Perturbation analysis of a matrix differential equation x˙=ABx\dot x=ABx

Two complex matrix pairs $(A,B)$ and $(A',B')$ are contragrediently equivalent if there are nonsingular $S$ and $R$ such that $(A',B')=(S^{-1}AR,R^{-1}BS)$. M.I. Garc\'{\i}a-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair $(A,B)$ for contragredient equivalence; that is, a simple normal form to which all matrix pairs $(A + \widetilde A, B+\widetilde B)$ close to $(A,B)$ can be reduced by contragredient equivalence transformations that smoothly depend on the entries of $\widetilde A$ and $\widetilde B$. Each perturbation $(\widetilde A,\widetilde B)$ of $(A,B)$ defines the first order induced perturbation $A\widetilde{B}+\widetilde{A}B$ of the matrix $AB$, which is the first order summand in the product $(A +\widetilde{A})(B+\widetilde{B}) = AB + A\widetilde{B}+\widetilde{A}B+ \widetilde A \widetilde B$. We find all canonical matrix pairs $(A,B)$, for which the first order induced perturbations $A\widetilde{B}+\widetilde{A}B$ are nonzero for all nonzero perturbations in the normal form of Garc\'{\i}a-Planas and Sergeichuk. This problem arises in the theory of matrix differential equations $\dot x=Cx$, whose product of two matrices: $C=AB$; using the substitution $x = Sy$, one can reduce $C$ by similarity transformations $S^{-1}CS$ and $(A,B)$ by contragredient equivalence transformations $(S^{-1}AR,R^{-1}BS)$

A precise characterisation of the top quark electro-weak vertices at the ILC

Top quark production in the process $e^+e^- \to t\bar{t}$ at a future linear electron positron collider with polarised beams is a powerful tool to determine indirectly the scale of new physics. The presented study, based on a detailed simulation of the ILD detector concept, assumes a centre-of-mass energy of $\sqrt{s}=500\,$GeV and a luminosity of $\mathcal{L}=500\,{\rm fb}^{-1}$ equally shared between the incoming beam polarisations of $\mathcal{P}_{e^-}, \mathcal{P}_{e^+} =\pm0.8,\mp0.3$. Events are selected in which the top pair decays semi-leptonically and the cross sections and the forward-backward asymmetries are determined. Based on these results, the vector, axial vector and tensorial $CP$ conserving couplings are extracted separately for the photon and the $Z^0$ component. With the expected precision, a large number of models in which the top quark acts as a messenger to new physics can be distinguished with many standard deviations. This will dramatically improve expectations from e.g. the LHC for electro-weak couplings of the top quark.Comment: This work is an update of arXiv:1307.8102, minor changes w.r.t. v1 (typos, wrong grammar, incomplete sentences etc.

Tunable gauge potential for neutral and spinless particles in driven lattices

We present a universal method to create a tunable, artificial vector gauge potential for neutral particles trapped in an optical lattice. The necessary Peierls phase of the hopping parameters between neighboring lattice sites is generated by applying a suitable periodic inertial force such that the method does not rely on any internal structure of the particles. We experimentally demonstrate the realization of such artificial potentials, which generate ground state superfluids at arbitrary non-zero quasi-momentum. We furthermore investigate possible implementations of this scheme to create tuneable magnetic fluxes, going towards model systems for strong-field physics

Kinematic studies of transport across an island wake, with application to the Canary islands

Transport from nutrient-rich coastal upwellings is a key factor influencing biological activity in surrounding waters and even in the open ocean. The rich upwelling in the North-Western African coast is known to interact strongly with the wake of the Canary islands, giving rise to filaments and other mesoscale structures of increased productivity. Motivated by this scenario, we introduce a simplified two-dimensional kinematic flow describing the wake of an island in a stream, and study the conditions under which there is a net transport of substances across the wake. For small vorticity values in the wake, it acts as a barrier, but there is a transition when increasing vorticity so that for values appropriate to the Canary area, it entrains fluid and enhances cross-wake transport.Comment: 28 pages, 13 figure

Scanning Tunneling Spectroscopy study of paramagnetic superconducting β’’-ET4[(H3O)Fe(C2O4)3]•C6H5Br crystals

