Zeta function continuation and the Casimir energy on odd- and even-dimensional spheres

The zeta function continuation method is applied to compute the Casimir energy on spheres SN. Both odd and even dimensional spheres are studied. For the appropriate conformally modified Laplacian A the Casimir energy $is shown to be finite for all dimensions even though, generically, it should diverge in odd dimensions due to the presence of a pole in the associated zeta function ζA(s). The residue of this pole is computed and shown to vanish in our case. An explicit analytic continuation of ζA(s) is constructed for all values of N. This enables us to calculate$ exactly and we find that the Casimir energy vanishes in all even dimensions. For odd dimensions δ is never zero but alternates in sign as N increases through odd values. Some results are also derived for the Casimir energy of other operators of Laplacian type

Chiral Fermions and Spinc structures on Matrix approximations to manifolds

The Atiyah-Singer index theorem is investigated on various compact manifolds which admit finite matrix approximations (``fuzzy spaces'') with a view to applications in a modified Kaluza-Klein type approach in which the internal space consists of a finite number of points. Motivated by the chiral nature of the standard model spectrum we investigate manifolds that do not admit spinors but do admit Spinc structures. It is shown that, by twisting with appropriate bundles, one generation of the electroweak sector of the standard model, including a right-handed neutrino, can be obtained in this way from the complex projective space Bbb CBbb P2. The unitary grassmannian U(5)/(U(3) Ã U(2)) yields a spectrum that contains the correct charges for the Fermions of the standard model, with varying multiplicities for the different particle states

The Standard Model Fermion Spectrum from Complex Projective spaces

It is shown that the quarks and leptons of the standard model, including a right-handed neutrino, can be obtained by gauging the holonomy groups of complex projective spaces of complex dimensions two and three. The spectrum emerges as chiral zero modes of the Dirac operator coupled to gauge fields and the demonstration involves an index theorem analysis on a general complex projective space in the presence of topologically non-trivial SU(n)xU(1) gauge fields. The construction may have applications in type IIA string theory and non-commutative geometry

On non-L2L^2 solutions to the Seiberg-Witten equations

We show that a previous paper of Freund describing a solution to the Seiberg-Witten equations has a sign error rendering it a solution to a related but different set of equations. The non-$L^2$ nature of Freund's solution is discussed and clarified and we also construct a whole class of solutions to the Seiberg-Witten equations.Comment: 8 pages, Te

Effects of edge-stiffened web openings on the behaviour of cold-formed steel channel sections under compression

The use of cold-formed steel (CFS) channel sections are becoming popular as the load-carrying members in building structures, and such channel sections often include web openings for the ease of installation of services. Traditional web openings are normally punched, and are unstiffened which can restrict the size and spacing of web openings. Recently, a new generation of CFS channel sections with edge-stiffened web openings has been developed, and is widely used in New Zealand. However, no experimental investigation has been reported in the literature for such channel sections under compression. In this paper, a total of 75 results comprising 26 axial compression tests and 49 finite element analysis results are reported on the compression resistance of CFS channel sections with both edge-stiffened and unstiffened web openings. For comparison, channel sections without web openings were also tested. For all specimens, initial imperfections were measured using a laser scanner. A nonlinear elasto-plastic finite element model was also developed, and the results showed good agreement with the test results. A parametric study was conducted using the validated finite element model to investigate the effect of opening spacing and column length on compression resistance of channel sections. It is shown that for the case of a channel section having seven edge-stiffened web openings, the compression resistance increased by as much as 22%, compared to a plain channel section. For comparison, the same section having unstiffened web openings had a 20% reduction in compression resistance, compared to a plain channel section

Modular Invariance of Finite Size Corrections and a Vortex Critical Phase

We analyze a continuous spin Gaussian model on a toroidal triangular lattice with periods $L_0$ and $L_1$ where the spins carry a representation of the fundamental group of the torus labeled by phases $u_0$ and $u_1$. We find the {\it exact finite size and lattice corrections}, to the partition function $Z$, for arbitrary mass $m$ and phases $u_i$. Summing $Z^{-1/2}$ over phases gives the corresponding result for the Ising model. The limits $m\rightarrow0$ and $u_i\rightarrow0$ do not commute. With $m=0$ the model exhibits a {\it vortex critical phase} when at least one of the $u_i$ is non-zero. In the continuum or scaling limit, for arbitrary $m$, the finite size corrections to $-\ln Z$ are {\it modular invariant} and for the critical phase are given by elliptic theta functions. In the cylinder limit $L_1\rightarrow\infty$ the ``cylinder charge'' $c(u_0,m^2L_0^2)$ is a non-monotonic function of $m$ that ranges from $2(1+6u_0(u_0-1))$ for $m=0$ to zero for $m\rightarrow\infty$.Comment: 12 pages of Plain TeX with two postscript figure insertions called torusfg1.ps and torusfg2.ps which can be obtained upon request from [email protected]

