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The dual exponential coupled cluster theory proposed by Tribedi et al.[J. Chem. Theory Comput. 16, 10, 6317–6328 (2020)] performs significantly better for a wide range of weakly correlated systems than the coupled cluster theory with singles and doubles excitations due to the implicit inclusion of high-rank excitations. The high-rank excitations are included through the action of a set of vacuum annihilating scattering operators that act non-trivially on certain correlated wavefunctions and are determined via a set of local denominators involving the energy difference between certain excited states. This often leads the theory to be prone to instabilities. In this paper, we show that restricting the correlated wavefunction, on which the scattering operators act, to be spanned by only the singlet-paired determinants can avoid catastrophic breakdown. For the first time, we present two nonequivalent approaches to arrive at the working equations, viz., the projective approach with sufficiency conditions and the amplitude form with many-body expansion. Although the effect of the triple excitation is quite small around molecular equilibrium geometry, this scheme leads to a better qualitative description of the energetics in the regions of strong correlation. With many pilot numerical applications, we have demonstrated the performance of the dual-exponential scheme with both the proposed solution strategies while restricting the excitation subspaces coupled to the corresponding lowest spin channels. [ABSTRACT FROM AUTHOR]

As shown by W. H. Miller in a seminal article [J. Chem. Phys. 53, 3578 (1970)], the most convenient and accurate semiclassical (SC) theory of molecular scattering in action-angle coordinates is based on the initial value representation (IVR) and the use of shifted angles, which are different from the natural angles usually used in the quantum and classical treatments. Here, we show for an inelastic molecular collision that the initial and final shifted angles define three-segment classical paths that are exactly those involved in the classical-limit of Tannor–Weeks quantum scattering theory [J. Chem. Phys. 98, 3884 (1993)], provided that the translational wave packets |g+⟩ and |g−⟩ into play in this theory are both taken at |0⟩. Assuming this to be the case, using van Vleck propagators, and applying the stationary phase approximation, Miller's SCIVR expression of S-matrix elements is found, with an additional cut-off factor canceling the energetically forbidden transition probabilities. This factor, however, is close to unity in most practical cases. Furthermore, these developments show that the Møller operators underlie Miller's formulation, thus confirming, for molecular collisions, the results recently established in the simpler case of light-induced rotational transitions [L. Bonnet, J. Chem. Phys. 153, 174102 (2020)]. Last but not least, we show, based on the previous results, that for processes involving long-range anisotropic forces, implementing the Skinner–Miller method [Chem. Phys. Lett. 300, 20 (1999)] in shifted coordinates makes its predictions both easier and more accurate than in natural coordinates. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the tempered subdiffusive Black–Scholes model. The main part of our work consists of the finite difference method as a numerical approach to option pricing in the considered model. We derive the governing fractional differential equation and the related weighted numerical scheme. The proposed method has an accuracy order 2 - α with respect to time, where α ∈ (0 , 1) is the subdiffusion parameter and 2 with respect to space. Furthermore, we provide stability and convergence analysis. Finally, we present some numerical results. [ABSTRACT FROM AUTHOR]

Small‐angle scattering (SAS) is a key experimental technique for analyzing nanoscale structures in various materials. In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting. This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models. The performance of the method is assessed through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that this proposed analysis approach yields highly accurate and interpretable results. The ability of the method to analyze a range of mixing ratios and particle size ratios for mixed components is also discussed, along with its precision in model evaluation by the degree of fitting. The proposed method effectively facilitates quantitative analysis of nanoscale sample structures in SAS, which has traditionally been challenging, and is expected to contribute significantly to advancements in a wide range of fields. [ABSTRACT FROM AUTHOR]

We consider the Schrödinger operator with regular short range complex-valued potential in dimension d ≥ 1 . We show that, for d ≥ 2 , the unitarity of scattering operator for this Hamiltonian at high energies implies the reality of the potential (that is Hermiticity of Hamiltonian). In contrast, for d = 1 , we present complex-valued exponentially localized soliton potentials with unitary scattering operator for all positive energies and with unbroken PT symmetry. We also present examples of complex-valued regular short range potentials with real spectrum for d = 3 . Some directions for further research are formulated. [ABSTRACT FROM AUTHOR]

A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex probabilities is motivated by a recent reinterpretation of the real-time path integral as the expectation value of a potential functional with respect to a complex probability distribution on cylinder sets of paths. The discrete formulation in this work is based on a discrete version of the Weyl algebra that can be applied to any observable with a finite number of outcomes. The origin of the complex probability in this work is the completeness relation. In the discrete formulation the complex probability exactly factors into products of conditional probabilities and exact unitarity is maintained at each level of approximation. The approximation of infinite dimensional quantum systems by discrete systems is discussed. The method is illustrated by applying it to scattering theory and quantum field theory. The implications of these applications for quantum computing is discussed. [ABSTRACT FROM AUTHOR]

Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the stability estimate for the Helmholtz equation in a deterministic periodic structure is established. For the stochastic case, by introducing a variable transform, the variational formulation of the scattering problem in a random domain is reduced to that in a definite domain with random medium. Combining the stability result for the deterministic case with regularity and stochastic regularity of the scattering surface, Pettis measurability theorem and Bochner's Theorem further yield the stability result for the scattering problem by random periodic structures. Both stability estimates are explicit with respect to the wavenumber. [ABSTRACT FROM AUTHOR]

