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A theoretical framework for the rational approximation of optical response functions in resonant photonic systems is introduced. The framework is based on the AAA algorithm and further allows to solve the underlying nonlinear eigenproblems and to efficiently model sensitivities. An adaptive sampling strategy exploits the predominance of resonances in the physical response. A chiral metasurface is investigated and it is shown that the chiroptical response on parameter variations can be accurately modeled in the vicinity of the relevant resonance frequencies. [ABSTRACT FROM AUTHOR]

We consider a non-self-adjoint H acting on a complex Hilbert space. We suppose that H is of the form H = H 0 + C W C where C is a bounded, positive definite and relatively compact with respect to H 0 , and W is bounded. We suppose that C (H 0 − z) − 1 C is uniformly bounded in z ∈ ℂ ∖ ℝ. We define the regularized wave operators associated to H and H 0 by W ± (H , H 0) : = s-lim t → ∞ e ± i t H r ∓ (H) Π p (H ⋆) ⊥ e ∓ i t H 0 where Π p (H ⋆) is the projection onto the direct sum of all the generalized eigenspaces associated to eigenvalues of H ⋆ and r ∓ is a rational function that regularizes the "incoming/outgoing spectral singularities" of H. We prove the existence and study the properties of the regularized wave operators. In particular, we show that they are asymptotically complete if H does not have any spectral singularity. [ABSTRACT FROM AUTHOR]

The triboelectric nanogenerator (TENG) is a new type of energy conversion technology capable of transforming various forms of environmental energy into electricity. However, most of the existing spring‐assisted TENGs (S‐TENGs) are based on the vertical contact‐separation mode, which has low energy‐harvesting efficiency and insufficient research on the performance output of TENG under near‐resonant frequency conditions. In this article, a low‐cost S‐TENG with independent layer mode is designed for vibration energy harvesting. The effects of different vibration parameters and structural parameters on the output performance are comprehensively investigated. In the experimental results, it is shown that the output voltage of the S‐TENG reaches its peak at a frequency of 50 Hz, achieving ≈40 V. To validate the capability of S‐TENG in powering low‐power devices, 20 LED lights are successfully lit. It is found that the maximum output power across the external resistor of 8 MΩ is 0.4 mw. It is also investigated that the output characteristics of S‐TENG under resonance and the results showed that higher output electric power can be achieved when the vibration frequency is close to the intrinsic frequency of the S‐TENG. In this finding, the potential of S‐TENG in optimized energy‐harvesting applications, particularly in resonance‐enhanced scenarios. [ABSTRACT FROM AUTHOR]

We show that the wave operators for Schrödinger scattering in R 4 have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator. [ABSTRACT FROM AUTHOR]

We show that the wave operators for Schrödinger scattering in R 4 have a particular form which depends on the existence of resonances. As a consequence of this form, we determine the contribution of resonances to the index of the wave operator. [ABSTRACT FROM AUTHOR]

The low-lying eigenvalues of the generator of a Langevin process are known to satisfy the Eyring--Kramers law in the low temperature regime under suitable assumptions. These eigenvalues are generically real. We construct generators whose spectral gap is given by nonreal eigenvalues or by a real eigenvalue having a Jordan block. [ABSTRACT FROM AUTHOR]

We give a criterion based on reflection symmetries in the spirit of Jitomirskaya--Simon to show absence of point spectrum for (split-step) quantum walks and Cantero--Moral--Velázquez (CMV) matrices. To accomplish this, we use some ideas from a recent paper by the authors and collaborators to implement suitable reflection symmetries for such operators. We give several applications. For instance, we deduce arithmetic delocalization in the phase for the unitary almost-Mathieu operator and singular continuous spectrum for generic CMV matrices generated by the Thue--Morse subshift. [ABSTRACT FROM AUTHOR]

In this paper, we prove an inverse resonance theorem for the half-solid with vanishing stresses on the surface via Weyl-Titchmarsh function. Using a semi-classical approach, it is possible to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. The goal of the paper is to establish a method to recover the potential from eigenvalues and resonances through the Weyl-Titchmarsh function for non-self-adjoint problems and to establish a one-toone and onto map between suitable function spaces. Moreover, we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances, via the spectral data. [ABSTRACT FROM AUTHOR]

