Unusual Symmetries in the Kugel-Khomskii Hamiltonian

The Kugel-Khomskii Hamiltonian for cubic titanates describes spin and orbital superexchange interactions between $d^1$ ions having three-fold degenerate $t_{2g}$ orbitals. Since orbitals do not couple along "inactive" axes, perpendicular to the orbital planes, the total number of electrons in $|\alpha >$ orbitals in any such plane and the corresponding total spin are both conserved. A Mermin-Wagner construction shows that there is no long-range spin ordering at nonzero temperatures. Inclusion of spin-orbit coupling allows such ordering, but even then the excitation spectrum is gapless due to a continuous symmetry. Thus, the observed order and gap require more symmetry breaking terms.Comment: 4 pages (two column format with 2 figures), to appear in Phys. Rev. Lett. (submitted on Dec. 2002

Single cell phenotyping reveals heterogeneity among haematopoietic stem cells following infection.

The haematopoietic stem cell (HSC) niche provides essential micro-environmental cues for the production and maintenance of HSCs within the bone marrow. During inflammation, haematopoietic dynamics are perturbed, but it is not known whether changes to the HSC-niche interaction occur as a result. We visualise HSCs directly in vivo, enabling detailed analysis of the 3D niche dynamics and migration patterns in murine bone marrow following Trichinella spiralis infection. Spatial statistical analysis of these HSC trajectories reveals two distinct modes of HSC behaviour: (i) a pattern of revisiting previously explored space, and (ii) a pattern of exploring new space. Whereas HSCs from control donors predominantly follow pattern (i), those from infected mice adopt both strategies. Using detailed computational analyses of cell migration tracks and life-history theory, we show that the increased motility of HSCs following infection can, perhaps counterintuitively, enable mice to cope better in deteriorating HSC-niche micro-environments following infection

The hypervariable domain of the mitochondrial control region in atlantic spiny lobsters and its potential as a marker for investigating phylogeographic structuring.

Atlantic spiny lobsters support major fisheries in northeastern Brazilian waters and in the Caribbean Sea. To avoid reduction in diversity and elimination of distinct stocks, understanding their population dynamics, including structuring of populations and genetic diversity, is critical. We here explore the potential of using the hypervariable domain in the control region of the mitochondrial DNA as a genetic marker to characterize population subdivision in spiny lobsters, using Panulirus argus as the species model

Coupling of the lattice and superlattice deformations and hysteresis in thermal expansion for the quasi one-dimensional conductor TaS3_3

An original interferometer-based setup for measurements of length of needle-like samples is developed, and thermal expansion of o-TaS$_3$ crystals is studied. Below the Peierls transition the temperature hysteresis of length $L$ is observed, the width of the hysteresis loop $\delta L/L$ being up to $5 \cdot 10^{-5}$. The behavior of the loop is anomalous: the length changes so that it is in front of its equilibrium value. The hysteresis loop couples with that of conductivity. The sign and the value of the length hysteresis are consistent with the strain dependence of the charge-density waves (CDW) wave vector. With lowering temperature down to 100 K the CDW elastic modulus grows achieving a value comparable with the lattice Young modulus. Our results could be helpful in consideration of different systems with intrinsic superstructures.Comment: 4 pages, 3 figures. Phys. Rev. Lett., accepted for publicatio

Parametric generation of second sound in superfluid helium: linear stability and nonlinear dynamics

We report the experimental studies of a parametric excitation of a second sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity. The results on several topics in this system are presented: (i) The linear properties of the instability, namely, the threshold, its temperature and geometrical dependencies, and the spectra of SS just above the onset were measured. They were found to be in a good quantitative agreement with the theory. (ii) It was shown that the mechanism of SS amplitude saturation is due to the nonlinear attenuation of SS via three wave interactions between the SS waves. Strong low frequency amplitude fluctuations of SS above the threshold were observed. The spectra of these fluctuations had a universal shape with exponentially decaying tails. Furthermore, the spectral width grew continuously with the FS amplitude. The role of three and four wave interactions are discussed with respect to the nonlinear SS behavior. The first evidence of Gaussian statistics of the wave amplitudes for the parametrically generated wave ensemble was obtained. (iii) The experiments on simultaneous pumping of the FS and independent SS waves revealed new effects. Below the instability threshold, the SS phase conjugation as a result of three-wave interactions between the FS and SS waves was observed. Above the threshold two new effects were found: a giant amplification of the SS wave intensity and strong resonance oscillations of the SS wave amplitude as a function of the FS amplitude. Qualitative explanations of these effects are suggested.Comment: 73 pages, 23 figures. to appear in Phys. Rev. B, July 1 st (2001

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Band-width control in a perovskite-type 3d^1 correlated metal Ca_{1-x}Sr_xVO_3. I. Evolution of the electronic properties and effective mass

Single crystals of the perovskite-type $3d^{1}$ metallic alloy system Ca$_{1-x}$Sr$_x$VO$_3$ were synthesized in order to investigate metallic properties near the Mott transition. The substitution of a Ca$^{2+}$ ion for a Sr$^{2+}$ ion reduces the band width $W$ due to a buckling of the V-O-V bond angle from $\sim180^\circ$ for SrVO$_3$ to $\sim160^\circ$ for CaVO$_3$. Thus, the value of $W$ can be systematically controlled without changing the number of electrons making Ca$_{1-x}$Sr$_x$VO$_3$: one of the most ideal systems for studying band-width effects. The Sommerfeld-Wilson's ratio ($\simeq2$), the Kadowaki-Woods ratio (in the same region as heavy Fermion systems), and a large $T^{2}$ term in the electric resistivity, even at 300 K, substantiate a large electron correlation in this system, though the effective mass, obtained by thermodynamic and magnetic measurements, shows only a systematic but moderate increase in going from SrVO$_3$ to CaVO$_3$, in contrast to the critical enhancement expected from the Brinkmann-Rice picture. It is proposed that the metallic properties observed in this system near the Mott transition can be explained by considering the effect of a non-local electron correlation.Comment: 14 pages in a Phys. Rev. B camera-ready format with 10 EPS figures embedded. LaTeX 2.09 source file using "camera.sty" and "prbplug.sty" provided by N. Shirakawa. For OzTeX (Macintosh), use "ozfig.sty" instead of "psfig.sty". "ozfig.sty" can be also obtained by e-mail request to N. Shirakawa: . Submitted to Phys. Rev.

Towards a sustainable Cornwall: State of the Doughnut

This is the final version. Available from the Environment and Sustainability Institute, University of Exeter via the link in this recordUsing the 'doughnut economics' framework established by Kate Raworth to identify a safe and just operating space for humanity, this report presents an initial assessment of the ‘state of the Doughnut’ in Cornwall in 2020. The report provides a baseline from which to evaluate progress towards achieving a social foundation that meets human needs while also reducing environmental pressures. By developing a dataset that can be regularly revisited to assess progress this assessment has longer-term potential to inform reporting to the Cornwall and Isles of Scilly Leadership Board on ecological and social trends. The report aims to assist Cornwall Council and other key stakeholders to identify appropriate indicators that can be used to track progress across the wider context in which their decision-making wheel is used. By assessing available data and identifying gaps, this ‘state of the Doughnut’ report is designed to provide a benchmark to help sustainable development in Cornwall. Where available, we also include data for the Isles of Scilly.UKRI Strategic Priorities Fun