It is well known that propagation of waves in homogeneous linearized elastic materials of infinite extent is not dispersive. Motivated by the work of Rubin, Rosenau, and Gottlieb, we develop a generalized continuum model for the response of strain-limiting materials that are dispersive. Our approach is based on both a direct inclusion of Rivlin–Ericksen tensors in the constitutive relations and writing the linearized strain in terms of the stress. As a result, we derive two coupled generalized improved Boussinesq-type equations in the stress components for the propagation of pure transverse waves. We investigate the traveling wave solutions of the generalized Boussinesq-type equations and show that the resulting ordinary differential equations form a Hamiltonian system. Linearly and circularly polarized cases are also investigated. In the case of unidirectional propagation, we show that the propagation of small-but-finite amplitude long waves is governed by the complex Korteweg–de Vries (KdV) equation. [ABSTRACT FROM AUTHOR]

In this work the scattering of time-harmonic thermoelastic waves by a multi-layered thermoelastic body is considered. The mathematical formulation of the scattering problem is presented in a unified four-dimensional form. Using the thermoelastic analogue of Betti's identity, the transmission conditions and asymptotic analysis in the dyadic fundamental solution of thermoelasticity, an integral representation of the scattered field as well as formulas of the thermoelastic far-field patterns containing the physical parameters of the scatterer's layers are constructed. Via the Rellich's Lemma for vector fields, the Helmholtz decomposition of thermoelastic waves and the Kupradze's radiation conditions, uniqueness of solution is proved. Setting the solution to be a linear combination of single- and double- layer thermoelastic potentials and using their jump relations, the scattering problem is transformed into a system of integral equations written in a matrix form. Using the regularity properties of the potentials and the Riesz-Fredholm's theory existence of solution is obtained. [ABSTRACT FROM AUTHOR]

Purpose: To quantify operator dose in interventional CT fluoroscopy (CTF) procedures and compare to catheterization laboratory and interventional radiology procedures. Methods: Fifteen studies quantifying operator scatter dose for c‐arm fluoroscopy and CTF were reviewed from a literature survey. The dose provided in each study was normalized to skin entrance air kerma and air kerma rate including backscatter. The average air kerma rate and exposure duration were calculated and compared between c‐arm fluoroscopy and CTF. To enable operator scatter dose calculations in CTF procedures, a model was created which scaled the dose from a reference condition. Results: Our literature survey indicated that for CTF relative to c‐arm fluoroscopy: (1) the mean air kerma rate is 3.5 times higher, while (2) the mean exposure duration is 31.6 times lower. On average, a physician would have to perform 9.1 times (i.e., 31.6/3.5) more CTF procedures relative to c‐arm fluoroscopy procedure to receive equal operator scatter doses. Our own experimental measurements provided scaling factors allowing physician scatter dose to be obtained at any rotation time, tube current, beam collimation, or beam energy. Conclusion: Our results shed light onto a currently mis‐understood issue in radiology. Namely, that physicians receive more dose from CT relative to c‐arm fluoroscopy motivating them to retreat from the room during interventional exposures. Our literature review and experimental measurements indicate the opposite it true; interventional CT produces on average nine times less physician dose relative to c‐arm procedures. Our method allows for prospective/retrospective determination of an individual's dose. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the scattering function and discrete spectrum of the impulsive Sturm‐Liouville type differential operator with a turning point and nonlinear eigenparameter‐dependent boundary condition. Using hyperbolic type representations of the fundamental solutions, the operator's discrete spectrum was constructed. We presented asymptotic equations for the fundamental solutions and the Jost function. Finally, we stated an example to demonstrate the paper's major points. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to examine the scattering analysis of a multiplicative Sturm-Liouville boundary value problem. Firstly, we find the Jost solution of this problem and give the Jost function to construct the scattering function of the problem. Secondly, we obtain asymptotic equations for Jost solution and investigate some properties of the Jost function. Moreover, we present other solutions of the problem by giving the relations between these solutions and Jost solution. Finally, we define the scattering function of this problem by using the Jost function and examine the basic properties of the scattering function. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method to approximate operators resulted from solving the scattering Problem in electromagnetism by dielectrically coated conducting bodies, using integral equations and high order impedance boundary condition. We introduce the variational Problem and we prove its well‐posedness. After discretization, we find that operators arising from the high‐order impedance boundary conditions are not well‐defined. We present the new theoretical approach and highlight its potential through numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper we consider time-harmonic acoustic wave propagation in a half-plane filled by inhomogeneous periodic medium. If the refractive index depends on the horizontal coordinate only, we define upward and downward radiating modes by solving a one-dimensional Sturm-Liouville eigenvalue problem with a complex-valued periodic coefficient. The upward and downward radiation conditions are introduced based on a generalized Rayleigh series. Using the variational method, we then prove uniqueness and existence for the scattering of an incoming wave mode by a grating located between an upper and lower half plane with such inhomogeneous periodic media. The solution operator of the quasiperiodic boundary value problem yields a well-defined scattering operator, the numerical approximation of which is nothing else but the S-matrix in scattering matrix algorithms like Rigorous Coupled Wave Analysis (RCWA) or Fourier Modal Method (FMM). [ABSTRACT FROM AUTHOR]