In this paper we investigate some number theoretic properties of the frequencies of the Korteweg--de Vries equation on the torus, relevant for the stability of finite gap solutions. [ABSTRACT FROM AUTHOR]

The CcdAB system expressed in the E.coli cells is a prototypical example of the bacterial toxin-antitoxin (TA) systems that ensure the survival of the bacterial population under adverse environmental conditions. The solution and crystal structures of CcdA, CcdB and of CcdB in complex with the toxin-binding C-terminal domain of CcdA have been reported. Our interest lies in the dynamics of CcdB-CcdA complex formation. Solution NMR studies have shown that CcdB_G100T, in presence of saturating concentrations of CcdA-c, a truncated C-terminal fragment of CcdA exists in equilibrium between two major populations. Sequence specific backbone resonance assignments of both equilibrium forms of the ~ 27 kDa complex, have been obtained from a suite of triple resonance NMR experiments acquired on 2H, 13C, 15N enriched samples of CcdB_G100T. Analysis of 1H, 13Cα, 13Cβ secondary chemical shifts, shows that both equilibrium forms of CcdB_G100T have five beta-strands and one alpha-helix as the major secondary structural elements in the tertiary structure. The results of these studies are presented below. [ABSTRACT FROM AUTHOR]

In this paper, we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb's problem. Using a semiclassical approach, we are able to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. We obtain asymptotic values on the number and the location of the resonances with respect to the wave number. Moreover, we prove that the mapping from real compactly supported potentials to the Jost functions in a suitable class of entire functions is one-to-one and onto and we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances. [ABSTRACT FROM AUTHOR]

We prove a general Levinson’s theorem for Schrödinger operators in two dimensions with threshold obstructions at zero energy. Our results confirm and simplify earlier seminal results of Bollé, Gesztesy et al., while providing an explicit topological interpretation. We also derive explicit formulas for the wave operators, and so show that they are elements of a C -algebra introduced by Cordes. As a consequence of our approach, we provide an evaluation of the spectral shift function at zero in the presence of p-resonances. [ABSTRACT FROM AUTHOR]

We present an algorithm for the computation of scattering poles for an impenetrable obstacle with Dirichlet or Robin boundary conditions in acoustic scattering. This paper builds upon the previous work of Cakoni et al. (2020) titled 'A duality between scattering poles and transmission eigenvalues in scattering theory' (Cakoni et al. 2020 Proc. A.476, 20200612 (doi:10.1098/rspa.2020.0612)), where the authors developed a conceptually unified approach for characterizing the scattering poles and interior eigenvalues corresponding to a scattering problem. This approach views scattering poles as dual to interior eigenvalues by interchanging the roles of incident and scattered fields. In this framework, both sets are linked to the kernel of the relative scattering operator that maps incident fields to scattered fields. This mapping corresponds to the exterior scattering problem for the interior eigenvalues and the interior scattering problem for scattering poles. Leveraging this dual characterization and inspired by the generalized linear sampling method for computing the interior eigenvalues, we present a novel numerical algorithm for computing scattering poles without relying on an iterative scheme. Preliminary numerical examples showcase the effectiveness of this computational approach. [ABSTRACT FROM AUTHOR]

In a semiclassical approach, we investigate the superradiation of two parallel ultra-thin layers doped with active centers exhibiting Λ-scheme operation transitions in an absorbing medium. The initial population of the upper state of the active centers varies from full inversion to inversion-less superradiation regimes. We demonstrate the resonant influence of interlayer interference of counterpropagating waves on the intensity dynamics of the fields emitted from the bilayer system, depending on the phase factor characterizing the distance between the layers. In this model, both relaxation processes associated with homogeneous and inhomogeneous broadening of the spectral lines of the active centers are taken into account. [ABSTRACT FROM AUTHOR]

We consider two-dimensional, non-relativistic quantum system with asymptotically straight soft waveguide. We show that the local deformation of the symmetric waveguide can lead to the emerging of the embedded eigenvalues living in the continuous spectrum. The main problem of this paper is devoted to the analysis of weak perturbation of the symmetric system. We show that the original embedded eigenvalues turn to the second sheet of the resolvent analytic continuation and constitute resonances. We describe the asymptotics of the real and imaginary components of the complex resonant pole depending on deformation. Finally, we generalize the problem to three dimensional system equipped with a soft layer. [ABSTRACT FROM AUTHOR]

