pinecone/core-2020-05-10-deduplication huggingface dataset:
A nonlinear problem for the Laplace equation with a degenerating Robin condition

We investigate the behavior of the solutions of a mixed problem for the Laplace equation in a domain ?. On a part of the boundary ??, we consider a Neumann condition, whereas in another part, we consider a nonlinear Robin condition, which depends on a positive parameter ? in such a way that for ??=?0 it degenerates into a Neumann condition. For ? small and positive, we prove that the boundary value problem has a solution u(?,?). We describe what happens to u(?,?) as ??0 by means of representation formulas in terms of real analytic maps. Then, we confine ourselves to the linear case, and we compute explicitly the power series expansion of the solutionpublishersversionPeer reviewe
Fully non-homogeneous problem of two-dimensional second grade fluids

This article studies the solutions of a two-dimensional grade-two fluid model
with a fully non-homogeneous boundary condition for velocity u. Compared to
problems with a homogeneous or tangential boundary condition, studied by many
authors , we must add a boundary condition, otherwise the problem is no longer
well-posed. We propose two conditions on z = curl (u -- $\alpha$$\Delta$u),
which differ according to the regularity of z, on the portion of
$\partial$$\Omega$ where $\alpha$u. n \textless{} 0. Following the approach of
V. Girault and L.R. Scott in the tangential boundary case, we split the problem
into a system with a generalized Stokes problem and a transport problem. But,
compared to the study of these authors, we are now led to solve transport
problems with boundary conditions. In two previous articles, we studied these
transport problems. The results obtained in these articles allow us, by a
fixed-point argument, to establish existence of the solutions for the fully
non-homogeneous grade-two problem. Uniqueness requires the boundary condition
with z in H 1
Two different fractional Stefan problems which are convergent to the
  same classical Stefan problem

Two fractional Stefan problems are considered by using Riemann-Liouville and
Caputo derivatives of order $\alpha \in (0,1)$ such that in the limit case
($\alpha =1$) both problems coincide with the same classical Stefan problem.
For the one and the other problem, explicit solutions in terms of the Wright
functions are presented. We prove that these solutions are different even
though they converge, when $\alpha \nearrow 1$, to the same classical solution.
This result also shows that some limits are not commutative when fractional
derivatives are used.Comment: 14 pages, 1 figur
On Two Topologies that were suggested by Zeeman

The class of Zeeman topologies on spacetimes in the frame of relativity
theory is considered to be of powerful intuitive justification, satisfying a
sequence of properties with physical meaning, such as the group of
homeomorphisms under such a topology is isomorphic to the Lorentz group and
dilatations, in Minkowski spacetime, and to the group of homothetic symmetries
in any curved spacetime. In this article we focus on two distinct topologies
that were suggested by Zeeman as alternatives to his Fine topology, showing
their connection with two orders: a timelike and a (non-causal) spacelike one.
For the (non-causal) spacelike order, we introduce a partition of the null cone
which gives the desired topology invariantly from the choice of the hyperplane
of partition. In particular, we observe that these two orders induce topologies
within the class of Zeeman topologies, while the two suggested topologies by
Zeeman himself are intersection topologies of these two order topologies
(respectively) with the manifold topology. We end up with a list of open
questions and a discussion, comparing the topologies with bounded against those
with unbounded open sets and their possible physical interpretation
Existence and concentration of positive ground state solutions for
  nonlinear fractional Schr\"odinger-Poisson system with critical growth

