163 research outputs found
Stable Approximations of Set-Valued Maps
A good descriptive model of a dynamical phenomenon has inherent stability of its solution, by that one means that small changes in data will result only in "small" changes in the solution. It is thus a criterion that can, and should, be used in the evaluation of dynamical models. This report, that develops approximation results for set-valued functions, provides stability criteria based on generalized derivatives. It also provides estimates for the region of stability
Glauber dynamics in a single-chain magnet: From theory to real systems
The Glauber dynamics is studied in a single-chain magnet. As predicted, a
single relaxation mode of the magnetization is found. Above 2.7 K, the
thermally activated relaxation time is mainly governed by the effect of
magnetic correlations and the energy barrier experienced by each magnetic unit.
This result is in perfect agreement with independent thermodynamical
measurements. Below 2.7 K, a crossover towards a relaxation regime is observed
that is interpreted as the manifestation of finite-size effects. The
temperature dependences of the relaxation time and of the magnetic
susceptibility reveal the importance of the boundary conditions.Comment: Submitted to PRL 10 May 2003. Submitted to PRB 12 December 2003;
published 15 April 200
Estimates for the Sobolev trace constant with critical exponent and applications
In this paper we find estimates for the optimal constant in the critical
Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow
\|u\|^p_{W^{1,p}(\Omega)} that are independent of . This estimates
generalized those of [3] for general . Here is the
critical exponent for the immersion and is the space dimension. Then we
apply our results first to prove existence of positive solutions to a nonlinear
elliptic problem with a nonlinear boundary condition with critical growth on
the boundary, generalizing the results of [16]. Finally, we study an optimal
design problem with critical exponent.Comment: 22 pages, submitte
Identification of the bulk pairing symmetry in high-temperature superconductors: Evidence for an extended s-wave with eight line nodes
we identify the intrinsic bulk pairing symmetry for both electron and
hole-doped cuprates from the existing bulk- and nearly bulk-sensitive
experimental results such as magnetic penetration depth, Raman scattering,
single-particle tunneling, Andreev reflection, nonlinear Meissner effect,
neutron scattering, thermal conductivity, specific heat, and angle-resolved
photoemission spectroscopy. These experiments consistently show that the
dominant bulk pairing symmetry in hole-doped cuprates is of extended s-wave
with eight line nodes, and of anisotropic s-wave in electron-doped cuprates.
The proposed pairing symmetries do not contradict some surface- and
phase-sensitive experiments which show a predominant d-wave pairing symmetry at
the degraded surfaces. We also quantitatively explain the phase-sensitive
experiments along the c-axis for both Bi_{2}Sr_{2}CaCu_{2}O_{8+y} and
YBa_{2}Cu_{3}O_{7-y}.Comment: 11 pages, 9 figure
Existence and uniqueness for stochastic 2D Euler flows with bounded vorticity
The strong existence and the pathwise uniqueness of solutions with (Formula presented.) -vorticity of the 2D stochastic Euler equations are proved. The noise is multiplicative and it involves the first derivatives. A Lagrangian approach is implemented, where a stochastic flow solving a nonlinear flow equation is constructed. The stability under regularizations is also proved
On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
In this paper we consider the global existence of weak solutions to a class
of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in
the energy norm. These type of models, initially proposed by Madelung, have
been extensively used in Physics to investigate Supefluidity and
Superconductivity phenomena and more recently in the modeling of semiconductor
devices . Our approach is based on various tools, namely the wave functions
polar decomposition, the construction of approximate solution via a fractional
steps method, which iterates a Schr\"odinger Madelung picture with a suitable
wave function updating mechanism. Therefore several \emph{a priori} bounds of
energy, dispersive and local smoothing type allow us to prove the compactness
of the approximating sequences. No uniqueness result is provided
TRY plant trait database – enhanced coverage and open access
Plant traits—the morphological, anatomical, physiological, biochemical and phenological characteristics of plants—determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits—almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives
Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model
We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society
Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)
[no abstract available
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