arXiv subjects

K. Silva

Publications and source records attributed to K. Silva.

5 recordsLinked to original sources

arXiv2026

A unified treatment of degenerate nonlocal elliptic problems

We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having sublinear or asymptotically linear growth. By combining the study of a suitable auxiliary problem and fixed-point techniques with careful parameter analysis, we establish existence, non-existence, and multiplicity results for positive solutions. Our method reveals sharp parameter thresholds and provides a comprehensive description of the solution set. Finally, for powerlike nonlinearities (including superlinear and singular ones) we provide a more direct approach, based on homogeneity.

math.AP↗

arXiv2023

On a Perturbed Critical p-Kirchhoff-Type Problem

In this paper we deal with a stationary non-degenerate $p-$Kirchhoff type problem with critical non-linearity and a subcritical parametrized perturbation. We work on bounded domains of the Euclidean space, without any restriction on the dimension or on $p>0$. Variational methods will be utilized in combination with an analysis of the fibering functions of the energy functional, in order to obtain ground state solutions, as well as Mountain Pass solutions, depending on the values of the parameter. A local analysis of the energy functional will allow us to obtain non-trivial solutions even beyond the extremal parameter.

math.AP↗

arXiv2021

Dielectric Strength of Noble and Quenched Gases for High Pressure Time Projection Chambers

Dielectric breakdown strength is one of the critical performance metrics for gases and mixtures used in large, high pressure gas time projection chambers. In this paper we experimentally study dielectric breakdown strengths of several important time projection chamber working gases and gas-phase insulators over the pressure range 100 mbar to 10 bar, and gap sizes ranging from 0.1to 10 mm. Gases characterized include argon, xenon, CO2, CF4, and mixtures 90-10 argon-CH4,90-10 argon-CO2and 99-1 argon-CF4. We develop a theoretical model for high voltage breakdown based on microphysical simulations that use PyBoltz electron swarm Monte Carlo results as input to Townsend- and Meek-like discharge criteria. This model is shown to be highly predictive at high pressure, out-performing traditional Paschen-Townsend and Meek-Raether models significantly. At lower pressure-times-distance, the Townsend-like model is an excellent description for noble gases whereas the Meek-like model provides a highly accurate prediction for insulating gases.

physics.ins-det↗

arXiv2020

On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension

The present paper deals with a parametrized Kirchhoff type problem involving a critical nonlinearity in high dimension. Existence, non existence and multiplicity of solutions are obtained under the effect of a subcritical perturbation by combining variational properties with a careful analysis of the fiber maps of the energy functional associated to the problem. The particular case of a pure power perturbation is also addressed. Through the study of the Nehari manifolds we extend the general case to a wider range of the parameters.

math.AP↗

arXiv2019

Tips and Tricks in linear imaging polarimetry of extended sources with FORS2 at the VLT

Context: Polarimetry is a very powerful tool to uncover various properties of astronomical objects that remain otherwise hidden in standard imaging or spectroscopic observations. However, the reliable measurement of the low polarization signal from astronomical sources requires a good control of spurious instrumental polarization induced by the various components of the optical system and the detector. Aims: We perform a detailed multi-wavelength calibration study of the FORS2 instrument at the VLT operating in imaging polarimetric mode (IPOL) to characterize the spatial instrumental polarization that may affect the study of extended sources. Methods: We use imaging polarimetry of a) high signal-to-noise blank fields BVRI observations during full-moon, when the polarization is expected to be constant across the field-of-view and deviations originate from the instrument and b) a crowded star cluster in broad-band RI and narrow-band H{\alpha} filters, where individual polarization values of each star across the field can be measured. Results: We find an instrumental polarization pattern that increases radially outwards from the optical axis of the instrument reaching up to 1.4% at the edges, depending on the filter. Our results are well approximated by an elliptical paraboloid down to less than {\sim0.05\%} accuracy,and {\sim0.02\%} when using non-analytic fits. We present 2D maps to correct for this spurious instrumental polarization. We also give several tips and tricks to analyze polarimetric measurements of extended sources. Conclusions: FORS2 is a powerful instrument allowing to map the linear polarimetry of extended sources. We present and discuss a methodology to measure the polarization of such sources, and to correct for the spatial polarization induced in the optical system. This methodology could be applied to polarimetric measurements using other dual-beam polarimeters.

astro-ph.IM↗