In this paper, we study the following fractional Schr\"{o}dinger-Poisson
system involving competing potential functions \begin{equation*} \left\{
  \begin{array}{ll}
  \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u=K(x)f(u)+Q(x)|u|^{2_s^{\ast}-2}u, &
\hbox{in $\mathbb{R}^3$,}
  \varepsilon^{2t}(-\Delta)^t\phi=u^2,& \hbox{in $\mathbb{R}^3$,}
  \end{array} \right. \end{equation*} where $\varepsilon>0$ is a small
parameter, $f$ is a function of $C^1$ class, superlinear and subcritical
nonlinearity, $2_s^{\ast}=\frac{6}{3-2s}$, $s>\frac{3}{4}$, $t\in(0,1)$, $V(x)$
$K(x)$ and $Q(x)$ are positive continuous function. Under some suitable
assumptions on $V$, $K$ and $Q$, we prove that there is a family of positive
ground state solutions with polynomial growth for sufficiently small
$\varepsilon>0$, of which it is concentrating on the set of minimal points of
$V(x)$ and the sets of maximal points of $K(x)$ and $Q(x)$. The methods are
based on the Nehari manifold, arguments of Brezis-Nirenberg and concentration
compactness of P. L. Lions
ASYMPTOTIC BEHAVIOUR OF CURVED RODS BY THE UNFOLDING METHOD

International audienceWe consider in this work general curved rods with a circular cross-section of radius . Our aim is to study the asymptotic behaviour of such rods as $\delta\to 0$, in the framework of the linear elasticity according to the unfolding method. It consists in giving some decompositions of the displacements of such rods, and then in passing to the limit in a xed domain. A first decomposition concerns the elementary displacements of a curved rod which characterize its translations and rotations, and the residual displacements related to the deformation of the cross-section. The second decomposition concerns the displacements of the middle-line of the rod. We prove that such a displacement can be written as the sum of an inextensional displacement and of an extensional one. An extensional displacement will modify the length of the middle-line, while an inextensional displacement will not change this length in a rst approximation. We show that the $H1$-norm of an inextensional displacement is of order 1, while that of an extensional displacement is in general, of order $\delta$ . A priori estimates are established and convergence results as $\delta \to 0$, are given for the displacements. We give their unfolded limits, as well as the unfolded limits of the strain and stress tensors. To prove the convergence of the strain tensor, the introduction of elementary and residual displacements appears as essential. By passing to the limit as $\delta\to 0$ in the linearized system of the elasticity, we obtain on the one hand, a variational problem that is satis ed by the limit extensional displacement, and on the other hand, a variational problem coupling the limit of inextensional displacements and the limit of the angle of torsion
On similarity solutions for boundary layer flows with prescribed heat
  flux

This paper is concerned with existence, uniqueness and behavior of the
solutions of the autonomous third order nonlinear differential equation
$f'''+(m+2)ff''-(2m+1)f'^2=0$ on $\mathbb{R}^+$ with the boundary conditions
$f(0)=-\gamma$, $f'(\infty)=0$ and $f''(0)=-1$. This problem arises when
looking for similarity solutions for boundary layer flows with prescribed heat
flux. To study solutions we use some direct approach as well as blowing-up
coordinates to obtain a plane dynamical system.Comment: v2: new page-settin
Essential spectrum in vibrations of thin shells in membrane
  approximation. Propagation of singularities

The spectral problem of thin elastic shells in membrane approximation does
not satisfy the classical properties of compactness and so there exists an
essential spectrum. In the first part, we propose to determinate this spectrum
and the weakness directions in the shell. We particularly study the case of
homogeneous and isotropic shells with some examples. In the second part, we
consider an elementary model problem to study the propagation of singularities
and their reflections at the boundary of the domain. In the last, we study the
problem of propagation for an isotropic cylindrical shell and we show that the
equation of propagation does not depend on the Poisson coefficient
The Forced Non-Linear Schroedinger Equation with a Potential on the
  Half-Line

In this paper we prove that the initial-boundary value problem for the forced
non-linear Schroedinger equation with a potential on the half-line is locally
and (under stronger conditions) globally well posed, i.e. that there is a
unique solution that depends continuously on the force at the boundary and on
the initial data. We allow for a large class of unbounded potentials. Actually,
for local solutions we have no restriction on the grow at infinity of the
positive part of the potential, and for global solutions very mild assumptions
that allow, for example, for exponential grow.Comment: 23 page
Derivation of macroscopic equations for individual cell-based models. A formal approach

