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C. Klein

Publications and source records attributed to C. Klein.

At least 19 recordsLinked to original sources
arXiv2026

Gamma irradiation of ATLAS18 ITk strip sensors affected by static charge

Construction of the new all-silicon ITk, developed by the ATLAS collaboration to be able to track charged particles produced at the HL- LHC, started in 2021 and is expected to continue until 2028. The ITk detector will include ~18,000 highly segmented and radiation hard n+-in-p silicon strip sensors, which are being manufactured by HPK. Upon their delivery, the ATLAS ITk strip sensor collaboration performs detailed measurements of sensors to monitor quality of all fabricated pieces. QC electrical tests include IV and CV tests, full strip tests, and a measurement of the long-term stability of the sensor leakage current. While most sensors demonstrate excellent performance during QC testing, we have nevertheless observed that a number of sensors from several production batches failed the electrical tests. Accumulated data indicates a strong correlation between observed electrical test failures and high electrostatic charge measured on the sensor surface during initial reception tests. This electrostatic charge enhances the risk of "Local trapped charge" events during manufacturing, shipping, and handling procedures, resulting in failed electrical QC tests. In the presented study, we have investigated whether the TID expected in the real experiment can effectively resolve early breakdown or low interstrip isolation caused by the electrostatic charge. Selected charge-affected sensors were irradiated with gamma rays from a 60Co source for a number of TID values. The results of this study indicate that the negative effects of the electrostatic charge on the critical sensors characteristics disappear after a very small amount of an accumulated TID, which actually corresponds to one or two days in the experiment. This finding gives us confidence in mitigating the issue of electrostatic charge during the operation of the ITk strip sensors in the real experiment.

physics.ins-det↗
arXiv2026

Enhanced Superconducting Nanowire Single Photon Detector Performances using Silicon Capping

Niobium Titanium nitride (NbTiN) based superconducting nanowire single photon detectors (SNSPDs) are known for their high performance across a wide spectral range, from the X-ray to the mid-infrared. Nonetheless, fabrication challenges and performance degradation attributable to surface oxidation and lack of uniformity in films thinner than 5 nm remain a significant barrier for achieving high-quality detectors. In this work, we study the influence of a Silicon capping layer on film properties and on the performance of SNSPDs. A Silicon capping layer effectively suppresses oxidation and increases the superconducting transition temperature. This enables superconductivity in films as thin as 3 nm at 3 K, increases critical current in patterned nanowires and significantly extends the saturation plateau from the visible to the near infrared (up to 2050 nm): These detectors maintain sub-50 ps timing jitter, even for nanowires as wide as 250 nm and with detection areas of 20x20{\mu}m2. Our results establish that thinner films protected by a capping layer allow for the fabrication of wider wires, decreasing nanofabrication challenges and extending the operating temperature range for efficient single photon detection.

quant-ph↗
arXiv2025

Numerical study of the Amick-Schonbek system in 2D

A numerical study of the 2D Amick-Schonbek Boussinesq system is presented. Numerical evidence is given for the transverse stability of the 1D solitary waves that are line solitary waves of the 2D equations. It is shown that initial data not satisfying the non-cavitation condition can lead to the formation of a gradient catastrophe in finite time. The numerical propagation of localised smooth initial data does not lead to the formation of stable structures localised in both spatial directions. For initial data satisfying the non-cavitation condition, smooth solutions appear to exist for all times.

math.AP↗
arXiv2024

Instrument design and performance of the first seven stations of RNO-G

The Radio Neutrino Observatory in Greenland (RNO-G) is the first in-ice radio array in the northern hemisphere for the detection of ultra-high energy neutrinos via the coherent radio emission from neutrino-induced particle cascades within the ice. The array is currently in phased construction near Summit Station on the Greenland ice sheet, with 7~stations deployed during the first two boreal summer field seasons of 2021 and 2022. In this paper, we describe the installation and system design of these initial RNO-G stations, and discuss the performance of the array as of summer 2024.

astro-ph.IM↗
arXiv2024

On the Kaup-Broer-Kupershmidt systems

The aim of this paper is to survey and complete, mostly by numerical simulations, results on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. It is the only member of the so-called (abcd) family of Boussinesq systems known to be completely integrable.

math.AP↗
arXiv2024

Visualisation of counter-rotating dust disks using ray tracing methods

A detailed study of ray tracing in the space-time generated by a disk of counter-rotating dust is presented. The space-time is given in explicit form in terms of hyperelliptic theta functions. The numerical approach to ray tracing is set up for general stationary axisymmetric space-times and tested at the well-studied example of the Kerr solution. Similar features as in the case of a rotating black hole, are explored in the case of a dust disk. The effect of the central redshift varying between a Newtonian disk and the ultrarelativistic disk, where the exterior of the disk can be interpreted as the extreme Kerr solution, and the transition from a single component disk to a static disk is explored. Frame dragging, as well as photon spheres, are discussed.

gr-qc↗
arXiv2024

Multi-domain spectral approach to rational-order fractional derivatives

We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multi-domain approach; after transformations in accordance with the underlying $Z_{q}$ curve ensuring analyticity of the respective integrands, the integrals over the different domains are computed with a Clenshaw-Curtis algorithm. As an example, we consider solitary waves for fractional Korteweg-de Vries equations and compare these to results obtained with a discrete Fourier transform.

math.NA↗
arXiv2023

On the Benjamin and related equations

We consider in this paper various theoretical and numerical issues on classical one dimensional models of internal waves with surface tension.They concern the Cauchy problem, including the long time dynamic, localized solitons or multisolitons, the soliton resolution property. We survey known results, present a few new ones together with open questions and conjectures motivated by numerical simulations. A major issue is to emphasize the differences of the qualitative behavior of solutions with those of the same equations without the capillary term.

