5 research outputs found
First results of dust injection in T-10 plasma
First results of T-10 injection experiments of the carbon dust particles with 2-10 mm diameter and 40-300 m/s velocity are presented. Different scenarios of the dust injection were tested. The dust particles ablation was studied. An approach for determination of a dust particle penetration length was developed. Measured penetration depths (3-7 cm) are compared with the simulation by the ablation model. The mm range of the separate dust particle diameters derived from the ablation data was close to sizes of the dust injected assuming that an acceleration of the separate particle is similar to the large carbon pellet in the pellet injector.ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½ΠΎ ΠΏΠ΅ΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΈ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΡΠ² ΠΏΠΎ ΡΠ½ΠΆΠ΅ΠΊΡΡΡ Π²ΡΠ³Π»Π΅ΡΠ΅Π²ΠΈΡ
ΠΏΠΈΠ»ΠΎΠ²ΠΈΡ
ΡΠ°ΡΡΠΎΠΊ Π΄ΡΠ°ΠΌΠ΅ΡΡΠΎΠΌ 2-10 ΠΌΠΊΠΌ Π·Ρ ΡΠ²ΠΈΠ΄ΠΊΠΎΡΡΡΠΌΠΈ 40-300 ΠΌ/Ρ Ρ Π’-10. ΠΡΠΎΡΠ΅ΡΡΠΎΠ²Π°Π½ΠΎ ΡΡΠ·Π½Ρ ΡΡΠ΅Π½Π°ΡΡΡ ΡΠ½ΠΆΠ΅ΠΊΡΡΡ ΠΏΠΈΠ»Ρ. ΠΠΎΡΠ»ΡΠ΄ΠΆΠ΅Π½ΠΎ Π²ΠΈΠΏΠ°Ρ ΠΏΠΈΠ»ΠΎΠ²ΠΈΡ
ΡΠ°ΡΡΠΎΠΊ. Π ΠΎΠ·ΡΠΎΠ±Π»Π΅Π½ΠΎ ΠΏΡΠΈΠ±Π»ΠΈΠ·Π½Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΡ Π²ΠΈΠ·Π½Π°ΡΠ΅Π½Π½Ρ Π³Π»ΠΈΠ±ΠΈΠ½ΠΈ ΠΏΡΠΎΠ½ΠΈΠΊΠ½Π΅Π½Π½Ρ ΠΏΠΈΠ»ΠΎΠ²ΠΈΡ
ΡΠ°ΡΡΠΎΠΊ. ΠΠ±ΠΌΡΡΡΠ½Ρ Π³Π»ΠΈΠ±ΠΈΠ½ΠΈ ΠΏΡΠΎΠ½ΠΈΠΊΠ½Π΅Π½Π½Ρ (3-7 ΡΠΌ) ΠΏΠΎΡΡΠ²Π½ΡΠ²Π°Π»ΠΈΡΡ Π· ΡΠΎΠ·ΡΠ°Ρ
ΡΠ½ΠΊΠ°ΠΌΠΈ ΠΏΠΎ ΠΌΠΎΠ΄Π΅Π»Ρ Π²ΠΈΠΏΠ°ΡΡ. ΠΡΡΠ½Π΅Π½Ρ ΠΌΡΠΊΡΠΎΠ½Π½Ρ Π΄ΡΠ°ΠΌΠ΅ΡΡΠΈ ΡΠ°ΡΡΠΎΠΊ, ΠΎΡΡΠΈΠΌΠ°Π½Ρ Π· Π΄Π°Π½ΠΈΡ
ΠΏΠΎ Π²ΠΈΠΏΠ°ΡΡ, Ρ Π±Π»ΠΈΠ·ΡΠΊΠΈΠΌΠΈ Π΄ΠΎ ΡΠΎΠ·ΠΌΡΡΡΠ² ΡΠ½ΠΆΠ΅ΠΊΡΠΎΠ²Π°Π½ΠΎΠ³ΠΎ ΠΏΠΈΠ»Ρ, Ρ ΠΏΡΠΈΠΏΡΡΠ΅Π½Π½Ρ ΡΠΎΠ³ΠΎ, ΡΠΎ ΠΎΠΊΡΠ΅ΠΌΡ ΡΠ°ΡΡΠΊΠΈ ΠΏΡΠΈΡΠΊΠΎΡΡΡΡΡΡΡ ΡΠ°ΠΊ ΡΠ°ΠΌΠΎ, ΡΠΊ Ρ ΠΏΡΠΈ ΡΠ½ΠΆΠ΅ΠΊΡΡΡ Π²Π΅Π»ΠΈΠΊΠΈΡ
ΠΏΠ΅Π»Π΅ΡΡΠ².ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΠΏΠ΅ΡΠ²ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΠΏΠΎ ΠΈΠ½ΠΆΠ΅ΠΊΡΠΈΠΈ ΡΠ³Π»Π΅ΡΠΎΠ΄Π½ΡΡ
ΠΏΡΠ»Π΅Π²ΡΡ