In this paper we review the theory of cells (particles) that evolve according to a dynamics determined by friction and that interact between themselves by means of suitable potentials. We derive by means of elementary arguments several macroscopic equations that describe the evolution of cell density. Some new results are also obtained — a formal derivation of a limit equation in the case of attractive potential as well as in the case of repulsive potential with a hard-core part are presented Finally, we discuss the possible relevance of those results within the framework of individual cell-based models. Several classes of potentials, including hard-core, repulsive and potentials with attractive parts are discussed. The effect of noise terms in the equation is also considered.\u
New anisotropic models from isotropic solutions

We establish an algorithm that produces a new solution to the Einstein field
equations, with an anisotropic matter distribution, from a given seed isotropic
solution. The new solution is expressed in terms of integrals of known
functions, and the integration can be completed in principle. The applicability
of this technique is demonstrated by generating anisotropic isothermal spheres
and anisotropic constant density Schwarzschild spheres. Both of these solutions
are expressed in closed form in terms of elementary functions, and this
facilitates physical analysis.Comment: 23 pages, To appear in Math. Meth. Appl. Sc
Generating potentials via difference equations

The condition for pressure isotropy, for spherically symmetric gravitational
fields with charged and uncharged matter, is reduced to a recurrence equation
with variable, rational coefficients. This difference equation is solved in
general using mathematical induction leading to an exact solution to the
Einstein field equations which extends the isotropic model of John and Maharaj.
The metric functions, energy density and pressure are well behaved which
suggests that this model could be used to describe a relativistic sphere. The
model admits a barotropic equation of state which approximates a polytrope
close to the stellar centre.Comment: 11 pages, To appear in Math. Meth. Appl. Sc
Asymptotics for steady state voltage potentials in a bidimensional highly contrasted medium with thin layer

International audienceWe study the behavior of steady state voltage potentials in two kinds of bidimensional media composed of material of complex permittivity equal to 1 (respectively α) surrounded by a thin membrane of thickness h and of complex permittivity α (respectively 1). We provide in both cases a rigorous derivation of the asymptotic expansion of steady state voltage potentials at any order as h tends to zero, when Neumann boundary condition is imposed on the exterior boundary of the thin layer. Our complex parameter α is bounded but may be very small compared to 1, hence our results describe the asymptotics of steady state voltage potentials in all heterogeneous and highly heterogeneous media with thin layer. The asymptotic terms of the potential in the membrane are given explicitly in local coordinates in terms of the boundary data and of the curvature of the domain, while these of the inner potential are the solutions to the so-called dielectric formulation with appropriate boundary conditions. The error estimates are given explicitly in terms of h and α with appropriate Sobolev norm of the boundary data. We show that the two situations described above lead to completely different asymptotic behaviors of the potentials
A continuum theory for first-order phase transitions based on the balance of structure order

First-order phase transitions are modelled by a non-homogeneous, time-dependent scalar valued order parameter or phase field. The time dependence of the order parameter is viewed as arising from a balance law for the structure order. The gross motion is disregarded and hence the body is regarded merely as a heat conductor. Compatibility of the constitutive functions with thermodynamics is exploited by expressing the second law through the classical Clausius-Duhem inequality. First a model for conductors without memory is set up and the order parameter is shown to satisfy a maximum theorem. Next, heat conductors with memory are considered. Different evolution problems are established through a system of differential equations whose form is related to the way the memory property is represented
High efficiency and high linearity power amplifier design

The optimum high-frequency Class-F loading conditions are inferred, accounting for the effects of actual output device behavior, and deriving useful charts for an effective\ud
design. The important role of the biasing point selection is stressed, demonstrating that it must\ud
be different from the Class-B theoretical one to get the expected improvement. The IMD behavior of the Class-F amplifier is presented and the large-signal sweet-spot origin in the\ud
IMD output characteristics is discussed, together with possible strategies to improve intermodulation\ud
distortion performances. The control of the sweet spot position is demonstrated\ud
via proper terminating impedances, both at fundamental and harmonic frequencies and low frequencies
Design of a 4.2-5.4 GHz differential LC VCO using 0.35 mu m SiGeBiCMOS technology for IEEE 802.11a applications