We consider the Cancrids meteor shower and analyze its dynamical parameters. For each branch of the shower we determined radiants, their displacements, and radiation areas. The dependences of the semi-major axis and eccentricity on magnitude were studied. Resonances from Jupiter were determined for the meteor shower. It is concluded that the branches of the shower have different evolutionary mechanisms of origin. [ABSTRACT FROM AUTHOR]

The design of high-speed simply supported bridges in critical conditions, such as road or canal crossings, is a matter of concern, particularly under two-way crossings with sequential wheel loads. Contrarily to simple classical support, elastic bearings can serve towards vibration mitigation under high speed. In this paper, a non-dimensional framework is developed to understand the impact mechanism of an elastically supported (ES) beam under the action of single as well as opposite traversing loads. A good agreement with the available literature has been confirmed for the one-way crossing using the present methodology. Moreover, a parametric study is conducted for an ES beam, in which the effects of speed parameter (η), speed parameter ratio between two trains (R), interspatial distance between loads to the length of the bridge (ϵ), damping ζ, stiffness parameter (κ), and traversing time difference between two trains (t os ) are investigated. The theoretical results suggest the effective use of the ES beam under higher values of η for one-way and R for two-way traffic. Additionally, various resonances and cancellation speed ratios under particular values of ϵ have been identified under varying values of κ. [ABSTRACT FROM AUTHOR]

This paper deals with the action of the fractional order derivative on nonlinear resonances and its analysis on the chaotic dynamics of an excited rotating gyroscope has been investigated. After the mathematical modeling of the system, we determined the possible resonances of the system using the method of multiple scales. The stability conditions for each resonance were obtained using the Routh-Hurwitz criterion. The different system parameters have been studied and it is concluded that the different resonance states can be controlled by each of the system parameters. Moreover, using bifurcation diagrams, Lyapunov exponents, phase portraits and time series, it was shown that for certain values of the parameters the considered gyroscope exhibits several rich dynamics. The chaos has been reduced, even eliminated with the progressive increase of the other parameters, in particular of the order μ of the fractional derivative up to a certain value. [ABSTRACT FROM AUTHOR]

We consider Schrôdinger equations with energy-dependent potentials that are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent Schrôdinger equations without eigenvalues, defined with Miura potentials and boundary conditions at the origin. We solve the inverse resonance problem in this case and describe sets of isoresonance potentials and boundary condition parameters. Our strategy consists of exploiting a correspondence between Schrôdinger and Dirac equations on the half-line. As a byproduct, we describe similar sets for Dirac operators and show that the scattering problem for a Schrôdinger equation or Dirac operator with an arbitrary boundary condition can be reduced to the scattering problem with the Dirichlet boundary condition. [ABSTRACT FROM AUTHOR]

The possibility and effectiveness of using an automated zenith telescope to determine selenodetic rotation parameters by computer simulation of observations using a telescope installed on the lunar surface are considered, in particular, modeling of star tracks at an automated zenith telescope and the possibilities of astrophysical research, development of a space observations program. [ABSTRACT FROM AUTHOR]

This article presents a new method to reconstruct slowly varying width defects in two-dimensional waveguides using one-side section measurements at locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide up to a "cut-off"" position. In this particular point, the local width of the waveguide can be recovered. Given multifrequency data measured on a section of the waveguide, we perform an efficient layer stripping approach to recover, section by section, the shape variations. It provides an L infinity-stable method to reconstruct the width of a slowly monotonous varying waveguide. We validate this method on numerical data and discuss its limits. [ABSTRACT FROM AUTHOR]

Gas-phase anions present an ideal playground for the exploration of excited-state dynamics. They offer control in terms of the mass, extent of solvation, internal temperature, and conformation. The application of a range of ion sources has opened the field to a vast array of anionic systems whose dynamics are important in areas ranging from biology to star formation. Here, we review recent experimental developments in the field of anion photodynamics, demonstrating the detailed insight into photodynamical and electron-capture processes that can be uncovered. We consider the electronic and nuclear ultrafast dynamics of electronically bound excited states along entire reaction coordinates; electronically unbound states showing that photochemical concepts, such as chromophores and Kasha's rule, are transferable to electron-driven chemistry; and nonvalence states that straddle the interface between bound and unbound states. Finally, we consider likely developments that are sure to keep the field of anion dynamics buoyant and impactful. [ABSTRACT FROM AUTHOR]

