- Light-time correction

by Manoj Agravat29 Jul 2015 02:56 - Electroweak physics

by Dr. Emmanuel Lipmanov27 Jan 2015 18:53 - Poisson distribution

by Mahdi Ranjbar Zefreh20 Dec 2014 20:47 - Thermalisation

by Mahdi Ranjbar Zefreh18 Dec 2014 14:11 - Quadrature

by Nicolas Guarin Zapata11 Oct 2014 01:22 - Minimal Dark Matter

by Dr. Marco Cirelli05 Dec 2010 22:13 - Andreev reflection

by Prof. Carlo Beenakker08 Dec 2010 13:33 - Dzyaloshinskii-Moriya interaction

by Dr. George Jackeli28 Aug 2009 09:41 - Leptogenesis

by Dr. Sacha Davidson08 Dec 2010 13:32 - Universal Conductance Fluctuations

by Prof. Carlo Beenakker08 Dec 2010 13:33

- Analysis of the peculiar velocities of galaxies should take account of the uncertainties in both redshifts and distances. We show how this can be done by a numerical application of the action principle. The method is applied to an improved catalog of the galaxies and tight systems of galaxies within 4$h_{75}^{-1}$ Mpc, supplemented with a coarser sample of the major concentrations at 4$h_{75}^{-1}$ Mpc to 20$h_{75}^{-1}$ Mpc distance. Inclusion of this outer zone improves the fit of the mass tracers in the inner zone to their measured redshifts and distances, yielding best fits with reduced $\chi ^2$ in redshift and distance in the range 1.5 to 2. These solutions are based on the assumption that the galaxies in and near the Local Group trace the mass, and a powerful test would be provided by observations of proper motions of the nearby galaxies. Predicted transverse galactocentric velocities of some of the nearby galaxies are confined to rather narrow ranges of values, and are on the order of 100 km~s$^{-1}$, large enough to be detected and tested by the proposed SIM and GAIA satellite missions.GalaxyRelaxationNearby galaxiesAndromeda galaxyLuminosityLocal groupMilky WayPeculiar velocityMass to light ratioVirgo Cluster...
- Conformal invariance is spontaneously broken in many physical systems leading to the appearance of a single massless Goldstone mode in the spectrum, the dilaton. The dilaton soft limit is shown to generically encode the action of both the dilatation and the special conformal transformation on observables. For massive on-shell legs these take the form of sub-leading soft theorems. At loop level, we show how anomalous dimensions for coupling constants and fields can be included. We illustrate the general analysis with a variety of formal and phenomenological applications.DilatonCoupling constantAnomalous dimensionGoldstone bosonConformal invarianceSpecial conformal transformationVacuum expectation valueScaling dimensionDimensionsSpontaneously broken conformal invariance...
- According to the long-standing received wisdom, a "small" value of the Higgs mass - as for instance implied by general unitarity constraints - is highly "unnatural" and essentially $\mbox{requires}$ new physics to be present at or near currently accessible energy scales. Following the discovery of a new, Higgslike boson at the LHC facility in 2012, but with no sign of new physics after having explored a large region of parameter space, a dilemma thus seems to present itself : either the newly discovered boson is indeed the long-sought Higgs boson of the standard model of particle physics (or some appropriate variant of that model) and the new physics at the TeV scale, supposedly required by the naturalness argument, is still waiting to be discovered, possibly by LHC-II, or the identification of the new boson as the Higgs cannot be maintained. It is shown that this apparent dilemma is in fact a false one, in that nothing in contemporary particle physics dictates that a small Higgs mass be unnatural in any way.Standard ModelRenormalizationQuantum field theoryQuantum electrodynamicsEffective field theoryHiggs boson massDimensionsCoupling constantRenormalization groupLandau pole...
- Our goal is to interpret the energy equation from Doubly Special Relativity (DSR) of Magueijo-Smolin with an invariant Planck energy scale in order to obtain the speed of light with an explicit dependence on the background temperature of the expanding universe. We also investigate how other universal constants, including the fine structure constant, have varied since the early universe and, thus, how they have evoluted over the cosmological time related to the temperature of the expanding universe. For instance, we show that both the Planck constant and the electron charge were also too large in the early universe. However, we finally conclude that the fine structure constant has remained invariant with the age and temperature of the universe, which is in agreement with laboratory tests and some observational data.ThermalisationFine structure constantThe early UniverseExpanding universeQuasarSpeed of lightParticle massCosmologyPlanck energyPlanck mission...
- The objective of this work is to understand how the characteristics of relativistic MHD turbulence may differ from those of nonrelativistic MHD turbulence. We accomplish this by studying the ideal invariants and energy spectrum in the relativistic case and comparing them to what we know of nonrelativistic turbulence. Although much work has been done to understand the dynamics of nonrelativistic systems (mostly for ideal incompressible fluids), there is minimal literature explicitly describing the dynamics of relativistic MHD turbulence. Many researchers simply assume that relativistic turbulence has the same invariants and obeys the same dynamics as non-relativistic systems our results show that this assumption is incorrect.TurbulenceRelativistic magnetohydrodynamicsCompressibilityHelicityMagnetohydrodynamic turbulenceMagnetic helicityFluid dynamicsErgodicityDissipationEvolution equation...
- The origin of cosmic magnetism is an issue of fundamental importance in astrophysics. We review here some of the ideas of how large scale magnetic fields in the universe, particularly in galaxies and galaxy clusters could arise. The popular paradigm involves the generation of a seed magnetic field followed by turbulent dynamo amplification of the seed field. We first outline various seed field generation mechanisms including Biermann batteries. These in general give a field much smaller than the observed field and so they require further amplification by dynamo action. The basic idea behind fluctuation dynamos, as applied to cluster magnetism and the mean-field helical dynamo as applied to disk galaxies, are outlined. Major difficulties with the dynamo paradigm are considered. It is particularly important to understand the nonlinear saturation of dynamos, and whether the fields produced are coherent enough on large-scales to explain the observed fields in galaxies and clusters. At the same time the alternative possibility of a primordial field lacks firm theoretical support but can have very interesting observational consequences.HelicityTurbulenceMean fieldGalaxyIntergalactic mediumQuenchingActive Galactic NucleiDisk galaxyMagnetic helicityCluster of galaxies...