math.AP↗
arXiv2023

Numerical study of the Amick-Schonbek system

The aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one-dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint-Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow-up of solutions for initial data not satisfying the non-cavitation condition as well as the appearence of dispersive shock waves are studied.

math.AP↗
arXiv2023

Numerical study of the Serre-Green-Naghdi equations in 2D

A detailed numerical study of solutions to the Serre-Green-Naghdi (SGN) equations in 2D with vanishing curl of the velocity field is presented. The transverse stability of line solitary waves, 1D solitary waves being exact solutions of the 2D equations independent of the second variable, is established numerically. The study of localized initial data as well as crossing 1D solitary waves does not give an indication of existence of stable structures in SGN solutions localized in two spatial dimensions. For the numerical experiments, an approach based on a Fourier spectral method with a Krylov subspace technique is applied.

math.AP↗
arXiv2023

Computational approach to the Schottky problem

We present a computational approach to the classical Schottky problem based on Fay's trisecant identity for genus $g\geq 4$. For a given Riemann matrix $\mathbb{B}\in\mathbb{H}^{g}$, the Fay identity establishes linear dependence of secants in the Kummer variety if and only if the Riemann matrix corresponds to a Jacobian variety as shown by Krichever. The theta functions in terms of which these secants are expressed depend on the Abel maps of four arbitrary points on a Riemann surface. However, there is no concept of an Abel map for general $\mathbb{B} \in \mathbb{H}^{g}$. To establish linear dependence of the secants, four components of the vectors entering the theta functions can be chosen freely. The remaining components are determined by a Newton iteration to minimize the residual of the Fay identity. Krichever's theorem assures that if this residual vanishes within the finite numerical precision for a generic choice of input data, then the Riemann matrix is with this numerical precision the period matrix of a Riemann surface. The algorithm is compared in genus 4 for some examples to the Schottky-Igusa modular form, known to give the Jacobi locus in this case. It is shown that the same residuals are achieved by the Schottky-Igusa form and the approach based on the Fay identity in this case. In genera 5, 6 and 7, we discuss known examples of Riemann matrices and perturbations thereof for which the Fay identity is not satisfied.

math.AG↗
arXiv2021

Spectral approach to Korteweg-de Vries equations on the compactified real line

We present a numerical approach for generalised Korteweg-de Vries (KdV) equations on the real line. In the spatial dimension we compactify the real line and apply a Chebyshev collocation method. The time integration is performed with an implicit Runge-Kutta method of fourth order. Several examples are discussed: initial data bounded but not vanishing at infinity as well as data not satisfying the Faddeev condition, i.e. with a slow decay towards infinity.

math.NA↗
arXiv2021

Numerical study of Davey-Stewartson I systems

An efficient high precision hybrid numerical approach for integrable Davey-Stewartson (DS) I equations for trivial boundary conditions at infinity is presented for Schwartz class initial data. The code is used for a detailed numerical study of DS I solutions in this class. Localized stationary solutions are constructed and shown to be unstable against dispersion and blow-up. A finite-time blow-up of initial data in the Schwartz class of smooth rapidly decreasing functions is discussed.

math.AP↗
arXiv2021

Multi-domain spectral approach for the Hilbert transform on the real line

A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and functions with algebraic decay towards infinity. Several examples of these and other types of functions are discussed. As an application solitons to generalized Benjamin-Ono equations are constructed.

math.NA↗
arXiv2020

Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Korteweg-de Vries equation, though, not completely integrable. This equation is $L^2$-subcritical, and thus, solutions exist globally, for example, in the $H^1$ energy space. We first study stability of solitons with various perturbations in sizes and symmetry, and show asymptotic stability and formation of radiation, confirming the asymptotic stability result in \cite{FHRY2020} for a larger class of initial data. We then investigate the solution behavior for different localizations and rates of decay including exponential and algebraic decays, and give positive confirmation toward the soliton resolution conjecture in this equation. Finally, we investigate soliton interactions in various settings and show that there is both a quasi-elastic interaction and a strong interaction when two solitons merge into one, in all cases always emitting radiation in the conic-type region of the negative $x$-direction.

math.AP↗
arXiv2020

On soliton (in-)stability in multi-dimensional cubic-quintic nonlinear Schr\"odinger equations

We consider the nonlinear Schr\"odinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion of stability of solitary waves. We recall the two standard notions of orbital stability in the context of nonlinear Schr\"odinger equations, and show that they must be considered as independent from each other. We investigate numerically the notion of orbital stability of ground states in the radially symmetric case, confirming existing conjectures or leading to new ones.

math.AP↗
arXiv2020

On the modified fractional Korteweg-de Vries and related equations

We consider in this paper modified fractional Korteweg-de Vries and related equations (modified Burgers-Hilbert and Whitham). They have the advantage with respect to the usual fractional KdV equation to have a defocusing case with a different dynamics. We will distinguish the weakly dispersive case where the phase velocity is unbounded for low frequencies and tends to zero at infinity and the strongly dispersive case where the phase velocity vanishes at the origin and goes to infinity at infinity. In the former case, the nonlinear hyperbolic effects dominate for large data, leading to the possibility of shock formation though the dispersive effects manifest for small initial data where scattering is possible. In the latter case, finite time blow-up is possible in the focusing case but not the shock formation. In the defocusing case global existence and scattering is expected in the energy subcritical case, while finite time blow-up is expected in the energy supercritical case. We establish rigorously the existence of shocks with blow-up time and location being explicitly computed in the weakly dispersive case, while most of the results on the strongly dispersive case are derived via numerical simulations, for large solutions. Moreover, the shock formation result can be extended to the weakly dispersive equation with some generalized nonlinearity. We will also comment briefly on the BBM versions of those equations.

math.AP↗