On deformation and classification of V-systems

The V-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of V-systems are known but their classification is an open problem. We derive the relations describing the infinitesimal deformations of V-systems and use them to study the classification problem for V-systems in dimension 3. We discuss also possible matroidal structures of V-systems in relation with projective geometry and give the catalogue of all known irreducible rank 3 V-systems.Comment: Slightly revised version, one of the figures correcte

Magnetic properties of the spin-1 two-dimensional J1−J3J_1-J_3 Heisenberg model on a triangular lattice

Motivated by the recent experiment in NiGa$_2$S$_4$, the spin-1 Heisenberg model on a triangular lattice with the ferromagnetic nearest- and antiferromagnetic third-nearest-neighbor exchange interactions, $J_1 = -(1-p)J$ and $J_3 = pJ, J > 0$, is studied in the range of the parameter $0 \leq p \leq 1$. Mori's projection operator technique is used as a method, which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature several phase transitions are observed. At $p \approx 0.2$ the ground state is transformed from the ferromagnetic order into a disordered state, which in its turn is changed to an antiferromagnetic long-range ordered state with the incommensurate ordering vector at $p \approx 0.31$. With growing $p$ the ordering vector moves along the line to the commensurate point $Q_c = (2 \pi /3, 0)$, which is reached at $p = 1$. The final state with the antiferromagnetic long-range order can be conceived as four interpenetrating sublattices with the $120\deg$ spin structure on each of them. Obtained results offer a satisfactory explanation for the experimental data in NiGa$_2$S$_4$.Comment: 2 pages, 3 figure

In search for a perfect shape of polyhedra: Buffon transformation

For an arbitrary polygon consider a new one by joining the centres of consecutive edges. Iteration of this procedure leads to a shape which is affine equivalent to a regular polygon. This regularisation effect is usually ascribed to Count Buffon (1707-1788). We discuss a natural analogue of this procedure for 3-dimensional polyhedra, which leads to a new notion of affine $B$-regular polyhedra. The main result is the proof of existence of star-shaped affine $B$-regular polyhedra with prescribed combinatorial structure, under partial symmetry and simpliciality assumptions. The proof is based on deep results from spectral graph theory due to Colin de Verdiere and Lovasz.Comment: Slightly revised version with added example of pentakis dodecahedro

Phase diagram of the three-dimensional Anderson model of localization with random hopping

We examine the localization properties of the three-dimensional (3D) Anderson Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM) and finite-size scaling (FSS). The nearest-neighbor hopping elements are chosen randomly according to $t_{ij} \in [c-1/2, c + 1/2]$. We find that the off-diagonal disorder is not strong enough to localize all states in the spectrum in contradistinction to the usual case of diagonal disorder. Thus for any off-diagonal disorder, there exist extended states and, consequently, the TMM converges very slowly. From the TMM results we compute critical exponents of the metal-insulator transitions (MIT), the mobility edge $E_c$, and study the energy-disorder phase diagram.Comment: 4 pages, 5 EPS figures, uses annalen.cls style [included]; presented at Localization 1999, to appear in Annalen der Physik [supplement

Insights on star formation histories and physical properties of 1.2≤z≲41.2 \leq z \lesssim 4 Herschel-detected galaxies

We test the impact of using variable star forming histories (SFHs) and the use of the IR luminosity (LIR) as a constrain on the physical parameters of high redshift dusty star-forming galaxies. We explore in particular the stellar properties of galaxies in relation with their location on the SFR-M* diagram. We perform SED fitting of the UV-NIR and FIR emissions of a large sample of GOODS-Herschel galaxies, for which rich multi-wavelength observations are available. We test different SFHs and imposing energy conservation in the SED fitting process, to face issues like the age-extinction degeneracy and produce SEDs consistent with observations. Our models work well for the majority of the sample, with the notable exception of the high LIR end, for which we have indications that our simple energy conservation approach cannot hold true. We find trends in the SFHs fitting our sources depending on stellar mass M* and z. Trends also emerge in the characteristic timescales of the SED models depending on the location on the SFR-M* diagram. We show that whilst using the same available observational data, we can produce galaxies less star-forming than usually inferred, if we allow declining SFHs, while properly reproducing their observables. These sources can be post-starbursts undergoing quenching, and their SFRs are potentially overestimated if inferred from their LIR. Fitting without the IR constrain leads to a strong preference for declining SFHs, while its inclusion increases the preference of rising SFHs, more so at high z, in tentative agreement with the cosmic star formation history. Keeping in mind that the sample is biased towards high LIR, the evolution shaped by our model appears as both bursty (initially) and steady-lasting (later on). The global SFH of the sample follows the cosmic SFH with a small scatter, and is compatible with the "downsizing" scenario of galaxy evolution.Comment: 28 pages, 26 figures, one appendix, Accepted for publication in Astronomy & Astrophysic

