Sentence examples for expansion exponentially from inspiring English sources

The property gradation in FGMs is considered by varying shear-modulus, mass density, thermal conductivity and coefficient of thermal expansion exponentially along the gradation direction.

Previous studies [35, 36] confirm that the orthonormal polynomials chosen from the Askey scheme for a given probability measure μ make the PC expansion converge exponentially with the rate of, where κ is a constant.

To provide insight into this aspect of data analysis, we have simulated population expansion with exponentially distributed inter-division times where the birth rates increase linearly with time and fitted the simulated data with the predictions of the model where the birth rates increase with the division class.

The material is assumed linearly elastic and nonlinear isotropic hardening with elastic modulus, yield strength and the thermal expansion coefficient varying exponentially through the thickness of the plate.

In this model, the shape of European population history is assumed to start by a constant ancestral population, followed by a population bottleneck with a reduction in effective size, and then by an exponentially expansion of the population until to the present.

Recently, by an extension of the method of matched asymptotic expansions that retains exponentially small terms, Korzec et al.[17] derived a new type of stationary solutions of the one-dimensional sixth-order Cahn-Hilliard equation.

Korzec et al. [3] studied equation (1.1) with f ( x, t ) = 0. New types of stationary solutions of one-dimensional driven sixth-order Cahn-Hilliard type equation (1.1) are derived by an extension of the method of matched asymptotic expansions that retains exponentially small terms.

Young's modulus, conduction coefficient, coefficient of thermal expansion are taken as exponentially varying functions of the depth coordinate where as Poisson ratio and thermal diffusivity are assumed to be constant.

Objects moving towards a fly with a constant velocity induce not a constantly but exponentially increasing expansion pattern on the retina.

The amount of data available has increased exponentially since the expansion of new biological drug development.

Inflation is the exponentially fast initial expansion of a universe [ 83- 85].