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 $\Lambda_{\overline{MS}}$ 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, $gA_0$ 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