- We study the production of sterile neutrinos in the early universe from $\pi \rightarrow l \nu_s$ shortly after the QCD phase transition in the absence of a lepton asymmetry while including finite temperature corrections to the $\pi$ mass and decay constant $f_{\pi}$. Sterile neutrinos with masses $\lesssim 1 MeV$ produced via this mechanism freeze-out at $T_f \simeq 10 MeV$ with a distribution function that is highly non-thermal and features a sharp enhancement at low momentum thereby making this species \emph{cold} even for very light masses. Dark matter abundance constraints from the CMB and phase space density constraints from the most dark matter dominated dwarf spheroidal galaxies provide upper and lower bounds respectively on combinations of mass and mixing angles. For $\pi \rightarrow \mu \nu_s$, the bounds lead to a narrow region of compatibility with the latest results from the $3.55 \mathrm{KeV}$ line. The non-thermal distribution function leads to free-streaming lengths (today) in the range of $\sim \mbox{few kpc}$ consistent with the observation of cores in dwarf galaxies. For sterile neutrinos with mass $\lesssim 1 eV$ that are produced by this reaction, the most recent accelerator and astrophysical bounds on $U_{ls}$ combined with the non-thermal distribution function suggests a substantial contribution from these sterile neutrinos to $N_{eff}$.Sterile neutrinoThermalisationQCD phase transitionFreeze-outPhase space densityCosmologyDark matterFree streamingActive neutrinoNeutrino...
- The chiral magnetic and chiral separation effects---quantum-anomaly-induced electric current and axial current along an external magnetic field in parity-odd quark-gluon plasma---have received intense studies in the community of heavy-ion collision physics. We show that analogous effects occur in rotating trapped Fermi gases with Weyl-Zeeman spin-orbit coupling where the rotation plays the role of an external magnetic field. These effects can induce a mass quadrupole in the atomic cloud along the rotation axis which may be tested in future experiments. Similar effects also exist in rotating trapped Bose gases with Weyl-Zeeman spin orbit coupling. Our results suggest that the spin-orbit coupled atomic gases are potential simulators of the chiral magnetic and separation effects.Spin-orbit interactionChiralityAtomic gasesChiral separation effectHeavy ion collisionChiral magnetic effectHamiltonianIntensityQuark-gluon plasmaAtomic clouds...
- Lectures at the 1998 Les Houches Summer School: Topological Aspects of Low Dimensional Systems. These lectures contain an introduction to various aspects of Chern-Simons gauge theory: (i) basics of planar field theory, (ii) canonical quantization of Chern-Simons theory, (iii) Chern-Simons vortices, and (iv) radiatively induced Chern-Simons terms.Chern-Simons termGauge fieldChern-Simons theoryEffective actionGauge transformationLarge gauge transformationQuantum mechanicsScalar fieldLowest Landau LevelWavefunction...
- Observations of exotic structures in the $J/\psi p$ channel, that we refer to as pentaquark-charmonium states, in $\Lambda_b^0\to J/\psi K^- p$ decays are presented. The data sample corresponds to an integrated luminosity of 3/fb acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude analysis is performed on the three-body final-state that reproduces the two-body mass and angular distributions. To obtain a satisfactory fit of the structures seen in the $J/\psi p$ mass spectrum, it is necessary to include two Breit-Wigner amplitudes that each describe a resonant state. The significance of each of these resonances is more than 9 standard deviations. One has a mass of $4380\pm 8\pm 29$ MeV and a width of $205\pm 18\pm 86$ MeV, while the second is narrower, with a mass of $4449.8\pm 1.7\pm 2.5$ MeV and a width of $39\pm 5\pm 19$ MeV. The preferred $J^P$ assignments are of opposite parity, with one state having spin 3/2 and the other 5/2.HelicityPentaquarkLHCbInvariant massPhase spaceOrbital angular momentum of lightSystematic errorP-valueIntegrated luminosityDecay product...
- We perform a new analysis of electron-proton scattering data to determine the proton electric and magnetic radii, enforcing model-independent constraints from form factor analyticity. A wide-ranging study of possible systematic effects is performed. An improved analysis is developed that rebins data taken at identical kinematic settings, and avoids a scaling assumption of systematic errors with statistical errors. Employing standard models for radiative corrections, our improved analysis of the 2010 Mainz A1 Collaboration data yields a proton electric radius $r_E = 0.895(20)$ fm and magnetic radius $r_M = 0.776(38)$ fm. A similar analysis applied to world data (excluding Mainz data) implies $r_E = 0.916(24)$ fm and $r_M = 0.914(35)$ fm. The Mainz and world values of the charge radius are consistent, and a simple combination yields a value $r_E = 0.904(15)$ fm that is $4\sigma$ larger than the CREMA Collaboration muonic hydrogen determination. The Mainz and world values of the magnetic radius differ by $2.7\sigma$, and a simple average yields $r_M= 0.851(26)$ fm. The circumstances under which published muonic hydrogen and electron scattering data could be reconciled are discussed, including a possible deficiency in the standard radiative correction model which requires further analysis.Form factorSystematic errorTwo-photon exchangeRadiative correctionKinematicsMuonic hydrogenStatistical errorElectron scatteringCharge radiusVacuum polarization...
- The proton radius puzzle questions the self-consistency of theory and experiment in light muonic and electronic bound systems. Here, we summarize the current status of virtual particle models as well as Lorentz-violating models that have been proposed in order to explain the discrepancy. Highly charged one-electron ions and muonic bound systems have been used as probes of the strongest electromagnetic fields achievable in the laboratory. The average electric field seen by a muon orbiting a proton is comparable to hydrogenlike Uranium and, notably, larger than the electric field in the most advanced strong-laser facilities. Effective interactions due to virtual annihilation inside the proton (lepton pairs) and process-dependent corrections (nonresonant effects) are discussed as possible explanations of the proton size puzzle. The need for more experimental data on related transitions is emphasized.Proton radiusVirtual particleMuonic hydrogenAxionLorentz violationMuonStrong magnetic fieldAxion-like particlePseudoscalarCoupling constant...