Scanning tunnelling spectroscopy (STS) and microscopy (STM) were performed on the paramagnetic molecular superconductor beta''-ET4[(H3O)Fe(C2O4)(3)]C6H5Br. Under ambient pressure, this compound is located near the boundary separating superconducting and insulating phases of the phase diagram. In spite of a strongly reduced critical temperature T-c (T-c = 4.0 K at the onset, zero resistance at T-c = 0.5 K), the low temperature STS spectra taken in the superconducting regions show strong similarities with the higher T-c ET kappa-derivatives series. We exploited different models for the density of states (DOS), with conventional and unconventional order parameters to take into account the role played by possible magnetic and non-magnetic disorder in the superconducting order parameter. The values of the superconducting order parameter obtained by the fitting procedure are close to the ones obtained on more metallic and higher T-c organic crystals and far above the BCS values, suggesting an intrinsic role of disorder in the superconductivity of organic superconductors and a further confirmation of the non-conventional superconductivity in such compounds

Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, precisely and physically identified from experimental examples, together give a physical justification for the `chronometric hypothesis' of general relativity. Indeed, we show that, with a lack of these latter two ingredients, no clock paradox solution exists in which the clock and message functions are solely at the origin of the asymmetry. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian sheaf structure. In addition, the proper time parameterizations, as two point functions, cannot be defined irrespective of the processes in the relative changes of physical characteristics. These processes are included via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension. As such, the differential aging differs far beyond the first and second clock effects in Weyl geometries, with the latter finally appearing to not be suitable.Comment: 25 pages, 2 figure

How long before the end of inflation were observable perturbations produced?

We reconsider the issue of the number of e-foldings before the end of inflation at which observable perturbations were generated. We determine a plausible upper limit on that number for the standard cosmology which is around 60, with the expectation that the actual value will be up to 10 below this. We also note a special property of the $\lambda \phi^4$ model which reduces the uncertainties in that case and favours a higher value, giving a fairly definite prediction of 64 e-foldings for that model. We note an extreme (and highly implausible) situation where the number of e-foldings can be even higher, possibly up to 100, and discuss the shortcomings of quantifying inflation by e-foldings rather than by the change in $aH$. Finally, we discuss the impact of non-standard evolution between the end of inflation and the present, showing that again the expected number of e-foldings can be modified, and in some cases significantly increased.Comment: 7 pages RevTeX4 file with one figure incorporated. Minor updates to match version accepted by Physical Review

IVUS-based imaging modalities for tissue characterization: similarities and differences

Gray-scale intravascular ultrasound (IVUS) is the modality that has been established as the golden standard for in vivo imaging of the vessel wall of the coronary arteries. The use of IVUS in clinical practice is an important diagnostic tool used for quantitative assessment of coronary artery disease. This has made IVUS the de-facto invasive imaging method to evaluate new interventional therapies such as new stent designs and for atherosclerosis progression-regression studies. However, the gray-scale representation of the coronary vessel wall and plaque morphology in combination with the limited resolution of the current IVUS catheters makes it difficult, if not impossible, to identify qualitatively (e.g. visually) the plaque morphology similar as that of histopathology, the golden standard to characterize and quantify coronary plaque tissue components. Meanwhile, this limitation has been partially overcome by new innovative IVUS-based post-processing methods such as: virtual histology IVUS (VH-IVUS, Volcano Therapeutics, Rancho Cordova, CA, USA), iMAP-IVUS (Bostoc Scientific, Santa Clara, CA, USA), Integrated Backscatter IVUS (IB-IVUS) and Automated Differential Echogenicity (ADE)

PARTOS - Passive and Active Ray TOmography Software: description and preliminary analysis using TOMO-ETNA experiment’s dataset.

In this manuscript we present the new friendly seismic tomography software based on joint inversion of active and passive seismic sources called PARTOS (Passive Active Ray TOmography Software). This code has been developed on the base of two well-known widely used tomographic algorithms (LOTOS and ATOM-3D), providing a robust set of algorithms. The dataset used to set and test the program has been provided by TOMO-ETNA experiment. TOMO-ETNA database is a large, highquality dataset that includes active and passive seismic sources recorded during a period of 4 months in 2014. We performed a series of synthetic tests in order to estimate the resolution and robustness of the solutions. Real data inversion has been carried out using 3 different subsets: (i) active data; (ii) passive data; and (iii) joint dataset. Active database is composed by a total of 16,950 air-gun shots during 1 month and passive database includes 452 local and regional earthquakes recorded during 4 months. This large dataset provides a high ray density within the study region. The combination of active and passive seismic data, together with the high quality of the database, permits to obtain a new tomographic approach of the region under study never done before. An additional user-guide of PARTOS software is provided in order to facilitate the implementation for new users.PublishedS04351V. Storia e struttura dei sistemi vulcaniciJCR Journalope