4,907 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
The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit
In the present paper we study the following scaled nonlinear Schr\"odinger
equation (NLS) in one space dimension: This equation represents a nonlinear Schr\"odinger
equation with a spatially concentrated nonlinearity. We show that in the limit
, the weak (integral) dynamics converges in to
the weak dynamics of the NLS with point-concentrated nonlinearity: where is the
laplacian with the nonlinear boundary condition at the origin
and
. The convergence occurs for every if and for every otherwise. The same
result holds true for a nonlinearity with an arbitrary number of
concentration pointsComment: 10 page
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
Characterisation of flow dynamics within and around an isolated forest, through measurements and numerical simulations
The case study of ‘Bosco Fontana’, a densely-vegetated forest located in the north of Italy, is analysed both
experimentally and numerically to characterise the internal ventilation of a finite forest with a vertically
non-homogeneous canopy. Measurements allow for the evaluation of the turbulent exchange across the forest
canopy. The case study is then reproduced numerically via a two-dimensional RANS simulation, successfully
validated against experimental data. The analysis of the internal ventilation leads to the identification of
seven regions of motion along the predominate-wind direction, for whose definition a new in-canopy stability
parameter was introduced. In the vertical direction, the non-homogeneity of the canopy leads to the separation
of the canopy layer into an upper foliage layer and a lower bush layer, characterised respectively by an
increasing streamwise velocity and turbulence intensity, and a weak backflow. The conclusions report an
improved description of the dynamic layer and regions of motion presented in the literature
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
Nurses’ behavior regarding pain treatment in an emergency department: A single-center observational study
Purpose: The aim of this prospective study was to assess the behavior of emergency department (ED) nurses with regard to pain and their role in pain management in a real-life clinical setting. Methods: A total of 509 consecutive patients were enrolled during a 6-week period. A case-report form was used to collect data on nurses’ approaches to pain, time to analgesia provision, and patient-perceived quality of analgesia. Results: Triage nurses actively inquired about pain in almost every case, but they did not estimate pain intensity in a third of patients. In the majority of cases, triage nurses did not report pain-related findings to the physician, who was the only professional that could prescribe analgesia to patients. The assignment of the color-coding of triage by nurses appears to be related to the perceived severity of the clinical case and a more comprehensive evaluation of pain. More than half of patients were at least fairly satisfied with analgesia. Conclusion: Pain is increasingly screened during triage, but its comprehensive assessment and management still lack systematic application. We believe that further education and implementation of analgesia protocols may empower nurses to manage ED patients’ pain more effectively and in a more timely manner
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
The Combined Impact of Canopy Stability and Soil NOx Exchange on Ozone Removal in a Temperate Deciduous Forest
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