Active nematic and polar gels
An active gel, a nematic tensor or a polarisation transported in the Stokes flow of its own stresses.
- Name:
active_gels - Field:
physics/active_matter - Formalism: ordinary differential equations
- References: Marchetti et al. 2013; arXiv:1207.2929; Kruse et al. 2005; Voituriez, Joanny, and Prost 2005; Giomi et al. 2012; arXiv:1110.4338
Factory
@register_model(
field='physics/active_matter',
tags=('field', 'active matter', 'nematic', 'polar', 'tensor', 'gel', 'stokes flow', 'active turbulence', 'pde'),
references=(
'Marchetti et al. 2013',
'arXiv:1207.2929',
'Kruse et al. 2005',
'Voituriez, Joanny, and Prost 2005',
'Giomi et al. 2012',
'arXiv:1110.4338',
),
defaults={'until': 0.5, 'dt': 0.025, 'solver': RK4Solver(dt=5e-4)},
settings=_gel_settings,
observables=lambda system: [
ObservableSpec('u_x', _velocity_x, group='gel', reduce=_sites),
ObservableSpec('u_y', _velocity_y, group='gel', reduce=_sites),
],
)
def active_gels(
shape: Sequence[int] | None = None,
*,
order: str = 'nematic',
spacing: float | None = None,
a: float | None = None,
c: float | None = None,
K: float = 1.0,
xi: float | None = None,
gamma: float = 1.0,
eta: float = 1.0,
zeta: float | None = None,
film: bool = False,
perturbation: float | None = None,
random_state: int | np.random.Generator | None = 0,
) -> System:
"""Return an active gel, a nematic tensor or a polarisation transported in the Stokes flow of its own stresses.
On a periodic lattice with spectral operators, the order parameter follows its co-rotational derivative in the flow,
Section III of Marchetti et al. The flow solves the overdamped Stokes equation of the elastic stress and the active
stress, `-zeta Q` for the nematic and `-zeta p p` for the polar gel, and the elastic energy relaxes the order. An
extensile nematic, `zeta > 0`, is unstable to bend, and a contractile polar gel, `zeta < 0`, is unstable to splay
above a threshold.
The defaults of the nematic are the chaotic state of Giomi et al. 2012, cited by Marchetti et al., whose free energy
has the same form: a box of side 10, the critical density `3 pi / 2`, the density twice that, which give `a` and
`c`, the activity `3` times the squared density, and the flow alignment 0.1, in units of the elastic constant, the
rotational viscosity, and the viscosity. The density stays uniform here. At these defaults pairs of `+1/2` and
`-1/2` defects move in a chaotic flow, active turbulence.
The nematic starts from the tensor along the first axis at the order `sqrt(-2 a / c)`, and the polar gel from the
polarisation along the first axis at the length `sqrt(-a / c)`, both with noise. With `film=True` the polarisation
along the second axis is odd about the sites 0 and `shape[1] / 2` of the second axis, and the other one even, which
holds the polarisation along the first axis at these two walls, with stress-free flow there.
Args:
shape:
The number of sites along every axis of the periodic lattice, in two dimensions, or `None` for `(128, 128)`
for the nematic and `(32, 32)` for the polar gel.
order:
`'nematic'` or `'polar'`.
spacing:
The distance between neighbouring sites, or `None` for a nematic box of side 10 along the first axis and 1
for the polar gel.
a:
The coefficient of the quadratic energy, negative in the ordered phase, or `None` for `-3 pi / 4` for the
nematic and -1 for the polar gel.
c:
The coefficient of the quartic energy, or `None` for `3 pi` for the nematic and 1 for the polar gel.
K:
The elastic constant.
xi:
The flow-alignment parameter, or `None` for 0.1 for the nematic and 0 for the polar gel.
gamma:
The rotational viscosity.
eta:
The viscosity of the flow.
zeta:
The activity, or `None` for `3 (3 pi)^2` for the nematic and -0.5 for the polar gel.
film:
Whether the polar gel lies between walls of fixed polarisation.
perturbation:
The standard deviation of the initial noise of the order parameter, or `None` for 0.1 for the nematic and
0.01 for the polar gel.
random_state:
The seed or generator of the initial noise.
Returns:
system:
The model, with the field `gel.Q` or `gel.p`.
Raises:
ValidationError:
The order is unknown, or a nematic is asked to lie in a film.
Examples:
>>> from skcomplex.models.physics.active_matter import active_gels
>>> active_gels((8, 8), order='polar').elements[0].values['zeta']
-0.5
>>> active_gels(order='polar').elements[0].space.shape
(32, 32)
"""
if order not in GEL_ORDERS:
error_msg = f'The order of the gel is {order!r}. Use one of {", ".join(GEL_ORDERS)}.'
raise ValidationError(error_msg)
if film and order != 'polar':
error_msg = 'A film of the gel holds a polarisation at its walls. Use order=polar.'
raise ValidationError(error_msg)
polar = order == 'polar'
shape = ((32, 32) if polar else (128, 128)) if shape is None else tuple(shape)
sites = int(np.prod(shape))
rng = np.random.default_rng(random_state)
quadratic = (-1.0 if polar else (NEMATIC_CRITICAL_DENSITY - NEMATIC_DENSITY) / 2) if a is None else a
cubic = (1.0 if polar else NEMATIC_DENSITY) if c is None else c
activity = (-0.5 if polar else NEMATIC_ACTIVITY * NEMATIC_DENSITY**2) if zeta is None else zeta
alignment = (0.0 if polar else NEMATIC_XI) if xi is None else xi
distance = (1.0 if polar else NEMATIC_BOX / shape[0]) if spacing is None else spacing
amplitude = (0.01 if polar else 0.1) if perturbation is None else perturbation
noise = amplitude * rng.standard_normal((sites, 2))
size = np.sqrt(-quadratic / cubic) if polar else np.sqrt(-2 * quadratic / cubic) / 2
start = np.column_stack([np.full(sites, size), np.zeros(sites)]) + noise if quadratic < 0 else noise
values = {
'p' if polar else 'Q': start,
'a': quadratic,
'c': cubic,
'K': K,
'xi': alignment,
'gamma': gamma,
'eta': eta,
'zeta': activity,
}
symmetry = {'p': ((None, 'even'), (None, 'odd'))} if film else None
gel = FieldElement(
'gel',
element=PolarGelSiteElement if polar else NematicGelSiteElement,
space=LatticeSpace(shape, spacing=distance),
values=values,
discretization='spectral',
symmetry=symmetry,
)
return System(elements=[gel])
Components
class NematicGelSiteElement(Element):
"""Site of an active nematic gel, a symmetric traceless tensor `Q` carried by an overdamped Stokes flow.
The tensor follows `Q_t = -corotational(Q, u, xi) + H / gamma`, with the molecular field `H` of the Landau-de Gennes
energy. The velocity solves `eta laplacian(u) - grad(P) + div(sigma) = 0`, `div(u) = 0`, with the stress
`sigma = -xi H + Q H - H Q - zeta Q`. An activity `zeta > 0` is extensile and an activity `zeta < 0` contractile.
Args:
label:
The label of the site or the field.
visual:
How the site is drawn, or `None` for `default_visual_`.
Q:
The initial tensor, its independent components `Q_xx` and `Q_xy`.
a:
The coefficient of `tr(Q^2) / 2` of the energy, negative in the ordered phase.
c:
The coefficient of `tr(Q^2)^2 / 4` of the energy.
K:
The elastic constant.
xi:
The flow-alignment parameter.
gamma:
The rotational viscosity.
eta:
The viscosity of the flow.
zeta:
The activity.
Attributes:
default_visual_:
The visual of the element when it sets none.
