s
stringlengths
1
39
o
stringclasses
996 values
p
stringlengths
7
77
confidence
float64
0.4
1
predicate_class
stringclasses
2 values
community
int64
0
14
equation_name
stringlengths
14
73
equation_latex
stringlengths
5
217
equation_sympy
stringclasses
617 values
equation_form
stringclasses
472 values
variables
stringlengths
2
85
domain
stringclasses
119 values
scm_name
stringclasses
165 values
source
stringlengths
9
50
extraction_method
stringclasses
8 values
k
t
urn:hailstone:chemistry_physics:structural_equation[ab28a55e8c99]
1
structural_equation
2
arxiv.physics.class-ph.2604.27525v1.eq_421
Φ(θ) = 2k\,r(θ)\sqrt{1-β^2\sin^2θ}/(1-β^2)
arxiv_extracted
["q", "t", "r", "s", "k"]
arxiv
arxiv
arxiv:physics.class-ph:2604.27525v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[ef8e34effc3e]
1
structural_equation
2
arxiv.physics.class-ph.2603.29035v1.eq_422
χ^2/\mathrm{dof}=0.50
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2603.29035v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[9474c4071f4d]
1
structural_equation
2
arxiv.physics.class-ph.2603.19887v1.eq_423
\mathrm{d}ΔT/\mathrm{d}t = -[γ_0 + \mathcal{M}Q(t)][ΔT - \mathcal{I}Q(t)]
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2603.19887v1
cross_domain_amplification
d
E
urn:hailstone:chemistry_physics:structural_equation[1383e09133db]
1
structural_equation
2
arxiv.physics.class-ph.2602.07577v1.eq_424
\dot{E}=0
arxiv_extracted
["t", "d", "E", "o"]
arxiv
arxiv
arxiv:physics.class-ph:2602.07577v1
cross_domain_amplification
t
w
urn:hailstone:chemistry_physics:structural_equation[9e70faf653f1]
1
structural_equation
2
arxiv.physics.class-ph.2602.03790v2.eq_425
t_{\text{w}}=τ
arxiv_extracted
["t", "w", "e", "x"]
arxiv
arxiv
arxiv:physics.class-ph:2602.03790v2
cross_domain_amplification
a
m
urn:hailstone:chemistry_physics:structural_equation[aa6e35db5602]
1
structural_equation
2
arxiv.physics.class-ph.2601.16325v1.eq_426
Δa/g = κ(q/m)
arxiv_extracted
["g", "m", "q", "a"]
arxiv
arxiv
arxiv:physics.class-ph:2601.16325v1
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[3d221c96c754]
1
structural_equation
2
arxiv.physics.class-ph.2512.22285v1.eq_427
\mathbf{F}=\mathbf{F}^e\mathbf{F}^r_α\mathbf{F}^d_α
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2512.22285v1
cross_domain_amplification
j
x
urn:hailstone:chemistry_physics:structural_equation[35ba436b5bc1]
1
structural_equation
2
arxiv.physics.class-ph.2512.20123v1.eq_428
j_{-1}(x) = \cos x / x
arxiv_extracted
["j", "o", "s", "c", "x"]
arxiv
arxiv
arxiv:physics.class-ph:2512.20123v1
cross_domain_amplification
b
y
urn:hailstone:chemistry_physics:structural_equation[f7419cfd31c1]
1
structural_equation
2
arxiv.physics.class-ph.2510.25981v1.eq_429
\boldsymbol{δF}=-γ_nv^{n-1}\boldsymbol{v}
arxiv_extracted
["y", "o", "s", "b", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2510.25981v1
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[cef8b1ebb29e]
1
structural_equation
2
arxiv.physics.class-ph.2510.17750v4.eq_430
\mathbf{k}_{\parallel} = \mathbf{0}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2510.17750v4
cross_domain_amplification
f
f
urn:hailstone:chemistry_physics:structural_equation[86757bd4a726]
1
structural_equation
2
arxiv.physics.class-ph.2509.17821v2.eq_431
f^N(q)=\pm\frac{q}{|q|^2}
arxiv_extracted
["f", "q", "m", "p", "N"]
arxiv
arxiv
arxiv:physics.class-ph:2509.17821v2
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[ccdd0a079c06]
1
structural_equation
2
arxiv.physics.class-ph.2509.12601v1.eq_432
Δ_{1} = 23~\mathrm{meV}
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2509.12601v1
cross_domain_amplification
m
m