- Big-bang nucleosynthesis (BBN) describes the production of the lightest nuclides via a dynamic interplay among the four fundamental forces during the first seconds of cosmic time. We briefly overview the essentials of this physics, and present new calculations of light element abundances through li6 and li7, with updated nuclear reactions and uncertainties including those in the neutron lifetime. We provide fits to these results as a function of baryon density and of the number of neutrino flavors, N_nu. We review recent developments in BBN, particularly new, precision Planck cosmic microwave background (CMB) measurements that now probe the baryon density, helium content, and the effective number of degrees of freedom, n_eff. These measurements allow for a tight test of BBN and of cosmology using CMB data alone. Our likelihood analysis convolves the 2015 Planck data chains with our BBN output and observational data. Adding astronomical measurements of light elements strengthens the power of BBN. We include a new determination of the primordial helium abundance in our likelihood analysis. New D/H observations are now more precise than the corresponding theoretical predictions, and are consistent with the Standard Model and the Planck baryon density. Moreover, D/H now provides a tight measurement of N_nu when combined with the CMB baryon density, and provides a 2sigma upper limit N_nu < 3.2. The new precision of the CMB and of D/H observations together leave D/H predictions as the largest source of uncertainties. Future improvement in BBN calculations will therefore rely on improved nuclear cross section data. In contrast with D/H and he4, li7 predictions continue to disagree with observations, perhaps pointing to new physics.Big bang nucleosynthesisCosmic microwave backgroundAbundanceStandard ModelCosmologyStarLight element abundancesLikelihood functionHelium abundanceHalo star...
- Recent results from the NA48/2 and NA62 kaon decay-in-flight experiments at CERN are presented. A precision measurement of the helicity-suppressed ratio RK of the K+- to e+- nu and K+- to mu+- nu decay rates has been performed using the full dedicated data set collected by the NA62 experiment (RK phase); the result is in agreement with the Standard Model expectation. New measurements of the K+- to pi+- gamma gamma decay at the NA48/2 and NA62 experiments provide further tests of the Chiral Perturbation Theory. A planned measurement of the branching ratio of the ultra-rare K+ to pi+ nu anti-nu decay at 10% precision is expected to represent a powerful test of the Standard Model.Standard ModelNA62 experimentKaonCERNSpectrometersKaon decayKinematicsBranching ratioMuonChiral perturbation theory...
- I first review the status of Digital Sky Surveys. The focus will be on extragalactic surveys with an area of more than 100 sq.deg. The Sloan Digital Sky Survey is the archetype of such imaging surveys and it is its great success that has prompted great activity in this field. The latest surveys explore wider, fainter and higher resolution and also a longer wavelength range than SDSS. Many of these surveys overlap particularly in the S Hemisphere where we now have Pan-STARRS, DES and the ESO VST surveys, and our aim here is to compare their properties. Since there is no dedicated article on the VST ATLAS in this symposium, we shall especially review the properties of this particular survey. This easily fits onto our other main focus which is to compare overlapping Southern Surveys and see how they best fit with the available NIR imaging data. We conclude that the Southern Hemisphere will soon overtake the North in terms of multiwavelength imaging. However we note that the South has more limited opportunities for spectroscopic follow-up and this weakness will persist during the LSST era. Some new perspectives are offered on this and other aspects of survey astronomy.Digitized Sky SurveySloan Digital Sky SurveySky surveysPan-STARRSLarge Synoptic Survey TelescopeATLAS Experiment at CERNF4SurveysResolutionWavelength...
- We assess a model of late cosmic reionization in which the ionizing background radiation arises entirely from high redshift quasars and other active galactic nuclei (AGNs). The low optical depth to Thomson scattering reported by the Planck Collaboration pushes the redshift of instantaneous reionization down to z=8.8^{+1.7}_{-1.4} and greatly reduces the need for significant Lyman-continuum emission at very early times. We show that, if recent claims of a numerous population of faint AGNs at z=4-6 are upheld, and the high inferred AGN comoving emissivity at these epochs persists to higher redshifts, then active galaxies may drive the reionization of hydrogen and helium with little contribution from normal star-forming galaxies. We discuss an AGN-dominated scenario that satisfies a number of observational constraints: the HI photoionization rate is relatively flat over the range 2<z<5, hydrogen gets fully reionized by z=5.7, and the integrated Thomson scattering optical depth is tau=0.056, in agreement with measurements based on the Lya opacity of the intergalactic medium (IGM) and Cosmic Microwave Background (CMB) polarization. It is a prediction of the model that helium gets doubly reionized before redshift 4, the heat input from helium reionization dominates the thermal balance of the IGM after hydrogen reionization, and z>5 AGNs provide a significant fraction of the unresolved X-ray background at 2 keV. Singly- and doubly-ionized helium contribute about 13% to tau, and the HeIII volume fraction is already 50% when hydrogen becomes fully reionized.ReionizationActive Galactic NucleiIntergalactic mediumIonizationQuasarLyman recombination continuaPlanck missionCosmic X-ray backgroundStar-forming galaxyLuminosity function...
- We investigate the non-spherical density structure of dark halos of the dwarf spheroidal (dSph) galaxies in the Milky Way and Andromeda galaxies, based on revised axisymmetric mass models from our previous work. The models we adopt here fully take into account velocity anisotropy of tracer stars confined within a flattened dark halo. Applying our models to the available kinematic data of the twelve bright dSphs, we find that these galaxies associate, in general, elongated dark halos even considering the effect of this velocity anisotropy of stars. We also find that the best-fit parameters, especially for the shapes of dark halos and velocity anisotropy, are susceptible to both the availability of velocity data in the outer regions and the effect of the lack of sample stars in each spatial bin. Thus, to obtain more realistic limits on dark halo structures, we require photometric and kinematic data over much larger areas in the dSphs than previously explored. The results obtained from the currently available data suggest that the shapes of dark halos in the dSphs are more elongated than those of $\Lambda$CDM subhalos. This mismatch needs to be solved by theory including baryon components and the associated feedback to dark halos as well as by further observational limits in larger areas of dSphs. It is also found that more diffuse dark halos may have undergone consecutive star-formation history, thereby implying that dark-halo structure plays an important role in star-formation activity.Dark matter haloStarDwarf spheroidal galaxyDark matter subhaloMilky WayLine of sight velocityEllipticityKinematicsStar formationVelocity dispersion...
