5,400 research outputs found
Eisenstein Series and String Thresholds
We investigate the relevance of Eisenstein series for representing certain
-invariant string theory amplitudes which receive corrections from BPS
states only. may stand for any of the mapping class, T-duality and
U-duality groups , or respectively.
Using -invariant mass formulae, we construct invariant modular functions
on the symmetric space of non-compact type, with the
maximal compact subgroup of , that generalize the standard
non-holomorphic Eisenstein series arising in harmonic analysis on the
fundamental domain of the Poincar\'e upper half-plane. Comparing the
asymptotics and eigenvalues of the Eisenstein series under second order
differential operators with quantities arising in one- and -loop string
amplitudes, we obtain a manifestly T-duality invariant representation of the
latter, conjecture their non-perturbative U-duality invariant extension, and
analyze the resulting non-perturbative effects. This includes the and
couplings in toroidal compactifications of M-theory to any
dimension and respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms
renumbered, plus minor corrections; v3: relation (1.7) to math Eis series
clarified, eq (3.3) and minor typos corrected, final version to appear in
Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde
Biofilm growth in a biological plate tower, BPT, for VOC air pollution treatment
The growth of microorganisms in biofilters and biotrickling filters always leads to the occurrence of clogging. A
good efficiency of removal makes it happen faster. To solve clogging and making that kind of process easy to operate steadily
for a long time, a new concept of reactor was designed and tested with air polluted with toluene and Pseudomonas putida. The
BPT is a cascade of plates to whose surface the bacteria attaches. Water flows down and air flows upwards. The reactor shows
very good hydrodynamic performance and operates continuously without problem. When the thickness of the biofilm reaches
the maximum value allowable, the set of plates is simply replaced by a clean one and the biomass is dealt with outside the
reactor
Biodegradation of toluene in a trickling filter
A trickling filter packed with PVC 16 mm Raschig
rings was used to study the degradation of toluene in a polluted air stream, by means of a bacterial biofilm of Pseudomonas putida ATCC 17484. A polluted stream was simulated by blending air with a controlled amount of
toluene. The mixing was accomplished in a special mixing chamber designed for that purpose. Induction of the enzymes of the toluene degradative pathway and adaptation
of the inoculum were done in batch cultures with minimum mineral media and phenol. The continuous experiments were monitored by mass spectrometry for the quantification of the various gases and of toluene removal.
A 94% toluene removal was achieved with contacting times above one minute and toluene concentrations up to 400 ppm
Comment on the Adiabatic Condition
The experimental observation of effects due to Berry's phase in quantum
systems is certainly one of the most impressive demonstrations of the
correctness of the superposition principle in quantum mechanics. Since Berry's
original paper in 1984, the spin 1/2 coupled with rotating external magnetic
field has been one of the most studied models where those phases appear. We
also consider a special case of this soluble model. A detailed analysis of the
coupled differential equations and comparison with exact results teach us why
the usual procedure (of neglecting nondiagonal terms) is mathematically sound.Comment: 9 page
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