Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the P'eclet number in the current application. The effectiveness of the algorithm is demonstrated on two problems for the linear advection-diffusion equation. © 2011 Published by Elsevier Ltd

Finite-temperature reaction-rate formula: Finite volume system, detailed balance, T→0T \to 0 limit, and cutting rules

A complete derivation, from first principles, of the reaction-rate formula for a generic process taking place in a heat bath of finite volume is given. It is shown that the formula involves no finite-volume correction. Through perturbative diagrammatic analysis of the resultant formula, the detailed-balance formula is derived. The zero-temperature limit of the formula is discussed. Thermal cutting rules, which are introduced in previous work, are compared with those introduced by other authors.Comment: 35pages (text) plus 4pages (figures

Gap equation in scalar field theory at finite temperature

We investigate the two-loop gap equation for the thermal mass of hot massless $g^2\phi^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution of the gap equation beyond $g^2$ order in perturbation theory. We have solved the gap equation and obtain the real and the imaginary part of the thermal mass which are correct up to $g^4$ order in perturbation theory.Comment: 13 pages, Latex with axodraw, Minor corrections, Appendix adde

Anomaly-Induced Magnetic Screening in 2+1 dimensional QED at Finite Density

We show that in 2+1 dimensional Quantum Electrodynamics an external magnetic field applied to a finite density of massless fermions is screened, due to a $2+1$-dimensional realization of the underlying $2$-dimensional axial anomaly of the space components of the electric current. This is shown to imply screening of the magnetic field, i.e., the Meissner effect. We discuss the physical implications of this result.Comment: 8 pages, DFTT-93-10 [ Eq.(15) and (16) were scrambled in previous version

Induced Parity Breaking Term at Finite Temperature

We compute the exact induced parity-breaking part of the effective action for 2+1 massive fermions in $QED_3$ at finite temperature by calculating the fermion determinant in a particular background. The result confirms that gauge invariance of the effective action is respected even when large gauge transformations are considered.Comment: to be published in Physical Review Letters. 5 pages, Revtex, no figure

The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation does reproduce the generalized Frenet equation. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of $C_\beta$ carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this $C_\beta$ framing relates intimately to the discrete Frenet framing. We also explain how inflection points can be located in the loops, and clarify their distinctive r\^ole in determining the loop structure of foldel proteins.Comment: 14 pages 12 figure

Abelian and Non-Abelian Induced Parity Breaking Terms at Finite Temperature

We compute the exact canonically induced parity breaking part of the effective action for 2+1 massive fermions in particular Abelian and non Abelian gauge field backgrounds. The method of computation resorts to the chiral anomaly of the dimensionally reduced theory.Comment: 13 pages, RevTeX, no figure

On The Finite Temperature Chern-Simons Coefficient

We compute the exact finite temperature effective action in a 0+1-dimensional field theory containing a topological Chern-Simons term, which has many features in common with 2+1-dimensional Chern-Simons theories. This exact result explains the origin and meaning of puzzling temperature dependent coefficients found in various naive perturbative computations in the higher dimensional models.Comment: 11 pages LaTeX; no figure

Contemporary strain rates in the northern Basin and Range province from GPS data

We investigate the distribution of active deformation in the northern Basin and Range province using data from continuous GPS (CGPS) networks, supplemented by additional campaign data from the Death Valley, northern Basin and Range, and Sierra Nevada–Great Valley regions. To understand the contemporary strain rate field in the context of the greater Pacific (P)–North America (NA) plate boundary zone, we use GPS velocities to estimate the average relative motions of the Colorado Plateau (CP), the Sierra Nevada–Great Valley (SNGV) microplate, and a narrow north-south elongate region in the central Great Basin (CGB) occupying the longitude band 114–117°W. We find that the SNGV microplate translates with respect to the CP at a rate of 11.4 ± 0.3 mm yr^(−1) oriented N47 ± 1°W and with respect to NA at a rate of ∼12.4 mm yr^(−1) also oriented N47°W, slower than most previous geodetic estimates of SNGV-NA relative motion, and nearly 7° counterclockwise from the direction of P-NA relative plate motion. We estimate CGB-CP relative motion of 2.8 ± 0.2 mm yr^(−1) oriented N84 ± 5°W, consistent with roughly east-west extension within the eastern Great Basin (EGB). Velocity estimates from the EGB reveal diffuse extension across this region, with more rapid extension of 20 ± 1 nstr yr^(−1) concentrated in the eastern half of the region, which includes the Wasatch fault zone. We estimate SNGV-CGB relative motion of 9.3 ± 0.2 mm yr^(−1) oriented N37 ± 2°W, essentially parallel to P-NA relative plate motion. This rate is significantly slower than most previous geodetic estimates of deformation across the western Great Basin (WGB) but is generally consistent with paleoseismological inferences. The WGB region accommodates N37°W directed right lateral shear at rates of (1) 57 ± 9 nstr yr^(−1) across a zone of width ∼125 km in the south (latitude ∼36°N), (2) 25 ± 5 nstr yr^(−1) in the central region (latitude ∼38°N), and (3) 36 ± 1 nstr yr^(−1) across a zone of width ∼300 km in the north (latitude ∼40°N). By construction there is no net extension or shortening perpendicular to SNGV-CGB relative motion. However, we observe about 8.6 ± 0.5 nstr yr^(−1) extension on average in the direction of shear from southeast to northwest within the Walker Lane belt, comparable to the average east-west extension rate of 10 ± 1 nstr yr^(−1) across the northern Basin and Range but implying a distinctly different mechanism of deformation from extension on north trending, range-bounding normal faults. An alternative model for this shear parallel deformation, in which extension is accommodated across a narrow, more rapidly extending zone that coincides with the central Nevada seismic belt, fits the WGB data slightly better. Local anomalies with respect to this simple kinematic model may reveal second-order deformation signals related to more local crustal dynamic phenomena, but significant improvements in velocity field resolution will be necessary to reveal this second-order pattern

The effective action of (2+1)-dimensional QED: the effect of finite fermion density

The effective action of (2+1)-dimensional QED with finite fermion density is calculated in a uniform electromagnetic field. It is shown that the integer quantum Hall effect and de Haas-van Alphen like phenomena in condensed matter physics are derived directly from the effective action.Comment: 10 pages, Revtex, No figure