Nonlinear supratransmission in multicomponent systems

A method is proposed to solve the challenging problem of determining the supratransmission threshold (onset of instability of harmonic boundary driving inside a band gap) in multicomponent nonintegrable nonlinear systems. It is successfully applied to the degenerate three-wave resonant interaction in a birefringent quadratic medium where the process generates spatial gap solitons. No analytic expression is known for this model showing the broad applicability of the method to nonlinear systems.Comment: 4 pages, 3 figure

Four-dimensional ultrafast electron microscopy of phase transitions

Reported here is direct imaging (and diffraction) by using 4D ultrafast electron microscopy (UEM) with combined spatial and temporal resolutions. In the first phase of UEM, it was possible to obtain snapshot images by using timed, single-electron packets; each packet is free of space–charge effects. Here, we demonstrate the ability to obtain sequences of snapshots ("movies") with atomic-scale spatial resolution and ultrashort temporal resolution. Specifically, it is shown that ultrafast metal–insulator phase transitions can be studied with these achieved spatial and temporal resolutions. The diffraction (atomic scale) and images (nanometer scale) we obtained manifest the structural phase transition with its characteristic hysteresis, and the time scale involved (100 fs) is now studied by directly monitoring coordinates of the atoms themselves

Scattering of slow-light gap solitons with charges in a two-level medium

The Maxwell-Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering whith charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schroedinger model in an external potential related to the charges (the electrostatic permanent background component of the field).Comment: RevTex, 14 pages with 5 figures, to appear in J. Phys. A: Math. Theo

Are N=1 and N=2 supersymmetric quantum mechanics equivalent?

After recalling different formulations of the definition of supersymmetric quantum mechanics given in the literature, we discuss the relationships between them in order to provide an answer to the question raised in the title.Comment: 15 page

Clinical characteristics and patient-reported outcomes in patients with inadequately controlled rheumatoid arthritis despite ongoing treatment

Background Despite the wide array of treatments available for rheumatoid arthritis (RA), some patients continue to report unmet clinical needs. We investigated the extent of inadequate disease control in patients with RA. Methods Data were drawn from the Adelphi 2014 RA Disease-Specific Program in France, Germany, Italy, Spain and the UK. Rheumatologists provided patient demographics, comorbidities, satisfaction with RA control and other clinical details. Patients reported their level of satisfaction and completed the EuroQoL 5-Dimensions Health Questionnaire and Work Productivity and Activity Impairment Questionnaire. Patients had been on their current therapy 653 months and had 28-joint disease activity scores (DAS28) reported. Adequately controlled (DAS28 643.2) and inadequately controlled (DAS28 >3.2) patient cohorts were compared using univariate tests. Results Of 1147 patients, 74% were women, the mean age was 52 years and the mean time since RA diagnosis was 7 years. Twenty-seven percent of patients had inadequately controlled RA, whereas 73% had adequately controlled RA. Inadequately controlled patients were more affected clinically versus adequately controlled patients; 69% vs 13% had moderate/severe RA, the current level of pain was 4.6 vs 2.3, and 67% vs 41% experienced flares, respectively (all p<0.0001). Inadequately controlled patients had higher rates of depression (16% vs 5%; p<0.0001), worse health state, greater work and activity impairment, and lower satisfaction rates among the patients and their physicians than the adequately controlled cohort. Conclusion RA was insufficiently controlled in over a quarter of patients despite their current therapy and this had a negative impact on the patients