Nonlinear denoising of transient signals with application to event related potentials

We present a new wavelet based method for the denoising of {\it event related potentials} ERPs), employing techniques recently developed for the paradigm of deterministic chaotic systems. The denoising scheme has been constructed to be appropriate for short and transient time sequences using circular state space embedding. Its effectiveness was successfully tested on simulated signals as well as on ERPs recorded from within a human brain. The method enables the study of individual ERPs against strong ongoing brain electrical activity.Comment: 16 pages, Postscript, 6 figures, Physica D in pres

A laser gyroscope system to detect the Gravito-Magnetic effect on Earth

Large scale square ring laser gyros with a length of four meters on each side are approaching a sensitivity of 1x10^-11 rad/s/sqrt(Hz). This is about the regime required to measure the gravitomagnetic effect (Lense Thirring) of the Earth. For an ensemble of linearly independent gyros each measurement signal depends upon the orientation of each single axis gyro with respect to the rotational axis of the Earth. Therefore at least 3 gyros are necessary to reconstruct the complete angular orientation of the apparatus. In general, the setup consists of several laser gyroscopes (we would prefer more than 3 for sufficient redundancy), rigidly referenced to each other. Adding more gyros for one plane of observation provides a cross-check against intra-system biases and furthermore has the advantage of improving the signal to noise ratio by the square root of the number of gyros. In this paper we analyze a system of two pairs of identical gyros (twins) with a slightly different orientation with respect to the Earth axis. The twin gyro configuration has several interesting properties. The relative angle can be controlled and provides a useful null measurement. A quadruple twin system could reach a 1% sensitivity after 3:2 years of data, provided each square ring has 6 m length on a side, the system is shot noise limited and there is no source for 1/f- noise.Comment: 9 pages, 6 figures. 2010 Honourable mention of the Gravity Research Foundation; to be published on J. Mod. Phys.

Ultrasensitive 3He magnetometer for measurements of high magnetic fields

We describe a 3He magnetometer capable to measure high magnetic fields (B > 0.1 Tesla) with a relative accuracy of better than 10^-12. Our approach is based on the measurement of the free induction decay of gaseous, nuclear spin polarized 3He following a resonant radio frequency pulse excitation. The measurement sensitivity can be attributed to the long coherent spin precession time T2* being of order minutes which is achieved for spherical sample cells in the regime of motional narrowing where the disturbing influence of field inhomogeneities is strongly suppressed. The 3He gas is spin polarized in-situ using a new, non-standard variant of the metastability exchange optical pumping. We show that miniaturization helps to increase T2* further and that the measurement sensitivity is not significantly affected by temporal field fluctuations of order 10^-4.Comment: 27 pages, 7 figure

Lack of humidification may harm the patient during continuous positive airway pressure

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Multifractal analysis of the metal-insulator transition in anisotropic systems

We study the Anderson model of localization with anisotropic hopping in three dimensions for weakly coupled chains and weakly coupled planes. The eigenstates of the Hamiltonian, as computed by Lanczos diagonalization for systems of sizes up to $48^3$, show multifractal behavior at the metal-insulator transition even for strong anisotropy. The critical disorder strength $W_c$ determined from the system size dependence of the singularity spectra is in a reasonable agreement with a recent study using transfer matrix methods. But the respective spectrum at $W_c$ deviates from the ``characteristic spectrum'' determined for the isotropic system. This indicates a quantitative difference of the multifractal properties of states of the anisotropic as compared to the isotropic system. Further, we calculate the Kubo conductivity for given anisotropies by exact diagonalization. Already for small system sizes of only $12^3$ sites we observe a rapidly decreasing conductivity in the directions with reduced hopping if the coupling becomes weaker.Comment: 25 RevTeX pages with 10 PS-figures include