969 research outputs found
On the stability of travelling waves with vorticity obtained by minimisation
We modify the approach of Burton and Toland [Comm. Pure Appl. Math. (2011)]
to show the existence of periodic surface water waves with vorticity in order
that it becomes suited to a stability analysis. This is achieved by enlarging
the function space to a class of stream functions that do not correspond
necessarily to travelling profiles. In particular, for smooth profiles and
smooth stream functions, the normal component of the velocity field at the free
boundary is not required a priori to vanish in some Galilean coordinate system.
Travelling periodic waves are obtained by a direct minimisation of a functional
that corresponds to the total energy and that is therefore preserved by the
time-dependent evolutionary problem (this minimisation appears in Burton and
Toland after a first maximisation). In addition, we not only use the
circulation along the upper boundary as a constraint, but also the total
horizontal impulse (the velocity becoming a Lagrange multiplier). This allows
us to preclude parallel flows by choosing appropriately the values of these two
constraints and the sign of the vorticity. By stability, we mean conditional
energetic stability of the set of minimizers as a whole, the perturbations
being spatially periodic of given period.Comment: NoDEA Nonlinear Differential Equations and Applications, to appea
Molecular mechanisms of hematogenous tumor - metastasis
The present manuscript demonstrates that B16F10 melanoma cells activate the enzyme acid sphingomyelinase in thrombocytes via the surface molecule P-selectin, by which ceramide is released. Metastasis of tumor cells in the lung is decreased by up to 95% by genetic deficiency of P-selectin molecule or deficiency of acid sphingomyelinase. After activation of wild type thrombocytes by B16F10 melanoma cells there is a rapid increase in acid sphingomyelinase activity and ceramide production as compared to acid sphingomyelinase-deficient thrombocytes or P-selectin-deficient thrombocytes. A lack of interaction of B16F10 melanoma cells and thrombocytes was excluded by activation of PLCγ, JNK and MAP kinase, indicating that these signaling events are stimulated in both, wild-type and P-selectin-deficient platelets, proving that B16F10 melanoma cells interact with and activate P-selectin-deficient thrombocytes. The molecular mechanisms of tumor metastasis are currently fairly incomplete, though metastasis plays a crucial clinical role in cancer patients. Acid sphingomyelinase is
iidentified as a novel target molecule for the inhibition of tumor metastasis. In order to pharmacologically inhibit the thrombocytic P-selectin system, an intravenous injection of fucoidan showed a decrease of tumor metastasis of B16F10 melanoma cells by approximately
75%. This indicates that tumor metastasis can be blocked pharmacologically, which is of great clinical interest
On the existence of an inertial manifold for a deconvolution model of the 2D mean Boussinesq equations
We show the existence of an inertial manifold (i.e. a globally invariant,
exponentially attracting, finite-dimensional manifold) for the approximate
deconvolution model of the 2D mean Boussinesq equations. This model is obtained
by means of the Van Cittern approximate deconvolution operators, which is
applied to the 2D filtered Boussinesq equations
A gene regulatory network armature for T lymphocyte specification
Choice of a T lymphoid fate by hematopoietic progenitor cells depends on sustained Notch–Delta signaling combined with tightly regulated activities of multiple transcription factors. To dissect the regulatory network connections that mediate this process, we have used high-resolution analysis of regulatory gene expression trajectories from the beginning to the end of specification, tests of the short-term Notch dependence of these gene expression changes, and analyses of the effects of overexpression of two essential transcription factors, namely PU.1 and GATA-3. Quantitative expression measurements of >50 transcription factor and marker genes have been used to derive the principal components of regulatory change through which T cell precursors progress from primitive multipotency to T lineage commitment. Our analyses reveal separate contributions of Notch signaling, GATA-3 activity, and down-regulation of PU.1. Using BioTapestry (www.BioTapestry.org), the results have been assembled into a draft gene regulatory network for the specification of T cell precursors and the choice of T as opposed to myeloid/dendritic or mast-cell fates. This network also accommodates effects of E proteins and mutual repression circuits of Gfi1 against Egr-2 and of TCF-1 against PU.1 as proposed elsewhere, but requires additional functions that remain unidentified. Distinctive features of this network structure include the intense dose dependence of GATA-3 effects, the gene-specific modulation of PU.1 activity based on Notch activity, the lack of direct opposition between PU.1 and GATA-3, and the need for a distinct, late-acting repressive function or functions to extinguish stem and progenitor-derived regulatory gene expression
A Novel Potassium Channel in Lymphocyte Mitochondria