The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering centres are, on average, at rest. It is common therefore to use a mixed coordinate system, wherein space and time are measured in a fixed inertial frame, while momenta are measured in a 'co-moving' frame. To facilitate analytical and numerical solutions, the momentum dependence of the phase-space density may be expanded as a series of spherical harmonics, typically truncated at low order. A method for deriving the system of equations for the expansion coefficients of the spherical harmonics to arbitrary order is presented in the limit of isotropic, small-angle scattering. The method of derivation takes advantage of operators acting on the space of spherical harmonics. The matrix representations of these operators are employed to compute the system of equations. The computation of matrix representations is detailed and subsequently simplified with the aid of rotations of the coordinate system. The eigenvalues and eigenvectors of the matrix representations are investigated to prepare the application of standard numerical techniques, e.g. the finite volume method or the discontinuous Galerkin method, to solve the system. [ABSTRACT FROM AUTHOR]

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. The attenuating and scattering properties of the medium are assumed known. For scattering kernels of finite Fourier content in the angular variable, we show how to recover the anisotropic radiative sources from boundary measurements. The approach is based on the Cauchy problem for a Beltrami-like equation associated with A-analytic maps. As an application, we determine necessary and sufficient conditions for the data coming from two different sources to be mistaken for each other. [ABSTRACT FROM AUTHOR]

Mesoporous polysaccharide aerogels are versatile functional materials for drug delivery and wound dressing devices. The hydration and wetting of these aerogels control their application‐related performance, e.g. the release of encapsulated drugs. Reported here is a detailed small‐angle neutron scattering (SANS) analysis of the hydration mechanism of a calcium alginate aerogel, based on mathematical modelling of the scattering. The model accounts for the hierarchical structure of the material comprising a mesoporous structure, the solid skeleton of which is made up of water‐swollen polymers. At large scale, the mesoporous structure is modelled as a random collection of elongated cylinders, which grow in size as they absorb water and aggregate. The small‐scale inner structure of the skeleton is described as a Boolean model of polymer coils, which captures the progressive transition from a dense dry polymer to a fully hydrated gel. Using known physico‐chemical characteristics of the alginate, the SANS data are fitted using the size of the cylinders as the only adjustable parameter. The alginate aerogel maintains a nanometre‐scale, albeit altered, structure for low water contents but it collapses into micrometre‐sized structures when the water content approaches one gram of water per gram of alginate. In addition to the wetting of aerogels, the model might be useful for the small‐angle scattering analysis of the supercritical drying of gels. [ABSTRACT FROM AUTHOR]

In this paper, the Cauchy problem for the nonlinear Schrodinger system {idtu1(x,t)== ∆u1(x, t)− |u1(x, t)| p−1u1(x, t)− |u2(x, t)| p−1u1(x, t), idtu2(x, t) = ∆u2(x, t) − |u2(x, t)| p−1u2(x, t) − |u1(x, t)| p−1u2(x, t), was investigated in d space dimensions. For 1 < p ≤ 1 + 2/d, the nonexistence of asymptotically free solutions for the nonlinear Schrödinger system was proved based on mathematical analysis and scattering theory methods. The novelty of this paper was to give the proof of pseudo-conformal identity on the nonlinear Schrödinger system. The present results improved and complemented these of Bisognin, Sepúlveda, and Vera(Appl. Numer. Math. 59(9)(2009): 2285–2302), in which they only proved the nonexistence of asymptotically free solutions when d = 1, p = 3. [ABSTRACT FROM AUTHOR]

The diffusive wave model is one of the simplified forms of Saint-Venant equations, and it is often used instead of the full model. In this paper, we present an analytical solution for the linearized diffusive wave model represented by a simultaneous system of two first-order partial differential equations focused on spatial variation of a lateral inflow in a finite channel. A concentrated lateral inflow from a small-width tributary is considered through the Dirac delta function. We use the Laplace transform method to solve these equations analytically. Two types of upstream boundaries are considered here in the form of a flow-discharge hydrograph and a flow-depth hydrograph, while keeping a flow-depth hydrograph as the downstream boundary. Using unit-step responses of the lateral inflow, the effect of different boundaries on the flow-depth responses and the flow-discharge responses is studied for different values of the Peclet number ( P e ). The flow depth is observed to be more sensitive to the downstream boundary and other parameters used in this work. Consideration of the flow depth as the upstream boundary reflects the effect of all the parameters on the unit-step responses presented. These responses are compared with the available semi-infinite channel responses, which are found to be an inappropriate substitute for the finite channel responses for P e < 5 which implies that the downstream boundary cannot be ignored for these cases. However, for the case P e > 5 , although the semi-infinite channel responses are found to satisfactorily estimate the discharge along the entire channel, they can approximate the flow depth at the locations closer to the upstream boundary only. [ABSTRACT FROM AUTHOR]

