14,860 research outputs found
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
In this paper we study the semiclassical limit of the Schr\"odinger equation.
Under mild regularity assumptions on the potential which include
Born-Oppenheimer potential energy surfaces in molecular dynamics, we establish
asymptotic validity of classical dynamics globally in space and time for
"almost all" initial data, with respect to an appropriate reference measure on
the space of initial data. In order to achieve this goal we prove existence,
uniqueness and stability results for the flow in the space of measures induced
by the continuity equation.Comment: 34 p
MACRO constraints on violation of Lorentz invariance
The energy spectrum of neutrino-induced upward-going muons in MACRO has been
analysed in terms of relativity principles violating effects, keeping standard
mass-induced atmospheric neutrino oscillations as the dominant source of
transitions. The data disfavor these exotic
possibilities even at a sub-dominant level, and stringent 90% C.L. limits are
placed on the Lorentz invariance violation parameter at = 0 and at = 1. These limits can also be
re-interpreted as upper bounds on the parameters describing violation of the
Equivalence Principle.Comment: 3 pages, 2 figures. Presented at NOW 2006: Neutrino Oscillation
Workshop, Conca Specchiulla, Otranto, Italy, Sep 2006. To be published in
Nucl. Phys. B (Proc. Suppl.
Infinitely many periodic solutions for a class of fractional Kirchhoff problems
We prove the existence of infinitely many nontrivial weak periodic solutions
for a class of fractional Kirchhoff problems driven by a relativistic
Schr\"odinger operator with periodic boundary conditions and involving
different types of nonlinearities
Multiple solutions for a fractional -Laplacian equation with sign-changing potential
We use a variant of the fountain Theorem to prove the existence of infinitely
many weak solutions for the following fractional p-Laplace equation
(-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=f(x,u) in R^N, where ,,, is the fractional -Laplace operator, the
nonlinearity f is -superlinear at infinity and the potential V(x) is allowed
to be sign-changing
Mountain pass solutions for the fractional Berestycki-Lions problem
We investigate the existence of least energy solutions and infinitely many
solutions for the following nonlinear fractional equation (-\Delta)^{s} u =
g(u) \mbox{ in } \mathbb{R}^{N}, where , ,
is the fractional Laplacian and is an
odd function satisfying Berestycki-Lions type
assumptions. The proof is based on the symmetric mountain pass approach
developed by Hirata, Ikoma and Tanaka in \cite{HIT}. Moreover, by combining the
mountain pass approach and an approximation argument, we also prove the
existence of a positive radially symmetric solution for the above problem when
satisfies suitable growth conditions which make our problem fall in the so
called "zero mass" case
Periodic solutions for a superlinear fractional problem without the Ambrosetti-Rabinowitz condition
The purpose of this paper is to study -periodic solutions to
[(-\Delta_{x}+m^{2})^{s}-m^{2s}]u=f(x,u) &\mbox{in} (0,T)^{N} (P)
u(x+Te_{i})=u(x) &\mbox{for all} x \in \R^{N}, i=1, \dots, N
where , , , and is a continuous
function, -periodic in and satisfying a suitable growth assumption
weaker than the Ambrosetti-Rabinowitz condition. The nonlocal operator
can be realized as the Dirichlet to Neumann map for a
degenerate elliptic problem posed on the half-cylinder
. By using a variant of the Linking
Theorem, we show that the extended problem in admits a
nontrivial solution which is -periodic in . Moreover, by a
procedure of limit as , we also prove the existence of a
nontrivial solution to (P) with
Concentrating solutions for a fractional Kirchhoff equation with critical growth
In this paper we consider the following class of fractional Kirchhoff
equations with critical growth: \begin{equation*} \left\{ \begin{array}{ll}
\left(\varepsilon^{2s}a+\varepsilon^{4s-3}b\int_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right)(-\Delta)^{s}u+V(x)u=f(u)+|u|^{2^{*}_{s}-2}u
\quad &\mbox{ in } \mathbb{R}^{3}, \\ u\in H^{s}(\mathbb{R}^{3}), \quad u>0
&\mbox{ in } \mathbb{R}^{3}, \end{array} \right. \end{equation*} where
is a small parameter, are constants, , is the fractional critical
exponent, is the fractional Laplacian operator, is a
positive continuous potential and is a superlinear continuous function with
subcritical growth. Using penalization techniques and variational methods, we
prove the existence of a family of positive solutions which
concentrates around a local minimum of as .Comment: arXiv admin note: text overlap with arXiv:1810.0456
Maximum allowable temperature during quench in Nb3Sn accelerator magnets
This note aims at understanding the maximum allowable temperature at the hot
spot during a quench in Nb3Sn accelerator magnets, through the analysis of
experimental results previously presented.Comment: 4 pages, Contribution to WAMSDO 2013: Workshop on Accelerator Magnet,
Superconductor, Design and Optimization; 15 - 16 Jan 2013, CERN, Geneva,
Switzerlan
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