The two-loop massless (lambda/4!)phi(4) model in nontranslational invariant domain

We study the (lambda/4!)phi(4) massless scalar field theory in a four-dimensional Euclidean space, where all but one of the coordinates are unbounded. We are considering Dirichlet boundary conditions in two hyperplanes, breaking the translation invariance of the system. We show how to implement the perturbative renormalization up to two-loop level of the theory. First, analyzing the full two and four-point functions at the one-loop level, we show that the bulk counterterms are sufficient to render the theory finite. Meanwhile, at the two-loop level, we must also introduce surface counterterms in the bare Lagrangian in order to make finite the full two and also four-point Schwinger functions. (c) 2006 American Institute of Physics.

Applicability of the linear delta expansion for the lambda phi(4) field theory at finite temperature in the symmetric and broken phases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Energy localization in the Phi(4) oscillator chain

We study energy localization in a finite one-dimensional Phi(4) oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. on the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrodinger equation approximating the dynamics, to support and explain the numerical results.

Electrical resistivity, formation factors, and sound velocity at DSDP Holes 75-530A and 75-530B

From 0 to 277 m at Site 530 are found Holocene to Miocene diatom ooze, nannofossil ooze, marl, clay, and debrisflow deposits; from 277 to 467 m are Miocene to Oligocene mud; from 467 to 1103 m are Eocene to late Albian Cenomanian interbedded mudstone, marlstone, chalk, clastic limestone, sandstone, and black shale in the lower portion; from 1103 to 1121 m are basalts. In the interval from 0 to 467 m, in Holocene to Oligocene pelagic oozes, marl, clay, debris flows, and mud, velocities are 1.5 to 1.8 km/s; below 200 m velocities increase irregularly with increasing depth. From 0 to 100 m, in Holocene to Pleistocene diatom and nannofossil oozes (excluding debris flows), velocities are approximately equivalent to that of the interstitial seawater, and thus acoustic reflections in the upper 100 m are primarily caused by variations in density and porosity. Below 100 or 200 m, acoustic reflections are caused by variations in both velocity and density. From 100 to 467 m, in Miocene-Oligocene nannofossil ooze, clay, marl, debris flows, and mud, acoustic anisotropy irregularly increases to 10%, with 2 to 5% being typical. From 467 to 1103 m in Paleocene to late Albian Cenomanian interbedded mudstone, marlstone, chalk, clastic limestone, and black shale in the lower portion of the hole, velocities range from 1.6 to 5.48 km/s, and acoustic anisotropies are as great as 47% (1.0 km/s) faster horizontally. Mudstone and uncemented sandstone have anisotropies which irregularly increase with increasing depth from 5 to 10% (0.2 km/s). Calcareous mudstones have the greatest anisotropies, typically 35% (0.6 km/s). Below 1103 m, basalt velocities ranged from 4.68 to 4.98 km/s. A typical value is about 4.8 km/s. In situ velocities are calculated from velocity data obtained in the laboratory. These are corrected for in situ temperature, hydrostatic pressure, and porosity rebound (expansion when the overburden pressure is released). These corrections do not include rigidity variations caused by overburden pressures. These corrections affect semiconsolidated sedimentary rocks the most (up to 0.25 km/s faster). These laboratory velocities appear to be greater than the velocities from the sonic log. Reflection coefficients derived from the laboratory data, in general, agree with the major features on the seismic profiles. These indicate more potential reflectors than indicated from the reflection coefficients derived using the Gearhart-Owen Sonic Log from 625 to 940 m, because the Sonic Log data average thin beds. Porosity-density data versus depth for mud, mudstone, and pelagic oozes agree with data for similar sediments as summarized in Hamilton (1976). At depths of about 400 m and about 850 m are zones of relatively higher porosity mudstones, which may suggest anomalously high pore pressure; however, they are more probably caused by variations in grain-size distribution and lithology. Electrical resistivity (horizontal) from 625 to 950 m ranged from about 1.0 to 4.0 ohm-m, in Maestrichtian to Santonian- Coniacian mudstone, marlstone, chalk, clastic limestone, and sandstone. An interstitial-water resistivity curve did not indicate any unexpected lithology or unusual fluid or gas in the pores of the rock. These logs were above the black shale beds. From 0 to 100 m at Sites 530 and 532, the vane shear strength on undisturbed samples of Holocene-Pleistocene diatom and nannofossil ooze uniformly increases from about 80 g/cm**2 to about 800 g/cm**2. From 100 to 300 m, vane shear strength of Pleistocene-Miocene nannofossil ooze, clay, and marl are irregular versus depth with a range of 500 to 2300 g/cm**2; and at Site 532 the vane shear strength appears to decrease irregularly and slightly with increasing depth (gassy zone). Vane shear strength values of gassy samples may not be valid, for the samples may be disturbed as gas evolves, and the sediments may not be gassy at in situ depths.