Polarimetric target decomposition algorithms have played an important role in extracting the scattering characteristics of buildings, crops, and other fields. However, there is limited research on the scattering characteristics of grasslands and a lack of volume scattering models established for grasslands. To improve the accuracy of the polarimetric target decomposition algorithm applicable to grassland environments, this paper proposes an adaptive polarimetric target decomposition algorithm (APD) based on the anisotropy degree (A). The adaptive volume scattering model is used in APD to model volume scattering in forest and grassland regions separately by adjusting the value of A. When A > 1, the particle shape becomes a disk, and the grassland canopy is approximated as a cloud layer composed of randomly oriented disk particles; when A < 1, the particle shape is a needle, simulating the scattering mechanism of forests. APD is applied to an L-band AirSAR dataset from San Francisco, a C-band AirSAR dataset from Hunshandak grassland in Inner Mongolia Autonomous Region, and an X-band COSMO-SkyMed dataset from Xiwuqi grassland in Inner Mongolia Autonomous Region to verify the effectiveness of this method. Comparison studies are carried out to test the performance of APD over several target decomposition algorithms. The experimental results show that APD outperforms the algorithms tested in terms of this study in decomposition accuracy for grasslands and forests on different bands of data. [ABSTRACT FROM AUTHOR]

This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic set-ups. It provides an overview of the physical ideas involved in setting up the mathematical problem, the mathematical challenges that need to be overcome once the problem is posed, as well as the main new results we will obtain in upcoming work. From the physical perspective, this includes a discussion of how post-Newtonian theory provides a prediction on the gravitational radiation emitted by N infalling masses from the infinite past in the intermediate zone, i.e. up to some finite advanced time. From the mathematical perspective, we then take this prediction, together with the condition that there be no incoming radiation from I− , as a starting point to set up a scattering problem for the linearized Einstein vacuum equations around Schwarzschild and near spacelike infinity, and we outline how to solve this scattering problem and obtain the asymptotic properties of the scattering solution near i0 and I+. The full mathematical details will be presented in the sequel to this paper. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'. [ABSTRACT FROM AUTHOR]

This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, (1) A multiple scattering strategy that decomposes a given interior time-domain problem into a sequence of limited-duration time-domain problems of scattering by overlapping open arcs, each one of which is reduced (by means of the Fourier transform) to a sequence of Helmholtz frequency-domain problems ; (2) Boundary integral equations on overlapping boundary patches for the solution of the frequency-domain problems in point (1); (3) A smooth "Time-windowing and recentering" methodology that enables both treatment of incident signals of long duration and long time simulation; and, (4) A Fourier transform algorithm that delivers numerically dispersionless, spectrally-accurate time evolution for given incident fields. By recasting the interior time-domain problem in terms of a sequence of open-arc multiple scattering events, the proposed approach regularizes the full interior frequency domain problem—which, if obtained by either Fourier or Laplace transformation of the corresponding interior time-domain problem, must encapsulate infinitely many scattering events, giving rise to non-uniqueness and eigenfunctions in the Fourier case, and ill conditioning in the Laplace case. Numerical examples are included which demonstrate the accuracy and efficiency of the proposed methodology. [ABSTRACT FROM AUTHOR]

Asymptotic normalization coefficients (ANCs) of the 0 1 + , 0 2 + , 1 1 - , 2 1 + , 3 1 - ( l ith π ) bound states of 16 O are deduced from the phase shift data of elastic α - 12 C scattering at low energies. S matrices of elastic α - 12 C scattering are constructed within cluster effective field theory (EFT), in which both bound and resonant states of 16 O are considered. Parameters in the S matrices are fitted to the precise phase shift data below the p- 15 N breakup energy for the partial waves of l = 0 , 1 , 2 , 3 , 4 , 5 , 6 , and the ANCs are calculated by using the wave function normalization factors of 16 O propagators for l = 0 , 1 , 2 , 3 . We review the values of ANCs, which are compared with other results in the literature, and discuss uncertainties of the ANCs obtained from the elastic α - 12 C scattering data in cluster EFT. [ABSTRACT FROM AUTHOR]

In this paper, we study the direct scattering problem on the half-line for the Dirac system of differential equations in the case of finite density with the boundary condition . The spectrum is studied, the resolvent is constructed, and the spectral expansion in the eigenfunctions of the Dirac operator is obtained. [ABSTRACT FROM AUTHOR]

The multichannel scattering problem for the stationary Schrödinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the Jost solutions as functions of the spectral parameter is described. Unitarity of the scattering matrix is proved in the general case when some of the scattering channels can be closed and the thresholds can be different at left and right infinities on the line. The symmetry relations of the S -matrix are established. The condition determining the bound states is obtained. The asymptotics of the Jost functions and of the transition matrix are derived for a large spectral parameter. [ABSTRACT FROM AUTHOR]

The normalization of scattering states is more than a rote step necessary to calculate expectation values. This normalization actually contains important information regarding the density of the scattering spectrum (along with useful details on the bound states). For many applications, this information is more useful than the wavefunctions themselves. In this paper, we show that this correspondence between scattering state normalization and the density of states is a consequence of the completeness relation, and we present formulas for calculating the density of states, which are applicable to certain potentials. We then apply these formulas to the delta function potential and the square well. We then illustrate how the density of states can be used to calculate the partition function for a system of two particles with a point-like (delta potential) interaction. [ABSTRACT FROM AUTHOR]

We derive a new system of integrable derivative non-linear Schrödinger equations with an L operator, quadratic in the spectral parameter with coefficients belonging to the Kac–Moody algebra A 2 (1) . The construction of the fundamental analytic solutions of L is outlined and they are used to introduce the scattering data, thus formulating the scattering problem for the Lax pair L , M . [ABSTRACT FROM AUTHOR]

