Crosstalk Correction in Atomic Force Microscopy

Commercial atomic force microscopes usually use a four-segmented photodiode to detect the motion of the cantilever via laser beam deflection. This read-out technique enables to measure bending and torsion of the cantilever separately. A slight angle between the orientation of the photodiode and the plane of the readout beam, however, causes false signals in both readout channels, so-called crosstalk, that may lead to misinterpretation of the acquired data. We demonstrate this fault with images recorded in contact mode on ferroelectric crystals and present an electronic circuit to compensate for it, thereby enabling crosstalk-free imaging

Contrast Mechanisms for the Detection of Ferroelectric Domains with Scanning Force Microscopy

We present a full analysis of the contrast mechanisms for the detection of ferroelectric domains on all faces of bulk single crystals using scanning force microscopy exemplified on hexagonally poled lithium niobate. The domain contrast can be attributed to three different mechanisms: i) the thickness change of the sample due to an out-of-plane piezoelectric response (standard piezoresponse force microscopy), ii) the lateral displacement of the sample surface due to an in-plane piezoresponse, and iii) the electrostatic tip-sample interaction at the domain boundaries caused by surface charges on the crystallographic y- and z-faces. A careful analysis of the movement of the cantilever with respect to its orientation relative to the crystallographic axes of the sample allows a clear attribution of the observed domain contrast to the driving forces respectively.Comment: 8 pages, 8 figure

Comparing and characterizing some constructions of canonical bases from Coxeter systems

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a pre-canonical structure, relative to which the well-known Kazhdan-Lusztig basis of $\mathcal{H}$ is a canonical basis. Lusztig and Vogan have defined a representation of a modified Iwahori-Hecke algebra on the free $\mathbb{Z}[v,v^{-1}]$-module generated by the set of twisted involutions in $W$, and shown that this module has a unique pre-canonical structure satisfying a certain compatibility condition, which admits its own canonical basis which can be viewed as a generalization of the Kazhdan-Lusztig basis. One can modify the parameters defining Lusztig and Vogan's module to obtain other pre-canonical structures, each of which admits a unique canonical basis indexed by twisted involutions. We classify all of the pre-canonical structures which arise in this fashion, and explain the relationships between their resulting canonical bases. While some of these canonical bases are related in a trivial fashion to Lusztig and Vogan's construction, others appear to have no simple relation to what has been previously studied. Along the way, we also clarify the differences between Webster's notion of a canonical basis and the related concepts of an IC basis and a $P$-kernel.Comment: 32 pages; v2: additional discussion of relationship between canonical bases, IC bases, and P-kernels; v3: minor revisions; v4: a few corrections and updated references, final versio

Constraints on AGN feedback from its Sunyaev-Zel'dovich imprint on the cosmic background radiation

We derive constraints on feedback by active galactic nuclei (AGN) by setting limits on their thermal Sunyaev-Zel'dovich (SZ) imprint on the cosmic microwave background. The amplitude of any SZ signature is small and degenerate with the poorly known sub-mm spectral energy distribution of the AGN host galaxy and other unresolved dusty sources along the line of sight. Here we break this degeneracy by combining microwave and sub-mm data from $\textit{Planck}$ with all-sky far-infrared maps from the AKARI satellite. We first test our measurement pipeline using the Sloan Digital Sky Survey (SDSS) redMaPPer catalogue of galaxy clusters, finding a highly significant detection (>20$\sigma$) of the SZ effect together with correlated dust emission. We then constrain the SZ signal associated with spectroscopically confirmed quasi-stellar objects (QSOs) from SDSS data release 7 (DR7) and the Baryon Oscillation Spectroscopic Survey (BOSS) DR12. We obtain a low-significance (1.6$\sigma$) hint of an SZ signal, pointing towards a mean thermal energy of $\simeq$5 × 10$^{60}$ erg, lower than reported in some previous studies. A comparison of our results with high-resolution hydrodynamical simulations including AGN feedback suggests QSO host masses of $M_{200c}$ ~ 4 × 10$^{12}h^{-1}$M$_\odot$, but with a large uncertainty. Our analysis provides no conclusive evidence for an SZ signal specifically associated with AGN feedback.BS acknowledges support from an Isaac Newton Studentship at the University of Cambridge and from the Science and Technology Facilities Council (STFC). TG acknowledges support from the Kavli Foundation and STFC grant ST/L000636/1. DS acknowledges support by the STFC and the ERC Starting Grant 638707 ‘Black holes and their host galaxies: coevolution across cosmic time’. This research is based on observations obtained with Planck (http://www.esa.int/Planck), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA and Canada. Furthermore, it is, in parts, based on observations with AKARI, a JAXA project with the participation of ESA. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration

Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

This is the second of a series of four articles studying various generalisations of Khovanov's diagram algebra. In this article we develop the general theory of Khovanov's diagrammatically defined "projective functors" in our setting. As an application, we give a direct proof of the fact that the quasi-hereditary covers of generalised Khovanov algebras are Koszul.Comment: Minor changes, extra sections on Kostant modules and rigidity of cell modules adde

Super duality and irreducible characters of ortho-symplectic Lie superalgebras

We formulate and establish a super duality which connects parabolic categories $O$ between the ortho-symplectic Lie superalgebras and classical Lie algebras of $BCD$ types. This provides a complete and conceptual solution of the irreducible character problem for the ortho-symplectic Lie superalgebras in a parabolic category $O$, which includes all finite-dimensional irreducible modules, in terms of classical Kazhdan-Lusztig polynomials.Comment: 30 pages, Section 5 rewritten and shortene

Three-dimensionality of space and the quantum bit: an information-theoretic approach

It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry "minimal amounts of direction information", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.Comment: 13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39

Economic damages from on-going climate change imply deeper near-term emission cuts

Pathways toward limiting global warming to well below 2 ∘C, as used by the IPCC in the Fifth Assessment Report, do not consider the climate impacts already occurring below 2 ∘C. Here we show that accounting for such damages significantly increases the near-term ambition of transformation pathways. We use econometric estimates of climate damages on GDP growth and explicitly model the uncertainty in the persistence time of damages. The Integrated Assessment Model we use includes the climate system and mitigation technology detail required to derive near-term policies. We find an optimal carbon price of $115 per tonne of CO2 in 2030. The long-term persistence of damages, while highly uncertain, is a main driver of the near-term carbon price. Accounting for damages on economic growth increases the gap between the currently pledged nationally determined contributions and the welfare-optimal 2030 emissions by two thirds, compared to pathways considering the 2 ∘C limit only