In this paper, a 4.2-5.4 GHz, -Gm LC voltage controlled oscillator (VCO) for IEEE 802.11a standard is presented. The circuit is designed with AMS 0.35 mu m SiGe BiCMOS process that includes high-speed SiGe Heterojunction Bipolar Transistors (HBTs). According to post-layout simulation results, phase noise is -110.7 dBc/Hz at 1 MHz offset from 5.4 GHz carrier frequency and -113.4 dBc/Hz from 4.2 GHz carrier frequency. A linear, 1200 MHz tuning range is obtained from the simulations, utilizing accumulation-mode varactors. Phase noise was also found to be relatively low because of taking advantage of differential tuning concept. Output power of the fundamental frequency changes between 4.8 dBm and 5.5 dBm depending on the tuning voltage. Based on the simulation results, the circuit draws 2 mA without buffers and 14.5 mA from 2.5 V supply including buffer circuits leading to a total power dissipation of 36.25 mW. The circuit layout occupies an area of 0.6 mm(2) on Si substrate, including DC and RF pads
Double U-slots patch antenna for tri-band wireless systems

File shown is the pre-print version of the published paper, with the title "Connected u-slots pathch antenna for WiMAX applications"ABSTRACT: A compact microstrip patch antenna with two U-slots shape is presented.\ud
Detailed simulation and experimental investigation are conducted to understand the behavior\ud
of the two U-slots. The proposed antenna generates three resonant frequencies at 2.7, 3.3, and\ud
5.3 GHz. It can, therefore, be used in Worldwide Interoperability for Microwave Access compliant\ud
communication equipment. The proposed antenna has two U-slot shaped and two\ud
bridge elements to connect both shapes together to adapt the structure to the desired interest\ud
operating frequency. A comprehensive parametric study has been applied to understand the\ud
effect of each U-slot on the antenna’s performance. Moreover, the current distribution for the\ud
three bands is investigated to give further understanding of the antenna behavior. The proposed\ud
antenna is verified experimentally and the simulated and measured results are in good\ud
agreement
Synthesis of Frequency-Independent Phase Shifters Using Negative Group Delay Active Circuit

International audienceThis article describes a synthesis method dedicated to the design of frequency-independent phase shifters (PSs). This innovative PS structure consists in a transmission line cascaded with a negative group delay (NGD) active circuit so that the absolute constant group delays generated by both of them are identical but of opposite signs. So, in principle, it exhibits a constant overall phase and a group delay close to zero. Broadband linear positive phase slopes are obtained through use of an NGD active circuit whose characteristics are recalled prior to the extraction of the PS synthesis relations. The design and simulations of a PS of compact size are reported. The experimental results confirm the expected frequency-independent transmission-phase value of 145° with an insertion gain of 2 dB over a 160% relative frequency band. At last, future prospects allowed by the specific properties of this PS are presente
Cost-effective global surrogate modeling of planar microwave filters using multi-fidelity Bayesian support vector regression

A computationally efficient method is presented for setting up accurate Bayesian support vector regression (BSVR) models of the highly nonlinear |S21| responses of planar microstrip filters using substantially reduced finely discretized training data (compared to traditional design of experiments techniques). Inexpensive coarse-discretization full-wave simulations are exploited in conjunction with the sparseness property of BSVR to identify the regions of the input space requiring denser sampling. The proposed technique allows for substantial reduction (by up to 51%) of the computational expense necessary to collect the finely discretized training data, with negligible loss in predictive accuracy. The accuracy of the reduced-data BSVR models is confirmed by their use within a space mapping optimization algorithmIcelandic Centre for Research (RANNIS) Grants 110034021 and 120016021.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-047Xhb201
Printed monopole antenna with tunable band-notched characteristic for use in mobile and ultra-wide band applications