- Masses of clusters of galaxies from weak gravitational lensing analyses of ever larger samples are increasingly used as the reference to which baryonic scaling relations are compared. In this paper we revisit the analysis of a sample of 50 clusters studied as part of the Canadian Cluster Comparison Project. We examine the key sources of systematic error in cluster masses. We quantify the robustness of our shape measurements and calibrate our algorithm empirically using extensive image simulations. The source redshift distribution is revised using the latest state-of-the-art photometric redshift catalogs that include new deep near-infrared observations. Nonetheless we find that the uncertainty in the determination of photometric redshifts is the largest source of systematic error for our mass estimates. We use our updated masses to determine b, the bias in the hydrostatic mass, for the clusters detected by Planck. Our results suggest 1-b=0.76+-0.05(stat)}+-0.06(syst)}, which does not resolve the tension with the measurements from the primary cosmic microwave background.GalaxyEllipticityLensing signalNavarro-Frenk-White profileSystematic errorMultiplicative biasSignal to noise ratioStarSubaru telescopeCanada-France-Hawaii Telescope...
- We present weak lensing and X-ray analysis of 12 low mass clusters from the CFHTLenS and XMM-CFHTLS surveys. We combine these systems with high-mass systems from CCCP and low-mass systems from COSMOS to obtain a sample of 70 systems, spanning over two orders of magnitude in mass. We measure core-excised Lx-Tx, M-Lx and M-Tx scaling relations and include corrections for observational biases. By providing fully bias corrected relations, we give the current limitations for Lx and Tx as cluster mass proxies. We demonstrate that Tx benefits from a significantly lower intrinsic scatter at fixed mass than Lx. By studying the residuals of the bias corrected relations, we show for the first time using weak lensing masses that galaxy groups seem more luminous and warmer for their mass than clusters. This implies a steepening of the M-Lx and M-Tx relations at low masses. We verify the inferred steepening using a different high mass sample from the literature and show that variance between samples is the dominant effect leading to discrepant scaling relations. We divide our sample into subsamples of merging and relaxed systems, and find that mergers may have enhanced scatter in lensing measurements, most likely due to stronger triaxiality and more substructure. For the Lx-Tx relation, which is unaffected by lensing measurements, we find the opposite trend in scatter. We also explore the effects of X-ray cross-calibration and find that Chandra calibration leads to flatter Lx-Tx and M-Tx relations than XMM-Newton.GalaxyPhotometric redshiftNavarro-Frenk-White profileWeak lensing mass estimateLensing signalVirial cluster massCanada-France-Hawaii Telescope Legacy SurveyCluster of galaxiesCFHTLenS surveyCosmology...
- We present a new non-parametric method for determining mean 3D density and mass profiles from weak lensing measurements around stacked samples of galaxies or clusters, that is, from measurement of the galaxy-shear or cluster-shear correlation functions. Since the correlation function is statistically isotropic, this method evades problems, such as projection of large-scale structure along the line of sight or halo asphericity, that complicate attempts to infer masses from weak lensing measurements of individual objects. We demonstrate the utility of this method in measuring halo profiles, galaxy-mass and cluster-mass cross-correlation functions, and cluster virial masses. We test this method on an N-body simulation and show that it correctly and accurately recovers the 3D density and mass profiles of halos. We find no evidence of problems due to a mass sheet degeneracy in the simulation. Cross-correlation lensing provides a powerful method for calibrating the mass-observable relation for use in measurement of the cluster mass function in large surveys. It can also be used on large scales to measure and remove the halo bias and thereby provide a direct measurement of Omega_m * sigma_8.Two-point correlation functionGalaxyWeak lensingStatisticsVirial massLine of sightCosmologyLarge scale structureCross-correlationN-body simulation...
- We report weak-lensing masses for 51 of the most X-ray luminous galaxy clusters known. This cluster sample, introduced earlier in this series of papers, spans redshifts 0.15 < z_cl < 0.7, and is well suited to calibrate mass proxies for current cluster cosmology experiments. Cluster masses are measured with a standard `color-cut' lensing method from three-filter photometry of each field. Additionally, for 27 cluster fields with at least five-filter photometry, we measure high-accuracy masses using a new method that exploits all information available in the photometric redshift posterior probability distributions of individual galaxies. Using simulations based on the COSMOS-30 catalog, we demonstrate control of systematic biases in the mean mass of the sample with this method, from photometric redshift biases and associated uncertainties, to better than 3%. In contrast, we show that the use of single-point estimators in place of the full photometric redshift posterior distributions can lead to significant redshift-dependent biases on cluster masses. The performance of our new photometric redshift-based method allows us to calibrate `color-cut` masses for all 51 clusters in the present sample to a total systematic uncertainty of ~7% on the mean mass, a level sufficient to significantly improve current cosmology constraints from galaxy clusters. Our results bode well for future cosmological studies of clusters, potentially reducing the need for exhaustive spectroscopic calibration surveys as compared to other techniques, when deep, multi-filter optical and near-IR imaging surveys are coupled with robust photometric redshift methods.Systematic errorCalibrationVirial cluster massObjectWeak lensingPhotometric redshiftPoint spread functionWeak lensing mass estimateNavarro-Frenk-White profilePhotometry...
- Locating the centers of dark matter halos is critical for understanding the mass profiles of halos as well as the formation and evolution of the massive galaxies that they host. The task is observationally challenging because we cannot observe halos directly, and tracers such as bright galaxies or X-ray emission from hot plasma are imperfect. In this paper we quantify the consequences of miscentering on the weak lensing signal from a sample of 129 X-ray selected galaxy groups in the COSMOS field with redshifts 0<z<1 and halo masses in the range 10^13 - 10^14 M_sun. By measuring the stacked lensing signal around eight different candidate centers (such as the brightest member galaxy, the mean position of all member galaxies, or the X-ray centroid), we determine which candidates best trace the center of mass in halos. In this sample of groups, we find that massive galaxies near the X-ray centroids trace the center of mass to <~75 kpc, while the X-ray position and centroids based on the mean position of member galaxies have larger offsets primarily due to the statistical uncertainties in their positions (typically ~50-150 kpc). Approximately 30% of groups in our sample have ambiguous centers with multiple bright or massive galaxies, and these groups show disturbed mass profiles that are not well fit by standard models, suggesting that they are merging systems. We find halo mass estimates from stacked weak lensing can be biased low by 5-30% if inaccurate centers are used and the issue of miscentering is not addressed.Lensing signalDark matter subhaloStellar massVirial massWeak lensingMassive galaxiesMass profileDark matter haloNavarro-Frenk-White profilePhotometric redshift...
