Large deviations for many Brownian bridges with symmetrised initial-terminal condition

Consider a large system of $N$ Brownian motions in $\mathbb{R}^d$ with some non-degenerate initial measure on some fixed time interval $[0,\beta]$ with symmetrised initial-terminal condition. That is, for any $i$, the terminal location of the $i$-th motion is affixed to the initial point of the $\sigma(i)$-th motion, where $\sigma$ is a uniformly distributed random permutation of $1,...,N$. Such systems play an important role in quantum physics in the description of Boson systems at positive temperature $1/\beta$. In this paper, we describe the large-N behaviour of the empirical path measure (the mean of the Dirac measures in the $N$ paths) and of the mean of the normalised occupation measures of the $N$ motions in terms of large deviations principles. The rate functions are given as variational formulas involving certain entropies and Fenchel-Legendre transforms. Consequences are drawn for asymptotic independence statements and laws of large numbers. In the special case related to quantum physics, our rate function for the occupation measures turns out to be equal to the well-known Donsker-Varadhan rate function for the occupation measures of one motion in the limit of diverging time. This enables us to prove a simple formula for the large-N asymptotic of the symmetrised trace of ${\rm e}^{-\beta \mathcal{H}_N}$, where $\mathcal{H}_N$ is an $N$-particle Hamilton operator in a trap

Genetic characterization of flea-derived Bartonella species from native animals in Australia suggests host-parasite co-evolution

Fleas are important arthropod vectors for a variety of diseases in veterinary and human medicine, and bacteria belonging to the genus Bartonella are among the organisms most commonly transmitted by these ectoparasites. Recently, a number of novel Bartonella species and novel species candidates have been reported in marsupial fleas in Australia. In the present study the genetic diversity of marsupial fleas was investigated; 10 species of fleas were collected from seven different marsupial and placental mammal hosts in Western Australia including woylies (Bettongia penicillata), western barred bandicoots (Perameles bougainville), mardos (Antechinus flavipes), bush rats (Rattus fuscipes), red foxes (Vulpes vulpes), feral cats (Felis catus) and rabbits (Oryctolagus cuniculus). PCR and sequence analysis of the cytochrome oxidase subunit I (COI) and the 18S rRNA genes from these fleas was performed. Concatenated phylogenetic analysis of the COI and 18S rRNA genes revealed a close genetic relationship between marsupial fleas, with Pygiopsylla hilli from woylies, Pygiopsylla tunneyi from western barred bandicoots and Acanthopsylla jordani from mardos, forming a separate cluster from fleas collected from the placental mammals in the same geographical area. The clustering of Bartonella species with their marsupial flea hosts suggests co-evolution of marsupial hosts, marsupial fleas and Bartonella species in Australia

Cooling atoms in an optical trap by selective parametric excitation

We demonstrate the possibility of energy-selective removal of cold atoms from a tight optical trap by means of parametric excitation of the trap vibrational modes. Taking advantage of the anharmonicity of the trap potential, we selectively remove the most energetic trapped atoms or excite those at the bottom of the trap by tuning the parametric modulation frequency. This process, which had been previously identified as a possible source of heating, also appears to be a robust way for forcing evaporative cooling in anharmonic traps.Comment: 5 pages, 5 figure

Reproducing Kernels of Generalized Sobolev Spaces via a Green Function Approach with Distributional Operators

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function $G$ with respect to $L:=\mathbf{P}^{\ast T}\mathbf{P}$ now becomes a conditionally positive definite function. In order to support this claim we ensure that the distributional adjoint operator $\mathbf{P}^{\ast}$ of $\mathbf{P}$ is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function $G$ can be isometrically embedded into or even be isometrically equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant $s_{f,X}$ to data values sampled from an unknown generalized Sobolev function $f$ at data sites located in some set $X \subset \mathbb{R}^d$. We provide several examples, such as Mat\'ern kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are isometrically equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator $\mathbf{P}$. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the "best" kernel function for kernel-based approximation methods.Comment: Update version of the publish at Num. Math. closed to Qi Ye's Ph.D. thesis (\url{http://mypages.iit.edu/~qye3/PhdThesis-2012-AMS-QiYe-IIT.pdf}

Enhanced stability of layered phases in parallel hard-spherocylinders due to the addition of hard spheres

There is increasing evidence that entropy can induce microphase separation in binary fluid mixtures interacting through hard particle potentials. One such phase consists of alternating two dimensional liquid-like layers of rods and spheres. We study the transition from a uniform miscible state to this ordered state using computer simulations and compare results to experiments and theory. We conclude that (1) there is stable entropy driven microphase separation in mixtures of parallel rods and spheres, (2) adding spheres smaller then the rod length decreases the total volume fraction needed for the formation of a layered phase, therefore small spheres effectively stabilize the layered phase; the opposite is true for large spheres and (3) the degree of this stabilization increases with increasing rod length.Comment: 11 pages, 9 figures. Submitted to Phys. Rev. E. See related website http://www.elsie.brandeis.ed

