Articles — Page 7

Kelvin WedgeReading Note

Relations among Rays, Group Velocity, Phase Velocity, and the Wave Number Vector in Water Waves

In dispersive water waves (e.g., surface gravity waves on deep or shallow water), several concepts describe how waves travel, how energy moves, and how the wave patterns evolve.…

Fluid Mechanics
Kelvin WedgeReading Note

Pressure Forcing on a Free Surface and Far-Field Waves in Lamb’s Hydrodynamics

We summarise Lamb’s treatment of a pressure disturbance on a free surface in a uniform stream, emphasising the contour‐integral evaluation of the far-field wavetrain, the…

Fluid Mechanics
Kelvin WedgeReading Note

Wave Patterns from Ray Theory: Centered Waves, Wake Angles, and Phase Geometry

We collect the ray-theoretic relations for wave patterns generated by a point source, derive the slope of characteristics and their connection to the group-velocity symbol…

Fluid Mechanics

Gaussian Integrals and Related Fourier–Bessel Identities

We collect closed-form formulas for one- and \(n\)-dimensional Gaussian integrals with linear and oscillatory terms, derive even-moment integrals, and list several useful…

Mathematics

我的小院

原想写一些剖析自我的文字,却不知如何下笔,也罢,就写写最近的杂绪吧。 早春,院子里的不知名的树依然光秃着树干,纹丝不动地点缀着视野里的红墙,肃杀而冷淡。又是一个冬去了,除却偶或光临的故乡的喜鹊,在小院凌乱的大戏台,唱着故园情、天涯愁。素常,小院是安静的,百无聊赖,当我抬头,它便饮喜若狂的挤到窗前叽叽喳喳,可是啊,这冰冷的窗显然冻住那些炙热的陈情,定格成了…

随想 Reflections
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