Radiation damage in the LHCb vertex locator

The LHCb Vertex Locator (VELO) is a silicon strip detector designed to reconstruct charged particle trajectories and vertices produced at the LHCb interaction region. During the first two years of data collection, the 84 VELO sensors have been exposed to a range of fluences up to a maximum value of approximately 45 × 1012 1 MeV neutron equivalent (1 MeV neq). At the operational sensor temperature of approximately −7 °C, the average rate of sensor current increase is 18 μA per fb−1, in excellent agreement with predictions. The silicon effective bandgap has been determined using current versus temperature scan data after irradiation, with an average value of Eg = 1.16±0.03±0.04 eV obtained. The first observation of n+-on-n sensor type inversion at the LHC has been made, occurring at a fluence of around 15 × 1012 of 1 MeV neq. The only n+-on-p sensors in use at the LHC have also been studied. With an initial fluence of approximately 3 × 1012 1 MeV neq, a decrease in the Effective Depletion Voltage (EDV) of around 25 V is observed. Following this initial decrease, the EDV increases at a comparable rate to the type inverted n+-on-n type sensors, with rates of (1.43±0.16) × 10−12 V/ 1 MeV neq and (1.35±0.25) × 10−12 V/ 1 MeV neq measured for n+-on-p and n+-on-n type sensors, respectively. A reduction in the charge collection efficiency due to an unexpected effect involving the second metal layer readout lines is observed

Some results about diagonal operators on Köthe echelon spaces

[EN] Several questions about diagonal operators between Köthe echelon spaces are investigated: (1) The spectrum is characterized in terms of the Köthe matrices defining the spaces, (2) It is characterized when these operators are power bounded, mean ergodic or uniformly mean ergodic, and (3) A description of the topology in the space of diagonal operators induced by the strong topology on the space of all operators is given.This research was partially supported by MINECO Project MTM2016-76647-P and the grant PAID-01-16 of the Universitat Politècnica de València.Rodríguez-Arenas, A. (2019). Some results about diagonal operators on Köthe echelon spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):2959-2968. https://doi.org/10.1007/s13398-019-00663-yS295929681134Agathen, S., Bierstedt, K.D., Bonet, J.: Projective limits of weighted (LB)-spaces of continuous functions. Arch. Math. 92, 384–398 (2009)Albanese, A.A., Bonet, J., Ricker, W.J.: Mean ergodic operators in Fréchet spaces. Ann. Acad. Sci. Fenn. Math. 34(2), 401–436 (2009)Bennett, G.: Some elementary inequalities. Quart. J. Math. 38, 401–425 (1987)Bennett, G.: Factorizing the classical inequalities. Mem. Am. Math. Soc. (1996). https://doi.org/10.1090/memo/0576Bierstedt, K.D.: An introduction to locally convex inductive limits, Functional analysis and its applications (Nice, 1986), 35–133, ICPAM Lecture Notes. World Sci. Publishing, Singapore (1988)Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 97(2), 159–188 (2003)Bierstedt, K.D., Meise, R., Summers, W.H.: Köthe sets and Köthe sequence spaces, Functional Analysis, Holomorphy and Approximation Theory. North-Holland Math. Studies 71, 27–91 (1982)Bonet, J., Jordá, E., Rodríguez-Arenas, A.: Mean ergodic multiplication operators on weighted spaces of continuous functions. Mediterr. J. Math 15, 108 (2018)Crofts, G.: Concerning perfect Fréchet spaces and transformations. Math. Ann. 182, 67–76 (1969)Kellogg, C.N.: An extension of the Hausdorff–Young theorem. Michig. Math. J. 18, 121–127 (1971)Krengel, U.: Ergodic Theorems. de Gruyter, Berlin (1985)Meise, R., Vogt, D.: Introduction to Functional Analysis. Oxford University Press, New York (1997)Vasilescu, F.H.: Analytic Functional Calculus and Spectral Decompositions. D. Reidel Publ. Co., Dordrecht (1982)Wengenroth, J.: Derived Functors in Functional Analysis. Springer, Berlin (2003)Yosida, K.: Functional Analysis. Springer, Berlin (1980

Translation Representations and Scattering By Two Intervals

Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U (t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator, and scattering matrix. We illustrate our results in the Lax-Phillips model where (U (t), H) represents an acoustic wave equation in an exterior domain; and in quantum tunneling for dynamics of quantum states