- We present the cluster mass-richness scaling relation calibrated by a weak lensing analysis of >18000 galaxy cluster candidates in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). Detected using the 3D-Matched-Filter cluster-finder of Milkeraitis et al., these cluster candidates span a wide range of masses, from the small group scale up to $\sim10^{15} M_{\odot}$, and redshifts 0.2 $\lesssim z\lesssim$ 0.9. The total significance of the stacked shear measurement amounts to 54$\sigma$. We compare cluster masses determined using weak lensing shear and magnification, finding the measurements in individual richness bins to yield 1$\sigma$ compatibility, but with magnification estimates biased low. This first direct mass comparison yields important insights for improving the systematics handling of future lensing magnification work. In addition, we confirm analyses that suggest cluster miscentring has an important effect on the observed 3D-MF halo profiles, and we quantify this by fitting for projected cluster centroid offsets, which are typically $\sim$ 0.4 arcmin. We bin the cluster candidates as a function of redshift, finding similar cluster masses and richness across the full range up to $z \sim$ 0.9. We measure the 3D-MF mass-richness scaling relation $M_{200} = M_0 (N_{200} / 20)^\beta$. We find a normalization $M_0 \sim (2.7^{+0.5}_{-0.4}) \times 10^{13} M_{\odot}$, and a logarithmic slope of $\beta \sim 1.4 \pm 0.1$, both of which are in 1$\sigma$ agreement with results from the magnification analysis. We find no evidence for a redshift-dependence of the normalization. The CFHTLenS 3D-MF cluster catalogue is now available at cfhtlens.org.GalaxyCluster samplingPhotometric redshiftSDSS-MaxBCG Cluster CatalogCFHTLenS surveyCovarianceConcentration-mass relationSloan Digital Sky SurveyNavarro-Frenk-White profileLuminosity...
- The propagation of TeV gamma rays can be strongly modified by B-field induced conversion to axionlike particles (ALPs). We show that, at such high energies, photon dispersion is dominated by background photons - the only example where photon-photon dispersion is of practical relevance. We determine the refractive index for all energies and find that, for fixed energy density, background photons below the pair-production threshold dominate. The cosmic microwave background alone provides an "effective photon mass" of (m_gamma)^2 = -(1.01 neV * E/TeV)^2 for E < 1000 TeV. The extragalactic background light is subdominant, but local radiation fields in the galaxy or the source regions provide significant contributions. Photon-photon dispersion is small enough to leave typical scenarios of photon-ALP oscillations unscathed, but big enough to worry about it case by case.TeV gamma raysCosmic microwave backgroundExtragalactic background lightIndex of refractionAxion-like particlePair productionAbsorptivityStarThermalisationElectromagnetism...
- The main physics results obtained by the CMS experiment during the first three years of operation of the CERN Large Hadron Collider (2010--2013, aka. Run 1) are summarized. The advances in our understanding of the fundamental particles and their interactions are succinctly reviewed under the following physics topics: (i) Quantum Chromodynamics, (ii) Quark Gluon Plasma, (iii) Electroweak interaction, (iv) Top quark, (v) Higgs boson, (vi) Flavour, (vii) Supersymmetry, (viii) Dark Matter, and (ix) other searches of physics beyond the Standard Model.Standard ModelSupersymmetryDark matterLarge Hadron ColliderBosonizationPartonTurbulent jetQCD jetCurve of marginal stabilityQuantum chromodynamics...
- We perform a detailed study of the weak interactions of standard model neutrinos with the primordial plasma and their effect on the resonant production of sterile neutrino dark matter. Motivated by issues in cosmological structure formation on small scales, and reported X-ray signals that could be due to sterile neutrino decay, we consider $7$ keV-scale sterile neutrinos. Oscillation-driven production of such sterile neutrinos occurs at temperatures $T \gtrsim 100$ MeV, where we study two significant effects of weakly charged species in the primordial plasma: (1) the redistribution of an input lepton asymmetry; (2) the opacity for active neutrinos. We calculate the redistribution analytically above and below the quark-hadron transition, and match with lattice QCD calculations through the transition. We estimate opacities due to tree level processes involving leptons and quarks above the quark-hadron transition, and the most important mesons below the transition. We report final sterile neutrino dark matter phase space densities that are significantly influenced by these effects, and yet relatively robust to remaining uncertainties in the nature of the quark-hadron transition. We also provide transfer functions for cosmological density fluctuations with cutoffs at $k \simeq 10 \ h \ {\rm Mpc}^{-1}$, that are relevant to galactic structure formation.NeutrinoSterile neutrinoPhase space densityLepton asymmetryStandard ModelMuon neutrinoDark matterThermalisationLattice QCDActive neutrino...
- We present a method to recover the shape and amplitude of the power spectrum of mass fluctuations, P(k), from observations of the high redshift \lya forest. The method is motivated by the physical picture of the \lya forest that has emerged from hydrodynamic cosmological simulations and related semi-analytic models, which predicts a tight correlation between the \lya optical depth and the underlying matter density. We monotonically map the QSO spectrum to a Gaussian density field, measure its 3-d P(k), and normalize by evolving cosmological simulations with this P(k) until they reproduce the observed power spectrum of the QSO flux. Imposing the observed mean \lya opacity as a constraint makes the derived P(k) normalization insensitive to the choice of cosmological parameters, ionizing background spectrum, or reionization history. Thus, in contrast to estimates of P(k) from galaxy clustering, there are no uncertain "bias parameters" in the recovery of the mass power spectrum. We test the full procedure on SPH simulations of 3 cosmological models and show that it recovers their true mass power spectra on comoving scales ~1-10/h Mpc, the upper scale being set by the size of the simulation boxes. The procedure works even for noisy (S/N ~ 10), moderate resolution (~40 km/s pixels) spectra. We present an illustrative application to Q1422+231; the recovered P(k) is consistent with an \Omega=1, \sigma_8=0.5 CDM model. Application to large QSO samples should yield the power spectrum of mass fluctuations on small scales at z ~ 2-4. (Compressed)QuasarFlux power spectrumCosmological parametersLine of sightQuasar spectrumAbsorptivityCosmological modelIntergalactic mediumMean transmitted fluxLyman-alpha forest...
