8,064 research outputs found
Ill-posedness of waterline integral of time domain free surface Green function for surface piercing body advancing at dynamic speed
In the linear time domain computation of a floating body advancing at a
dynamic speed, the source formulation for the velocity potential of the
hydrodynamic problem is commonly used so that the velocity potential is
expressed as the integral of time domain free surface sources distributed on
the two-dimensional wetted body surface and the one-dimensional waterline,
which is the intersection of the wetted body surface and the mean free water
surface. A time domain free surface source is corresponding to the time domain
free surface Green function associated with a suitable source strength, which
is to be solved from body boundary condition and normal velocity boundary
integral equation of the source formulation.
The normal velocity boundary integral equation contains an integral of the
normal derivative of the time domain free surface Green function on the
waterline. It is shown that the waterline integral is ill-posed. Thus the
source strength of velocity potential is not obtainable
Steady-state bifurcation analysis of a strong nonlinear atmospheric vorticity equation
The quasi-geostrophic equation or the Euler equation with dissipation studied
in the present paper is a simplified form of the atmospheric circulation model
introduced by Charney and DeVore [J. Atmos. Sci. 36(1979), 1205-1216] on the
existence of multiple steady states to the understanding of the persistence of
atmospheric blocking. The fluid motion defined by the equation is driven by a
zonal thermal forcing and an Ekman friction forcing measured by . It
is proved that the steady-state solution is unique for while
multiple steady-state solutions exist for with respect
to critical value .
Without involvement of viscosity, the equation has strong nonlinearity as its
nonlinear part contains the highest order derivative term. Steady-state
bifurcation analysis is essentially based on the compactness, which can be
simply obtained for semi-linear equations such as the Navier-Stokes equations
but is not available for the quasi-geostrophic equation in the Euler
formulation. Therefore the Lagrangian formulation of the equation is employed
to gain the required compactness.Comment: 20 pages, 0 figures, 30 reference
New formulation of the finite depth free surface Green function
For a pulsating free surface source in a three-dimensional finite depth fluid
domain, the Green function of the source presented by John [F. John, On the
motion of floating bodies II. Simple harmonic motions, Communs. Pure Appl.
Math. 3 (1950) 45-101] is superposed as the Rankine source potential, an image
source potential and a wave integral in the infinite domain . When
the source point together with a field point is on the free surface, John's
integral and its gradient are not convergent since the integration
of the corresponding integrands does not tend to zero in a
uniform manner as tends to . Thus evaluation of the Green
function is not based on direct integration of the wave integral but is
obtained by approximation expansions in earlier investigations. In the present
study, five images of the source with respect to the free surface mirror and
the water bed mirror in relation to the image method are employed to
reformulate the wave integral. Therefore the free surface Green function of the
source is decomposed into the Rankine potential, the five image source
potentials and a new wave integral, of which the integrand is approximated by a
smooth and rapidly decaying function. The gradient of the Green function is
further formulated so that the same integration stability with the wave
integral is demonstrated. The significance of the present research is that the
improved wave integration of the Green function and its gradient becomes
convergent. Therefore evaluation of the Green function is obtained through the
integration of the integrand in a straightforward manner. The application of
the scheme to a floating body or a submerged body motion in regular waves shows
that the approximation is sufficiently accurate to compute linear wave loads in
practice.Comment: 24 pages, 7 figure
Instability of the Kolmogorov flow in a wall-bounded domain
In the magnetohydrodynamics (MHD) experiment performed by Bondarenko and his
co-workers in 1979, the Kolmogorov flow loses stability and transits into a
secondary steady state flow at the Reynolds number . This problem is
modelled as a MHD flow bounded between lateral walls under slip wall boundary
condition. The existence of the secondary steady state flow is now proved. The
theoretical solution has a very good agreement with the flow measured in
laboratory experiment at . Further transition of the secondary flow
is observed numerically. Especially, well developed turbulence arises at
On the number of representations of n as a linear combination of four triangular numbers II
Let and be the set of integers and the set of positive
integers, respectively. For let be the
number of representations of by , and let
be the number of representations of by
). In this paper we reveal the connections
between and . Suppose and . We show that for and . We also obtain
explicit formulas for in the cases $(a,b,c,d)=(1,1,2,8),\
(1,1,2,16),(1,2,3,6),\ (1,3,4,12),\ (1,1,3,4),\ (1,1,5,5),\ (1,5,5,5),\
(1,3,3,12),\ (1,1,1,12),\ (1,1,3,12)(1,3,3,4)$.Comment: 22 page
Global large solutions and incompressible limit for the compressible flow of liquid crystals
The present paper is dedicated to the global large solutions and
incompressible limit for the compressible flow of liquid crystals under the
assumption on almost constant density and large volume viscosity. The result is
based on Fourier analysis and involved so-called critical Besov norm.Comment: 19 page
Global large solutions and incompressible limit for the compressible Navier-Stokes equations
The present paper is dedicated to the global large solutions and
incompressible limit for the compressible Navier-Stokes system in
with . We aim at extending the work by Danchin and Mucha
(Adv. Math., 320, 904--925, 2017) in structure to that in a critical
framework. The result implies the existence of global large solutions
initially from large highly oscillating velocity fields.Comment: The final version for publis
On the number of representations of n as a linear combination of four triangular numbers
Let and be the set of integers and the set of positive
integers, respectively. For
let be the number of representations of
by ). In this paper we obtain explicit formulas
for in the cases
, $(1,3,9,9),\
(1,1,3,9)(1,3,3,9)(1,1,9,9),\ (1,9,9,9)(1,1,1,9).$Comment: 18 page
Fermion Masses and Flavor Mixing in A Supersymmetric SO(10) Model
we study fermion masses and flavor mixing in a supersymmetric SO(10) model,
where , and Higgs multiplets
have Yukawa couplings with matter multiplets and give masses to quarks and
leptons through the breaking chain of a Pati-Salam group. This brings about
that, at the GUT energy scale, the lepton mass matrices are related to the
quark ones via several breaking parameters, and the small neutrino masses arise
from a Type II see-saw mechanism. When evolving renormalization group equations
for the fermion mass matrices from the GUT scale to the electroweak scale, in a
specific parameter scenario, we show that the model can elegantly accommodate
all observed values of masses and mixing for the quarks and leptons,
especially, it's predictions for the bi-large mixing in the leptonic sector are
very well in agreement with the current neutrino experimental data.Comment: LaTeX2e, 14 pages, 2 figure
Entanglement entropy in quasi-symmetric multi-qubit states
We generalize the symmetric multi-qubit states to their q-analogs, whose
basis vectors are identified with the q-Dicke states. We study the entanglement
entropy in these states and find that entanglement is extruded towards certain
regions of the system due to the inhomogeneity aroused by q-deformation. We
also calculate entanglement entropy in ground states of a related q-deformed
Lipkin-Meshkov-Glick model and show that the singularities of entanglement can
correctly signify the quantum phase transition points for different strengths
of q-deformation.Comment: 11 pages, 2 figure
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