Luttinger-Liquid Behavior in the Alternating Spin-Chain System Copper Nitrate

We determine the phase diagram of copper nitrate Cu(NO$_3$)$_2\cdot$2.5D$_2$O in the context of quantum phase transitions and novel states of matter. We establish this compound as an ideal candidate to study quasi-1D Luttinger liquids, 3D Bose-Einstein-Condensation of triplons, and the crossover between 1D and 3D physics. Magnetocaloric effect, magnetization, and neutron scattering data provide clear evidence for transitions into a Luttinger liquid regime and a 3D long-range ordered phase as function of field and temperature. Theoretical simulations of this model material allow us to fully establish the phase diagram and to discuss it in the context of dimerized spin systems.Comment: 5 pages, 4 figure

The role of Hand2 in branchial arch and head-shoulder patterning

Comprehending gnathostome evolution requires insights into key cellular and molecular components of craniofacial and shoulder development. For the work of this PhD, I made use of genetically modified mouse models to study aspects of mammalian head and shoulder morphogenesis by triple fluorescent RNA in situ hybridisation, immunohistochemistry and high resolution imaging. First- I use a genetically defined sentinel cell population labelled by the Hand2-Cre transgene to establish the expansion of the distal-most branchial arch domain and correlate this by triple fluorescent RNA in situ hybridisation with the system controlling proximo-distal branchial arch patterning, the Dlx system. I find that the axis of the Dlx system does not correspond to the proximo-distal but an endodermal-ectodermal axis of the arch and rotates during development; the overall expansion of the arch is explicable by telescopic outgrowth along this new axis. Second- I study the cellular and molecular characteristics of head/ shoulder skeleto-muscular connectivity and the contribution of limb lateral plate mesoderm to the shoulder girdle, which allows me to identify part of the manubrium sterni as the ‘lost’ mammalian procoracoid and to demonstrate that the interaction between lateral plate mesodermal subpopulations is non-random. Third- I establish novel roles for Hand2 in lower incisor ameloblasts and in laminar dermal bone formation, suggesting a fundamental role for Hand2 in epithelial and mesenchymal cell layer arrangements. My detailed study of the murine frontal bone reveals that the establishment of an internal and an external layer initiates dermal bone formation; the latter shows intermediate molecular periosteal/ perichondrial characteristics and generates the intermediate layer by a Hand2-dependent invagination process. For a comparative amphibian data set, I begin to establish genetic lineage labelling as technique in Xenopus tropicalis. I generate and test a Xenopus Hand2-Cre transgene and establish a stable generic Xenopus tropicalis Cre-reporter line by I-SceI mediated transgenesis

Magnetic Hamiltonian and phase diagram of the quantum spin liquid Ca10Cr7O28

A spin liquid is a new state of matter with topological order where the spin moments continue to fluctuate coherently down to the lowest temperatures rather than develop static long range magnetic order as found in conventional magnets. For spin liquid behavior to arise in a material the magnetic Hamiltonian must be frustrated , where the combination of lattice geometry, interactions, and anisotropies gives rise to competing spin arrangements in the ground state. Theoretical Hamiltonians which produce spin liquids are spin ice, the Kitaev honeycomb model, and the kagome antiferromagnet. Spin liquid behavior, however, in real materials is rare because they can only approximate these Hamiltonians and often have weak higher order terms that destroy the spin liquid state. Ca10Cr7O28 is a new quantum spin liquid candidate with magnetic Cr5 ions that possess quantum spin number S . The spins are entirely dynamic in the ground state and the excitation spectrum is broad and diffuse, as is typical of spinons which are the excitations of a spin liquid. In this paper we determine the Hamiltonian of Ca10Cr7O28 using inelastic neutron scattering under high magnetic field to induce a field polarized paramagnetic ground state and spin wave excitations that can be fitted to extract the interactions. We further explore the phase diagram by using inelastic neutron scattering and heat capacity measurements and establish the boundaries of the spin liquid phase as a function of magnetic field and temperature. Our results show that Ca10Cr7O28 consists of distorted kagome bilayers with several isotropic ferromagnetic and antiferromagnetic interactions where, unexpectedly, the ferromagnetic interactions are stronger than the antiferromagnetic ones. This complex Hamiltonian does not correspond to any known spin liquid model and points to new directions in the search for quantum spin liquid behavio

Weighted ergodic theorems for Banach-Kantorovich lattice Lp(∇^,μ^)L_{p}(\hat{\nabla},\hat{\mu})

In the present paper we prove weighted ergodic theorems and multiparameter weighted ergodic theorems for positive contractions acting on $L_p(\hat{\nabla},\hat{\mu})$. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.Comment: 11 page

