207,207 research outputs found
The gravitational field of a global monopole
We present an exact solution to the non-linear equation which describes a
global monopole in the flat space. We re-examine the metric and the geodesics
outside the global monopole. We will see that a global monopole produces a
repulsive gravitational field outside the core in addition to a solid angular
deficit. The lensing property of the global monopole and the global
monopole-antimonopole annihilation mechanism are studied.Comment: 8 pages, no figure
Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
This paper is concerned with a generalized type of Darboux transformations
defined in terms of a twisted derivation satisfying
where is a homomorphism. Such twisted derivations include regular
derivations, difference and -difference operators and superderivatives as
special cases. Remarkably, the formulae for the iteration of Darboux
transformations are identical with those in the standard case of a regular
derivation and are expressed in terms of quasideterminants. As an example, we
revisit the Darboux transformations for the Manin-Radul super KdV equation,
studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140,
(1997). The new approach we take enables us to derive a unified expression for
solution formulae in terms of quasideterminants, covering all cases at once,
rather than using several subcases. Then, by using a known relationship between
quasideterminants and superdeterminants, we obtain expressions for these
solutions as ratios of superdeterminants. This coincides with the results of
Liu and Ma\~nas in all the cases they considered but also deals with the one
subcase in which they did not obtain such an expression. Finally, we obtain
another type of quasideterminant solutions to the Main-Radul super KdV equation
constructed from its binary Darboux transformations. These can also be
expressed as ratios of superdeterminants and are a substantial generalization
of the solutions constructed using binary Darboux transformations in earlier
work on this topic
Prediction of combustion instability limit cycle oscillations by combining flame describing function simulations with a thermoacoustic network model
Accurate prediction of limit cycle oscillations resulting from combustion instability has been a long-standing challenge. The present work uses a coupled approach to predict the limit cycle characteristics of a combustor, developed at Cambridge University, for which experimental data are available (Balachandran, Ph.D. thesis, 2005). The combustor flame is bluff-body stabilised, turbulent and partially-premixed. The coupled approach combines Large Eddy Simulation (LES) in order to characterise the weakly non-linear response of the flame to acoustic perturbations (the Flame Describing Function (FDF)), with a low order thermoacoustic network model for capturing the acoustic wave behaviour. The LES utilises the open source Computational Fluid Dynamics (CFD) toolbox, OpenFOAM, with a low Mach number approximation for the flow-field and combustion modelled using the PaSR (Partially Stirred Reactor) model with a global one-step chemical reaction mechanism for ethylene/air. LES has not previously been applied to this partially-premixed flame, to our knowledge. Code validation against experimental data for unreacting and partially-premixed reacting flows without and with inlet velocity perturbations confirmed that both the qualitative flame dynamics and the quantitative response of the heat release rate were captured with very reasonable accuracy. The LES was then used to obtain the full FDF at conditions corresponding to combustion instability, using harmonic velocity forcing across six frequencies and four forcing amplitudes. The low order thermoacoustic network modelling tool used was the open source OSCILOS (http://www.oscilos.com). Validation of its use for limit cycle prediction was performed for a well-documented experimental configuration, for which both experimental FDF data and limit cycle data were available. The FDF data from the LES for the present test case was then imported into the OSCILOS geometry network and limit cycle oscillations of frequency 342 Hz and normalised velocity amplitude of 0.26 were predicted. These were in good agreement with the experimental values of 348 Hz and 0.21 respectively. This work thus confirms that a coupled numerical prediction of limit cycle behaviour is possible using an entirely open source numerical framework
I=2 Two-Pion Wave Function and Scattering Phase Shift
We calculate a two-pion wave function for the I=2 -wave two-pion system
with a finite scattering momentum and estimate the interaction range between
two pions, which allows us to examine the validity of a necessary condition for
the finite size formula presented by Rummukainen and Gottlieb. We work in the
quenched approximation employing the plaquette gauge action for gluons and the
improved Wilson action for quarks at on
lattice. The quark masses are chosen to give , 0.488 and . We find that the energy dependence of the interaction range is
small and the necessary condition is satisfied for our range of the quark mass
and the scattering momentum, . We also find that the
scattering phase shift can be obtained with a smaller statistical error from
the two-pion wave function than from the two-pion time correlator.Comment: 23 pages, 7 figures, added a reference (Phys.Rev.D73:054503,2006) in
v