Examples:
>>> from skcomplex.models.physics.active_matter import NematicGelSiteElement
>>> NematicGelSiteElement('site').zeta
0.5
"""
def __init__(
self,
label: str,
visual: VisualSpec | None = None,
*,
Q: Annotated[npt.ArrayLike, StateSpec(tensor='traceless')] = 0.0,
a: Annotated[float, ParameterSpec()] = -1.0,
c: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 2.0,
K: Annotated[float, ParameterSpec(domain=RealSet.closed_open(0, oo))] = 1.0,
xi: Annotated[float, ParameterSpec()] = 0.0,
gamma: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 1.0,
eta: Annotated[float, ParameterSpec(domain=RealSet.open(0, oo))] = 1.0,
zeta: Annotated[float, ParameterSpec()] = 0.5,
) -> None:
super().__init__(label, visual=visual)
self.Q = Q
self.a = a
self.c = c
self.K = K
self.xi = xi
self.gamma = gamma
self.eta = eta
self.zeta = zeta
@staticmethod
def _velocity(s: SimpleNamespace) -> FreeModuleElement:
"""Return the velocity of the Stokes flow of the elastic and active stresses at a site."""
field = LandauDeGennesEnergyInteraction._molecular_field(s.Q, s.a, s.c, s.K)
stress = -s.xi * field + s.Q * field - field * s.Q - s.zeta * s.Q
force = tensor_divergence(stress)
return leray_projection(force.apply_map(lambda item: inverse_laplacian(-item / s.eta)))
def _get_laws(self, namespace: SimpleNamespace) -> list[BaseLaw]:
"""Return the rate of the tensor, its transport in the flow and its relaxation.
Args:
namespace:
The namespace of the symbols the laws can use.
Returns:
laws:
The rate of `Q`.
"""
s = namespace
field = LandauDeGennesEnergyInteraction._molecular_field(s.Q, s.a, s.c, s.K)
return [RateLaw(s.Q, -corotational(s.Q, self._velocity(s), s.xi) + field / s.gamma)]
Equations
gel.Q_xx[i]: diff(Q_gel_xx(t), t) == -(Q_gel_xy(t)*partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) + Q_gel_xx(t)*partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 0) - Q_gel_xx(t)*partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 1) + Q_gel_xy(t)*partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0))*xi_gel*(2*Q_gel_xx(t) + 1) + xi_gel*(2*Q_gel_xx(t) + 1)*partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 0) + (xi_gel*(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0)) + partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) - partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0))*Q_gel_xy(t) - (2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))/gamma_gel - upwind(Q_gel_xx(t), 1, inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1)) - upwind(Q_gel_xx(t), 0, inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0))
gel.Q_xy[i]: diff(Q_gel_xy(t), t) == -2*(Q_gel_xy(t)*partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) + Q_gel_xx(t)*partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 0) - Q_gel_xx(t)*partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 1) + Q_gel_xy(t)*partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0))*xi_gel*Q_gel_xy(t) + xi_gel*Q_gel_xy(t)*partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 0) + xi_gel*Q_gel_xy(t)*partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 1) + 1/4*(xi_gel*(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0)) - partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0))*(2*Q_gel_xx(t) + 1) - 1/4*(xi_gel*(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0)) + partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0), 1) - partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1), 0))*(2*Q_gel_xx(t) - 1) - (2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))/gamma_gel - upwind(Q_gel_xy(t), 1, inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 1)) - upwind(Q_gel_xy(t), 0, inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0) - partial(inverse_helmholtz(partial(inverse_helmholtz(-(partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel - zeta_gel*Q_gel_xx(t), 0) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 1))/eta_gel, 0), 0) + partial(inverse_helmholtz(-(partial(-(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*xi_gel + zeta_gel*Q_gel_xx(t), 1) + partial((2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*xi_gel + 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xy(t) + a_gel*Q_gel_xy(t) - K_gel*laplacian(Q_gel_xy(t)))*Q_gel_xx(t) - 2*(2*(Q_gel_xx(t)^2 + Q_gel_xy(t)^2)*c_gel*Q_gel_xx(t) + a_gel*Q_gel_xx(t) - K_gel*laplacian(Q_gel_xx(t)))*Q_gel_xy(t) - zeta_gel*Q_gel_xy(t), 0))/eta_gel, 0), 1), 0), 0))