urn:hailstone:chemistry_physics:structural_equation[7d97c9e2780b]
1
structural_equation
2
arxiv.physics.class-ph.2509.12601v1.eq_433
Δ_{2} = 6~\mathrm{meV}
arxiv_extracted
["a", "t", "m", "h", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2509.12601v1
cross_domain_amplification
C
c
urn:hailstone:chemistry_physics:structural_equation[e5489f0c7607]
1
structural_equation
2
arxiv.physics.class-ph.2509.09973v2.eq_434
θ_{C}=60^{\circ}
arxiv_extracted
["c", "r", "C", "i"]
arxiv
arxiv
arxiv:physics.class-ph:2509.09973v2
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[6092da9843b3]
1
structural_equation
2
arxiv.physics.class-ph.2508.16689v2.eq_435
\mathbf{\nabla}\cdot{\bf B}=0
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2508.16689v2
cross_domain_amplification
s
y
urn:hailstone:chemistry_physics:structural_equation[66180ce23db5]
1
structural_equation
2
arxiv.physics.class-ph.2507.20660v1.eq_436
s_{\infty} = \ln (z)
arxiv_extracted
["f", "t", "y", "i", "s", "n"]
arxiv
arxiv
arxiv:physics.class-ph:2507.20660v1
cross_domain_amplification
S
r
urn:hailstone:chemistry_physics:structural_equation[c78cb90ba203]
1
structural_equation
2
arxiv.physics.class-ph.2507.20660v1.eq_437
S_{\mathrm{molar}} = R \ln 12 \approx 20.7 \, \mathrm{J/mol \cdot K}
arxiv_extracted
["a", "t", "m", "h", "S", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2507.20660v1
cross_domain_amplification
v
p
urn:hailstone:chemistry_physics:structural_equation[62b3f8a6cbb6]
1
structural_equation
2
arxiv.physics.class-ph.2506.08799v3.eq_438
\varkappa=0
arxiv_extracted
["a", "p", "r", "k", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2506.08799v3
cross_domain_amplification
L
m
urn:hailstone:chemistry_physics:structural_equation[3ad72c29ae6f]
1
structural_equation
2
arxiv.physics.class-ph.2505.12062v4.eq_439
Δ_L(0) = 6.9 \pm 1.2
arxiv_extracted
["p", "m", "L"]
arxiv
arxiv
arxiv:physics.class-ph:2505.12062v4
cross_domain_amplification
p
m
urn:hailstone:chemistry_physics:structural_equation[4e2f4d3a6c08]
1
structural_equation
2
arxiv.physics.class-ph.2505.03551v4.eq_440
p^μp_μ= m^2
arxiv_extracted
["m", "p", "p_\u03bc"]
arxiv
arxiv
arxiv:physics.class-ph:2505.03551v4
cross_domain_amplification
f
f
urn:hailstone:chemistry_physics:structural_equation[574f57378102]
1
structural_equation
2
arxiv.physics.class-ph.2504.01471v1.eq_441
f^N(q)=\pm\frac{q}{|q|^3}
arxiv_extracted
["f", "q", "m", "p", "N"]
arxiv
arxiv
arxiv:physics.class-ph:2504.01471v1
cross_domain_amplification
e
m
urn:hailstone:chemistry_physics:structural_equation[e7ee346f3c11]
1
structural_equation
2
arxiv.physics.class-ph.2503.19972v1.eq_442
e_{\text{max}}^2-e^2=h=l\left(1-\cosθ\right)
arxiv_extracted
["e", "t", "m", "x"]
arxiv
arxiv
arxiv:physics.class-ph:2503.19972v1
cross_domain_amplification
b
y
urn:hailstone:chemistry_physics:structural_equation[1fb42cd11cd7]
1
structural_equation
2
arxiv.physics.class-ph.2503.19972v1.eq_443
\boldsymbolα=\textbf{j}+\textbf{e}, \boldsymbolβ=\textbf{j}-\textbf{e}
arxiv_extracted
["y", "o", "s", "b", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2503.19972v1
cross_domain_amplification
d
l
urn:hailstone:chemistry_physics:structural_equation[9d30e73163a7]
1
structural_equation
2
arxiv.physics.class-ph.2503.19972v1.eq_444
\dot{\boldsymbolα}=2\partial_{\boldsymbolα} φ\times \boldsymbolα
arxiv_extracted
["t", "o", "b", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2503.19972v1
cross_domain_amplification
d
l
urn:hailstone:chemistry_physics:structural_equation[748d6f62a483]
1
structural_equation
2
arxiv.physics.class-ph.2503.19972v1.eq_445
\dot{\boldsymbolβ}=2\partial_{\boldsymbolβ} φ\times \boldsymbolβ