Aberrant posterior cingulate connectivity classify first-episode schizophrenia from controls: A machine learning study
Background Posterior cingulate cortex (PCC) is a key aspect of the default mode network (DMN). Aberrant PCC functional connectivity (FC) is implicated in schizophrenia, but the potential for PCC related changes as biological classifier of schizophrenia has not yet been evaluated. Methods We conducted a data-driven approach using resting-state functional MRI data to explore differences in PCC-based region- and voxel-wise FC patterns, to distinguish between patients with first-episode schizophrenia (FES) and demographically matched healthy controls (HC). Discriminative PCC FCs were selected via false discovery rate estimation. A gradient boosting classifier was trained and validated based on 100 FES vs. 93 HC. Subsequently, classification models were tested in an independent dataset of 87 FES patients and 80 HC using resting-state data acquired on a different MRI scanner. Results Patients with FES had reduced connectivity between PCC and frontal areas, left parahippocampal regions, left anterior cingulate cortex, and right inferior parietal lobule, but hyperconnectivity with left lateral temporal regions. Predictive voxel-wise clusters were similar to region-wise selected brain areas functionally connected with PCC in relation to discriminating FES from HC subject categories. Region-wise analysis of FCs yielded a relatively high predictive level for schizophrenia, with an average accuracy of 72.28% in the independent samples, while selected voxel-wise connectivity yielded an accuracy of 68.72%. Conclusion FES exhibited a pattern of both increased and decreased PCC-based connectivity, but was related to predominant hypoconnectivity between PCC and brain areas associated with DMN, that may be a useful differential feature revealing underpinnings of neuropathophysiology for schizophrenia
Method for classifying multiqubit states via the rank of the coefficient matrix and its application to four-qubit states
We construct coefficient matrices of size 2^l by 2^{n-l} associated with pure
n-qubit states and prove the invariance of the ranks of the coefficient
matrices under stochastic local operations and classical communication (SLOCC).
The ranks give rise to a simple way of partitioning pure n-qubit states into
inequivalent families and distinguishing degenerate families from one another
under SLOCC. Moreover, the classification scheme via the ranks of coefficient
matrices can be combined with other schemes to build a more refined
classification scheme. To exemplify we classify the nine families of four
qubits introduced by Verstraete et al. [Phys. Rev. A 65, 052112 (2002)] further
into inequivalent subfamilies via the ranks of coefficient matrices, and as a
result, we find 28 genuinely entangled families and all the degenerate classes
can be distinguished up to permutations of the four qubits. We also discuss the
completeness of the classification of four qubits into nine families
Spectral properties of photon pairs generated by spontaneous four wave mixing in inhomogeneous photonic crystal fibers
The photonic crystal fiber (PCF) is one of the excellent media for generating
photon pairs via spontaneous four wave mixing. Here we study how the
inhomogeneity of PCFs affect the spectral properties of photon pairs from both
the theoretical and experimental aspects. The theoretical model shows that the
photon pairs born in different place of the inhomogeneous PCF are coherently
superposed, and a modulation in the broadened spectrum of phase matching
function will appear, which prevents the realization of spectral factorable
photon pairs. In particular, the inhomogeneity induced modulation can be
examined by measuring the spectrum of individual signal or idler field when the
asymmetric group velocity matching is approximately fulfilled. Our experiments
are performed by tailoring the spectrum of pulsed pump to satisfy the specified
phase matching condition. The observed spectra of individual signal photons,
which are produced from different segments of the 1.9 m inhomogeneous PCF,
agree with the theoretical predictions. The investigations are not only useful
for fiber based quantum state engineering, but also provide a dependable method
to test the homogeneity of PCF.Comment: to appear in Phys. Rev.
South Asian summer monsoon projections constrained by the Intedacadal Pacific Oscillation
A reliable projection of future South Asian summer monsoon (SASM) benefits a large population in Asia. Using a 100-member ensemble of simulations by the Max Planck Institute Earth System Model (MPI-ESM) and a 50-member ensemble of simulations by the Canadian Earth System Model (CanESM2), we find that internal variability can overshadow the forced SASM rainfall trend, leading to large projection uncertainties for the next 15 to 30 years. We further identify that the Interdecadal Pacific Oscillation (IPO) is, in part, responsible for the uncertainties. Removing the IPO-related rainfall variations reduces the uncertainties in the near-term projection of the SASM rainfall by 13 to 15% and 26 to 30% in the MPI-ESM and CanESM2 ensembles, respectively. Our results demonstrate that the uncertainties in near-term projections of the SASM rainfall can be reduced by improving prediction of near-future IPO and other internal modes of climate variabilit
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