In this work, for the first time, an exact solution of the contact problem of interaction with a multilayer base of two semi-infinite stamps, the ends of which are parallel to each other, is constructed. The stamps are assumed to be absolutely rigid, and the distance between them can have any finite value. The task is an important stage in the algorithm for constructing models of a new type of crack in materials of different rheologies. The mechanism of destruction of the medium by cracks of a new type is radically different from the mechanism of destruction of the medium by Griffiths cracks, and has so far been little studied. Griffiths formed his cracks with a smooth border as a result of compression from the sides of an elliptical cavity in the plate. Cracks of a new type have a piecewise smooth border, resulting from the replacement of an ellipse with a rectangle compressed from the sides. The problem considered in this article can be considered as the result of the formation of a new type of crack with absolutely rigid banks and a deformable lower boundary. Thanks to it, after the solution, it becomes possible to switch to deformable stamps and a crack of a new type in the rheological medium. The solution of this problem turned out to be possible due to the construction of exact solutions of the Wiener–Hopf integral equations on a finite segment. This paper shows how the solution of one of the previously unsolved problems allows us to investigate and solve exactly other problems and to identify previously unknown properties and resonances. As a result of constructing an exact solution to the problem, the fact that the solution of dynamic contact problems for stamp systems is not unique was confirmed and a dispersion equation for finding resonant frequencies was constructed. [ABSTRACT FROM AUTHOR]

We consider the (in)stability problem of the inviscid 2D Boussinesq equations near a combination of a shear flow v = (y , 0) and a stratified temperature θ = α y with α > 1 4 . We show that for any ϵ > 0 there exist non-trivial explicit solutions, which are initially perturbations of size ϵ , and grow to size 1 on a time scale ϵ - 2 . Moreover, the (simplified) linearized problem around these non-trivial states exhibits improved upper bounds on the possible size of norm inflation for frequencies larger and smaller than ϵ - 4 . [ABSTRACT FROM AUTHOR]

We consider standard-like/Froeschlé dissipative maps with a dissipation and nonlinear perturbation. That is, where , are the dynamical variables. We fix a frequency and study the existence of quasi-periodic orbits. When there is dissipation, having a quasi-periodic orbit of frequency requires selecting the parameter , called the drift. We first study the Lindstedt series (formal power series in ) for quasi-periodic orbits with independent frequencies and the drift when . We show that, when is irrational, the series exist to all orders, and when is Diophantine, we show that the formal Lindstedt series are Gevrey. The Gevrey nature of the Lindstedt series above was shown in [3] using a more general method, but the present proof is rather elementary. We also study the case when , but the quasi-periodic orbits have only one independent frequency (lower-dimensional tori). Both when and when , we show that, under some mild nondegeneracy conditions on , there are (at least two) formal Lindstedt series defined to all orders and that they are Gevrey. [ABSTRACT FROM AUTHOR]

We consider the 2-dimensional Boussinesq equations with viscous but without thermal dissipation and observe that in any neighborhood of Couette flow and hydrostatic balance (with respect to local norms) there are time-dependent traveling wave solutions of the form ω = 1 + f(t) cos(x ty), θ = α y + g(t) sin(x ty). As our main result we show that the linearized equations (with some technical simplifications) around these waves for ∞ = 0 exhibit echo chains and norm inflation despite viscous dissipation of the velocity. Furthermore, we construct initial data in a critical Gevrey 3 class, for which temperature and vorticity diverge to infinity in Sobolev regularity as t ∞ but for which the velocity still converges. [ABSTRACT FROM AUTHOR]

Using some classical theorems on entire functions, we determine the asymptotic for the counting function of the resonances for 2 × 2 matrix Schrödinger operator in one dimension for potentials with compact support. [ABSTRACT FROM AUTHOR]