In this paper, an SM-PB (Sparse Matrix Canonical Grid method-Physics Based Two Grid) acceleration algorithm is proposed which can be used to calculate electromagnetic scattering from two-dimensional rough surfaces with large dielectric constants. Firstly, a two-dimensional rough surface model is established based on the Monte Carlo method and Gaussian spectral function, and a conical incident wave with Gaussian characteristics is introduced to eliminate the error caused by artificial truncation of the rough surface. In the scattering calculation, the integral equation of the rough surface is processed by the SMCG algorithm, and then the matrix equation is further processed by applying the PBTG algorithm to decompose the matrix equation into the very near-field matrix, near-field matrix, and far-field matrix. The FFT method is then used to calculate the matrix vector product during the iteration for fast computation. The proposed algorithm and MoM algorithm were compared from the perspectives of computational accuracy and efficiency. Through comparison, it was found that the two algorithms produced highly consistent results, validating the effectiveness of the proposed algorithm. The proposed algorithm demonstrated a significant advantage in computational efficiency, with considerable efficiency also observed for large-scale rough surfaces. The electromagnetic scattering from rough surfaces with large dielectric constants was calculated, and the influence of the correlation distance rd and dielectric constant on the electromagnetic scattering characteristics was investigated. It was found that it is important to set a reasonable value of rd in order to balance calculation accuracy and calculation efficiency. [ABSTRACT FROM AUTHOR]

Recent years have witnessed rapid progress in observations of the epoch of reionization (EoR). These have enabled high-dimensional inference of galaxy and intergalactic medium (IGM) properties during the first billion years of our Universe. However, even using efficient, seminumerical simulations, traditional inference approaches that compute 3D lightcones on-the-fly can take 105 core hours. Here we present 21cmemu : an emulator of several summary observables from the popular 21cmfast simulation code. 21cmemu takes as input nine parameters characterizing EoR galaxies, and outputs the following summary statistics: (i) the IGM mean neutral fraction; (ii) the 21-cm power spectrum; (iii) the mean 21-cm spin temperature; (iv) the sky-averaged (global) 21-cm signal; (vi) the ultraviolet (UV) luminosity functions (LFs); and (vii) the Thomson scattering optical depth to the cosmic microwave background (CMB). All observables are predicted with sub- per cent median accuracy, with a reduction of the computational cost by a factor of over 104. After validating inference results, we showcase a few applications, including: (i) quantifying the relative constraining power of different observational data sets; (ii) seeing how recent claims of a late EoR impact previous inferences; and (iii) forecasting upcoming constraints from the sixth observing season of the Hydrogen Epoch of Reionization Array (HERA) telescope. 21cmemu is publicly available, and is included as an alternative simulator in the public 21cmmc sampler. [ABSTRACT FROM AUTHOR]

The Green's function approach is well‐established and widely used for modeling the surface mass loading displacements. Global mean Green's functions (MGFs) are commonly applied without considering local variations of the crustal structure. Derived from the modified layered Earth structure, the local Green's functions (LGFs) are theoretically beneficial to generate more accurate deformation, since they consider interior information of the local crust. This paper analyzed the differences among MGFs from Gutenberg–Bullen A model and two sets of LGFs derived from modified PREM Earth models consolidating with two crust models TEA12 and CRUST1.0, hereafter called PREMTEA and PREMCRU, respectively. Utilizing MGFs and two sets of LGFs, we modeled the corresponding 3D atmospheric loading displacements for 984 ITRF2014 stations and compared them with the ITRF2014 residuals. The results show that LGFs from PREMTEA and PREMCRU perform well in further promoting scatter reduction for ∼72%, ∼56%, and ∼85% of stations for the Up, East and North components, respectively. The improvements for the North components are significant (up to 3.6%). In particular, stations in the east coastal areas of North America and the west edge of Greenland exhibit further promoting scatter reduction for the East components (up to ∼2.5%), while those located in west coastline of North America show better performance for the North components. Nevertheless, there are significant anomalies in northern Europe for PREMCRU, the mutation margin of which should be carefully considered when using a resolution higher than 1°. In the area around station MORP (358.31°W, 55.21°N, sited at coastline of Britain), we suggest using PREMTEA model. Plain Language Summary: In any location worldwide, we employ a consistent set of numbers, known as load Green's functions that characterize the elastic properties of the Earth, to model the deformation caused by mass transfer on Earth's surface, which is referred to as surface mass loading effects. Most research and data products adopt same set of global mean Green's functions for any location on Earth, which neglects the differences in elastic properties of various regions of the Earth, leading to modeling errors to some extent. This study aims to optimize the modeling using local load Green's functions, with the objective of obtaining results that are more theoretically valuable. "Local" means that the Green's functions for each site are derived from an Earth model that takes into account the local crustal structure. The modeled atmospheric loading displacements exhibit enhanced alignment with GNSS position time series. This, in turn, further elucidates that deformations can be more attributed to atmospheric loading. Moreover, the model shows improved performance in the horizontal components when compared to the vertical components. Key Points: Local load Green's Functions enable a more precise modeling of loading displacements than global mean Green's FunctionsThe modeled atmospheric loading displacements based on Local Green's Functions can improve scatter reduction of GNSS position time seriesTwo sets of local load Green's Functions, based on CRUST1.0 model and TEA12 model, are compared. We recommend TEA12 for European region [ABSTRACT FROM AUTHOR]