YesA tunable band-notch printed monopole antenna is presented, exhibiting a wide impedance bandwidth from 1.5 to 5.5 GHz with good impedance matching (VSWR ≤ 2) and a tunable rejected frequency band from 2.38 to 3.87 GHz.  The band-notching is achieved by adding an inner chorded crescent element within a driven element of a similar shape. By varying the value of the varactor which is placed between the inner and outer arcs, the desired variable rejected can be obtained. Simulated and measured results show wide impedance bandwidth with a tunable band notch, stable radiation patterns, and consistent nearly constant gain. The antenna is suitable for mobile and portable applications
Semi fractal three leaf clover-shaped CPW antenna for triple band operation

This article presents a unique and compact coplanar waveguide (CPW) antenna that exhibits triband operation with circular polarization. The single antenna was designed to operate simultaneously in the following bands: WiMAX (3.3–3.6 GHz), wireless local area network (WLAN) (5.15–5.825 GHz), ITS (5.795–6.400 GHz), and ITU-R (7.725–8.5 GHz). The realization of the triband antenna was achieved by using two semi fractal ring patches resembling the shape of a three leaf clover, and by introducing a pair of symmetrical L-shaped slits in its ground plane. The antenna’s physical parameters were investigated to fully understand their affect on the antenna’s performance. The salient parameters obtained from this analysis enabled the optimization of the antenna’s overall characteristics.The design concept was confirmed by fabricating the antenna prototype and measuring its characteristics. The proposed antenna has dimensions of 20 3 20 3 1 mm3. Measured results show the antenna exhibits circular polarization in WiMAX and ITU-R bands, and linear polarization in the WLAN band. The antenna radiates omnidirectionally in the H-plane, and approximately bidirectionally in the E-plane. In addition, the antenna presents stable gain over the triband
Reduced-cost microwave filter modeling using a two-stage Gaussian process regression approach

A technique for the reduced-cost modeling of microwave filters is presented.
Our approach exploits variable-fidelity electromagnetic (EM) simulations, and Gaussian process
regression (GPR) carried out in two stages. In the first stage of the modeling process, a
mapping between EM simulation filter models of low and high fidelity is established. The mapping
is subsequently used in the second stage, making it possible for the final surrogate model
to be constructed from training data obtained using only a fraction of the number of highfidelity
simulations normally required. As demonstrated using three examples of microstrip
filters, the proposed technique allows us to reduce substantially (by up to 80%) the central
processing unit (CPU) cost of the filter model setup, as compared to conventional (single-stage)
GPR—the benchmark modeling method in this study. This is achieved without degrading the
model generalization capability. The reliability of the two-stage modeling method is demonstrated
through the successful application of the surrogates to surrogate-based filter design
optimization.Icelandic Centre for Research (RANNIS) Grants 120016021 and 13045051.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-047X2016-06-30hb201
Synthesis of slow-wave structures based on capacitive-loaded lines through aggressive space mapping (ASM)

This article is focused on the automated synthesis of slow-wave structures based on microstrip lines loaded with patch capacitors. Thanks to the presence of the shunt capacitors, the effective capacitance of the line is enhanced, and the phase velocity of the structure can be made significantly smaller than the one of the unloaded line. The target is to achieve the layout of the slow-wave structure able to provide the required slow-wave ratio, characteristic (Bloch) impedance and electrical length (i.e., the usual specifications in the design of slow-wave transmission lines). To this end, a two-step synthesis method, based on the aggressive space mapping (ASM) algorithm, is proposed for the first time. Through the first ASM algorithm, the circuit schematic providing the target specifications is determined. Then, the second ASM optimizer is used to generate the layout of the structure. To illustrate the potential of the proposed synthesis method, three application examples are successfully reported. The two-step ASM algorithm is able to provide the layout of the considered structures from the required specifications, without the need of an external aid in the proces