8,708 research outputs found
An abstract version of the concentration compactness principle
We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains.We prove an abstract version of concentration compactness principle in Hilbert space and show its applications to a range of elliptic problems on unbounded domains
Almost sure asymptotic behaviour of Birkhoff sums for infinite measure-preserving dynamical systems
We consider a conservative ergodic measure-preserving transformation T of a Ï-finite measure space (X,B,ÎŒ) with ÎŒ(X)=â. Given an observable f:Xââ we study the almost sure asymptotic behaviour of the Birkhoff sums S_Nf(x). In infinite ergodic theory it is well known that the asymptotic behaviour of SNf(x) strongly depends on the point xâX, and if fâL^1(X,ÎŒ), then there exists no real valued sequence (b(N)) such that lim S_Nf(x)/b(N)=1 almost surely. In this paper we show that for dynamical systems with strong mixing assumptions for the induced map on a finite measure set, there exists a sequence (α(N)) and m:XĂâââ such that for fâL^1(X,ÎŒ) we have lim S_{N+m(x,N)}f(x)/α(N)=1 for ÎŒ-a.e. xâX. Moreover if fâL1(X,ÎŒ) we give conditions on the induced observable such that there exists a sequence (G(N)) depending on f, for which lim S_Nf(x)/G(N)=1 holds for ÎŒ-a.e. xâX
Low-T_c Josephson junctions with tailored barrier
Nb/Al_2O_3/Ni_{0.6}Cu_{0.4}/Nb based
superconductor-insulator-ferromagnet-superconductor (SIFS) Josephson tunnel
junctions with a thickness step in the metallic ferromagnetic
\Ni_{0.6}\Cu_{0.4} interlayer were fabricated. The step was defined by optical
lithography and controlled etching. The step height is on the scale of a few
angstroms. Experimentally determined junction parameters by current-voltage
characteristics and Fraunhofer pattern indicate an uniform F-layer thickness
and the same interface transparencies for etched and non-etched F-layers. This
technique could be used to tailor low-T_c Josephson junctions having controlled
critical current densities at defined parts of the junction area, as needed for
tunable resonators, magnetic-field driven electronics or phase modulated
devices.Comment: 6 pages, 6 figures, small changes, to be published by JA
Magellan Spectroscopy of the Galaxy Cluster RX J1347.5-1145: Redshift Estimates for the Gravitationally Lensed Arcs
We present imaging and spectroscopic observations of the gravitationally
lensed arcs in the field of RX J1347.5-1145, the most X-ray luminous galaxy
cluster known. Based on the detection of the [OII] 3727 emission line, we
confirm that the redshift of one of the arcs is z = 0.806. Its color and [OII]
line strength are consistent with those of distant, actively star forming
galaxies. In a second arc, we tentatively identify a pair of absorption lines
superposed on a red continuum; the lines are consistent with Ca II H & K at z =
0.785. We detected a faint blue continuum in two additional arcs, but no
spectral line features could be measured. We establish lower limits to their
redshifts based on the absence of [OII] emission, which we argue should be
present and detectable in these objects. Redshifts are also given for a number
of galaxies in the field of the cluster.Comment: To appear in The Astrophysical Journal (September 2002). 6 page
Implications of surface noise for the motional coherence of trapped ions
Electric noise from metallic surfaces is a major obstacle towards quantum
applications with trapped ions due to motional heating of the ions. Here, we
discuss how the same noise source can also lead to pure dephasing of motional
quantum states. The mechanism is particularly relevant at small ion-surface
distances, thus imposing a new constraint on trap miniaturization. By means of
a free induction decay experiment, we measure the dephasing time of the motion
of a single ion trapped 50~m above a Cu-Al surface. From the dephasing
times we extract the integrated noise below the secular frequency of the ion.
