Search results for "scattering [p p]"
showing 10 items of 39 documents
Determining a Random Schrödinger Operator : Both Potential and Source are Random
2020
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We then derive two unique recovery results in determining the rough strengths of the random source and the random potential, by using the corresponding far-field data. The first recovery result shows that a single realization of the passive scattering measurements uniquely recovers the rough strength of the random source. The second one shows that, by a single realization of the backscattering data, the rough strength of the random potential can be recovered…
Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation
2019
International audience; The inverse scattering approach for the defocusing Davey–Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.
Explicit Characterization of Inclusions in Electrical Impedance Tomography
2001
In electrical impedance tomography one seeks to recover the spatial conductivity distribution inside a body from knowledge of the Neumann--Dirichlet map. In many practically relevant situations the conductivity is smooth apart from some inhomogeneities where the conductivity jumps to a higher or lower value. An explicit characterization of these inclusions is developed in this paper. To this end a class of dipole-like indicator functions is introduced, for which one has to check whether their boundary values are contained in the range of an operator determined by the measured Neumann--Dirichlet map. It is shown that this holds true if and only if the dipole singularity lies inside the inhom…
Proposal of Up-to-Date Standards on Methods of Measuring Noise Parameters of Microwave Transistors
1994
One of the most interesting topics for microrwave community is the characterization of low-noise transistors. After so many years, the Standards suggested by IEEE in 1960 are considered obsolete by the experimenters. A new methodology is here proposed as a standard. To support this proposal, an original measuring system for the complete characterization of microwave transistors in terms of noise, gain and scattering parameters from noise figure measurements only is presented.
Role of Levinson’s theorem in neutron-deuteron quartetS-wave scattering
1990
The real part of the phase shift for elastic neutron-deuteron scattering in the quartet {ital S} wave channel, as calculated with the exact three-body theory, assumes at threshold the value {pi} if normalized to zero at infinity; that is, it does not comply with the expectations raised by a naive application of Levinson's theorem since no bound state exists in this channel. A description of this situation on an equivalent two-body level via a potential, constructed by means of the Marchenko inverse scattering theory, necessitates the introduction of a fictitious bound state. This predominantly attractive, equivalent local potential can be related via supersymmetry to a strictly phase equiva…
Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method
1999
A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the corresponding soliton solutions that can be constructed using the Belinskii-Zakharov inverse-scattering technique is determined.
Full characterization of low-noise HEMTs using only noise figure measurements
1993
A method for the complete characterization of microwave transistors in terms of noise, gain and scattering parameters using a computer-controlled noise figure measuring set-up only is presented. Selection of the optimum measuring conditions, all the steps of the experimental procedure, the data collecting and processing to derive all the parameters, are fully driven by an original (unpublished) software, even without the presence of an (unskilled) operator. Results are presented about the complete characterization of a series of ten pseudomorphicHEMTs in the 8-16 GHz range. The S-parameters are also compared with those measured by an ANA.
Noise and gain performance of PSA transistor series for personal communication systems vs. emitter number and operating conditions
1995
The booming market of communication system applications in the low microwave range put greater demands on the component performance at lower supply voltages and limited current consumption, as well as on production cost and integration level. In this work, we present the results of an extensive characterization activity carried out on several advanced polysilicon bipolar transistors as requested by the manufacturer. The devices were grouped according to their emitter finger number and were characterized over the 2-6 GHz frequency range in terms of noise, gain and scatterino parameters at different bias conditions. A comparative analysis has been performed to explore how the transistor perfo…
Free boundary methods and non-scattering phenomena
2021
We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point. These facts are proved by invoking results from t…
Nonrecursive multiple shock formation via four-wave mixing: theory and experiment
2002
We show theoretically and experimentally that a beat signal propagating along a normally dispersive fiber can trigger the formation of multiple shocks. This phenomenon critically depends on the input frequency separation and power of the beat signal.