- We measure the weak lensing shear around galaxy troughs, i.e. the radial alignment of background galaxies relative to underdensities in projections of the foreground galaxy field over a wide range of redshift in Science Verification data from the Dark Energy Survey. Our detection of the shear signal is highly significant (10 to 15sigma for the smallest angular scales) for troughs with the redshift range z in [0.2,0.5] of the projected galaxy field and angular diameters of 10'...1{\deg}. These measurements probe the connection between the galaxy, matter density, and convergence fields. By assuming galaxies are biased tracers of the matter density with Poissonian noise, we find agreement of our measurements with predictions in a fiducial LambdaCDM model. The prediction for the lensing signal on large trough scales is virtually independent of the details of the underlying model for the connection of galaxies and matter. Our comparison of the shear around troughs with that around cylinders with large galaxy counts is consistent with a symmetry between galaxy and matter over- and underdensities. In addition, we measure the two-point angular correlation of troughs with galaxies which, in contrast to the lensing signal, is sensitive to galaxy bias on all scales. The lensing signal of troughs and their clustering with galaxies is therefore a promising probe of the statistical properties of matter underdensities and their connection to the galaxy field.Galaxy countsLensing signalThe Dark Energy SurveyBackground galaxyWeak lensingTangential shearSignal to noise ratioVoidForeground galaxyGalaxy bias...
- We address the impact of a modified $W \ell \nu$ coupling on a wide range of observables, such as $\tau$ leptonic and mesonic decays, leptonic decays of pseudoscalar mesons, as well as semileptonic meson decays. In particular, we concentrate on deviations from lepton flavour universality, focusing on the ratios $R_{P} = \Gamma (P \to \ell \nu) / \Gamma (P \to \ell' \nu)$, with $P=K, \pi, D, D_s$, $R(D)={\Gamma (B^+ \to D \tau^+ \nu)}/{\Gamma (B^+ \to D\ell^+ \nu)}$, $R \tau={\Gamma (\tau\to \mu\nu\nu)}/{\Gamma (\tau\to e\nu\nu)}$, $R^{\ell \tau}_P=\Gamma(\tau\to P\nu)/\Gamma(P\to \ell \nu)$, and $\text{BR}(B \to \tau \nu)$. We further consider leptonic gauge boson decays, such as $W\to \ell \nu $ and $Z \to \nu \nu$. For all the above observables, we provide the corresponding complete analytical expressions, derived for the case of massive neutrinos. Working in the framework of the Standard Model extended by additional sterile fermions, which mix with the active (left-handed) neutrinos, we numerically study the impact of active-sterile mixings on the above mentioned observables.Standard ModelSterile neutrinoNeutrinoDecay widthUnitarityMeson decaysActive-sterile neutrino mixingLepton flavour universalityKinematicsCosmology...
- We discuss the effective string theory of vortex lines in ordinary fluids and low-temperature superfluids, by describing the bulk fluid flow in terms of a two-form field to which vortex lines can couple. We derive the most general low-energy effective Lagrangian that is compatible with (spontaneously broken) Poincare invariance and worldsheet reparameterization invariance. This generalizes the effective action developed by Lund and Regge and by Endlich and Nicolis. By applying standard field-theoretical techniques, we show that certain low-energy coupling constants -- most notably the string tension -- exhibit RG running already at the classical level. We discuss applications of our techniques to the study of Kelvin waves, vortex rings, and the coupling to bulk sound modes.WorldsheetSuperfluidEffective actionPhononTwo-formRenormalizationEffective theoryGauge invarianceKelvinGoldstone boson...
- A new subtraction procedure for removal both ultraviolet and infrared divergences in Feynman integrals is proposed. This method is developed for computation of QED corrections to the electron anomalous magnetic moment. The procedure is formulated in the form of a forest formula with linear operators that are applied to Feynman amplitudes of UV-divergent subgraphs. The contribution of each Feynman graph that contains propagators of electrons and photons is represented as a finite Feynman-parametric integral. Application of the developed method to the calculation of 2-loop and 3-loop contributions is described.GraphFeynman diagramInfrared divergenceRenormalizationAnomalous magnetic dipole momentMonte Carlo methodFeynman parametrizationFeynman parameterSelf-energyIntegral domain...
- Recently, the effects of spin-orbit coupling (SOC) in correlated materials have become one of the most actively studied subjects in condensed matter physics, as correlations and SOC together can lead to the discovery of new phases. Among candidate materials, iridium oxides (iridates) have been an excellent playground to uncover such novel phenomena. In this review, we discuss recent progress in iridates and related materials, focusing on the basic concepts, relevant microscopic Hamiltonians, and unusual properties of iridates in perovskite- and honeycomb-based structures. Perspectives on SOC and correlation physics beyond iridates are also discussed.IridatesMagnetismDopingSpin liquidFerromagnetMott insulatorMagnetic orderOxideTopological insulatorAntiferromagnet...
- This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing the amplitude and phase information of a modulated carrier wave. Particle transmission events are modeled as the outcome of a process of signal accumulation that occurs in an extra (non-spacetime) dimension. Besides giving a natural interpretation of the wavefunction and the Born rule, the model accommodates the collapse of the wave packet and other quantum paradoxes such as EPR and the Ahanorov-Bohm effect. The model also gives a new perspective on the 'relational' nature of quantum mechanics: that is, whether the wave function of a physical system is "real" or simply reflects the observer's partial knowledge of the system. We simulate the model for a 2-slit experiment, and indicate possible deviations of the model's predictions from conventional quantum mechanics. We also indicate how the theory may be extended to a field theory.Quantum mechanicsWavefunctionWave packetDouble-slit experimentEventCommunicationParticlesField...
- In this paper we give the Bohr-Sommerfeld-Heisenberg quantization of the mathematical pendulum.QuantizationLine bundleHamiltonianIntegral curveCovarianceBundleManifoldDiffeomorphismCovariant derivativePhase space...
- Proof Designer is a computer software program designed to help Mathematics students learn to write mathematical proofs. Under the guidance of the user, Proof Designer assists in writing outlines of proofs in elementary set theory. Proof Designer was designed by Daniel Velleman in association with his book "How To Prove It: A Structured Approach" to help students apply the methods discussed in the book, making classes based on the book more interactive. This article is an early report on the progress of our effort to "bring set theory to the masses" by developing Proof Maker, a new Proof Designer-inspired software that ports Proof Designer to hand-held devices such as smart-phones and tablets. Proof Maker, when completed, will allow students to use Proof Designer with the ease of a touch, literally, on their smart devices. Our goal behind developing Proof Maker is to enable any one who is interested enough to develop elementary set theory proofs anywhere he or she might be (think of doing proofs while waiting at a bus stop!) and at any time he or she wishes (think of writing proofs before going to bed, or even in bed!). In this paper we report on the improvements we made to Proof Designer so far, and on the (many) steps remaining for us to have a fully-functioning Proof Maker "in our hands".Set theoryMathematical proofUser InterfaceNatural languageObjectArithmeticNumber theoryLucidGroup theoryMass...