We find that none of the most commonly discussed surface noise models for ion
traps describes both, the observed heating as well as the measured dephasing,
satisfactorily. Thus, our measurements provide a benchmark for future models
for the electric noise emitted by metallic surfaces.Comment: (5 pages, 4 figures
Lay conceptions of âbeing movedâ (âbewegt seinâ) include a joyful and a sad type: Implications for theory and research
Being moved has received increased attention in emotion psychology as a social emotion that fosters bonds between individuals and within communities. This increased attention, however, has also sparked debates about whether the term âbeing movedâ refers to a single distinct profile of emotion components or rather to a range of different emotion profiles. We addressed this question by investigating lay conceptions of the emotion components (i.e., elicitors, cognitive appraisals, subjective feelings, bodily symptoms, and consequences for thought/action) of âbewegt seinâ (the German term for âbeing movedâ). Participants (N = 106) provided written descriptions of both a moving personal experience and their conceptual prototype of âbeing moved,â which were subjected to content analysis to obtain quantitative data for statistical analyses. Based on latent class analyses, we identified two classes for both the personal experiences (joyfully-moved and sadly-moved classes) and the being-moved prototype (basic-description and extended-description classes). Being joyfully moved occurred when social values and positive relationship experiences were salient. Being sadly moved was elicited by predominantly negative relationship experiences and negatively salient social values. For both classes, the most frequently reported consequences for thought/action were continued cognitive engagement, finding meaning, and increased valuation of and striving for connectedness/prosociality. Basic descriptions of the prototype included âbeing movedâ by positive or negative events as instances of the same emotion, with participants in the extended-description class also reporting joy and sadness as associated emotions. Based on our findings and additional theoretical considerations, we propose that the term âbeing movedâ designates an emotion with an overall positive valence that typically includes blends of positively and negatively valenced emotion components, in which especially the weight of the negative components varies. The emotionâs unifying core is that it involves feeling the importance of individuals, social entities, and abstract social values as sources of meaning in oneâs life
Hosting the plant cells in vitro : recent trends in bioreactors
Biotechnological production of high-value metabolites and therapeutic proteins by plant in vitro systems has been considered as an attractive alternative of classical technologies. Numerous proof-of-concept studies have illustrated the feasibility of scaling up plant in vitro system-based processes while keeping their biosynthetic potential. Moreover, several commercial processes have been established so far. Though the progress on the field is still limited, in the recent years several bioreactor configurations has been developed (e.g., so-called single-use bioreactors) and successfully adapted for growing plant cells in vitro. This review highlights recent progress and limitations in the bioreactors for plant cells and outlines future perspectives for wider industrialization of plant in vitro systems as âgreen cell factoriesâ for sustainable production of value-added molecules
Second-layer nucleation in coherent Stranski-Krastanov growth of quantum dots
We have studied the monolayer-bilayer transformation in the case of the
coherent Stranski-Krastanov growth. We have found that the energy of formation
of a second layer nucleus is largest at the center of the first-layer island
and smallest on its corners. Thus nucleation is expected to take place at the
corners (or the edges) rather than at the center of the islands as in the case
of homoepitaxy. The critical nuclei have one atom in addition to a compact
shape, which is either a square of i*i or a rectangle of i*(i-1) atoms, with
i>1 an integer. When the edge of the initial monolayer island is much larger
than the critical nucleus size, the latter is always a rectangle plus an
additional atom, adsorbed at the longer edge, which gives rise to a new atomic
row in order to transform the rectangle into the equilibrium square shape.Comment: 6 pages, 4 figures. Accepted version, minor change
Concentration analysis and cocompactness
Loss of compactness that occurs in may significant PDE settings can be
expressed in a well-structured form of profile decomposition for sequences.
Profile decompositions are formulated in relation to a triplet , where
and are Banach spaces, , and is, typically, a
set of surjective isometries on both and . A profile decomposition is a
representation of a bounded sequence in as a sum of elementary
concentrations of the form , , , and a remainder that
vanishes in . A necessary requirement for is, therefore, that any
sequence in that develops no -concentrations has a subsequence
convergent in the norm of . An imbedding with this
property is called -cocompact, a property weaker than, but related to,
compactness. We survey known cocompact imbeddings and their role in profile
decompositions
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