4,717 research outputs found
Constrained energy minimization and orbital stability for the NLS equation on a star graph
We consider a nonlinear Schr\"odinger equation with focusing nonlinearity of
power type on a star graph , written as , where is the selfadjoint operator
which defines the linear dynamics on the graph with an attractive
interaction, with strength , at the vertex. The mass and energy
functionals are conserved by the flow. We show that for the energy at
fixed mass is bounded from below and that for every mass below a critical
mass it attains its minimum value at a certain \hat \Psi_m \in H^1(\GG)
, while for there is no minimum. Moreover, the set of minimizers has
the structure {\mathcal M}={e^{i\theta}\hat \Psi_m, \theta\in \erre}.
Correspondingly, for every there exists a unique
such that the standing wave is orbitally
stable. To prove the above results we adapt the concentration-compactness
method to the case of a star graph. This is non trivial due to the lack of
translational symmetry of the set supporting the dynamics, i.e. the graph. This
affects in an essential way the proof and the statement of
concentration-compactness lemma and its application to minimization of
constrained energy. The existence of a mass threshold comes from the
instability of the system in the free (or Kirchhoff's) case, that in our
setting corresponds to \al=0.Comment: 26 pages, 1 figur
Variational properties and orbital stability of standing waves for NLS equation on a star graph
We study standing waves for a nonlinear Schr\"odinger equation on a star
graph {} i.e. half-lines joined at a vertex. At the vertex an
interaction occurs described by a boundary condition of delta type with
strength . The nonlinearity is of focusing power type. The
dynamics is given by an equation of the form , where is the Hamiltonian operator which
generates the linear Schr\"odinger dynamics. We show the existence of several
families of standing waves for every sign of the coupling at the vertex for
every . Furthermore, we determine the ground
states, as minimizers of the action on the Nehari manifold, and order the
various families. Finally, we show that the ground states are orbitally stable
for every allowed if the nonlinearity is subcritical or critical, and
for otherwise.Comment: 36 pages, 2 figures, final version appeared in JD
Willingness to pay more for value-added pomegranate juice (Punica granatum L.): An open-ended contingent valuation.
A Quantum Model of Feshbach Resonances
We consider a quantum model of two-channel scattering to describe the
mechanism of a Feshbach resonance. We perform a rigorous analysis in order to
count and localize the energy resonances in the perturbative regime, i.e., for
small inter-channel coupling, and in the non-perturbative one. We provide an
expansion of the effective scattering length near the resonances, via a
detailed study of an effective Lippmann-Schwinger equation with
energy-dependent potential.Comment: 29 pages, pdfLaTe
Fast solitons on star graphs
We define the Schr\"odinger equation with focusing, cubic nonlinearity on
one-vertex graphs. We prove global well-posedness in the energy domain and
conservation laws for some self-adjoint boundary conditions at the vertex, i.e.