The main subject of this study is the low‐frequency (with the periods longer than 2 hr) wave processes in the coupled regional system of the Ross Ice Shelf (RIS), the Ross Sea and the atmosphere above them. We investigate possible causal relationships between the wave activity in the three media using a unique set of geophysical instruments: a hydrophone measuring pressure variations on the seafloor, a network of seismometers measuring vertical displacements of the RIS surface, and a Dynasonde system measuring wave characteristics at the ionospheric altitudes. We present an extension of the previously introduced theoretical model of the coupled resonance vibrations of the RIS that quantifies the connection between the ocean tide and the resonance vibrations of the RIS. The ocean tide is confirmed as the most significant source of excitation of the resonances. Analysis of average power spectra in year‐long data sets reveals multiple harmonics of the tide (eight) detected by the RIS seismometers while only three are detected by the seafloor sensor. This may represent a confirmation of the effect of resonance‐related broadband amplification predicted by the model. Several peaks in the spectrum of RIS vibrations have periods different from the periods of nearby tidal constituents and may be associated with broad‐scale resonance RIS vibrations. Resonances may play a role in maintaining the coupled atmosphere‐ocean wave activity. Our results reveal a statistically significant correlation between the spectra of the vertical displacements of the RIS and the spectra of the atmospheric waves. Plain Language Summary: This study explores how low‐frequency waves interact in the Ross Ice Shelf, the Ross Sea, and the atmosphere above them. By using a unique set of tools like hydrophones, seismometers, and a Dynasonde system, the researchers investigate the connection between waves in these three areas. They expand on a previous theoretical model, confirming that ocean tides are the main source of these interactions. The study finds that the ice shelf picks up more tidal harmonics than the seafloor sensor, which might support the idea of resonance‐related amplification. Additionally, some vibrations in the ice shelf have different periods than nearby tidal movements, which could be due to broad‐scale resonance vibrations. These resonances might play a role in maintaining the overall wave activity in the atmosphere and ocean. The research shows a significant correlation between the ice shelf's vertical movements and the atmospheric waves. Key Points: Ocean tides represent a major source of energy for exciting resonance vibrations of the Ross Ice Shelf (RIS)There is an empirical evidence for resonance‐related amplification effect predicted by the theory of forced ice shelf vibrationsSpectral correlation results confirm existence of the wave coupling above the noise level between atmosphere, ocean and the RIS [ABSTRACT FROM AUTHOR]

The form of modern guitars were shaped by Spanish luthiers in the XIX century. Especially Antonio de Torres Jurado is the one, whose designs are an inspiration for modern constructions. From the very beginning, guitars are struggling with not sufficient sound levels for all the desired applications. Apart from electroacoustic amplification, there were several attempts to modify the construction of the sound hole or the soundboard. Higher sound pressure levels were often connected with distorted sound, sometimes not acceptable to musicians. In this paper, inequalities in the frequency characteristics of the sound generated by the guitar with modern sound holes are presented. Resonant frequencies of the soundboard were pointed as being responsible for the too high amplitude of sound in the 600-800 Hz frequency range. Using optimization and finite element method modelling, the best patterns of bracings were proposed to equalize the frequency spectrum and improve the sound of the instrument. [ABSTRACT FROM AUTHOR]

Opacity determines radiation transport through material media. In a plasma source, the primary contributors to atomic opacity are bound–bound line transitions and bound-free photoionization into the continuum. We review the theoretical methodology for state-of-the-art photoionization calculations based on the R-matrix method as employed in the Opacity Project, the Iron Project, and solution of the heretofore unsolved problem of plasma broadening of autoionizing resonances due to electron impact, Stark (electric microfields), Doppler (thermal), and core-excitations. R-matrix opacity calculations entail huge amount of atomic data and calculations of unprecedented complexity. It is shown that in high-energy-density (HED) plasmas, photoionization cross sections become 3-D energy–temperature–density-dependent owing to considerable attenuation of autoionizing resonance profiles. Hence, differential oscillator strengths and monochromatic opacities are redistributed in energy. Consequently, Rosseland and Planck mean opacities are affected significantly. [ABSTRACT FROM AUTHOR]

We propose an iterative method to find pointwise exponential growth rates in linear problems posed on essentially one-dimensional domains. Such pointwise growth rates capture pointwise stability and instability in extended systems and arise as spectral values of a family of matrices that depends on a spectral parameter, obtained via a scattering-type problem. Different from methods in the literature that rely on computing determinants of this nonlinear matrix pencil, we propose and analyze an inverse power method that allows one to locate robustly the closest spectral value to a given reference point in the complex plane. The method finds branch points, eigenvalues, and resonance poles without a priori knowledge. [ABSTRACT FROM AUTHOR]