- Beginning from two simple assumptions, i) the speed of light is a universal constant, or its equivalent, the spacetime intervals are Lorentz invariant, and ii) there are mutually interacting particles, with a covariant `source-field' equation, one arrives at a class of field equations of which the standard electromagnetism (EM) and electrodynamics (ED) are special cases. The formalism, depending on how one formulates the source-field equation, allows one to speculate magnetic monopoles, massive photons, non-linear EM's, and more.ElectromagnetismCovarianceCharged currentMagnetic monopoleMagnetDualityLorentz invariantSpeed of lightMassive photonKinematics...
- Surprisingly, an interesting property of the Noether charge that it is by itself invariant under the corresponding symmetry transformation is never discussed in quantum field theory or classical mechanics textbooks we have checked. This property is also almost never mentioned in articles devoted to Noether's theorem. Nevertheless, to prove this property in the context of Lagrangian formalism is not quite trivial and the proof, outlined in this article, can constitute an useful and interesting exercise for students.Field theoryNoether's theoremEuler-Lagrange equationLagrangian formalismQuantum field theoryGeneralized coordinatesContinuous symmetryVariational principleDegree of freedomInfinitesimal transformation...
- We prove global existence of appropriate weak solutions for the compressible Navier--Stokes equations for more general stress tensor than those covered by P.-L. Lions and E. Feireisl's theory. More precisely we focus on more general pressure laws which are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining precise quantitative regularity estimates: This requires a more precise analysis of the structure of the equations combined to a novel approach to the compactness of the continuity equation. These two cases open the theory to important physical applications, for instance to describe solar events (virial pressure law), geophysical flows (eddy viscosity) or biological situations (anisotropy).CompressibilityEntropyRegularizationWeak solutionBarotropicViscous stressViscosityNavier-Stokes equationsContinuity equationRenormalization...
- Starting with the early alchemists, a holy grail of science has been to make desired materials by modifying the attributes of basic building blocks. Building blocks that show promise for assembling new complex materials can be synthesized at the nanoscale with attributes that would astonish the ancient alchemists in their versatility. However, this versatility means that making direct connection between building block attributes and bulk behavior is both necessary for rationally engineering materials, and difficult because building block attributes can be altered in many ways. Here we show how to exploit the malleability of the valence of colloidal nanoparticle "elements" to directly and quantitatively link building block attributes to bulk behavior through a statistical thermodynamic framework we term "digital alchemy". We use this framework to optimize building blocks for a given target structure, and to determine which building block attributes are most important to control for self assembly, through a set of novel thermodynamic response functions, moduli and susceptibilities. We thereby establish direct links between the attributes of colloidal building blocks and the bulk structures they form. Moreover, our results give concrete solutions to the more general conceptual challenge of optimizing emergent behaviors in nature, and can be applied to other types of matter. As examples, we apply digital alchemy to systems of truncated tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that self assemble diamond, FCC, and icosahedral quasicrystal structures, respectively.Self-assemblyColloidStatisticalNanoparticleQuasicrystalMaterialsThermodynamicsDiamond...
- The new model of modified $F(R)$ gravity theory with the function $F(R) = R+(a/\gamma) \arcsin(\gamma R)$ is suggested and investigated. Constant curvature solutions corresponding to the extremum of the effective potential are obtained. We consider both the Jordan and Einstein frames, and the potential and the mass of the scalar degree of freedom are found. It was shown that the de Sitter space-time is unstable but the flat space-time is stable. We calculate the slow-roll parameters $\epsilon$, $\eta$, and the $e$-fold number of the model. Critical points of autonomous equations for the de Sitter phase and the matter dominated epoch are obtained and learned.Constant curvatureDe Sitter spaceEinstein frameCritical pointSlow roll parametersEffective potentialDark energyGeneral relativityCurvatureDegree of freedom...
- A cornerstone equation of optics, Snell's law, relates the angles of incidence and refraction for light passing through an interface between two media. It is built on two fundamental constrains: the conservation of tangential momentum and the conservation of energy. By relaxing the classical Snell law photon momentum conservation constrain when using space-gradient phase discontinuity, optical metasurfaces enabled an entirely new class of ultrathin optical devices. Here, we show that by eradicating the photon energy conservation constrain when introducing time-gradient phase discontinuity, we can further empower the area of flat photonics and obtain a new genus of optical devices. With this approach, classical Snell relations are developed into a more universal form not limited by Lorentz reciprocity, hence, meeting all the requirements for building magnetic-free optical isolators. Furthermore, photons experience inelastic interaction with time-gradient metasurfaces, which modifies photonic energy eigenstates and results in a Doppler-like wavelength shift. Consequently, metasurfaces with both space- and time-gradients can have a strong impact on a plethora of photonic applications and provide versatile control over the physical properties of light.MetasurfaceAngle of incidenceRelaxationReciprocityPhotonOpticsMomentumEnergySnell's lawUniverse...
- We present a comprehensive analysis of strong-lensing, weak-lensing shear and magnification data for a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters selected from the CLASH survey. Our analysis combines constraints from 16-band HST observations and wide-field multi-color imaging taken primarily with Subaru/Suprime-Cam. We reconstruct surface mass density profiles of individual clusters from a joint analysis of the full lensing constraints, and determine masses and concentrations for all clusters. We find internal consistency of the ensemble mass calibration to be $\le 5\% \pm 6\%$ by comparison with the CLASH weak-lensing-only measurements of Umetsu et al. For the X-ray-selected subsample, we examine the concentration-mass relation and its intrinsic scatter using a Bayesian regression approach. Our model yields a mean concentration of $c|_{z=0.34} = 3.95 \pm 0.35$ at $M_{200c} \simeq 14\times 10^{14}M_\odot$ and an intrinsic scatter of $\sigma(\ln c_{200c}) = 0.13 \pm 0.06$, in excellent agreement with LCDM predictions when the CLASH selection function based on X-ray morphological regularity and the projection effects are taken into account. We also derive an ensemble-averaged surface mass density profile for the X-ray-selected subsample by stacking their individual profiles. The stacked mass profile is well described by a family of density profiles predicted for cuspy dark-matter-dominated halos, namely, the NFW, Einasto, and DARKexp models, whereas the single power-law, cored isothermal and Burkert density profiles are disfavored by the data. We show that cuspy halo models that include the two-halo term provide improved agreement with the data. For the NFW halo model, we measure a mean concentration of $c_{200c} = 3.79^{+0.30}_{-0.28}$ at $M_{200c} = 14.1^{+1.0}_{-1.0}\times 10^{14}M_\odot$, demonstrating robust consistency between complementary analysis methods.Cluster Lensing And Supernova survey with HubbleNavarro-Frenk-White profileWeak lensingStrong gravitational lensingVirial cluster massCalibrationCosmologyLarge scale structureMass profileIntrinsic scatter...