Towards the deconstruction of M-theory

We argue that there is an equivalence of M-theory on T^3 \times A_{N-1} with a four-dimensional non-supersymmetric quiver gauge theory on the Higgs branch. The quiver theory in question has gauge group SU(N)^{N_4N_6N_8} and is considered in a strong coupling and large N_{4,6,8} limit. We provide field- and string-theoretical evidence for the equivalence making use of the deconstruction technique. In particular, we find wrapped M2-branes in the mass spectrum of the quiver theory at low energies.Comment: LaTeX, 15 pages, 4 figures, added reference

Sun exposure behaviour, seasonal vitamin D deficiency, and relationship to bone health in adolescents

YesContext: Vitamin D is essential for bone health in adolescence, where there is rapid bone mineral content accrual. As cutaneous sun-exposure provides vitamin D, there is no recommended oral intake for UK adolescents. Objective: Assess seasonal vitamin D status and its contributors in white Caucasian adolescents, and examine bone health in those found deficient. Design: Prospective cohort study. Setting: Six schools in Greater Manchester, UK. Participants: 131 adolescents, 12–15 years. Intervention(s): Seasonal assessment of circulating 25-hydroxyvitamin D (25OHD), personal sunexposure and dietary vitamin D. Adolescents deficient (25OHD <10 ng/mL/25 nmol/L) in ≥one season underwent dual-energy X-ray absorptiometry (lumbar spine, femoral neck), with bone mineral apparent density (BMAD) correction for size, and peripheral quantitative computed tomography (distal radius) for volumetric (v)BMD. Main Outcome Measure: Serum 25OHD; BMD. Results: Mean 25OHD was highest in September: 24.1 (SD 6.9) ng/mL and lowest in January: 15.5 (5.9) ng/mL. Over the year, 16% were deficient in ≥one season and 79% insufficient (25OHD <20 ng/mL/50 nmol/L) including 28% in September. Dietary vitamin D was low year-round while personal sun-exposure was seasonal and predominantly across the school week. Holidays accounted for 17% variation in peak 25OHD (p<0.001). Nineteen adolescents underwent bone assessment, which showed low femoral neck BMAD versus matched reference data (p=0.0002), 3 with Z≤ -2.0 distal radius trabecular vBMD. Conclusions: Sun-exposure levels failed to provide adequate vitamin D, ~one-quarter adolescents insufficient even at summer-peak. Seasonal vitamin D deficiency was prevalent and those affected had low BMD. Recommendations on vitamin D acquisition are indicated in this age-group.The Bupa Foundation (Grant number TBF-M10-017)

Superfluid toroidal currents in atomic condensates

The dynamics of toroidal condensates in the presence of condensate flow and dipole perturbation have been investigated. The Bogoliubov spectrum of condensate is calculated for an oblate torus using a discrete-variable representation and a spectral method to high accuracy. The transition from spheroidal to toroidal geometry of the trap displaces the energy levels into narrow bands. The lowest-order acoustic modes are quantized with the dispersion relation $\omega \sim |m| \omega_s$ with $m=0,\pm 1,\pm 2, ...$. A condensate with toroidal current $\kappa$ splits the $|m|$ co-rotating and counter-rotating pair by the amount: $\Delta E \approx 2 |m|\hbar^2 \kappa < r^{-2}>$. Radial dipole excitations are the lowest energy dissipation modes. For highly occupied condensates the nonlinearity creates an asymmetric mix of dipole circulation and nonlinear shifts in the spectrum of excitations so that the center of mass circulates around the axis of symmetry of the trap. We outline an experimental method to study these excitations.Comment: 8 pages, 8 figure

Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical point of the energy subject to the constraint that the momentum is fixed. We prove the existence of a minimiser of the energy subject to the constraint that the momentum is fixed and small. The existence of a small-amplitude solitary wave is thus assured, and since the energy and momentum are both conserved quantities a standard argument may be used to establish the stability of the set of minimisers as a whole. `Stability' is however understood in a qualified sense due to the lack of a global well-posedness theory for three-dimensional water waves.Comment: 83 pages, 1 figur

Reply to N.M. Vegter ‘Discussion on the kinetics of the elution of gold from activated carbon’

Mr Vetger has analysed, in some depth, the approximations made in the treatment of the kinetic data presented in the original by ourselves..