Some numerical examples are also
given to illustrate the accuracy and applicability of the presented
method.
Abstract: Comparison of two approaches for the simulation of
the dynamic behaviour of a permanent magnet linear actuator is
presented. These are full coupled model, where the electromagnetic
field, electric circuit and mechanical motion problems are solved
simultaneously, and decoupled model, where first a set of static
magnetic filed analysis is carried out and then the electric circuit and
mechanical motion equations are solved employing bi-cubic spline
approximations of the field analysis results. The results show that the
proposed decoupled model is of satisfactory accuracy and gives more
flexibility when the actuator response is required to be estimated for
different external conditions, e.g. external circuit parameters or
mechanical loads.
Abstract: We present a novel scheme to evaluate sinusoidal functions with low complexity and high precision using cubic spline interpolation. To this end, two different approaches are proposed to find the interpolating polynomial of sin(x) within the range [- π , π]. The first one deals with only a single data point while the other with two to keep the realization cost as low as possible. An approximation error optimization technique for cubic spline interpolation is introduced next and is shown to increase the interpolator accuracy without increasing complexity of the associated hardware. The architectures for the proposed approaches are also developed, which exhibit flexibility of implementation with low power requirement.