On Breakdown Criteria for Nonvacuum Einstein Equations

The recent "breakdown criterion" result of S. Klainerman and I. Rodnianski stated roughly that an Einstein-vacuum spacetime, given as a CMC foliation, can be further extended in time if the second fundamental form and the derivative of the lapse of the foliation are uniformly bounded. This theorem and its proof were extended to Einstein-scalar and Einstein-Maxwell spacetimes in the author's Ph.D. thesis. In this paper, we state the main results of the thesis, and we summarize and discuss their proofs. In particular, we will discuss the various issues resulting from nontrivial Ricci curvature and the coupling between the Einstein and the field equations.Comment: 62 pages This version: corrected minor typos, expanded Section 6 (geometry of null cones

Spin splitting and precession in quantum dots with spin-orbit coupling: the role of spatial deformation

Extending a previous work on spin precession in GaAs/AlGaAs quantum dots with spin-orbit coupling, we study the role of deformation in the external confinement. Small elliptical deformations are enough to alter the precessional characteristics at low magnetic fields. We obtain approximate expressions for the modified $g$ factor including weak Rashba and Dresselhaus spin-orbit terms. For more intense couplings numerical calculations are performed. We also study the influence of the magnetic field orientation on the spin splitting and the related anisotropy of the $g$ factor. Using realistic spin-orbit strengths our model calculations can reproduce the experimental spin-splittings reported by Hanson et al. (cond-mat/0303139) for a one-electron dot. For dots containing more electrons, Coulomb interaction effects are estimated within the local-spin-density approximation, showing that many features of the non-iteracting system are qualitatively preserved.Comment: 7 pages, 7 figure

Sub-Riemannian Calculus on Hypersurfaces in Carnot Groups

We develope basic geometric quantities and properties of hypersurfaces in Carnot groups

IMRT beam angle optimization using electromagnetism-like algorithm

The selection of appropriate beam irradiation directions in radiotherapy – beam angle optimization (BAO) problem – is very impor- tant for the quality of the treatment, both for improving tumor irradia- tion and for better organs sparing. However, the BAO problem is still not solved satisfactorily and, most of the time, beam directions continue to be manually selected in clinical practice which requires many trial and error iterations between selecting beam angles and computing fluence patterns until a suitable treatment is achieved. The objective of this pa- per is to introduce a new approach for the resolution of the BAO problem, using an hybrid electromagnetism-like algorithm with descent search to tackle this highly non-convex optimization problem. Electromagnetism- like algorithms are derivative-free optimization methods with the ability to avoid local entrapment. Moreover, the hybrid electromagnetism-like algorithm with descent search has a high ability of producing descent directions. A set of retrospective treated cases of head-and-neck tumors at the Portuguese Institute of Oncology of Coimbra is used to discuss the benefits of the proposed algorithm for the optimization of the BAO problem.Fundação para a Ciência e a Tecnologia (FCT

Complex patterns of spontaneous initiations and terminations of reentrant circulation in a loop of cardiac tissue

A two-component model is developed that consists of a discrete loop of cardiac cells that circulates action potentials together with a cardiac pacing mechanism. Physiological properties of cells such as restitutions of refractoriness and of conduction velocity are given via experimentally measured functions. The dynamics of circulating pulses and their interactions with the pacer are regulated by two threshold relations. Patterns of spontaneous initiations and terminations of reentry (SITR) generated by this system are studied through numerical simulations and analytical observations. These patterns can be regular or irregular; causes of irregularities are identified as the threshold bistability of reentrant circulation (T-bistability) and in some cases, also phase-resetting interactions with the pacer.Comment: 27 pages, 10 figures, 61 references; A version of this paper (same results) is to appear in the Journal of Theoretical Biology; arXiv V2 adds helpful commments to facilitate reading and corrects minor errors in presentatio