ΡΠ°ΡΡΠΈΡ Π΄ΠΈΠ°ΠΌΠ΅ΡΡΠΎΠΌ 2-10 ΠΌΠΊΠΌ ΡΠΎ ΡΠΊΠΎΡΠΎΡΡΡΠΌΠΈ 40-300 ΠΌ/Ρ Π² Π’-10. ΠΡΠΎΡΠ΅ΡΡΠΈΡΠΎΠ²Π°Π½Ρ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠ΅ ΡΡΠ΅Π½Π°ΡΠΈΠΈ ΠΈΠ½ΠΆΠ΅ΠΊΡΠΈΠΈ ΠΏΡΠ»ΠΈ. ΠΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΎ ΠΈΡΠΏΠ°ΡΠ΅Π½ΠΈΠ΅ ΠΏΡΠ»Π΅Π²ΡΡ
ΡΠ°ΡΡΠΈΡ. Π Π°Π·ΡΠ°Π±ΠΎΡΠ°Π½Π° ΠΏΡΠΈΠ±Π»ΠΈΠ·ΠΈΡΠ΅Π»ΡΠ½Π°Ρ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ° ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ Π³Π»ΡΠ±ΠΈΠ½Ρ ΠΏΡΠΎΠ½ΠΈΠΊΠ½ΠΎΠ²Π΅Π½ΠΈΡ ΠΏΡΠ»Π΅Π²ΡΡ
ΡΠ°ΡΡΠΈΡ. ΠΠ·ΠΌΠ΅ΡΠ΅Π½Π½ΡΠ΅ Π³Π»ΡΠ±ΠΈΠ½Ρ ΠΏΡΠΎΠ½ΠΈΠΊΠ½ΠΎΠ²Π΅Π½ΠΈΡ (3-7 ΡΠΌ) ΡΡΠ°Π²Π½ΠΈΠ²Π°Π»ΠΈΡΡ Ρ ΡΠ°ΡΡΠ΅ΡΠ°ΠΌΠΈ ΠΏΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΈΡΠΏΠ°ΡΠ΅Π½ΠΈΡ. ΠΡΠ΅Π½Π΅Π½Π½ΡΠ΅ ΠΌΠΈΠΊΡΠΎΠ½Π½ΡΠ΅ Π΄ΠΈΠ°ΠΌΠ΅ΡΡΡ ΡΠ°ΡΡΠΈΡ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΠΈΠ· Π΄Π°Π½Π½ΡΡ
ΠΏΠΎ ΠΈΡΠΏΠ°ΡΠ΅Π½ΠΈΡ, Π±Π»ΠΈΠ·ΠΊΠΈ ΠΊ ΡΠ°Π·ΠΌΠ΅ΡΠ°ΠΌ ΠΈΠ½ΠΆΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΠΏΡΠ»ΠΈ, Π² ΠΏΡΠ΅Π΄ΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠΈ ΡΠΎΠ³ΠΎ, ΡΡΠΎ ΠΎΡΠ΄Π΅Π»ΡΠ½ΡΠ΅ ΡΠ°ΡΡΠΈΡΡ ΡΡΠΊΠΎΡΡΡΡΡΡ ΡΠ°ΠΊ ΠΆΠ΅, ΠΊΠ°ΠΊ ΠΈ ΠΏΡΠΈ ΠΈΠ½ΠΆΠ΅ΠΊΡΠΈΠΈ ΠΊΡΡΠΏΠ½ΡΡ
ΠΏΠ΅Π»Π»Π΅ΡΠΎΠ²
Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes
Different initial and boundary value problems for the equation of vibrations
of rods (also called Fresnel equation) are solved by exploiting the connection
with Brownian motion and the heat equation. The analysis of the fractional
version (of order ) of the Fresnel equation is also performed and, in
detail, some specific cases, like , 1/3, 2/3, are analyzed. By means
of the fundamental solution of the Fresnel equation, a pseudo-process ,
with real sign-varying density is constructed and some of its properties
examined. The equation of vibrations of plates is considered and the case of
circular vibrating disks is investigated by applying the methods of
planar orthogonally reflecting Brownian motion within . The composition of
F with reflecting Brownian motion yields the law of biquadratic heat
equation while the composition of with the first passage time of
produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure