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Investigation of the moment distribution in a bent circular plate by speckle-shearing interferometry

K.V.S. Gnaneswara Rao D.V.Krishna Rao 《Optics and Lasers in Engineering》1983,4(3):187-194

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Homogenization of piezoelectric solid and thermodynamics

R. Wojnar 《Reports on Mathematical Physics》1997,40(3):585-598

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Laser pulse heating: a formulation of desired temperature at the surface

M. Kalyon B. S. Yilbas 《Optics and Lasers in Engineering》2003,39(1):109-119

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Singularity formation for Prandtl’s equations

F. Gargano M. Sammartino V. Sciacca 《Physica D: Nonlinear Phenomena》2009,238(19):1975-1991

Si tratta di una memoria in cui si espongono alcuni progressi matematici recentemente compiuti nello studio delle equazioni di strato limite de Prandtl. Gli argomenti principali trattati sono la derivazione rigorosa delle equazioni stesse, la teoria matematica del problema di valore iniziale associato e la teoria delle soluzioni di similarità.

Abstract

Этa-излoжитeльнaя paбoтa o нeкoтopых мaтeмaтихecких ycпeхaх в изyхeнии ypaвнeний гpaнихнoгo cлoя Пpaндтля. Ocнoвныe paccмaтpывaeмыe вoпpocы: cтpoгий вывoд ypaвнeний, мaтe-мaтихecкaя тeopия cвязaннoй зaдaхи нaхaльнoгo знaхeния, и тeopия пoдoбнocтых pэшeний.

Contents

1. Introduction		4
	1.1. The basic questions	4
	1.2. Other approaches	8
	1.3. Outline of the paper	11
2. Adiabatic accessibility and construction of entropy		12
	2.1. Basic concepts	13
	2.2. The entropy principle	19
	2.3. Assumptions about the order relation	21
	2.4. The construction of entropy for a single system	24
	2.5. Construction of a universal entropy in the absence of mixing	29
	2.6. Concavity of entropy	32
	2.7. Irreversibility and Carathéodory’s principle	35
	2.8. Some further results on uniqueness	36
3. Simple systems		38
	3.1. Coordinates for simple systems	40
	3.2. Assumptions about simple systems	42
	3.3. The geometry of forward sectors	45
4. Thermal equilibrium		54
	4.1. Assumptions about thermal contact	54
	4.2. The comparison principle in compound systems	59
	4.3. The role of transversality	64
5. Temperature and its properties		67
	5.1. Differentiability of entropy and the existence of temperature	67
	5.2. Geometry of isotherms and adiabats	73
	5.3. Thermal equilibrium and uniqueness of entropy	75
6. Mixing and chemical reactions		77
	6.1. The difficulty in fixing entropy constants	77
	6.2. Determination of additive entropy constants	79
7. Summary and conclusions		88
	7.1. General axioms	88
	7.2. Axioms for simple systems	88
	7.3. Axioms for thermal equilibrium	88
	7.4. Axiom for mixtures and reactions	89
Acknowledgements		92
Appendix A		92
	A.1. List of symbols	92
	A.2. Index of technical terms	93
References		94

Constant	H₂CO	D₂CO	Unit
$ν_{0}$	1746.011	1701.620	cm^?1
$A′$	281807.8 ± 6.	141696.6 ± 7.	MHz
$B′$	38608.7 ± 5.	32068.4 ± 7.	MHz
$C′$	33738.7 ± 3.	25998.6 ± 10.	MHz
μ″	2.328 ± 0.006	2.344 ± 0.006	Debye
μ′	2.344 ± 0.006	2.364 ± 0.005	Debye

²⁰Ne	²²Ne
Neenergy (keV)	239.12±0.14	230.49±0.88
width (keV)	15.43±0.41	12.65±3.51

$J + 1 ← J$	$M_{J}$		μ/D
2 ← 1	0		5.627
	1		5.601
4 ← 3	3		5.608
		Mean	5.612

	$ν_{2}$		$ν_{5}$
$ν_{0}$	1 028.67275 (15)		1 059.96970 (11)	(cm^?1)
$A$	78 765.20 (89)		78 030.21 (109)	(MHz)
$B^{1}$	10 805.29 (26)		10 860.10 (13)	(MHz)
$Aζ_{5}$			?25 080.77 (99)	(MHz)
$D$		8 756.0 (43)		(MHz)
μ	1.90741 (33)		1.90607 (36)	(D)
μ(ground state)		1.90597 (33)		(D)

State	$T_{v}$	$B_{v}$	$d (hfs)$
$Ω′ = 4.5 (System XXI)$	18 882.388 (2)	0.353001 (18)	0.12403 (71)
$Ω′ = 4.5 (System XVII)$	16 594.075 (1)	0.353736 (20)	0.12977 (67)
$Ω ″ = 3.5$	3 887.15 (16)	0.35751 (28)	—
$Ω ″ = 3.5$	2 931.66 (15)	0.35712 (21)	—
$Ω ″ = 4.5$	2 155.16 (30)	0.36264 (67)	—
$Ω ″ = 5.5$	2 099.16 (31)	0.35079 (71)	—
$Ω ″ = 3.5$	2 064.34 (13)	0.35654 (20)	—
$Ω″ = 4.5 (System XXI)$	217.383 (1)	0.362134 (20)	0.27744 (66)
$Ω″ = 3.5 (System XVII)$	0.0	0.360948 (16)	?0.00809 (85)

$ν_{0}$	$B′$	$D′ × 10^{7}$	$B″$	$D″ × 10^{7}$
18 665.19(1)	0.3530(1)	1.80(5)	0.3622(1)	2.85(1)
18 613.22(1)	0.3517(1)	0.4(3)	0.3606(1)	2.4(2)
17 842.32(1)	0.3560(1)	3.0(1)	0.3621(1)	2.7(1)
17 796.09(4)	0.3532(3)	2.4(8)	0.3604(2)	2.7(6)
18 628.22(3)	0.3530(6)	1.8(8)	0.3620(5)	2.7(7)
14 426.12(2)	0.3519(1)	5.5(6)	0.3620(1)	1.9(6)
13 541.44(2)	0.3500(2)	3.7(5)	0.3605(2)	2.3(5)
13 645.78(8)	0.3511(3)	3.1(5)	0.3620(2)	2.8(5)
12 961.98(4)	0.3445(4)	4.5(4)	0.3603(3)	2.3(7)
9 600.47(1)	0.3454(1)	2.8(2)	0.3620(1)	3.0(3)
16 591.29(1)	0.3536(1)	0.5(2)	0.3610(1)	2.6(1)
11 912.89(1)	0.3480(2)	8.5(8)	0.3610(1)	2.2(6)
10 429.62(2)	0.3450(1)	3.1(1)	0.3610(1)	3.0(3)

Constant	Ground state	$v_{3} = 1$ state	Units
$ν_{0}$		1724.267	cm^?1
$A$	198 119.75	198 210.4	MHz
$B$	34 910.646	34 676.6	MHz
$C$	29 561.488	29 331.3	MHz
$μ_{a}$	2.3302	2.3486	D
$μ_{b}$	0.195	0.190	D

System	Ω′	$T′_{0} (cm^{?1})$	$Ω″$	$T″_{0} (cm^{?1})$
VI	5.5	11102	4.5	2157
IX	4.5	16597	3.5	3887
X	5.5	13259	4.5	220
XI	5.5	13865	4.5	220
XIV	5.5	16595	4.5	2157
XVI	5.5	19169	4.5	3720
XVII	4.5	16597	3.5	0
XVIII	7.5	21321	6.5	3965
XIX	6.5	19687	5.5	2111
XX	5.5	18069	4.5	220
XXI	4.5	18885	4.5	220
XXII	5.5	19169	4.5	220