- There are few opportunities in introductory physics for a genuine discussion of the philosophy of science, especially in cases where the physical principles are straightforward and the mathematics is simple. Terrestrial classical mechanics satisfies these requirements, but students new to physics usually carry too many incorrect or misleading preconceptions about the subject for it to be analyzed epistemologically. The problem of dark matter, and especially the physics of spiral galaxy velocity rotation curves, is a straightforward application of Newton's laws of motion and gravitation, and is just enough removed from everyday experience to be analyzed from a fresh perspective. It is proposed to teach students about important issues in the philosophy of physics, including Bacon's induction, Popper's falsifiability, and the Duhem-Quine thesis, all in light of the dark matter problem. These issues can be discussed in an advanced classical mechanics course, or, with limited simplification, at the end of a first course in introductory mechanics. The goal is for students to understand at a deeper level how the physics community has arrived at the current state of knowledge.Dark matterRotation CurveSpiral galaxyObjectPlanetStarUranusSunGeneral relativityGalaxy mass...
- Data from social media are providing unprecedented opportunities to investigate the processes that rule the dynamics of collective social phenomena. Here, we consider an information theoretical approach to define and measure the temporal and structural signatures typical of collective social events as they arise and gain prominence. We use the symbolic transfer entropy analysis of micro-blogging time series to extract directed networks of influence among geolocalized sub-units in social systems. This methodology captures the emergence of system-level dynamics close to the onset of socially relevant collective phenomena. The framework is validated against a detailed empirical analysis of five case studies. In particular, we identify a change in the characteristic time-scale of the information transfer that flags the onset of information-driven collective phenomena. Furthermore, our approach identifies an order-disorder transition in the directed network of influence between social sub-units. In the absence of a clear exogenous driving, social collective phenomena can be represented as endogenously-driven structural transitions of the information transfer network. This study provides results that can help define models and predictive algorithms for the analysis of societal events based on open source data.EntropyDirected networkSocial systemsTime SeriesEventMeasurementNetworks...
- With the help of quantum entanglement, quantum communication can be achieved between arbitrarily distant places without passing through intermediate locations by quantum teleportation. In the laboratory, quantum teleportation has been demonstrated over short distance by photonic and atomic qubits. Using fiber links, quantum teleportation has been achieved over kilometer distances. Long distance quantum teleportation is of particular interest and has been one of the holy grails of practical quantum communication. Most recently, quantum teleportation over 16 km free-space link was demonstrated. However, a major restriction in this experiment is that the unknown quantum state cannot directly come from outside. Here, based on an ultra-bright multi-photon entanglement source, we demonstrate quantum teleportation, closely following the original scheme, for any unknown state created outside, between two optical free-space links separated by 97 km. Over a 35-53 dB high-loss quantum channel, an average fidelity of 80.4(9) % is achieved for six distinct initial states. Besides being of fundamental interest, our result represents an important step towards a global quantum network. Moreover, the high-frequency and high-accuracy acquiring, pointing and tracking (APT) technique developed in our experiment can be directly utilized for future satellite-based quantum communication.EntanglementQuantum teleportationLasersAlice and BobTelescopesQuantum channelQuantum communicationTurbulenceQubitQuantum entanglement...
- Accepting that galactic mass discrepancies are due to modified dynamics, I show why it is specifically the MOND paradigm that is pointed to cogently. MOND is thus discussed here as a special case of a larger class of modified dynamics theories whereby galactic systems with large mass discrepancies are described by scale-invariant dynamics. This is a novel presentation that uses more recent, after-the-fact insights and data (largely predicted beforehand by MOND). Starting from a purist set of tenets, I follow the path that leads specifically to the MOND basic tenets. The main signposts are: (i) Space-time scale invariance underlies the dynamics of systems with large mass discrepancies. (ii) In these dynamics, $G$ must be replaced by a single "scale-invariant" gravitational constant, Q0 (in MOND, Q0=A0=Ga0, where a0 is MOND's acceleration constant). (iii) Universality of free fall points to the constant q0=Q0/G as the boundary between the G-controlled, standard dynamics, and the Q0-controlled, scale-invariant dynamics (in MOND, q0=a0). (iv) Data clinches the case for q0 being an acceleration (MOND).Modified Newtonian DynamicsScale invarianceDimensionsMass discrepancyRotation CurveNewtonian dynamicsDark matterCosmologyLuminosityGalactic masses...
- The electric dipole moments (EDMs) of electron and nucleons are the promising probe of the new physics. In the generic high-scale supersymmetric (SUSY) scenarios such as models based on mixture of the anomaly and gauge mediations, gluino has an additional contribution to the nucleon EDMs. In this paper, we estimated the effect of the CP-violating gluon Weinberg operator induced by the gluino chromoelectric dipole moment in the high-scale SUSY scenarios, and we evaluated the nucleon and electron EDMs in these scenarios. We found that in the generic high-scale SUSY models, the nucleon EDMs may receive the sizable contribution from the Weinberg operator. Thus, it is important to compare the nucleon EDMs with the electron EDM in order to discriminate among the high-scale SUSY models.Electric dipole momentGluinoWeinberg operator for neutrino massesSupersymmetryGauginoRenormalisation group equationsHiggsinoStandard ModelMinimal supersymmetric Standard ModelGauge coupling constant...
- Complex network theory has been applied to solving practical problems from different domains. In this paper, we present a general framework for complex network applications. The keys of a successful application are a thorough understanding of the real system and a correct mapping of complex network theory to practical problems in the system. Despite of certain limitations discussed in this paper, complex network theory provides a foundation on which to develop powerful tools in analyzing and optimizing large interconnected systems.Complex network