Determining the Energy Barrier for Decay out of Superdeformed Bands

An asymptotically exact quantum mechanical calculation of the matrix elements for tunneling through an asymmetric barrier is combined with the two-state statistical model for decay out of superdeformed bands to determine the energy barrier (as a function of spin) separating the superdeformed and normal-deformed wells for several nuclei in the 190 and 150 mass regions. The spin-dependence of the barrier leading to sudden decay out is shown to be consistent with the decrease of a centrifugal barrier with decreasing angular momentum. Values of the barrier frequency in the two mass regions are predicted.Comment: v1: 4 pages, 1 figure, 1 table. v2: 5 pages, 1 figure, 1 table; minor corrections and clarification

Chloride Anion Controlled Molecular “Switching”. Binding of 2,5,7-Trinitro-9-dicyanomethylenefluorene-C60 by Tetrathiafulvalene Calix[4]pyrrole and Photophysical Generation of Two Different Charge-Separated States

The binding of the snake-like trinitrodicyanomethylenefluorene-C60 derivative (TNDCF-C60) to the dynamic receptor, tetrathiafulvalene calix[4]pyrrole (TTF-calix[4]pyrrole), may be controlled via the use of a chloride anion as an external trigger. Whereas, in the absence of a chloride anion, the TNDCF ?tail? of the trinitrodicyanomethylenefluorene-C60 substrate binds to the TTF?calix[4]pyrrole in a 2:1 (substrate/receptor) stoichiometry in CH2Cl2 solution, addition of a chloride anion (yellow) leads the TNDCF tail to be displaced in favor of a bound C60 ?head?, a process that leads to the formation of a complex with overall 1:2:2 substrate/receptor/chloride anion stoichiometry. These chemical switching events are reflected in easy-to-visualize color changes, as well as in the production of two different kinds of charge-separated states following selective femtosecond photoexcitation

Binding studies of tetrathiafulvalene-calix[4]pyrroles with electron-deficient guests

The neutral meso-octamethylporphyrinogen derivative, tetraTTF-calix[4]pyrrole 1 (TTF=tetrathiafulvalene), acts as a multi-faceted receptor in that it interacts with an assortment of different guests in different ways. The conformation of receptor 1 can be reversibly switched between the 1,3-alternate conformation (i.e., 1, Fig. 1) and the cone conformation (i.e., 1·Cl−, Fig. 2) by the repetitive addition of chloride and sodium ions. In this paper, the results of detailed and systematic complexation studies involving both 1 and its chloride-bound complex, 1·Cl−, with a variety of guests are described. Receptor 1 binds quasi-planar nitroaromatic guests in its 1,3-alternate conformation, while release of these guests takes place upon addition of chloride anions. On the other hand, spherical fullerene guests are strongly bound by 1·Cl−. Finally, it was found that a bidentate guest, consisting of a quasi-planar 2,5,7-trinitro-9-dicyanomethylenefluorene moiety tethered to a spherical C60 fullerene, could be recognized by receptor 1 in either its 1,3-alternate or its chloride-bound cone conformation, albeit through very different binding modes

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Search for the standard model Higgs boson decaying into two photons in pp collisions at sqrt(s)=7 TeV

A search for a Higgs boson decaying into two photons is described. The analysis is performed using a dataset recorded by the CMS experiment at the LHC from pp collisions at a centre-of-mass energy of 7 TeV, which corresponds to an integrated luminosity of 4.8 inverse femtobarns. Limits are set on the cross section of the standard model Higgs boson decaying to two photons. The expected exclusion limit at 95% confidence level is between 1.4 and 2.4 times the standard model cross section in the mass range between 110 and 150 GeV. The analysis of the data excludes, at 95% confidence level, the standard model Higgs boson decaying into two photons in the mass range 128 to 132 GeV. The largest excess of events above the expected standard model background is observed for a Higgs boson mass hypothesis of 124 GeV with a local significance of 3.1 sigma. The global significance of observing an excess with a local significance greater than 3.1 sigma anywhere in the search range 110-150 GeV is estimated to be 1.8 sigma. More data are required to ascertain the origin of this excess.Comment: Submitted to Physics Letters