Kirchhoff boundary condition and the so called and boundary
conditions. Moreover, in the same setting we study the collision of a fast
solitary wave with the vertex and we show that it splits in reflected and
transmitted components. The outgoing waves preserve a soliton character over a
time which depends on the logarithm of the velocity of the ingoing solitary
wave. Over the same timescale the reflection and transmission coefficients of
the outgoing waves coincide with the corresponding coefficients of the linear
problem. In the analysis of the problem we follow ideas borrowed from the
seminal paper \cite{[HMZ07]} about scattering of fast solitons by a delta
interaction on the line, by Holmer, Marzuola and Zworski; the present paper
represents an extension of their work to the case of graphs and, as a
byproduct, it shows how to extend the analysis of soliton scattering by other
point interactions on the line, interpreted as a degenerate graph.Comment: Sec. 2 revised; several misprints corrected; added references; 32
page
On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles
We consider a non relativistic quantum system consisting of heavy and
light particles in dimension three, where each heavy particle interacts with
the light ones via a two-body potential . No interaction is assumed
among particles of the same kind. Choosing an initial state in a product form
and assuming sufficiently small we characterize the asymptotic
dynamics of the system in the limit of small mass ratio, with an explicit
control of the error. In the case K=1 the result is extended to arbitrary
. The proof relies on a perturbative analysis and exploits a
generalized version of the standard dispersive estimates for the
Schr\"{o}dinger group. Exploiting the asymptotic formula, it is also outlined
an application to the problem of the decoherence effect produced on a heavy
particle by the interaction with the light ones.Comment: 38 page
Acute nephrotoxicity of NSAID from the foetus to the adult
NSAIDs are generally considered to be safe and well tolerated, but, even with the advent of selective COX-2 inhibitors, nephrotoxicity remains a concern. An impaired renal perfusion caused by the inhibition of prostaglandin synthesis is claimed like the more frequent cause of an acute renal failure due to NSAIDs, while a chronic interstitial nephritis or an analgesic nephropathy are believed the causes of a chronic renal failure. The real incidence of renal side effects of NSAIDs is still unclear and it differs between the age of the patients and the reports present in the literature. The occurrence of renal side effects following prenatal exposure to NSAIDs seems to be rare considering the large number of pregnant woman treated with indomethacin or other prostaglandin inhibitors. NSAID-related nephrotoxicity remains an important clinical problem in the newborns, in whom the functionally immature kidney may exert a significant effect on the disposition of the drugs. Instead, nephrotoxicity is a rare event in children and the risk is lower than adults. In healthy adult patients the incidence of renal adverse effects is very low, less than 1%. The risk increased with age. The elderly are at higher risk, and it is correlated at the presence of pretreatment renal disease, hypovolemia due to use of diuretics, diabetes, congestive heart failure or alteration of NSAID pharmacokinetics
Struggling with COVID-19 in Adult Inborn Errors of Immunity Patients: A Case Series of Combination Therapy and Multiple Lines of Therapy for Selected Patients
Background: The SARS-CoV-2 infection is now a part of the everyday lives of immunocompromised patients, but the choice of treatment and the time of viral clearance can often be complex, exposing patients to possible complications. The role of the available antiviral and monoclonal therapies is a matter of debate, as are their effectiveness and potential related adverse effects. To date, in the literature, the amount of data on the use of combination therapies and on the multiple lines of anti-SARS-CoV-2 therapy available to the general population and especially to inborn error of immunity (IEI) patients is small. Methods: Here, we report a case series of five adult IEI patients managed as inpatients at three Italian IEI referral centers (Rome, Treviso, and Cagliari) treated with combination therapy or multiple therapeutic lines for SARS-CoV-2 infection, such as monoclonal antibodies (mAbs), antivirals, convalescent plasma (CP), mAbs plus antiviral, and CP combined with antiviral. Results: This study may support the use of combination therapy against SARS-CoV-2 in complicated IEI patients with predominant antibody deficiency and impaired vaccine response
COVID-19 case fatality ratio of Latino America countries with temperate climate partially follows european and oceania trends according to seasonal change
The objective of our study is, therefore, to verify whether the trend of the pandemic regarding the lethality of the virus is similar in Argentina and Chile to that which emerged in the temperate countries of Europe and Oceania. The CFRs were derived from the John Hopkins University database. To check the trend of the Case Fatality Ratio and Argentina, Chile we calculated this index on the same dates in which it was calculated for comparison in European countries and in Australia and New Zealand: i.e., May 6th and from May 6th to the September 21st. We continued comparing the other countries of the southern hemisphere, recalculating the CFR as of 11th November. For comparing a period of year homogeneous, late spring, we calculate the change if CFR from 20th March to 15th April in the North Hemisphere. Our study's results seem to confirm in Latin America a possible influence of the climate and the changing of the seasons in the lethality of the virus. For the same exceptions, it is evident that the study shows that this factor is not the only one nor probably the most important. The obvious exception concerns Argentina, which does not show any summer improvement of the CFR, unfortunately; for this, nation-specific data are not available to verify if the trend is homogeneous in the different climates that the vast territory presents. Other very important factors come into play, among which the diffusivity of the virus also seems to play a role
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