کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5773657 | 1631342 | 2017 | 38 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
New exact and numerical solutions of the (convection-)diffusion kernels on SE(3)
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We consider hypo-elliptic diffusion and convection-diffusion on R3âS2, the quotient of the Lie group of rigid body motions SE(3) in which group elements are equivalent if they are equal up to a rotation around the reference axis. We show that we can derive expressions for the convolution kernels in terms of eigenfunctions of the PDE, by extending the approach for the SE(2) case. This goes via application of the Fourier transform of the PDE in the spatial variables, yielding a second order differential operator. We show that the eigenfunctions of this operator can be expressed as (generalized) spheroidal wave functions. The same exact formulas are derived via the Fourier transform on SE(3). We solve both the evolution itself, as well as the time-integrated process that corresponds to the resolvent operator. Furthermore, we have extended a standard numerical procedure from SE(2) to SE(3) for the computation of the solution kernels, that is directly related to the exact solutions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 53, August 2017, Pages 182-219
Journal: Differential Geometry and its Applications - Volume 53, August 2017, Pages 182-219
نویسندگان
J.M. Portegies, R. Duits,