Spacetime triangle diagram technique (original) (raw)

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In physics and mathematics, the spacetime triangle diagram (STTD) technique, also known as the Smirnov method of incomplete separation of variables, is the direct space-time domain method for electromagnetic and scalar wave motion. (en)

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left (en)
right (en)

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Canonical variables (en)
Initial variables (en)

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STTD for a source limited from right by plane , i.e. (en)
Canonical variables ξ, η. (en)
Initial variables z, τ. (en)
STTD for a finite travelling source pulse. (en)
STTD for a semi-infinite travelling source pulse. (en)
The same STTD sequence for a "long" pulse. (en)
STTD for a source limited from left by plane , i.e. , which is the case, e.g., for a travelling source propagating along a semi-infinite radiator . (en)
STTD for a source limited from both sides, i.e. , which is the case, e.g., for a travelling source propagating along a radiator of finite length . (en)
A sequence of generic STTDs for a "short", finite source pulse of duration propagating along a finite radiator with a constant velocity . In this case the source can be expressed in the form : where is the Heaviside step function. (en)
STTD for a finite travelling source pulse propagating along a semi-infinite radiator . (en)

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horizontal (en)
vertical (en)

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The simplest STTD representing a triangle integration domain resulted from the Riemann–Volterra integral formula. (en)

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center (en)

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Static limitations to the source area (en)
Combined action of limitations of different type, see Refs. for details and more complicated examples (en)

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F140910a_STTDmethod_F_RotatedDomain.gif (en)
F140910a_STTDmethod_F_zTauDomain.gif (en)
F140910a_STTDmethod_F_zTau_l.gif (en)
F140910a_STTDmethod_F_zTau_z0.gif (en)
F140911a_STTDmethod_F_zTau_frntBack.gif (en)
F140911a_STTDmethod_F_zTau_frntBack_z0.gif (en)
F140911a_STTDmethod_F_zTau_front.gif (en)
F140911a_STTDmethod_F_zTau_z0l.gif (en)
F140913a_STTDmethod_F_zTau_z0lT_L_all.gif (en)
F140913a_STTDmethod_F_zTau_z0lT_S_all.gif (en)

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In physics and mathematics, the spacetime triangle diagram (STTD) technique, also known as the Smirnov method of incomplete separation of variables, is the direct space-time domain method for electromagnetic and scalar wave motion. (en)

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Spacetime triangle diagram technique (en)

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