516 research outputs found
Low regularity bounds for mKdV
We study the local well-posedness in the Sobolev space H^s for the modified
Korteweg-de Vries (mKdV) equation on the real line. Kenig-Ponce-Vega
\cite{KPV2} and Christ-Colliander-Tao established that the data-to-solution map
fails to be uniformly continuous on a fixed ball in H^s when s<1/4. In spite of
this, we establish that for -1/8 < s < 1/4, the solution satisfies global in
time H^s(R) bounds which depend only on the time and on the H^s(R) norm of the
initial data. This result is weaker than global well-posedness, as we have no
control on differences of solutions. Our proof is modeled on recent work by
Christ-Colliander-Tao and Koch-Tataru employing a version of Bourgain's Fourier
restriction spaces adapted to time intervals whose length depends on the
spatial frequency.Comment: 22 page
Color-Coulomb Force Calculated from Lattice Coulomb Hamiltonian
The static color-Coulomb potential is calculated as the solution of a
non-linear integral equation. This equation has been derived recently as a
self-consistency condition which arises in the Coulomb Hamiltonian formulation
of lattice gauge theory when the restriction to the interior of the Gribov
horizon is implemented. The potential obtained is in qualitative agreement with
expectations, being Coulombic with logarithmic corrections at short range and
confining at long range. The values obtained for the string tension and
are in semi-quantitative agreement with lattice Monte
Carlo and phenomenological determinations.Comment: 4 pages (including 1 figure); (latex using espcrc2.sty). Talk
presented at LATTICE96(poster
Stability engineering of the human antibody repertoire
AbstractHuman monoclonal antibodies often display limited thermodynamic and colloidal stabilities. This behavior hinders their production, and places limitations on the development of novel formulation conditions and therapeutic applications. Antibodies are highly diverse molecules, with much of the sequence variation observed within variable domain families and, in particular, their complementarity determining regions. This has complicated the development of comprehensive strategies for the stability engineering of the human antibody repertoire. Here we provide an overview of the field, and discuss recent advances in the development of robust and aggregation resistant antibody therapeutics
An Empirical Analysis of Web Site Stickiness
Even though we have seen an exponential growth in the number of Web sites and the number of users, little is known about Web usage at the level of the individual. This paper aims to overcome this lack of knowledge on individual usage patterns. Based on previous findings on saturation of Web usage, we use data from 1995-1998 on residential Web usage conducted as part of the HomeNet project to examine if groups of Web users differ in loyalty to Web sites. We also measure the stickiness of the most popular Web sites in the HomeNet sample. The results help us to understand how one should think of Internet usage and have important implications for Internet marketing and strategy
On the Mutual Interaction between Mechanical Stresses and Internal Corrosion during Isothermal and Cyclic Oxidation of Nickel-Base Superalloys
Thermal cycling has been observed to cause a transition from superficial alumina formation to internal oxidation and nitridation, an effect that was shown to depend on the specimen thickness and geometry, which can be described by a spalling-probability model. Once protection by a dense and adherent alumina scale got lost, the internal-corrosion rate is determined by the diffusivity and solubility of nitrogen and oxygen in the alloy. These parameters seem to depend not only on the temperature and the alloy composition but also on the applied mechanical stress. Internal nitridation under a superimposed creep loading was found to follow a higher rate constant than under just isothermal exposure. This effect can probably be attributed to dislocation-pipe diffusion, a mechanism which has been claimed also to be relevant for outward solvent diffusion during internal corrosion, a phenomenon, which was observed as a stress-relief mechanism during various internal-reaction processes
On the Mutual Interaction between Mechanical Stresses and Internal Corrosion during Isothermal and Cyclic Oxidation of Nickel-Base Superalloys
Thermal cycling has been observed to cause a transition from superficial alumina formation to internal oxidation and nitridation, an effect that was shown to depend on the specimen thickness and geometry, which can be described by a spalling-probability model. Once protection by a dense and adherent alumina scale got lost, the internal-corrosion rate is determined by the diffusivity and solubility of nitrogen and oxygen in the alloy. These parameters seem to depend not only on the temperature and the alloy composition but also on the applied mechanical stress. Internal nitridation under a superimposed creep loading was found to follow a higher rate constant than under just isothermal exposure. This effect can probably be attributed to dislocation-pipe diffusion, a mechanism which has been claimed also to be relevant for outward solvent diffusion during internal corrosion, a phenomenon, which was observed as a stress-relief mechanism during various internal-reaction processes
Renormalizable Non-Covariant Gauges and Coulomb Gauge Limit
To study ``physical'' gauges such as the Coulomb, light-cone, axial or
temporal gauge, we consider ``interpolating'' gauges which interpolate linearly
between a covariant gauge, such as the Feynman or Landau gauge, and a physical
gauge. Lorentz breaking by the gauge-fixing term of interpolating gauges is
controlled by extending the BRST method to include not only the local gauge
group, but also the global Lorentz group. We enumerate the possible divergences
of interpolating gauges, and show that they are renormalizable, and we show
that the expectation value of physical observables is the same as in a
covariant gauge. In the second part of the article we study the Coulomb-gauge
as the singular limit of the Landau-Coulomb interpolating gauge. We find that
unrenormalized and renormalized correlation functions are finite in this limit.
We also find that there are finite two-loop diagrams of ``unphysical''
particles that are not present in formal canonical quantization in the Coulomb
gauge. We verify that in the same limit, the Gauss-BRST Ward identity holds,
which is the functional analog of the operator statement that a BRST
transformation is generated by the Gauss-BRST charge. As a consequence,
is invariant under renormalization, whereas in a covariant gauge, no component
of the gluon field has this property.Comment: 37 pages, latex; 3 postscript figure
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