103,059 research outputs found
Well-posedness of the Ericksen-Leslie system
In this paper, we prove the local well-posedness of the Ericksen-Leslie
system, and the global well-posednss for small initial data under the physical
constrain condition on the Leslie coefficients, which ensures that the energy
of the system is dissipated. Instead of the Ginzburg-Landau approximation, we
construct an approximate system with the dissipated energy based on a new
formulation of the system.Comment: 16 page
Long-range coupling of prefrontal cortex and visual (MT) or polysensory (STP) cortical areas in motion perception
To investigate how, where and when moving
auditory cues interact with the perception of object-motion
during self-motion, we conducted psychophysical, MEG, and
fMRI experiments in which the subjects viewed nine textured
objects during simulated forward self-motion. On each trial,
one object was randomly assigned its own looming motion
within the scene. Subjects reported which of four labeled objects
had independent motion within the scene in two conditions:
(1) visual information only and (2) with additional moving-
auditory cue.
In MEG, comparison of the two conditions showed: (i) MT
activity is similar across conditions, (ii) late after the stimulus
presentation there is additional activity in the auditory cue
condition ventral to MT, (iii) with the auditory cue, the right
auditory cortex (AC) shows early activity together with STS,
(iv) these two activities have different time courses and the
STS signals occur later in the epoch together with frontal
activity in the right hemisphere, (v) for the visual-only condition
activity in PPC (posterior parietal cortex) is stronger than
in the auditory-cue condition. fMRI conducted for visual-only
condition reveals activations in a network of parietal and frontal
areas and in MT.
In addition, Dynamic Granger Causality analysis showed
for auditory cues a strong connection of the AC with STP but
not with MT suggesting binding of visual and auditory information
at STP. Also, while in the visual-only condition PFC is
connected with MT, in the auditory-cue condition PFC is connected
to STP (superior temporal polysensory) area.
These results indicate that PFC allocates attention to the
“object” as a whole, in STP to a moving visual-auditory object,
and in MT to a moving visual object.Accepted manuscrip
Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals
The equations for the three-dimensional incompressible flow of liquid
crystals are considered in a smooth bounded domain. The existence and
uniqueness of the global strong solution with small initial data are
established. It is also proved that when the strong solution exists, all the
global weak solutions constructed in [16] must be equal to the unique strong
solution
On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability
In this paper we investigate the role of Parodi's relation in the
well-posedness and stability of the general Ericksen-Leslie system modeling
nematic liquid crystal flows. First, we give a formal physical derivation of
the Ericksen-Leslie system through an appropriate energy variational approach
under Parodi's relation, in which we can distinguish the
conservative/dissipative parts of the induced elastic stress. Next, we prove
global well-posedness and long-time behavior of the Ericksen-Leslie system
under the assumption that the viscosity is sufficiently large. Finally,
under Parodi's relation, we show the global well-posedness and Lyapunov
stability for the Ericksen-Leslie system near local energy minimizers. The
connection between Parodi's relation and linear stability of the
Ericksen-Leslie system is also discussed
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