Implementation and testing of the first prompt search for gravitational wave transients with electromagnetic counterparts

Aims. A transient astrophysical event observed in both gravitational wave (GW) and electromagnetic (EM) channels would yield rich scientific rewards. A first program initiating EM follow-ups to possible transient GW events has been developed and exercised by the LIGO and Virgo community in association with several partners. In this paper, we describe and evaluate the methods used to promptly identify and localize GW event candidates and to request images of targeted sky locations. Methods. During two observing periods (Dec 17 2009 to Jan 8 2010 and Sep 2 to Oct 20 2010), a low-latency analysis pipeline was used to identify GW event candidates and to reconstruct maps of possible sky locations. A catalog of nearby galaxies and Milky Way globular clusters was used to select the most promising sky positions to be imaged, and this directional information was delivered to EM observatories with time lags of about thirty minutes. A Monte Carlo simulation has been used to evaluate the low-latency GW pipeline's ability to reconstruct source positions correctly. Results. For signals near the detection threshold, our low-latency algorithms often localized simulated GW burst signals to tens of square degrees, while neutron star/neutron star inspirals and neutron star/black hole inspirals were localized to a few hundred square degrees. Localization precision improves for moderately stronger signals. The correct sky location of signals well above threshold and originating from nearby galaxies may be observed with ~50% or better probability with a few pointings of wide-field telescopes.Comment: 17 pages. This version (v2) includes two tables and 1 section not included in v1. Accepted for publication in Astronomy & Astrophysic

Formula for the nnth kk-Generalized Fibonacci-like Number

In this paper we provided a formula for the $n$th term of the $k$-generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having $k$ arbitrary initial terms, where the succeeding terms are obtained by adding its previous $k$ terms. The formula for the $n$th term of the $k$-generalized Fibonacci-like sequence was obtained by observing patterns in the derived formula for the nth term of the Fibonacci-like, Tribonacci-like, and Tetrabonacci-like sequence. The formula for the $k$-generalized Fibonacci sequence was also derived and was used in the process of proving the main result of this paper

Active fixturing: literature review and future research directions

Fixtures are used to fixate, position and support workpieces and represent a crucial tool in manufacturing. Their performance determines the result of the whole manufacturing process of a product. There is a vast amount of research done on automatic fixture layout synthesis and optimisation and fixture design verification. Most of this work considers fixture mechanics to be static and the fixture elements to be passive. However, a new generation of fixtures has emerged that has actuated fixture elements for active control of the part–fixture system during manufacturing operations to increase the end product quality. This paper analyses the latest studies in the field of active fixture design and its relationship with flexible and reconfigurable fixturing systems. First, a brief introduction is given on the importance of research of fixturing systems. Secondly, the basics of workholding and fixture design are visited, after which the state-of-the-art in active fixturing and related concepts is presented. Fourthly, part–fixture dynamics and design strategies which take these into account are discussed. Fifthly, the control strategies used in active fixturing systems are examined. Finally, some final conclusions and prospective future research directions are presented

Phonons in mesoporous silicon The influence of nanostructuring on the dispersion in the Debye regime

We present a comprehensive scattering study of nanostructured silicon. Neutron and x ray scattering experiments elucidate structural and dynamical properties of electrochemically etched, porous silicon membranes with pores roughly 8 nm across. In particular, inelastic cold neutron scattering techniques reveal the phonon dispersion of the nanostructured, single crystalline samples in the linear Debye regime for energy transfers up to 4 meV. A modified dispersion relation characterized by systematically reduced sound velocities manifests itself in altered elastic properties of porous silicon when compared to bulk silicon. Its relevance for nanostructured silicon as thermoelectric material of interest is discusse

The magnetic phase diagram of the frustrated spin chain compound linarite, PbCuSO4_4(OH)2_2, as seen by neutron diffraction and 1^1H-NMR

We report on a detailed neutron diffraction and $^1$H-NMR study on the frustrated spin-1/2 chain material linarite, PbCuSO$_4$(OH)$_2$, where competing ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor interactions lead to frustration. From the magnetic Bragg peak intensity studied down to 60 mK, the magnetic moment per Cu atom is obtained within the whole magnetic phase diagram for $H \parallel b$ axis. Further, we establish the detailed configurations of the shift of the SDW propagation vector in phase V with field and temperature. Finally, combining our neutron diffraction results with those from a low-temperature/high-field NMR study we find an even more complex phase diagram close to the quasi-saturation field suggesting that bound two-magnon excitations are the lowest energy excitations close to and in the quasi-saturation regime. Qualitatively and semi-quantitatively, we relate such behavior to $XYZ$ exchange anisotropy and contributions from the Dzyaloshinsky-Moriya interaction to affect the magnetic properties of linarite