arxiv_extracted
["t", "o", "b", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2503.19972v1
cross_domain_amplification
b
y
urn:hailstone:chemistry_physics:structural_equation[2c3d7bc8e1fa]
1
structural_equation
2
arxiv.physics.class-ph.2503.19972v1.eq_446
\boldsymbolα^2=\boldsymbolβ^2=1
arxiv_extracted
["y", "o", "s", "b", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2503.19972v1
cross_domain_amplification
d
x
urn:hailstone:chemistry_physics:structural_equation[03714a48e9c5]
1
structural_equation
2
arxiv.physics.class-ph.2501.08424v2.eq_447
\ddot{x} - (1/2x) \dot{x}^2 + 2 ω^2 x - 1/8x = 0
arxiv_extracted
["t", "d", "x", "o"]
arxiv
arxiv
arxiv:physics.class-ph:2501.08424v2
cross_domain_amplification
A
p
urn:hailstone:chemistry_physics:structural_equation[c2164e66457e]
1
structural_equation
2
arxiv.physics.class-ph.2501.04743v1.eq_448
A \frac{\partial {\bf q}}{\partial t}+\sum_{i=1}^n B_i \frac{\partial {\bf q}}{\partial x_i}=0,
arxiv_extracted
["f", "a", "p", "A", "r", "c"]
arxiv
arxiv
arxiv:physics.class-ph:2501.04743v1
cross_domain_amplification
h
a
urn:hailstone:chemistry_physics:structural_equation[e264ac0cfa34]
1
structural_equation
2
arxiv.physics.class-ph.2501.01995v3.eq_449
[\hat{x},\hat{k}]=i
arxiv_extracted
["t", "x", "h", "a"]
arxiv
arxiv
arxiv:physics.class-ph:2501.01995v3
cross_domain_amplification
h
a
urn:hailstone:chemistry_physics:structural_equation[38ffa4e68639]
1
structural_equation
2
arxiv.physics.class-ph.2501.01995v3.eq_450
[\hat{x},\hat{p}]=i\hbar
arxiv_extracted
["t", "x", "h", "a"]
arxiv
arxiv
arxiv:physics.class-ph:2501.01995v3
cross_domain_amplification
f
e
urn:hailstone:chemistry_physics:structural_equation[6811bf39fb32]
1
structural_equation
2
arxiv.physics.class-ph.2412.13221v3.eq_451
\frac{\text{d}}{\text{d}\text{t}}\oint_{s(t)}\vec{E}\cdot\text{d}\vec{s}(t)=\frac{I^{(s)}_{\text{in}}(t)}{ε_0}
arxiv_extracted
["f", "e", "a", "t", "r", "c"]
arxiv
arxiv
arxiv:physics.class-ph:2412.13221v3
cross_domain_amplification
d
k
urn:hailstone:chemistry_physics:structural_equation[57c817c72a25]
1
structural_equation
2
arxiv.physics.class-ph.2412.09100v3.eq_452
\ddot{x} + k x \dot{x} + ω^2 x + (k^2/9) x^3 = 0
arxiv_extracted
["t", "o", "d", "k", "x"]
arxiv
arxiv
arxiv:physics.class-ph:2412.09100v3
cross_domain_amplification
d
J
urn:hailstone:chemistry_physics:structural_equation[893b57fd4a36]
1
structural_equation
2
arxiv.physics.class-ph.2412.09100v3.eq_453
\ddot{z} + J(z) \dot{z}^2 + F(z) \dot{z} + G(z) = 0
arxiv_extracted
["z", "t", "o", "J", "d"]
arxiv
arxiv
arxiv:physics.class-ph:2412.09100v3
cross_domain_amplification
b
y
urn:hailstone:chemistry_physics:structural_equation[4010e9765416]
1
structural_equation
2
arxiv.physics.class-ph.2412.10408v1.eq_454
\boldsymbol{E}(\boldsymbol{r},t)=\nabla\times\boldsymbolΘ(\boldsymbol{r},t)
arxiv_extracted
["y", "o", "s", "b", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2412.10408v1
cross_domain_amplification
v
i
urn:hailstone:chemistry_physics:structural_equation[f5309d30f30a]
1
structural_equation
2
arxiv.physics.class-ph.2410.00877v1.eq_455
\varphi(x) = (\it{x/D})^{4/3}
arxiv_extracted
["a", "h", "i", "p", "r", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2410.00877v1
cross_domain_amplification
v
i
urn:hailstone:chemistry_physics:structural_equation[187ee5957323]
1
structural_equation
2
arxiv.physics.class-ph.2410.00877v1.eq_456
\varphi(x) = (x/D)^{3/2}
arxiv_extracted
["a", "h", "i", "p", "r", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2410.00877v1
cross_domain_amplification
v
i
urn:hailstone:chemistry_physics:structural_equation[0dac7ab6f832]
1
