Strong-coupling expansion for the momentum distribution of the Bose Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies and correlation functions of the Bose Hubbard model is developed. We illustrate the general formalism, which includes all possible inhomogeneous effects in the formalism, such as disorder, or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third-order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator to superfluid transition along with a generalization of the RPA-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions; the accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling theory results are benchmarked against numerically exact QMC simulations in two and three dimensions and against DMRG calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.Comment: 48 pages 14 figures RevTe

Development of Zwitterionic Hydrophilic Liquid Chromatography (ZICⓇHILIC-MS) metabolomics method for Shotgun analysis of human urine

Urine is a product of the body’s metabolism and the majority of the metabolic products exiting via the renal system are rendered polar in order to be water soluble. Resolution of urinary metabolites for metabolomic studies requires the development of HPLC separation techniques that match this feature of biological chemistry. ZIC –HILIC is an ideal candidate to take forward resolution of such metabolites where reverse phase is unable to give adequate separation. Metabolomic data has to be processed by Shotgun multivariate analysis to sift through thousands of analytes and their variables such as ion intensity. In the development of ZIC-HILIC separation with mass spectrometric (IT-ToF) detection, methodological variability have to be minimized so that any Shotgun data analysis does not reveal potential biomarker analytes that are artifacts or are adversely affected of the separation and detection technique. Here, we report the development of a ZIC-HILIC mass spectrometry method that is suitable for SIMCA P+ data analysis of urine. Variables such as resolution, run reproducibility and sample storage temperature were evaluated in tandem with SIMCA P+ data analysis and quality control pre-processing. The developed method couples quality control runs that pre-process and exclude analytes that are insufficiently robust for further candidate biomarker studies. This meant labile analytes that could not be reproduced in 70% of QC runs (which are pools of all samples run that day) were excluded. However, urine samples stored at 4°C for more than 9 months will contain metabolites that will alter and produce small molecule marker artifacts when compared to samples stored at -20°C. In conclusion, the developed method is a robust method of ZIC-HILIC mass spectrometry shotgun analysis suitable for urinary metabolome discovery of robust biomarkers

Primordial Magnetic Field Limits from Cosmic Microwave Background Bispectrum of Magnetic Passive Scalar Modes

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabatic-like scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \sim 6-9 \times 10^{-16}$, for a magnetic field of $B_0 \sim 3$ nG, assuming a nearly scale-invariant magnetic spectrum . We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \approx -1.4 \times 10^{-16}$. These values are more than $\sim 10^6$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of $B_0 \sim 2$ nG on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on $B_0$ based on the compensated mode bispectrum.Comment: 9 page

Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator

Recent experiments have emphasized that our understanding of the interplay of electron correlations and randomness in solids is still incomplete. We address this important issue and demonstrate that particle-hole (ph) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when ph-symmetry is preserved, and shows the opposite behavior, i.e. conductivity increases with increasing disorder, when ph-symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is ph-symmetry, whereas in its absence the gap diminishes with increasing disorder.Comment: 4 pages, 4 figure

Topology of pocket formation in turbulent premixed flames

© 2018 The Combustion Institute. In turbulent premixed flame propagation, the formation of isolated pockets of reactants or products is associated with flame pinch-off events which cause rapid changes in the flame surface area. Previous topological analysis of these phenomena has been carried out based on Morse theory and Direct Numerical Simulation (DNS) in two spatial dimensions. The present work extends the topological analysis to three dimensions with emphasis on the formation and subsequent burnout of reactant pockets. Singular behaviour observed previously for terms of the Surface Density Function (SDF) transport equation in the two-dimensional case is shown to occur also in three dimensions. Further singular behaviour is observed in the displacement speed close to reactant pocket burnout. The theory is compared against DNS data from hydrogen-air flames and good agreement is obtained

Time Dependence of Tip Morphology during Cellular/Dendritic Arrayed Growth

Succinonitrile-1.9 wt pct acetone has been directionally solidified in 0.7 X 0.7-cm-square cross section pyrex ampoules in order to observe the cell/dendrite tip morphologies, not influenced by the 'wall effects', which are present during growth in the generally used thin (about 200 gm) crucibles. The tips do not maintain a steady-state shape, as is generally assumed. Instead, they fluctuate within a shape envelope. The extent of fluctuation increases with decreasing growth speed, as the micro structure changes from the dendritic to cellular. The influence of natural convection has been examined by comparing these morphologies with those grown, without convection, in the thin ampoules

Outcome of fracture of intra articular distal femur treated with distal femur locking compression plate

Background: Intra articular fracture of the distal femur is a composite and complex injury that poses various challenges for orthopaedic surgeon starting from management of fracture to a protracted recovery of the patient.Methods: We have done retrospective study of 25 patients with intra articular distal femur fracture operated during the period of 2008 to 2014. NEER score is used as criteria for evaluation of patients.Results: With use of DFLCP, anatomical reduction and rigid fixation, early mobilization and aggressive physiotherapy can be started with the use of these plates.Conclusions: Our study shows that distal femur locking compression plate (DFLCP) is the evolving approach to treat distal femur fractures