The margatoxin-sensitive Kv1.3 is the major potassium channel in the plasma membrane of T lymphocytes. Electron microscopy, patch clamp, and immunological studies identified the potassium channel Kv1.3, thought to be localized exclusively in the cell membrane, in the inner mitochondrial membrane of T lymphocytes. Patch clamp of mitoplasts and mitochondrial membrane potential measurements disclose the functional expression of a mitochondrial margatoxin-sensitive potassium channel. To identify unambiguously the mitochondrial localization of Kv1.3, we employed a genetic model and stably transfected CTLL-2 cells, which are genetically deficient for this channel, with Kv1.3. Mitochondria isolated from Kv1.3-reconstituted CTLL-2 expressed the channel protein and displayed an activity, which was identical to that observed in Jurkat mitochondria, whereas mitochondria of mock-transfected cells lacked a channel with the characteristics of Kv1.3. Our data provide the first molecular identification of a mitochondrial potassium conductance
Direct Light-Enabled Access to α-Boryl Radicals: Application in the Stereodivergent Synthesis of Allyl Boronic Esters
Operationally simple strategies to assemble boron containing organic frameworks are highly enabling in organic synthesis. While conventional retrosynthetic logic has engendered many platforms focusing on the direct formation of C−B bonds, α-boryl radicals have recently reemerged as versatile open-shell alternatives to access organoborons via adjacent C−C bond formation. Direct light-enabled α-activation is currently contingent on photo- or transition metal-catalysis activation to efficiently generate radical species. Here, we disclose a facile activation of α-halo boronic esters using only visible light and a simple Lewis base to enable homolytic scission. Intermolecular addition to styrenes facilitates the rapid construction of highly versatile E-allylic boronic esters. The simplicity of activation permits the strategic merger of this construct with selective energy transfer catalysis to enable the complimentary stereodivergent synthesis of Z-allylic boronic esters
On the constants in a Kato inequality for the Euler and Navier-Stokes equations
We continue an analysis, started in [10], of some issues related to the
incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus
T^d. More specifically, we consider the quadratic term in these equations; this
arises from the bilinear map (v, w) -> v . D w, where v, w : T^d -> R^d are two
velocity fields. We derive upper and lower bounds for the constants in some
inequalities related to the above bilinear map; these bounds hold, in
particular, for the sharp constants G_{n d} = G_n in the Kato inequality | < v
. D w | w >_n | <= G_n || v ||_n || w ||^2_n, where n in (d/2 + 1, + infinity)
and v, w are in the Sobolev spaces H^n, H^(n+1) of zero mean, divergence free
vector fields of orders n and n+1, respectively. As examples, the numerical
values of our upper and lower bounds are reported for d=3 and some values of n.
When combined with the results of [10] on another inequality, the results of
the present paper can be employed to set up fully quantitative error estimates
for the approximate solutions of the Euler/NS equations, or to derive
quantitative bounds on the time of existence of the exact solutions with
specified initial data; a sketch of this program is given.Comment: LaTeX, 39 pages. arXiv admin note: text overlap with arXiv:1007.4412
by the same authors, not concerning the main result
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
This paper is concerned with the analysis of the Cauchy problem of a general
class of two-dimensional nonlinear nonlocal wave equations governing anti-plane
shear motions in nonlocal elasticity. The nonlocal nature of the problem is
reflected by a convolution integral in the space variables. The Fourier
transform of the convolution kernel is nonnegative and satisfies a certain
growth condition at infinity. For initial data in Sobolev spaces,
conditions for global existence or finite time blow-up of the solutions of the
Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes.
Accepted for publication in Nonlinearit
On the Clark-alpha model of turbulence: global regularity and long--time dynamics
In this paper we study a well-known three--dimensional turbulence model, the
filtered Clark model, or Clark-alpha model. This is Large Eddy Simulation (LES)
tensor-diffusivity model of turbulent flows with an additional spatial filter
of width alpha (). We show the global well-posedness of this model with
constant Navier-Stokes (eddy) viscosity. Moreover, we establish the existence
of a finite dimensional global attractor for this dissipative evolution system,
and we provide an anaytical estimate for its fractal and Hausdorff dimensions.
Our estimate is proportional to , where is the integral spatial
scale and is the viscous dissipation length scale. This explicit bound is
consistent with the physical estimate for the number of degrees of freedom
based on heuristic arguments. Using semi-rigorous physical arguments we show
that the inertial range of the energy spectrum for the Clark- model has
the usual Kolmogorov power law for wave numbers and
decay power law for This is evidence that the
Clark model parameterizes efficiently the large wave numbers within
the inertial range, , so that they contain much less translational
kinetic energy than their counterparts in the Navier-Stokes equations.Comment: 11 pages, no figures, submitted to J of Turbulenc
Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
In this paper we provide a sufficient condition, in terms of only one of the
nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity
vector field, for the global regularity of strong solutions to the
three-dimensional Navier-Stokes equations in the whole space, as well as for
the case of periodic boundary conditions
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