We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems: in terms of zeros of reflection coefficient and in terms of poles of reflection coefficients (i.e. resonances). Moreover, we prove the following: 1) a zero of the reflection coefficient can be arbitrarily shifted, such that we obtain the sequence of zeros of the reflection coefficient for another compactly supported potential, 2) the set of "isoresonance potentials" is described, 3) the forbidden domain for resonances is estimated, 4) asymptotics of the resonances counting function is determined, 5) these results are applied to canonical systems. [ABSTRACT FROM AUTHOR]

The experimentally observed first and second sound resonances caused by vibrations of a closed quartz tuning fork in superfluid helium mixtures are studied. Taking into account the full set of hydrodynamic modes of the system allows us to explain the unusual behavior of second sound resonances observed in experiments due to the redistribution of energy between the dissipative mode and the second sound mode. [ABSTRACT FROM AUTHOR]

Many new particles, mostly hadrons, are produced in high-energy collisions between atomic nuclei. The most popular models describing the hadron-production process are based on the creation, evolution and decay of resonances, strings or quark–gluon plasma. The validity of these models is under vivid discussion, and it seems that a common framework for this discussion is missing. Here, for the first time, we explicitly introduce the diagram of high-energy nuclear collisions, where domains of the dominance of different hadron-production processes in the space of laboratory-controlled parameters, the collision energy and nuclear-mass number of colliding nuclei are indicated. We argue that the recent experimental results suggest the location of boundaries between the domains, allowing for the first time to sketch an example diagram. Finally, we discuss the immediate implications for experimental measurements and model development following the proposed sketch of the diagram. [ABSTRACT FROM AUTHOR]

The waves (including acoustic, electromagnetic and elastic ones) propagating in the presence of a cluster of inhomogeneities undergo multiple interactions between them. When these inhomogeneities have sub-wavelength sizes, the dominating field due to the these multiple interactions is the Foldy–Lax field. This field models the multiple interactions between the equivalent point-like scatterers, located at the centers of the small inhomogeneities, with scattering coefficients related to geometrical/material properties of each inhomogeneities, as polarization coefficients. One of the related questions left open for a long time is whether we can reconstruct this Foldy–Lax field from the scattered field measured far away from the cluster of the small inhomogeneities. This would allow us to see (or detect) the multiple interactions between them. This is the Foldy–Lax approximation (or Foldy–Lax paradigm). In this work, we show that this approximation is indeed valid as soon as the inhomogeneities enjoy critical scales between their sizes and contrasts. These critical scales allow them to generate resonances which can be characterized and computed. The main result here is that exciting the cluster by incident frequencies which are close to the real parts of these resonances allows us to reconstruct the Foldy–Lax field from the scattered waves collected far away from the cluster itself (as the farfields). In short, we show that the Foldy–Lax approximation is valid using nearly resonating incident frequencies. This result is demonstrated by using, as small inhomogeneities, dielectric nanoparticles for the 2D TM model of electromagnetic waves and bubbles for the 3D acoustic waves. [ABSTRACT FROM AUTHOR]

In (2017 Nonlinearity 30 2667–86) Slipantschuk, Bandtlow and Just gave concrete examples of Anosov diffeomorphisms of T 2 for which their resonances could be completely described. Their approach was based on composition operators acting on analytic anisotropic Hilbert spaces. In this note we present a construction of alternative anisotropic Hilbert spaces which helps to simplify parts of their analysis and gives scope for constructing further examples. [ABSTRACT FROM AUTHOR]

Copyright of Educar is the property of Universitat Autonoma de Barcelona, Servei de Publicacions and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

High-resolution vibrational spectra of C–H, O–H, and N–H stretches depend on both molecular conformation and environment as well as provide a window into the frequencies of many other vibrational degrees of freedom as a result of mode mixing. We review current theoretical strategies that are being deployed to both aid and guide the analysis of the data that are encoded in these spectra. The goal is to enhance the power of vibrational spectroscopy as a tool for probing conformational preferences, hydrogen bonding effects away from equilibrium, and energy flow pathways. Recent years have seen an explosion of new methods and strategies for solving the nuclear Schrödinger equation. Rather than attempt a comprehensive review, this work highlights specific molecular systems that we have chosen as representing bonding motifs that are important to chemistry and biology. We focus on the choices theoretical chemists make regarding the level of electronic structure theory, the representation of the potential energy surface, the selection of coordinates, preferences in basis sets, and methods of solution. [ABSTRACT FROM AUTHOR]