A simple yet efficient solution to the problem of transverse electric (TE) scattering by a two-dimensional right trapezoidal groove placed in a perfect electric conductor (PEC) surface is presented. Using superposition of plane waves and applying the Neumann boundary condition at the groove walls, the transverse magnetic field is expressed as the sums of infinite series of waveguide modes. Considering the equivalent magnetic current on the aperture, a Fredlholm's integral equation with logarithmic singular kernel is extracted and then discretised by a collocation method based on a piecewise constant approximant. The extracted linear system of equations can be easily solved by the matrix methods for the unknown coefficients. Numerous examples are presented to verify the results and show the ability of the proposed method. Finally, this method is employed to examine the effect of the groove parameters and incidence angle on the scattering signatures. [ABSTRACT FROM AUTHOR]

This paper explores the dynamic behavior of the (2 + 1) -dimensional Boussinesq equation, which is a nonlinear water wave equation used to model wave packets in dispersive media with weak nonlinearity. Specifically, we investigate the equation's traveling wave solutions using the Riccati equation mapping method. Our results include solitary and soliton solutions, each with their own set of parameter values. To provide a comprehensive understanding of these solutions, we present them in general form and visualize their significance using various graphs, such as 3D, 2D, and contour plots. The computational effort and resulting outcomes highlight the efficacy of our approach, which has the potential to be applied to other nonlinear physical problems in fields such as mathematical physics, engineering, and nonlinear science. [ABSTRACT FROM AUTHOR]

Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely. An interesting example is that of problems with cubic nonlinearities in one space dimension. The method of testing by wave packets was introduced by the authors as a tool to efficiently capture the asymptotic equations associated to such flows, and thus establish the modified scattering mechanism in a simpler, more efficient fashion, and at lower regularity. In these expository notes we describe how this method can be applied to problems with general dispersion relations. [ABSTRACT FROM AUTHOR]

You might have heard about various mathematical properties of scattering amplitudes such as analyticity, sheets, branch cuts, discontinuities, etc. What does it all mean? In these lectures, we will take a guided tour through simple scattering problems that will allow us to directly trace such properties back to physics. We will learn how different analytic features of the S-matrix are really consequences of causality, locality of interactions, unitary propagation, and so on. These notes are based on a series of lectures given in Spring 2023 at the Institute for Advanced Study in Princeton and the Higgs Centre School of Theoretical Physics in Edinburgh. [ABSTRACT FROM AUTHOR]

In this paper, effect of small deviations in the parameters that appear either in the definition or determination of a physical problem to the resultant calculated value. Within the study, Perturbation theory and Asymptotic Series expansions have been used as mathematical tools. In this work, perturbation theory has been handled in two alternative ways: numerical and analytical. Electromagnetic waves has been dealed extensively. Electromagnetic propagation equation has been nondimensionalised and presented via asymptotic series approach. Spatial Fourier transformation provides singular perturbation application to the equation. Validity of the solution has been investigated. This manuscript also concerns the electromagnetic feature extraction of the multilayered properties by the inverse scattering theory approach. In this work, in order to characterize the unknown or ambiguous part of the structure, random modeling of the parameters was introduced. Monte Carlo methods are used to calculate the resultant randomness effect. The description of any parameter, including thickness, with any probability density function (pdf) to represent nonnegative/bounded/unbounded cases and any combination of all these parameters, is represented in a framework. Skewness and kurtosis values are added to the output structure in order to lead complex analysis on the output descriptions. In this work, depending on the structure or aim of the analysis, the permittivity or the permeability of a layer is randomized. The overall reflection coefficient is calculated via recursive analysis. [ABSTRACT FROM AUTHOR]

We study massless one-dimensional Dirac–Coulomb Hamiltonians, that is, operators on the half-line of the form D ω , λ : = - λ + ω x - ∂ x ∂ x - λ - ω x . We describe their closed realizations in the sense of the Hilbert space L 2 (R + , C 2) , allowing for complex values of the parameters λ , ω . In physical situations, λ is proportional to the electric charge and ω is related to the angular momentum. We focus on realizations of D ω , λ homogeneous of degree - 1 . They can be organized in a single holomorphic family of closed operators parametrized by a certain two-dimensional complex manifold. We describe the spectrum and the numerical range of these realizations. We give an explicit formula for the integral kernel of their resolvent in terms of Whittaker functions. We also describe their stationary scattering theory, providing formulas for a natural pair of diagonalizing operators and for the scattering operator. We describe the point spectrum of their nonhomogeneous realizations. It is well-known that D ω , λ arise after separation of variables of the Dirac–Coulomb operator in dimension 3. We give a simple argument why this is still true in any dimension. Furthermore, we explain the relationship of spherically symmetric Dirac operators with the Dirac operator on the sphere and its eigenproblem. Our work is mainly motivated by a large literature devoted to distinguished self-adjoint realizations of Dirac–Coulomb Hamiltonians. We show that these realizations arise naturally if the holomorphy is taken as the guiding principle. Furthermore, they are infrared attractive fixed points of the scaling action. Beside applications in relativistic quantum mechanics, Dirac–Coulomb Hamiltonians are argued to provide a natural setting for the study of Whittaker (or, equivalently, confluent hypergeometric) functions. [ABSTRACT FROM AUTHOR]