structural_equation
2
arxiv.physics.class-ph.2410.00877v1.eq_457
\varphi(x) = (x/D)^ξ
arxiv_extracted
["a", "h", "i", "p", "r", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2410.00877v1
cross_domain_amplification
Q
r
urn:hailstone:chemistry_physics:structural_equation[3268215e1f1b]
1
structural_equation
2
arxiv.physics.class-ph.2408.15773v2.eq_458
δQ^\text{rev}/T = dS
arxiv_extracted
["e", "Q", "t", "r", "x"]
arxiv
arxiv
arxiv:physics.class-ph:2408.15773v2
cross_domain_amplification
n
c
urn:hailstone:chemistry_physics:structural_equation[b3e72424eb3d]
1
structural_equation
2
arxiv.physics.class-ph.2407.09570v2.eq_459
\nabla \cdot \vec{P}=-ρ, \ \partial \vec{P}/\partial t + c \nabla \times \vec{M} = \vec{J}
arxiv_extracted
["a", "n", "b", "c", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2407.09570v2
cross_domain_amplification
m
c
urn:hailstone:chemistry_physics:structural_equation[8a4c9c8efd50]
1
structural_equation
2
arxiv.physics.class-ph.2402.04047v2.eq_460
{\mc E}=mc^2
arxiv_extracted
["E", "c", "m"]
arxiv
arxiv
arxiv:physics.class-ph:2402.04047v2
cross_domain_amplification
T
E
urn:hailstone:chemistry_physics:structural_equation[0055bc233daf]
1
structural_equation
2
arxiv.physics.class-ph.2308.16159v1.eq_461
T^{*}=T|E|^{3/2}<80
arxiv_extracted
["E", "T"]
arxiv
arxiv
arxiv:physics.class-ph:2308.16159v1
cross_domain_amplification
S
q
urn:hailstone:chemistry_physics:structural_equation[16e7e76350aa]
1
structural_equation
2
arxiv.physics.class-ph.2308.15369v1.eq_462
S(q',q'',T)=S(q',Q,t_1)+S(Q,q'',t_2)
arxiv_extracted
["T", "q", "S"]
arxiv
arxiv
arxiv:physics.class-ph:2308.15369v1
cross_domain_amplification
t_1
T
urn:hailstone:chemistry_physics:structural_equation[a9de97357c87]
1
structural_equation
2
arxiv.physics.class-ph.2308.15369v1.eq_463
t_1+t_2=T
arxiv_extracted
["t_2", "T", "t_1"]
arxiv
arxiv
arxiv:physics.class-ph:2308.15369v1
cross_domain_amplification
v
i
urn:hailstone:chemistry_physics:structural_equation[053b2d1a4aed]
1
structural_equation
2
arxiv.physics.class-ph.2307.04810v1.eq_464
\vec{r}_i,\,i=1,2,3
arxiv_extracted
["e", "i", "r", "c", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2307.04810v1
cross_domain_amplification
v
h
urn:hailstone:chemistry_physics:structural_equation[54685b532a69]
1
structural_equation
2
arxiv.physics.class-ph.2307.04810v1.eq_465
\vec{f}_i=\hat{r}_i+\vec{e}_i
arxiv_extracted
["e", "f", "h", "i", "c", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2307.04810v1
cross_domain_amplification
N
n
urn:hailstone:chemistry_physics:structural_equation[1cf753a70fa3]
1
structural_equation
2
arxiv.physics.class-ph.2306.07897v1.eq_466
N = 1, n = 2
arxiv_extracted
["n", "N"]
arxiv
arxiv
arxiv:physics.class-ph:2306.07897v1
cross_domain_amplification
N
n
urn:hailstone:chemistry_physics:structural_equation[1cf753a70fa3]
1
structural_equation
2
arxiv.physics.class-ph.2306.07897v1.eq_467
N = 1, n = 2
arxiv_extracted
["n", "N"]
arxiv
arxiv
arxiv:physics.class-ph:2306.07897v1
cross_domain_amplification
J_1
x
urn:hailstone:chemistry_physics:structural_equation[0726822cb048]
1
structural_equation
2
arxiv.physics.class-ph.2305.08869v1.eq_468
J_1(x)=0
arxiv_extracted
["x", "J_1"]
arxiv
arxiv
arxiv:physics.class-ph:2305.08869v1
cross_domain_amplification
J_0
x
urn:hailstone:chemistry_physics:structural_equation[cefaab47906e]
1
structural_equation
2
arxiv.physics.class-ph.2305.08869v1.eq_469
J_0(x)=0
arxiv_extracted
["J_0", "x"]
arxiv
arxiv
arxiv:physics.class-ph:2305.08869v1
cross_domain_amplification
J_1
x
urn:hailstone:chemistry_physics:structural_equation[0726822cb048]
1
structural_equation
2
arxiv.physics.class-ph.2305.08869v1.eq_470