Complex eigenvalues of random matrices J = GUE + i γ diag (1 , 0 , ... , 0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions N ≫ 1 the eigenvalue density of J undergoes an abrupt restructuring at γ = 1 , the critical threshold beyond which a single eigenvalue outlier ("broad resonance") appears. We provide a detailed description of this restructuring transition, including the scaling with N of the width of the critical region about the outlier threshold γ = 1 and the associated scaling for the real parts ("resonance positions") and imaginary parts ("resonance widths") of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite N in terms of the associated large deviation function. [ABSTRACT FROM AUTHOR]

Copyright of Filigrane: Revue de Psychanalyse is the property of Revue Sante Mentale au Quebec and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Planets and stars have liquid layers that can support internal gravity waves and inertial waves respectively restored by the buoyancy and Coriolis forces. Both types of waves are excited by tides, leading to resonantly amplified dissipation. We review the theoretical formalism to compute these resonances and present some challenges and methods to overcome them. [ABSTRACT FROM AUTHOR]

The short-lived hadronic resonances are used to study the properties of the hot and dense medium produced in the relativistic heavy-ion collisions. The resonance masses and widths, yields and mean transverse momenta measured in the hadronic decay channels probe different stages of the nuclear collisions and are most sensitive to strangeness production, collective flow and hadronization mechanisms as well as to lifetime and density of the hadronic phase. In this contribution, we discuss line shape modifications for short-lived resonances and their consequences for the yields and shapes of the production spectra measured in heavy-ion collisions at intermediate collision energies, s NN ∼ 1 0 GeV. Capabilities of the MPD facility at NICA to reconstruct resonances in Bi+Bi collisions at s NN = 9. 2 GeV are presented and discussed. [ABSTRACT FROM AUTHOR]

Given an N-planet system with coplanar, low eccentricity orbits, and under the effects of an external non-conservative force, we derive necessary conditions for the orbital migration to undergo global convergent migration and allow the formation of a mean-motion resonance chain. Since the conditions are expressed in terms of the time-derivatives of the semimajor axes, the method is applicable to any non-conservative force, including disk–planet interactions and tides. Although the number of possible conditions increase exponentially with the number of bodies, the calculations may be enormously simplified adopting a tree diagram for the decision process. We deduce explicit expressions for N = 3 and N = 4 together with applications to Kepler-60 and Kepler-223 assuming a simple prescription for Type-I migration and no inner disk edge. This disk model is chosen for simplicity and to highlight the applicability of the method. We also present all the necessary steps for the implementation of an algebraic tree algorithm for the general N-planet case, and discuss possible implications for the migration history of the TOI-178 and TRAPPIST-1 systems. [ABSTRACT FROM AUTHOR]

We study the dynamics of two homogeneous rigid ellipsoids subject to their mutual gravitational influence. We assume that the spin axis of each ellipsoid coincides with its shortest physical axis and is perpendicular to the orbital plane. Due to such assumptions, the problem is planar and depends on particular parameters of the ellipsoids, most notably, the equatorial oblateness and the flattening with respect to the shortest physical axes. We consider two models for such configuration: while in the full model, there is a coupling between the orbital and rotational motions, in the Keplerian model, the centers of mass of the bodies are constrained to move on coplanar Keplerian ellipses. The Keplerian case, in the approximation that includes the coupling between the spins of the two ellipsoids, is what we call spin–spin problem, that is a generalization of the classical spin–orbit problem. In this paper we continue the investigations of Misquero (Nonlinearity 34:2191–2219, 2021) on the spin–spin problem by comparing it with the spin–orbit problem and also with the full model. Beside detailing the models associated to the spin–orbit and spin–spin problems, we introduce the notions of standard and balanced resonances, which lead us to investigate the existence of periodic and quasi-periodic solutions. We also give a qualitative description of the phase space and provide results on the linear stability of solutions for the spin–orbit and spin–spin problems. We conclude by providing a comparison between the full and the Keplerian models with particular reference to the interaction between the rotational and orbital motions. [ABSTRACT FROM AUTHOR]

