scholarly journals Asymptotic spreading of interacting species with multiple fronts Ⅰ: A geometric optics approach

2020 ◽  
Vol 40 (6) ◽  
pp. 3683-3714 ◽  
Author(s):  
Qian Liu ◽  
◽  
Shuang Liu ◽  
King-Yeung Lam ◽  
Keyword(s):  
Geometric Optics ◽  
Interacting Species ◽  
Asymptotic Spreading

scholarly journals Light shaping from a physical-optics point of view

2020 ◽  
Vol 238 ◽  
pp. 02006
Author(s):  
Liangxin Yang ◽  
Irfan Badar ◽  
Christian Hellmann ◽  
Frank Wyrowski
Keyword(s):  
Fourier Transform ◽  
Optical Element ◽  
Initial Guess ◽  
Point Of View ◽  
Physical Optics ◽  
Diffraction Effect ◽  
Geometric Optics ◽  
Design Task ◽  
Tracing Techniques

In the design of optical element for light shaping, a geometric-optics assumption is usually used, where the validity of the assumption is rarely discussed in literature. In this work, the field tracing techniques for modeling light-shaping systems are presented, which reveals the optical element resulted from those geometric-base algorithm is not always accurate enough for the design task. An example is demonstrated with the functional embodiment of the element. The simulation result shows that diffraction effect may occur, especially in paraxial situation. However, the designed result start with the assumption is well-introduced initial guess for further optimization with the iterative Fourier transform algorithm (IFTA).

scholarly journals Kerr-spacetime geometric optics for vortex beams

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Fabrizio Tamburini ◽  
Fabiano Feleppa ◽  
Ignazio Licata ◽  
Bo Thidé
Keyword(s):  
Geometric Optics ◽  
Kerr Spacetime ◽  
Vortex Beams

An evolutional free-boundary problem of a reaction–diffusion–advection system

2017 ◽  
Vol 147 (3) ◽  
pp. 615-648 ◽  
Author(s):  
Ling Zhou ◽  
Shan Zhang ◽  
Zuhan Liu
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Ecological Model ◽  
Reaction Diffusion ◽  
Spreading Speed ◽  
Heterogeneous Environment ◽  
Long Run ◽  
Strong Competition ◽  
Asymptotic Spreading

In this paper we consider a system of reaction–diffusion–advection equations with a free boundary, which arises in a competition ecological model in heterogeneous environment. The evolution of the free-boundary problem is discussed, which is an extension of the results of Du and Lin (Discrete Contin. Dynam. Syst. B19 (2014), 3105–3132). Precisely, when u is an inferior competitor, we prove that (u, v) → (0, V) as t→∞. When u is a superior competitor, we prove that a spreading–vanishing dichotomy holds, namely, as t→∞, either h(t)→∞ and (u, v) → (U, 0), or limt→∞h(t) < ∞ and (u, v) → (0, V). Moreover, in a weak competition case, we prove that two competing species coexist in the long run, while in a strong competition case, two species spatially segregate as the competition rates become large. Furthermore, when spreading occurs, we obtain some rough estimates of the asymptotic spreading speed.

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