J_1(x)=0
arxiv_extracted
["x", "J_1"]
arxiv
arxiv
arxiv:physics.class-ph:2305.08869v1
cross_domain_amplification
D
i
urn:hailstone:chemistry_physics:structural_equation[a1c3c45770de]
1
structural_equation
2
arxiv.physics.class-ph.2305.04125v5.eq_471
\Ddotθ + ω^{2} \sinθ = H\cos{ωt}
arxiv_extracted
["D", "t", "o", "i", "s", "d"]
arxiv
arxiv
arxiv:physics.class-ph:2305.04125v5
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[3eddb946f6bc]
1
structural_equation
2
arxiv.physics.class-ph.2303.18204v1.eq_472
{\mathbf q} = [{\mathbf q}_1, {\mathbf q}_2, \dots, {\mathbf q}_N] \in {\mathbb R}^{3N}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2303.18204v1
cross_domain_amplification
r_{ij}
b
urn:hailstone:chemistry_physics:structural_equation[7aaabf8d6184]
1
structural_equation
2
arxiv.physics.class-ph.2303.18204v1.eq_473
r_{ij} = |{\mathbf q}_i - {\mathbf q}_j |
arxiv_extracted
["a", "r_{ij}", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2303.18204v1
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[6e1a7dad139b]
1
structural_equation
2
arxiv.physics.class-ph.2302.10224v1.eq_474
ω\mathbf{A}_{0}=\mathbf{k}φ_{0}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2302.10224v1
cross_domain_amplification
c
v
urn:hailstone:chemistry_physics:structural_equation[c5f1a14d6022]
1
structural_equation
2
arxiv.physics.class-ph.2302.10224v1.eq_475
ω^{2}=c^{2}\left\vert \mathbf{k}\right\vert^{2}
arxiv_extracted
["e", "f", "t", "c", "l", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2302.10224v1
cross_domain_amplification
c
r
urn:hailstone:chemistry_physics:structural_equation[e76d406e2050]
1
structural_equation
2
arxiv.physics.class-ph.2301.10469v1.eq_476
{\cal L}=1+\frac{n}{2}
arxiv_extracted
["f", "a", "L", "r", "c", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2301.10469v1
cross_domain_amplification
c
L
urn:hailstone:chemistry_physics:structural_equation[439483270181]
1
structural_equation
2
arxiv.physics.class-ph.2301.10469v1.eq_477
{\cal L}=2,3
arxiv_extracted
["L", "c", "l", "a"]
arxiv
arxiv
arxiv:physics.class-ph:2301.10469v1
cross_domain_amplification
R
s
urn:hailstone:chemistry_physics:structural_equation[bf2a9446d712]
1
structural_equation
2
arxiv.physics.class-ph.2301.05360v2.eq_478
Re[s]=1/2
arxiv_extracted
["e", "s", "R"]
arxiv
arxiv
arxiv:physics.class-ph:2301.05360v2
cross_domain_amplification
a
a
urn:hailstone:chemistry_physics:structural_equation[4382fdb265a2]
1
structural_equation
2
arxiv.physics.class-ph.2212.07005v1.eq_479
a(x + y) = ax + ay
arxiv_extracted
["y", "a", "x"]
arxiv
arxiv
arxiv:physics.class-ph:2212.07005v1
cross_domain_amplification
o
t
urn:hailstone:chemistry_physics:structural_equation[d7455048f961]
1
structural_equation
2
arxiv.physics.class-ph.2211.13213v2.eq_480
\operatorname{curl} \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}
arxiv_extracted
["e", "a", "t", "o", "p", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2211.13213v2
cross_domain_amplification
o
t
urn:hailstone:chemistry_physics:structural_equation[06a28b0b1417]
1
structural_equation
2
arxiv.physics.class-ph.2211.13213v2.eq_481
\operatorname{curl} \mathbf{H} = \frac{\partial \mathbf{D}}{\partial t} + \mathbf{j}
arxiv_extracted
["e", "a", "t", "o", "p", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2211.13213v2
cross_domain_amplification
o
t
urn:hailstone:chemistry_physics:structural_equation[417fd95441fe]
1
structural_equation
2
arxiv.physics.class-ph.2211.13213v2.eq_482
\operatorname{div} \mathbf{D} = \varrho
arxiv_extracted
["e", "a", "t", "o", "p", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2211.13213v2