We are interested in the resonant electromagnetic scattering by all-dielectric metasurfaces made of a two-dimensional lattice of nanoparticles with high refractive indices. In [Ammari, Li, and Zou, Trans. Amer. Math. Soc., 376 (2023), pp. 39--90], it has been shown that a single high-index nanoresonator can couple with the incident wave and exhibit a strong magnetic dipole response. Recent physics experiments reveal that when the particles are arranged in certain periodic configurations, they may have different anomalous scattering effects in the macroscopic scale, compared to the single-particle case. In this work, we shall develop a rigorous mathematical framework for analyzing the resonant behaviors of all-dielectric metasurfaces. We start with the characterization of subwavelength scattering resonances in such a periodic setting and their asymptotic expansions in terms of the refractive index of the nanoparticles. Then we show that real resonances always exist below the essential spectrum of the periodic Maxwell operator and that they are the simple poles of the scattering resolvent with the exponentially decaying resonant modes. By using group theory, we discuss the implications of the symmetry of the metasurface on the subwavelength band functions and their associated eigenfunctions. For the symmetric metasurfaces with the normal incidence, we use a variational method to show the existence of embedded eigenvalues (i.e., real subwavelength resonances embedded in the continuous radiation spectrum). Furthermore, we break the configuration symmetry either by introducing a small deformation of particles or by slightly deviating from the normal incidence and prove that Fano-type reflection and transmission anomalies can arise in both of these scenarios. [ABSTRACT FROM AUTHOR]

The scattering phase, defined as log detS(\lambda)/2\pi i where S(\lambda) is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Kre\u {\i}n's spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for nonradial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM. [ABSTRACT FROM AUTHOR]

The Stark operator with a step-like potential is considered. An explicit form of special solutions to the corresponding Stark equation is found. The scattering problem for the operator L is studied. A formula for expansion in terms of eigenfunctions of a continuous spectrum is obtained. [ABSTRACT FROM AUTHOR]

We prove that the wave operators of the scattering theory for the fourth order Schrödinger operator δ¹ + V(x) on R4 are bounded in Lp(R4) for the set of p's of .1;1/depending on the kind of spectral singularities of H at zero which can be described by the space of bounded solutions of (δ-2 + V(x))u(x) + 0. [ABSTRACT FROM AUTHOR]

We study the (characteristic) Cauchy problem for the Maxwell‐Bloch equations of light‐matter interaction via asymptotics, under assumptions that prevent the generation of solitons. Our analysis clarifies some features of the sense in which physically‐motivated initial‐boundary conditions are satisfied. In particular, we present a proper Riemann‐Hilbert problem that generates the unique causal solution to the Cauchy problem, that is, the solution vanishes outside of the light cone. Inside the light cone, we relate the leading‐order asymptotics to self‐similar solutions that satisfy a system of ordinary differential equations related to the Painlevé‐III (PIII) equation. We identify these solutions and show that they are related to a family of PIII solutions recently discovered in connection with several limiting processes involving the focusing nonlinear Schrödinger equation. We fully explain a resulting boundary layer phenomenon in which, even for smooth initial data (an incident pulse), the solution makes a sudden transition over an infinitesimally small propagation distance. At a formal level, this phenomenon has been described by other authors in terms of the PIII self‐similar solutions. We make this observation precise and for the first time we relate the PIII self‐similar solutions to the Cauchy problem. Our analysis of the asymptotic behavior satisfied by the optical field and medium density matrix reveals slow decay of the optical field in one direction that is actually inconsistent with the simplest version of scattering theory. Our results identify a precise generic condition on an optical pulse incident on an initially‐unstable medium sufficient for the pulse to stimulate the decay of the medium to its stable state. [ABSTRACT FROM AUTHOR]

We have developed a fast method of using Multiple Scattering Theory-Broadband Green’s Function (BBGF-MST) for band field calculations. In this paper, we successfully extended the method to the vector electromagnetic case of 3D periodic structures. In the MST-BBGF approach, the broadband transformation to vector spherical waves for 3D is derived using the Broadband Green’s function. The band eigenvalue problem is expressed in terms of the single scatterer T matrix which is independent of the periodic lattice nor the Bloch vector. For the first five bands, the dimension of the KKR eigen equation is merely 6, as 6 vector spherical waves are utilized for the scattered waves. We make extensive comparisons of the results with the commercial software COMSOL in both accuracy and computation efficiency. The CPU requirement on a standard laptop for the MST-BBGF method is merely 0.309 seconds for the first 5 bands. The MST-BBGF method is accurate and is at least two orders of magnitude faster than commercial software COMSOL. In the band field calculations, we employ the approach of extended coefficient to use the low order eigenvector of 6 to extend to 240 vector spherical wave coefficients without the need of recalculating the eigenvalue nor the eigenvector of the KKR equation. The extended coefficients approach gives accurate band field solutions for the entire (0, 0, 0) cell. [ABSTRACT FROM AUTHOR]