Road-building materials in Texas

UT Librarie

BENCH-SCALE STEAM REFORMING OF ACTUAL TANK 48H WASTE

Fluidized Bed Steam Reforming (FBSR) has been demonstrated to be a viable technology to remove >99% of the organics from Tank 48H simulant, to remove >99% of the nitrate/nitrite from Tank 48H simulant, and to form a solid product that is primarily carbonate based. The technology was demonstrated in October of 2006 in the Engineering Scale Test Demonstration Fluidized Bed Steam Reformer1 (ESTD FBSR) at the Hazen Research Inc. (HRI) facility in Golden, CO. The purpose of the Bench-scale Steam Reformer (BSR) testing was to demonstrate that the same reactions occur and the same product is formed when steam reforming actual radioactive Tank 48H waste. The approach used in the current study was to test the BSR with the same Tank 48H simulant and same Erwin coal as was used at the ESTD FBSR under the same operating conditions. This comparison would allow verification that the same chemical reactions occur in both the BSR and ESTD FBSR. Then, actual radioactive Tank 48H material would be steam reformed in the BSR to verify that the actual tank 48H sample reacts the same way chemically as the simulant Tank 48H material. The conclusions from the BSR study and comparison to the ESTD FBSR are the following: (1) A Bench-scale Steam Reforming (BSR) unit was successfully designed and built that: (a) Emulated the chemistry of the ESTD FBSR Denitration Mineralization Reformer (DMR) and Carbon Reduction Reformer (CRR) known collectively as the dual reformer flowsheet. (b) Measured and controlled the off-gas stream. (c) Processed real (radioactive) Tank 48H waste. (d) Met the standards and specifications for radiological testing in the Savannah River National Laboratory (SRNL) Shielded Cells Facility (SCF). (2) Three runs with radioactive Tank 48H material were performed. (3) The Tetraphenylborate (TPB) was destroyed to > 99% for all radioactive Bench-scale tests. (4) The feed nitrate/nitrite was destroyed to >99% for all radioactive BSR tests the same as the ESTD FBSR. (5) The radioactive Tank 48H DMR product was primarily made up of soluble carbonates. The three most abundant species were thermonatrite, [Na{sub 2}CO{sub 3} {center_dot} H{sub 2}O], sodium carbonate, [Na{sub 2}CO{sub 3}], and trona, [Na{sub 3}H(CO{sub 3}){sub 2} {center_dot} 2H{sub 2}O] the same as the ESTD FBSR. (6) Insoluble solids analyzed by X-Ray Diffraction (XRD) did not detect insoluble carbonate species. However, they still may be present at levels below 2 wt%, the sensitivity of the XRD methodology. Insoluble solids XRD characterization indicated that various Fe/Ni/Cr/Mn phases are present. These crystalline phases are associated with the insoluble sludge components of Tank 48H slurry and impurities in the Erwin coal ash. The percent insoluble solids, which mainly consist of un-burnt coal and coal ash, in the products were 4 to 11 wt% for the radioactive runs. (7) The Fe{sup +2}/Fe{sub total} REDOX measurements ranged from 0.58 to 1 for the three radioactive Bench-scale tests. REDOX measurements > 0.5 showed a reducing atmosphere was maintained in the DMR indicating that pyrolysis was occurring. (8) Greater than 90% of the radioactivity was captured in the product for all three runs. (9) The collective results from the FBSR simulant tests and the BSR simulant tests indicate that the same chemistry occurs in the two reactors. (10) The collective results from the BSR simulant runs and the BSR radioactive waste runs indicates that the same chemistry occurs in the simulant as in the real waste. The FBSR technology has been proven to destroy the organics and nitrates in the Tank 48H waste and form the anticipated solid carbonate phases as expected

Long-term exposure to environmental concentrations of the pharmaceutical ethynylestradiol causes reproductive failure in fish

International audienceHeightened concern over endocrine-disrupting chemicals is driven by the hypothesis that they could reduce reproductive success and affect wildlife populations, but there is little evidence for this expectation. The pharmaceutical ethynylestradiol (EE(2)) is a potent endocrine modulator and is present in the aquatic environment at biologically active concentrations. To investigate impacts on reproductive success and mechanisms of disruption, we exposed breeding populations (n = 12) of zebrafish (Danio rerio) over multiple generations to environmentally relevant concentrations of EE(2). Life-long exposure to 5 ng/L EE(2) in the F, generation caused a 56% reduction in fecundity and complete population failure with no fertilization. Conversely, the same level of exposure for up to 40 days in mature adults in the parental F(0) generation had no impact on reproductive success. Infertility in the F, generation after life-long exposure to 5 ng/L EE(2) was due to disturbed sexual differentiation, with males having no functional testes and either undifferentiated or intersex gonads. These F, males also showed a reduced vitellogenic response when compared with F(0) males, indicating an acclimation to EE(2) exposure. Deputation studies found only a partial recovery in reproductive capacity after 5 months. Significantly, even though the F(0) males lacked functional testes, they showed male-pattern reproductive behavior, inducing the spawning act and competing with healthy males to disrupt fertilization. Endocrine disruption is therefore likely to affect breeding dynamics and reproductive success in group-spawning fish. Our findings raise major concerns about the population-level impacts for wildlife of long-term exposure to low concentrations of estrogenic endocrine disruptors