cross_domain_amplification
o
t
urn:hailstone:chemistry_physics:structural_equation[712f6ba86577]
1
structural_equation
2
arxiv.physics.class-ph.2211.13213v2.eq_483
\operatorname{div} \mathbf{B} = 0
arxiv_extracted
["e", "a", "t", "o", "p", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2211.13213v2
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[55e8ea8f21a9]
1
structural_equation
2
arxiv.physics.class-ph.2211.13213v2.eq_484
\mathbf{D} = \varepsilon_0 \mathbf{E}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2211.13213v2
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[6be6fb27d5d7]
1
structural_equation
2
arxiv.physics.class-ph.2211.13213v2.eq_485
\mathbf{B} = μ_0 \mathbf{H}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2211.13213v2
cross_domain_amplification
t
P
urn:hailstone:chemistry_physics:structural_equation[56d2b2193f40]
1
structural_equation
2
arxiv.physics.class-ph.2210.05601v1.eq_486
\tilde{P} = \boldsymbol{\tilde{p}} -\,\frac{1}{c}\,\boldsymbol{\tilde{M}}
arxiv_extracted
["e", "t", "P", "i", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2210.05601v1
cross_domain_amplification
t
J
urn:hailstone:chemistry_physics:structural_equation[f14f3ca3795b]
1
structural_equation
2
arxiv.physics.class-ph.2210.05601v1.eq_487
\tilde{J} = J -\,c\,\nabla\cdot\tilde{P}
arxiv_extracted
["e", "t", "i", "J", "d", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2210.05601v1
cross_domain_amplification
d
e
urn:hailstone:chemistry_physics:structural_equation[3d2a9a493663]
1
structural_equation
2
arxiv.physics.class-ph.2210.05601v1.eq_488
\dot{T}\left(\dot{\nabla}\right) = \frac{1}{c}\,J \cdot F = f
arxiv_extracted
["e", "t", "d", "o", "T", "l"]
arxiv
arxiv
arxiv:physics.class-ph:2210.05601v1
cross_domain_amplification
v
s
urn:hailstone:chemistry_physics:structural_equation[be1899b61f6b]
1
structural_equation
2
arxiv.physics.class-ph.2207.11508v1.eq_489
\varepsilon(z) = 1 + αχ(z)
arxiv_extracted
["e", "a", "p", "r", "s", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2207.11508v1
cross_domain_amplification
m
a
urn:hailstone:chemistry_physics:structural_equation[6729771ae87e]
1
structural_equation
2
arxiv.physics.class-ph.2206.12996v2.eq_490
\mathcal{N}=2
arxiv_extracted
["a", "t", "m", "h", "c"]
arxiv
arxiv
arxiv:physics.class-ph:2206.12996v2
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[d6cfa03f8704]
1
structural_equation
2
arxiv.physics.class-ph.2206.00764v3.eq_491
\mathbf{V}= \sqrt{\mathbf{B}}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2206.00764v3
cross_domain_amplification
m
f
urn:hailstone:chemistry_physics:structural_equation[520707caa15a]
1
structural_equation
2
arxiv.physics.class-ph.2206.00764v3.eq_492
\mathbf{E}_{\text{Bell}} = \mathbf{V}-\mathbf{I}
arxiv_extracted
["f", "a", "t", "m", "h", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2206.00764v3
cross_domain_amplification
r
T
urn:hailstone:chemistry_physics:structural_equation[3126280665e6]
1
structural_equation
2
arxiv.physics.class-ph.2205.01832v1.eq_493
ω_{\rm R} = 2π/T
arxiv_extracted
["T", "m", "r", "R"]
arxiv
arxiv
arxiv:physics.class-ph:2205.01832v1
cross_domain_amplification
b
A
urn:hailstone:chemistry_physics:structural_equation[2edeb438a643]
1
structural_equation
2
arxiv.physics.class-ph.2204.03952v1.eq_494
{\bf f}^{\rm Aterm} = [(\varepsilonμ-1)/c^2] \partial/\partial t ({\bf E}\times {\bf H})
arxiv_extracted
["f", "m", "A", "r", "b"]
arxiv
arxiv
arxiv:physics.class-ph:2204.03952v1
cross_domain_amplification
v
e
urn:hailstone:chemistry_physics:structural_equation[fedfa7dfc248]
1
structural_equation
2
arxiv.physics.class-ph.2203.05150v1.eq_495
