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dbr:Victor_Borisov
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Spacetime triangle diagram technique
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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.
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Canonical variables Initial variables
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STTD for a semi-infinite travelling source pulse. 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 . 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 . STTD for a source limited from right by plane , i.e. Canonical variables ξ, η. STTD for a finite travelling source pulse. 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. The same STTD sequence for a "long" pulse. STTD for a finite travelling source pulse propagating along a semi-infinite radiator . Initial variables z, τ.
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The simplest STTD representing a triangle integration domain resulted from the Riemann–Volterra integral formula.
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Static limitations to the source area Combined action of limitations of different type, see Refs. for details and more complicated examples
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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.
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