interacting particle systems modeling various processes in non-equilibrium statistical mechanics. Stochastic partial differential equations describe dynamics subjected to random noises. The methods from the two
The meshgrid function generates a grid of points, and the surface is constructed using parametric equations. The surf function generates the 3D surface plot. Use: Surface of revolution visualizations are used in fields like geometry, solid modeling, and mechanical engineering to model 3D objects ...
Further, he asserted that numbers cannot be regarded as elements in the same sense as words. Sentences can be explained in"telling"but mathematical equations must be expressed by"showing."For example, to prove "two plus two equals four " one can show two oranges first and two oranges later....
Third and fourth graders learned to solve equivalent equations in one of two ways that involved different manual actions for the assigned condition. Participants using the two-handed ‘bucket’ strategy were significantly more likely to use both hands when solving post-test and transfer problems, ...
It is also worth emphasizing that if a dimension is changed, all the formulation of the equilibrium equations is deeply modified too, like the boundary conditions and space distribution of the loading. On the other hand, the advantages gained by using such simplified models in structural analysis...
in particular, this function acts on any vertex Vi as (3.6) so that we can easily prove that all the previous conditions are easily satisfied [14]. According to the above equations, each edge transforms as (3.7) where . 3.1. Variation Law of the p-Faces of σ The variation law of...
Equations (13) and (10) together with computer programs like Maple are used to create a system of equations. Consequently, the values of constants a0, a1, a2, and d1 are given below: a0 ¼ a0, a1 ¼ À3EF þ 2F2 þ E2 þ 2F À E a2 ¼ ÀðE À F À ...
It is one of the most widely used methods for analyz- ing fractional differential equations in a chaotic manner (see [52,53] for more details on the predictor–corrector method). To investigate the effects of the time-varying fractional derivative, we present the results of the model with ...
The parameters and functions used in the equations are defined as previously described. 3 Analysis of the model 3.1 The non-negativity of the solutions in the model Ensuring the non-negativity of solutions in biological models is necessary.Lemma 3.1...
2020, Chaos, Solitons and Fractals Citation Excerpt : As a rule, these equations are different generalizations of the nonlinear Schrödinger equation but unlike the nonlinear Schrödinger equation, most of these equations do not belong to the class of integrable equations, and the Cauchy problem ...