{\vec τ}=d{\vec L} / dt
arxiv_extracted
["e", "c", "d", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2203.05150v1
cross_domain_amplification
v
t
urn:hailstone:chemistry_physics:structural_equation[f8b0cb615f6f]
1
structural_equation
2
arxiv.physics.class-ph.2201.10856v4.eq_496
\vec{\mathcal{E}}(x)=\vec{E}(Λ^{-1}x)
arxiv_extracted
["e", "a", "t", "m", "c", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2201.10856v4
cross_domain_amplification
v
t
urn:hailstone:chemistry_physics:structural_equation[0cb8698b7934]
1
structural_equation
2
arxiv.physics.class-ph.2201.10856v4.eq_497
\vec{\mathcal{B}}(x)=\vec{B}(Λ^{-1}x)
arxiv_extracted
["e", "a", "t", "m", "c", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2201.10856v4
cross_domain_amplification
R
R
urn:hailstone:chemistry_physics:structural_equation[aa26bdcca646]
1
structural_equation
2
arxiv.physics.class-ph.2108.05070v1.eq_498
R_\pm=\pm R
arxiv_extracted
["p", "m", "R"]
arxiv
arxiv
arxiv:physics.class-ph:2108.05070v1
cross_domain_amplification
T_c
m
urn:hailstone:chemistry_physics:structural_equation[96ca8f6af83b]
1
structural_equation
2
arxiv.physics.class-ph.2108.02843v1.eq_499
T_c^*=403 \pm 1
arxiv_extracted
["p", "m", "T_c"]
arxiv
arxiv
arxiv:physics.class-ph:2108.02843v1
cross_domain_amplification
T_o
m
urn:hailstone:chemistry_physics:structural_equation[83ec0cf3b684]
1
structural_equation
2
arxiv.physics.class-ph.2108.02843v1.eq_500
T_o^*=373 \pm 1
arxiv_extracted
["p", "m", "T_o"]
arxiv
arxiv
arxiv:physics.class-ph:2108.02843v1
cross_domain_amplification
X_t
N
urn:hailstone:chemistry_physics:structural_equation[4b97f2c4261c]
1
structural_equation
2
arxiv.physics.class-ph.2103.15562v1.eq_501
X_t^N = \sum_{i=1}^N ω_i Y_t^{x_i}
arxiv_extracted
["m_{i", "u", "X_t", "s", "N"]
arxiv
arxiv
arxiv:physics.class-ph:2103.15562v1
cross_domain_amplification
h
r
urn:hailstone:chemistry_physics:structural_equation[e41f6edde105]
1
structural_equation
2
arxiv.physics.class-ph.2102.10857v1.eq_502
\hbar = 1
arxiv_extracted
["b", "r", "h", "a"]
arxiv
arxiv
arxiv:physics.class-ph:2102.10857v1
cross_domain_amplification
v
b
urn:hailstone:chemistry_physics:structural_equation[718e7bd58ffd]
1
structural_equation
2
arxiv.physics.class-ph.2101.10118v1.eq_503
\vec{\nabla}\cdot\vec{B}=0
arxiv_extracted
["e", "a", "n", "b", "c", "v"]
arxiv
arxiv
arxiv:physics.class-ph:2101.10118v1
cross_domain_amplification
E_{vh}
C_VT
urn:hailstone:chemistry_physics:structural_equation[3dc052997e29]
1
structural_equation
2
arxiv.physics.class-ph.2012.14787v1.eq_504
E_{vh}=C_VT^2 /2
arxiv_extracted
["C_VT", "E_{vh}"]
arxiv
arxiv
arxiv:physics.class-ph:2012.14787v1
cross_domain_amplification
U
t
urn:hailstone:chemistry_physics:structural_equation[b688c4a1ccd6]
1
structural_equation
2
arxiv.physics.class-ph.2011.03412v1.eq_505
. Using the height H of the fluid layer, we introduce the non-dimensional Biot number Bi* =
arxiv_extracted
["g", "t", "n", "i", "s", "U"]
arxiv
arxiv
arxiv:physics.class-ph:2011.03412v1
cross_domain_amplification
H
i
urn:hailstone:chemistry_physics:structural_equation[a78b51f1b710]
1
structural_equation
2
arxiv.physics.class-ph.2011.03412v1.eq_506
H. Varying Bi* allows us to transition from fixed temperature for Bi* = +
arxiv_extracted
["V", "a", "H", "y", "i", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2011.03412v1
cross_domain_amplification
t
g
urn:hailstone:chemistry_physics:structural_equation[e74ff71b529a]
1
structural_equation
2
arxiv.physics.class-ph.2010.15514v1.eq_507
t(=τ_1+τ_2=τ_3=3/\sqrt{2g})=0.67
arxiv_extracted
["g", "q", "t", "r", "s"]
arxiv
arxiv
arxiv:physics.class-ph:2010.15514v1