In this study, we consider two nonlinear Schrödinger-type models that are derived by R L. Frank, F. Méhats, C. Sparber (2017) to study 3D nonlinear Schrödinger equations under strong magnetic fields. One model is derived by spatial scaling and the other is obtained by averaging the spatial scaled model over time. We study these models in the energy space to obtain global solutions and improve the convergence result over an arbitrarily long time. Regarding the nonic nonlinear power of the time averaged model, we prove a scattering result under a scaling-invariant small-energy condition, which underlines energy-criticality of the nonic case. [ABSTRACT FROM AUTHOR]

The modified transmission eigenvalue (MTE) problem was introduced in [S. Cogar, D. Colton, S. Meng and P. Monk, Modified transmission eigenvalues in inverse scattering theory, Inverse Problems 33 2017, 12, Article ID 125002] and used as a target signature for nondestructive testing. In this paper, we study the inverse spectral problem to reconstruct the modified transmission eigenvalues using Cauchy data. We propose a reciprocity gap functional method and show that the MTEs can be determined by solving some linear ill-posed integral equations. Numerical examples for both absorbing and non-absorbing media are presented to validate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

We discuss various aspects of nonlocal electrical transport in anisotropic metals. For a metal with circular Fermi surface, the scattering rates entering the local conductivity and viscosity tensors are well-defined, corresponding to eigenfrequencies of the linearized collision operator. For anisotropic metals, we provide generalized formulas for these scattering rates and use a variational approximation to show how they relate to microscopic transition probabilities. We develop a simple model of a collision operator for a metal of arbitrary Fermi surface with finite number of quasi-conserved quantities, and derive expressions for the wavevector-dependent conductivity σ (q) and the spatially-varying conductivity σ (x) for a long, narrow channel. We apply this to the case of different rates for momentum-conserving and momentum-relaxing scattering, deriving closed-form expressions for σ (q) and σ (x) — beyond generalizing from circular to arbitrary Fermi surface geometry, this represents an improvement over existing methods which solve the relevant differential equation numerically rather than in closed form. For the specific case of a diamond Fermi surface, we show that, if transport signatures were interpreted via a model for a circular Fermi surface, the diagnosis of the underlying transport regime would differ based on experimental orientation and based on whether σ (q) or σ (x) was considered. Finally, we discuss the bulk conductivity. While the common lore is that "momentum"-conserving scattering does not affect bulk resistivity, we show that crystal momentum-conserving scattering — such as normal electron-electron scattering — can affect the bulk resistivity for an anisotropic Fermi surface. We derive a simple formula for this contribution. [ABSTRACT FROM AUTHOR]

For layered metamaterial devices, the reflection and transmission coefficients at an interface typically depend on the properties of the coupling between different layers. In this paper, we set out to engineer the reflection/transmission behaviour at boundaries to obtain desirable properties such as achieving total reflection and transmission. Based on the quantum graph formulation for modelling metamaterials developed in Sci. Rep. 12 (1), 18006 (2022), we tailor the interface reflection and transmission coefficients by patterning the boundary with resonant elements at each interface vertex. By tuning the internal lengths of the resonant elements, we demonstrate both minimization and maximization of the reflection coefficient via a scattering formulation. In addition, we present an interface set-up incorporating beyond-nearest-neighbour connections, which yields narrow-band transmission for certain angles only, creating an angular filtering interface. [ABSTRACT FROM AUTHOR]

It is vital to consider acoustic scattering when using geometrical acoustic simulation techniques, such as ray tracing. However, there are few methods for modelling scattering, and most rely on strong assumptions of uniformity on the distribution of scattered energy. In this paper, a model for directional scattering in ray tracers is presented. The model is based on an idealized model of a 1D scatterer, which is then used to extend the most commonly used scattering algorithm in ray tracers today. The developed algorithm is implemented in a ray tracer and tested to evaluate its performance compared to existing methods. It is found that the directional scattering algorithm can be used to replicate measured effects on room acoustic parameters caused by changes in the orientation of 1D scatterers. [ABSTRACT FROM AUTHOR]

Previous work involving integro-difference equations of a single species in a homogenous environment has emphasized spreading behavior in unbounded habitats. We show that, under suitable conditions, a simple scalar integro-difference equation incorporating a strong Allee effect and overcompensation can produce solutions where the population persists in an essentially bounded domain without spread despite the homogeneity of the environment. These solutions are robust in that they occupy a region of full measure in parameter space. We develop orbit diagrams showing various patterns of nonspreading solutions from stable equilibria, period-two, to higher periodicity. We show that from a relatively uniform initial density with small stochastic perturbations, a population consisting of multiple isolated patches can emerge. In ecological terms, this work suggests a novel endogenous mechanism for the creation of patch boundaries. [ABSTRACT FROM AUTHOR]

In this paper we examine necessary conditions for an inhomogeneity to be non‐scattering, or equivalently, by negation, sufficient conditions for it to be scattering. These conditions are formulated in terms of the regularity of the boundary of the inhomogeneity. We examine broad classes of incident waves in both two and three dimensions. Our analysis is greatly influenced by the analysis carried out by Williams in order to establish that a domain, which does not possess the Pompeiu Property, has a real analytic boundary. That analysis, as well as ours, relies crucially on classical free boundary regularity results due to Kinderlehrer and Nirenberg, and Caffarelli. [ABSTRACT FROM AUTHOR]