We consider non-local Schrödinger operators with kinetic terms given by several different types of functions of the Laplacian and potentials decaying to zero at infinity and derive conditions ruling embedded eigenvalues out. Our goal in this paper is to advance techniques based on virial theorems, Mourre estimates, and an extended version of the Birman–Schwinger principle, previously developed for classical Schrödinger operators but thus far not used for non-local operators. We also present a number of specific cases by choosing particular classes of kinetic and potential terms and discuss existence/non-existence of at-edge eigenvalues in a basic model case in function of the coupling parameter. [ABSTRACT FROM AUTHOR]

Nearly 60 years ago, Weinberg suggested a criterion for particle "compositeness", which has acquired a new life with the discovery of new, exotic hadrons. His idea resonates with model-based intuition. I discuss the role it plays in the context of another of Weinberg's creations, the model-independent framework of effective field theories. [ABSTRACT FROM AUTHOR]

In this paper a wavefunction-centered description of decaying states that are coupled to an external potential of general time-dependence is investigated. We present the application of non-Hermitian spectral calculations merged with the (t, t′)-formalism to estimate the possible time-dependent potential induced corrections to the lifetime of quasi-stationary states. The appliance of the formalism is demonstrated on some specific potential models as illustrative examples that represent decaying systems. We argue, that the presented framework and computational technique might provide a way to evaluate the lifetime of quasi-stationary states of different types of physical decaying systems that are subjected to perturbative, time-dependent drivings. [ABSTRACT FROM AUTHOR]

Quasi-bound states in the continuum (quasi-BICs) supported in all-dielectric metasurfaces (MTS) are known for their confinement in real space and the notably high values of the quality factor Q. Recently, the properties of quasi-BICs have been employed to achieve polarization conversion with all-dielectric MTS. However, one of the main disadvantages of the current approaches is the dependence on the chirality of either the meta-atoms or their disposition. We present the possibility of achieving polarization conversion by using all-dielectric MTS with square and rectangular lattices of nano-disks. The precise tuning of the lattice and disks parameters allows to transform linearly polarized light into circularly polarized light with near unity polarization rates while maintaining the high Q values of quasi-BICs. Moreover, by using double accidental BICs it is possible to obtain right and left circularly polarized light on demand just by varying the angle of incidence. [ABSTRACT FROM AUTHOR]

Terahertz (THz) propagation in periodic structures has attracted great attention because of its captivating electrical and optical properties. However, the created THz band gaps are usually considered to be caused by Bragg resonances. Here, we theoretically and numerically investigate THz resonances and their related band gap properties in a periodically corrugated plate waveguide with arbitrary wall profiles. It has been found that the corrugated structure can cause not only the interaction between the same transverse modes, called the Bragg resonance, but also the strong interference between different transverse standing wave modes, which occurs in a higher frequency range with quite different features. Unlike the well-known Bragg resonance, the excited resonances between different transverse modes can produce the stronger energy attenuation and wider frequency band gap. The dispersion diagram is depicted to clearly describe the relationship between these resonances and waveguide geometries. Using this method, we can properly estimate the band gap structure of THz waveguides, which has been confirmed by the simulated results. In addition, these two resonances can be easily manipulated by changing the symmetry of waveguide structures. These findings on THz propagation in periodic waveguides could be applicable in high performance devices, such as filters, modulators and switches. [ABSTRACT FROM AUTHOR]

We analyse the scattering and absorption of a terahertz-range plane wave by a thin circular dielectric disk with two graphene covers. Assuming that the thickness of the whole composite disk is much smaller than the free-space wavelength, we reduce the complexity of the problem with the aid of the generalized boundary conditions. This yields a set of singular integral equations for the effective electric and magnetic currents, induced on an equivalent zero-thickness disk. The adopted advanced numerical solution technique is a version of the method of analytical preconditioning, which uses weighted polynomials as expansion functions in the discretization of the integral equations. Then, the resulting matrix equation has Fredholm second-kind property that enables us to control the computational error by the matrix size and reduce it to the desired level. This accurate analysis reveals resonances on several types of natural modes, best understood via visualization of in-resonance near-fields. They are the plasmon-mode resonances of the graphene disk, perturbed by the presence of the dielectric filler, and the dielectric disk modes, perturbed by the graphene covers. Additionally, quasi-full disk transparency is observed if the transverse resonance condition is fulfilled. Special attention is paid to the tunability of the found effects with the aid of graphene's chemical potential. [ABSTRACT FROM AUTHOR]