cross_domain_amplification
t
g
urn:hailstone:chemistry_physics:structural_equation[fc2ecfdeb8ea]
1
structural_equation
2
arxiv.physics.class-ph.2010.15514v1.eq_508
t(=τ_4=2/\sqrt{g})=0.63
arxiv_extracted
["g", "q", "t", "r", "s"]
arxiv
arxiv
arxiv:physics.class-ph:2010.15514v1
cross_domain_amplification
t
B
urn:hailstone:chemistry_physics:structural_equation[a3d0a82c9ede]
1
structural_equation
2
arxiv.physics.class-ph.2010.15514v1.eq_509
t=τ_B=0.58
arxiv_extracted
["t", "B"]
arxiv
arxiv
arxiv:physics.class-ph:2010.15514v1
cross_domain_amplification
i
c
urn:hailstone:chemistry_physics:structural_equation[f7d9d2ea008e]
1
structural_equation
2
arxiv.physics.class-ph.2010.15514v1.eq_510
ν\in (0, ν_c=0.09653)
arxiv_extracted
["n", "c", "i"]
arxiv
arxiv
arxiv:physics.class-ph:2010.15514v1
cross_domain_amplification
s
B
urn:hailstone:chemistry_physics:structural_equation[38ed572b9a91]
1
structural_equation
2
arxiv.physics.class-ph.2010.15514v1.eq_511
=1/\sqrt{2g}=τ_2) < τ_B
arxiv_extracted
["g", "q", "B", "t", "r", "s"]
arxiv
arxiv
arxiv:physics.class-ph:2010.15514v1
cross_domain_amplification
U_{rad}
t
urn:hailstone:chemistry_physics:structural_equation[e1445f1d13e5]
1
structural_equation
2
arxiv.physics.class-ph.2009.05844v1.eq_512
U_{rad}=const\timesω,
arxiv_extracted
["s", "t", "o", "U_{rad}", "n", "c"]
arxiv
arxiv
arxiv:physics.class-ph:2009.05844v1
cross_domain_amplification
r_{ij}
f
urn:hailstone:chemistry_physics:structural_equation[7108a74214b4]
1
structural_equation
2
arxiv.physics.class-ph.2007.11959v5.eq_513
r_{ij}=\mid {\bf r}_i - {\bf r}_j\mid
arxiv_extracted
["f", "r_{ij}", "m", "i", "b", "d"]
arxiv
arxiv
arxiv:physics.class-ph:2007.11959v5
cross_domain_amplification
i
r_{ij}
urn:hailstone:chemistry_physics:structural_equation[4e109b5f3eb1]
1
structural_equation
2
arxiv.physics.class-ph.2007.11959v5.eq_514
ρ_{ij}=r_{ij}^2
arxiv_extracted
["j", "r_{ij}", "i"]
arxiv
arxiv
arxiv:physics.class-ph:2007.11959v5
cross_domain_amplification
b
B
urn:hailstone:chemistry_physics:structural_equation[b667fd6669b9]
1
structural_equation
2
arxiv.physics.class-ph.2006.03162v2.eq_515
{\bf A}=Γ_1{\bf B}Γ_1
arxiv_extracted
["f", "b", "A", "B"]
arxiv
arxiv
arxiv:physics.class-ph:2006.03162v2
cross_domain_amplification
m_a
c
urn:hailstone:chemistry_physics:structural_equation[0a9d7094411f]
1
structural_equation
2
arxiv.physics.class-ph.2006.03455v1.eq_516
m_a/a=m_b/b=m_c/c=ρ
arxiv_extracted
["a", "m_b", "m_c", "m_a", "b", "c"]
arxiv
arxiv
arxiv:physics.class-ph:2006.03455v1
cross_domain_amplification
H_{0k}
p_{0k}
urn:hailstone:chemistry_physics:structural_equation[4c3f4393700a]
1
structural_equation
2
arxiv.physics.class-ph.2006.00288v1.eq_517
{H_{0k}} = n{p_{0k}}ω
arxiv_extracted
["n", "H_{0k}", "p_{0k}"]
arxiv
arxiv
arxiv:physics.class-ph:2006.00288v1
cross_domain_amplification
f
r
urn:hailstone:chemistry_physics:structural_equation[1f89084d1880]
1
structural_equation
2
arxiv.physics.class-ph.2001.10375v2.eq_518
\frac{d^2r(t)}{dt^2} = r^a
arxiv_extracted
["f", "a", "d", "r", "c"]
arxiv
arxiv
arxiv:physics.class-ph:2001.10375v2
cross_domain_amplification
r
t
urn:hailstone:chemistry_physics:structural_equation[7997b1af68e2]
1
structural_equation
2
arxiv.physics.class-ph.2001.10375v2.eq_519
r(t=0) =0
arxiv_extracted
["t", "r"]
arxiv
arxiv
arxiv:physics.class-ph:2001.10375v2
cross_domain_amplification
f
r
urn:hailstone:chemistry_physics:structural_equation[038938f566c7]
1
structural_equation
2
arxiv.physics.class-ph.2001.10375v2.eq_520
\frac{dr(t)}{dt}\mid_{r(t=0)} =0
arxiv_extracted
["f", "a", "d", "r", "c"]
arxiv
arxiv
arxiv:physics.class-ph:2001.10375v2
cross_domain_amplification